Computer Calculation of Dose Distributions in Radiotherapy

TECHNICAL REPORTS SERIES No. 57

INTERNATIONAL ATOMIC ENERGY AGENCY,VIENNA, 1966

COMPUTER CALCULATION OF DOSE DISTRIBUTIONS IN RADIOTHERAPY The following States ate Members of the International Atomic Energy Agency:

AFGHANISTAN GABON NICARAGUA ALBANIA GERMANY, FEDERAL NIGERIA ALGERIA REPUBLIC OF NORWAY ARGENTINA GHANA PAKISTAN AUSTRALIA GREECE PANAMA AUSTRIA GUATEMALA PARAGUAY BELGIUM HAITI PERU BOLIVIA HOLY SEE PHILIPPINES BRAZIL HONDURAS POLAND' BULGARIA HUNGARY PORTUGAL BURMA ICELAND ROMANIA BYELORUSSIAN SOVIET INDIA SAUDI ARABIA SOCIALIST REPUBLIC INDONESIA SENEGAL CAMBODIA IRAN SOUTH AFRICA CAMEROON IRAQ SPAIN CANADA ISRAEL SUDAN CEYLON ITALY SWEDEN CHILE IVORY COAST SWITZERLAND CHINA JAMAICA SYRIAN ARAB REPUBLIC COLOMBIA JAPAN THAILAND CONGO, DEMOCRATIC JORDAN TUNISIA REPUBLIC OF KENYA TURKEY COSTA RICA KOREA, REPUBLIC OF UKRAINIAN SOVIET SOCIALIST CUBA KUWAIT REPUBLIC CYPRUS LEBANON UNION OF SOVIET SOCIALIST CZECHOSLOVAK SOCIALIST LIBERIA REPUBLICS REPUBLIC LIBYA UNITED ARAB REPUBLIC DENMARK LUXEMBOURG UNITED KINGDOM OF GREAT DOMINICAN REPUBLIC MADAGASCAR BRITAIN AND NORTHERN ECUADOR MALI IRELAND EL SALVADOR MEXICO UNITED STATES OF AMERICA ETHIOPIA MONACO URUGUAY FINLAND MOROCCO VENEZUELA FRANCE . NETHERLANDS VIET-NAM NEW ZEALAND YUGOSLAVIA

The Agency's Statute was approved on 23 October 1956 by the Conference on the Statute of the IAEA held at United Nations Headquarters, New York; it entered into force on 29 July 1957. The Headquarters of the Agency are situated in Vienna. Its principal objective is "to accelerate and enlarge the contribution of atomic energy to peace, health and prosperity throughout the world".

Permission to reproduce or translate the information contained in this publication may be obtained by writing to the International Atomic Energy Agency, KSrntner Ring 11, Vienna I, Austria.

1 Printed by the IAEA in Austria

June 1966 TECHNICAL REPORTS SERIES No. 57

COMPUTER CALCULATION OF DOSE DISTRIBUTIONS IN RADIOTHERAPY

REPORT OF A PANEL HELD IN VIENNA 18-22 OCTOBER 1965

INTERNATIONAL ATOMIC ENERGY AGENCY VIENNA, 1966 International Atomic Energy Agency. Computer calculation of dose distributions in radiotherapy. Report of a Panel held in Vienna, 18 - 22 October 1965. Vienna, the Agency, 1966. 215 p. (IAEA, Technical reports series no. 57)

615.849 681.3 '

COMPUTER CALCULATION OF DOSE DISTRIBUTIONS IN RADIOTHERAPY, IAEA, VIENNA, 1966 STI/DOC/lO/57 FOREWORD

As in most areas of scientific endeavour, the advent of electronic computers has made a significant impact on the investigation of the physical aspects of radiotherapy. Since the first paper on the subject was published in 1955 the literature has rapidly expanded to include the application of computer techniques to problems of external beam, and intracavitary and interstitial dosimetry. By removing the tedium of lengthy repetitive calculations, the availability of automatic computers has encouraged physicists and radiotherapists to take a fresh look at many fundamental physical problems of radiotherapy. The most important result of the automation of dosage calculations is not simply an increase in the quantity of data but an improvement in the quality of data available as a treatment guide for the therapist. In October 1965 the International Atomic Energy Agency convened a panel in Vienna on the "Use of Computers for Calculation of Dose Distribu- tions in Radiotherapy" to assess the current status of work, provide guide- lines for future research, explore the possibility of international co- operation and make recommendations to the Agency. The panel meeting was attended by 15 participants from seven countries, one observer, and two representatives of the World Health Organization. Participants contributed 20 working papers which served as the bases of discussion. By the nature of the work, computer techniques have been developed by a few advanced centres with access to large computer installations. How- ever, several computer methods are now becoming "routine" and can be used by institutions without facilities for research. It is hoped that the report of the Panel will provide a comprehensive view of the automatic computation of radiotherapeutic dose distributions and serve as a means of communication between present and potential users of computers.

CONTENTS

INTRODUCTION AND REPORT

INTRODUCTION 3

REPORT ON PROCEEDINGS OF THE PANEL 9 1. Production of isodose charts for single, multiple and moving beams 9 2. Provision of corrections for body shape and tissue inhomogeneity 11 3. Sealed source calculations 12 4. Presentation and evaluation of results '.. 14 5. Economics 18 6. Organization and international co-operation 19 7. Philosophy and future 23 8. Recommendations 24

WORKING PAPERS

1. Single field distribution derived by theoretical methods as compared with empirical data 2 7 T. D. Sterling 2. Computation of dose distributions using wedge and compensating filters: correction for irregular body contours 36 J. van de Geijn 3. Computation of multiple and moving beam'distributions 53 J. R. Cunningham 4. Computer-assisted external-beam dosimetry with special reference to correction calculations and presentation of data . 63 J.S. Clifton 5. Correction of single-field distributions to allow for tissue inhomogeneity 74

Aê Dutreix 6. Effect of tissue inhomogeneities on external radiation therapy dose distributions 79 W. Siler and C. Dymytryshak 7. Computer calculations in interstitial seed therapy: I. Radiation treatment planning 83 II. Dose control after seed implantation 92 M. Busch 8. Automatic calculation of isodose curves from implants of radiation sources 100 С,. W. Batten and R.J. Shalek 9. Calculation of dose distributions for multi-field and moving beam irradiations and methods of presenting results 107 G. Schoknecht 10. The optimization of treatment plans 118 C.S. Hope, M.J.E. Laurie and J. S. Orr 11. Clinical evaluation of treatment plans: Criteria used to select optimum plan 129 H. Perry ; ; 12. Economics of computer dosimetry 146 I. Ragnhult 13. Systematic study of therapeutic radiation dose distributions ... 151 К. C. Tsien . ' ' 14. Evaluation of integral absorbed dose and other physical parameters characterizing the radiation field in external radiotherapy 157 I. Ragnhult 15. Organization of a computer facility in a hospital physics department 164 W. Siler 16. International co-operation in the use of computers 167 К. C. Tsien ' 17. Transmission of data: Digital processing of isodose patterns .. 168 К. C. Tsien 18. International co-operation in use of computers 171 T. D. Sterling 19. Clinical evaluation of treatment plans 177 E.W. Emery 20. Physicist or computer specialist? 182

BIBLIOGRAPHY 187

APPENDIX I: Glossary ...: 197

APPENDIX II: Questionnaire on use of computers for calculation of dose distributions in radiotherapy 201

APPENDIX III: Institutions using computers for dosimetric calculations in radiotherapy • • 211

LIST OF PARTICIPANTS 213 INTRODUCTION AND REPORT

INTRODUCTION

During the past few years there has been a rapid development in the use of automatic digital computers in radiotherapy. Several hospitals, particularly in the United States of America, are using such computers for routine treatment planning both in teletherapy and in interstitial and intracavitary therapy. Many other hospitals are acquiring their own computers or are arranging for access to an outside computer. These facilities are not necessarily intended, or even suitable, for dosimetric purposes in radiotherapy since there are various other uses for a computer in a hospital, e.g. payroll, inventory, documentation. However, it is probable that many hospitals would be interested in the dosimetric applications if the advantages of computers in this field were more widely known. Furthermore, even where a hospital has no prospect of acquiring computing facilities in the near future - as in most developing countries - it should at least be aware of the wide range of useful radiotherapeutic data that could be made available by other institutes which are using computers in this field. A small panel of physicists, radiotherapists and computer specialists, drawn from 7 countries, was convened in Vienna from 18 to 22 October 1965. The purpose of the meeting was to review the present position with regard to the use of digital computers for calculating dose distributions in radiotherapy, to consider possible future developments, and to make recommendations both to those working in the field and to the International Atomic Energy Agency. (The Panel did not feel itself competent to discuss analogue computers in detail, although it was aware that such machines have a potentially useful role in radiotherapy. ) A number of working papers on different aspects of the subject were prepared by the participants and were distributed in advance of the meeting. These papers were not presented formally, but served as background material and as a basis for discussion. Edited versions of the working papers are appended to the present publication, except for those which have since been published in scientific journals. The discussions of the Panel, occupying five working days, were too lengthy to reproduce verbatim. The present volume therefore contains only a summary report of the discussions which nevertheless, we hope, includes all the highlights and will convey a little of the meat and flavour of the ex- changes as well as the bare bones. Since the conclusion of the meeting two additional documents have been prepared and are included in this volume: a glossary of the most common terms used in computing science; and a survey of the computing applications, with details concerning such factors as time and cost, ' based on a questionnaire sent to all the institutes represented in the Panel. In addition, a list of institutions using computers in radiotherapy has befen compiled, mainly on the basis of information given in paper 15. Finally, the present volume contains a summary of the proceedings and conclusions of the Panel, and a number of recommendations and suggestions for future projects in this field. The use of automatic computers in radiotherapy is hardly more than 10 years old. The first paper was published by Tsien (1955). At about the

3 4 INTRODUCTION same time began the world-wide conversion from orthovoltage X-ray machines to cobalt teletherapy units and supervoltage X-ray machines that has been such an important feature of the development of radiotherapy in the past decade. Even during this transitional period the main application of computers in radiotherapy dosimetry has been in the high-energy rather than the orthovoltage range, and this will undoubtedly be the case in the future. The present publication is concerned essentially with high-energy radiation. Many of the working papers included in this volume contain short historical introductions. It is tempting to collect this material together to form a single historical survey covering all aspects of the use of computers in radiotherapy dosimetry. However, it is quite impossible to obtain an overall historical perspective at the present time. To change the metaphor: the first trees were planted only 10 or a dozen years ago, most of the growth has occurred in the past three or four years, and we are now standing in the middle of a forest which is expanding so rapidly that we can discern neither its present shape not its pattern of growth. It might, however, be useful and relevant to say a few words about what happened before the first trees were planted, since this aspect is hardly touched upon in the working papers. To revert to more scientific language: the basic problem in treatment planning in radiotherapy is to determine the dose at any point in an absorbing and scattering medium for a single stationary beam of radiation. The addition of the contributions from several fields and the assessment of the effect of movement, while by no means negligible tasks, are in many ways secondary to the problem of the single field. If corrections are to be applied, for oblique incidence, for body heterogeneity or for a modifying filter, they must be inserted at the single-field stage rather than after the fields have been summed. In most radiotherapy centres the problem of single-field distributions is solved, up to a certain point, by measuring isodose curves in a homogeneous phantom, usually a tank of water. However, the measurement of a large number of fields, for different radiation conditions, can be laborious; furthermore, information may subsequently be required on fields that have not been measured. Thus, from an early stage in the history of radiotherapy dosimetry, mathematics was looked to as an alternative to measurement. Unfortunately it proved impossible to dispense with measurement altogether; the best that could be done was to confine the measured data to the central axis of the beam and to utilize these data to calculate the dose at non-axial points and hence deduce isodose curves if required. The calculation depends on the fact that the dose at any point in an absorbing medium is the sum of the contributions due to the primary beam and to scattered radiation. The primary component presents no real difficulty and the main problem is the calculation of the contribution due to scatter, especially for orthovoltage X-rays in which the scatter component at a point may be several times larger than the primary component. Clarkson (1941) deduced a general expression for the dose at a point due to the scatter from an elementary pencil of radiation of cross-sectional area A at distance r from the point. However, this expression involved a function (the "scatter-radius" function) which Clarkson did not attempt to put into mathematical form, and the method therefore depended on numerical INTRODUCTION 5 addition of a series of finite, equally-spaced elements. The nest step was taken by Meredith and Neary (1944) who showed that the scatter-radius function could be represented by a modified Bessel function involving two arbitrary constants which could be determined for each set of irradiation conditions (half-value layer and source-surface distance) and for each depth. Meredith and Neary determined the values of the constants and of the integrated function - the "scatter integral" - to fit the experimental central axis data of Mayneord and Lamerton (1941), while a more comprehensive analysis was made by Quimby et al. (1956). The methods of Clarkson and of Meredith and Neary both use published central axis data to derive information on non-axial points. If the accepted central axis data are changed, the calculations must be re-worked. Thus, for example, the replacement of the Mayneord and Lamerton tables by those in Supplement No. 5 of the British Journal of Radiology (1953), and later by Supplement No. 10 (1961), necessitated the recalculation of the constants. This work was undertaken by Meredith in connection with the atlas of single- field isodose charts for orthovoltage X-rays by Tsien and Cohen (1962). In principle, a calculation method originally developed for medium- energy radiation can also be used for high-energy radiation provided that the constants are appropriately adjusted. Day has shown (1962) that the method of equivalent fields (Day, 1950) is valid over a very wide energy range, from soft X-rays to high-energy radiation, and he has applied the method to the calculation of single-field dose distributions (Suppl. 10 to Brit. J. Radiol., Appendix). On the other hand, the relative simplicity of high- energy dose distributions, arising from the fact that there is much less scatter than at lower energies, facilitates the use of empirical or semi- analytical formulae which describe the whole distribution and thereby avoid the need to split the dose at each point into its primary and secondary components. However, in at least one calculation method currently under development the two-component concept is re-introduced (see section 1 of the Report following this Introduction). A further property of high-energy dose distributions is that they appear to obey empirical but useful rules which enable a complete distribution to be plotted from measurements at a limited number of points. For example, the "decrement lines" described by Orchard (1964) for cobalt 7-rays are effectively straight lines which permit isodose curves to be obtained by interpolation and extrapolation based on a few points only. The same method has been used by Orr et al. (Í964) for 4- MV X-rays although the difficulty here is that the decrement lines are no longer effectively straight. The comparative simplicity of high-energy radiation dose distributions is, however, only one aspect of the use of these radiations. There are three other important aspects which should be mentioned here. Firstly, bolus packing on the surface of the patient is usually avoided with high-energy radiation, in order to preserve build-up effects, and the need therefore arises to correct or compensate for oblique incidence. Secondly, wedge filter techniques are much more useful with high-energy radiation than with orthovoltage X-rays, because the wedges are easier to design, the improved depth doses allow more versatility in the geometries employed, and the problem of "hot spots" is greatly reduced. Certainly wedge techniques, which were formerly confined to a few enthusiasts, are now in widespread use. 6 INTRODUCTION 6

Thirdly, although in principle the corrections for body heterogeneity are smaller for high-energy radiation, the possibility of giving effective treatment to deep-seated tumours has focussed attention of the heterogeneity problem. The tank of water (with perhaps one or two rule-of-thumb corrections whose main function is to satisfy the enquiring visitor) is no longer considered adequate. All these problems, and their solutions, exist independently of the digital computer. Summaries have been presented in ICRU Report lOd (1963), in a recent review by Cohen (in press), and in paper 5 of this Report. The unique contribution of the computer is not so much that it makes possible new solutions of old problems, but that existing solutions are lifted from the level at which corrections for one or two points in selected patients are obtained by slow and laborious arithmetic, to the level at which fully corrected isodose distributions are attainable for every patient. Finally, in this introductory section, a few words should be said on interstitial and intracavitary therapy with sealed sources. The panel was concerned with those types of therapy as well as with teletherapy, although admittedly the emphasis tended to fall on external beam therapy. However, it can be argued that, in the long run, the role of the computer in interstitial and intracavitary therapy will be even more important than in teletherapy. During the first half the century interstitial, intracavitary and surface therapy were virtually synonymous with radium therapy. Two stages can be distinguished: (i) The empirical stage, in which treatments were carried out entirely on the basis of personal experience and preference. Dosimetry was non- existent and the "dose" was specified simply by the total radium strength (mg) and the treatment time (hours). (ii) The systematic stage, in which some order was introduced into the chaotic situation engendered by stage (i). In the early 1930's Edith Quimby, in New York, investigated the dose in rontgens (first defined in 1928) arising from a regular array of needles used as a surface mould or as an implant. Shortly afterwards Paterson and Parker, in Manchester, published the classic papers in which they demonstrated how a given amount of radium could be arranged in a stated geometrical pattern so as to produce a defined dose in a treatment plane or within a treatment volume. Subsequently Quimby modified and extended her system in the light of the Manchester experience, and today most radiotherapy centres throughout the world would probably claim to follow either the Paterson-Parker or the Quimby system. The disadvantage of any radium system is that (except for surface moulds which are in any case of comparatively little importance) it is hard to translate theory into practice. The ideal array of co-planar, parallel needles is liable to be transformed into an irregular jumble within the living patient. The Paterson-Parker system is the most widely used and the most comprehensive, but is also the most complex and has the further disadvantage that its use requires a rather extensive stock of radium sources of different (though related) linear strengths. In both the Paterson-Parker and Quimby systems the dose is specified by a single number and this can be regarded as both advantageous and disadvantageous: advantageous because the dosimetry is thereby greatly simplified but disadvantageous because the number thus stated may not be the most INTRODUCTION 7 meaningful number with respect to the implant as a whole. Indeed, not only are the dose specifications completely different under the two systems, so that they are by no means interchangeable, but many people practising radium therapy have no clear idea as to what these specifications represent. Parallel with the development of the Quimby and Pater son-Parker systems for surface and implant dosimetry, the methods and dosimetry for intracavitary therapy of cancer of the cervix uteri were systematized. The methods now in use 'are generally modifications of the techiques which are usually called by their cities of origin: Paris, Stockholm or Manchester. All involve essentially a line of radium tubes placed in the uterine canal andtwosourcesplacedinthevaginalfornices. The dose is usually calculated at one or two anatomical points only and even so certain simplifying assumptions have to be made, chiefly with regard to the geometrical relationship between the uterine and vaginal sources. Interstitial and intracavitary therapy has now entered its third stage. An important factor here is undoubtedly the introduction of automatic computers but there are three other important contributory developments: (i) The substitution of artificial radioisotopes for traditional radium and radon. (ii) Development of "afterloading" techniques. Although these techniques were originally conceived as a means of improving the radiation pro- tection they also have important therapeutic advantages in so far as the geometrical pattern of inert containers may be carefully adjusted before the active sources are inserted. (iii) Development of improved methods of radiographic localization of sources within tissue. The role of the computer in the third stage is not yet fully known, but several interesting possibilities have already emerged: exact dosimetry based on the actual positions of sources in the patient; substitution of a full dose distribution for a single dosage figure; production of atlases of dose distributions to illustrate the effect of various geometrical errors. Perhaps the most exciting possibility, as the work of Fletcher and Stovall (1962) has demonstrated, is the correlation of dosage with clinical results in individual cases. Whichever of these avenues proves to be the most fruitful, the future of the computer in interstitial and intracavitary therapy seems well assured.

REPORT ON PROCEEDINGS OF THE PANEL

1. Production of isodose charts for single, multiple and moving beams ) The working papers presented to the panel are concerned mainly with the use of computers in treatment planning, i. e. the computation of dose distributions for multiple or moving beams. Only one paper (No. 1) deals with single fields per se. Nevertheless single-field data are basic to the calculation of more complex distributions, since the first task is to calculate the depth dose at a point due to a single stationary beam: the addition of the contributions at that point from many beams is a relatively minor matter. Clearly the output data can refer to either single fields or more complex situations, as required. Much of the discussion in the first part of the panel meeting was, in fact, devoted to the production and/or utilization of single- field data. Two approaches are used. In the first, the single-field dose at a particular point is obtained by interpolation in a table of depth doses which is itself derived from measured data. If the measurements are originally in the form of isodose curves, the distribution must be digitized on a suitable grid system - this is usually carried out by hand - to provide the table of input data for the computer. The second approach utilizes a mathematical generating function to calculate each dose ab initio. This function may be one of three types. Firstly, it may be theoretical, i.e. based on the distribution of radiation in an absorbing and scattering medium as derived from first principles. However, as Dr. Sterling pointed out (see paper 1), these techniques have not yet passed beyond the research stage. Secondly, the generating function may be semi- analytical, i.e. derived by analysing the measured data from a physical standpoint. Finally, it may be empirical, i.e. a mathematical expression whose sole virtue is-that it fits the measured data. The method of Meredith and Neary, discussed in the Introduction above, is an early example of an empirical generating function. However, the emphasis in computer work has tended to lie with the semi-analytical function. Clearly, in those computer methods using the interpolation of depth dose measurements, depth doses for wedge fields provide no difficulty. Some workers who have developed generating functions have also attempted to include wedge fields but at the present time no one is able to compute dose distributions for a wide variety of wedge fields. Methods using measured data directly can be employed with any quality of radiation but generating functions usually apply only to one quality, though Dr. Sterling reported that this empirical function derived for 60Co 7-rays has been successfully adapted for 4-MV X-rays with the change of some constants. The danger that a semi-analytical or purely empirical function may contain inaccuracies which are difficult to detect when observing a completed treatment plan was discussed by the Panel. Clearly, in deriving such functions, any approximation used should have a sound physical basis, and very great care should be taken over any introduced merely for convenience

9 10 REPORT

in programming a computer. However, the use of functions has an advantage in that some steps in interpolation can be avoided. Furthermore, these functions are less susceptible to the errors which arise in hand-digitizing of isodose curves. Human errors of this latter type are avoided in some centres by recording depth dose measurements in a form directly acceptable to a computer (e.g. paper tape). In general the Panel felt that for calculating dose distributions in a homogeneous phantom better results are obtained from the direct use of measured data, but formulae come into their own when corrections for inhonwgeneities are made and when three-dimensional distibutions are computed. The consideration of the relative accuracy of these two approaches led to the question of the accuracy of computer methods in general. Dr. Nickson expressed the desire for the accuracy to be stated on each computed dose distribution. Some figures on the accuracy of computed percentage depth doses relative to measured data were given. Mr. van de Geijn stated that his method gave inaccuracies of the order of -2% (i.e. computed value is always less than measured value) but that at regions near the geometrical edge of the beam and at depths of 4 to 5 cm errors of -5% could occur. In the case of wedge fields this value could be -7% on the side of the wedge maximum. Inaccuracies of the same order occur in cross-firing techniques and here the value stated is relative to the tumour maximum. It was pointed out by Dr. Cohen that an error of about 5% of tumour maximum could give rise to an uncertainty of 20 to 25% in the dose to a vital anatomical structure receiving around 20% of tumour dose. Mr. van de Geijn stated that in such cases transverse data at depths other than the nominal depth (see paper 2) could be ùsed by the computer to increase the accuracy in such regions. Dr. Sterling stated that his empirical function gave inaccuracies of about ±1 to 2 % over most of the field but that this figure rises to ±4 to 5% in the penumbra. The figures apply to depths greater than 1 cm and to field axes smaller than 20 cm. Mr. van de Geijn suggested that the standard deviation in the cumulative probability integral (see paper 1) should vary with different fields. In reply Dr. Sterling described investigations now underway of the effect on the standard deviation of variations in depth, collimation and field axis, Mr. Kalnaes (in press) described his method of computing depth doses which is derived from that of Dr. Sterling. In it the standard deviation has been made to vary with depth and an empirical term for the electron build-up has been included. The accuracy was stated to be ± 1 to 2% over most of a single field and ±5%, relative to the surface dose of one field, for a multiple field dose distribution. A general statement on the accuracy of computer methods relative to conventional hand methods was made by Mr. Siler and is quoted below: "The accuracy of a computer treatment plan depends upon essentially the same factors as a manually prepared plan, with one additional factor and one additional hazard. The potential sources of error which are common to both methods are: (1) Inaccurate input data (2) Inaccurate assumptions about the patient, e.g. neglect of body curvature and inhomogeneities (3) Inaccurate calculation methods. REPORT U

The additional factor is the substitution of the machine for the man, and this eliminates human error (other than in iput data). However, a source of strength is also eliminated, the ability to exercise human judgement in the course of the calculation, and internal data checks must be built into a computer programme. Since in treatment planning the main need for human judgement is to detect human error, some compensation for this loss is present. Human error tends to be random, computer error on the other hand is consistent and once eliminated is gone forever. The additional hazard in computer calculations arises from the incom- pleteness of available experimental dose data to confirm the calculations. This is particularly true of the three-dimensional dose distributions, with corrections for patient curvature and inhomogeneities, which are now possible. An effort should be made to provide suitable data so that the computer's ability to produce information of greater quantity and accuracy than is possible by manual methods can become an advantage instead of a danger". It was generally agreed that Mr. Siler's statement provided the link, necessary to the radiotherapist, between manual and computer produced treatment plans. Furthermore, to express the error on a treatment plan meant giving a number of different confidence intervals pertaining to different regions of the plan and to do this in relation to measured data provided no problem to the computer. In the course of the general discussion on methods, Dr. Cunningham outlined his more recent work (see Appendix I of paper 3). This method involves a reversion to the orthovoltage techniques of breaking down measured depth dose data into primary and scattered components and a new function called the scatter-air-ratio is defined which is independent of source to surface distance. The choice of reference grids was briefly discussed. Polar co-ordinates are particularly useful when dealing with intersecting beams and have the economic advantage that points are closer together in the region where more information is required. However, since the transformation of co-ordinates is a trivial matter for a computer, it is possible to choose any co-ordinate system which seems favourable. In particular where dose distributions are to be plotted by machine a cartesian system for the patient grid is advantageous. In the course of the discussions on methods and accuracy it became clear that some confusion was arising from the terms used by computer specialists. Dr. Cohen and Dr. Nickson proposed that a sub-committee should be formed to produce a glossary of computer terms, used in the Panel discussions. The resulting glossary is given in section 5 of this report.

2. Provision of corrections for body shape and tissue inhomogeneity

The discussions of the last topic were in general addressed to considerations of the ability of computers to produce dose distributions in a homogeneous medium (a tank of water) by combining or predicting the effects of fields incident normal to the medium. In this section more detailed consideration is given to the methods in which more realistic approximations to the patient treatment situation are used. 12 REPORT

The Panel discussions showed (see papers 2, 4, 5 and 6) that there is no difficulty, in a computer programme, of making adequate corrections for body shape. The distinction between making such corrections and the alternative of using compensating filters was made by Mr. van de Geijn in whose paper (No. 2) equipment for simplifying the construction of such compensators is described. This equipment was shown to the Panel and its use demonstrated. It was suggested that, in some circumstances, the use of compensating filters and a correspondingly simplified method for calculating dose distributions might be more economical than direct correction by the computer. The importance of corrections for tissue inhomogeneities was highlighted by Madame Dutreix, who stated that the effect of tissue inhomogeneities on high-energy photons could give rise to errors of 20 to 30% in doses calculated on the assumption that a patient could be considered as a homogeneous water phantom of the same shape. Mr.Siler described a programme in which tissue inhomogeneity is included in the calculation of the dose distribution, but stated that there is a grave shortage of experimental data to confirm the calculated depth doses in a heterogeneous medium. Also it is very difficult to establish the positions of the boundaries of anatomical regions in individual patients. This point was discussed in some detail. The necessity of radiological equipment to carry out transverse axial tomography on the patient in the position of treatment was stressed. It appears that no equipment of this sort is commercially available at this time, though a Japanese company is reported to have produced one. Other equipment to do this, which should be available soon, includes modified versions of standard buCo and linear accelerator simulators. A design for similar equipment has been made by the Regional Radiotherapy Department. Newcastle General Hospital, UK. Mr. Siler pointed out that his work had indicated that a problem of equal importance was the establishment of reliable density values for anatomical structures such as lung. A measurement technique perhaps based on exit or transit dose is required. In parallel with the difficulty of producing detailed information on inhomogeneities is the problem of how to relate this information to the computer. A piece of peripheral equipment under development by various groups in the United States can assist here. This is Sketch Pad, a device consisting of a cathode ray oscilloscope and a 'light pen1. By means of this equipment it is possible both to display the results of a calculation (e.g. isodose curves) and to input data to the computer by altering the display manually with the 'light pen'. It is likely that this equipment when available commercially will be very expensive. However, as Dr. Cunningham pointed out. developments of this kind are increasing the potential of computer methods beyond the possibilities of manual computation.

3. Sealed source calculations

There are two distinct problems in interstitial and intracavitary therapy; these are the design of ideal implants to deliver a fixed minimum or average dose to a fixed shape of tumour, and the calculation of dose distributions in the vicinity of actual implants. Computers can assist in both these problems as papers 7 and 8 illustrate. REPORT 13

Interstitial and intracavitary implantations of sources present at least three problems which are not found inteletherapy: (i) it is usually technically impossible to carry out the treatment exactly according to plan; (ii) because of the short treatment distance, small errors in the source geometry can cause a large deviation from the planned dose; and (iii) because of the relatively short overall treatment'time of 2 to 7 days, dosimetric information must be provided very quickly if necessary changes are to be made in the treatment. v In view of these problems, for many years the practice in interstitial implants has been to calculate a dose rate based on the geometry of the actual implant as shown by radiography. The assessment of the dose rate is facilitated by the use of radium systems, such as the Paterson-Parker system (1934), in which the needles are implanted according to certain rules and the dose rate is then easily calculated using the tables associated with the system. Although the Paterson-Parker system has been used with success, there are obvious limitations to the "system" approach to interstitial dosimetry: the variation about the calculated dose rate is dependent on the placement of sources, and furthermore the radiotherapist is presented with only one number to represent a complex radiation distribution. The dosimetry of intracavitary applications, when based on manual calculations, is normally limited to obtaining the dose at a few points of particular interest, such as Points A and В for cervix treatment. It is now possible to calculate complete isodose distributions for individual patients by computer, giving the radiotherapist information which he has never had before. Also, where needed, a computer can be used to formulate new methods of planning implants and to make a systematic analysis of implants of various sizes and distributions. Dr.Busch presented his work with reference to seed implants in which he has used a computer both to plan ideal implants and to assess the dose from actual implants. Although the seed spacing was thought by somé radiotherapists present to be rather large it was pointed out that these were 10-mCi seeds and that the earlier versions of the methods described had been applied to around two hundred patients with good results over the last four years. Miss Stovall, who introduced Dr. Shalek's paper, felt that a sufficient number of systems is already available for the design of needle implants and consequently the computer developments in this field are limited to the estimation of dose in practical situations. The radiographic location of sources is very important in sealed source work. Two radiographs at right angles with computer correction for magnifi- cation are in common use and give the most accurate results. In some situations transverse tomography or stereo films are used to facilitate the identification of sources when a large number is present. An interesting feature of Dr. Busch's programme (see paper 7) was that up to 150 seeds can be recognized and located by the computer from the data from two radiographs at right angles. Some interesting developments which make the input measurements from radiographs easier were reported. Dr. Sterling described an additional feature of the on-line Sketch Pad being developed at Washington University, St. Louis, USA. This consists of a viewing box with an arrangement of 14 REPORT mechanical arms, by means of which the co-ordinates of any point on the viewing box can be directly transmitted to a computer. A much simpler off-line device was reported by Mr. Hope which produces the co-ordinates, on paper tape, of points located manually by sin electric stylus. This latter machine is available commercially. Miss Stovall reported that the computer programme described in paper 8 has now reached the point where the main problem involves the evaluation by the radiotherapist of the data produced. Time-dose-volume studies have to be undertaken and here the computer's assistance will probably be necessary. Mr. Siler reported some work (Baiter et al., in press) in which 25 seed implant treatments have been analysed. The results indicated that the average dose was an important factor and he suggested that this dose needs to be stated in addition to the "Paterson-Parker dose" in order to assess the effect of an implant.

4. Presentation and evaluation of results

This topic of the agenda embraces two closely associated subjects which, for the convenience of this report, can be treated separately. Dealing firstly with the presentation of results, it may be said that, if a computer is programmed to print calculated dose data in the form of a list or table, a great deal of the benefit of the computer's speed will be lost in transcribing these data into a form which permits rapid visual assessment of the dose distribution. This is particularly true when the computer is to be used routinely, as visual presentation is essential to the radiotherapist in the evaluation of a treatment plan. Many of the working papers (see papers V, 9-13) give examples of the use of ordinary output devices to make plots, to scale, of dose distributions. The techniques for doing this vary. One method is to print the value of the dose at each point of a predetermined grid. Isodose curves are then interpolated and drawn by hand. Alternatively, the computer itself carries out interpolations to find the co-ordinates of points on isodose curves. A character is then printed in the nearest available print position for each isodose point located. A third variation is, in effect, a combination of these two: a code character is printed at every available print position on the printer. The code is such that a single character represents a range of dose values and the resulting print-out exhibits a shading effect in the various dosage zones. This method was the subject of some discussion. Dr. Sterling, the originator of the method just mentioned, tabled a pre- print of a paper entitled "Automation of Radiation Treatment Planning. V. Calculation and Visualization of the Total Treatment Volume" by Sterling, Perry and Weinkam (1965). The discussion centred on a figure from that paper which is reproduced here as Fig. 1. Dr. Meredith expressed doubt that a field arrangement, such as was used in the production of the figure, could produce virtually square isodose curves as the printing of the letter с in the figure exemplifies. Dr. Sterling pointed out that in this symbolic print-out each symbol represents a band of percentage depth dose of ± 5 on the value stated in the key (given at the bottom of the figure). Furthermore, with such a representation a line of с characters REPORT 15

FIELO PO*T»l-SIIE CO-Q.Ol ЧАТЕ OF ENTRY CO-OaOINMES OF EUT tt PHA uEISHT BE I.

6.00 6.SO

FIG. I. Dose distribution for plane marked Z = 2 could, and in this case did, conceal a shallow curve of the isodose line for the depth dose value 130. Dr. Meredith asked Dr. Perry if he did not find this misleading in some cases, and Dr. Perry replied that the symbolic print-out was a crude pattern which gave a general idea of the distribution and that a print-out of doses is also produced on which isodose curves are drawn. This latter print-out is used for the detailed assessment of the treatment. Dr. Sterling in reply to further questions said that no correction for body curvature was included in this particular calculation, and that the difficulty in accepting the shape of the dose distribution was the result of a lack of experience in seeing distributions in planes other than those parallel to that defined by the central axes of the radiation fields. Dr. Cunningham doubted if any more information could be obtained from such planes and felt that curvature corrections could be carried out more easily on conventionally oriented planes. In reply, Dr. Perry stated that the conventional planes were produced in actual cases and this particular set of distributions was produced only for this paper, to illustrate the freedom which the therapist had in requesting information from the computer. Dr. Sterling made it clear 16 REPORT that this was only one of many displays which Dr. Perry uses and that it allows him to make a quick assessment of possible treatments while more quantitative displays are used when finer evaluations are being carried out. In recent years two further computer output devices have been introduced into the field of dose distribution presentation. These are graph plotting machines and cathode-ray oscilloscope display units. Examples of the use of these are contained in the work of Shalek (paper 8) at the M. D. Anderson Hospital, USA, and Bentley (1964) at the Institute of Cancer Research, UK. Graph plotters produce much more accurate and visually pleasing isodose patterns than standard printing machines, but two points should be noted. To provide continuously varying data for a plotter, the dose at many more points must be calculated, either directly or by interpolation. Furthermore, a graph plotter is very slow relative to the speed of production of dose data. In most installations it is likely that it will be operated off-line with its own magnetic tape input equipment for maximum economy. Oscilloscope display units permit very fast communication of information from the computer directly to the therapist but it is important that some means of recording information should also be available. This may be achieved either by photographing the display or by including a section in the programme which produces a supplementary printed record. Future developments in the display of dose distributions would seem to depend on the availability of graph plotters, oscilloscope display units and even more sophisticated machines such as Sketch Pad, mentioned above. Various machines of this type are being developed, particularly in the United States, and will soon be available. Sketch Pad is a very important step forward in man-machine communication since it has both an analogue output, via a cathode-ray oscilloscope, and an analogue input, whereby the operator may draw pictorial information on the oscilloscope with a 'light pen'. As has been stated above, the evaluation of a treatment plan demands visual presentation of the dose distribution. Thereafter the basic difference between evaluating a computer produced distribution and a manually produced one arises from the amount of detail which is available from the computer. This is nowhere more clear than in interstitial treatments. A detailed dose distribution in three dimensions can now be obtained by the computer where formerly only a single dose-rate value, or at best dose-rates at a few selected points, was produced. In teletherapy, also, three-dimensional distributions are available and, in both calculations, corrections for tissue inhomogeneity can be carried out. What does all this additional detailed information mean to the therapist? The answer to this question cannot be given at present. It requires time for the analysis of effects and for the accumulation of experience based on such analyses. The desire to improve treatment plans leads to the concept of the optimum plan for an individual treatment. The ease with which a computer can produce a treatment plan makes it realistic to seek the optimum distribution. Several approaches to computer optimization are presently being examined. One of them is the subject of paper 10. In this approach an attempt is being made to define a set of score functions, each of which awards a score according to the value of some attribute of a treatment plan. It follows, therefore, that in defining such functions a knowledge of the features which the therapist uses to evaluate the plan is essential. REPORT 17

In the panel discussion, Mr. Hope indicated that the system presented in the working paper was, as yet, purely experimental and that the score functions used were the products of the experience of a group of radiotherapy physicists. The project did not have the direct participation of radiotherapists. Dr. Emery expressed the view that this was a serious deficiency in any new system for radiotherapy. Dr. Sterling felt that in defining mathematical expressions there was a danger of losing communication with therapists whose training in mathematics was slight. Dr. Nickson agreed and in reply Mr. Hope stated that communication need not be lost if the therapist defined the score function as a curve on paper. It was then the computer specialist's task to fit a suitable mathematical function to that curve. Once the computer has produced an optimum plan it would be printed- out in a form permitting visual assessment and the therapist would then be able to judge its value in the usual way. Dr. Sterling suggested that the standard computer programmes for producing treatment plans permitted an approach to optimization which was more acceptable to the therapist. These plans allowed the therapist to investigate quite quickly such variations in a treatment specification as he felt were necessary. This is the arrangement which has been in use for some time in Cincinnati. Mr. Hope pointed out that there is a danger in many computer tasks of producing much more information than can be assessed by any manual process. Dr. Perry, in introducing his paper (paper 11), reaffirmed the benefit of the system which he and Dr. Sterling operated and stressed the importance of having an accessible computing installation in close proximity to the radiotherapy centre. This makes replanning a simple matter when changes in the tumour occur during treatment. Mr. Siler felt that human assessment of plans in three dimensions was very difficult and that score functions might have an important part to play here. Dr. Cohen suggested that much of the detail of a computer produced treatment plan was ignored by the therapist who, in practice, would examine certain criteria and judge the plan on these. He felt, therefore, that the approach of Hope to optimization was very important since he tried to define these essential criteria and thereby to avoid computing unnecessary data. In reply, Drs Nickson and Perry suggested that, while it was true that some of the data now produced could not be used, this was due to the inexperience of radiotherapists, who had not yet learned to interpret a full dose distribution. The question of the number of criteria required in an optimizing system was raised. Dr. Sterling expressed the view that computer methods of pattern analysis were not as good as the human observer. Mr. Hope stated that he had come to no conclusion on the number of criteria required, and that essentially an optimization system had to remain ready to receive additional criteria as knowledge of physical and radiobiological processes developed. Dr. Nickson stressed the importance of retrospective and prospective analyses of treatments for the production of the knowledge necessary to evaluate plans. Mrs. Ragnhult described some work in which she has been considering various factors in the evaluation of a plan. She has defined risk zones rather than score functions pertaining to the values of the factors studied. These are carefully recorded with the intention of correlating them with effects 18 REPORT at a later date. One of the factors studied is integral dose (see paper 14) and this was discussed at some length. Mrs. Ragnhult suggested that the distribution of the integral dose throughout a treatment plan was very important. Madame Dutreix stated that, although the patient's reaction to similar treatments might be related to integral dose, the comparison of different treatment techniques, such as multiple fixed fields and moving fields, required a more complex factor. Dr. Emery thought it desirable to calculate the distribution of integral dose for every plan so that its usefulness could be examined, even though the total integral dose is not closely correlated with the patient's reaction. An analysis of betatron treatments was reported by Dr. Perry who had been unable to correlate either response or systemic reaction with integral dose. On the basis of this study, and a similar one on 60 Co treatments, he concluded that the particular region of the body is important and that the integral dose cannot be used in isolation. Dr. Cohen introduced the "integral dose efficiency factor" into the discussion; he stated that rarely does an external beam treatment achieve an efficiency of greater than 0.25. He asked for the opinions of the radiotherapists on the usefulness of this factor. Dr. Emery said that it was desirable to establish a useful measure of healthy tissue irradiation. Dr. Nickson suggested using the factor to test the validity of the assumption that maximum energy should be delivered to the target with minimum energy outside. Dr. Perry outlined some further studies of white cell counts, which again stressed the importance of the position of the irradiated tissue in the body. Mr. van de Geijn reported a study of the distribution of integral dose in 28 bladder cases having similar treatment specifications and again no correlation with the effects on the patient was found. Madame Dutreix described a similar lack of correlation in implants, where the efficiency is high. It was concluded that, as yet, no direct correlation has been established between tumour response or systemic reaction and the integral dose definitions so far examined. Such factors as patient size, tumour size and position in the body may play an important part and have not yet been fully investigated. Dr. Nickson suggested that the effects may be associated with biological rather than physical parameters, though it was important that the physical aspects, about which more is known, should be studied.

5. Economics

The cost of producing a treatment plan by computer is a factor which must be considered when routine use is envisaged. Unfortunately, it is a factor which is very difficult to define, owing to differences in the computer techniques used. The bare cost of a plan is a function of its detail and accuracy, the computer used, of the efficiency of the programme and of the organization of the computer installation. A careful study of costs is presented in paper 12. Some additional information, with various sets of conditions, was given by members of the Panel. These additional data on costs are set out in Tables I and II in which there are many blanks and manv inconsistencies. For more detailed enquiry into methods and costs the

2* REPORT 19 reader is referred to the working papers and to the other published work of the individuals concerned. It is apparent from Table I that the cost of computer produced plans for teletherapy treatments does not vary greatly between centres. Comparing computer costs with manual costs, the table indicates that fixed field plans are more expensive by computer, but this is compensated for by the additional detail of the information obtained. Moving field plans are less expensive by computer, and again more detail is produced. Costs for interstitial and intracavitary distributions are shown in Table II. In general, these calculations are more expensive than for teletherapy because of the greater number of sources involved. No comparison between manual and computer methods is possible because the time required for manual calculation of detailed dose distributions for sealed sources exceeds the treatment time and such calculations are never carried out. It may be concluded that the cost of a treatment plan increases with the number of sources, the amount of detail, the accuracy and the realism of the assumptions about the patient. It decreases with the use of larger and faster computers, particularly if plans can be batched. As Dr. Nickson pointed out in the discussion, the use of computers in treatment planning is a technique which is at present carrying heavy development costs. It is encouraging that, even so, the costs are comparable with manual processes where development costs, in the main, have long ago been met. The comparison was highlighted by Mr. Clifton who felt that the cost of computing as a service to a radiotherapy department, while an important factor, must be considered in relation to the overall cost of treating a patient. In his centre, in one year, computer costs for radiotherapy are around £1000. This is comparable with the salary of the technician who would otherwise be required for this work. Dr. Emery said that the bare cost is only a small fraction of the overall cost of patient care. Further- more, the most rewarding feature of the computer investigations is that the whole field of treatment planning is receiving a thorough reappraisal.

6. Organization and international co-operation

Under this broad heading five topics were considered by the Panel; the organization of facilities within a hospital, the exchange of ideas between active groups, the exchange of more detailed information suchas programmes and systems between active groups, co-operative projects and the possibilities of using centralized computing installations. The reader is referred to papers 15, 16, 17 and 18. The standard methods of exchanging ideas are scientific journals, conferences, specialist group meetings and personal communication. Journals have two disadvantages which gravely limit their usefulness. Firstly the time lapse between the submission of a paper and its appearance in print is. seldom less than nine months. Secondly, the number of joúrnals, which a specialist in any field must examine, is such that a large amount of his time is absorbed with no guaranteed return. Conferences provide a better means of exchanging new ideas, but they must be attended by all interested parties because the time lapse in producing proceedings is comparable with journal delays. At most large conferences the greatest benefit to the individual is 20 REPORT

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TABLE II

COSTS OF COMPUTATION OF INTERSTITIAL AND INTRACAVITARY DOSE DISTRIBUTIONS

Panel Member Computer Calculation type Number of points Cost per plan (US$)

Hope Sirius Intracavitary 300 28

Shalek IBM 7094 Interstitial and 2500 7 intracavitary

Siler CDC 160 A Interstitial - 100 and up gained by personal contact with other participants or attenders. Specialist group meetings are better still since they have the advantage of a narrower field of interest. Personal contact either by visits or written communication is the best means of exchange, and it was suggested by the Panel that the Agency might take a part in exchanging information at a pre-publication stage between co-operating groups. The exchange of programmes and systems is hedged with complications. The manufacturers of computing machines do not co-operate in providing users with unified programming languages or unified control of input and output. Though some attempts to correct this are being made by writing compilers for a few commonly used languages, the fact is that rarely can a programme for one machine be run on another without major alterations. Even if the language problem were overcome there is a further complication. Rarely do two installations, even when based on the same central processor, possess precisely the same configuration of input units, output units and backing stores. Thus programme or system exchange is not a practical reality. As Dr. Curiningharrç pointed out, even if programme exchange were possible , no physicist in one centre would accept a programme from another without knowing completely the methods of calculation used in it. Algorisms (the mathematical statements of the method) can, however, usefully be exchanged, and the information in the documentation of the programme is more important than the programme itself. In the panel discussions it became clear that in a number of areas of study there is a great need for more work and that in many cases this need could best be satisfied by groups co-operating rather than competing. It was suggested that the Agency might foster such co-operation, and the proposed areas of study are contained in the Panel's recommendations to be found in the conclusion of this report (section 2.8). The final topic, the possibilities of using centralized computing installations, was discussed by various Panel Members who have experience in this field. Dr. Sterling stated that his centre at Cincinnati was within two days reach, by air mail, of any point in the United States. Consequently, if a treatment set-up were specified by telephone, the detailed plan could be received in around 48 hours. A 24-hour service operating in a smaller area is probably more acceptable to radiotherapists, particularly where REPORT 23 interstitial and intracavitary calculations are required. For optimizing treatment plans by trying different arrangements, an on-line console at each treatment centre is possible. This is expensive and is only satisfactory with a time-sharing computer. However, such costs, can be shared by several departments in a general hospital. Mr. van de Geijn expressed his interest in such a service for a small country like Holland. As a result of his studies, he suggested input by Telex line and output by mail. Mr. Clifton described his experience with Telex lines in which one of the difficulties is in the coding of information on paper tape. The code used by the General Post Office in Great Britain is different from that used by the computer at his centre. This means that conversions have to be carried out and this in turn complicates visual checking of results. Furthermore, there are no automatic checks of data sent with data received and such checks have to be introduced. In general, it may be concluded that the data links at present available are expensive and, until costs are reduced, the more conventional methods of post, telephone and human messenger are superior. During the discussion of the question of aids to communication Dr. Tsien introduced the method described in paper 16. This method eases the problem of the transmission of graphical data and has some interesting additional features for analysing dose distributions.

7. Philosophy and future

In considering the philosophy of the use of computers in radiotherapy treatment planning and the future of this field, it is well to review the present situation in the words of Mr. Siler. "This is not a field which is finalized. We are engaged in a process of iteration which will continue for some time. Three paths are being followed; (1) routine work, the automation of standard hand methods at reasonable cost and with reasonable accuracy; (2) research studies, the investigation of factors not previously considered (e.g. three-dimensional distributions, tissue inhomogeneity and optimization); (3) development work, the production of data for atlases and the development of new hand methods (e.g. implant design and systematic studies)." Three papers (papers 13, 19 and 20) formed the basis of the discussion. Dr. Emery made a plea for not advancing too rapidly. He felt that computers should first be used to replace, and where necessary to improve, existing hand methods. All radiotherapy centres should be brought up to this level before further advances were made. Numerous speakers stressed the danger that automation could tend to abrogate the responsibility of the clinician to the patient. It was felt that, while this danger was easily overcome, measures must be taken to guard against the more subtle effects on the training of radiotherapists. Mr. Clifton stressed the necessity of the computer for routine work, while Dr. Tsien favoured research and development projects. Dr. Meredith pointed out that, with each advance in accuracy and in detail, the radiotherapist could lose sight of the important clinical correlations accumulated in his own experience with treatments based on less accurate concepts. At each stage the therapist needs to establish new base lines to connect past and future (practice. 24 REPORT

The importance of analysing old case histories was discussed and the difficulties in carrying this out, owing to inadequate clinical records, was recognized. It follows that in all current treatment processes good records should be kept for future studies, and,here the computer has a part to play. •Mr. Siler raised question, should there be general agreement on the facilities contained in a computer programme? If a 'universal1 programme were produced, radiotherapists would have the freedom to examine the potential of techniques which are not normally used at their centres. The possibilities of automation of the whole therapy process, though outside the scope of the Panel, were mentioned. Dr. Sterling stated that radiotherapy should proceed according to reasonable rules and such rules could be taught to a computer. One could conceive, for example, of a treatment machine which could sense a movement by the patient and alter its position accordingly to maintain the treatment specification. One less futuristic possibility introduced by Mr. Clifton was the production of a field specification on punched cards for a treatment plan. These cards could then be read by the treatment machine which would set its portal size and source position automatically. It is clear that a treatment plan, however accurate and however detailed, is only a part of the treatment process. Variable factors, including tumour location, biological response, accuracy of applying the planned treatment and treatment machine calibration must also be considered when a treatment is evaluated. It is to be hoped that developments in all aspects of treatment will be stimulated by the developments in treatment planning brought about by the use of computers.

8. Recommendations

At the close of the discussions, the Panel set forth several recommendations concerning the role of th Agency in encouraging further activity in this field: (1) The Agency should continue its interest and encouragement of meetings such as the present one. (2) The Agency should consider the provision of a service for the distribution of preprints of papers, possibly on a subscription basis. (3) The Panel noted that the accuracy of computed dose distributions was as good as, and should be better than, hand computed data, but felt that to test the computations now available, more experimental measurements are desirable. The agency should encourage this. (4) Retrospective studies should be undertaken or the correlation between dose distributions and results of treatment, in teletherapy, interstitial and intracavitary therapy. The Agency could facilitate this work by co-ordinating the projects of different institutes and by arranging co- operative efforts where necessary. The Agency's programme of "cost-free" research contracts could provide a suitable framework for such co-ordination. WORKING PAPERS

SINGLE FIELD DISTRIBUTION DERIVED BY THEORETICAL METHOD AS COMPARED WITH EMPIRICAL DATA

T.D. STERLING MEDICAL COMPUTING CENTER, COLLEGE OF MEDICINE, UNIVERSITY OF CINCINNATI, OHIO, UNITED STATES OF AMERICA

There are three fundamental approaches to the calculation of the dose at any point in space. First is the theoretical derivation of the dose distribution from fundamental principles describing the behaviour of nuclear materials. The second fits a general field equation to available empirical data without being concerned whether or not the mathematical expressions derived have any bearing on the understanding of the physical nature of the universe. The third method of calculation derives estimates of the dose at a particular point by approximation and interpolation from known values of nearest points in a physically measured space. All three approaches are pursued today with the help of the computer, albeit at different levels of sophistication.

THEORETICAL DERIVATION OF A GENERAL FIELD EXPRESSION

The numerous methods developed by the physicist for calculating the distributions and energy spectra of scattered gamma rays in space have not resulted so far in any neat formal solution to dosimetry problems, although some progress has been achieved. Most of it has been summarized by Aaronson and Goldstein (1953). Fundamentally, the big problem that has not been solved yet is to describe the penetration diffusion of X-rays in such a way that solvable equations can be derived from more general statements. What has happened instead is that numerous numerical methods have been developed to approximate solutions for complex formal expressions. One of the more promising of these has been the "Moments Methods" developed largely by Fano et al. (1960). Their calculation technique is limited to infinite homogeneous media and is most easily handled for simple source geometries, although there is considerable flexibility here. An extensive series of calculations on the penetration of gamma rays in infinite homogeneous media using the moments method was done by Goldstein and Wilkins (1954). Spectra of scattered photons, due to mono-energetic sources ranging in energy from 0.5to lOMeV, were obtained at distances up to 20 mean free path lengths in eight materials whose atomic numbers varied from 0 to 92. Recently other numerical approaches have been developed using Monte Carlo techniques. These are techniques by which the random movement of particles are re-created and libraries of such movements constructed. These approaches have suffered, however, from two basic drawbacks. First of all they are not really formal derivations of solutions to scatter problems derived from first principles. They are numerical techniques

27 28 STERLING

(based on a good bit of theoretical work)'for-solving the integro-differential Boltzmann equation for certain simple geometries. In the second place they require rather large amounts of computer time.

FITTING A GENERAL FIELD-DISTRIBUTION EQUATION TO EMPIRICAL DATA

Equations that describe the dose distribution generated by an irradiating source can be based also on the possible geometries and relationships that exist within the parameters of the dose distribution. Successful "fittings" have resulted in equations which have all the advantages of calculating dose at a point except that they may have no theoretical content. This lack tends to disturb the empiricist less than.the theoretician. From the point of view of calculating dose for treatment purposes, empirical curve fitting frees the user from the many shackles imposed on him by theoretical development. Above all, he is able to seek the fastest, cheapest, and most accurate method of calculation available to him without regard to any other considerations. The end product of the curve fitting process ought to be a measure of dose at a particular point expressed as some fraction of dose at a standard point. This comparative measure is usually referred to as the "per cent

depth dose", R(P)(X> Vi zl. The reference point for R(P) may be any point below the surface of the skin, although it is usual to place it at the location of the largest electron build-up, and (x, y, z) are its co-ordinates. (In our notation, x describes the length of the field, y its width, and z the depth below the surface along the central axis. All distances are understood to be expressed in centimetres. R(PVo,o,0.5) = 100.00% is the dimension of the dose at the point of the highest electron build up for cobalt-60 and similar energies.) Despite the short history of the attempt to develop empirical expressions, two divergent approaches are already emerging. One of these is based on first calculating "Dose in Air" and then introducing proper tissue absorption factors (which are obtained from measurements) to convert dose in air into per cent depth dose in tissue. The second approach develops expressions directly for per cent depth dose.

Computation using dose in air

A quick method of calculating doses can be based on computing the dose in air at a point and then converting this dose into a per cent depth dose by what is called the "tumour air ratio" or "tissue air ratio":

(R(P)(MiF+z)=R(D)(x,yiF+z)d(A) (1)

where R(D)iXiVi f+2) is equal to dose in air to a point that lies within the length and width co-ordinates x and y in the field and at a depth given by the skin source distance, F, and the distance below surface, z. The expression d(A) stands for some function which determines the absorption factor. In this general expression, R(D)^x, v, F+z) cannot be assumed to be completely PAPER 1 29 independent of all factors except the inverse square law and the quality of radiation at some point. Dose in air at a point depends also on field size and on the amount of divergence from the central axis of the beam. The absorption function, d(A) definitely is a function of field size, SSD, depth below surface, and divergence from the central axis.

Direct calculation of per cent depth dose

A newer approach seeks to develop a mathematical expression for per cent depth dose directly.

R(P)(x,y,z) = g(F,S,z,0) ' (2)

where g(F, S, z, 0) represents a function of skin source distance, F, size of the field, S, distance below surface, z, and angle of divergence, 0. We have talked so far only about beams entering normal to the surface. For both approaches of calculation, additional factors are introduced for beams that enter the medium at an angle, for the curvature and inhomogeneities of the medium, for wedges, and for other factors. All these will be ignored here and in subsequent discussions partially for the sake of sim-

plicity and partially because there are still many unknown factors involved ч in developing such equations. There are a number of good reasons why the direct approach to the computation of per cent depth dose is preferable to computing dose in air as an interim step.

(1) Calculation by computer of R(D)(Xiy>p+Z) may be as complex as computing R(P)(x,y, F+z) directly for all practical purposes. (2) The absorption function, d(A) has not been studied adequately and while tables of tissue air ratios are available and more can be determined empirically, the factors determining d(A) are many and need separate calculations. Even when these factors can be determined satisfactorily and an adequate equation for absorption exists it is still necessary to undertake two calculations if a dose in air approach is taken. (3) Recent breakthroughs have reduced the number of parameters needed

for calculating R(P)(X, y, F+Z) directly. In fact it is potentially simpler now to compute per cent depth dose directly even if no computer should be available. Thus, for the purposes of radiation treatment planning and other related needs, a shorter and less costly calculation is made possible by the direct method.

DIRECT CALCULATION OF R(P)(X,Y,F + Z)

A number of attempts some years ago fitted curves with varying de- grees of success to.per cent depth dose data (Meredith and Neary, 1944; Quimby et al. , 1956). Because of limitations imposed by the then computer- less world, the results of these early procedures are relatively difficult to calculate and have fairly large errors of estimate. Also, these equations cannot be expanded to describe doses off the central plane. The more recent 30 STERLING procedures give the value of per cent depth dose at a point in a medium by the following expression (Sterling et al. , 1964; Sterling et al., 1965).

R(P>(x,y.F + z) = R

(0,0,F + z) f(P> (3) where R(P)(o,o, f+Z) is the per cent depth dose on the central axis and f(p) is a function describing the divergence factor from the central axis. Calculation of R(P)(o,o, f+Z) is made easy because of the discovery that dose along the central axis is simply a function of field size, S, for any F and quality of radiation (Pfalzner, 1960; Sterling et al., 1964). The exact relation was found by Sterling (1964) to be as follows:

i Ti/ni u , i /Area of field surface \ ... 1 n R(P)(o. o. F+i) = hi + mi (perimeter of field surfacej (4) where h¡ = intercept constant and m¡ = slope constant. The fact that this function turns out to be linear is welcome and simplifies calculations considerably. Even more convenient is that both h and m are linear functions of depth below the surface (see Figs. 1, 2, and 3 taken from Sterling, et al., (1964). As an aside it ought to be mentioned that similar relationships appear to be true for the central axis dose in air also

Log ( AREA / PERIMETER )

FIG.1. Change in per cent depth dose on the major axis by log ^per'meteIJ different cobalt-60 portal sizes at 80 cm SSD for distance of 3, 7,11.15 and 20 cm from the surface PAPER 1 31

.250-1

.200"

2.1 50-

10 20 30 Distance Below Surface in cm / area \ FIG. 2. Change in slope of axial per cent depth dose as function of log of the treatment field y peri meter J with distance below surface

i.800-

I .700-

1.500-

1.300

1.000 10 20 30 Distance, cm

FIG. 3. Change of intercept of axial per cent depth dose as function of log of the treatment field with distance below surface

(Pfalzner, 1960). Constants h¡ and m¡ can be determined by simple measurements. They are also related simply to SSD. The uniform expression for any point at the central axis is then given by

r,/T-, v , и , /Area of field at surface ) (5) H(P)(o.o,F+z)= [t(F.z) + t>(F.z)]ln ( perimeter of field at surface^ " 32 STERLING

FIG.4. Schematic diagram showing notation where t(F, z) and t'(F, z) are both functions of SSD and depth below surface and estimate h¡ and m¡ respectively.

An evaluation of f(p) for expression (3)

Sterling et al. (1964) found this function simple to determine. It depends essentially on the value of a single parameter. The crucial relationships are shown in Fig. 4. P¡ indicates the dose for a point off the central axis anywhere in the treatment volume. C¡ is the geometric image of p on the central axis of the beam with source S. P;C¡S form a plane. L is the distance in this plane and on the surface from the central axis to the point at which the skin dose drops to fifty per cent of the value at the central axis; i is the distance between the central axis and the intersection of Pi S with the skin. R(P)(x,y,F+i) • the dose at P¡ is given by Eq. (6)

R p (6) < )(x,y,F + i) = f(i/L) R(C),( o. 0, F + i)

and f(j?/L) is given by a simple derivative of the cumulative probability integral:

where a rough empirical estimate of a is 0.17. Detailed methods for evaluating this integral quickly and easily both by hand and by computer are given by Sterling et al. (1964), Sterling et al. (1965), and Sterling and Pollack (in press). Insofar as the only factor determining dose at any point off the central axis is the ratio i/L, the dose at any point'in the volume of the beam may be,determined simply and easily by the use of vector notation and matrix algebra. This.makes the calculation for one point practically trivial as far PAPER 1 33 as computer time is concerned. (Short calculation methods are given by Sterling et al. (1965) and Sterling and Pollack (in press).) Although

APPROXIMATION METHODS BASED ON INTERPOLATION BETWEEN MEASURED POINTS

Early methods of dosimetry with a computer used hand digitized measurements obtained from printed isodose curves which were themselves empirically derived approximations. With automatic measurement of large three-dimensional grids of points, as are obtained now in our laboratory, it would of course be possible to extend the range of interpolation procedures as well as to make them more accurate. It might seem that with adequate equations available, approximation procedures based on measured data are superfluous. However, this is not quite true. It may well be that for really fast approximation to the dose at a point a simple look-up procedure for the nearest dose value may be a per- fectly adequate procedure. Bentley (1964) uses such a simple procedure which assigns to a point the same dose as that of the nearest point for which an actual measurement is available. The first automatic calculation method was developed by Tsien (1955) and later expanded and modified by Sterling et al. (1961). The approach used by them might be called the best "exact summation1' method. In this method, dose distributions are digitized in such a way that by super—imposition of doses the computer can be used to sum doses at specifically pre-determined points in a polar co-ordinate grid. The accuracy of this method is limited only by the accuracy of the dose measurements. The disadvantage of the exact method is that the preparation of data for'it is simply immense. Dose values in different polar co-ordinate grids have to be established for so талу different possible combinations of treatments, that for all practical purposes an infinite number of data points are necessary. The approximation proce-

3 34 STERLING dure by Sterling et al. (1963a, 1963b) decreased the number of data points needed for each isodose curve to one single grid by interpolating between the nearest measured points. In this method a single hand-digitized Cartesian co-ordinate grid is obtained for each portal size. The central axis of the beam serves as the ordinate and its perpendicular through the skin line as the abscissa. Each point of interest is located by its perpendicular distance from the ordinate and abscissa. The intersection of ordinate and abscissa serves as the origin. When a digitized grid for a single beam is superimposed on the outline of a patient, the points for which dose values are given do not usually coincide with the points in the area of interest for which the dose values are to be found. Rather each of the points in the grid describing dose in the patient is bracketed by the four nearest points of each of the digitized isodoses. Figure 5 shows a point P for which the dose is to be computed and the four points with doses Di, D2, Цз, D4, respectively of one of the digitized isodose grids which are adjacent to it. It is necessary, however, to translate the co-ordinates of P in the treatment field to the co-ordinates of P in the particular beam which lies in the treatment field, or, more particularly, to the position of the origin, ordinate, and abscissa of each of the digitized grids of the separate treatment beams. This is done as follows: Let M denote the major field and S¡ denote the digitized sub-field of the ith treatment beam. Le (X, Y) denote the co-ordinates of P and M and (Xi Y¡) denote the co-ordinates of P in Si. Let a¡ denote the angle of incidence of the major axis of the treatment beam with the ordinate of the basic grid. Let (h¡, kj) be the co-ordinates of the origin of the digitized treatment beam Si in M. Then

X = (Y - kj) sin a¡ + (X - h¡) cos a¡ (8a)

Y i = (У - k¡) cos a¡ - (X -h¡)sino.¡ (8b)

give the co-ordinates of P in S¡. The programme has to test to determine whether Xi and Y¡ are within the range of values in which the dose is non- zero. If one or the other is out of range it immediately sets the dose at P, Dpi = 0. The programme now has to find X¡ and Y¡ , the largest values of the X and Y co-ordinates in the grid of the treatment beam, which are just smaller than X¡ and Y¡, and computes

AX¡= X¡ - Xi (9a)

Д Y¡ = Y¡ - Y, (9b)

The dose at P contributed by the ith field, Dpi is now given by:

Dpi = W¡ (1- AX¡) [(1- AYi)Di;+AYi D3¡] + AX¡[(1 - ДY; ) D2¡ + Д Y¡ D4¡ ]] (10)

th where W¡ is the proportion of dose supplied by the i beam.

3- PAPER 1 35

FIG. 5. Geometrical relationships involved in calculating dose at Point P using dose rates at points D|, D2,

D3, and D4 on a digitized isodose grid

An extension of this method is of course possible for instances where measurements of doses in three dimensions are available. The same methods of interpolation can be used, but now, interpolations are done between the nearest eight points which surround the points in question. As has already been mentioned, Bentley has adopted an even simpler method of approximation by which the dose value of the point nearest to the desired point is simply substituted for the desired dose. In concluding the discussion of calculation from hand digitized or otherwise obtained dose values we stress again that the importance of this procedure will depend purely on computational convenience. At the moment the approach to dose calculation by a general equation is preferable. However, the day might come when computer memories are large enough to contain large numbers of three-dimensional grid points. It might then be simpler to move the grid points over each other in memory and simply interpolate among them or even adopt to the nearest highest value, than to use equations. If the main desire of the therapist is to investigate possibilities for better treatment, these latter methods might very well become important again. At the moment, however, they seem to be trivial. COMPUTATION OF DOSE DISTRIBUTIONS USING WEDGE AND COMPENSATING FILTERS; CORRECTION FOR IRREGULAR BODY CONTOURS

J. VAN DE GEIJN RONTGENAFDELING, ZIEKENHUIS VAN DE H. JOANNES DE DEO, WESTEINDE, THE HAGUE, THE NETHERLANDS

1. "INTRODUCTION

The title includes three separate subjects and, conventionally treated, they require rather different techniques in clinical practice. Only with the availability of computers has it become possible to treat these subjects together. They are three different aspects of the problem of a radiation beam interacting with a tissue equivalent medium, assuming the beam to be incident at right angles to a flat surface. Looking at the methods of calculation of dose distributions in general before computers became available, the basis for all techniques was the isodose chart, representing the empirical distribution of absorbed dose in one plane, thus limiting the irradiation techniques mainly to co-planar set- ups. With the help of a computer, using digitized isodose charts, the same calculation can be done much faster, though giving no more information. However, radiation beams produce three-dimensional distributions and' they need not necessarily give the best distribution in co-planar combinations. Here we touch the essence of an important problem: is it possible to give a general mathematical formulation for the dose distribution (a) at least in a limited range of energy (b) at least in a homogeneous medium (c) possibly in inhomogeneous media (d) possibly for a class or range of classes of radiation machines. There are some methods being developed; for example Sterling et al. (1964, 1965) use a generating function found by analysing depth dose data with curve-fitting techniques. They use this for stationary straight beam techniques, requiring adequate compensation in the case of oblique incidence or irregular surfaces. It is outside the scope of the present paper to discuss this further. In Great Britain Orchard (1964) has developed the decrement line system which, in two-dimensional problems, seems more versatile. Its main merit seems to be the possibility of generating conventional isodose charts much more easily, i.e. with less measured data. It is also useful for wedged beams. Correction for irregular surfaces is performed along empirical lines. The author has been developing, since the beginning of 1963, a generalized three-dimensional mathematical model for a beam of eoCo gamma radiation in a water-equivalent medium; the model can also be used for wedge field techniques, individualized compensation techniques and corrections for body contour irregularities. Details of this method, as far as straight stationary

36 PAPER 1 37 beam techniques, moving beams and wedge fields are concerned, were recently published (van de Geijn, 1965a), with some aspects of the adaptation for use of a computer. A paper on a new technique for individualized compensation was published recently (van de Geijn, 1965b). In this paper a condensed mathematical description of the model will be given, together with a brief review of the computational aspects of wedge field techniques and the correction for body outline. The problem of individualized compensation will be treated in detail. One must be careful to avoid a possible by-product of the great speed with which a computer produces great amounts of detailed results; an im- pression of accuracy can be given where it is not possible to be accurate. Therefore, generally speaking, conventional X-ray dose calculations should not be undertaken with computers. The three systems mentioned above are concerned with high-energy radiation only.

2. THEORETICAL MODEL OF A RECTANGULAR BEAM OF HIGH ENERGY ELECTROMAGNETIC RADIATION

A theory of the author (van de Geijn, 1965) is reviewed here, using a co-ordinate system consistent in all three fields of application considered and paying attention to the physical basis.

2.1. The co-ordinate system: notation

We shall consider the source as a point source, being the origin of a system of rays. The central ray is taken as the Y-axis. The point y - 0 is always taken at the source-surface-distance f. The rays are identified by co-ordinates x and z, measured in cm at a distance f from the source. The surface thus defined is called the nominal surface. For the range of field sizes and the values of f used in clinical practice, the nominal surface

is treated as flat. Quantities subscripted with a zero (P0 , d0, etc. ) refer to nominal situations, by which we mean perpendicular incidence of the beam axis at a flat surfâce. Otherwise we refer to gene ral situations.

2. 2. The physical basis ' - •

We limit our attention to 60Co-gamma rays and "equivalent" X-rays (2-6 MV) where virtually the only interaction mechanism is the Compton effect, which occurs between photons and free electrons. In this medium and for this energy range, all electrons can be treated as free. The electron density is only slightly dependent on atomic number in general, and, in the human body is sufficiently independent to the use of water as a reference medium.

2.2.1. The secondary electron produced in each "first" scatter phenomenon travels only a few millimetres and can (except in the first few millimetres beyond the surface) be treated as absorbed on the spot, at least for the present descriptive purposes. 38 VAN DE GEIJN

2.2.2. The predominant direction of the once scattered photon is forward, in a narrow cone around the original direction of propagation.

2.2.3. The fraction of once scattered photons, after a layer t, can be given by:

a^l-e"*'

Similarly, the fraction of n times scattered photons can be given approximately as:

стп = (1-e^i1). (l-e^t ). (l-e""nt)

Where цп represents the effective linear absorption coefficient for the nth

interaction per photon. The only thing we can say is that цп increases with n, slowly with n small. Also, the forward tendency will, in general, be preseryed for the first few scatter interactions, per primary photon.

2.2.4. The important suggestion emerging from this very qualitative consideration is that it seems worth while to investigate the possibility that scatter equilibrium might exist far into the penumbra, even for small fields. In other words, the lateral "reach" of contributions from second or higher order scatter phenomena could be sufficiently low to use the following model (fig.1).

2.2.5. For mathematical purposes, a beam of high-energy electromagnetic radiation (60Co and equivalent X-rays) in a water equivalent medium can be treated as composed of independent infinitesimal beams (rays), emitted by a point source. The behaviour of absorbed dose along each ray is governed by the same function g(d), where d represents the length of ray in the medium. The distribution across the beam is governed by a function p (x, z) depending mainly on geometrical parameters (field size, length of collimator, source-surface distance, source diameter).

2.2. 6. It was shown that, in the XY-plane, in a nominal situation, this leads to the following expression for the percentage depth dose

P0(x,y)=g{d0(x.y)} ^ Р(х.Уг) (D

where p (x, yt) =P0(x, yr)/P0(0, yr) do(x, y) =the depth of (x, y), for practical purposes measured parallel to the central axis (the y-axis); hence, here, d0(x, y) =y

g(d) =P0(o,d) ¿

yr =the reference depth for p(x) PAPER 1 39

FIG.l. Schematic cross-section, in the XY plane, of a beam entering a flat surface (nominal situation)

В =the back scatter factor f =the source surface distance

PQ С' У) = the central axis percentage depth dose at a depth y.

The quantities p, g, В and P0 depend on field size. The quantities g and В are, for a given field size, independent of f. Formula (1) is an approximation. To achieve optimal overall agreement, yr has to be chosen carefully. 2.2.7. In the general situation, we find (Fig. 2) in the XY-plane:

г,, v г „ 100 /f+0.5\2 P(x, y) - g {d(x, y)} — f+y J p(x, yr) (2)

2.2.8. Expansion for the third dimension (Fig.3) We now consider a rectangular beam as composed of flat beam elements, containing a ray through (0,0, z) and a line parallel to the X-axis. We assume that each beam element, in the nominal situation, shows a dose distribution point by point proportional to the distribution in the XY-plane, or

2 P0 (x. У, z) = gid0(x. У» z)} ^ (^f) P(x,yr,0) p(0,yr,z) (3) 40 VAN DE GEIJN

FIG.2. Schematic cross-section, in the XY plane, of a beam entering an irregular surface

In the general situation, this becomes, similar to Eq.(2)

P(x,y,z) = g{d(x,y,z)} ^ (^ïrf) p(x,yr,0) • p(0,yr,z) (4)

For straight rectangular beams, p(x, yt,0) and p(0,yr,z) are symmetrical about the Y-axis.

2.2.9. Application to the problem of individualized compensation for body contour By "adequate compensation for the effect of irregular body shape" we mean the combination of the application of a patient-adapted intensity modifying filter in front of the diaphragm and the corresponding setting-up of the patient. The desired effect (Fig. 4) is the production of a dose distribution in the irradiated part of the body resembling quantitatively a.s closely as possible the distribution obtained in the corresponding nominal situation. Complete compensation is possible only when applying a fitted block of unit density material directly to the surface. This technique, apart from being very time consuming as far as construction is concerned, destroys the skin-sparing effect. It is not further considered here. PAPER 1 41

•FIG.3. Schematic three-dimensional representation of a beam entering a flat surface

Let us consider the case illustrated in Fig. 4. The nominal contribution at (x, y) is given by

P0 (1)

Without compensation, we have

P(x,y)=g{d(x,y)} P(x,yr) (2)

It follows, that exact compensation, at (x, y) can be effected by a filter thickness, in the ray through (x, y), corresponding to

e"Xt(X) =g{d0(x,y)}/g{d(x,y)} or

t(x) = ^ [loge g{d(x, y)} - loge gído(x. У)}] (5)

In three dimensions:

t(x, z) = i [loge g {d(x, y, z)} - loge g{d0(x,y,z)}] (6) 42 VAN DE GEIJN

FIG.4. Schematic cross-section, in the XY plane, of a beam entering an irregular surface with the addition of a wedge filter. The reulting dose distribution is equivalent to one obtained with a flat surface (nominal situation)

Putting

d0(x, У» z) = A(X> z) + d(x, y, z)

this becomes

t(x, z) [loge g { d(x, y, z)} - loge g{ z) + d(x, y, z)}] (7)

establishing a direct relationship between filter thickness and "missing tissue" thickness. We shall now investigate the influence of the choice of j| (the actual depth, at a ray (x, z) for which exact compensation is obtained) upon the accuracy of compensation at other points (x, y1, z) along the same ray, for various values of Д. PAPER 1 43

The error introduced at (x, y', z), expressed in percentage (nominal) depth dose, is given by

"g{A(x, z) + d(x, y, z)} gd(x, y',z) Л 5(x, y',z)=P0(x, y»,z) g{d(x,y,z)} g{A(x,z) + d(x,y',z)} " J 1 '

(see Table I).

TABLE I

UPPER LIMITS OF ô(x,y', z) CALCULATED WITH EQ.(8)

Field size: 10 X 10 cm; f = 50 cm. (For symbols see Fig. 4)

d(x,y' .z)

d(x,y,z) л /

1 2 4 6 10 16

2 -0.5 0.0 +1.9 +1.8 +1.6 +1.0

2 4 -1.5 0.0 +2.0 +2.0 +1.7 +1.3

10 -1.0 0.0 +1.4 +1.8 +2.0 +1.2

2 -2.5 -2.4 0.0 +0.1 +0.8 +0.6

4 4 -3.5 -2.2 0.0 +0.4 +0.5 . +0.5

10 -2.4 -1.3 0.0 +0.6 +1.3 +0.8

2 -3.2 -2.4 -1.3 0.0 +0.2 +0.3

6 4 -4.0 -2.7 -0.5 0.0 +0.2 +0.3

10 -3.4 -2.3 -0.7 0.0 +0.6 +0.4

2 -3.8 -3.2 -0.7 -0.5 0.0 0.0

10 4 -4.6 -3.3 -0.7 -0.3 0.0 +0.2

10 -4.6 -3.4 -1.6 -0.9 0.0 0.0

As will be discussed later, it appears that the best overall compensation is effected when taking d = 4 cm. This results in the filter conversion function, for any one field size:

t(x, z) = ^ [loge g (4) - loge g{A(x, z) + 4}] (9) 44 VAN DE GEIJN

Another interesting problem is the influence of using a filter, based on the conversion function of an n X n field for an m X m field, m * n. This error can be given as

~gn{4+A(x,z)} gm{d(x, y',z)} 0™=P

Replacing pft") (x, y\ z) by Pf) (0, y', 0), we have the upper limit of this error for straight fields (Table II).

TABLE II

UPPER LIMITS OF 6™(x,y',z) CALCULATED WITH EQ.(ll)

Field sizes: 4 X 4, 10 X 10, and 15 X 15 cm, using d(x, y, z) = 4 cm as reference depth and the conversion function for the 10 X 10 cm field as a basis; i.e. m = 4, 10, and 15, and n = 10

d(x,y', z)

m xm

1 2 4 6 10 16

2 +1.6 +2.2 +3.1 +2.4 +2.2 +1.5

4x4 4 +1.0 +2.2 +2.3 +2.0 +1.8 +1.5

10 +2.6 +3.3 +3.7 +3.0 +2.9 +1.8

2 -2.5 -2.4 0.0 +0.1 +0.8 +0.6

10X10 4 -3.5 -2.2 0.0 +0.4 +0.5 +0.5

10 -2.4 -1.3 0.0 +0.6 +1.3 +0.8

2 -2.8 -2.6 -1.1 -0.5 0.0 0.0

15x15 4 -4.8 -3.9 -1.5 -0.8 -0.3 -0.1

10 -5.3 -4.1 -2.4 -1.5 -0.9 -0.5

It was decided to use, in practice, three conversion functions, based on (a) a 5 cm X 5 cm field, for the fields equivalent to squares less than 6 cm X 6 cm (b) an 8 cm X 8 cm field, for the field size interval 6 cm X 6 cm to 10 cm X 10 cm (c) a 12 cm X 12 cm field for larger fields. In Table III, values of all three are tabulated. They are independent ofSSD. PAPER 1 45

ю w о i0H0 о о? оо о о

M с- ю с- Ен i-соt 00 00 с- t-4 о о о & Q И H о са < 1 ÏT JЕ- X оо ю о с- ¡э СО со со S m* о о о w X Й m О ,, нн ш H ф ю ю о N и •iH со со са со Й to о о о ¡Э ь i—•v1 d) й •iH p4 со с-

со о о о тЧ о о о о о

сюз 00 гЧ о о осо о о о

2 и U5 сэ •бH X X X гН

í 46 VAN DE GEIJN

3. EXPERIMENTAL INVESTIGATIONS

It has been shown (van de Geijn, 1965a) that the present theory is adequate for the description of straight beams in both nominal and general situations, when taking yr = 10 cm. For wedged beams only nominal situations were investigated, with y, = 7 cm. For moving beam technique, yr was taken as 15 cm. All these reference depths are chosen in the middle of the usual range of depths of clinical interest when using the corresponding techniques. Significant deviations were found only in the first few centimetres beyond the real surface, and then only in a relatively narrow region just inside the geometrical edge of the beam. This is caused by the lack of scatter equilibrium. The errors are not unacceptable for clinical purposes. In the chapter on adaptation for use with a computer, a method will be indicated to correct for this effect.

3.1. The compensation method

In Table IV, a survey is given of the accuracy of the theoretical description. It shows the results of checking experimentally the calculations leading to Table II.

4. PRACTICAL APPLICATION OF THE COMPENSATION METHOD

The present theory offers no fundamental conclusion as to the density of the filter material. It was shown previously that on geometrical grounds high density material is preferable for wedge type intensity modifying filters (1963). It will be shown that the same holds for irregular filters constructed in the way described below and schematically illustrated in Fig. 5. The employment of square metal columns for the construction of irregular filters was introduced by Ellis et al. (1959). It involves the approximation to the continuous actual surface by a discontinuous one. In the context of the present work this means the approximation to the continuous function Д(х, z) by a step function A*(xj, z¡) with a step size b in both the x- and z-direction in the XZ-plane. If с is the filter-surface-distance, the side a of the columns is related to b by

a=^b (11)

and the length is t(A*(x¡, Zj)), found by substituting Д*(х;, zj) in Eq.(5). In most practical cases, a step size b = 1 cm involves errors not exceeding ± 2% of the nominal maximum, so it was decided to base the filter on rays through x and z at integer centimetres. Now we are faced with the problem of rectangular columns to deal with oblique divergent beam elements (Fig. 5). 1548 PAPER 1

fe ш Ф tí 01 И (tí ni о H g t-H ce (tí Í с „ со' b; G ° О •"-> ,o 5 ю H с ü G-* и +-> «! aS i ф rt fe Ф tí P cSe SO í te оЙ 8 от ai Й <2 л Ф <1 О d H св ,ГН С 0 ад 3 Й Sd £^ Sud ф S С О >1 b и о +оJ J +"> r-H ítí с fe So* и Й d a и св д д a ? ? e a * 5 ¡S о Ф О) и Д Д Я w + ОТ JH X Д J о « s Ф s- SÍ s и со •s з <в св X -н» о о ф г- со ш s о тс <н Д ТО> ) а 1 . . •а* L I 'и S от ^ фs ад 0 С св H й * g Л m •гН 01 Ф от S Я s < Оe d « «"H ® ul Ф Ctí Й ф m Ф - ю О ф в * д Ф 01

fe ai ья О > от Ф H -а Ф д <Й H 48 VAN DE GEIJN

FIG. 5. Illustration, in the XY plane, of the relation between the oblique beam element icentred by the: ray through (X¡ ,0), length Д* (X¿, О) and the right column, length t(A*)

The fraction of the rays entering the column centred by the ray (x¡, z¡ ) satis- fying condition (9) for A*(x¡, z¡) is given by

A=ja-b! t(A*(Xi,Zj))} |а-1^(Д*(х^))}/а2

or substituting Eq.(ll) for a and ignoring the quadratic term, we find

hl+hl A = 1 - J1 1(Д*(х;,2].))

Obviously, A should be as close to unity as possible. For any given ray, f and с being fixed, the only variable remaining is the length of the column, which can be decreased by increasing the density. We decided to.use brass (X = 0.443 cm-1) with increments of 0.1 cm in thickness, corresponding roughly to 0.9 cm steps in Д*. The clinical application of this system is illustrated by the use of a specially developed "surface copying device" consisting, in principle, of PAPER 1 49 a bundle of divergent rods aligned with rays (x¡, Zj). In the zero position the tops are in the nominal surface. The central needle can be used as a front pointer. The rods are kept in place in any position by the friction produced by a slab of foam plastic through which they are placed. They can be brought into contact with the actual surface simply by pushing them gently by hand from behind (Fig. 6). The displacement per rod is then equal to A*(x¡, Zj). The actual central axis SSD is given by the displacement of the central needle. The corresponding values t(A*(x¡, Zj)) are read, row by row, from a chart calibrated directly in mm of brass (Fig. 7). The values t(A*(x¡, Zj)) are written down in an XZ-grid serving as the prescription for the actual filter. The brass columns are glued pnto aPerspex base plate which in turn is mounted upon a slide (Fig. 8). The latter is positioned and fixed in front of the diaphragm. The whole procedure, from taking a print of the patient's surface up to and including the mounting of the filter, takes about three-quarters of an hour. Both the brass pieces and the base plate are recovered after the treatment is finished.

FIG. 6. Application of the surface copying device

5. USE OF A COMPUTER

As described so far, we have succeeded in developing a general generating function describing the relative dose distribution produced by a single rectangular beam in a water equivalent medium. The step from this single beam to cross-fire techniques with several stationary beams, or to moving beam methods, involves in principle merely transformations of co-ordinates

3 50 VAN DE GEIJN

FIG.7. Typical "print" in the process of being read in terms of millimetres of brass

and weighting factors. The number of fixed, machine and beam defining data has been discussed previously. Whether steps of 1 cm in the functions p(x) and in the grid to be scanned, as well as 20° intervals in moving beam cases are adequate in all circumstances is a problem currently under investigation. in the present paper, points oí paramount interest seem to be (a) the number and the organization of the variable data defining the dose distribution for the three irradiation techniques considered here, and (b) the presentation of the results.

5.1. Compensation for irregular surfaces etc.

It was shown that using intensity modifying filters as described above the difference between the "nominal" distributions and the actual ones can be ignorêd beyond the first 3 cm. Near the surface, the errors are small enough to be ignored also for all practical purposes. Then, the computation of the dose distribution in such cases is reduced to the regular, normal incidence to a flat surface type.

4' PAPER 1 51

FIG. 8. The parts involved in the application of a filter. From left to right: a Perspex base plate with some brass blocks, a finished filter, and the slide upon which it can be mounted. The slide is positioned first by means of the cross hairs. The filter can be attached upon the four columns and fixed by two nuts placed diagonally

We need: (1) the number of fields, (2) the field dimensions plus the side of the equivalent square, (3) the co-ordinates of the effective points of entry of the central axes, (4) the directions of the various central axes, with respect to a reference direction, (5) the weighting factors, and (6) for reasons of "elegance" of the display, the patient's outline (18 points, see below). In all: for a three field combination: 40 numbers.

5. 2. Correction for irregular surfaces etc.

We assume that the central axis enters the surface at the nominal SSD, f cm. We need the same variable data as in A, except that we now must use the outline of the patient. This curve is made available to the computer as follows. A point is chosen inside the contour (Fig. 9), from which, beginning (in our case) at left horizontal, 18 radii are drawn, at 20-degree intervals . Their lengths are measured, in clockwise sequence, and read into storage. The programme then approximates the actual outline with a 18-point polygon. By suitable choice of the origin, sufficiently detailed information in irregular regions can always be obtained.

5. 3. Wedge fields

The same general approach can be followed. The variable data are the same as in B, plus a special indication for the orientation of the wedge. So far we have not included wedge fields in our computer programme, merely because of lack of time. 52 VAN DE GEIJN

5. 4. Processing time and display of results

Since July 1965 we have had access to an IBM 7094/11, which was then the fastest IBMmachine. A 600-point scan takes of the order of 0.72 seconds per field, per plane. The results are printed by an IBM 1401 with a 600 lines per minute printer. The output consists of four parts per plane: (a) The administrative page, giving details of patient, institute, diagnosis, date, treatment plan, etc,. (b) A 1-1 scale print-out of the dose distribution inside the outline (also printed), along horizontal lines, 1/3 inch apart. This distribution is given by means of numerals 9 to 1, corresponding to 90...... 10% of the maximum (M) and printed on the correct line and in the nearest column. Horizontally, there is an uncertainty of ±li mm in the location of the numerical, although the real position is usually derivable to a better degree of accuracy. (c) A table containing relative surface area integral dose values for various percentage intervals and various efficiency factors. (d) A table with interpolation results for vertical lines.. These results can be used to improve manually the print-out mentioned under (b) above.

ACKNOWLEDGEMENTS

I should like to express my sincere thanks to Dr. G. Kok, radiotherapist, for his continuous encouragement and guidance in clinical aspects, and to the Queen Wilhelmina Fund for Cancer Research for financial support. Also, the expert and kind help from the IBM-staff, especially Mr. J. Roukens and Mr. A. Hylkema, accelerated the development of the computer programme greatly. COMPUTATION OF MULTIPLE ' AND MOVING BEAM DISTRIBUTIONS*

J. R, CUNNINGHAM PHYSICS DIVISION. ONTARIO CANCER INSTITUTE. TORONTO, ONT., CANADA

INTRODUCTION

Individual isodose distributions for moving beam therapy treatments are seldom drawn by hand due to the excessive amount of labour involved. Distributions have been produced either by direct measurement in a phantom or by using calculations based on fixed field isodose charts. Representative of the direct measurement technique is the work of Hultberg et al. (1959) who measured a very large number of distributions in a mix D phantom using Sievert ionization chambers. Rather more numerous have been the attempts to develop a method for calculating the desired distributions. Manual preparation of a complete distribution usually involves the rather tedious procedure of laying a single field isodose chart over a contour at each of a series of angles and noting the contributions to a grid of points. Corrections for variations in.SSD (source- to-surface distance) or contour shape must be calculated to weight the contribution to each point. Summation, normalization, interpolation, and curve plotting complete the procedure. Since the whole task must be repeated for each distribution required, this is a problem which lends itself to machine calculation. Historically, we at the Ontario Cancer Institute embarked on a programme to precalculate sets of rotational isodose distributions in 1962 when it was realized that to study systematically and display the effects of changes in various parameters in rotation, therapy it was necessary to use as few sources of primary data as possible and to compute all of the required distributions by a common and self-consistent method. This project was accordingly coupled with the aims of sub-committee III of the IAEA panel on "Physical Data for Dose Distributions with High Energy Radiation" (1960), of which the author was a member, to produce the majority of the isodose charts that are to be included in the Atlas (Tsien et al., in press). The computation method described in this paper is a refinement of the method that was used for that task. Radiation in a phantom consists of primary and scattered radiation. The primary beam can sometimes be described by a simple analytical model, as in the case of a monoenergetic beam, but the scattered radiation is always complex. Over the years a number of concepts such as depth dose, tissue- air ratio, scatter functions and the extensive use of single-field isodose charts have been developed (Johns, 1961; H.P. A., 1961) to describe carefully and systematically measured beams of radiation. In choosing a method

* Work done in collaboration vjithDr. D. ]. Wright of the Ontario Cancer Institute and Mr. К. C. Tsien,. then of the IAEA.

53 54 CUNNINGHAM of computation it seemed most logical to make the maximum use of this already amassed and well-known data rather than to àttempt to generate new empirical expressions or to try to base the computations on theory. The basic approach to the problem follows that of Jones et al. (1956), who constructed a numerical polar co-ordinate representation of a single- field isodose chart. This was then applied to a contour from a number of directions and the contributions to a grid of points were totalled. They also applied modifying or weighting factors which were empirically determined, to take account of the variation in SSD in the form of "tissue deficit" or "tissue excess" compared to the distance for which the single-field isodose chart was measured. Tsien (1955; 1958) independently developed a similar approach and introduced the use of automatic computing machinery.

BASIC COMPUTATION

The fundamental elements of data are the single-field isodose charts and a table of tissue-air ratios. Figure 1 shows an isodose chart superposed on a polar grid of points, the origin of which is on the central axis of the beam at the distance from the source equal to the source-to-axis distance (SAD) of the therapy machine. Let the dose values read off the chart at the grid points be the array of numbers Ay where the index i refers to the radial distance the point is from the origin and the index j refers to the angular co-ordinate 0j. A value Ay may describe either the relative dose at a co-ordinate point r¡, 0j within the beam or the relative dose along a phantom axis from a beam directed at an angle 9¡ to this axis. If rotation were about a circular phantom n the summation t Ay is then proportional to the total dose contribution from n fields to a point a distance r¡ from the axis. The summation of the Ay , being the contributions at the axis of rotation, is in the same way proportional to the total dose at the axis of rotation as the ratio of the two summations is to the relative dose at a distance rj from the axis. Consider next an actual contour such as is shown in Fig. 2. Let Rj be the radial distances from the centre to the contour corresponding to the angles 0j. The dose at the axis of rotation from a single beam applied at angle 6>j is by definition equal to:

D0 = Da T(Rj) (1) where Da is the dose in air at the position of the axis of rotation (measured inasmall amount of phantom material under electronic equilibrium conditions) and T(Rj) is the tissue-air ratio (Johns, 1961) corresponding to the phantom depth Rj. The relative doses, as given by the isodose chart, at other points in the phantom bear a fixed relation to the dose at the centre, so the dose along a reference axis at a distance r¡ from the centre from a field directed along the angle d¡ is then given by

(2) PAPER7. II 55

FIG.l. Isodose chart superposed on a polar grid of points

Since all of the Alf are the same (all being the value on the isodose chart at the origin of the co-ordinates), and Da is an arbitrary constant, the total relative dose at the co-ordinate point rj(Q) is then from n fields:

n 11

X dq =Z aü т(кР (з) j=l .

The tissue-air ratios are thus by definition the basic weighting factors to use for a series of radially applied fields, and if the angular intervals are made equal then Eq. (3) describes the relative dose for a beam moving around the contour with constant angular velocity. Expression (3), however, yields the relative dose only for points r¡ along a single line forming the co-ordinate axis (such as Rj in Fig. 2). The dose values along the next radial line are obtained by first advancing the T(Rj) values by one angular interval and then again multiplying as in Eq. (3). This is equivalent to a rotation of the co-ordinate system by one angular interval. The A¡j form a two-dimensional matrix of numbers and the T(Rj) form a vector. Expression (3) is the formal multiplication of a matrix by a vector, 56 CUNNINGHAM

along the radical line R4 an operation well suited to machine calculation. The expression given in Eq.(3) is the basic element in the method of computation being described. For arc therapy, the weighting factors T(Rj) can be set equal to zero for some directions and if only a limited number of the T(Rj) are non-zero the distribution resulting will be for multiple fields.

CORRECTIONS TO THE BASIC CALCULATION

The original A¡j (the isodose chart) strictly apply only to the conditions under which they were measured. This can be explained by referring again to Fig. 2, where 0 is the axis of rotation and the origin of the co-ordinate system and SAO is the central ray of the beam. SA is the source-surface distance for which the isodose chart was measured but SA' is the source- surface' distance for the beam applied along the line SO. If A(P) is the dose read off the isodose chart at point P then the ratio A(P)/A(0) does not quite correctly describe the relative dose at point P from this field and in fact will slightly over-estimate it. The extent of the error may be seen by referring to a numerical example. Let SO be 80 cm, OA be 15 cm, OA' be 10 cm and OP be 8 cm. If the radiation is from 60Co, the field size 8X8 cm and A(0) = 100, then the isodose chart would indicate 191.2 for A(P). An isodose chart that was measured for source-surface distance SA' = 70 cm would on the other hand indicate a value of 178.0 for the relative dose at point P. The difference is not large, being only 7.5%. (These numbers are obtained from a separate computer project, discussed briefly in Appendix I, for the compu- PAPER7. II 57 tationof dose at any point in anirradiatedphantom.) This example illustrates the magnitude of the error that is being accounted for. In a similar but perhaps more obvious way for. a point Q, the ratio A(Q)/A(0) will not be quite correct. In this case there will be an additional "tissue deficit" equal to B'C which will cause the relative dose at Q to be higher still than that given by the A¡j (= A(Q)). In the work done for the IAEA Atlas these errors were accounted for by three separate empirically derived correction factors which were computed for each grid point for each applied field. The derivations of these corrections will not be discussed in this paper but are described elsewhere (Tsien et al. , in press). Since that time it has been noted that the correction could be made more simply and more rigorously by an additional use of tissue- air ratios. It is necessary first to state the relationship between per cent depth doses and tissue-air ratios which is:

T(d,Zd) (F+y)2 D(d,Zy,(S-y)) = 100¥TF^-) (¥Tiy-2 (4)

where d is the depth below the surface of the phantom, y is the depth at which the depth dose data were normalized, Zy is a field dimension at depth y, Zd is the field dimension at depth d and F is the source-to-surface distance. S is the SAD and (S-y) is the SSD. The derivation of this relation is shown in Appendix II. The subsequent relation that is of interest is the relation between two depth doses at a constant point in space for two different SSD's. This is equivalent to measuring the dose in a water phantom and then changing the water level and remeasuring the dose at the same point. This is also equivalent to comparing the dose at point P in Fig. 2, referred to the contour (or at least the surface A'B'), with the dose at point P referred to the surface AB. The dose at P for surface A'B1 is:

T (A'P, Zp) (so)2 D(A'P,Z0,SA') = 100T(A,0) zPo) ^ (5)

and for the surface AB is

T (AP, Zp) (SO)2 D(AP, Zp,SA) = 100 T(AO>Zo) ^Jy (6)

The quantity D(AP, Z0, SA) is the matrix element A¡j at the co-ordinate point P. The ratio of (5) to (6) gives the desired correction factor.

T(A'P, Zp) T(A0, ZQ) A'.. (P) = Ац (P) T(APj Zp) ' T (A'O, Z„) (7)

The quantity T(A0, Z0) is a constant factor for all steps in the computation and so would cancel out in the normalization and the quantity T(A'0, Z0) is identical with the tissue-air ratios T (Rj) that were used in Eq. (3) so they 58 CUNNINGHAM would cancel out if the above ratio is used as a multiplier to augment Eq.(3). It is clear from this, however, that the first ratio term in Eq. (7) could replace the factor T (Rj) in Eq. (3) and it would appear logical to omit the step described by Eq. (3) and go directly to Eq. (7). Because of the extreme simplicity of the basic calculation, and the rather small effect on the resulting distributions, it has been retained and the whole of the correction term in Eq.(7) is used as a separate and optional correction factor. The above considerations have dealt solely with a point on the central axis of the beam, but the argument applies, although less accurately, to a point such as Q (Fig. 2), off the axis of the beam. In this case the depth of tissue overlying the point is reduced to QC. An assessment of the applicability of this method'of correction for oblique incidence is shown in Fig. 3 where a beam of 6(JCo radiation is directed at an angle of 30° to a phantom surface. The calculated curve, obtained from applying the above correction to a single-field isodose chart, is compared with measured dose values for the altered conditions. The effect of the general correction on a rotation distribution is shown in Fig. 4 where a distribution for a 180° arc using only the basic calculation (Eq. 3) has been superposed on one for which the more refined method has been used. The net effect can be seen to be quite small, for the isodose lines are shifted by no more than a few millimetres except near the extreme edges of the contour. In this diagram only half the distribution has been shown because of symmetry.

PROGRAMMING

The computer used was an IBM 7090 (University of Toronto, Institute of Computer Science) and the Fortran language was employed. The basic data, the Ay, need only be punched on cards once for a given field size and SAD and then retained for future use. Also needed is a set of tissue-air ratios for the field size corresponding to the Ац. The shape of the contour and the position of the centre of rotation in it are specified by the set of radii Rj, one corresponding to each applied field. The programme subsequently determines the weighting factors T(Rj) appropriate to the contour. The correction factors described in Eq. (7) are obtained first by determining the depth the point of calculation is below the contour surface (such as QC in Fig. 2). Then a search is carried out to find which two points on the contour (such as X and Y) the ray from the source will pass between. Once this is determined a linear interpolation gives a very good approximation to the distance QC. The tissue-air ratios called for by Eq. (7) must then be obtained by interpolation from the table. It must be noted that in this latter case the field size for which the tissue-air ratio is specified is the size of the beam at the level of calculation. A second set of weighting factors, which are either 1.0, 0.5 or 0.0, have been employed to enable calculations for arc or multiple field distributions with the minimum repunching of cards. This factor is 1.0 if the field is to be applied, 0.0 if there is to be no field from that angle, and 0.5 at the ends of arcs. The answers.are obtained in the form of the calculated relative dose at the polar grid of points or, alternatively, an interpolation can be used to PAPER7. II 59

FIG.3. Comparison of measured and calculated isodose lines for a beam inclined 30° to the perpendicular to the surface. The dashed lines are obtained by adjusting an isodose chart for normal incidence according to Eq.(7)

FIG.4. Isodose chart for a 180° arc about the centre of an oval phantom with and without the correction for oblique incidence and variation of source-to-surface distance produce the radii at which a set of pre-determined isodose lines will fall. Optional features of the programme include provision for change of co- ordinates and the addition of a mirror image distribution so that rotation about more than one centre can be studied. The computer could be programmed to draw thè dose distributions directly but this has not been done to date. 60 CUNNINGHAM

SUMMARY AND CONCLUSIONS

This paper has only briefly touched on past methods of computing rotation isodose distributions. It has not touched at all the voluminous literature on this topic. Instead, the author has described a method of computation which has been used rather extensively by him and his colleagues over the past four years. The method is simple and has as its basic operation the multiplication of a matrix by a vector. The input data are a single-field isodose chart in digital form, a tablé of tissue-air ratios, and a set of radii describing a contour. Corrections for oblique incidence and surface proximity are included. This programme has been used exclusively for the production of pre- calculated distributions. No.effort has been made to put the patient "on line" with the computer. Rotation distributions are on the whole rather insensitive to changes in contour and it is felt that little, if any, gain would result to the patient from this type of endeavour although the author is quite aware of the general usefulness of this approach in other matters.

APPENDIX I

COMPUTATION OF DOSE AT ANY POINT WITHIN A PHANTOM

The author has recently (Gupta and Cunningham, in press; Johns, in press) defined a new quantity to describe the scattered radiation within a phantom. From lack of inspiration in finding a better term, it has been given the name Scatter-air ratio because it bears almost the same relationship to tissue-air ratio as scatter functions do to central axis depth dose data. It is defined as:

Sar (d, Zd) = Tar(d, Zd) - Tar (d, Q) where Tar (d, Zd) is the tissue-air ratio for a depth d in a phantom for a field having dimensions Zd at depth d. Tar(d, 0) is the tissue-air ratio at the same depth for a field of zero area. Tar(d, 0) is in fact a description of the primary beam and would be a simple exponential for monoenergetic radiation. The scatter-air ratio is thus as independent of source-to-surface distance as is the tissue-air ratio and becomes a universal scatter function for a given quality of radiation. Tables of scatter-air ratios have been produced by the author for 60Co radiation as well as a number of the other qualities of radiation which are tabulated in Suppl. No. 10 of the British Journal of Radiology. The use of this quantity allows the very rapid calculation of depth dose data or isodose curves for any shape of field for a very wide range of source- to-surface distances. The relation between scatter-air ratio and scatter function is:

S(d Z F) 2 &с IA 7 \ - - y (F + d)2 аг '"> ^d' 100 (F+y) PAPER7. II 61

where Zy is the field dimension at depth y, in this case the depth of maximum dose, and F is the source-surface distance. The dose at any point at a depth d in a phantom is given by:

Sar(R(0)) D(d) = Da(d) Te(d.0)+/-^de 2tf

where Da(d) is the dose in air at the point of calculation and R(0) is the distance, in a plane perpendicular to the central ray of the beam, from the point of calculation to the geometrical edge of the beam at an angle в with respect to an axis in this plane. Integration is around the perimeter of the beam, with the integral reduced to a summation for machine calculation. To test the method, scatter-air ratios have been determined from the published measurements (Suppl. 5 of the British Journal of Radiology) for circular fields at SSD = 80 cm for 60Co and used to calculate all of the data for b0Co in Suppl. 10 of the British Journal of Radiology. Agreement was everywhere within 2% except for large fields for SSD = 50 cm where the agreement was only slightly poorer. The programme has also been used to obtain isodose curves and has been enlarged somewhat to allow for the use of a non-uniform primary beam as would be the case with wedge filters or incidence on an irregular surface. It is hoped that it can be developed still further in an attempt to allow for phantom inhomogeneities. This programme has also been coupled with the programme described in the main body of the paper so that the A¡j of the single field have been calculated rather than read off an isodose chart.

APPENDIX II

A RELATIONSHIP BETWEEN TISSUE-AIR RATIO AND PERCENTAGE DEPTH DOSE

The tissue-air ratio at depth d is defined as

tíT(d л Zd7 )\ - ' - Da(d)

where, as in Appendix I, Zd is a field dimension at depth d, D(d) is the dose

in the phantom at depth d and Da(d) is the dose in a small portion of phantom material at the same point in air. • The per cent depth dose is

D(d,:Zy,F) = §^ 100

where у is the depth at which'the depth dose is normalized (where 100%

occurs) and is usually the depth of the maximum dose but need not be. Zy is a field dimension at depth у and F is the source to surface distance. 62 CUNNINGHAM

Eliminating D(d) between the two relations, introducing the inverse square law, and substituting:

Ti7 Z ) Da(y) ' y gives:

T(d, Z.) (F + y)2 D(d,Zy,F) = 100 ^^

which is the desired relation. COMPUTER-ASSISTED EXTERNAL-BEAM DOSIMETRY WITH SPECIAL REFERENCE TO CORRECTION CALCULATIONS AND PRESENTATION OF DATA

J. S. CLIFTON DEPARTMENT OF MEDICAL PHYSICS, UNIVERSITY COLLEGE HOSPITAL, LONDON, UNITED KINGDOM

INTRODUCTION

Any computation of a dosage distribution requires three sets of data: the first describing the radiation fields; the second, the parameters of the patient and the proposed arrangement of fields; and, the third, a set of instructions covering the output format. The method adopted for data insertion determines the types and limits of correction that can be applied for effects of irregular body contours etc., whilst the inaccuracies in the inter-stage processing to obtain the final output lead to a further loss of information.

1. DATA INPUT

1.1. Radiation fields

The provision of data concerning radiation fields in a form suitable for a computer (i. e. digitized to give the dose at a specific point or matrix of points) can be approached in three ways: (1) Conversion of existing experimentally determined isodose charts (2) Derivation from an empirical mathematical expression (3) Computation from suitable equations using limited experimental data specially obtained for this purpose. The first use of a computer for external beam dosimetry, described by Tsien (1955), used a method of digitizing the isodose chart in polar co- ordinates. Similar techniques have been described by Sterling et al. (1961), Wood (1962) and van de Geijn (1963). We have used a Cartesian co-ordinate system in which the dose grid interval may be varied. Sterling (1963) has converted his system to Cartesian co-ordinates with a fixed interval of |in.X i in. The use of a digitized isodose chart suffers from a number of disadvantages: (1) The hand conversion of an isodose chart invariably leads to inaccuracies in data (2) The accuracy of subsequent interpolation depends on the separation of the individual dose points (3) If a small grid interval is used excessive computer storage space is required. The advantage of this method is that any isodose chart may be converted to a form suitable for the computer and no new experimental data are required.

63 64 CLIFTON

An alternative to the hand conversion of the isodose chart is to construct an interpolation routine so that the computer can produce the grid of points. This is done in the following manner. From each percentage curve on a given isodose chart a number of points are read, points being placed in close proximity where the curvature changes rapidly (Fig. 1). The programme assumes that the isodose curve can be represented by straight line segments between these points. To find the dose at any point on the isodose grid, the four isodose chart points which surround the point P are determined and the dose at P found by interpolation. The interpolation routine is least accurate at the 'knee' of the isodose curve. Since a computer is ideally suited to the solution of mathematical equations and repetitive calculations, attempts have been made to find an empirical mathematical expression that would permit the direct computation of the dose at a given point in a matrix without recourse to an isodose chart distribution. The method of Siler et al. (1964) for use in rotation dose distributions n treats the digitized field of radiation dose as a matrix of the form A = £ UV i=l which is the product of two matrices U, the primary beam dose matrix, and V, the scatter dose matrix. The total dose matrix is found to be of rank one and may be rewritten as the outer product of two vectors: One dependent on depth only and equivalent to tumour-air-ratio (TAR), (Johns 1953) with inverse square law correction, and the other dependent on the angle of divergence from the beam centre-line or off-centre-line-ratio (OCR). The final form is given by:

Dose = TAR X OCR X Inverse square correction

Data input is reduced by using vector representation, and correction for curvature and inhomogeneities is achieved by modification of the TAR vector. PAPER7. II 65

Sterling (1964), using computer analysis of experimental data, has devised an empirical relationship for the central axis dose at a given point of the form:

log q = h¡+ m ¡log (A/P) where Ci is the per cent depth dose on the central axis at depth Di, A/P is the ratio of area of field to field perimeter and hi and m¡ are intercept and slope constants. The dose at any point Pi off the central axis is found to be related to the ratio 1/L where L is half the field width and 1 is the intercept on the surface of the line joining P to the source, i.e. Pi/Ci = (l/L) =K. К is found empirically to be a cumulative normal probability integral. Whilst satisfactory agreement between empirical equations and experimentally measured doses are obtained within the volume irradiated by the primary beam, agreement is not usually so satisfactory in the penumbra region where scattered radiation predominates. Since the unknown scatter function limits the universal applicability of an empirical equation for dose distribution, a number of solutions have been suggested which require the acquisition of only a limited amount of experimental data. Van de Geijn(1965) has derived a generalized three-dimensional dose distribution for 60Co radiation, in which the dose at any point within the geometrical beam is obtained from central axis depth dose tables, and that for a point outside the beam by use of a scatter function evaluated from two sets of measurements taken parallel to the two principal axes of the field at a given depth. We have adopted an experimental approach based on the decrement line system described by Orchard (1964). Fundamentally, this states that the points А, В, C, in Fig. 2 have the identical percentage value of the central axis depth dose at that level, in this instance 80%. The line ABC is known as the 80% decrement line. It is found experimentally that for most 60Co units, and our units in particular, the decrement lines are in fact straight for a plain field. To construct any isodose curve it is only necessary to obtain two sets of experimental data down to less than 5% of the central axis value, at known depths perpendicular to the central axis. These, together with the appropriate central axis depth dose data, allow the decrement lines to be set up and hence the isodose chart constructed or, alternatively, a matrix of dose points obtained. ' The variation of scatter dose with field size has been investigated for various field sizes and if the decrement lines are measured for an intermediate value of field length for a given width, all isodose distributions for that field width, for field lengths varying from 4 cm to 20 cm, can be constructed. The isodose lines are correct from 90 to 20%, the maximum uncertainty of the 10% line is 1.5 mm, and the 5% line 2 to 3 mm. The system is applicable to both axes of a given field, and work is at present in hand to extend our investigations to three dimensions using this method. Wedge fields are also treated in this manner, but within the primary beam the decrement lines are curved. The decrement line system has the following advantages: (1) Information on field widths at any depth is immediately available, no matter how the width may be specified. 66 CLIFTON

FIG.2. Illustration of the basis of the decrement line system

(2) Information may be interpolated for any desired interval with an accuracy equal to that of the original measurement. (3) Information on the variation of dose across a beam is presented with an accuracy which is independent of depth. The conventional isodose curve has an accuracy of presentation which decreases with depth. (4) Information can readily be provided outside the limits of the 5% or 10% isodose line, which normally gives the limit of information with a' conventional curve. A similar system evolved for 4-MV X-rays has been described by Orr et al. (1964).

1. 2. Patient dose distribution

The evaluation of the dosage distribution produced by multiple fields, arc, or rotation treatment requires the specification of a matrix of points within the patient outline, for each individual point of which the dose is calculated. For confocal field arrangements, arc and rotktion, a polar co- ordinate system can be used, Tsien (1955), Sterling (1961), Wood (1962), van de Geijn (1963), Siler et al. (1964). It has the advantage that the matrix is closely spaced in the region of greatest interest. It can be extended in a limited fashion, Sterling (1963), to cope with non-confocal arrangements, but corrections for tissue excess or deficit are virtually impossible where both patient dose matrix and digitized radiation field are specified in this way. Where the tumour-air-ratio system is used for rotation treatment planning, suitable corrections are possible, Siler (1964), van de Geijn (1963). However, the major disadvantage of the polar co-ordinate system is incompatibility with output devices, all forms of which are designed for rectilinear Cartesian co-ordinates. This incompatibility caused Sterling (1963) to change his system to rectangular Cartesian co-ordinates. Since he wished to use a standard teleprinter as his output device, he chose a fixed matrix interval of \ in.X \ in. This leads to errors of up to 4% in calculated dose. We have used a Cartesian co-ordinate system for both isodose matrix and

5' PAPER7. II 67 patient matrix, the interval of the matrix being variable for different specified areas within the patient.

2. CALCULATION OF DOSE AT A MATRIX POINT

The total dose at a given point in the patient matrix will be the sum of the contributions from all radiation fields used in the treatment plan. If the patient surface is assumed to be flat, or is made artificially flat by use of wax or bolus, it is sufficient to translate the patient matrix point into the matrix of the radiation field to obtain the dose at that point from a given field. If correction for the patient contour is to be made, the total absorption path (EP) along the ray S. P. must be determined (Fig. 3). Siler (1964) uses this value, in conjunction with the measured off-axis- ratio, OAR, to modify the tumour air ratio in rotation treatment plans, whilst van de Geijn (1965) derives his scatter function from a similar value, but uses the distance parallel to the central axis. This leads to errors of the order of 7% in certain circumstances. We apply this type of off-axis adjustment to our digitized isodose chart, using either an exponential or an inverse square law, correction for tissue excess or deficit and obliquity of applied fields. Also, as the computation method is generalized, it can be applied to fixed field, arc, or rotation treatment plans with equal felicity. The use of a variable Cartesian co-ordinate grid system allows the accuracy of determination of the patient dose distribution to be controlled over the whole treatment area. Further, the specification of the patient outline in Cartesian co-ordinates, with no restriction on the number of outline points, means that sharply changing curvatures in outline can be accurately represented. Compensating blocks, Hall and Oliver (1961), or wedges, van de Geijn (1963), could also be used with this system.

3. PRESENTATION OF DATA

If the full value of the multiple point dose distribution, complete with all the appropriate corrections, is to be realized the format of the output must be accurate and easily comprehensible. The print-out of a matrix of total doses (Sterling 1963) requires further interpolation by hand, with consequent loss in accuracy, to obtain the isodose contours. Whilst the introduction of special symbols for dose values (Sterling 1964) provides an immediate representation of the distribution, exact positioning of the isodose contours requires further hand interpolation. Siler (1964) uses a print-out in which multiple marks are used to indicate the value of the isodose contour at a given point. This system is not easily interpreted and does not match in accuracy the preceding calculations. Van de Geijn (1965) mentions the use of a Calcomp plotter to print his results, but it is not clear whether continuous lines are drawn for the percentage isodose distribution, or numbers printed at predetermined intervals. 68 CLIFTON

FIG.3. Geometrical relationships used in correcting dose for irregular patient contours (d = distance from actual irregular surface to assumed flat surface)

Our initial investigations into the use of a computer for dosimetry led us to the conclusion that if the full value were to be extracted from the system the final output must be: (1) Immediately comprehensible without further hand interpolation (2) As accurate as the preceding calculations. With these objects in mind a number of search and interpolation routines were written to operate on the total 'dose matrix initially produced.

3.1. Search and scale

A search is made for the highest matrix dose value, this value is noted, normalized to 100%,and all other values scaled in percentage accordingly. Alternatively, an area is specified over which the modal dose is required; this is evaluated and all doses scaled according to this modal dose.

3. 2. Contour interpolation

The values of the requrred contours (e.g. 90%, 80% etc.) are specified to the computer, and an interpolation is made (scanning in both axes) between the matrix of dose points to obtain the co-ordinates of the points which lie on a given contour. This routine may be used without previously scaling to maximum or modal dose, but the value of the highest contour must then be estimated and specified.

3. 3. Teleprinter output

A teleprinter can be used as a plotter in a similar manner to that described by Sterling (1963). Since the contour co-ordinates have been pre- PAPER7. II 69 viously evaluated it is only necessary to allocate a single symbol to each contour. There are obvious disadvantages to this'method of presentation. The space between letters on a given line is 1/12 in. and the space between lines is 1/6 in. which leads to a maximum error in placing of 2.5 mm. Further, where the distribution changes rapidly, there is a risk of over- printing, thus it is necessary to arrange to print only the highest isodose contour - with consequent loss of information.

3. 4. X-Yplotter output

An "off-line" device has been built for us by a commercial firm, in which an x-y plotter is used to'produce isodose contours directly. The equipment consists of four units: (1) a tape reader, (2) a manual keyboard, (3) a digital to analogue converter, and (4) an x-y plotting table. The writing head for this equipment can be either: (1) a direct writing pen, or (2) a symbol, printer. The symbol printer has thirteen alternative symbols which can be changed automatically by the digital to analogue converter from instructions included on the data tape, at the end of each contour. The table area is 37 cm X 25 cm, the linearity 0.1% of full scale de- flection, pen writing speed 70 cm per second. When using the symbol printer, movement sensing logic is introduced which withholds the print pulse until the printing head is stationary. When using the pen to draw closed loops it is necessary to have a pen lift and pen lower instruction at the end of each completed contour. The data tapes, which are produced directly by the computer from the contour interpolation routine, carry both pen lift and symbol change instructions. The logic in the digital to analogue converter is arranged so that it selects instructions appropriate to.the writing head in use. Thus the same tape can be used to produce curves either continuously drawn or printed with symbols.

4.. ACCURACY

The accuracy of the dose distribution produced by any programme depends on the validity of the assumptions made in the calculation routines.

4.1. Radiation field data

Sterling (1961) has described a graphical method for interpolation of the dose matrix from an isodose grid which is claimed to be very accurate. The isodose chart is digitized in polar co-ordinates, but the same chart must be repeatedly digitized with the origin of the polar co-ordinates moving down the central axis in successive 1 cm intervals. With this system the maximum error in positioning of the isodose chart with respect to the patient surface is 0.5 cm. This method has been adapted (Sterling 1963) to produce a matrix of dose points in Cartesian co-ordinates. However, the spacing of the points in this matrix is i in. in each direction; thus there will be loss of accuracy in subsequent interpolation of dose values for patient points which occur near the edge of the isodose chart. 70 CLIFTON

When interpolating our dose matrix we have used a grid interval of 1.0 cm along the central axis and 0.5 cm perpendicular to this axis. With this interval the results obtained are accurate to 2% and since the accuracy of the isodose chart is not better than ±2% this is acceptable. With the decrement line system it is possible to obtain the dose at a point accurate to 1%. It also eliminates the errors inherent in any manual conversion of existing charts.

4. 2. Patient dose distribution

In those systems which rely on a second interpolation, from the isodose matrix to the patient matrix, to find the initial uncorrected dose value at a given point in the patient, the limits of accuracy will depend on: (1) The spacing of the points in the initial isodose matrix (2) The accuracy of the interpolation routine. Clearly this double interpolation must of necessity introduce calculation errors, and direct methods for calculation of dose at a given point are to be preferred, provided a sufficiently accurate mathematical representation can be obtained. At the present time it would appear the errors with both systems are likely to be of the same order of magnitude.

4. 3. Fixed field plans

4.3.1. Use of correction calculations Figure 4 shows a comparison of the effect of exponential and inverse square law corrections when used to compute a simple four field treatment on a symmetrical elliptical body. The lower two segments are strictly comparable, since the same patient grid interval has been used. It is evident that there is little significant difference between the two.

4.3.2. Effect of patient matrix interval

The effect of the size of matrix interval is also illustrated in this figure. The top right-hand segment was calculated taking points in the patient at 0.5 cm intervals, and the improved accuracy of the 100% contour is evident. Since the computer has to interpolate between the doses calculated for grid points to obtain contour points it is obvious that the smaller the grid interval, the greater will be the accuracy of the interpolation. However, the maximum difference in position of an isodose contour, when calculated on a 1 cm grid as opposed to 0.5 cm grid, is 3 mm. On the other hand, it is clear from the top left-hand segment, which was calculated on a 2-cm interval grid, that there is a distinct loss of information.

4.3.3. Deficiencies in isodose data

There is a distinct discontinuity in the 20% contour which is not repeated in the 10% contour. This is a true discontinuity, not a fault in the programme and it occurs for the following reason. The isodose chart when first programmed into the computer stopped at the 5% level, as is common with most isodose charts. PAPER 7. II 71

«FIELDS 6x6cm 61.cm SSD

field treatment

2x60° ARCS 6cm FIELD 61cm SSD

exponential corrections

Consequently, when a grid point fell outside the 5% isodose line the computer assumed the contribution to be zero. Hence the 20% contour, which is composed of the 10% contours of the parallel opposed fields, exhibits a sudden discontinuity where it strikes the 5% edge of the other two fields. The 10% contour is unaffected since it is composed of the 5% isodose lines of two fields only. Thus this discontinuity results from a lack of information in the original isodose data.

4.4. Rotational plans

Figure 5 shows the results obtained by altering some of the many variables in rotation treatment. The treatment plan is two 60° arcs of a 72 CLIFTON

6 cm X 6 cm field, separated by 40°, the set-up being symmetrical about the vertical.

4.4.1. Effect of source position interval

Take first the left-hand side. The method of correction used here is the axial exponential method described by Jones et al. (1956), the SCD is 73.5 cm, and computation has been made for the same two 60° arcs, using source positions at 10° and 4° intervals. There is a striking difference between these two. Along the bisector of the arc, the 70% contour is increased by 5 mm and the 60% contour by 19 mm in the 4° interval case. Thus it appears that whilst the 90% and 80% contours are little affected by the change of interval, the use of the 10° interval leads to a serious under- estimate of dose in the centre of the treatment arc. This is in agreement with the calculations of Craig (1963).

4.4.2. Axial and off-axis exponential correction

The right-hand side of Fig. 5 shows the comparison between axial and off-axis exponential correction using an SCD of 76 cm. There is little difference between the distributions produced by these alternative methods of correction. On the vertical centre line, the isodose contours are raised some 4 mm in the direction of the irradiated surface when calculated by the "off-axis" method. This would be expected since the method gains in accuracy over the axial correction as the obliquity increases. Along the bisector of the arc the "off-axis" correction reduces the 60% contour by 7 mm. The 4° interval case using off-axis correction, which is not shown here, results in an increase of 13 mm in the 70% contour and 29 mm in the 60% contour, thus confirming the difference in distribution produced by using more frequent source positions.

5. COMMENTS AND CONCLUSIONS

The present system of radiotherapy treatment planning is wedded to the concept of the isodose chart. The application of the high-speed digital computer to the task of treatment plan calculation brings this concept into question. It is clear that if the full value is to be made of computer techniques, and treatment plans produced which are: (1) Three dimensional (2) Corrected for: (a) obliquity of field, (b) tissue excess or deficit, (c) inhomogeneity, then the system must be tailored to match the needs of the computer. This implies that a suitable form of mathematical equation must be found which will enable the dose at a point in a three-dimensional system to be calculated directly, and in such a way that all appropriate corrections are included. However, it must be emphasized that radiotherapy is a clinical science, and the isodose chart is the means by which the radiotherapist PAPER7. II 73 visualizes the treatment fields applied to the patient. Thus whilst mathematical forms must be developed to facilitate calculation, serious consideration must be given to the input and output systems in order that the radiotherapist can visualize the proposed plan and exercise his clinical judgement. The results of the computation should be presented within a very short interval of time in a form which is immediately comprehensible. In considering these latter requirements there is much to be said for the introduction of analogue techniques. The areas for development would thus seem to be: (1) Development of a generalized mathematical form to enable the dose at a point to be calculated in any form of treatment plan (2) Extension of treatment planning calculations to three dimensions (3) Improvement of input and output systems, with particular reference to accuracy and visual presentation. CORRECTION OF SINGLE-FIELD DISTRIBUTIONS TO ALLOW FOR TISSUE INHOMOGENEITY

A. DUTREIX UNITE DE RADIOPHYSIQUE, INSTITUT GUSTAVE-ROUSSY, VILLEJUIF (SEINE), FRANCE

The two main inhomogeneities encountered in the tissues are lung and bone. A difference in composition (bone) leads to a variation of the absorbed dose; a difference in density (bone or lung) leads to a modification of the exposure dose, the only problem which we consider in this report.

1. CORRECTION OF TUMOUR DOSE USING A PRESET CORRECTION FACTOR

Several authors, Batho (1964), Keller (1963) and Massey (1962), have proposed the use of pre-established coefficients to correct the tumour dose. These coefficients depend only on some simple parameters such as energy of radiation, region which is irradiated (chest, abdomen, skull), thickness of the patient and direction of the beam (lateral or antero- posterior). The value of such an arbitrary correction can be discussed if we know the spread of the actual individual corrections. Keller (1963) made a large number of transit dose measurements on patients for different qualities of X or 7-rays and found that the correction for the thorax varies from 1. 1 to 1. 85 at 200 kVp and from 1. 0 to 1. 3 with Co -y-rays. Nahon (1955) found for 250 kVp X-rays very large variations among individuals for transmitted doses through the thorax, with no relation between exit dose and thickness of patients. He found no significant difference between exit dose through the abdomen measured with full backscatter and standard depth doses. Schulz et al. (1961) showed that the correction for irradiation of chest by 6°Co can vary from 1. 00 to 1. 34 depending on the size and the position of the tumour and concluded that as much error was introduced by an arbitrary correction factor as would be incurred by using standard depth dose data alone. For this reason many workers have studied the problem of individual corrections. There are two groups of corrections, those based on individual dose measurements, i.e. transit or exit dose measurements and those based on calculations after determination of the individual structure of patients.

2. TRANSIT OR EXIT DOSE MEASUREMENTS

It is usual to distinguish between exit or transit dose. In this report exit doses refer to doses measured at the exit part of the beam with no collimation of the chamber, i. e. the dosimeter measures the scattered dose

74 PAPER7. II 75 from the patient. These measurements are made with or without back- scattering material. Transit doses refer to doses measured in good geometry conditions, i. e. doses due to primary radiations only, measured with a well collimated chamber, far from the patient.

2. 1. Exit dose measurements

Neuman and Wachsmann (1942) were the first to do such measurements with a non-collimated chamber at 250 kV. They established graphs to determine the tumour dose as a function of the size of the patient and the eccentricity of the axis of rotation. At 250 kV Robbins and Meszaros (1954) established calibration curves giving relation between tumour dose and exit dose in percentage of the air dose while Kornelsen (1954) determined an effective absorption coefficient of the patient. Woodley et al. (1960) calibrated their exit chamber by measurements with a phantom to determine an effective patient thickness for 250-kV X-rays and 2-MV Van de Graaff X-rays.

2. 2 . Transit dose measurements

To avoid special calibrations due to the presence of an unknown amount of scattered radiation, many workers preferred to measure only the primary radiation. O1 Connor (1956) determined in such a way the water-equivalent thickness of patients at 200 kV. Many workers use a similar technique for 60Co y-rays, Braestrup (1958), Bur lin (1957), Fedoruk (1957), Pfalzner (1956, 1958), Schulz (1961).

2. 3. Discussion

Calculation of an equivalent thickness, or an effective linear attenuation coefficient, based upon exit or transit dosimetry assumes the patient to be homogeneous. It gives information about the gross absorption properties of the patient but it is unable to distinguish between an homogeneous absorber and one composed of tissues of widely differing densities. It could be applied without discussion to those cases where tissue is homogeneous throughout the treatment beam or where the tumour is centred between a symmetrical arrangement of non-uniform tissues. In the case of a midline lesion treated with opposed fixed fields or with a symmetrical rotation technic, it was demonstrated that errors due to asymmetry of inhomogeneities average out, and that the final error is negligible relative to the magnitude of the correction. This notion was tested by Kornelsen (1954) for 200-kV X-rays and by Schulz et al. (1961) for 60Co 7-rays who agree on the value of the method. 76 DUTREIX

3. CALCULATION OF CORRECTED DOSES

The transit or exit dose methods can provide average factors to correct depth dose, but are unable to give information on the overall dose distribution. In general, the thickness of overlying lung or bone and the distance from them will be different for each point and the correction to be applied will be different too. A point-by-point correction implies three steps: (1) determination of anatomical structure of individual patients, (2) evaluation of correction factors as a function of nature, thickness and position of inhomogeneities, (3) calculation of the actual doses.

3. 1. Anatomical structure

The determination of the contour of the patient together with position and size of inhomogeneities is not an easy problem. The simplest way is certainly to use transverse axial tomograms to draw "maps" of the region of interest. The use of a body cross-section atlas alone cannot help for an individual estimation; however such an atlas can be useful for the interpretation of two conventional radiographs without which it is quite impossible to estimate anatomical structures.

3. 2. Correction factors

Attenuation coefficients have been determined for bone by Haas and Sandberg (1957) from 50 kV to 18 MeV. Attenuation coefficients for bone, fat and lung have been measured by Jacobson and Knauer (1956) for Co vrays and conventional X-rays as a function of field area with an arbitrary geometry. The correction for bone is always less than 10% for e0Co while the correction for lung can be as large as 40%. For this reason we shall now especially consider lung. There is not only a greater transmission of radiation by the lung than by the equivalent thickness of soft tissue which it re- places, but there is also a reduction in the amount of scattered radiation generated in the lung, thus leading to a reduction in the scattered radiation dose to the tissue beyond the lung. This last factor leads to an increase in the correction factor to be applied, with the distance increased between lung and point of interest. This effect has been studied experimentally for 60Co 7-rays by Burlin (Í957), Dutreix et al. (1959) and Massey (1962). Batho (1964) found very similar values by theoretical calculations usingthe tumour- air-ratio (TAR). Furthermore the scattered radiation dose outside the shadow of the lung is modified in a very complex way. This modification can be neglected for 60<¿p as demonstrated by Dutreix (1959) and Greene (1965) but not for conventional X-rays.

3. 3. Practical calculations

An approximate method of correcting the dose can be developed if an exponential attenuation can be accepted. That is the case for high-energy X- or 7-rays provided the point at which the dose is being estimated is several centimetres beyond the inhomogeneity. PAPER7. II 77

If the effective linear attenuation coefficient is ^ for the soft tissue and ц ' for the inhomogeneity, the correction factor is e^-f')* where x is the thickness of the inhomogeneity. Since (ц -ц1 ) is generally small the approximate correction factor [ 1 + {ц - ц 1 )x] can be used in the case where x is small enough. But if an accurate correction is desired, it is necessary to use the exact value of the correction factor, which is a function of the nature of inhomogeneity, its thickness, its distance from the point of interest, the quality of the radiation and the field size. Values of these correction factors can be taken from curves or tables in literature - for instance for cobalt in papers by Burlin (1957), Dutreix (1959), or Batho (1964), and for 4 MV in a paper by Massey (1962). If many points have to be corrected this method is very laborious and time consuming. Another method of correction was proposed by Greene (1965). It is very similar to the "two-thirds'1 rule used for correcting for the effect of oblique incidence (Dutreix, 1962). The authors propose to move the isodose lines by an amount equal to n times the thickness of the inhomogeneity measured along a line parallel to the central axis and passing through the point of interest. The isodoses must be moved proximally in the case of bone and distally in the case of air cavity or lung. The values of n were determined experimentally and are independent of the field size; they are the same for 60Co Y-rays and 4-MV X-rays, and probably for all high-energy X-rays: n = 0. 6 for air cavity n = 0. 4 for lung n = 0. 5 for hard bone n = 0. 25 for spongy bone. The doses determined by this method agree with measured doses to an accuracy of about 2 per cent of the local dose. For conventional X-rays, the authors propose n = 0. 5 for hard bone, air cavities and lung and this simple rule leads to an accuracy of about 5 per cent for the points in the shadow of the heterogeneity. Thus the whole isodose chart can be corrected by simple graphical procedures with accuracy and rapidly.

4. USE OF COMPUTERS FOR THESE CORRECTIONS

It doès not seem realistic to use computers to calculate the dose at the centre of the tumour only. This calculation can be made easily and rapidly by classical procedures and does not require electronic equipment. Transit or exit dose measurements cannot be of a great help when computers are used for dose distribution calculations. Elsewhere we can probably suppose that if computers are available for dosimetry in a country, high-energy beams are also available to treat deep tumours. Therefore for a first stage at least, we should consider only corrections for high-energy beams. Every time a calculation method can be represented by a mathematical law it is probably possible to use it in a computer programme. The use of a table of numerical values is technically possible but its storage poses an economic problem. 78 DUTREIX

The exponential correction can be probably easily demanded of a computer, if thickness and co-ordinates of the heterogeneity are introduced in the data. The correction proposed by Greene can be summarized in a mathematical transformation of co-ordinates of the point. Let us suppose for instance that the orthogonal co-ordinates of a point P are x and y, the x axis being the central axis of the beam. If the beam traverses a lung thickness 1 along the parallel to the central axis passing through P, the dose to the point P is equal to the dose to the point P' in homogeneous tissue whose co-ordinates x' and y' are x1 = -0. 4X1 and y1 = y. For the points beyond the inhomogeneity, this transformation depends only on the value of y since 1 is a function of y. Thus, it seems possible to find a method of calculation among those actually used in practice which can be used in computer programmes. The choice of the correction method will depend upon the computer programming used to calculate doses in homogeneous tissues. EFFECT OF TISSUE INHOMOGENEITIES ON EXTERNAL RADIATION THERAPY DOSE DISTRIBUTIONS*

W. SILER AND C. DYMYTRYSHAK DOWNSTATE MEDICAL CENTER, BROOKLYN, NEW YORK, UNITED STATES OF AMERICA

While considerable attention has been paid to the use of computers in the calculation of radiation therapy dose distributions, little work has been done on the effects of body inhomogeneities on the dose distributions. The usual assumptions for computer calculations are two in number: first, that the surface of the patient is flat and perpendicular to the centre line of the X-ray beam; and second, that the patient is homogeneous and water equivalent. Hallden et al. (1963) have published a method which permits the surface of the patient, while still flat, to meet the centre-line of the X-ray beam at oblique angles; Mauderli and Fitzgerald (1964) allow for patient curvature, as does Clifton (1964). The problem of correction for inhomogeneities has received less attention; the only working programme known to the authors which corrects for these effects is that of Siler et al. (1964). The scarcity of computer programmes for dealing with inhomogeneities reflects, we believe, a corresponding lack of theoretical and experimental work in this field. While attention has been paid to the inhomogeneity problem by such workers as Dutreix et al. (1959), Bahretal. (1964), the very early work of Spiers, and the electron beam work of Laughlin (1964), much of this work.is not directly applicable to the effect of gross tissue inhomogeneities on the overall radiation therapy dose distributions. It should also be mentioned that virtually all investigators using computers in dose distribution calculations restrict themselves to a centre-line plane of the X-ray field. Sterling (1965) has gone to three-dimensional representations. The theoretical solution for the problem of inhomogeneity corrections is not easy. If one can safely assume that the interactions are Compton, the Boltzmann transport equation with Klein-Nishina cross-sections governs the actual dose distribution. However, the boundary conditions under which this equation may be numerically solved with the Klein-Nishina cross- sections are extremely restrictive, requiring infinite absorbing medium and very simple source geometries. The theoretical method is then not presently capable of being applied to the inhomogeneity problems. One can employ a Monte Carlo method, as has been done in nuclear reactor shielding problems, and this method has begun to be employed by Bahr. However, extensive computer time is required for the calculation of real patient situation dose distributions, and the authors do not know of such calculations actually being carried out, although the techniques for so doing are well-known.

* Partially supported by USPHS Research Grant CA-06102.

79 80 SILER and DYMYTRYSH A К

Two methods then remain: the use of a highly simplified analytical technique, with attendant theoretical imperfections; or the employment of purely empirical methods, based upon measured dose distributions in inhomogeneous phantoms. Unfortunately, the data for the second of these are not available in sufficient quantity to warrant the development of empirical formulatives. Therefore, we have employed a formulation which is theoretically correct for the primary beam, but not for scattered radiation. This method's validity depends upon a predominance of primary over scattered radiation and its usefulness is restricted to supervoltage radiation. The basic model for these calculations, as given originally in Siler and Laughlin (1962) and further developed in Siler et al. (1964), is:

-12 D = TAR (E Oit.) OCR (а) (1) in which D = dose at point P, TAR = tissue-air-ratio, pi = density of ith inhomogeneity, tj = thickness of ith inhomogeneity traversed by ray from source to point P, OCR = off-centre-line ratio,

n (2)

i=l

in which X¡, u¡ and v¡ are the eigenvalues, eigenvectors of Ml, and eigenvectors of M2, and in which M is the number of eigenvalues which are significantly different from zero. We here note that n is then the effective rank of matrix M. It was expected that the supervoltage radiation matrices would be of rank 1, and that the orthovoltage matrices would be of rank 2, as described in Siler et al. (1964). In fact,the supervoltage matrices were indeed of rank 1, but there were three or perhaps four eigenvalues of the orthovoltage matrices which were quite different from zero. The problem of matrix reconstruction is now being worked on, to find out how many eigenvalues for the orthovoltages matrices must be used. It is hoped that the matrices will be such that they can be reconstructed within experimental

6 82 SILER and DYMYTRYSH A К error by the use of two non-zero eigenvalues. This hope is based upon a paper by Worfhley and Wheatley (1952). The separation of a matrix into factors consisting of the eigenvalues and eigenvectors in the way described may be done in infinitely many ways if the matrix is of rank 2 or greater. The particular decomposition obtained by the use of eigenvectors and eigenvalues is hased upon orthogonality of the eigenvectors. However, in actual fact, the decomposition should not be based upon orthogonality, but should be based upon the known relationship between primary radiation and scattered beam which occurs at the point at which back scatter is measured, which is conventionally at the maximum point on the centre-line of the X-ray beam. Given this condition, it is hoped that the condition of orthogonality may be foregone, and by the choice of a new vector base, new vectors chosen which will properly represent the amount of scattered radiation present at the maximum point. These factors should then represent a decomposition of the dose matrix into primary and scattered radiation. We do not at present know whether or not this method will be successful. Another possibility for separation of the dose matrix into primary and scattered beam is the experimental measurements of transit data on orthovoltage radiation through various thicknesses of absorber ranging from zero to approximately 30 cm. Such data would establish the vectors for the primary beam, and the matrix of secondary radiation can be immediately obtained by subtraction of the calculated primary beam matrix from the measured total dose matrix. Unfortunately, such data are not presently available to the authors. It then appears that the four methods available for calculation of inhomogeneities are: (1) the simplified analytical method based upon primary beam characteristics; (2) the separation of primary beam and scattered radiation by the matrix manipulations here described; (3) separation of primary beam from scattered radiation by experimental transit measurements plus matrix manipulations; (4) Monte Carlo calculations. In any case, the acquisition of reliable experimental data on the effects of inhomogeneities for checking the calculated results is very desirable. COMPUTER CALCULATIONS IN INTERSTITIAL SEED THERAPY! I. RADIATION TREATMENT PLANNING

M. BUSCH ABTEILUNG FÜR RONTGEN-RADIUM-THERAPIE DER MEDIZINISCHÈN UNIVERSITATSKLINIK, FREIBURG/BRSG. , FEDERAL REPUBLIC OF GERMANY

In interstitial seed therapy computers can be used for radiation treatment planning and for dose control after implantation. In interstitial therapy with radioactive seeds there are much greater differences between planning and carrying out radiation treatment than in teletherapy with cobalt-60 or X-rays. Because of the short distance between radioactive sources and tumour tissue, even slight deviations from the planned implantation geometry cause considerable dose deviations. Furthermore, the distribution of seeds in an actual implant is inhomogeneous. During implantation the spatial distribution of seeds cannot be examined exactly, though X-rays are used to control the operation. The afterloading technique of Henschke allows a more exact implantation geometry, but I have no experience of this method. In spite of the technical difficulty of achieving optimum geometry, interstitial therapy still has certain advantages when compared with teletherapy: the dose in the treated volume can be kept smaller than in teletherapy, the radiation can be better concentrated in the tumour volume, the treatment can be restricted to one or two operations, and localized inoperable tumours may be cured more easily. The latter may depend on an optimal treatment time, a relatively high tumour dose and a continuous exponentially decreasing dose rate during the treatment time. A disadvantage of interstitial therapy is the high personnel dose, which may be reduced by the afterloading technique of Henschke (1956). However, the afterloading method requires much greater personnel and instrumental expense than free implantation of radiogold seeds and causes greater trauma for the patient. Radioactive seeds can be considered as point sources and using this assumption the mathematical treatment of dosimetry in interstitial seed therapy is rather simple (Frost, 1960). The dose around a seed is approximately proportional to the inverse square of the distance and proportional to a fuction of absorption and scattering of the gamma rays in soft tissue:

D = K^ (1)

where D = dose rate from seed to an arbitrary point, d = distance from seed to point, and a(d) = absorption + scattering function. The value of К varies with the type of seed and can be calculated from the following expressions:

83 84 BUSCH

K= A Iygt for seeds of long-lived nuclides (cobalt-60)

A0IygT for radiogold seeds which are not removed

A0IygT (1 -exp(-t/T)) for seeds which are removed before full decay (afterloading method)

where A = activity of a seed (mCi), A0 = radioactivity at the moment of implantation (mCi), Iy = gamma dose rate of the nuclide (R/mCi h at 1 cm), g = radiation energy absorption of soft tissue (0. 966 rad/R) (Frost, 1960) t = treatment time, T = average life of the nuclide. (If T is the hálf-life, T = T / - In 0. 5 = T/0. 693). The function a(d) can be replaced by an exponential function, if no better function is available:

a(d) := exp(-Aid) (2)

where ц = 1/d and d = dm/-ln 0. 5 = dm/0. 693 (dm is the half-value layer of the gamma radiation in water or soft tissue). If the co-ordinates of the calculated point are a, b, c, and those of the seed x¡, уь z¡, then the distance d¡ between point and seed can be calculated as follows:

di = Л(х; = а)2+(у;-Ь)2+(21-с)2 (3)

If we have n seeds, we must sum the single doses, D¡, of each seed to obtain the total dose, D:

n n P^D^K^aidO/df , (4) i=l 1=1

How well the calculated dose distribution corresponds to the measured one is shown in Figs 1 and 2. Dose distributions around a number of geometrical seed arrangements were calculated using Eqs (l)-(4); some of these arrangements are shown in Fig. 3. One can see that the minimum superficial dose may be expected at the point indicated by a cross (Fig. 3)-. .Five hundred and seven different implant designs have been investigated: these have a maximum rank of 11 seeds and a maximum number of 200 seeds. The superficial minimum dose was kept constant by an iterative variation of spacing. The minimum dose of 6000 rads, for instance, was of special interest. The number of seeds in every implant was then put in relation first to the volume, second to the spacing and third to the surface of the implant. In the 507 different geometrical implants the number of seeds used for implantation is nearly proportional to the surface of the implant (for the same superficial minimum dose), independent ot the type of implantation (plane, volume or surface) and independent of the elongation. How well the surfaces of the examined implants correspond with the number of seeds is PAPER 7. II 85

FIG.l. Comparison between measured dose distribution of a flat square radium filter

(32.25 R/h) (21.45 R/h) (10.75 R/h) ( 5J» R/h)

FIG.2. Comparison between measured and calculated • dose distributions of a seed arrangement (radiogold seeds). shown in Figs 4 and 5. One may expect that cylindrical, spherical, or other implants are not exceptions but perhaps this ought to be investigated. The straight line in Figs 4 and 5 can be expressed by the equation

N= 0. 18 S + 5 where S is the surface of the radiated area in square centimetres and N the number of seeds. 86 BUSCH

-о—ы plane implant

Л ^

-- -- 1

tX- - -- volume implant yl y\ У!

surface implant

FIG.3. Basic types of seed arrangements which are examined

In practice it is impossible to arrange the seeds exactly. Therefore the surface of the radiation area is enlarged by a factor of about 1.1. Then we get the following equation:

N= 0. 2 S + 5 (5) PAPER 7. II 87

àJ . minimum dose at surface: 6000 rods N Number of seeds

FIG.4. Dependence of the number of seeds used for implantation on the surface of the implant (radiation area) (square basic implantation type) for the same superficial minimum dose of 6000 rads (Busch). In the left upper corner the nuclides are shown, for which Eq.(5) is available (dose rate of 182Ta :6.1 (R/mCih at 1 cm) (Gauwerky))

Number of seeds

FIG.5. Dependence of the number of seeds used for implantation on the surface of the implant (triangular basic type) for the same superficial minimum dose of 6000 rads 88 BUSCH

N number of seeds

200-

100-

'• ' • plane implants .S • volume SO—I • surface •• •• a.» %•

volume of implant

WOO ISOO 2000 V (err?i

FIG.6. Dependence of the number of seeds used for implantation on the volume of the implant (radiation area) for the same minimum dose of 6000 rads. Here the same geometrical implants are examined as in Fig. 4

The tumour volume is less suited for dosimetric purposes in seed implantations than the tumour surface (Fig. 6). (See Laughlin et al., 1963). The accuracy of fit of a straight line in the volume method is 52%, while the accuracy of the surface method, at a number of 150 seeds, is below ±6%. In the left upper corner of Fig. 4 the activities and treatment times for tantalum-182, iridium-192 and cobalt-60 seeds are specified, with regard to the dosimetric instructions given in Eq. (5). These three kinds of seeds are assigned for the afterloading method. Because radiogold seeds are not removed, the treatment time is theoretically infinite, the biological efficiency may perhaps last for two or three weeks. In clinical use of interstitial seed therapy one often must avoid pressing the tumour to prevent a penetration of tumour cells into the blood stream. In such cases the advantage of surface implantation arrangements is evident. One must consider that, in surface implants larger in the smallest diameter than 4 cm, the central minimum dose is usually smaller than the peripheral minimum dose. In such cases an implantation of some seeds into the tumour centre is unavoidable. Generally the minimum peripheral dose can be obtained in the tumour centre by implanting half of the number of the seeds into the centre as would be needed for a volume implant. To calculate the number of seeds by Eq. (5) one needs the surface area of the tumour. In rectangular slab implants the surface S can be calculated by the following equation (Fig. 7):

S= 2(AB+AC + BC) (6)

А, В, С are the three axial dimensions of the tumour. PAPER 7.1 89

A .'/ / / A

[JEÉEEÎ/

FIG. 7. Calculation of the surface of a seed implant

N number surface volume of seeds implants implants Л--Л 200-

150- plane implants

100-

50-

spacing

13 U IS IS 11 18 19 20 21 22 23 2i 25 26 27 mm FIG. 8. Spacing of the examined implants related to the number of seeds for 6000 rads peripheral minimum dose, for seeds specified in Fig. 4

If one proposes an implantation in an ellipsoidal shape, Eq. (6) must be altered. There is no simple equation for the surface S e of an ellipsoidal solid, however the surface varies between

ж/3 (AB + AC + ВС)

A sphere requires the factor 7r/3 — 1. 05, a flat disc the factor 7T/2 — 1. 57. A mean factor may be 1. 15 to 1.3. Figure 8 shows the spacing of the different seed arrangements for 6000 rads peripheral minimum dose and for seeds specified in Fig. 4. In 90 BUSCH

Minimum dose Activity (mCil per seed

Factor F

FIG. 9. Dependence of the factor F (Eq. 7) on the minimum dose at different activities per seed

volume implants one must consider the elongation of the implant. Other peripheral minimum doses than 6000 rads, and other activities per seed than those given in Fig. 4 are desirable. One can then write the dosage Eq. (5) for interstitial seed therapy as follows:

N = FS + 5 (7)

where F is 0. 2 in the case of radiogold seeds of 10 mCi each to obtain a superficial minimum dose of 6000 rads. In addition to this relationship, the dependence of the factor F (Eq. (7)) on the radioactivity of the single seeds and on the minimum dose has been examined. The dependence of the factor F on the minimum dose is linear, independent of the radioactivity of the seeds (Fig. 9). On the other hand, the dependence of the factor F on the reciprocal value of the radioactivity per seed is also linear, independent of the minimum dose (Fig. 10). According to this result one gets the following general equation for the dosage in interstitial seed therapy:

N = (К^" +0. 008^1 S + 5 (8) V AO ;

where N = number of the seeds, D = minimum dose (krad), A0 = activity per . seed (mCi), S= surface of the tumour (cm'2), and K= proper constant of the use nuclide:

198AU, t = oo : K= 0.32 (5 to 15 mCi/seed)

60Co, t= 93 h: K= 0. 055 (1 to 2 mCi/seed) 192Ir, t= 91 h: K= 0. 1 j (3 to 7 mCi/seed) 182Ta, t= 92 h: K= 0. 13 (2 to 5 mCi/seed) PAPER 7. II 91

FIG. 10. Dependence of the factor (Eq.7) on the reciprocal value of the radioactivity per seed at different minimum doses

Equation (8) is valid for volume, surface, and plane implants with seeds distributed homogeneously. The error is perhaps 0% to 12% of the minimum dose (20 to 150 seeds). COMPUTER CALCULATIONS IN INTERSTITIAL SEED THERAPY: II DOSE CONTROL AFTER SEED IMPLANTATION

M. BUSCH ABTEILUNG FÜR RÔNTGEN-RADIUM-THERAPIE DER MEDIZINISCHE UNIVERSITATSKLINIK, FREIBURG/BRSG., FEDERAL REBUBLIC OF GERMANY

After seed implantation exact dose control is desirable. In clinical practice a measurement of dose in a depth of tissue is hardly possible. A measurement may be possible by the method of three-dimensional reconstruction of the seed arrangement in water. To reconstruct an identical seed arrangement one must know the co-ordinates of the "seeds. How can one measure the co-ordinates of the seeds in tissue? Several methods are given in the literature (Adams and Meurk, 1964; Nuttall and Spiers, 1946; Pierquin et al., 1960) but all seem to be somehow imperfect, because of the difficulties in correcting faults of projection and identifying individual seeds. The laborious procedure of correcting manually for projection enlargement, identifying of seeds and correcting for adjustment faults in making radiographs may be the reason for such methods not being used in routine practice. A computer programme has been written to correct central projection, to correct the two most important adjustment faults and to identify seeds in perpendicular radiographs. The method of determining the dose distribution after seed implantation consists of two parts, a manual part and a computer part. The manual part has three working steps: (1) Making radiograms in perpendicular planes of the subject, (2) Measuring co-ordinates of seed pictures in the radiographs, (3) Feeding the measured and other data into the computer.

MANUAL STEP 1

The radiographs in perpendicular planes can be made in the sitting or the lying position. One must avoid a mixed position technique, where the patient is sitting in one plane and lying in the other. In the lateral view the patient must keep his left side towards the film, and in the antero-posterior view he must turn his backside towards the film, although the seed implant is sometimes localized on the opposite side. The reason for this order depends on the computer procedure of correcting central projection into parallel projection. On the other side the orientation of inverse calculated dose distributions is difficult. In Fig. 1 the normal position of the patient and Cartesian axes are shown. The zero point of the co-ordinate system is identical with the crossing point of the central axes of the two perpendicular views. This point marks the position of the subject. The transit spots of the two central beams are

92 PAPER 7. II 93

marked by longitudinal lines at the patient's skin before making the radiographs (Fig. 2). In Fig. 3 the exposure directions and the patient is shown once more. The two subject-film-distances must be measured to enable the computer to convert the central projection into parallel projection (Figs. 2and3). Only two errors in positioning the patient are allowed (and the first of them is nearly unavoidable), axial displacement and inclination of the subject from -20° to +20° from the correct position (Fig. 4). Because of the relative inaccuracy of manual measurement of seed co- ordinates on the radiographs only the two mentioned position errors can be corrected mathematically. Therefore one must avoid the other four possible adjustment faults.

MANUAL STEP 2

This consists of measurement of the co-ordinates of seeds in two perpendicular radiographs. Two straight lines are drawn at right angles in the centre of each radiograph (Fig. 5). By means of these lines the co-ordinates of the seeds in the concerning exposure plane can be easily measured (Fig. 6). On the measurement of co-ordinates of seeds the following manual procedure is of some value: the radiograph is put on millimetre paper, on which co-ordinate lines are drawn. The centre of the paper corresponds with the centre of the radiograph. The seed images are punched by a thin needle through the radiograph, and the perforations can be easily measured on the millimetre paper. The accuracy of measurement is better than 0.3 mm, the values are written down in 0.1 mm. 94 BUSCH

FIG.2. Measuring the two subject-film-distances from, the marked transit spots of the central beam

FIG. 3. The two views of exposure and the two subject-film-distances

MANUAL STEP 3

This consists of compilation and punching the data. The measured values and the other data are punched on cards and on tape respectively and are fed into the machine after the programme is set up. Figure 7 shows the print-out of a punched tape. The manual work now is finished, and the automatic calculations may start. PAPER 7. II 95

FIG.4. The left-hand diagram shows the two positioning mistakes, axial displacement and inclination of the patient. These two mistakes are allowed

FIG. 5. Two perpendicular views of the seeds arrangement in a case of a tumour of the mouth floor. The co-ordinates of the seeds pictures can be measured after drawing the cross lines into the centre of the radio graphs

THE COMPUTER PROGRAMME

The principles of automatic correction of projection and position faults and of identification can be described as follows: the lateral view (i. e. the measured data from it) is slowly turned in the computer from -20° to +20°. And this is done until the z-co-ordinates of the lateral view correspond best with those of the antero-posterior view. The turning is done in steps of 1°, and with each step the following is executed: the z-co-ordinates are arranged according to size, the enlargement of the projection is put into normal 96 BUSCH

FIG. 6. Measurement of the co-ordinates of seeds pictures in the case of the lateral view

[AA KAPPAJ

2052 PROPORTIONAL ITAETSFAKTOR;

».495b-J SCHWAECHUNGSKOEFFIZIENT, GLEITKOMMAZAHL; 16a SE ITENLAENGE DES BERECHNETEN QUADRATES IN MM ; o,o,o KOORDINATEN DER MITTE DES BERECHNETEN QUADRATES IN MM; 2o ANZAHL DER VERWENDETEN SEEDS; o,l,o BERECHNUNG EINES QUERSCHNITTES; 2ooo FOKUS-FILM-DISTANZ IN MM; 27o OBJEKT-FILM-DI STANZ IN MM BEI D£R SE I TENA'JFNAHME; 16o OBJEKT-FILM-DISTANZ IN MM BEI DER A-P-AUFNAHME;

[AA KOORDINATEN]

: X. zx ;

161, -488, -oo5, -5o2, -o63, -5o3, 2o7, -557, 163, -579, 13o, -626, o75, -646, 088, -664, 094, -7«4, 117, -7O7, 078, -755, 012, —788, 231, -792, -062, -871; lo9, -984, 25o,-lool, 243,-lol5, -o46,-le4o. o42,-lo45, o8o,-1151,

; Y, ZY ;

813, -318, 765, —32o, 952, -344, 887, —4oo, 97o, -43o, 8lo, -46o, 468, -462, 627, -463, 543, -522, 975, -563, 522, -574, 89o, -632, 747, -633, 752, -7o8, 696, -819, 661, -846, 496, -854, 660, -857, 561, -87o, 488, -975,

CSS ANFANG!

FIG. 7. Outprint of the compiled dates punched on tape

scale, and the lateral view is shifted to the" proper height (Fig. 8). Finally the minimum differences of the corresponding z-со-ordinates of all angle steps are compiled. From this compilation one gets the exact angle of inclination of the lateral view (Figs. 4 and 9). How the axial displacement of PAPER 7. II 97

axial displacement correction

I I I rillrL -10 -30 -20 Omm +10 +20 +30 +Í0

FIG.8. Correction of the axial displacement of the lateral view from a compilation of the differences of corresponding z-co-ordinates of the two views

m i • . I -w . 40° + 20°

FIG. 9. Investigation of the inclination of the lateral view from a compilation of the sum of the minimum differences of corresponding z-co-ordinates of the two views

the lateral view at each step can best be corrected without being influenced by possible faults of measurement is shown in Fig. 8. Actually we do not use this rather lengthy procedure to determine the angle of inclination. We use an iterative procedure, which is more complicated, but it needs perhaps only 25% of the calculation time of the method given above. Once the angle of inclination and the axial displacement are determined, the final identification of the seeds starts: the measurements which differ least when reduced to the original scale are compiled as identical in the z-co-ordinates. By this procedure the most identical measurements are placed at the top, and those with the least identity at the end of the compilation. The two still separate z-co-ordinates now are unified by forming the mean value. If it is evident that the two z-co-ordinates differ by more than 2 mm, the number of the measured value concerned and the difference is printed out by the machine. By this indication one can recognize each major fault of measurement or writing, which influences the correspondence of the z-co-ordinates. Now one can decide whether the programme will be stopped or not, depending on the significance of the fault. After this the calculation of dose distribution starts. These calculations are carried out by means of Eqs. (1) to (4) given in part I. The printout of the

7 98 BUSCH

FIG. 10. Outprint of a dose distribution in a case of a carcinoma of the mouth floor, treated with 20 radiogold seeds (lying position). All lines are drawn by hand dose distribution is not a mathematical problem. The printout is a sheet of 50X 50 cm2 (Fig. 10) in which 1500 single doses rounded to 10 rads are given. In addition, the original co-ordinates of the seeds are printed, so one can draw the seeds into the generally enlarged printout of the dose distribution. The enlargement of the printout one can find out from a scale on the left and upper margin of the sheet. In Fig. 10 one can see what such a dose distribution looks like. The isodose and other lines on this printout are manual work. It must be emphasized, that dose distributions can be calculated in all perpendicular planes through or outside the seed implant. PAPER 7. II 99

ACKNOWLEDGEMENTS

The calculations were carried out by the computer 2002, Leihgabe der Deutschen Forschungsgemeinschaft, at the Institut für Angewandte Mathe- matik ofthe University of Freiburg/Brsg. I thank Dr. Geis, headofthe Com- puting Centre Freiburg, for his benevolence. AUTOMATIC CALCULATION OF ISODOSE CURVES FROM IMPLANTS . OF RADIOACTIVE SOURCES*

G. W. BATTEN AND R.J. SHALEK DEPARTMENTS OF B10MATHEMAT1CS AND PHYSICS, THE UNIVERSITY OF TEXAS M. D. ANDERSON HOSPITAL AND TUMOUR INSTITUTE, HOUSTON, TEXAS, UNITED STATES OF AMERICA

INTRODUCTION

Within two years after its discovery in 1898, radium was employed in the treatment of malignant disease. In 1913, the survival of a patient treated seven years previously for carcinoma of the cervix was reported (Abbe, 1913). As in other forms of radiation therapy, techniques of treatment evolved by trial and error. For lack of better quantitation, the unit of milligram- hours as a measure of radiation treatment was employed. This unit for the description of radiation treatment gives the product of the amount of radioactive material and the time of treatment but tells nothing of the geometrical arrangement of the radiation sources or of the resulting distributions of absorbed radiation in the structures under treatment. Nonetheless, it was a useful unit which continues today to have some applicability as a rough indi- cator of requisite dose and patient tolerance. In the early 1930's, a tran- sition was made to calculations which were based upon the energy absorbed in the tissue rather than the source strength or the treatment time. However, because of the complexity of the dose distributions and calculations, systems were devised which permitted the calculation of a single average dose or the dose to one or a few points from tables. Not until the availability of automatic computers has it been feasible to calculate the radiation distributions in detail for individual cases. Of several systems which were invented for interstitial radium therapy, the Quimby system (Quimby, 1932) and the Pater son-Parker system (Pater son and Parker, 1934) continue in clinical use. The Quimby system supplied the calculative procedure for existing treatment methods which utilized uniform sources at equal spacings. The Paterson-Parker method prescribed geometries of sources of two strengths, one twice the other, so that the dose delivered at \ cm from a plane or the dose on lines through a volume were uniform within limits. These methods which permit the calculation of a single dose rate representing the complex radiation distribution around an array of needles have served for thirty years as successful guides to interstitial treatment. The dose so calculated is used to determine the time required for the implant to deliver a prescribed dose. Computer methods for implantations of radioactive seeds or needles permit the description of the

* Supported in part by grant CA 06294 and CA 06675 from the National Cancer Institute, US Public Health Service.

100 PAPER 7. II 101 full radiation'distributions resulting from a particular geometry of sources (Nelson and Meurk, 1958; Shalek arid Stovall, 1961; Stovall and Sh'al'ek, 1962; Laughlin et al., .1963; Busch, 1963; Hope et al., 1964; Powers ét al. / 1965). Since the placement of sources in the patient is never exaotly'as planned; the calculation of the dose distributions are most useful when they are based upon the array of sources as they exist in the individual^ patient. -The treatment of carcinoma of the uterine cervix by radium was one of the earliest uses for radium in the treatment of cancer and,' indeed; the treatment of this disease with local intracavitary radiation continues tó-'be a major method of therapy. This method of treatment has the advantage that a high radiation dose can be delivered to the tumour while a relatively low dose is delivered to normal tissues. In addition,' the placement of radiation sources is accomplished easily with little trauma to the patient. The calculation of the radiation dose resulting from treatment has been ignored by many practitioners infavourof a mg-h description of the treatment. Another method of dose control has been the calculation of the dose to two points which are located relative to the radium system (Tód and Meredith, 1938). More recently, à manùal method for the calculation of a singlé isodose curve in a single plane defined by the radium system has been described (Fletcher et al. , 1953). With computer methods, families of isodose curves in arbitrary planes can be calculated. From such dosimetric information, an estimate can be made of the sufficiency of the treatment in the tumour volume, of the dose delivered to other areas such as the nodes on the pelvic wall or the intestine, and of the precision of the matching of supplementary radiation delivered by external beam techniques. The computer programme described here was designed to calculate radiation distributions, around multiple radioactive sources in individual treatments, The sources may be seeds, needles, or tubes with radium or any other .isotope as the radioactive element. The radiation distribution is computed and isodose curves are automatically plotted for any number of planes of calculation; the locations of the planes of calculation with respect to the sources are arbitrary. The versatility, accuracy, and automatic plotting feature of this programme represent significant improvements over the computer method which has been in routine use at this institution for the last three years (Stovall and Shalek, 1962). • • , . .. r The programme, which has been written in Fortran algorismic language; can be readily adapted to any large computer. Because considerable effort was directed at developing .an efficient procedure, the,amount of computation per patient is rather moderate (less than 60 multiplication times per point per source; which, on the CDC 1604, amounts to.less, than 45 seconds for a patient with four sources for. which the computations are done-atthe points of three 40 X 40 plane arrays); :

NUMERICAL METHOD

As point sources have a simple (inverse square with exponential absorption) behaviour, the discussion here is concerned with linear sources only. 102 BATTEN an4 SHALEK

Consider a linear source of linear density p(mg/cm) surrounded by a cylindrical absorber of thickness d(cm) and absorption coefficient (i(cm"i)i, and imbedded in a medium whose absorption coefficient is (i'(cm'i). Let P be any point not co-linear with the source, and let x1 and yi be Cartesian co-ordinates in the plane containing P and the source, the co-ordinates chosen so that P lies on the positive y' axis and the source lies on the x' axis. Denote by yo(cm) the ordinate of P and by xi and хг(ст) the abscissas of the left and right endpoints, respectively of the source. Then the source produces at P a radiation intensity I(R/hr) given by

x2/y0

i i I(xi,x2,y0) = Груо1 J (1+S2)-1 exp[-Aíd(l+s2) -A¡'y0(l+s2) ]ds (1) xi/y

*2/Уо 1о(*1.*8.Уо) = ГрУо1/ (l+s2)-i exp[-/ud(l+s2)*]ds (2) x 1 /У о

Unfortunately, the numerical evaluation of Eq.(l) as it stands is un- satisfactory for the present purposes since the integral must be evaluated several thousand times for each source. A more satisfactory approach is to consider the tissue absorption separately as follows.

By the mean value theorem, there is a number г*, (x^ + y§)l

x х I(xi,x2,y0) =Io( i. 2.Уо) exp(-ju'r*) (3)

In applications, ц' is small; therefore, a rough approximation, r, to r* can be used in Eq. (3) to provide a good approximation I to I:

T(x1,x2,y0) = I0(x1,x2,y0) exp(-ju'r) (4)

Indeed, let us assume that |xj |< |x2| (this assumption is not restrictive since the co-ordinates can be redefined so that this condition is satisfied), and let ХЗ = (Х1+Х2)/2 (the abscissa of the midpoint of the source). Then, r* must be between (x? + yo)4 and (хз+уо)^. Let x = (x3 + x1)/2, and let

r = (x®+yjj)*. (5)

1 The value 0.170 cm"1 for 0.5 mm wall thickness and 0.150 cm"1 for 1 mm wall thickness is recommended as the absorption coefficient for platinum to radium gamma rays (Shalek and Stovall, in Attix and Tochlin (in press)). PAPER7. II 103

Then the fractional error in approximating I by I is

|(I-ï)/l| = |l-e-CP"'*) I (6) which is certainly no greater than

eii'lï-r*l - 1 < ef'PVi)/4 - 1 (7)

1 1 2 For typical values (ju = 0.02 cm" , x2-x1= 1.5 cm) , the maximum error is less than 1%. The maximum error occurs only very near and very far from the source; in between, in the region of most importance, the error is considerably less. For more accuracy, each needle can be replaced by several shorter needles. Thus, we have reduced the problem of approximating I to that of determining I0. Any convenient method of numerical integration can be used, but since I0 must be determined many times, it is more convenient to compute and store a table of

Ij{t) = jT (1 +S2)"1 exp [-/ud(l +s2} i]d (8) о and to determine I0 by table look-up using

х х 10( Ь 2>Уо) = Ii(x2/y) -Ijtxj/y) (9)

As 1 j( —t) = -Ii(t), it suffices to store a table of (t) for t^O. Input data to the computer also include a description of the planes in which radiation distributions are desired. There can by any number of planes of calculation and their locations are arbitrary; they may be any distance from and any angle to the reference plane. A plane of calculation may be a square or rectangle of any size. The grid size, or distance between points of calculation, for each plane of calculation is a variable. Output data for each plane of calculation are available in two forms: a series of isodose curves and a table of dose rates on the grid of points. In practice, the isodose curves provide the radiotherapist with sufficient dosimetric information, although the tabular listing may be useful for special studies. The plotter automatically draws and labels the isodose curves and plots the projection of the sources onto the plane of calculation. More details are given in the users manual for the programme (Batten, 1965) which is available from the author.

2 Use of this value results in an overestimation of the absorption of tissue. A more recent determination (Meisberger and Shalek, 1965) gives the effective absorption of water to radium gamma rays as:

Dose in water/dose in air = 0.994 + 1.18X 10"2г - 5.91X 10"®^ + 3.28X Ю^г3 where r is the distance from a point source in cm. Such an absorption can be substituted easily for the absorption used above. 104 BATTEN an4 SHALEK

Q-, H 6

а) <л •5 э а. ' ОДо —E' Е3 _ о) а о J2H « О.2 о, л м •s в g 0) _Л ев § Е • .У Е «О -а дО ) о с О) II 3 s í I S g •^к я« Sо .°. ! Яs a.g I •a.» ^ I в ï и § u S H Я ТЭ U щw —-« 3sс О« Ss S J •SI 00 •—2 —0,0 rt о 2 E 5b g .S ю .2 - T- TJ «

„ t- С «л О Л ^ 'С W "S И 2 иtí- ûс> ао, оСо PAPER7. II 105 106 BATTEN an4 SHALEK

The isodose curves in this paper are shown as they came from the plotter, with no manual drawing added. The isodose curves may be plotted actual size or the scale increased or decreased as desired, within the limits of the size of the recorder. The isodose curves in a plane bisecting a radium needle implant of the floor of the mouth are shown in Fig. 1. Conventional calculation of dosage from this implant using Paterson-Parker tables is particularly difficult because of the minimal separation between planes. lnFig.2, the distribution around a. radium application in the treatment of carcinoma of the cervix is shown. An interesting possibility of optimizing the dose by the selection of sources is feasible with afterloading applicators (Henschke, 1963; Suit, 1963). These applicators, without sources in place, are applied to the patient in the operating room; the sources are loaded later through the hollow handle of the applicators. From radiographs of the applicators in the treatment position, the calculation of the radiation distribution from loadings of several possible source strengths before inserting the sources into the applicators would permit the selection of the best combination of sources. In this way, a new flexibility of treatment is possible in which the sources are suited to the disease and to the geometry of the applicators. The question of the size of computer that is required for such calculations is an important economic question which can be answered in two ways. The programme described above requires the use of a large digital computer (32K word memory). A small size computer of the IBM 1620 or CDC 106A class has been used successfully for the computation of dose distributions around gynaecological radiation sources (Adams andMeurk, 1964; Adams et al., 1965). The output from these machines is less elaborate than from the larger machines and thus may require somewhat more human time for interpretation. A second possibility is the communication to a computer at a distance by remote input-output devices or by telephone data input and mail return. The latter method of telephone input and mail return has been used successfully for several years for interstitial implantations where the treatment times range from five to seven days. This method would not be as useful for gynaecological treatments which usually require three days or less of irradiation time. The cost of the calculations at commercial rates is from 10 to 25 dollars for each patient. Thus, the cost is in the range of minor diagnostic procedures and is a small fraction of other costs during radiation treatment. At this time, it seems likely that interstitial and intracavitary radiation distributions for individual treatments early in the treatment, or before the sources are applied with afterloading applicators. The possibility of utilizing computers at a distance has been demonstrated so that the methods described can be made available at places away from computation centres. CALCULATION OF DOSE DISTRIBUTIONS FOR MULTI- FIELD AND MOVING BEAM IRRADIATIONS AND METHODS OF PRESENTING RESULTS

G. SCHOKNECHT PHYSICAL LABORATORY, RADIATION DEPARTMENT, STXDTISCHES AUGUSTE-VIKTORIA-KRANKENHAUS, BERLIN-SCHÔNEBERG, FEDERAL REPUBLIC OF GERMANY

1. SURVEY OF CALCULATION METHODS

The use of computer techniques for the determination of dose distributions in teletherapy is generally limited today to high-energy gamma- or X-radiation. With this type of radiation, there is no great difference between different tissue substances from the point of view of radiation absorption and a water-equivalent absorption medium can be assumed for calculation purposes. This condition is approximately fulfilled in the case of 60Co-radiation and the X-radiation obtained with linear accelerators and betatrons. Because of their widespread use and universal applicability, digital computers are generally employed for dose determinations, although the problem can also be solved with analogue computers (Siler and Laughlin, 1962). When digital computers are used for dose determinations in moving beam irradiations, the necessary integrations are approximated by summations for various positions of the radiation source. This is why the computation methods developed for moving beam irradiations are also suitable for multi-field calculations. Generally speaking, the purpose of such calculations at the present time is to determine dose distributions on the basis of specific irradiation parameters (position of rotational axis and angle, field size, etc. ). On the other hand, the problem of determining the irradiation parameter values required to obtain a given dose distribution is still largely unsolved. Calculations are generally based on the dose distribution produced in the absorbing medium with a fixed source of radiation (stationary field dose distribution). The difficulty is to take into account the variations in the stationary field dose distribution brought about by movement and the resultant constantly changing distance between radiation source and body surface. The stationary field dose values needed in the calculations can be obtained directly through measurements or from isodose charts; alternatively, the computation method can include the calculation of the stationary field dose distribution in the calculation. The direct method for determining dose distributions is to sum a number of stationary fields which correspond to the geometrical situation at some moment. This method was described by Tsien (1955, 1958). The stationary field distribution is represented digitally by the values at the grid points of a polar co-ordinate grid so that the values to be added coincide when the radiation source rotates. Sterling, Perry and Bahr (1961) developed this method further. In calculations based on this method a relatively large

107 108 SCHOKNECHT number of figures has to be processed since one has to havë a set of dose values for different source-skin distances for every field size. The number of figures can be reduced considerably if for each field size use is made of only one stationary field distribution which is converted for particular source-skin distances. Wood (1962) and Dalrymple and Perez- Tamayo (1963) used the method devised by Jones, Gregory and Birchall(1956) in which a stationary field distribution determined for a particular distance is converted by means of an effective absorption coefficient. This conversion can also be carried out by means of the tissue-air ratio (Schoknecht, 1963a; Turner, Johnson and Whitfield, 1965; Mac.Donald, 1965) if, in accordance with the method suggested by Braestrup and Mooney (1955), the dose in the rotational axis of the irradiation apparatus is taken as the reference point. With this method use is made of polar co-ordinates. Ilallden, Ragnhult and Roos (1963), Sterling, Perry and Weinkam (1963b) and Mauderli and Fitzgerald (1965) used stationary field dose values of a Cartesian co-ordinate grid. Interpolation procedures thus have to be employed in the calculation. In the case of Halldén, .Ragnhult and Roos (1963), the stationary field dose distribution is converted for different distances in accordance with the inverse square law. All these various methods are only applicable to concentric irradiations in the first instance. They can be slightly modified, however, to ailow calculations to be carried out for tangential irradiations as well (Schoknecht, 1963b). Sterling, Perry and Weinkam (1963a) performed calculations for multi-axial irradiations, first of all determining the distribution for each rotational axis separately and then summing the individual distributions for a new system of co-ordinates by interpolation. Siler and Laughlin (1962) made use of the possibility of including the determination of the stationary field distribution in the calculation; They described the field as the product of dose values on the central beam and values in a direction perpendicular to the central beam. Here again the inverse square law is used to make the necessary conversion for different distances. Richter and Schirrmeister (1964, 1965a), Sterling, Perry and Katz (1964), van de Geijn (1965) and Schoknecht (1965) employed the same product representation together with an analytical expression for thé dose distribution on the central" beam. The determination of dose values at pointé outside the central beam is based on the decrement-line principle described by Orchard (1964). The exactness of the calculations can be improved by the use of corrections. The conversion of the fixed field dose distribution by one effective absorption coefficient or one tissue-air ratio factor for different source-skin distances is not quite exact. MacDonald (1965) thereforé uses two or three fixed field distributions for each field size, each of which is valid for a certain range of source-skin distance. A method for consideration of oblique incidence was described by Mauderli and Fitzgerald (1965). Richter and Schirrmeister (1965b) showed one way to estimate the influence of tissue inhomogeneities in the calculations. Almost all computer techniques are confined to thé calculation of dose distributions in one plane.' Van de Geijn (1965) showed that the product representation of the stationary field distribution can also be extended to three PAPER 7. II 109 dimensions. Busch (1964a) made calculations of stationary fields in three dimensions by constructing them on the basis of elementary fields.

2. PRINT-OUT TECHNIQUES

The advantages of.utilizing computers for short-term irradiation planning are particularly obvious if the results of the calculations can be supplied in a form suitable for further use. The earlier methods used yielded results in tabular from and the tabulated values then had to be converted into scale drawings. Halldén, Ragnhult and Roos (1963) and Sterling, Perry and Weinkam (1963b) were the first to calculate dose values at the grid points of a Car- tesian co-ordinate grid and the values obtained were printed in lines on a 1:1 scale. In this way the cross-section of the patient's body can be transferred directly to the print-out. Similar scale print-out methods were described by Bentley (1964) and Rosenow (1965) and others. All these techniques involve interpolations in the course of the calculations. The need for interpolations can be avoided if the print-out points are allotted directly to a polar co-ordinate grid (Schoknecht, 1964). In this way the polar co-ordinate grid can be reproduced in spite of the linear motion of the printer.. Greater clarity in the scale print-out can be obtained by the use of uniform symbols for marking all points in which a particular dose is calculated. By drawing lines through equal symbols isodose curves can easily be obtained (Sterling, Perry and Katz, 1964; Bentley, 1964; Turner, Johnson and Whitfield, 1965). By the use of automatic plotting devices which are in connection with the computer it is possible to. get immediately drawings of the isodose curves (Maudérli and Fitzgerald, 19'65).

3-i STATUS OF A FAST COMPUTER ¡\IETHOD USED IN CLINICAL PRACTICE

3. 1. Description of stationary field

For calculations of two-dimensional dose distributions in BUCo teletherapy, use is made of a system of polar co-ordinates (r, ¥) having its origin in the rotational axis of the radiation apparatus. The dose rate D' at a point P(r, ?) within a water-equivalent absorbing medium irradiated with a 60Co source (source-rotational axis distance p, axis field size bXl) will be defined as

D'(r,T)=j = f(r,í)gJ¡ (1)

where f(r,^) = D'(r,¥)/D'(0,0) relative distribution of dose rate of stationary field referred to value at point P(0,0) g =D'(0,0)/J¿ (0,0) tissue-air ratio referred to J¿ 110 SCHOKNECHT

JJ standard ion dose rate in air at point p(0, 0) at maximum field size If calculations are made for deflected fields (e t 0, Schoknecht, 1963b), one has to use point Pc = P(rc,¥c) (Fig. 1) in place of point P(0,0); this point

Pc is also situated on the central beam and is separated from the source by the distance p.

3. 2. Calculations for moving beam irradiations

If the radiation source S is turned through angle ep from the 0U position, we obtain from Eq. (1)

D'(r,'5') = f(r,ï -q))g(cp) J' (2)

Integrating over irradiation time T, we obtain the dose

D(r,ï)=|f(rj-i)g(i)j; dt (3)

(T)

The convolution integral is approximated by summing for N intermediate values

1 = 0

Instead of calculating the dose D(r,Y), the following equation is evaluated on an IBM 1401

35 Ю0Г,, w . . . D(rk, 100 Y/^'Vilefi^ T У (4)

where r^ = к cm к = 0, 1, . . ., 15 fj = j 10° j = 0, 1, .... 35

This means, at all points P(ri(, Yj ) the dose rate D/T is thus calculated as percent of J^ . Since the movement of the radiation source no longer af- fects the calculation, Eq. (4) can also be used for calculations with multi- field irradiations. Figure 2a shows the printing-out concerning a moving beam irradiation over two arcs from 30° to 80° and from 280° to 330° . In this picture the

values calculated for the points P(rk, Yj) indicate the dose rate as per cent

of J's . The time required for the calculation of all 576 values is 1.2 minutes. After the calculation is finished the values stored in the computer will be printed out again. In this case the values are distributed according to the polar co-ordinate grid as well as possible (Fig. 2b). The figures indi- PAPER7. II 111

cate the dose rate as per cent of JJ . This printing-out lasts for 0.3 min. Onto this picture of dose distribution the body cross-section and the isodose curves can be drawn by hand.

3. 3. Addition of dose distributions

The computer programme makes it possible to add a number of dose distributions calculated on the basis of Eq. (4). If the total irradiation time T is made up of n partial irradiation times,

T = Tx + T2 + . . . + Tn where the different contributions are designated as an

ai=Ti/T... an=T„/T one obtains, if gn is replaced by angn

ajPi anDn\ 100 _Di+. . . + Dn 100

IL TN J J' T J's (5)

The total dose rate is thus calculated as per cent of J¿ . The times Tn for the partial irradiations have to be selected in accordance with the contributions an. 112 SCHOKNECHT

HNmminmN n л m fi гм и

, ** (ч «-л * <л о л л о N ® р»

< ел m и —ífrtf^^^^Ki^-í

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Г- О ^ Û -«f AJ vO

irv <с сс к •tmo^NOiM^mcDOMaHOosf'э-*гчо«лтт«>о~4Сч»40аэр»<осот^\таi > # (Л s r/ « к ^

f- о «-i О О ^О ^о о 'NflíOO-í'í^^ -О lA 00 í> СО о 1Л 1ÍI -О û л M •t <Г U~\ \Г\ U"\lí\kT»f\'Ainiríiri-Ú

KMnmininiTiinta

ОООООООООООСОООООООООООООООООООООООО

U1 со Z < LJ О г» h- о m -л m > 1Л 'О 1Л Z < m 1Л m m in МЛ 1Л 1П1Л 1Л о ш • UJ ОООООСЭОООООЭОООЭОЭОООООООООЭОООООООО О * О" О INÍ 1Л ONe^O^N m »л -о г» а> z z PAPER7. II 113 114 SCHOKNECHT

FIG.3. Diagram of automatic measuring unit for determining stationary field dose distributions

3. 4. Determination of initial values

Three methods have been used for determining the initial values f(rj<, i ¡): (1) Reading off values from isodose charts (2) Direct measurements (3) Calculation with computer. Reading off values from isodose charts gives rise to difficulties at low values since, for example, the AECL (Atomic Energy of Canada Ltd. ) charts used only give values down to 10% isodose curves. Direct measurements are more reliable; use was made of the automatic measurement unit shown in Fig. 3. In the calculation a product representation was used for f

f(r,ï) = fo(ro)f/"Y°) ' (6)

where the relationships r 0= r0(r, '?) and a0= ao(r, ¿ ) are obtained by (see Fig. 4)

r0 = p(l- cos e) + r cos (ï - e)

-psin e + r sin (e - í ) - Эп - P ^pco s e - r cos(i-e7ТГ ).

Function fo describes the distribution of relative dose rate in the central beam normalized to 100 at the point Pc and is given by F (CrC u)r +2 f0(r0)= 10 ' °

where F/u = bl/(2b+21) (area/perimeter). The dependence of C1 and C2 on oscillation radius for 60Co apparatus with oscillation radii from 50 to 100. cm is shown in Fig. 5. The same representation of fo is valid for wedge filter fields. The function fx(2ao/b) represents the normalized (ao divided by the half field width) dose distribution vertical to the central beam and is de- PAPER 10 115

C 1 2 C2 5

x10*3 xlO'2 \ cm"2 cm"' \ £ \

: \

50 p 100 cm 50 100cm

FIG. 5. Dependence of C^ and C2 on oscillation radius of irradiation apparatus

termined experimentally. The stationary field dose distribution f(rk, ff ) is calculated only once with an Si 2002 computer and the values are stored on magnetic tape. A print-out of the values for a 6 cmX 10 cm field is shown in Fig. 6. The tissue-air ratios g referred to J' at maximum field size used in the calculations (Fig. 7) are based on the results of experimental investigations.

3. 5. Future work in the use of computers

It is proposed to extend the scope of the calculation method by including an addition procedure to dose distributions with different positions of the rotational axes. As van de Geijn (1965) has shown,, it is not difficult to include the third dimension in the calculation. So far, however, no clear method of presenting the calculated data in three dimensions has been evolved. 116 SCHOKNECHT

FELD : 15~l o EPSI LON = 0 F/U = 1.88

2 -1 P =• • 55 CM Ci 51 0 .0017 CM C2 = 0.0 >447 CM C3 = 2

R 0 1 2 3 4 5 6 7 8 9 lo 11 12 13 14 15 PSI

0 loo lio 121 133 147 161 177 195 215 236 260 286 315 346 381 419 lo 1 po lio 121 133 146 160 176 192 2o9 225 243 26o 258 216 16.6 125 2n loo 109 12o 131 142 151 160 151 loo 6 3 51 46 43 42 39 38 3n loo 1 o9 113 126 132 122 67 4o 34 31 28 27 25 23 22 21 4o loo 10Я 115 119 I08 5o 31 26 23 21 19 18 15 1 3 11 7 5" loo I06 111 111 59 29 22 19 17 16 13 12 9 7 5 1 <0 loo I05 lo7 96 3 5 23 18 15 1 3 1 2 lo 8 6 4 1 0 7o loo lo3 1 0 3 76 27 19 15 13 11 9" 8 6 4 2 0. 0 По loo 10 2 99 63 24 17 1 3 11 9 8 6 5 3 1 0 0 9 о loo loo 96 59 22 15 1 2 lo 8 7 6 4 3 2 0 0 loo loo 98 9 3 61 22 15 1 1 9 . Я 6 5 4 3 2 1 0 11л loo 97 91 7o 24 15 1 1 9 8 6 5 4 3 3 2 1 12o loo 95 09 76 32 16 1 2 9 8 6 5 4 3 3 2 2 13o loo 94 88 78 51 21 13 lo 8 6 5 5 4 3 3 2 l4o loo 93 8 ó 78 68 41 2o 13 lo 8 6 5 5 4 3 3 150 loo 92 85 77 69 61 48 28 16 11 8 7 6 5 4 3 160 loo 91 84 76 7o 63 56 5o 45 37 26 18 13 9 7 6 170 loo 91 83 75 69 62 57 52 47 43 39 35 32 28 26 23 lflo loo 91 83 75 68 62 56 51 47 42 38 35 32 29 26 24 190 loo 91 83 75 69 62 57 52 47 43 39 35 32 28 26 23 2o 0 loo 91 84 76 7n 63 56 5o 45 37 26 18 13 9 7 6 21o loo 92 85 77 69 61 48 28 16 11 8 7 6 5 4 3 2?.o 1 óo 93 86 78 68 41 2o 13 lo 8 6 5 5 4 3 3 230 loo 94 88 78 51 21 1 3 lo 8 6 5 5 4 3 3 2 24 0 loo 95 89 76 3 2 16 12 9 8 6 5 4 3 3 2 2 250 loo 97 91 7o 24 15 1 1 9 8 6 5 4 3 3 2 1 2IÍ0 loo 98 9 3 61 22 IS 1 1 9 8 6 5 4 3 2 1 0 27o loo loo 96 59 22 15 1 2 lo 8 7 6 4 3 2 o 0 ЯП 0 loo 1 0 2 99 63 24 17 1 3 11 9 8 6 5 3 1 0 0 29 o loo 1 0 3 10 3 76 27 19 15 1 3 11 9 8 6 4 2 0 0 Зоо loo I05 I07 96 35 23 18 15 13 12 lo 8 6 4 1 0 ЗЮ Ion lo Л 111 111 59 29 22 19 17 16 13 12 9 7 5 1 32o loo 1оЯ US 119 I08 50 31 26 23 21 19 18 15 13 11 7 33o loo 1о9 118 126 132 122 67 4o 34 31 28 27 25 23 22 21 34 o loo I09 1 2o 131 142 151 I60 151 loo 63 51 46 4 3 42 39 38 З50 loo lio 121 133 146 1 60 176 192 2o9 225 243 260 258 216 166 125

TABE :LLE DER Fl (2-AO/B)

0 3 7 12 59 loo loo 41 11 6 2 0 3 7 13 82 loo 29 11 6 2 ó 4 8 14 92 loo 23 lo 6 2 0 4 8 15 95 100 2o lo 5 1 1 4 9 16 97 99 18 9 5 1 1 5 9 18 99 97 16 9 4 1 1 5 lo 2o loo 95 15 8 4 0 2 6 lo 23 loo 92 14 0 4 0 2 6 11 . 29 loo 82 13. 7 3 0 2 6 11 41 loo 59 12 7 3 0

FIG. 6. Computer print-out of a stationary field calculation

Calculated dose distributions for multi-field and moving beam irradiations are listed and this information is constantly being added to. The data obtained serve as a basis for the selection of irradiation parameters. PAPER 10 117

•*— Tissue-Air Ratio

25- cm

«S 20—

ВШ1я 50

Depth ^ 70

75 10— 80

100

о— 1 2 £ 3 4 cm u

FIG.7. Diagram for the determination of tissue-air ratio values THE OPTIMIZATION OF TREATMENT PLANS

C.S. HOPE, M.J. E, LAURIE AND J.S. ORR REGIONAL PHYSICS DEPARTMENT, WESTERN REGIONAL HOSPITAL BOARD, GLASGOW, UNITED KINGDOM

A GENERAL INTRODUCTION TO OPTIMIZATION

Optimization is the search for the most favourable conditions for some event to take place. The practice of optimization, formerly the realm of the astrologer, is mainly the activity of the economist and, with the advent of the high speed digital computer, the interest of the mathematician. The process of optimization comprises the maximizing or minimizing of a mathematical expression whose variables are subject to constraints on the values they may take. One class of optimizing problems includes those in which the expression and the constraints are linear in their variables and the general case may be described as the minimizing of the expression:

C = C1x1 + C2x2+ +Cnxn subject to constraints of the form:

a1x1+a2x2+ +anxn=b

where C¡, a¡ and b are constants and x¡ is a variable. The best known problem of this type is the transportation problem discussed by Hitchcock (1941). Satisfactory methods for solving such problems have been found, Vajda (1961), and most computer service bureaux now provide standard programmes for the purpose. Many problems when formulated do not present linear relationships and methods are currently being developed in cases where an approximate solution is known, Fletcher (1965). In these methods the obvious approaches of tabulation, random search, and improving each variable in turn have been discarded as inefficient and unreliable, and partial derivatives or gradients are used to obtain the optimum from the known approximate solution.

THE VALUE OF OPTIMIZED TREATMENT PLANNING

The desire to produce better treatment plans has led to many improvements in technique and to devices being produced which make planning more consistent and accurate. In particular, in the limited case of treatments using wedged fields, the studies of Cohen et al. (1960) have produced rules for optimized planning. An analogue computer devised by J.G. Stewart (personal communication) produces the angles at which wedged fields must

118 PAPER 10 119

be placed so that the dose gradient across the treatment area will be minimized. With the introduction of digital computers to radiation dosage problems the possibility of a more generalized optimizing procedure has been recognized. However, the calculating speed of a computer can only be fully used if the results are assessed at a comparable speed. The computer must con- duct this assessment and therefore a study must be made of the criteria of goodness by which a treatment is judged, so that rules can be built into the computer programme. A study of this kind requires repeated setting of rules and examination of results until lack of knowledge prevents further improvement. It may therefore open up new avenues of investigation into the requirements of a treatment plan and will produce a better understanding of the judgement criteria.

TREATMENT PLANNING AS AN OPTIMIZING PROBLEM

In optimizing fixed field treatment planning it is desired to minimize the badness of the treatment. In the assessment of a plan the badness can be expressed in terms of variables such as tumour dose, integral dose, dose gradient across the tumour, physical complexity of treating, etc. Each variable can have constraints imposed upon it, for example, minimum acceptable tumour dose, but these variables are dependent on a more basic set which includes number of fields, field positions, wedge angles and field weights, each having its own inherent constraints defined by available facilities. Further, the dependent variables, tumour dose etc., are hetero- dimensional and the assessment cannot be carried out by combining them directly; It is necessary to replace each dependent variable by a score function which relates the magnitude of a deviation from the ideal value to the importance of this deviation. The analogy between the optimizing process and curve fitting by least squares suggests that the individual scores should be added to evaluate badness. The score functions are, in fact, measures of the deviations. Deviations correspond to residuals which are squared and added to assess the goodness of fit of a curve, though in general the score functions in treatment planning will not be squares of the deviations. The two problems to be solved before optimized treatment planning is a practical reality are: (a) the organization of the search for the optimum; and (b) the definition of score functions to recognize it. In the next section score functions are considered while the problem of searching is examined later in the paper.

A STUDY OF SCORE FUNCTIONS

In a previous paper Hope and Orr (1965) presented a model optimizing programme which considered three criteria dependent on tumour dose, dose gradient across the tumour and a measure of integral dose. For each a score 120 HOPE et al. function of the form (КС)" or (К/С)" was used where К was a constant chosen to separate acceptable values of a dependent variable from unacceptable values, and n controlled both the severity of the penalty for values in the unacceptable range and the relative importance of values in the acceptable range. It was decided that the programme should be modified to include the choice of field width thereby permitting the inclusion of two further criteria dependent on doses to vulnerable points and the shape of the treated area. With only three criteria the values of К and n were set relatively simply and required only minor adjustments to give the desired effects. However, when the number of criteria is increased the interaction between their scores becomes much more complicated and it has been found necessary to embark on a preliminary investigation of this interaction. The investigation is being carried out with the aid of a programme which uses the vector representation of 4-MeV X-ray fields, described in the earlier paper, to evaluate measures of the criteria and from these the corresponding scores. The programme accepts the contour of a patient and a treatment site in polar co-ordinates at ten-degree angular increments and produces the scores and other details for externally selected arrangements of fields specified by field positions, wedge angles and weights. In finding the field width to be used for each individual field position the programme uses the maximum perpendicular distance from a treatment site perimeter point to the central axis. The field width obtained depends only on this distance, using the single criterion, coverage of the site. The score functions of the five interacting criteria which have been set initially in the programme are detailed below. In the discussion of these functions the word "dose11 is used for simplicity where percentage depth dose is meant.

Dose gradient score

From the vector representation the resultant vector of all the fields at the intersection point of their central axes can be obtained. The magnitude M of this vector gives the change in dose per centimetre, and it was decided that the initial acceptable limit of 10% of tumour dose across the treatment area was a reasonable value. The score function for dose gradient is:

M W D.G. Score: 0.1 ED

where W is the width of the treatment site in the direction of the resultant vector and ED is the tumour dose. The power 2 is applied to penalize values over the limit and to allow the score to reflect the desirability of a minimal value of M.

Tumour dose score

The score for tumour dose is identical to that used in the earlier programme, namely: PAPER 10 121

T.D. Score = where ED is the tumour dose. The acceptable limit is set at 120 and the sixth power severely penalizes tumour doses less than this but makes little distinction between greater values.

Integral dose score

The requirements of an integral dose score are that it should consider healthy tissue irradiation in relation to the size of the treatment area. It should also be simple for speedy evaluation. The integral dose score for the programme takes the form:

T _ _ E(AEL) I.D. Score = where A is the fipld axis at entry, E is the distance from entry to site perimeter, L is the weight to be applied to the field, W is the mean width of the treatment site and ED is the tumour dose introduced here as a normaliz- ing factor. No constant or power has been set initially since there are no obvious values for these to take.

Shape s со 1-е

When shape was first considered it was thought that a score based on a comparison between doses at treatment perimeter points and doses at points just outside the perimeter should be used. However the lack of information on what the ideal dose should be at these outer points and the desire for computational speed have led to a much simpler concept. A series of shape points is defined as lying one half centimetre radially outward from the treatment perimeter points and for each point the ratio of the number of fields in which it lies to the number of fields in the treatment is calculated. The score is a weighted average of these ratios:

N„ S.Score = E oo Ntotal

where Nin and Ntotal are self-explanatory and the power 2 performs the weighting of the average.

Vulnerable points score

Three classes of vulnerable points have been chosen, (1) individual points where a dose of more than 30% of tumour dose should be penalized, (2) individual points where a dose of more than 15% of tumour dose should 122 HOPE et al.

be penalized, and (3) groups of points where a mean dose of more than 15% of tumour dose should be penalized. Anatomical examples of the three classes are spinal cord, eye and lung. The programme calculates the dose at each individual point of class (1) or (2) and the mean dose at any group of class (3) points. The score is then based on the maximum vulnerable point dose since exceeding any one limit is sufficient to penalize a treatment plan. The score function is:

^max V.P. Score = 0. 3 ED 0.15 ED

depending on the class of the point with maximum dose. The power 6 is again used to provide a heavy penalty for exceeding the limit and to make little distinction if the limit is not exceeded. The investigation of score functions is clearly the crucial stage in the production of an optimizing system and will require much careful study before it is complete. One sample of the results from this programme is presented in the next section as an illustration of the process of improving score functions.

RESULTS OF A SCORE INVESTIGATION

The examination of score functions is carried out by selecting a number of representative body contours and treatment sites. The score investigation programme is then used to evaluate the badness of many arrangements of fields. Dose distributions are obtained for those arrangements which give low badness values and the study of distributions and scores indicates the score functions which are not producing the desired effects and the situations which require more detailed study. As an illustration of this process Fig.la shows the contour and site for a bronchus treatment. There are two vulnerable regions. The first is the spinal cord, marked by an individual point of class (1), the second is the unaffected lung marked by a series of ten points of class (3). The score for four of a series of trial field arrangements using this contour are presented in Table I. These arrangements all consist of a plain field and two 60° wedged fields. The position of the plain field varies as shown in the table and the wedged fields are kept at 50" on either side of it. All three fields have a weight of one. Figures la-d are the dose distributions for these four arrangements. Selecting the shape score for examination, it is apparent from the distributions that the shape of the 90% isodose line in the last arrangement is considerably better than in the other three. The score for shape, however, shows only a slight improvement. Therefore the score function chosen initially is inadequate. From a study of the distribution of the number of fields in which each shape point lies, it was apparent that a weighted average is not an appropriate basis for the score function. It was found that the area of each PAPER 10 123

в.7

FIG. la,b. Dose distributions and score functions of various field arrangements for treatment of the bronchus. Other data pertaining to these distributions are given in Table I 124 HOPE et al.

8.2 60°w

• •i

FIG .1 c, d. Dose distributions and score functions of various field arrangements for treatment of the bronchus. Other data pertaining to these distributions are given in Table I PAPER 10 125

TABLE I

SCORE FUNCTIONS FOR A SERIES OF FIELD ARRANGEMENTS

Plain Dose Internal Tumour Vulnerable Shape Total field gradient dose dose point score score position score score score score

280 0.5963 0.2217 0.1656 0.7840 5.406 7.17

290 0.4379 0.2182 0.1592 0.7840 0.7987 2.40

300 0.4155 0.2189 0.1581 0.8148 1.150 2.76

310 0.3434 0.1990 0.1422 0.7222 0.1644 1.57

overlap of the treated area beyond the treatment site was correlated with the number of adjacent shape points lying in all fields. It was decided that the relationship between the size of these overlaps and the importance of their badness should be S shaped. This is because a good fit is highly desirable but if gradient or vulnerability considerations require it, a parallel opposed field arrangement, giving a poor fit, is still acceptable. A suitable function for shape score is:

S. Score =0.4+0.25 tan"1 (n-5)

where n is the length of the maximum string of adjacent shape points lying in all fields of the treatment. This function is shown in Fig. 2. By using it, the treatment plan of Fig.la, having a maximum string of 7 points, has a score of 0. 675, while Fig.Id has a 4 point string and a score of 0. 205. Further investigations will show if this new function is adequate for scoring shape in all circumstances. When all the score functions have, been finalized the score investigation programme will have a search routine added to form the complete optimizing programme. The content of this search routine is considered in the next section.

THE SEARCH FOR THE OPTIMUM

In considering how to search for the optimum treatment it is necessary to examine the multi-dimensional surface of the badness expression. For any contour and site it is possible to find a best treatment using two 45° wedged fields and another which is the best using two 60" wedged fields. It is possible in certain situations that, if these two treatments have the same badness value, they are two points in a trough of uniform depth. The trivial case of a circular site in a concentric circular contour would permit many two field treatments with the same badness and in this case there is a single 126 HOPE et al.

FIG.2. Plot of shape score as a function of string length flat bottomed depression. However, in a practical situation there is more than one depression; for example, if a vulnerable point or a distinct variation in contour lies between the best angular position for a 45° wedged field and the corresponding 60° wedged field in the two best treatments, it is impossible to travel from one to the other without encountering a rise in the badness surface. Since the minimum value of badness may lie at the bottom of any one of these depressions the search must consider all of them and the only way to achieve this is by tabulation. The inherent objections to tabulations are the time taken and the possibility of missing a steep sided depression. However, in treatment planning minimum increments for a tabulation are imposed on the variables by practical considerations, such as the accuracy of setting the angular position of a field, and steep depressions within these minimum increments are of no interest. The time taken to carry out a tabulation has to be considered in some detail. The important factor is the time taken by a computer to score one treatment. From this we can establish the limitations which must be applied to the range of tabulation to produce an optimum in a reasonable time. The optimizing programme described in the earlier paper took one second to score each treatment. From the score investigation programme it is estimated that the addition and modification of score functions will increase this time to about five seconds. Both programmes are written in Sirius Autocode in which a store to store add time of 12 ms is a gauge of the operating speed. The I.C.T. 1902, which will soon be available for this work, has a store to store add time of 18 цs and to a first approximation the time to score one treatment will be about 8 ms. Defining a reasonable time to produce an optimized treatment plan as one hour, a process involving the examination of approximately 500 000 plans can be envisaged. An unrestricted tabulation might include 5° incremental placing of fields (72 entry points), 11 types of field (5 wedges, left and right handed andplain), PAPER 10 127 with 5 possible weightings, which gives approximately 4000 possible choices for each field, 16 X 10® two-field treatments and 64 X 10a three-field treatments. However, practical considerations in most cases can reduce this number. In the example used to illustrate the score investigation (see Fig.la) . there is no advantage in including entry points which would mean irradiating the vulnerable region before the tumour, also the linear accelerator used (at the Western Infirmary, Glasgow) cannot apply a posterior field at an angle greater than 130° from the vertical. Further it could be said at the outset that two-field treatments are of little value since one or both of the fields would have to penetrate a large depth of tissue to reach the tumour. The restricted posterior angle would prohibit three plain fields and the use of wedge angles smaller than 45° . This leaves for investigation a 45° or 60° wedged pair with an inter- vening plain field. The number of possible treatments is 18 000 without weighting, 90 000 with five possible weightings for the plain field and 2.2X 106 with five weightings for each field. If 10s incremental field positions are considered the corresponding numbers are 3000, 14 000 and 0. 34X 106. It is possible therefore with a fast modern computer to consider fairly detailed tabulations in a reasonable time. As experience of the depressions in the badness surface grows it may be possible to increase the size of the increments used and to introduce one of the methods currently being developed for non-linear constrained optimization, e.g. Box (1965), to. find the bottom of each depression after it has been approximately located by a restricted tabulation.

CONCLUSION

In' this paper it has been shown that the two problems which exist in computer optimization of radiotherapy treatment planning are the definition of a measure of the badness of a treatment, and the devising of a rapid reliable process for evaluating the treatment variables which give minimum badness. The study of judgement criteria is a continuous process which leads to successive improvements in the badness expression. Improvements may take the form of additional criteria as requirements are increased or better score functions as requirements are redefined. The improvement of procedures for searching for optima depends on developments which have considerable importance outside medical physics. These are the methods of function minimization referred to earlier and the understanding of computer learning processes. Learning processes offer a means of reducing the time taken for a search and two approaches are possible. The computer may be programmed to examine all previous optimal treatments to establish similarities in specifications. The introduction of learning then becomes a problem of data classification and information re- trieval. The second possible learning system consists of retrospective analyses of optimal treatment plans and the calculation of probabilities whereby a search may be guided in the directions most likely to succeed. 128 HOPE et al.

Important extensions to the formulation of the optimizing problem would be the introduction of treatment regions and contours in three dimensions and dose fractionation when more radiobiological data is available. The technical facilities offered by modern computer installations provide no restrictions in the solution of these problems. A useful but slightly limited optimizing programme can readily be achieved. A completely generalized procedure including the features suggested above could then be developed. CLINICAL EVALUATION OF TREATMENT PLANS: CRITERIA USED TO SELECT OPTIMUM PLAN

H. PERRY DEPARTMENT OF RADIOLOGY, UNIVERSITY OF CINCINNATI, COLLEGE OF MEDICINE, CINCINNATI, OHIO, UNITED STATES OF AMERICA

Treatment planning for external beam radiotherapy has been greatly simplified by the use of digital computers. The utilization of digital computers was first introduced and reported by К. C. Tsien in 1955. Since that time many authors have reported their work using digital computers in treatment planning for fixed field and rotation therapy. At the University of Cincinnati Medical Center a systematic approach has been followed in the development of techniques for radiation treatment planning with high-speed digital computers. Originally, hand digitized data were utilized for the determination of treatment plans. A tabular print-out was obtained which was then transcribed by hand onto a polar co-ordinate grid on which the patient's contour had been previously superimposed. Isodose lines were then formed by joining points of equal value (Sterling et al., 1961) (Figs 1, 2)-. A technique was next developed for treatment plans in which the central beams were non-convergent. This development made it possible to utilize treatment situations in which convergence of all central beams- at a common point of intersection was not essential for planning (Sterling et al., 1963a) (Fig.3). Next, a direct and to-scale print-out of dose distribution was developed which eliminated the intermediate step of transferring data from a tabulated print-out to a basic polar co-ordinate grid (Sterling et al., 1963b) (Fig. 4). Approximately three years ago an equation was derived which utilized only central axis data and from which the entire isodose distribution could be derived for any field and SSD for cobalt-60 gamma-ray therapy. This achievement also made it possible to visualize the entire dose distribution volume (with multiple planes ) rather than a single plane of interest (Sterling et al, 1964). In addition, a numeric as well as symbolic print-out was formulated which eliminated the drawing of isodose lines (Figs 5 and 6). The major criteria in clinical dosimetry for finding the optimal plan are (1) uniform dose distribution throughout the tumour-bearing volume, and (2) minimal dose to normal structures traversed by the beams of ionizing radiation as well as structures adjacent to the tumour-bearing volume. In an attempt to simplify as well as make uniform the presentation of dose values, Ellis and Oliver (1961) presented alternative definitions of the tumour dose. These were as follows: (1) Median dose: the average of the maximum and minimum values in the tumour volume (2) Average dose: the average of all doses in the tumour volume (3) Modal dose: the dose most frequently occurring in the tumour volume. Spiers and Meredith (1962), summarizing the results of a meeting of the Faculty of Radiologists in 1962, recommended the use of the modal dose as

129 130 PERRY PAPER 10 131

LESION: Co Thoracic Esophagus CO*0 80cm. S.S.D. s X IS cm fields at 40*. 140*,

FIG.2. Dose distribution produced by joining points of equal value shown in Fig. 1

FIG.3. Example of dose distribution produced by four non-convergent fields 132 PERRY

т!" '¡яг ;*s; """ 's^K;'.' ""• ! HI: I I II If is If II

Ангтюк

V-

POSTIKIOK

FIG.4. Print-out of grid of points with manually-drawn isodose curves the definition of tumour dose for 4 to 8 MV linear accelerators. At that time it was felt that its utilization would also be applicable to fixed-beam cobalt-60 teletherapy, but this had not been explored. Sundbom and Asard (1965) suggested that the average dose as defined by Ellis and Oliver (1961) be the best one to express the dose for fixed beam and rotation therapy when cobalt-60 gamma-ray therapy was used. The basic treatment planning procedure utilized at our institution has been previously reported (Sterling and Perry, 1964; 1965). All cases for radical radiotherapy are treated with a Theratron "A" cobalt-60 teletherapy beam unit. The following data for each plan are telephoned to the computing centre: the patient's name, diagnosis, source-skin distance for each field, treatment plan number, number of fields, the individual field size, and the co-ordinates of entry and exit of each field (indicated by the appropriate X, Y, and Z values on a Cartesian co-ordinate system), and the weight or amount PAPER 10 133

л.о. BECITRFKT CïfiCEH ÜFTERVI* _ PL4N l лIELO PCRIXl CO-GROIN4TES CO-ORDIN4IES WEIGHT SINE COSINE LOG sm or fmiv ет—шт l- lf'15.0 2ЛГ J.IÍ úíí I.DO -0.7'Tl -0.636 0~.33l5 2 6.0 X 15.0 9.44 0.94 1.ЬЧ 6.42 O.SO U.766 0.641 0.J315 3 6.0 x 1S.0 2.34 6.22 8.64 1.00 -0.Í93 0.6O6 0.3315 4 6.0 X 1S.0 9.64 6.44 3.S1 1.00 O.SO 0. 757 0.6S2 C.331S

£.0.00 INCHES 660VE CENTER Д.Q Р|оП I

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 B.O 6.5 9.0 9.5 10.0 10.5 li.O 11.S 12.0 12.

volume of irradiation to be applied to each field relative to the other fields. The resultant treatment plan or plans are presented in numeric and symbolic form as a series of planes spaced ^in. (1. 25 cm) apart. The data are printed out to scale for each plane. Selection of the best plan is then accomplished. The following criteria are used for the selection of the optimal treatment plan: (1) The minimum dose in the tumour-bearing volume must be not less than 90% of the maximum dose (2) The ratio of given dose to tumour dose must be less than 100:120 except where parallel opposed fields are used (3) The overall treatment plan is evaluated in terms of median, average, and modal doses (4) The dose to vital structures must be as low as possible, i.e. dose to the spinal cord (5) Replanning when there is change in the patient's anatomy and/or tumour size. The following examples illustrate use of the above criteria. Figure 7a illustrates the basic plan through the central plane utilizing four oblique 4. 5 cm X 15 cm fields for treatment of a primary carcinoma of the thoracic esophagus. The variation in dose throughout the tumour bearing 134 PERRY

A.C.

PLAN 1

FIELD ' PCftTAL • CO-ORDINATES CC-0R0INATES WEIGH! SINE COSINE L00

V.4¿ e#j515 ______2 6.0 X 15.0 9.44 C.94 2. 69 6.4? 0.50 0.Г66 0..64 1 0.3315

* 6.0 X 15.0 3.51 1.00 0.50 0.757 0..65 2 0.ЭЭ15

z* 2.00 INCHES ABOVE CENTER A.O. Plan X

0.Ô 6.9 i.o 1.5 2.0 2.5 Э.0 3.5 4 .0 «.5 5.0 5.5 6.0 6.5 7.0 7.5 e.o 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.

091 016 009 002

"Тог 064 022 Oil 001 006 026 OSO 060 071 090

10ff\106 100 099 012 012 029 018 097 068 069

099 106 l01NO96 092 090 091 019 091 076 068 069 070 067 029

062 090 096 092 492 111 199 162 119 092 OU

002 029 076 096 12J 099 077 061 010 006

001 022 069 096 169 16J/162 111 079 068 019 001

001 016 081 089 086 099 120 117 169 111 109 0>l 068 066 096 029 002

OSS 097 098 096 060 062 Oil 001

108 102/097 .069 070 069

107 101

FIG. 5b. Example of dose distributions in parallel planes, permitting visualization of dose for entire treated volume volume is seen to be less than 1% with rapid fall-off laterally as well as toward the spinal cord. Figure 7b shows maintenance of dose homogeneity below the edge of the lesion. Figure 8 illustrates a plan utilized for carcinoma of the urinary bladder with three oblique fields which have a common point of intersection. It is noted that the minimum dose is 90% of the maximum, which fits our criterion for dose homogeneity. Utilizing the dose concept of Ellis and Oliver it was found that the median, modal, and average dose in this particular example are all 141. The maximum dose is 148, the minimum is 134. The variation of the median, modal and average doses from the maximum is 5% and from the minimum dose is 5%. The to-scale digital print-out of our computer technique makes determination of the modal, median, and average doses, as well as their variations from the maximum and minimum doses, a simplified procedure. The treatment plan can be evaluated in this way by a separate or sub-programme on the computer or by manual means in less than five minutes. In many instances, to achieve a uniform dose throughout the tumour it is necessary that the given dose or applied dose to one or more of the treatment fields be weighted or unequal. Figure 9a shows a plan for carcinoma of the urinary bladder utilizing three oblique fields with significant fall-off PAPER 10 135

A. 0. REC. СЛ. OF THE CERVIX PIAN 1

£.0 X 1S.0 2.81 1.14 9.42 6.59 1.00 -0.TT1 -0.636 0.3315 6.0 X 15.0 9.44 0.94 2.09 6.42 0.50 0.T66 -0.641 0.3315 6.0 X 15.0 2.34 6.22 6.04 1.25 1.00 -0.193 0.60B 0.3315 6.0 X 13.0 9.84 6.44 3.51 1.00 0.50 0.75T 0.652 0.3315

Z'0.00 INCHES ABOVE CENTER Д.О. PI• Г1 I

1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 T.5 B.O 8.5 9.0 9.5 10.0 10.3 11.0 11.5 12.0 12.

OOSE/IO 00 01 02 03 04 05 06 07 OB 09 10 11 12 13 14 15 16 17 IB 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 3* 37 38 39 STHBOL 1234567B9.ABCOEFGH1-JKINHOPQRO/STUVWXV1

FIG. 6. Example of symbolic print-out which eliminates manual drawing of isodose curves in dose posteriorly which was improved by weighting the dose in favor of the posterior oblique fields. This change in plan is illustrated in Fig. 9b. Of further importance in the clinical evaluation of the optimal treatment plan is the dose received by adjacent normal structures. In Fig. 10a a treatment plan for carcinoma of the thoracic oesophagus is shown. It is noted that the anterior edge of the spinal cord received a dose almost as high as that received by the primary lesion. There was also significant high dose in the mediastinum. Reduction of the width of the treatment field resulted in significant diminution in the dose received by the spinal cord. This minor change in the treatment plan was rapidly accomplished on the computer, and there was maintenance of significant uniformity of dose throughout the tumour bearing volume (Fig. 10b). The problem of optimization is often complicated by a rapid change in the anatomy as well as size of the tumour, thus necessitating replanning of treatment. Figure 11a is the central plane of a treatment plan of a patient who presented with a large clinical Stage T4N3 carcinoma of the left inferior gingiva. 136 PERRY

FIELO PORTAL-SUE CO-ORPIHAIES OF ENTRY CO-QRÜINATES OF EXIT ALPHA WEICHT BETA X Г Z X Y I

1 X 15.0 2.50 1.20 0. B.40 7.10 0. 0 1.00 0 2 4.S X YS.O fl.40 V.30 О. 2.Ь0 7.20 0. Q 1.00 ^ 3 4.5 X 15.0 2.60 7.20 0. 6.40 1.30 0. 0 1.00 0 4 4.5 X 15.0 B.40 7.10 0. 2.50 1.20 0. 0 1.00 0. i * O: BUNNIE WINSLOH РГйП

0. 0.5 1.0 I.S 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 6.0 В.5 9.0 9.5 10.0 10.5 11.0 11.5

0.0

FIG. 7a. Dose distributions for four-field treatment of the thoracic esophagus: central plane

A mock wedge technique was utilized with rapid reduction in tumour size. Figure lib illustrates the second treatment plan, again using a false wedge technique with uniform dose to the lesion being maintained. Rapid replanning is possible with the computer to achieve the optimal or most ideal plan for the treatment conditions when change in the patient's contour and/or tumour volume occurs during treatment. The composite plan is illustrated in Fig. 11c. In summary, the clinical evaluation of the optimal treatment plan is greatly facilitated by digital computers. The rapid production of single or multiple plans as well as the direct visualization of dosage data on a direct and to-scale print-out with multiple planes throughout the treatment volume enhances the ability of the radiotherapist in choosing the optimal plan. Rapid visualization of dose homogeneity is available as well as determination of the dose levels administered to the adjacent and vital normal structures. Angle of entry, as well as field size, can be rapidly altered in an effort to achieve the optimal plan. In addition to the utilization of multiple planes to the treatment volume, rapid replanning is available and can be utilized in a short time for treatment of the patient. PAPER 10 137

FIELO ИЧИ-Slli CO—MPI WAT F S OF FH1HY CO-OtOlHAIES Of t»IT ALPHA «E1CH7 ИЧ X Y I I V Z

1 4. .5 X 15.. 0 г..5 0 1.20 0. 8.40 T.10 0. 0 1.00 0 2 4. .5 X 15.. 0 R.,4 0 1.Э0 0. 2.40 7.20 0. 0 1.00 0 3 4., S X 15.. 0 г.,6 0 7.20 0. 6.40 1.Э0 0. 0 1.00 0 4 4.. 5 X 15.> 0 A..4 0 T. 10 0. 2.50 1.20 0. 0 1.00 0

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O. 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 T.5 0.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5

0.0

FIG. 7b. Dose distributions for four-field treatment of the thoracic esophagus: 2. 5 cm below and parallel to central plane (edge of lesion)

At present, evaluation of correction factors for inhomogeneity of the structures traversed by the treatment beams, as well as for obliquity, is being conducted. The addition of these correction factors to the computer programmes would enhance the validity and value of the techniques now utilized in our department. Corrections are made manually for inhomogeneity, such as bone and lung, as well as for obliquity to see if there is significant error in the treatment plan as produced by the present computer programme. To date these errors have been small and within the range of clinical acceptance. 138 PERRY

0.00 INCHES ABOVE CENTER Rh-j r IÜÁ / 4- __

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 *.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5"

FIG.8. Dose distribution fot three-field treatment of the urinary bladder PAPER 10 139

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FIG. 9а. Dose distributions for three-field treatment of the urinary bladder: equal weighting for all fields 140 PERRY

0. 0.5 1.0 t.5 7.0 __2.5 1-0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 /.5 В.О а.5 9.0 9.5 [0.0 10.5 11.0 11.5 t7.ü

FIG. 9b. Dose distributions for three-field treatment of the urinary bladder: unequal weighting in favour of posterior fields PAPER 10 141

FIG. 10a. Dose distributions for four-field treatment of thoracic esophagus: original plan 142 PERRY

МЕЮ PORIAl-SIZE CO-OROINAftS Of ENIRf CO-OROINATES OF EXII ALPHA WEICHI BETA X У I X Y I

1.20 4.5 I 15.0 3.00 7.20 4.5 X 15.0 8.80 T.OO" ' 0~ ÎTTÔ O.BO

RACHEL COOPER PLAN 3 80 CM. SSD

0.5 UP 1.5 2.0 2.5 3.0 3.5 .0 4.5 5.0 5.5 6.0 6.5 7.0 1.5 8.0 8.5 9.0 9.5 10.0 10.5 П.О U.5 12.0 I

FIG. 10b. Dose distributions for four-field treatment of thoracic esophagus: field sizes reduced to decrease dose to spinal cord PAPER 10 143

IMM tWlNG CA. t. T. «W. «IN6IW mm • * t*URA CM|NC FIF-tP PflRT IP CO-C«f>lWâ»fS OF ENTRV C0-0H01MAT6S Of LUT М.ИИЛ UEICMt 8ЕТД XVI x V I

I 6.;: I tt.O s.20 Э.40 0. 1.50 U. 0 1.00 и 7 4.5 Я H,О 4.40 biO О. é.50 ê,5fi О. О 0*30 О 43 104..40 Xх я.п.О0 ),4).40Г 6.г«.1о0 О0. . 0.5Í.800 6.2Г.100 00. . ОО 1.0O.Ï0O Со • 0.50 LAURA CfclNt» 0.5 1.0 1.5 2.0 Ï.0 Ï.S 4.0 4.* Ч.О 5.5 6.0 i.5 Т.О ЦЧ 8.0 в.5 «.О «.5 10.0 10.S 11.0 II.S 12.0 II.*

FIG. lia. Dose distributions for four-field treatment of left inferior gingiva: original plan 144 PERRY

LMIá til IК

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i CU i:» 1:3 I: I'M >:В 8: í-fc&- i î:8 i:?. !:П — -í-teS-

FIG. 11b. Dose distributions for four-field treatment of left inferior gingiva: modified plan to allow for reduction in tumour size PAPER 11 145

* • в**° LAURA EWiNG O. O.S 1.0 1.9 2.0 2.5 J.O J.S 4.0 4.5 5.0 5.5 6.0 6.5 1.0 7.5 в.O í.5 «.0 9.5 10.0 10.« ||.0 ||.

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O. 40 в..0 1 8.0 9..2 0 >•60 0. 1.» в..9 0 0. 0. ..90 в.• 9С 0. O.H 6..9 X в.о 6..9 0 >.10 •.«o 6..2 0 0, 0.10 10.0 Ж в.0 >.6. 0 4.20 0* •.•o т..1 0 0. 0.11 4..9 X в.о 1..9 0 Т. 10 0. в.>9 0 0. 0.50 в,.0 X в.о 5,>1 0 >•60 0. 1.10 в..9 0 0. о.и 4..9 X в.о 9..в о 2.90 0. М1.1О0 6..2 0 0. 0.50 10.0 я в.о ).>9 0 «•20 0. t.10 т.>1 0 0. 0.19 6.,9 я в.о 6..1 0 Т. 10 0.

FIG. 11c. Dose distributions for four-field treatment of left inferior gingiva: composite of original and modified plans

10 ECONOMICS OF COMPUTER DOSIMETRY

I. RAGNHULT

RADIOPHYSICS LABORATORY, SAHLGRENSKA SJUKHUSET, GOTHENBURG, SWEDEN

1. INTRODUCTION

The literature concerning automatic dose planning methods contains sparse information about the time required and the cost. Bentley (1964) estimates the cost at £2 ($5. 60) for summation of digital dose-data from four fields in an array with 250 points on an ICT 1301, and states that the cost per plan will be lower if several plans are computed at the same time. Sterling, Perry and Katz (1964) have used three different IBM-computers and give the following times for the dose computation: IBM 1401: 4 min for one field; 16 min for four fields IBM 7040: 40 s for one field; 3 min for four fields . IBM 7090: 8 s for one field; 32 s for four fields. / With the analytical method described by Hope and Walters (1964) the summation time per field varies between \ and li min on a Ferranti Sirius computer. The type of computer and the calculation method used strongly influence the time required for the computation. The cost per minute for a high-speed computer is, however, very much higher than for a slow computer, and the great variations in computing times between different machines will not necessarily be reflected in the final cost. This will, on the other hand , always be proportional to the number of dose-data to be handled and it is thus expensive to use arrays with a great number of points for the input-fields and for the resulting distributions. Variations in technique make it difficult to compare different computer methods. These difficulties are, however, small compared with those which arise, when one tries to estimate and compare the manual techniques used at various hospitals.

2. COMPUTER CALCULATIONS

In applying computer techniques the initial stage involves a choice of method, the writing of a programme and thorough testing of this programme. This work is usually both expensive and time-consuming. For routine computations the same preparatory work will have to be done as for the ordinary manual calculations. The total procedure involves the following stages: (a) Filling in an order-form with code number for selected fields, co- ordinates for entry points, angles for central axes etc. (b) Transport of the order-form from the hospital to the computer (e.g. by mail or Telex, if the distance is great)

146

10* PAPER 10 147

(c) Transfer of data to the input medium to be used (e. g. paper tape) (d) Operation of the computer (e) Automatic computing (f) Output of data (e. g. by means of line-printer, typewriter or plotter) (g) Transport of results back to the hospital (h) Further treatment of results (e. g. drawing of isodose curves). The different stages are performed by: A Technician (T) whose work involves items (a) and (h) and sometimes (c) and an Operator (O) of the computer (items d-f). The information on time and cost for computer calculations which will be given here is based on experience in Gothenburg of dose computations with two different computers: (1) ALWAC. A small computer with drum memory (capacity 8191 words), paper tape for input of data and typewriter for print-out. Adding time: 5 ms, cost per minute: 2. 50 Sw. Cr. ($ 0. 50). (2) SAAB D-21. A considerably larger computer with core memory (capacity 16384 words), paper tape for input of order data, magnetic tape memory for storing of data and high-speed line-printer for print-out. Adding time: 9.6 MS, cost per minute: 20 Sw. Cr. ($4). The ALWAC computer handles single-field data in 10 cmX20 cm arrays with 231 points which are transformed and interpolated to give dose-values in 338 points with 1 on spacing in an array, 15 cm X 20 cm. Oblique incidence is corrected for (Halldén, Ragnhult and Roos, 1963). The fields used in the SAAB-programme are 30 cm X 30 cm (961 points) and the size of the resulting array 3 0 cmX40 cm (1271 points). Corrections for oblique incidence and the use of weighting factors for the different fields do not increase computing time. Other corrections, for instance for bone- or lung-tissue, increase computing time slightly. In the table dose-distribution calculations are given for four fixed fields and for an approximation to a moving-field irradiation consisting of 20 fixed fields.

3. MANUAL CALCULATIONS

Time and cost for the manual calculation of dose-distributions are difficult to estimate because many factors are hard to specify and there are variations from hospital to hospital. If corrections or weighting factors are introduced the time is greatly increased. The time required for the manual calculation of a simple 4-field distribution without corrections is given in Table 1. The resultingisodose-curves have been drawn from superposed single-field diagrams. The distributions for moving fields were obtained, (i) by adding dose values from 20 fields in about 300 points, a tedious method not much used in practice, and (ii) by adding single-field dose values in the pendulum axis only and interpolating the isodose curves from measured distributions. This latter procedure gives less dose-information and accuracy than the automatic method. 148 RAGNHULT

СГ- Cos t 0 . 5 0.1 7 с 0 . 5 о a ю , , ю ю •S .s rH Tim e "ed (min ) 411 3 Ma i Ma i (* ) 0 . 5 0 . 5 Cos t 30 . 0 31 . 0 <(J ^? 5 о ю , , о ю (30 0 points ) (30 0 points ) •H О iH OS Tim e (min ) с Movin g field s Movin g field s Movin g field s Movin g field s ($ ) (2 0 fixe d fields ) (2 0 fixe d fields ) (2 0 fixe d fields ) (2 0 fixe d fields ) 0 . 5 0 . 2 0 . 6 0 . 5 Cos t 20.0 0 21 . 8 0 SAA B SAA B ( 1 plan ) ( 1 plan ) Ю CD OS Ю Ю 1-H rH i Tim e (min ) (« ) 0.5 0 0 . 5 0.2 0 2.3 5 Cos t 15.0 0 18.5 5 ALWA C ALWA C ( 1 plan ) ( 1 plan ) тюН to CюO соо *-ю1

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О (M rt из 1 Tim e (min ) D-2 1 D-2 1 j ( > 10 0 fields ) j ( > 10 0 fields ) SAA B SAA B о Sí 0.3 3 0 . 6 0.4 7 U w 0.5 0 12.0 0 13.3 6 4 Fixe d field s 4 Fixe d field s 4 Fixe d field s 4 Fixe d field s ( 1 plan ) ( 1 plan ) о in с- со ю Tim e (min ) (« ) Cos t 0 . 3 1 . 0 5.0 0 0 . 5 о. 7 . 6 3 В • 0.8 0 ALWA C ALWA C ( 1 plan ) ( 1 plan ) TоH 1 юr-* ,-о1 . ,-юt 1 Tim e (min ) s У S H О H И О ' ' H 1

H о etc. , fil l i n order-for m compute r (outpu t etc . ) isodose s Wor k stag e Tota l cost s (a ) Selec t field s (d ) Operatio n o f (c ) Punchin g (f ) Extr a cost s (e ) Computin g (h ) Drawin g o f PAPER 10 149

4. COMPARISONS

4. 1. Simple plans

The figures for time and cost for the evaluation of dose-distributions by means of automatic and manual methods given here are rough estimates. Still, one observation is quite obvious: The simple computer-calculated plan is more expensive than the same plan produced by technicians. As long as the plan calculated by the computer does not contain more information or greater accuracy than the plan calculated by the technician it is certainly not economical to use the automatic procedure. The cost relation is still more unfavourable if we consider also the costs for writing and testinga programme. This work can take several months for a qualified programmer. The teaching and instruction period which is necessary before the technician can evaluate the dose distributions,and which most nearly corresponds to the programming- period for the computer, does not cost very much.

4.2. Complicated plans

• When we leave the simple dose-plans and consider more complicated ones, for instance a 4-field plan with different weights on the fields, oblique incidence and corrections, the technician1 s situation is drastically worsened, but the computer situation is much the same. This state of affairs is for moving field techniques still more pronounced. s

4.3. Amount of information

In the complicated cases the technician will have to simplify calculations and sum the doses from the different fields in a small number of points. The result from the manual calculation thus might contain considerably less information than the computer-result. The development of the computer dose-planning methods will give more complete dose-distributions, distributions in several planes and ultimately distributions in space. From the complete dose-distribution information of other kinds can also be obtained, for example parameters like the average dose in the tumour region and the integral dose efficiency factor.

5. CRITERIA FOR THE USE OF A COMPUTER

It appears from what has been said in the previous sections that the use of an automatic computer for calculation of isolated simple dose-plans is not justified. As soon as the situation is complex more detailed information is required, a great number of plans are to be executed in one run or different radiotherapy techniques are to be compared, the use of a computer must be regarded as justified. In our ALGOL-programme, written for the SAAB D-21 computer we have tried to avoid the inefficient use of the machine in short runs and to make the programme especially suited for runs with 100 to 200 fields simul- 150 RAGNHULT taneously. This programme is specially useful for series of dose- distributions in standard cases. The field-data are directly obtained from measured dose-values, corrections for lung- or bone-tissue can be introduced and the influence of small variations in different parameters can be studied.

6. CONCLUSIONS

Much work remains to be done before the automatic methods are fully developed and economical in practice. Different steps can be taken to reduce the high costs of the automatic dose-computations. An exchange of programmes between clinics is, for instance, one obvious way of reducing the expense. The programmes must then be written in standardized languages (e. g. Algol or Fortran) which can be interpreted by the various computers. Simplifications in the calculations, use of analytical expressions, vector methods (Hope and Orr, 1965), reduce computation time and cost and can justify the use of automatic methods even for simple dose plans. It should also be pointed out that a comparison between manual and automatic calculations on cost basis alone is not fair. The absolute time for a certain amount of calculation is also of great importance, e. g. when a new treatment procedure is developed, or when the physicist wants to investigate the influence of a certain parameter or set of parameters on the final dose- distribution. These spor'adic demands for calculations cannot be met by the employment for a short period of qualified technicians, but is easily and quickly met by an automatic computer, provided the suitable machine programme is available. SYSTEMATIC STUDY OF THERAPEUTIC RADIATION DOSE DISTRIBUTIONS

K.C. TSIEN DEPARTMENT OF RADIOLOGY, TEMPLE UNIVERSITY SCHOOL OF MEDICINE AND HOSPITAL, PHILADELPHIA, PA. , UNITED STATES OF AMERICA

The basic procedures and concepts used to make a systematic study of dose distributions with computers are not in any way different from those used without them. What is different however is that the use of computers opens up new areas of study by the amount and detail of the data that become available and the possibilities of analysing and comparing these data which would be hardly feasible without some mechanical assistance. The possible different approaches to a study of isodose patterns can be divided as follows: (i) the comparison of specific characteristics of the isodose curves, (ii) the comparison of the whole dose distributions using one or more specific indices as a criterion, and (iii) the generalization of relationships by study and analyses of selected series of data. Examples of these different approaches are given below.

1. THE COMPARISON OF SPECIFIC CHARACTERISTICS OF ISODOSE CURVES

1.1. The effect of the size of phantom on moving beam dose distributions

It is generally known that the effect of the size of the irradiated body is very small when high-energy radiations are used, but in the literature published so far there are no indications as to how small these variations actually are. By using computers to calculate a large number of cases, it is possible to detect the extent of the variation in the positions of isodose curves with the size of the phantom. One example is given below. Dose distributions of cobalt-60 360° planar rotation for eleven sizes of oval phantom with the same field size were calculated, and the results are presented in Table I (Tsien, Cunningham and Wright, in press). The data in this table are arranged in ascending order of the major/minor axis, ratio k, of the phantom. The range of к is from 1.07 for a phantom 28 cm X30 cm to 1. 60 for a phantom 25 cmX40 cm. Over this range, the increase in the distances on the minor axis of the 90 and 80% curves is 3 mm from the lowest к to the highest к value; the corresponding decrease along the major axis is 1 mm for the 90% curve and 2 mm for the 80% curve. The distance of the 50% curve from the centre increases 1. 1 cm on the minor axis and decreases 6 mm on the major axis from the lowest к to the highest к value of the phantom.

151 152 TSIEN

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1. 2. Effect of the displacement of the centime of rotation on the dose distributions

To study this effect, a comparison was made of the change of dose- gradient along one axis of the phantom. The example given here shows the dose profile on the arc-bisecting diameter of a 30-cm diameter phantom with cobalt-60 240" rotation (Fig. 1). This graph shows that the maximum dose is generally shifted from the centre of rotation towards the side of phantom with less tissue absorption. The relative magnitude of the maximum dose depends on the extent of the displacement of the centre of rotation from the geometrical centre of the phantom. This graph also shows that with 240° rotation it is possible to have the maximum dose remain at the centre of rotation when it is placed at a certain specific distance from the centre of the phantom on the side opposite to the beam entrance. ,

2. THE COMPARISON OF WHOLE DOSE DISTRIBUTIONS USING SPECIFIC INDEX AS A CRITERION

2. 1. Skin dose as a criterion for comparison

In using medium energy X-rays, the skin dose received is a useful indication for making comparisons of different treatment techniques. This is mainly because the skin dose often determines the magnitude of the tumour dose that can be applied. Quimby and Cohen (1957), for instance, have made a study of moving field dose distributions by comparing the ratio of the maximum skin dose to the tumour dose.

2. 2. Integral dose as a criterion for comparison

The integral dose has often been suggested for use as a guide for comparing dose distributions with different treatment plans. Recently Ragnhult et al. (1965) have made a comprehensive study, using a computer to compare the "integral dose efficiency factor" for different cases, other factors remaining constant.

2.3. The ratio of maximum dose to the centre dose on the combined central axis of two opposing fields

The change of the central axis depth doses of two opposing fields depends on the radiation quality, the source-surface distance, the field size, and the separation between the two fields. If we wish to compare the combined depth doses of HVL 3, 2 and 1-mm Cu and cobalt-60 radiation at eight different field sizes and two different source-surface distances and with separation from 6 to 25 cm there will be 4X8X2X20= 1280 cases. In each case on the average there are about 15 addition operations and 1 division operation,to calculate the maximum dose to centre dose ratio on the combined central axis. The total number of operations required is therefore about 20 000. 154 TSIEN

COBALT-60 240 d«g ROTATION

F.S. В x в cm 30 cm dio. CIRCULAR PHANTOM

FIG. 1. Dose profiles of cobalt-60 240-degree rotation on the arc bisecting diameter of a 30-cm circular phantom with a field size 8x8 cm . the centre of rotation at several different positions on the arc bisector

FIG. 2. Maximum permissible separation in using two opposing fields (Non-uniformity of dose along central axis limited at 20%) PAPER 10 155

t = F(lxw, mg. R) (1) Since mg is a function of IX w and mg/cm, R/h = F'(1X w, mg/cm) (2)

FIG.3. Flow chart of treatment time calculation for radium implant

This is an ideal application for a computer, to carry out the monotonous calculations and to print the results neatly. Calculations of this type were made some years ago (Tsien, 1958), and the results are shown in Fig. 2.

3. GENERALIZATION OF RELATIONSHIPS

An example is given here to illustrate the process of generalization as applied to dose calculations of radium planar implants (Tsien and Robbins, unpublished data). The usual procedure is first analysed with the aid of a flow chart (Fig. 3). In this chart

t = F(iXw, mg, R) (1)

Since mg is a function of Í Xw and mg/cm,

R/h = F'(iXw, mg/cm) (2)

With the use of a computer R/h for all possible arrangements of i and w cm can be calculated. An analysis of the results has yielded a useful generaliza- 156 TSIEN

tion (see next paragraph) which provides a practical guide in making an immediate estimate of the treatment time required before working out the calculation in detail. When the radium needles are placed at 1-cm intervals and the "basic" needles are of linear intensity 0. 33 mg/cm, the periphery of the plane being composed of needles of 0. 66 mg/cm, the dose rate, at 0. 5 cm depth, is 1250 R/d within ± 10% accuracy for all implanted areas from 20 to 350 cm2. For other linear intensities of the "basic" needles, p, the time in hours for 1000 R is equal to 6. 3/p . EVALUATION OF INTEGRAL ABSORBED DOSE AND OTHER PHYSICAL PARAMETERS CHARACTERIZING THE RADIATION FIELD IN EXTERNAL RADIOTHERAPY

I. RAGNHULT RADIOPHYSICS LABORATORY, SAHLGRENSKA SJUKHUSET, GOTHENBURG, SWEDEN

1. INTRODUCTION

The concepts mean, modal, and median tumour dose, efficiency factor, total integral absorbed dose, and various distribution functions of integral dose have all been introduced in order to have simple parameters describing and summarizing the physical characteristics of the complex radiation fields met with in radiotherapy. Necessarily, the loss of information inherent in the use of these parameters complicates the basic problems, i. e. of correlating biological effects with the radiation field and of giving figures-of-merit for different therapeutic techniques. The fuH physical description of the radiation field is, however, much too complex to render it meaningful in a correlation study, since this description should include the absorbed dose at every point (ultimately the microscopic dose distribution) as well as the quality and temporal distribution of the radiation energy, if the latter two factors are not kept constant in the study. On the other hand it is obvious that all the parameters that might conceivably influence a biological reaction can be calculated only from the full description. After some introductory remarks regarding the biological side of the problem and stressing the radiation effects on healthy tissue, the integral dose and some other physical dose-parameters will be discussed and the methods for their evaluation reviewed. The advantages of digital computers for the calculation of the dose-parameters are pointed out and the paper concludes with description of work in this field currently being done in Gothenburg.

2. RADIOBIOLOGICAL ASPECTS

The primary object of the radiation treatment of malignant tumours is to destroy the reproductive capacity of all the tumour cells. It is not possible, however, to deposit enough radiation energy in the tumour tissue without irradiating healthy tissue as well. An important question in all radiotherapy is thus how this unwanted radiation energy should be distributed to damage the patient as little as possible. We have quite a good knowledge of the physical parameters which charac- terize the radiation field. Among these the following four are deemed to be of paramount importance with respect to the biological effects: (i) the absolute magnitude of the absorbed dose, (ii) the spatial distribution of the ab-

157 158 RAGNHULT sorbed radiation energy, (iii) the temporal distribution of the energy absorption, including the instantaneous dose-rate, and (iv) the radiation quality. The parameters describing the biological effects are less well known. The haematologic response to radiation is the one most studied. The lymphocytes are especially sensitive and several attempts have been made to find relations between lymphocyte counts and integral dose. Ellis (1942) did not find any clear relation while Bush (1943), Kohn (1955) and Abbatucci et al. (1958) could correlate the integral dose with the degree of lymphopenia during radiation treatment. Changes in lymphocyte counts after irradiation can depend on damage induced in the lymphocyte precursors or to the lymphocytes themselves. Only the latter effect would be strongly correlated with the integral dose since the precursors are not as homogeneously distributed throughout the body as the lymphocytes circulating in the blood. The search for other biological indicators of radiation damage has not been particularly successful, a fact which, according to Roberts (1954), might be explained by the choice of the integral dose as the physical parameter in most investigations. In this connection I would like to raise a few questions: what is the clinical significance of the often large volumes of tissue which receive a comparatively low dose? How does the normal tissue, in which the absorbed dose is of the order of 100 to 200 rads react? Is there any general harmful effect on the organism when it is exposed to radiation at such a IQW dose- level? Is a radiation technique in which a smaller part of the body is given a somewhat higher dose tolerated better than one giving a low dose to a large region?

3. ABSOLUTE DOSE-PARAMETERS

The following physical parameters, listed in order of decreasing information content, have found or may conceivably find application in the study of general or regional clinical effects of radiotherapy:

(1) Absorbed dose at a number of points. In most practical cases the total dose distribution in space cannot be given. The number of dose-data has to be restricted somehow. The points should be selected in such a manner as to give the most essential information about the actual treatment. It is, for example, certainly of importance to know the location of that part of the tumour which receives the minimum dose and the dose value there. It is also important to know the maximum absorbed dose in vulnerable tissue, for instance in the kidney or in the eye. If carefully selected, a dozen points may give adequate dose-information in many treatment situations.

(2) Distribution of integral absorbed dose with respect to absorbed dose. The absorption pattern of radiation energy in the tumour tissue can be graphically depicted by plotting the differential integral absorbed dose as a function of absorbed dose. The area under this curve is thus proportional to the total integral dose received by the tumour (Ellis and Oliver, 1961). Corresponding distribution curves can be derived for a specific organ or body region and, of course, for the whole body (Dutreix, Dutreix and Galle, PAPER 10 159

1962; Tubiana et al., 1963). It appears that the differential distribution of volume or mass as a function of absorbed dose might give an even clearer picture of the spatial distribution of the absorbed dose. The integrals of these functions give the volume or mass of the region considered. From the distribution functions the following expressions are easily obtained: (i, ii) the mean and the modal tumour doses (Ellis and Oliver, 1961; Spiers and Meredith, 1962; Sundbom and Asard, 1965), (iii) the mean dose in a critical organ, and (iv) the mean dose in the total body. These simple parameters must of course be supplemented by information on the spread of the dose about the mean value before correlations with clinical findings can be hoped for. "(3) Integral absorbed dose. This can be derived from any of the sets of data discussed in the last sections or by more direct methods to be described in the following. If the integration is performed over the whole body the parameter contains actually very little information. When the integration is restricted to part of the body or to specified organs, the information content is somewhat increased owing to the greater homogeneity of the dose to be expected in these cases. Roberts (1954) discusses the total eneirgy absorbed by the tumour tissue, the active bone-marrow and other critical organs. Kohn et al. (1965) have used the integral absorbed dose in the pelvis as the physical parameter in a study of the influence of the radiation treatment of cervical cancer on the survival time of "cured" patients. When using co-planar irradiation techniques, knowledge of the dose conditions in one or a few representative planes is often considered satisfactory. In these cases the parameters discussed above are replaced by their two-dimensional analogues (for instance, volume distribution by area distribution).

4. RELATIVE DOSE PARAMETERS

The parameters listed in the last paragraph yield information to be applied in the study of relations between irradiation data and constitutional effects. When comparing various irradiation techniques, on the other hand, the absolute dose values are of less significance and hence relative values are often used. It should be also stated that probably the requirements concerning the information content of the physical parameters or sets of parameters are less severe in this case. A survey of the literature has yielded the following relative parameters: (1) Integral efficiency factor. This parameter, defined as the ratio between the integral absorbed dose in the tumour region and the total integral dose to the patient, gives information on how much of the absorbed energy is utilized (Wachsmann, 1954, Ellis and Oliver, 1961; ICRU Report 10 d, 1963). When used in combination with a few other relevant parameters, for instance relative absorbed dose or relative integral absorbed dose in critical organs, it is considered to be well suited for discrimination between alternative treatment techniques. In those cases in which special precautions should be taken in order to spare a particular organ, an analogous expression, namely the ratio between the unwanted radiation energy to this 160 RAGNHULT organ and the total integral dose, or perhaps better, the tumour integral dose, could be used in the optimizing procedure. This factor, in contrast to the efficiency factor, should be kept as low as possible. (2) Area efficiency factor or local efficiency factor. This is defined as the ratio between the area integral dose in the tumour region and the area integral dose to the patient, and is thus the two-dimensional analogue of (1) (Ellis and Oliver, 1961). The use of this parameter should perhaps be restricted to the frequent cases when co-planar irradiation techniques are applied. Obviously, the parameter will in these cases provide a good figure-of-me rit of different irradiation techniques. (3) Ratio of total integral absorbed dose and absorbed dose at a point. Such a ratio has often been used as a quantitative measure of the superiority of various radiation qualities or irradiation techniques, especially during the period of their introduction, for instance electron therapy (Schittenhelm, 1960). The reference point is usually placed on the skin or in the tumour region.

5. CALCULATION OF INTEGRAL ABSORBED DOSE

The mathematical definition of integral absorbed dose over a given mass

m is given by £ = Jm D dm where D is the absorbed dose in the mass element dm (Mayneord, 1940). It follows that £ is identical with "the energy imparted to matter in a given volume" (ICRU, Report 10 a, 1962), and also with the difference between incident and escaping energy with respect to this volume. The escaping energy is the sum of backscattered, transmitted and laterally lost ionizing radiation energy. Some of the methods which have been developed for the calculation of the total absorbed dose will be reviewed here: (1) From central depth dose data. When the isodose surfaces, which are usually curved, can be approximated by planes perpendicular to the beam axis, the integral absorbed dose within the geometrical limits of the radiation field is easily obtained by numerical integration over the central beam axis. For many radiation qualities the central depth dose can be approximated by an exponential function and the integration can then be performed analytically (Mayneord, 1940). A correction for the contribution to the integral dose from scattered radiation absorbed in the volume outside the geometrical limits of the radiation field can be made by using the central depth-dose curve not for the actual field but for a field of such dimensions that a further increase in area does not affect the depth-dose curve significantly. This is the method of "saturated scatter" (Happey, 1940 and 1941; Scarpa, 1960; Dutreix and Tubiana, 1961; Carlsson, 1963; Tubiana et al., 1963). In most radiotherapy situations the scatter contribution can also be allowed for by using the empirical scatter function given by Meredith and Neary (1944). It is stressed by ICRU (Report 10 d, 1963) that the latter method is quite general and the Commission recommends its use. (2) From energy fluence. The incident and escaping radiation energy can be calculated if the radiation spectrum is known. In several cases the incident spectrum is rather well defined but this is seldom true for the es- PAPER 14 161 caping radiation spectrum. Carlsson (1963) used experimentally determined X-ray spectra and calculated the incident energy per unit area and roentgen for radiation qualities with HVT less than 20 mm Al. The energy of the escaping radiation had to be evaluated by approximations. A fair agreement was found between integral dose values obtained by this method and those calculated from depth-dose data.

6. MEASUREMENTS OF INTEGRAL DOSE

The following somewhat condensed survey is intended only to give il- lustrative examples of the various techniques which have been used: (1) Integration of dose measured at points in a three-dimensional matrix. This is a straightforward although somewhat laborious method. It has been applied by Mayneord and Clarkson (1944) who used a large number of small detectors placed in an anatomical phantom. (2) Integration of dose measured at a restricted number of points. Wilson and Carruthers (1962) applied this method in an attempt to evaluate the total energy absorption in the active bone-marrow during whole-body irradiation. (3) Film measurements. Dutreix, Dutreix and Galle (1962) measured the dose distribution with photographic film in multiple and moving beam therapy and evaluated the integral dose by graphical techniques. (4) The Celluloid Man. This apparatus was made of a large number of parallel plate-ionization chambers connected in parallel and formed in the shape of the human body. The thickness of the celluloid plates and the width of the air-gaps were chosen to give the overall density 1.0. The total integral dose is obtained from the sum of the ionization currents (Grimmett, 1942; Boag, 1945; Bewley et al., 1959). (5) Chemical dosimeters. A Fricke solution in various phantoms was used by Dahl and Vikterlof (1959 and 1960) in measurements of the integral dose. This method is readily extended also to measurements of regional integral dose.

7. CALCULATION OF DOSE PARAMETERS WITH DIGITAL COMPUTERS

With automatic digital computers much more complex situations can be handled than with desk calculators or graphical techniques and by measurements. Thus all the parameters presented in section 3 can easily be derived from complete, automatically computed dose-distributions. Until now,, however, most of the automatic dose planning methods have,been confined to dose distributions in one plane only, and the parameters of greatest interest for the study of biological reactions have not been computed to any great extent. An attempt at computations in three dimensions has recently been reported by van de Geijn (1965) but usually the practical obstacle associated with the large number of data in the three-dimensional case has been too formidable. Since the parameters derived from two-dimensional distributions still may be of value as discussed earlier, their automatic evaluation wilbbe

11 162 RAGNHULT

discussed briefly. It can also be noted that the computational techniques applied in the two-dimensional case are easily converted to the three- dimensional distributions, although this may not be an economical procedure. (1) Distribution of area integral dose with respect to dose. After the primary plane dose-distribution has been calculated the computer is asked to sum the dose values at the points within the body contour according to dose value (i.e. < 11%, 11-20% etc. ). (2) Total integral dose. The computer is programmed to add the dose values within the body contour. (3) Area efficiency factor. According to its definition this parameter is calculated by first summing the dose values within the tumour area and the dose values within the body contour and then taking the ratio of the two sums.

8. PLAN OF CURRENT WORK IN GOTHENBURG

On the initiative of the IAEA we have started a study of integral absorbed dose and efficiency factors in external radiotherapy. The method used for the automatic computation of dose-distributions is a development of the method described by Halldén, Ragnhult and Roos (1963). According to the plan, the work will be carried out as follows: (1) Preliminary calculations. These are intended to establish: (i) the effect of the shape and size of the "tumour region" on the efficiency factor, (ii) the relationship between integral dose calculated in two and three dimensions, and (iii) the distribution of integral dose with respect to dose or the distribution of area with respect to dose. (2) Efficiency factor when the tumour site is kept constant. This will be studied as a function of (i) beam quality, (ii) source-skin distance, (iii) field size, (iv) penumbra and (v) body cross-section. (3) Efficiency factor for various tumour sites. This study will include three- and four-field cross-fire techniques, moving field techniques and wedge techniques. Most of the calculations will be made for 60Co and 5-MV X-ray radiation, but other types of radiation will be considered as well (for instance electron beams and 33-MV X-rays).

9. PRESENT STATUS OF THE GOTHENBURG WORK

Much preparatory work has been done, including measurements of 30 cmX 30 cm 6tCo and 5-MV linear accelerator fields, data reduction and storage of the measured and checked field-data on magnetic tape. Some preliminary calculations have been made of efficiency factors for tumour regions of different shapes and sizes and for three-, four- and moving-field techniques with ^o radiation. The original ALWAC programme has been rewritten in Algol and the first routine computations have recently been successfully executed. Some refinements in the subprogramme for integral dose calculations have to be introduced before we can start to calculate the different dose-parameters. Different calculation methods, suitable for the determination of single-field distributions in three-dimensions, have been PAPER 10 163 studied and the possibilities of extending the two-dimensional method of Day (1962) to three-dimensions has been examined.

10. CONCLUSIONS

The integral absorbed dose in the total body may be a parameter of some interest when the general radiation effects of fairly standardized radio- therapeutical treatments are studied. More sophisticated parameters will probably be needed if the search for correlations between the physical parameter and different clinical reactions are to be successful. Among the parameters discussed in this paper, the integral dose efficiency factor is particularly suited for the comparison of different radiation techniques. When the radiation effects on healthy tissue are in focus the distribution of absorbed radiation energy undoubtedly provides a better description. For the response of a particular organ attention should be centred on the radiation energy imparted to that organ, and, provided the radiation field is not too inhomogeneous, the mean organ dose may be a suitable parameter. Since most of the dose-parameters discussed here cannot be obtained with reasonable effort, unless an automatic dose-computation is performed, it appears self-evident that the automatic procedures will prove to be of extreme value in the future. As a final remark it can be said that the physicist's problem now is not how to calculate or measure a certain parameter but to find out which parameter should be provided.

ACKNOWLEDGEMENTS

I should like to express my sincere thanks to Dr. Bo Jung for helpful advice and criticism and to Mr. Ulf Larsson for programming work. The investigation is supported by grants from the Swedish Cancer Society. ORGANIZATION OF A COMPUTER FACILITY IN A HOSPITAL PHYSICS DEPARTMENT

W. SILER DOWNSTATE MEDICAL CENTER, BROOKLYN, NEW YORK, UNITED STATES OF AMERICA

The first question to be asked in determining the organization of computer activities in a hospital physics department is whether or not to acquire a computer at all. Most academic and medical institutions are vertically stratified; that is, the department head builds his protective fences around his department, and within these fences the flow of reports and direction of work proceeds up and down. The computer, unfortunately, is a general purpose tool in considerable demand by nearly all disciplines. It does not fit ¡nicely into a vertically stratified organization, and in some respects it makes about as much sense for one department to have its own computer as it would for one department to have its own laundry. A decision must be made as to whether or not the computer will be available to those outside the physics department. In either case, a policy has been laid down which will have to be defended. In any event, the basic problems to be considered are: space; staff; budget, direction of work; and choice of computer. None of these problems are easy ones. It is almost impossible to avoid under-estimating the amount of space which a computer facility requires. It is quite possible to fit a complete computer into 150 ft2 of floor space. It is, however, an extremely undesirable thing to do. Space is required for access for maintenance purposes which seems altogether unreasonable by conventional laboratory standards. In addition to the space required by the computer itself, auxiliary equipment is required, such as key punches or Flexowriters; this equipment is quite noisy and should be separate from the computer proper. The programming staff also requires office space. Since programming is a task which must be done with the utmost precision, quiet isolated offices for the programmers is an excellent idea. All told, a relatively modest computer facility employing a staff of about four programmers will usually require something like 2000 ft2 of floor space. Competent computer staff are hard to come by. A recent article in the Wall Street Journal states that the present supply of computer programmers is about 25 000 short of the demand. In addition, most computer programmers are not well trained in science or mathematics, and the performance standards for programmers are in general quite low. A thoroughly experienced computer programmer, with demonstrated talent and a good mathematical background, can now command in the United States of America a salary of about $15 000 a year. Trainees are available at less than half this figure; however, someone must train them and judge their performance. The best choice seems to be to develop a lead person from within the physics department, selecting one who has on his own initiative learned how to programme and who has acquired good practical experience. If this is not possible, a talented, experienced and expensive person should be hired to direct

164 PAPER 10 165 the programming effort. Of course, classes can be taught for the entire staff; however, the probability that a staff member will learn how to programme constantly is probably not better than 0.2. The computer budget is going to be a large one. If the computer is leased, rental costs of from two to five thousand dollars a month may be anticipated. If the computer is purchased, its cost will usually run into six figures. There are available bargain-basement computers at a cost of some tens of thousands of dollars. These include small, fast new computers selling at around $30 000, with limited capabilities, and also second-hand obsolete computers available at about the same price. The full time computer staff will probably command an average salary of about $10 000 a year, the number of staff probably being two to five. When supplies and auxiliary equipment such as oscilloscopes are added in, the budget is indeed a sub- stantial one. Here one must consider the source of funds: research grant money, institutional support, or a self-supporting centre which charges for its work. All of these have drawbacks. Mapping out the direction of work requires some major policy decisions. There are in general two types of computer work: the uninteresting routine work, such as statistical analysis of data, where the techniques for solving the problems are well known; and the interesting frontier work, in which the solution of the problem requires a certain degree of research into computer methodology itself. If too broad a scope of work is taken, a (probably small) computer staff may find themselves so swamped that it is difficult to do any work at all. The defining of the scope of work should be done very early in the game, since many other factors depend upon the choice here made. The choice of a computer is highly dependent upon the choice taken for direction of work, and in particular whether or not access to the computer is to be restricted to the physics department. If it is chosen to set up a computer facility which will be available to all, modern computer equipment with rapid access auxiliary storage should be acquired. A minimum facility here would consist of the computer itself, with memory of at least 4000 floating point words; two magnetic tape drives or a magnetic disc; line printer; card reader and punch; console typewriter; and possibly high-speed paper tape reader and punch, and digital graph plotter. If the computer is to be restricted to the physics department, the line printer may be left out. The addition of digital/analog converters and an oscilloscope with camera can provide very fast visual output. As the work requirements grow, more auxiliary storage as tapes or disc and more memory will be added. Some medium to large-scale computers now have time-sharing programmes which permit the operation of the computer from a number of remote teletype stations. These have proven quite useful at Massachusetts Institute of Technology, Dartmouth, and the General Electric Center in Phoenix, Arizona, units with which the writer is familiar. Teletype lines may be leased at low cost, which permit the operation of the computer from a remote teletype station thousands of miles away with no problems. However, the development of time-sharing programmes is not easy, and until computer companies furnish such programmes with the computers, it is doubtful if a small institution can time-share a small-scale computer successfully. However, the existence of time-sharing systems with remote teletype sta- 166 SILEfc tions in successful routine operation offers an alternative to the acquisition of a computer by a physics department; the possibility of installing a teletype link between the physics department and a large-scale remote computer should be investigated. The experience at Memorial Hospital in the computer section within the hospital physics department may be of interest. The first important automatic computation task at Memorial was the successful use of an accounting machine, sorter and key punch for radiation therapy dose calculations by Tsien (1955). Other members of the physics department had made occasional use of computers at the urging of the department chairman, Dr. Laughlin. In 1959, we became aware of the possibility of acquiring a low-cost digital computer in the range of fifty to one hundred thousand dollars purchase price. A machine-language programme for the Bendix G15 was written and operated successfully for dosimetry of radiation therapy in August of 1959. Appli- cation was then made to the hospital administration for the acquiring of a low-cost computer such as the G15. Unsuccessful in this attempt, we turned to the National Institutes of Health, and received a grant for support of a small-scale computer facility for a one year period. This was installed in October 1961. It was utilized for radiation therapy dose calculations, both external and internal X-ray spectroscopy and a number of other problems within the physics department and the biophysics department of Sloan Kettering Institute. Interest was displayed in the facility by members of other departments and divisions. A new application was made to the National Institutes of Health for the acquisition of a Control Data 160A computer, well adapted for hybrid work. This computer was received in October 1962. A supplemental application was made to add an analog computer and a Me- morial-designed interface to create a most advanced hybrid computer. This application was approved, with physiological data analysis in view. Work was begun on electrocardiogram analysis, electromyogram analysis, and the solution of compartment analysis problems by analog computer. The scope of . work continued to increase; statistical work was avoided, but physiological data analysis was actively sought. The programming staff was increased to one programmer plus a computer operator who programmed part-time. By this time, the role of the computer centre in the work of the entire institutional complex of Memorial, Sloan Kettering, New York Hospital and Cornell (from all of which computer projects were being received) was far from clear. A computer-oriented biomathematical centre was being set up at Cornell, with strong support from IBM, and there was some confusion regarding the relationship between the two centres. The author, in the mean- time, had slowly become converted from a radiological physicist to a computernik. Of course, since it is believed that the Memorial computer was the first to be installed in a hospital physics department or, indeed, in any hospital department at all, problems of all sorts were to be expected. By initially defining the scope of work, at least the problems can be anticipated. INTERNATIONAL CO-OPERATION IN THE USE OF COMPUTERS

K.C. TSIEN DEPARTMENT OF RADIOLOGY, TEMPLE UNIVERSITY SCHOOL OF MEDICINE AND HOSPITAL, PHILADELPHIA, PA., UNITED STATES OF AMERICA

EDITOR'S NOTE

This paper consisted of a short introduction and an extended bibliography on the use of digital computers in radiation treatment planning. As this bibliography has been included in the complete one covering the whole of this report (see below), it was considered unnecessary to print it here as well. Due acknowledgement should be paid, however, to the considerable work of Mr. Tsien in preparing his original bibliography.

167 TRANSMISSION OF DATA: DIGITAL PROCESSING OF ISODOSE PATTERNS

К.С. TSIEN DEPARTMENT OF RADIOLOGY, TEMPLE UNIVERSITY SCHOOL OF MEDICINE AND HOSPITAL, PHILADELPHIA. PA., UNITED STATES OF AMERICA

Communication technology has now reached a stage in which we can transmit almost any form of data from one place to another. While tele- vision is the best general form of transmission for visual data, the simplest and least expensive way is by coding the data into numerals. Transmission of data by numerical coding, however, requires decoding at the receiving end to restore it to the original form. The transmission of line curves is done most often by translating the curve into a series of points and then determining the co-ordinates of the points for transmission. The decoding of these data is generally time- consuming if there is no automatic plotter available. A new method of digitizing line drawings has been developed for use in pattern recognition, which simplifies greatly both coding and decoding in the transmission of line curves. This system can be readily adopted for use with isodose curves. In this system any curve is converted into a series of line segments on a square grid of a selected dimension. Using only line segments along the grid or along the diagonals of the grid, a section of the curve intersected by the grid lines may be represented by one of eight possible line segments, as shown in the key grid, Figure la, the line segment being always the one which has both the starting point and the end point nearest to the corresponding intersections of the curve with the grid lines. If we give each of these line segments a number, a curve can be translated into a series of numbers by means of this method. Figure 1 b shows how a curve AA1 is represented by line segments of a grid and coded. The numerical code can be furthea changed into a binary code and directly generated from a computer. When applying this system to translate isodose curves, a 5-mm grid is sufficiently accurate. An example of isodose curves, for a cobalt-60, 240° rotation, represented by line segments and coded is given in Fig. 2 and Table I. The first column in Table I gives the identification of the percentage of the curves and the position of the starting point of each curve. The advantage of this system is not only that it is easy to decode by plotting the numbers on a grid paper, by hand or by a simple machine, but it also makes it easier to analyse the characteristics of the isodose patterns, as for instance the area enclosed by any isodose curves, the distance between the end points of the curve in the direction of horizontal or vertical grid lines, etc. This system of coding line curves is relatively new and has not yet been used in dosimetry. Because of its simplicity it opens up new possibilities of distributing computerized dose data instantaneously from a single computer centre to more distant points.

168 PAPER 10 169

а Ь

FIG.l. (а) Key grid, (b) Example of curve plotted by coded line segments

ISODOSE CURVE

J DIGITIZED LINE 0 10 0

FIG.2. Example of cobalt-60 isodose curves represented by line segments 170 TSIEN

TABLE I

DIGITAL CODING OF ISODOSE CURVES Cobalt-60 240° rotation, SAD 75 cm, F.S. 8cmX 8 cm, 20 cmX 30 cm oval phantom

(1) Basic grid used, 5-mm square (2) The first column indicates the percentage of the isodose curve and the position (starting point) of the isodose curve on the minor axis of the phantom in reference to the centre of rotation.

100 X ooc 0000 1122 3334 34

90 X 21L 0000 1021 2122 2332 4334 44

80 X 32L 0000 1011 1221 2232 3234 3344 44

70 X 38L 0010 0101 1121 2222 2233 3243 3443 44

60 X 45L 0010- 0010 1111 1221 2322 3233 3334 3443 44

50 X 50L 0001 0001 0101 1111 1222 2232 3233 3333 4343 4344 4

40 X 56L 0000 0010 0101 0010 1001 0012 2122 3223 2232 3332 3333 433

30 X 65L 0000 1000 0100 0010 0000 0000 1

20 X 80L 0001 0000 1000 0000 0000 00

15 X 95L 0000 1001 0010 0000 000 INTERNATIONAL CO-OPERATION IN USE OF COMPUTERS

T.D. STERLING MEDICAL COMPUTING CENTRE, UNIVERSITY OF CINCINNATI, COLLEGE OF MEDICINE, CINCINNATI, OHIO, UNITED STATES OF AMERICA

INTERNATIONAL CO-OPERATION IN USE OF COMPUTERS

Computers are central parts of a total system of electronic and mechanical equipment that sense events in the environment and effect activities back on the environment itself. This total constellation of sensor-processor- effector make up what may best be described as the "robot", man's ultimate assistant who is willing and able to slave for him untiringly. It is obvious that this robot offers much needed help to the scientist and practitioner. However, to convert this collection of electronic and mechanical gear into a useful assistant requires an unusual complement of human intuition, ingenuity, creativity, and just plain hard work. While some countries may be wealthier than others and able to afford a more dazzling display of mechanical and electronic hardware, no place in this world has a monopoly on creativity. Fundamental contributions have come already from such diverse places as Holland, East Germany, England, Canada, a number of places in the United States of America, and will be forthcoming shortly from Australia. It is not even true that there are regional trends and differences in the kind of contributions. If this were so, then work done in Europe should have tended to be more theoretical since computer time is still more expensive and difficult to obtain there than in America. On the other hand, contributions from the United States should have tended to be more empirical and concerned more with mass computation and convenient display. However, nothing of this kind has happened. Theoretical and empirical work has progressed side by side. Where regional differences in approaches to computer-based radiation dosimetry have emerged, they were due to the diversity of temperaments and back- grounds of individuals. Different approaches plumb the subject matter from a variety of points of view and develop a firm foundation of new knowledge and techniques. We have found it extremely profitable to compare, learn from, and merge differences in approaches and techniques in our country. Almost all individuals actively interested in work on automatic dosimetry problems have met preceding the last three annual meetings of the Radiological So- ciety of North America. Their meetings were completely informal and, after a joint dinner, each of the participating individuals related his recent work and his plans for the future and offered suggestions and comments concerning the work described by others. These meetings have furthered greatly the work of all participants and have led to renewed interest by a number of other workers in diverse aspects of related research.

171 172 STERLING

Partially because these informal meetings have always had attendance and representation from Europe and partially because the general need for further information exchange obviously exists, there is a movement under way now to initiate regular meetings every two years between European and American workers. Present plans call for an international conference at Cambridge during next June and its repetition two years hence in the United States.

EXCHANGE OF PROGRAMMES AND COMMUNICATIONS CONCERNING CURRENT WORK

National and international co-operation takes on concreteness in the exchange of programmes and research results. On a practical level and for the exchange of actual techniques the diversity between computers and computer languages may offer almost overwhelming obstacles which can be overcome but not without considerable effort. If computing centres have similar constellations of hardware, then the exchange of programmes is of course routine. We were able to exchange programmes with the Cancer Institute Board at Melbourne, Australia. It turned out that our programmes, although developed for a 60Co teletherapy beam unit (Model Eldorado A), could be fitted to the dose distribution from the Melbourne 4-MeV linear accelerator with the change of a few constants. The work of fitting the equations themselves was done by the Melbourne group. Once the new constants were found it was a simple matter of transcribing our programme on a reel of magnetic tape and returning it to Melbourne. Treatment centres may have access to different computers. However, it is becoming increasingly true that different computers will be able to accept programmes written in many languages. Language compatibility makes it possible to take programmes and to rewrite them, at a very small cost, to fit another computer. Very often the only changes that have to be introduced are of "input-output" instructions. If this is the case, then a copy of the flow diagram and a print-out of the source programme is usually all that is needed to make a programme operational on a different machine. But even here we have found it desirable to send a programmer along so that resolution of detailed problems may be expedited. In this way we exchanged programmers with the Mallinckrodt Institute of Radiology at St.Louis, Mis- souri to make our own external beam methods compatible with their computer and to make their interstitial and intracavitary programmes operational on ours. If the computers are not the same and if they cannot accept each other's languages (especially if there are different principles of input and output involved), programmes cannot be exchanged but must be rewritten, often with changes in some of their principal components. An example would be the difficulties in exchanging our programmes with many British centres. British centres tend to use their own types of computers which are somewhat different from those of American manufacture. Predominantly there is a machine language difference here which would make it simply impossible to take a set of programmes written for an American machine and, merely by revising input and output statements, make these programmes operational on a British machine. But more serious than language differences is that PAPER 10 173

most of our programmes make maximum use of the display possibilities of high-speed printers or of on-line plotting devices. All programmes, for instance, include graphic and numeric display of results which make it easy for the radiotherapist to assess the general pattern of dose distributions. On the other hand, British machines have very limited display possibilities. Input and output of British machines is usually through paper tape and the teletype printer. This system is quite satisfactory if a great deal of computation is reduced to an output of a few numbers. However, it is completely inadequate to describe dose distributions graphically. Unless high-speed printers are available, our techniques of displaying dose distribution would simply make no sense at all for British computers. It is quite possible that within a few years most European computers will have the same type of display and output equipment as do American machines now so that this problem may very well be only temporary. The most useful means of transferring ideas and techniques from one country to another or from one centre to another is still personal contact. We have had a succession of British visitors in the United States and, con- versely, Americans have visited Britain. These meetings have been extremely useful and productive in exchanging techniques. It is interesting here that such contacts do not necessarily result in the saturation by one worker of ideas developed by the other. Rather, they tend to serve as a catalyst for the. work of both investigators, a phenomenon which is certainly not limited to radiation dosimetry. It ought to be mentioned also that the British Journal of Radiology has become the major international exchange medium for radiation dosimetry work on computers. Insofar as this journal has managed to concentrate contributions from all countries, it has become a valuable central reference for all individuals working in this field.

TRANSMISSION OF DATA USING CONVENTIONAL COMMUNICATION FOR HOSPITALS WITHOUT ACCESS TO LOCAL COMPUTERS

The actual use of programmes by hospitals, with and without access to local computers, is regulated mainly by two factors: time and cost. This is true not only for present uses of computers but also for those that will become practicable in the future. It is possible for hospitals and treatment centres which do not have their own computers to use existing techniques by making use of local or regional computing installations. Results of calculations can be mailed or in some other way conveyed to the user. It has been our experience that for external beam therapy a "turnover time" of two days is quite acceptable in most instances. (By turnover time is meant the time period that elapses between submission of a particular treatment plan to a centre and the receipt of the printed return. ) On the other hand, for interstitial or intracavitary treatment plans, a 24-h period for turnover time appears to be the permissible maximum. This means that minimal external beam therapy planning could be done by regional centres which are spaced fairly far apart. Specifications for treatment plans could be phoned in and print-outs returned by mail from and to any part of the United States within two days. The same is true for 174 STERLING

Europe. However, the demands of interstitial and intracavitary therapy would almost force the location of the computer installation within a one- day mail delivery distance. However, to optimize treatments, direct access to a computer is desirable and often necessary. Accessibility could be effected by having the computer located close enough to the treatment centre so that the radiotherapist can obtain physical access to the machine or it may be possible to give him an electronic display of his treatment plan and some means of communication with a more distant facility. This latter method may actually be preferable. Advances in computer technology have made it quite practicable to use a cathode ray or light board display. This light board displays the computer's memory by having the cells either "on" or "off" depending on the content of the memory. The result is a picture which can be held in a buffer and fed back through the oscilloscope so that a stable image appears. This image can be inspected and preserved by photography. In addition it is possible to use a so-called light pen to activate memory components directly from the light board. In this way the user may draw patient contours and other information directly on the light board and have representations of these drawings entered in the computer's memory. It is also possible, by the use of these light pens, to reprogramme or call out preprogrammed routines. The light board display may be controlled also by a console. Costs of such display devices depend very much on the constellation of equipment available to the therapist, the extent of use of the facility and its number of users, the programming system that is used, and on many other factors. Also, as far as computers are concerned, costs are constantly changing. Increases in speed of computation make themselves felt by decreases in cost to the user. As more users come into the picture, it is possible to cut the cost to all of them since each one has to carry less of the cost of unused time and of maintenance of a facility. It may be of interest to look at some admittedly rough cost estimates for different calculation and display methods. For a machine the size, speed, and cost of the IBM 7090, it would take 30 seconds of computer time to compute the dose distribution (by our method) for one plane of a field generated by three or four external treatment beams. It does not matter at which angle these treatment beams enter or where the plane is located. However, these 30 seconds of computer time are based on the assumption that the field comes in at right angles to the patient and that adjustments for curvature will be made by tissue compensators or bolus materials. For this 30 seconds of computer time the cost would be approximately $4. 60. To obtain five cuts through a patient would then cost approximately $23.00. In addition there is the cost for set-up time during which the programme is actually read into the computer. Set-up time may be from 30 s to 2 min and cost $4.60 to $18.40, depending on the type of operating system being used. Thus a treatment plan involving five cuts through a patient would cost somewhere between $28.00 to.$41. 00 if an IBM 7090 is used. These costs usually include the display of the dose distribution on a high-speed printer. Costs would go up steeply if adjustments for curvature were requested. Here computation time is no longer independent of the number of beams used and may be expected roughly to double or triple depending on the amount of curvature involved. Another complicating factor may be introduced by try- PAPER 10 175 ing to make allowances for heterogeneity of the medium. Heterogeneity of the medium is especially important where the beams go through air spaces within the body. However, to include corrections for heterogeneity would at the very least quadruple the costs of planning. Thus the cost of treatment planning could become quite high. We have found it necessary to split these costs between the patient, the therapy centre, and the computing installation. However, as the cost of computation time decreases and as computing centres learn to be more efficient in the use of available equipment, these costs may be expected to decrease sharply. If present trends are maintained then we can look forward to these costs decreasing by a factor of five within three years. To change systems and make use of the available additional power offered by cathode ray display and input devices would increase all expendi- tures considerably. Because of the high cost involved, it would not pay to have such light board displays unless there are a large number of users so that cost for each is a minimum. This is also true for all on-line time- sharing consoles for any computer. However, regardless of the number of users, the cost to a centre of the light board itself will be considerable. Adaptation of a basic computing system for accepting display devices involves the installation of interfaced equipment which mediates between the central system and the terminal device, allowing for the transmission of data in either direction. Since such equipment, once available, permits the addition of several terminal devices, the cost per terminal decreases as additional terminals are installed. Beyond a certain number of terminals, additional interfaced equipment must be acquired. These interacting factors are reflected in the approximate cost table given below (which does not include charges for phone and computer time):

Approximate rental Number of basic terminals (dollars per month)

1 570.00 2 620.00 3 770.00 8 1265.00

This type of unit provides a cathode ray display with a capacity of 960 characters. The display is for output purposes only. Communication back to the central computer is effected by means of a typewriter keyboard which contains both alphabetic and numeric characters. If expansion of capabilities is desired the design of most modern basic computing systems makes it possible to attach a single light board and light pen terminal without additional equipment. Such equipment, however, is required if more than one terminal is to be attached. The table given below shows the approximate price breakdown as above: 176 STERLING

Approximate rental Number of terminals (dollars per month)

1 750.00 2 1975.00 3 2725.00 8 7075.00

In addition to basic display and typewriter input, these terminals also provide a light pen for indicating points to be deleted or added directly on the light board. This pen may also be used to draw straight lines between any two points and have this information transmitted to the computer's memory. The capabilities of the typewriter keyboard are also considerably expanded in that the user may pre-programme a number of functions of his own choosing which can then be referenced by depressing single keys. Even if there is the expected decrease in cost it would still be profitable for a hospital to acquire such equipment if it can spread its cost over a large number of users. Thus the idea of a regional centre remains attractive. It would make much more sense to think of giving each community (consisting of a number of hospitals and treatment centres) a regional console which would be on-line to some distant computer or may have its own facility depending on the size of the community itself. The main thing would be to share the cost of the treatment console among the many hospitals in a region. The size of a "region" will increase as computing becomes more and more sophisticated. CLINICAL EVALUATION OF TREATMENT PLANS

E. W. EMERY RADIOTHERAPY DEPARTMENT, UNIVERSITY COLLEGE HOSPITAL, LONDON, UNITED KINGDOM

Since the start of radiotherapy, the aim of all radiotherapists has been to treat as many patients who suffer with malignant tumours as possible, so as to give an effective curative dose to the whole tumour, at the same time, doing as little damage as possible to normal tissues. Until 1945, damage to the skin was usually the limiting factor. Since the war, with the rapid development of more powerful X-ray machines and sources of irradiation, we have had at our disposal much more penetrating radiation, allowing us to give effective tumour doses, with little or no damage to the skin. However, with higher tumour doses, there is more likelihood of damage to structures in proximity to the tumour — i.e. bone, nerves, muscle, liver, kidney etc. This has focussed the interest of all radiologists on the need for careful planning, and physicists have worked out with great care the differential absorptions of X-rays on differing tissue, i.e. bone, muscle, fat etc. , so that very accurate and correct treatment planning can now be undertaken. This entails a great deal of accurate and complicated work and has had to be done by our physicist colleagues, who may take hours or days to work out a complicated treatment plan. The acceptance of the plan as being the most suitable for a patient is governed by these factors: (a) The dose must be given to the whole tumour area (b) The nearby structures, i.e. nerves, bowel, kidney etc. must not receive a dose which may cause serious damage (c) All parts of the tumour must have an effective dose (d) The integral dose must be such that the patient is not unduly upset. All these factors vary from patient to patient, and thus each plan has to be considered in conjunction with each individual patient so that, although patients have similar tunours, what may be an optimal plan for one may not be for another. Also clinicians themselves vary in their opinions on the size of tumour, general condition of the patient, and the amount of damage they think justifiable to inflict upon patients. When I first read the paper of Tsien (1958) on the use of computers in assisting this work, it seemed interesting but not very practical, as the computer could do no more than our physicists who were able and willing to do this work for us, and also computers were then something completely outside the domain of most hospitals. However, since those days, the role of the physicist in medicine has completely changed. The radiotherapist may claim the honour of introducing physicists into hospitals, but the physicists have now left us far behind, or at least to one side. Their work has increased enormously into all branches of medicine, and they are now really medical physicists and their departments are now often termed Departments of Nuclear Medicine.

177 12 178 EMERY

Naturally our experienced physicists are now heads of these departments and so do not have the time to spend hours a day working out treatment plans; they have to delegate this part of their work to juniors. When we reached this stage we often found ourselves having treatment plans made by physicists who hardly knew what we were aiming to do. Thus, although the physicists have greatly increased our knowledge of radiation dosimetry, we were finding difficulty in applying this knowledge. The paper by Sterling et al. (1963), showing us again how computers could help, had a much more enthusiastic reception at this stage and seemed to "offer practical help. Consequently, we contacted a computer firm. The firm, with their computer, was about 15 miles away from our hospital, and all ways of communicating with the computer were explored, i.e. telephone, post, messenger etc., and we soon learnt our first lesson, that to be of any real help the computer had to be in or near the hospital. We were fortunate in that the hospital as a whole became interested in the computer for working out wages, hospital records etc. and within a few months a computer was installed in the hospital almost underneath the physics department. Our chief physicist then worked out a programme for treatment planning using cobalt-60. This was tried and worked well. We as clinicians still had to do our original work, i. e. make an outline of the patient and put in the tumour area, the areas or tissues to be avoided, and the most likely size, direction, and number of fields. This information we gave to our physicist who, using the computer, brought back a print-out such as in Fig. 1. This mass of numbers, while probably quite intelligible to a physicist, we found difficult to understand; we required information in isodose form and with the use of an X-Y plotter, our physicists were then able to give us the same information from the computer as in Fig. 2 in a form with which we were familiar. I think this was the second lesson - to be of value, the information must be in a form which radiotherapists and radiographers easily recognise. In applying this help in our department, we soon found that the computer, although so near, could not spare us much time and eventually we worked out a practical method of using the computer for a few hours at the beginning and end of the working week. Patients are usually admitted to hospital over the weekend, their initial plans are made on Monday, the complete plans are available on Tuesday, and treatments are begun. The hours at the end of the week are used for patients admitted as emergencies or referred to us in the hospital during the week. The advantages to the patient and to us were soon apparent. The patients did not have to wait, there being rarely more than a day before starting their treatment. Most patients know their diagnosis and, while treatment is not an emergency as normally considered in medicine, they are naturally upset by any delay in starting their treatment. Other consultants are also upset by their beds being occupied by patients not yet receiving treatment; starting treatments as soon as possible makes fuller use of hospital beds and this helps to keep down the waiting lists. The rapidity with which plans can be made also, we think, helps to make better plans, as we now have no reason to be tempted, because of the time and work involved, to accept a treatment plan that is just reasonable. A plan can be repeated so quickly that the patient may easily have the best plan that we can devise. The junior physicists can now produce plans as

12* PAPER 10 179

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FIG.1. Print-out of plan from the computer quickly and as well as they had been done by our most experienced physicist, so that with the computer we have really not advanced, but have regained lost ground. To make a great advance, we shall have to devise a programme so that all we have to do is to give the physicist the outline plan of the patient, the tumour areas, areas which have to be spared, the dose required evenly distributed throughout the tumour, and the lowest possible integral dose to the patient, including the combination of interstitial and external radiation. The computer will then have to tell us how to carry this out. We are at present trying to do this but how successful we shall be in obtaining this optimum plan is not yet known. Will this enable us to cure more patients? I am sure that we shall be disappointed in this aspect, as there are so many unknown factors in treating patients with cancer. We cannot estimate accurately the size and spread of the tumour in all patients. In too many treatment plans, unfortunately, our depicted tumour areas are no more than an intelligent guess. How are we to estimate accurately the amounts of air, fat, and bone in the treated volume? Patients are individuals and, although their tumours may have similar histological patterns, the response of the tumour cells, for any given dose varies enormously. We all see patients whose tumours are apparently cured by very small doses, while in others, similar tumours seem to be 180 EMERY

FIG.2. Treatment plan of Fig. 1 using X-Y plotter practically unaffected by large doses. The patient's response to integral dose also cannot be estimated, some being upset by small amounts of radiation, others seeming to thrive on treatment. Thus a treatment plan is only one factor in controlling cancer, and is it worth while working out elaborate and accurate plans? There is in my opinion no doubt that it is well worth while. Certainly it will enable us to do the minimum damage to the patient. If all our patients in the department are planned in the same way, the results can be compared from patient to patient, and if other departments use the same or similar programmes, then comparison between patients treated in different departments may be more easily made. Thus, having a common treatment, one factor may be constant, making it easier to resolve our other unknown factors. What of the future? The treatment programme we have been using, although not an optimum programme, has been of great help. Already, our junior trainee radiotherapists have known no other way of planning than this, so that they do not plan patients themselves, and it will not be long before they will be completely dependent on the computer. No doubt a similar situation will occur with physicists. If and when an optimum programme develops, its use would undoubtedly spread rapidly through all departments. In underdeveloped areas of the world, where it is easy to obtain powerful sources of irradiation but difficult to obtain adequate physicist help, treatment planning by computer would be an undoubted benefit. The patients would have a much higher chance of cures without too much damage. PAPER 10 181

Is there any danger in producing treatment plans automatically? I think there could well be. We, have found that although computers do not make mistakes, human error can and does occur in putting information into the computer and the computer can also break down, so that the resulting plan may be wrong. Thus all plans must be carefully scrutinized by the clinician before being applied to the patient. A generation of radiotherapists brought up with computers may not be able to evaluate plans critically, knowing nothing about manual treatment planning. Thus the computer may in time dictate the treatment of the patient. Clinicians must be aware of this danger and aware of the fact that the treatment plan is only a method of treating a tumour. The clinician is treating a patient, will all the varying factors involved and must retain his critical view of any treatment plan accordingly. PHYSICIST OR COMPUTER SPECIALIST?

J.S. CLIFTON UNIVERSITY COLLEGE HOSPITAL, LONDON, UNITED KINGDOM

LANGUAGE BARRIER

Since to most clinicians physical science and computer science are two of the great mysteries of the world, the physicist in a hospital is expected by clinicians to be fully conversant with, and competent to make profound pronouncements on, all methods of computing, specific computing problems, and the suitability of computing machinery ranging from desk calculators to Atlas. This is not surprising since the proportion of the syllabus devoted to physics and mathematics in an M.B. degree is indeed meagre, and the word "computer" has been surrounded with an aura of mysticism which suggests that it is some fantastic piece of electronic gadgetry comprehensible only to a veritable genius. The clinician consequently turns to the only scientific colleague with whom he has direct contact - the medical physicist - and expects him to be an authority. The physicist is thus thrust, however unwillingly, into the forefront of the advance of computer assistance to scientific medicine. It is therefore essential for him to acquire sufficient knowledge of computing science to enable him to provide satisfactory answers for the clinicians' queries, to proffer more detailed advice as to programming convince clinicians that the computer is really a "simpleton" which can only add and subtract and even that only under instruction. In many applications of computers to clinical problems the first and most difficult barrier is one of common language. Here again the physicist must often play the role of interpreter between the clinical colleague on the one hand, and the computer programmer on the other. However, this approach can only serve as an initial introductory phase. Only if the problem is of relative simplicity can it be tackled without a common "language". If scientific or clinical "know-how" and experience are to form an integral part of the computer programme it is essential for each specialist to know something of the other's field. We have found during the three years that we have operated the Ex- perimental Medical Automation Unit in conjunction with Elliott Bros, that the most successful approach is to teach the would-be user of the computer to write his own programmes. The programmes produced in this fashion may not contain all the sophisticated routines that are at the command of the experienced programmer, but they do embody the vital experience and "know-how" of the specialist, correctly applied. This is the principal consideration since most computers are sufficiently endowed with core space and calculating facility to allow some latitude in the efficiency of programme writing. Universal languages, such as Algol and Fortran, permit a simplified programme writing technique and the Medcomp library of Sterling (1964) is a further step in the right direction - that of producing a programme language comprehensible to the clinician.

182 PAPER 10 183

COMPUTING FACILITIES

There are three approaches, not necessarily exclusive, to the provision of computing facilities for a hospital. (1) A scientific department, such as the physics department, may possess its own computer (2) The hospital may possess a computer, or computing unit, which provides a computing service to all departments (3) The hospital may hire time on a service basis on a computer placed some distance from the hospital. The development of data transmission links over Post Office lines and of very powerful computers such as Atlas makes the possession of an on-site computer less favourable on economic grounds. It is possible, using the teleprinter as a plotter, to transmit dose distributions in this manner. The greatest draw-back is the incompatibility of the various tele-codes and computer codes, it being necessary to convert the five-hole or eight-hole computer data tape to five-hole tele-code tape before transmission. Also it is essential to introduce suitable error checks in the data transmission to prevent waste of valuable computer time in calculations on data incorrectly transmitted.

THE ONE-DEPARTMENT MODEL

This is the simplest case, e.g. the Physics Department with its own computer. The computer will probably be a relatively small but high-speed machine with a number of special peripherals, operated on a time sharing basis, ideally suited to the problems of a scientific department, processing the results of experiments and storing data for subsequent analysis, and acting as part of a feed back loop to control complicated experiments. There are no "interface" problems, either machine or human. All equipment is designed to operate in conjunction with, and by direct access to, the computer. This system is not particularly applicable to radiation dosimetry or radiation record keeping where excessive amounts of data must be stored and repeatedly accessed.

THE TWO-DEPARTMENT MODEL

When the hospital possesses its own computer to which the Physics De- partment has direct access there exists the two-department model. Since the computer will be of the general purpose digital type, two problems arise: (1) An interface must be provided to convert data produced in the department into a form suitable for the computer (2) Experiments and available computer time must be scheduled to ensure smooth operation. The availability of a computer requires that the conventional approach to an experiment must be reversed, for, having defined the problem, the pattern in which the results are to be obtained is predetermined by the requirements of the computer to process them for the final answer. 184 CLIFTON

Data, in a form suitable for insertion into a general purpose computer, can be produced in one of two ways: (a) by recording manually and transferring the data to punched cards or tape; (b) by arranging for the equipment to drive a tape-punch, and produce its data directly. The greatest number of errors in data are invariably caused by human error, either incorrect reading of results, wrong conversion, or wrong punching. For this reason it is desirable, whenever possible, to arrange the experiment in such a way that the equipment pr©duces its results directly on punched card or punched tape suitable for the computer. There is also a large saving in labour cost. Generally, the experiments which are to be computer processed do not require immediate access to the machine. A delay of a few hours can be accepted. There are certain exceptions to this - particularly in isotope experiments where interpretation of "scanning data", blood loss, etc. are required for prompt diagnosis. This requires careful planning in conjunction with computer personnel to ensure that computer time is available when needed. In this respect an "on-site" computer is invaluable, since urgent priorities and minor adjustments of time-table can be achieved by first-hand negotiations. Clearly the larger the computer, the more essential to have a rigid time-table for economic reasons, and the less flexible the system becomes.

THE THREE-DEPARTMENT MODEL

This is the system in operation when attempting radiation treatment planning. As with any compartment system the complexity increases with increase in the number of compartments. The same basic problems arise as with the two-compartment model, except that it is now necessary to establish interfaces between all three departments, and the scheduling of computer time must also accommodate three- departmental requirements and the over-riding demand of minimum dead time between initiation of data and presentation of results. For treatment planning purposes there is a long established interface between the radiotherapist and the radiation physicist, but the transference of data is manual and in analogue form (i.e. isodose charts and treatment plans). The interface between physicist and computer also exists but, since the data started in analogue form, two hand conversions are necessary before it can be inserted in the computer. First, all isodose data must be converted into digital form and stored in the computer; secondly, the details of any treatment plan must be entered in a suitable pro-forma and then punched before presenting them to the computer. This acquisition and hand conversion of data causes a loss of time. The return links between computer and physicist, and physicist and radiotherapist also exist, but again hand conversion is often necessary to adapt the output of the computer into an analogue form acceptable to the radiotherapist, with another loss in time and accuracy. By far the most serious problem is the almost total lack of interface between the radiotherapist and the computer. There is now a range of techniques whereby the output of the computer is produced in analogue form by PAPER 10 185 a graph plotter in a manner acceptable to the radiotherapist, but these are not yet generally available. The non-existence of an interface between the radiotherapist and the computer means that a feed-back loop tends to develop between the physicist and the computer, which diminishes or even removes the clinical responsibility from the radiotherapist. To overcome this it will be necessary to develop an input device for the computer by which the radiotherapist, can use his clinical judgement to control the computation, and an output device which gives an immediate presentation of results. To meet these requirements and keep the system within a reasonable cost limit the input and output devices will have to be analogue in operation, incorporating analogue to digital conversion on the input, digital to analogue conversion on the output, and optical display, possibly by T. V. monitor. The combination of X-ray simulator, analogue computation unit, optical display, and data punch would enable clinical treatment planning to be carried out for the patient with presentation of the estimated dose distribution, followed by immediate production of a data tape. Detailed calculation including appropriate dosimetry corrections could then be made by the digital computer, with subsequent display of the final calculated result. This system would restore full clinical responsibility to the radiotherapist, eliminate the time delay in hand processing of data before computation and, with the availability of an "on-line" or "time-shared" computer for a short period each day, provide a complete treatment planning service. Without the direct interface between radiotherapist and computer, and with computer access only at predetermined times, it becomes essential to schedule the whole operation very carefully. Since the object of the exercise is the production of a suitable treatment plan for a given patient the time-table must start with the time of the planning clinic; also for economy in computer time, and hour must then be set by which time plans for computation are ready, time must now be allowed for the production of the pro-forma data sheet for each plan, and further time for these data sheets to be punched and verified. At this point computer time can be booked. Since booking must be made well in advance a period of time must be specified depending on the anticipated number of plans. If there are too many plans some must wait for the next available time; if there are too few, computer time is wasted. The cycle time of such a system is usually at least 24hours, of which about one hour is computer time. Clearly the inflexibility of this system both in time scale and in derivation of an optimum treatment plan are serious disadvantages, but those will only be overcome when a suitable interface is devised between the radiotherapist and the computer.

ECONOMICS

The question is often posed: is it economic to use a computer for radiation treatment planning? The answer must depend on the standpoint from which the problem is viewed. For simple fixed field treatments using simple methods of correction, and assuming the patient to be a homogeneous tank of water, the competent technician can produce an answer more economically than a computer, and 186 CLIFTON

the flexibility for modification is greater. However, when multiple fields, rotation, curvature and inhomogeneity are introduced into the calculation, the computer is more economical as well as more accurate. For interstitial dosimetry, the computer is the only answer. With the present steady decrease in the availability of suitably trained manpower to perform treatment planning calculations, the time will arrive shortly when treatment planning will only be possible by computer. A similar situation arises in the application of computers to Physics Department tasks. Where the programme is simply one to do automatically a task at present done manually the unit cost is usually unfavourable to the computer. If, however, the equipment is arranged to produce its own data tape the accuracy is unquestionably better. Also staff are freed to tackle other tasks, and the problem of finding a sufficiently qualified, conscientious technician prepared to do a routine job is removed.

CONCLUSION

The application of computer methods to medical problems is now a proven technique. In medical physics and more particularly radiation dosimetry the extent to which these techniques are applied will be largely dic- tated by the arrangements for the provision of computing facilities. For improved accuracy and extension of detailed calculation to complex dosimetry problems, the use of computers is adequately justified. For the less complicated problems at present dealt with by manual methods the economic justification is debatable, but the long term shortage of suitable labour must result in the eventual application of automation. BIBLIOGRAPHY

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LAUGHLIN, J. S., SILER, W. M. , HOLODNY, E. I., RITTER, F. W. , A dose description system for interstitial radiation therapy: seed implants, Am. J. Roentgenol. 89 (1963) 470.

LAUGHLIN, J. S. , SUMPF, R. , LUNDY, A., PHILLIPS, R., Electron beam treatment planning in inhomogeneous tissue, Radiology (in press). BIBLIOGRAPHY 191

LEDLEY, R. S., Programming and Utilizing Digital Computers, McGraw-Hill, New York (1962).

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MASSEY, J. B., Dose distribution problems in mega voltage therapy. I. The problem of air spaces, Brit. J. Radiol. 35 (1962) 736.

MAUDERLI, W., FITZGERALD, L. T., A computer programme for automatic rotational treatment planning, Phys. Med. Biol. 9 (1964) 102.

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PEREZ-TAMAYO, R., Digital Computers in Radiation Therapy; Progress in Radiation Therapy. Vol. Ill, Green and Stratton, New York and London (1965) 68-91. 192 BIBLIOGRAPHY

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QUIMBY, E. H. , COHEN, B. S. , Effects of radiation quality, target-axis distance, and field size on dose distribution in rotation therapy, Am. J. Roentgenol. (1957) 819.

RICHTER, J., SCHIRRMEISTER, D. , Ein Verfahren zur Berechnung der Dosisver'teilungen mit digitalen Rechen- automaten, Strahlentherapie 123 (1964) 45.

RICHTER, J. , SCHIRRMEISTER, D. , Die Ermittlung von Dosisverteilungen mit digitalen Rechenautomaten unter Berücksichtigung von Randabfall und Streuung, Strahlentherapie 126 (1965) 177.

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ROSENOV, U. , Programme zur Isodosenberechnung fiir die Pendel-, Kreuzfeuer- und konzentrische Mehrfelder- bestrahlung auf einer elektronischen Rechenmaschine, Strahlentherapie 127 (1965) 206.

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SCHITTENHELM, R. , Physikalischer Vergleich der Thérapie mit energiereichen Elektronen- und ultraharten ROntgenstrahlen, Strahlentherapie U2 (1960) 389. « SCHLESINGER, J. E. , PORTER, E. H. , Radium implant dosimetry with a small digital computer, Brit. J. Radiol. 39 (1966) 147.

SCHOKNECHT, G. , Dosisberechnung ftir die Kobalt-60 Bewegungsbestrahlung mit konstantem Pendelradius, Strahlentherapie 120 (1963) 525. BIBLIOGRAPHY 193

SCHOKNECHT, G., Berechnung der Dosisverteilung bei tangentialer Pendelbestrahlung mit Kobalt 60, Strahlen- therapie 122 (1963) 341.

SCHOKNECHT, G. , Berechnung und Ausdrucken von Dosisverteilungen ffir die Co-60-Teletherapie mit dem Datenverarbeitungssystem IBM 1401 nach experimenten bestimmten Ausgangswerten, Strahlentherapie 125 (1964) 75.

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SHALEK, R.J., STOVALL, M., The calculation of isodose distributions in interstitial implantations by a computer (Work in progress), Radiology TC (1961) 119.

SILER, W. , LAUGHLIN, J. S. , A computer method for radiation treatment planning, Comms Ass. comput. Mach. 5 (1962) 407.

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SILER, W. , BRONSTEIN, E. , LAUGHLIN, J. S. , RITTER, F. , A treatment planning computer method for analysis of effect of body inhomogeneities in radiation therapy, Radiology (in press).

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STERLING, T.D. , PERRY, H. , "Computation of radiation dosages", Computers in Biomedical Research (Vol. I), Academic Press, New York (1965).

STERLING, T.D., PERRY, H., BAHR, G. K. , A practical procedure for automating radiation treatment planning, Brit. J. Radiol. 34 (1961) 726.

STERLING, T.D. , PERRY, H. , Planning radiation treatment on the computer, Ann. N. Y. Acad. Sci. 1Л5 (1964) 976.

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STERLING, T.D. , PERRY, H. , WEINKAM, J.J. , Automation of radiation treatment planning. III. A simplified system of digitising isodoses and direct print-out of dose distribution, Brit. J. Radiol. 36 (1963) 522.

STERLING, T. D. , PERRY, H. , KATZ, L., Automation of radiation treatment planning. IV. Derivation of a mathematical expression for the per cent depth dose surface of cobalt 60 beams and visualisation of multiple field dose distributions, Brit. J. Radiol. 37 (1964) 544.

STERLING, T.D., PERRY, H. , WEINKAM, J.J. , Automation of radiation treatment planning. V. Calculation and visualization of the total treatment volume, Brit. J. Radiol. 38^ (1965) 906.

STERLING, T. D. , POLLACK, S. V. , Computers and the Life Sciences, Columbia Press, New York (in press).

STOVALL, M., SHALEK, R. J. , A study of the explicit distribution of radiation in interstitial implantations. I. A method of calculation with an automatic digital computer, Radiology 78 (1962) 950. 194 BIBLIOGRAPHY

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SUNDBOM, L. , ÂSARD, Р. E. , Tumor dose concept. Acta radiol. £ (New Series) (1965) 135.

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TSIEN, K.C. , The application of automatic computing machines to radiation treatment planning, Brit. J. Radiol. 2£ (1955) 432.

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TURNER, J.E. , JOHNSON, R.M. , WHITFIELD, S.M., A fast moving-field telecobalt tissue-dosage method for adding machine, tabulating machine, or electronic computer, Am. J. Roentgenol. 94 (1965) 865.

VAJDA, S., The Theory of Games and Linear Programming, Methuen and Co. Ltd. , London (1961).

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VAN DE GEIJN, J. , Dose distribution in moving beam cobalt 60 teletherapy: a generalized calculation method, Brit. J. Radiol. 36 (1963) 879.

VAN DE GEIJN, J., The computation of two and three dimensional dose distributions in cobalt 60 teletherapy, Brit. J. Radiol. 38 (1965) 369.

VAN DE GEIJN, J. , The construction of individualised intensity modifying filters in cobalt 60 teletherapy, Brit. J. Radiol. 38 (1965) 865.

WACHSMANN, F. , Definition des Begriffes "Relative Herdraumdosis" und Wert des Begriffes für die Beurteilung verschiedener Bestrahlungsmethoden, Strahlentherapie 93 (1954) 295.

WILSON, R. , CARRUTHERS, J. A., Measurement of bone-marrow dose in a human phantom for Co60 gamma- rays and low-energy X-rays, Hlth Phys. 7 (1962) 171.

WOOD, R. G., The computation of dose distributions in cobalt rotational therapy, Brit. J. Radiol. 35 (1962) 482.

WOODBURY, M. A. , SILER, W. , Factor analysis with missing data, Ann. N. Y. Acad. Sci. (in press). BIBLIOGRAPHY 195

WOODLEY, R.G. , BRONSTEIN, E.L. , LAUGHLIN, J. S. , Exit dosimeter for effective patient thickness. Radiology 74 (1960) 273.

YOUNG, M.E.J. , BATHO, H. F., Dose tables for linear radium sources calculated by an electronic computer, Brit. J. Radiol. 37 (1964) 38.

APPENDIX I

GLOSSARY

Computer

A machine which automatically carries out a calculation according to a predetermined design.

Digital computer

A computer which calculates by the usual arithmetic processes. It normally has the ability to carry out the four basic arithmetic actions of addition, subtraction, multiplication and division and is usually built for general purpose use.

Analogue computer

A machine which uses physical processes to represent mathematical operations. For example, since the voltage across a resistor is equal to the product of the current and the resistance, the product of Ax В can be computed by passing a current of A amps through a resistor of В ohms and measuring the voltage. Analogue computers are usually built for special purpose use.

Central processor

The basic unit of a digital computing installation, containing the arithmetic unit and a number store.

Peripherals

All units in a computing installation, other than the central processor.

Input peripherals

Machines which read data into a computer. They may be punched card readers, paper tape readers or, in some special cases, they may be analogue inputs which convert analogue information, e.g. the position of a knob, into its digital equivalent for processing.

Output peripherals

Machines which present the results of a calculation tothe operator. Digital outputs may be visual displays of numbers, character printers (electric typewriters) or line printers. Examples of analogue outputs are graph plotters and oscilloscope displays.

Backing store

Any storage machine attached to the central processor and used to hold blocks of information in excess of the capacity of the central processors fast store. These machines may be magnetic tape units, magnetic drum units, or magnetic card files. All such devices are capable of holding a large amount of information and of transferring it to the central processor more quickly than it could be obtained via an input peripheral. They can similarly receive the results of calculations and hold them for output at a later time.

On-line equipment

Any peripheral machine which is connected directly to and is controlled directly by the central processor.

197 198 GLOSSARY

Off-line equipment

Any peripheral machine which is not on-line. For instance, a graph plotter is a slow output machine, consequently it is usually operated off-line with its own magnetic tape input to save computer time.

Time-sharing

A method of using some very fast computers to work on more than one problem at one time. Peripherals work more slowly than the central processor and to permit the latter to work at full speed it can work on one problem while the data for another problem are being transferred from a peripheral unit.

Programme

A series of instructions to the computer which enables it to perform a desired task. Programmes are extremely detailed and must be correct in every detail before the computer will operate satisfactorily.

Error stop

A halt in calculation where the computer prints out a diagnostic message if an error has been recognized. Error stops must be built into each programme and, therefore, a computer can recognize only those errors which the programmer anticipates. For example, it is common practice for the computer to edit input data and halt if the data do not fall within the permitted range of values.

Language

The list of permissible programme instructions for a particular computer. Some computers can be in- structed in several different languages. Some languages can be used to instruct several different computers.

Machine language

The basic language ot a computer. It usually takes the form of a number code for each specific instruction possible on the computer.. Rarely, if ever, do two computers have identical machine codes.

Source language

Any language used to instruct a computer other than the machine language for that computer.

Source programme

A programme written in a source language. Such programmes are translated into their machine code equivalent by the computer.

Object programme

The machine language programme which results when a computer translates a source programme. It is the object programme which the computer obeys.

Symbolic language

A language in which the basic actions of the computer are defined in simple instructions involving symbols rather than machine language instructions. APPENDIX I 199

Symbolic assembler

A special programme written for a specific computer which translates a source programme in a symbolic language to a machine language programme for that computer.

Algebraic language

A highly sophisticated language in which the programme is written in readable English. It has the facility of accepting large algebraic expressions in a notation which is not very different from standard mathematical notation. Examples are Algol and Fortran'. These languages are available for most modern computers regardless of manufacturer.

Algebraic compiler

A special programme written for a specific computer which translates a source programme in an algebraic language into a machine language programme for that computer.

Algorism

A series of. mathematical statements or expressions which defines the method of calculating some desired quantity from available data.

Documentation

A collection of all the information necessary to understand what a programme does, how it does it, and how to use it.

Flow chart

A block diagram showing the major sections of a programme and the connections between them. The function of each section is shown and information about the flow and storage of data is given. The flow chart is a part of documentation.

Programme write-up

(1) A description of the function of each part of the programme. This is important since programmes are intricate and many subtle devices may be used by experienced programmers to make the programme run faster or use less storage. The more complicated a programme is the more necessary it is that its contents be explained in detail so that someone less familiar with it than the original programmer can make alterations or corrections at a later date. (2) The requirements of the programme in terms of machine storage and peripheral equipment are listed. (3) Information concerning input data is given, including permitted range of values, format, and instructions for preparation. (4) Running instructions giving the order of data are provided with a list of any error stops which are contained in the programme and the action the operator should take if they occur. All of the above items are part of documentation.

System

A programme which controls other programmes. In large computing installations, programmes and necessary data are assembled in machine storage before a computation begins. Furthermore many special purpose programmes use general purpose programmes for the more common tasks such as printing. A group of programmes and the data required for a calculation are brought together and controlled by a system. Many programmes written for large computers cannot be run outside a system.

Hardware

A general term for computing facilities provided by the manufacturer by means of electronic circuitry. 200 GLOSSARY

.*»'< >ttw;irc

A general term for computing facilities provided by the manufacturers (or other source) by means of special programmes or systems. Language assemblers and compilers are included in this class as well as libraries of programmes for general purposes. hi citrix

An array of numbers of two, or more, dimensions.

Veer or

A one-dimensional array of numbers.

Fixed point

When working in fixed point all numbers are regarded by the computer as having a decimal point in a fixed position, usually at the beginning or the end. That is to say, during any computation the programmer must take responsibility for the position of the decimal point and make allowance for the size of the numbers occurring in the processing.

Floating point

When working in floating point a computer'takes control of the size of the numbers it handles and the position of the decimal point. It does this by holding all numbers to a standard accuracy (fixed number of significant digits) and associated with each a scaling factor which gives the position of the decimal point. Normally all languages otherthan machine language work in floating point and unless SDecial hardware facilities are available a programme in such a language will run more slowly than a programme written in machine language for the same purpose. APPENDIX III

QUESTIONNAIRE ON USE OF COMPUTERS FOR CALCULATION OF DOSE DISTRIBUTIONS IN RADIOTHERAPY

Following the panel meeting all members were asked to complete a questionnaire in order to collect facts and figures which would give a clear picture of the use of computers in their institutions. The questionnaire is reproduced here. Thirteen participants are currently using computers and their collective answers are given in the questionnaire, with the exception of the answers concerning costs, which are shown in Tables I and II (see section 2). On the basis of the response to the questionnaire, the activities at these institutions have been summarized in a series of brief "profiles". While every effort has been made to maintain accuracy, it should be pointed out that the "profiles" were prepared by the Scientific Secretaries and have not been submitted to the respective members for approval.

SUMMARY OF THE QUESTIONNAIRE ON USE OF COMPUTERS FOR CALCULATION OF DOSE DISTRIBUTIONS IN RADIOTHERAPY

PART 1 GENERAL

13 1. Name of hospital or institute

2. Name of radiotherapist

physicist "

computer specialist answering

this questionnaire

3. Manufacturer and model of computer .IBM. .1.401(4).;, . IBM . 7094.(3);. .IBM 7040. . IBM . .1620 ;.

CDC 160 A; CDС .1604;.. ICT. Sirius;.. .Regneçentralen - GIER;.. Saab. _D-21;.Siemens 2002 (2).,.

Elliott. 803

4. Who owns or leases the computer?

The hospital A

A closely associated institute Л

An outside scientific institute Л

An outside commercial organization

5. How far away from the radiotherapy department is the computer located: 8 computers

6. Do you have "on-line" facilities

7. In which branches of radiotherapy have you used a computer! 13 Teletherapy

Seed implants 3

Needle implants 3

Cervix applications

If your work has involved more than one of the above, please indicate where the emphasis has fallen Yes, 8 out of 13, breakdown: Teletherapy 5; Seed 1; Needle 1; Cervix 1.

201 202 QUESTIONNAIRE

Seed Needle Cervix Teletherapy implants implants applications

8. TIME. How long does it take:

(1) To compute a dose distribution

in a single plane! Summarized I (ii) To print out the results ! in Tables I and И

(iii) To put the results in a form

suitable for evaluation (e. g. plotting

of isodose curves) if the first print-out,

(ii), is not already in that form!

(See also questions 20 and 22)

9. MONEY. What is the cost of

computing a dose distribution in a

single plane!

If possible, please break down this

figure into cost of:

(i) preparing data (e. g. punching)

(ii) computer time

(iii) print-out

(iv) further work after print-out

(v) other (specify)

Do the above costs depend on the number of plans

computed in a batch! Yes Yes Yes Yes No No No No

10. VALUE FOR MONEY. What is included

in the single plane distribution referred

to in (8) and (9) above!

(i) multiple-field distribution-

how many fields? 3,3,3,4,4, 5,6,36,72,

72, no limit APPENDIX II 203

Seed Needle Teletherapy implants implants

(ii) moving-beam distribution . Yes 10 No 2

(iii) number of computed points 196 1500 250 (2)

300

470

541

600

850

50-1000

1080

6-10 000

(iv) correction for body curvature Yes 9 No 3

(v) correction for body inhomogeneity Yes 1 No 11

(vi) correction for tissue absorption ... Yes 2 Yes 2 No 0 No 0

(vii) correction for oblique filtration ... Yes 1 No 1

(viii) full plotting of isodose curves Yes 4 Yes 0 Yes 1 No 8 No 2 No 1

(ix) other (specify)

11. How many planes are normally

computed per patient or treatment

plan ! 1(6)

1-2 2(2)

1-3 (2)

3 204 QUESTIONNAIRE

PART 2 TELETHERAPY

12. When did you start to use a computer for calculating dose distributions in teletherapy? ДЯ®Д» 1959 (2), 1960 (2), 1962 (2). 1963 (2), 1964, 1965 (2)

13. When did you start to use your present computer facilities for this purpose! J??9i Л?Й Jt?) i A®.®A (?).• 1965 (5)

14. For what purpose have you used the computer: g

(i) for treatment planning of individual patients

(ii) for fundamental investigations (analysis of parameters, optimization, etc.)

(iii) for production of a collection or atlas of dose distributions . ?

(iv) other (specify) . ?

Please indicate where the main emphasis has fallen if your work has involved more than one of the above 5 Щ 5 Í3' 3 <431 (some checked mote than one)

Questions 15-20 apply only if you are using the computer for treatment planning of individual

patients.

15. Do you use the computer for treatment planning routinely or only occasionally? ,9í"s.i?P?í1.X,:. .3 i Routinely: 6

16. Please state: approx. total number of teletherapy patients planned In past 12 months

approx. number of those planned by computer

(For this purpose teletherapy includes orthovoltage X-rays, supervoltage X-rays and gamma-ray beam

units but excludes superficial X-rays.)

Total Computer Computed m 1200 10 1

400 10 3 450 50 11

500 100 20

650 150 23 200 70 35 800 300 38

240 240 100 APPENDIX II 205

State radiation type(s) or energies for which computer planning is used ?.°.ЬЛ1Г.®°. . Í.^.Y .Х.~г.аУ.\

For each patient the radiotherapist presumably specifies the dose required, and where. In addition, does the radiotherapist usually:

(i) specify in advance the precise values of the physical parameters (field size, angulation, etc.)

he requires; Л

(ii) specify an approximate range of values! . ?

(iii) leave these details entirely to the physicist or computer specialist ! . ?

What is the process whereby the radiotherapist selects the final plan for the patient!

(i) Does he receive one plan which Is either accepted or sent back for modification! A

If the latter, does this modification process normally go beyond the second or third calculation! Yes 1; no 5

(ii) Does he receive a number of alternative plans! A

If so, are these plans complete dose distributions or rough (approximate) distributions; Complete? 3; Rough: 0

2 3-4 2-3

Also, how many alternative plans for an average patient 1 ..'....:

(iii) Is the selection process carried out entirely by the physicist or computer specialist !

If so, please supply additional information as in (ii) above

(iv) Is there some other process of selection, such as computer optimization by "score functions" ?..

(please specify)

How long does it take to give the radiotherapist a treatment plan after he has requested it ! . J.1?.'?* 1 d (6), 2-3 d (2), 7 d max.

If a modification process, as in 19(i), is carried out, how much further time does this involve! 5 min, 2 h, 1 d (4), 2-3d, 7 d max. 206 QUESTIONNAIRE

PART 3 INTERSTITIAL AND INTRACAVITARY THERAPY

(Four answered as routine plus one in develop- Seed Needle Cervix implants implants applications ment stage)

21. For what purpose do you use the computer?

0) 1 2 2

(ü) for investigation of dosage systems and rules 2 2 2

(iii) for producing a collection or atlas of dose

1 2

(iv) other (specify) 1

If more than one of the above applies, please indicate

(2).(2),(2) (1) (1)

22. If you use the computer for dosage control after

insertion of sources:

(i) Approx. number of patients for which such calculations have been made in past 12 months 10 10 40 45 250

(U) Approx. percentage represented by (i) of all patients receiving treatment of same type in

25% 100% 100%

95% 95%

(Ш) How long after insertion of sources does the radiotherapist receive the dose distributions? 2-7 d 2 d 2 d 1 d 1 d

Yes 1 Yes 0 Yes 0

No 1 No 2 No 2

(iv) Is the "stated dose" calculated from the computed

dose distribution, or according to a recognized Computer 2 Computer 1 Computer 1

System 0 System 0 System 0

(v) In approx. what percentage of cases is the geometry of the source arrangement modified 33% low

low APPENDIX II 207

Seed Needle Cervix implants implants applications

(vi) If you use afterloading technique, are the

computer calculations available before the Yes 0 Yes 0

No 2 No 2

PART 4 POSTSCRIPT

23. Please add any other relevant information or comments (apart from cursing the whole of this

questionnaire! )

il. Joannes de Deo Hospital, The Hague, Netherlands

(J. van de Geijn)

In 1963 this institution began development of a versatile computing system to be used by several independent hospitals on a co-operative basis. The system will be in routine use in the near future and will provide these hospitals with large-scale computing facilities which can be used for fundamental investigations in teletherapy dosimetry as well as treatment planning of individual patients. The machine in use is an IBM 7094, located at an outside commercial organization. The costs for distributions in a single plane are approximately $1.40 for four fixed-fields and $4.00 for 360° rotation.

Temple University Hospital, Philadelphia, Pennsylvania, USA

(К. C. Tsien)

Computers are being used for fundamental investigations of parameters and the production of atlases of isodose curves for fixed field and moving beam teletherapy. Treatment planning of individual patients by computer is not routine at this institution. The machines used are an IBM 1401 and IBM 1620, located at the university, and are available to the hospital free of charge.

University of Cincinnati, Cincinnati, Ohio, USA

(T. Sterling, H. Perry)

This institution has been using a computer since 1958 for calculation of teletherapy treatment plans. During the last year 240 patients received teletherapy and individual dose distributions for all of these patients were calculated by computer. In most cases, two or three alternate plans are presented to the radiotherapist, from which he selects one as the actual treatment guide. In addition to treatment planning of individual patients, the computer has been used in fundamental investigations of physical and geometric parameters. The machine being used currently is an IBM 7040 with IBM 1401 input-output and is adjacent to the hospital; with these facilities a fixed field dose distribution in a single plane can be computed in 30 seconds at a cost of approximately $5. 00. 208 QUESTIONNAIRE

Memorial Hospital, New York, USA

(W. Siler)*

Beginning in 1959, this institution has used a computer for dosimetry calculations in three areas: teletherapy, interstitial seed and needle implants, and cervix applications. The machine used at this time is a CDC 160 A and is located in the hospital. In teletherapy the emphasis has been on the systematic study of physical parameters. Individual planning by computer is routine for patients receiving cobalt-60 teletherapy; of 500 patients receiving all forms of teletherapy last year, 100 were planned using a computer. Costs for teletherapy computations in a single plane vary widely from $7 to 100, depending upon whether corrections are made for body curvature and tissue inhomogeneity. The dosimetry of seed implants has involved the study of systems and rules for implantation, while the approach to needle and cervix implants has been to provide individual dose distributions. During the past year, distributions were calculated by machine fór all patients receiving needle and cervix implants. The cost of computing a dose distribution in a single plane is approximately $8 for interstitial or intracavitary sources.

University of Texas M. D. Anderson Hospital, Houston, USA

(R.J. Shalek)

A computer has been used since 1960 for dosimetry of interstitial and intracavitary implants. The principal use has been for dosage control after insertion of sources, but a computer has also been used to investigate dosage systems and to produce an atlas of isodose curves. Isodose curves are drawn automatically by an off- line incremental plotter. Individual distributions are computed routinely for all patients receiving interstitial and intracavitary therapy. The cost of computing isodose curves in a single plane is approximately $5, if paid for on a commercial basis. A programme for computation of teletherapy distributions is being developed but is not yet in routine use. The present machine is an IBM 7094 and is located at a closely associated institute, adjacent to the hospital.

Stâdt. Auguste-Viktoria-Kiankenhaus, Berlin, Federal Republic of Germany

(C. Schoknecht)

A computer has been used for teletherapy dosimetry calculations since 1963. Studies using the computer include treatment planning of individual patients, fundamental investigations, and production of an atlas of isodose curves, with emphasis on the first. Last year computer calculations were done for 150 teletherapy patients out of a total of 650. For standard treatment conditions, the radiotherapist is given one treatment plan, which he accepts or rejects. Alternate plans (as many as 10) are computed when using new treatment techniques. The cost of computing the distribution in a single plane is approximately $1.15. The machines currently in use are a Siemens 2002, at an outside scientific institute, and an IBM 1401, at an outside commercial organization.

* Now at Downstate Medical Center, Brooklyn, New York, USA. APPENDIX II 209

Sahlgrenska Sjukhuset, Gothenburg, Sweden

(I. Ragnhult)

In 1962 a project was initiated to calculate teletherapy dose distributions with inclusion of integral doses and integral dose efficiency factors. Calculation of distributions for individual patients was routine until 12 months ago, when a new computer was installed. Development of the new programme will be completed in the near future and treatment planning will be routine again. Costs for distributions in a single plane are approximately $13 for a fixed-field arrangement and $20 for rotation therapy. The computer, a SAAB D-21, is located at the university, adjacent to the hospital.

Christie Hospital, Manchester, UK

(W.J. Meredith)

In 1960 this institution began using a computer to calculate dose distributions in moving beam teletherapy. A series of standard treatment plans were produced to form an atlas of dose distributions, in addition to treatment plans for individual patients. Since moving beam techniques are used for relatively few patients in this hospital, computer calculations have not been used to a large extent. An IBM 1401 is located at a closely associated institute and available free of charge to the hospital.

Radiumstatjonen, Arhus Kommunehospital, Denmark

(O. Kalnaes)

Since the beginning of 1965 this institution has used a computer to calculate dose distributions for fixed- field teletherapy. Individual dose distributions are calculated routinely for all treatments using three or more fields; last year 50 treatments were planned by computer, out of a total of 450 patients receiving teletherapy. Usually, two alternate plans are computed for each patient and the radiotherapist selects one as the treatment guide. Costs for distribution in one plane vary depending upon the corrections employed: $3 with no corrections, $7 with correction for body curvature, and $14 with corrections for curvature and tissue inhomogeneity. For development of programmes, a Regnecentralen GIER is used, located at an outside scientific institute ; routine work is done on a computer of the same model owned by an outside commercial organization.

Regional Physics Department, Western Infirmary, Glasgow, UK

(C.S. Hope)

This institution has used a computer since 1960 for calculation of dose distributions for teletherapy and cervical implants. The computer now in use is an I. С. T. Sirius, located at an outside commercial organization. In teletherapy dosimetry, a computer has been used for fundamental investigations, individual treatment planning, and production of an atlas of isodose curves. The emphasis has been on computer optimization by "score functions", although this is not in routine use at this time. Individual treatment planning by computer is routine and was done for 300 patients out of 800 last year. The cost of a teletherapy dose distribution in a single plane is approximately $6. In intracavitary dosimetry, the principal use has been to investigate dosage systems and rules for implantation , with a systemic collection of isodose curves for various treatment conditions. The computer has 210 QUESTIONNAIRE not been used for individual dosage control after insertion of sources. The cost of an intracavitary dose distribution in a single plane is $28.

Ontario Cancer Institute, Toronto, Canada

(J. R. Cunningham)

Since 1959 a computer has been used for teletherapy and interstitial implant dosimetry. The computer being used is an IBM "7094, located at the university. Costs are difficult to state since charges are not based on amount of time used. Teletherapy calculations have resulted in the analysis of primary and scattering radiation, isodose curves for an atlas of moving beam distributions, and depth dose data for special treatment techniques. The computer is used infrequently for treatment planning of individual patients. In the area of interstitial dosimetry, basic data have been collected in preparation for an atlas of dose distributions. Computations are not made for dosage control of individual implants.

University College Hospital, London, UK

(J. .4. Clifton, E. W. Emery)

In 1962 this institution began using a computer for fixed-field teletherapy dosimetry; programmes for the computation of interstitial and intracavitary dose distributions are under development. The machine used currently is an Elliott 803, located at an outside commercial organization which is adjacent to the hospital. Teletherapy planning of individual patients by computer is routine, with 70 out of 200 patients being planned last year. The radiotherapist is given a single plan which he either'accepts or returns for modification. Other teletherapy work includes collection of data for an atlas of dose distributions and computation of tables of treatment times for standard techniques. Cost for calculation of a dose distribution in a single plane is $12.

Klinisches Strahleninstitut der Universitât Freiburg, Federal Republic of Germany

(M. Busch)

Since 1964 a computer has been used for teletherapy treatment planning and investigation of a dosage system for interstitial seed implants. In teletherapy, physical parameters which produce optimal dose distributions have been determined for the irradiation of several sites; these data have been used to compile an atlas of dose distributions. The purpose of the dosage system for seed implants is to provide rules for the implantation of sources and to serve as a guide to the dosage delivered by an implant. The programme makes allowance for tissue absorption. The machine is rarely used for computation of distributions for individual patients receiving teletherapy or interstitial implants. The computer is a Siemens 2002, located at an outside scientific institute. Computer time is available to the hospital free of charge. APPENDIX III

INSTITUTIONS USING COMPUTERS FOR DOSIMETRIC CALCULATIONS IN RADIOTHERAPY

The following is a list of institutions known to have used computers in radiotherapeutic dosimetry and, in most cases, this work has been reported in the literature. The list is probably incomplete; omission implies only that the work of an institution in this field has not been brought to the Agency's attention. The individual listed with each institution is the person who should be contacted for information regarding the current use of computers at that hospital; he may or may not be the principal investigator concerned with this project.

Canada

Ontario Cancer Institute, 500 Sherbourne Street, Toronto 5, Ont. Physicist: J.R. Cunningham

British Columbia Cancer Institute, 2656 Heather Street, Vancouver 9, В. C. Physicist: H. F. Batho

Federal Republic of Germany

August-Viktoria Krankenhaus, Rubenstrasse 125, Berlin-Schoneberg Physicist: G. Schoknecht

Abteilung fur Rontgen-Radium-Therapie der Medizinischen Universitátsklinik, Freiburg, Brsg. Radiotherapist: M. Busch

Strahlenabteilung der Universitats-Frauenklinik, Güttingen Physicist: U. Rosenow

German Democratic Republic

Robert-ROssle-Klinik der Deutschen Akademie der Wissenschaften zu Berlin, Berlin-Buch Physicist: J. Richter

Netherlands

H. Joannes de Deo Hospital, Westeinde, The Hague Physicist: J. van de Geijn

Sweden

Radiophysics Institute, University of Gothenburg, Sahlgrenska Sjukhuset, Gothenburg .Physicist: I. Ragnhult

United Kingdom

Cardiff Radiotherapy Centre, Whitchurch, Cardiff Physicist: R.G. Wood

211 212 INSTITUTIONS USING COMPUTERS

Regional Physics Department, 9-13 West Graham Street, Glasgow, C. 4 Physicist: C. S. Hope

University College Hospital, Gower Street, London, W.C.I Physicist: J.S. Clifton

Christie Hospital and Holt Radium Institute, Withington, Manchester 20 Physicist: W.J. Meredith

Wessex Radiotherapy Unit, Royal South Hants Hospital, Southampton Physicist: P. G. Orchard

Institute ot Cancer Research, Royal Cancer Hospital, Belmont, Sutton, Surrey Physicist: R. E. Bentley

United States ot America

Massachusetts General Hospital, Boston 14, Mass. Computer Specialist: S. Lorch

Downstate Medical Center, 450 Clarkson Avenue, Brooklyn 3, N. Y. Physicist: W. Siler

Veterans Administration Research Hospital and Northwestern University Medical School, Chicago, 111. Physicist: R.M. Johnson

University of Cincinnati, College of Medicine, Eden and Bethesda Avenues, Cincinnati, Ohio 45219 Computer Specialist: T.D. Sterling

Penrose Cancer Hospital, Colorado Springs, Colorado Physicist: R. Perez-Tamayo

University of Colorado Medical Center, Denver, Colorado Radiotherapist: C.V. Dalrymple

University of Florida, Gainesville, Florida Physicist: W. Mauderli

Baylor University College of Medicine, Houston, Texas Radiotherapist: V.P. Collins

University of Texas M. D. Anderson Hospital and Tumor Institute, Houston, Texas 77025 Physicist: R.J. Shalek

Memorial Sloan- Kettering Cancer Center, New York, New York, 10021 Physicist: J.S. Laughlin

Temple University Medical School and Hospital, Philadelphia, Pennsylvania 19140 Physicist: К. C. Tsien

University of California School or" Medicine, San Francisco, California Physicist: R. Worsnop

Washington University School of Medicine and the Computer Center, St. Louis, Missouri Radiotherapist: W.E. Powers LIST OF PARTICIPANTS

PANEL MEMBERS

Meredith, W.J. (Chairman) Physics Department Christie Hospital and Holt Radium Institute Withington, Manchester 20 United Kingdom

Busch, M. Abteilung für Rôntgen-Radium-Therapie , der Medizinischen Universitâtsklinik Freiburg/Brsg. Federal Republic of Germany

Clifton, J.S. Department of Medical Physics University College Hospital Gower Street, London, W.C.I United Kingdom

Cunningham, J. R. Physics Division Ontario Cancer Institute 500 Sherbourne Street, Toronto 5 Canada

Dutreix, Mrs. A. Unité de Radiophysique Institut Gustave-Roussy Ville juif (Seine) France

Emery, E.W. Radiotherapy Department University College Hospital Gower Street, London, W.C.I United Kingdom

Van de Geijn, J. Rônt genaf deling Ziekenhuis van de H. Joannes de Deo Westeinde, The Hague Netherlands

Hope, C.S. Regional Physics Department 9-13 West Graham Street Glasgow, C.4, United Kingdom

Perry, H. University of Cincinnati Eden and Bethesda Avenues Cincinnati, Ohio 45219 United States of America •

213 214 LIST OF PARTICIPANTS

Ragnhult, Mrs. I. Radiophysics Laboratory Sahlgrenska Sjukhuset Gothenburg SV Sweden

Schoknecht, G. Strahlenabteilung Stâdt. Auguste -Viktoria Krankenhaus Rubensstrasse 125, Berlin 41 Federal Republic of Germany

Shalek, R.J. * Physics Department University of Texas M.D. Anderson Hospital and Tumor Institute Texas Medical Center Houston, Texas 77025 United States of America

Siler, W. Computing Center Downstate Medical Center 450 Clarkson Avenue Brooklyn 3, New York United States of America

Sterling, T.D. Computing Center University of Cincinnati Eden and Bethesda Avenues Cincinnati, Ohio 45219 United States of America

Tsien, К. C. Department of Radiology Temple University School of Medicine and Hospital 3401 North Broad Street Philadelphia, Pa. 19140 United States of America

OBSERVER

Kalnaes, O. Radiophysics Laboratory Radiumstationen Arhus Denmark

* Did not attend meeting but submitted working paper and other documents. 215 LIST OF PARTICIPANTS

Representatives of the World Organization

Nickson, J.J. Department of Radiotherapy Michael Reese Hospital Chicago, 111. United States of America

Parker, H. G. Radiation and Isotopes World Health Organization Geneva Switzerland

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