DEVELOPMENT OF ISODOSE CURVES FOR A 6 MV X-RAY BEAM
SD9800030
A THESIS SUBMITTED IN PARTIAL FULFILMENT FOR THE DEGREE OF MASTER OF SCIENCE IN PHYSICS
LAMYA ABBAS HIDAYTALLA
DEPARTMENT OF PHYSICS FACULTY OF SCIENCE UNIVERSITY OF KHARTOUM AUGUST 1994 29-52 We regret that some of the pages in this report may not be up to the proper legibility standards, even though the best possible copy was used for scanning (JJedicated to my (parents ABSTRACT
DEVELOPMENT OF FSODOSE CURVES FOR A 6 MV X-RAYBEAM
M.Sc. 1994 by LAMYA ABBAS HIDAYTALLA
In this thesis radiation distribution of 6 Mv X-ray beam in a water phantom is developed. The method is based on a simple empirical equation and the assumption that the X-ray source is a point source. This leads to a simple equation for the calculation and plotting of the isodose curves. The charts obtained for two fields, 6*6 and 12*12 cm show good agreement with the previous data used in the Isotope and Radiation Centre, Khartoum Hospital. It is suggested that further development should be carried out by writing a computer program for all the fields.
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ACKNOWLEDGEMENTS 5
TABLE OF CONTENTS 6
CHAPTER 1 9
INTRODUCTION 9
CHAPTER IL 10
II. I INTRODUCTION: 10 . II 2 Tin: PHYSICS Or X-RAYS: 10 11.2.a Production of X-rays: 10 11.2. b Interaction of X-rays with Matter: 10 II-Л UNITS AND DEFINITIONS: 14 П.За Radiation Quantities and Units: 14 11.3b Absorbed Dose Calculations: 15 ll.i.c Depth Dose Distribution: 15 CHAPTER III 20
CLINICAL USES OF X-RAYS 20
HI. I CONTACT THERAPY: 20 HI.2 ORTHOVOLTAOE THERAPY OR "DEEP THERAPY": 20 III.3 St TER VOLTAGE THERAPY: , 20 HI.4 MEGAVOI.TAGF. THERAPY 21 III.5 COBALT-60 UNIT: 23 CHAPTER IV 25
RADIATION DETECTORS AND EXPOSURE MEASUREMENTS 25
IV. 1 RADIATION DETECTORS: 25 IV. la Calonmetric: 25 IV l.b Chemical: 25 IVl.c Solid State Methods: 26 IV. 1 d Gas-Filled Detectors: 29 IV 2 EXPOSUREMEASUREMENTS: 31 IV. 2a Free-Air lomzation Chamber: 31 IV2.b Thimble Chambers: : 33 IV.2.с Practical Thimble Chambers: 55 IV. 2.d Electrometers: 37 CHAPTER V 39
EXPERIMENTAL SET UP AND HANDLING TECHNIQUE 39
V.I ENVIRONMENTAL CONDITIONS: 39 V.2 MEASUREMENT OF EXPOSURE.: 39 V.3 PHANTOMS: 40 V.4 MEASUREMENT OF ISODOSE CURVES: 40 V.5 PARAMETERS OF ISODOSE CURVES: 41 V.5.a Beam Quality: j, 41 V.5.b Source Size, SSD. andSDD-the Penumbra Effect: 42 V.5.с Collimation and Flattening: 42 V.S.d Field Size: 42 V.6 DA гл НАМИ ING- 4 Л CHAPTER VI 45
RESULTS AND DISCUSSIONS 45
VI 1 PKRCENTAGE CENTRAL AXIS DEPTH DOSE: 45 VI.2 PROFILES: 45 VI.3THEISODOSECIRVES: 49 CHAPTER VII 69
CONCLUSIONS AND SUGGESTIONS 69
APPENDIX „ 70
I. COMHTER PROGRAM LISTING .- 70 II. COMPUTER PROGRAM OITPIT 70 REFERENCES 73 Table Of Tables
TABIFI 46 T-\HLI: 2 47 TABLE 3 48 TAHI.K4 49 TABI.K5 50 TABLE 6 51 TABLE 7 52 TABLES 53 TABLE 9 -. 54 CHAPTER I
INTRODUCTION
In the 1950's the 4 MeV accelerators had proved to be reliable sources of high energy photons In order to provide for increase X-ray output, coupled with increased penetration, accelerators of high energies had been developed and the next decade saw a proliferation of both 6 MeV and 8 MeV accelerators in X-ray radiotherapy. X-rays in the range 6-25 MV are now of great use in radiotherapy. Since then comprehensive set of data, for this range, have been reported in several centers. Supplements were prepared by working parties setup by these centers. These sets include tables of doses for various depths, in particular the central axis depth dose data. These data, after comparing them with other centers, had been of value in clinical purpose (British Journal of Radiology, Supplement No 11, London, 1978). Tables of 6 MV depth doses, measured in water phantom, at 100 cm SSD have been reported by three British Centers ( Clatter Bridge, Cambridge and Queen Elizabeth Hospital ) and from other three overseas users of Varian "Clinic 6". From these data, cross plots of percentage isodose versus side length of the square field where made. Smooth curves were drawn to average the data at each depth. Since then a steady progress in developing the representation of these data was reported. It introduces the isodose curves to represent volumetric or planar variation in absorbed dose distributions. Then lines passing through points of equal % dose at regular intervals of absorbed dose, are expressed as percentage of the dose at a reference point. Correct placement of radiation fields relative to the patient anatomy is essential in radiotherapy in order to minimize serious side effects and to reduce the probability of recurrence of the tumors. In treatment planning, the position of the isodose lines is used to establish field sizes in order to verify the adequate dose area to be covered by the target. The initiative of this work is that it has bee-o reported by the Isotope and Radiation Center, Khartoum Hospital that the computerized machine used for the development of isodose curves and patient treatment planning'*?» faulty. Therefore it'-j<« necessary to develop a quick and reliable method for developing these curves. On the basis of this requirement, this work-<* carried out. CHAPTER II Th e©ГОДДСАЬ tWX H.I Introduction:
In this chapter the physics of X-rays is briefly reviewed. Namely the production of X-ray how they interact with matter and the units and definitions are given. Further the absorbed dose is defined as well as the distribution of this dose.
П.2 The Physics Of X-rays:
X-rays constitute part of the electromagnetic spectrum. They have wavelengths in the range of 0.005-1.0 nm (Nicholas Tsoulfanidis 1983).These short wavelengths are comparable to the interatomic distances and that is why X-rays are used in imaging techniques.
II.2.a Production of X-rays:
The conventional X-ray tube consists of a glass envelope which has been evacuated. Inside this tube a filament that emits electrons, when heated, forms the cathode. A thick rod at the end of which is placed a piece of target, forms the anode. When a high positive potential is applied to the anode, the electrons are emitted from the filament and are accelerated to the anode. The X-rays are produced by a sudden deflection or deceleration of the electrons when impinging the metal target. There are two mechanisms by which X-rays are produced. One mechanism gives rise to Bremsstrahlung X-rays (braking radiation) and the other to characteristic X-rays. The process of Bremsstrahlung is the result of interaction between a high speed electron and a nucleus field, where part or all of the electron kinetic energy is lost and propagated in space as electromagnetic radiation. Whereas in characteristic X-rays an incident electron with kinetic energy E, may interact with the atoms of the target ejecting an inner shell electron. Ал outer electron will fill the vacancy created .by the ejected electron, thus radiating energy in the form of electromagnetic radiation, which is called characteristic radiation.
The photon emitted will have energy hv = E2 - Ei where E] and E2 are the electron binding energies of the filling and ejected electron respectively, v is the frequency and h is Planck's constant. Inner shells transitions in high atomic number targets will result in emission of more energetic characteristic radiation. Characteristic radiation have discrete energies unlike Bremsstrahlung (Faiz, 1984)
II.2.b Interaction of X-rays with Matter:
When an X or у ray beam passes through a medium, interaction between photons and matter can take place with the result that energy is transferred to the medium. This involves the ejection of electrons from the atomic orbits, producing ionization or excitations of the atoms along their paths.
10 X-rays interact with matter in three diflV . nt ways the photoelectric effect, the Compton effect, and the pair production.
i)The Photoelectric Effect:
The photoelectric effect is a process in which the entire energy ,hv,of the photon is transfered to the inner atomic electrons (K, L, M or N )shel!s.The electron is ejected with a kinetic energy equal to hv - E , where E is the binding energy of the electron The vacancy created can be filled by an outer orbital electron with the emission of characteristic X-rays or Auger electrons which are monoenergetic electrons produced by the absortion of characteristic X-rays internally by the atom. Fig. II 1
Auger Electron *
^ -*f< ЛЗД' i i x • * ;• *jy^~-«~——'-Photon (hv) V */ * # У у* * *> *
,/"•*"•"• ' Atom
Fig. 11.1 Illustration of the photoelectric effect
For low Z materials, the energy of this characteristic photons is very low and almost locally absorbed, since the K-shell binding energy is about 0.5 KeV(Faiz, 1984)/The probability of photoelectric absorption depends on the photon energy ,E,and it can be shown that the photon energy is related to the attenuation coefficient by (Faiz, 1984)
P E> Where t/p(cm /g) is the attenuation coefficient. The data for various materials indicate that photoelectric attenuation strongly depends on the atomic number,Z, of the absorbing material as in
— ocZ3 II.2 P
This relationship is the basis of many applications in diagnostic radiology.By , the above two equtions we have: x Z3 - ос -у П.З p E3
The angular distribution of electrons emitted in this process depends on the ' о photon energy. At low energies, the photon is emitted '"• 3t 90 relative to the
11 direction of incident photon. As the energy increases, the photoclectrons are emitted in a more forward direction.
ii) Compton Effect:
In Compton process,fig.H.2, the photon interacts with an atomic electron of low binding energy (i.e., free electron) in comparison with the bombarding photon The electron 'sfecodb at an angle 9. The photon, with reduced energy, is scattered at an angle ф.
ё (Co/Tipton electron)
"Free" Electron «^(incident photon)
4 f (#) * ^'(scattered photon)
Fig. 11.2 Diagram illustrating the Compton effect By applying the law of conservation of energy and momentum, the following relationship can be found (Faiz, 1984): q(l - cos
Ф 1 where cot в - (1 + a) tan — and hvo, hv and E are the energies of the incident о - о l photon, scattered photon, and electron, respectively, and a = hvo/m cf Where m z is the rest energy of electron (0.511 MeV). If the incident photon has much less energy than the rest energy of the electron, the Compton scattered photons will have approximately the same energy as the original photons, since they are a dependent.However, if the incident photon has a very high energy, the photon loses most of its energy to the Compton electron and the scattered photon has much less energy. For high energy photons with a » 1 and ф = 90 А к, hv'=—-=0.5\\Mev (for<)>=900) II.6 a
12 *i/' = —= 0.255Л/ег (Гогф=180°) Н.7 2а As the photon energy increases beyond the binding enery of the К electron, the photoelectric effect decreases rapidly and the Compton effect becomes more dominant Compton interaction is independent of atomic number Z, because it involves essentially free electrons, but it depends on the number of electrons per gram.All mater except hydrogen have approximately the same number of electrons per gram. It follows that if the energy of the beam is in the region where Compton effect is the possible mode of interaction, approximately the same attenuation of the beam will occur in any material of equal density thickness (Faiz, 1984).
iii)Pair Production:
If the energy of the photon is greater than 1.02 MeV, pair production mechanism may take place.The photon interacts with the electromagnetic field of an atomic nucleus and gives up all its energy in the process of creating a pair consisting of a negative and positive electrons (e and e ). This energy is the minimum one needed to create pair of electrons, since the rest mass energy of the electron is equivalent to 0.51 MeV. Although the nucleus does not undergo any change, the photon energy in excess is shared between the particles as kinetic energy. At most, each particle acquire half the available kinetic energy, although any other distribution is possible. The pair production is an exampleof an evenj in which energy is converted into mass, as predicted by Einstein's equation, E = me . Annihilation radiation is the reverse process, in which mass is converted into energy The positron created in pair production loses its energy as it traverses matter, by the same type of interactions as an electron does.by ionization,excitation and bremsstrahlung at the end of its range the positron combines with one of the free electrons to give rise to two annihilation photons each having 0.51 MeV.Since momentum is conserved,the two photons are ejected in opposite directions,fig.ll.3. ^-~#-^ ё (electron)
Mev f / /IN
Pho\on \
-#• *s
•*- ё (positron)
Fig. 11.3 Diagram illustrating the pair production process
Since pair production results from an interaction with electromagnetic field of the nucleus.the probability of pair production increases rapidly with atomic number.
13 II-3 Units and Definitions:
An X-ray or y-ray consists of a large number of photons, usually with a variety of energies. A beam of photons can be described by the following terms:
a) Fluence: The fluence, ф, of photons is the quotient ф = — 11.8 da Where dN is the number of photons which enter an imaginary sphere of cross-sectional area da. b) Fluence Rate or Flux Density: is the fluence per unit time &> = —-' H.9 dt c) Energy Fluence, W:
vi/ Q_ if i n da Where dEj] is the sum of the energies of all photons which enter a sphere of cross-sectional area da.
d) Energy Fluence Rate or Energy Flux Density or Intensity, щ: is V|/=— П.11
Н.З.а Radiation Quantities and Units:
Exposure (X) is a measure of ionization produced in air by photons and is defined as: X ^ 11.12 dm where dQ is the absolute value of the total charge of the ions of one signal produced in air ,when all the electrons, liberated by photons in air of mass dm are stopped in air. The unit of exposure is the Roentgen, R, and is equal to: R = 2.58X lO^C/Kgair.
The quantity absorbed dose has been defined as the quantity of radiation for all types of ionization radiation. This includes charged and uncharged particles, all materials and energies. Absorbed dose is the quotient dE/dm, where dE is the mean energy imparted by ionizing radiation to material of mass dm. ( Faiz , 1984). The Gray is the unit for absorbed dose and is given by: 1 Gray = 1 J/Kg The centGray (cGY), is often used. Other units are the dose equivalent, H, defined as : H=D.Q.N
14 where D is the absorbed dose, Q is a quality factor for the radiation and N is^ a product of all other modifying factors. Ihe dose equivalent \& measured in Sievert. SV, defined as: 1SV= U/Kg
Н.З.Ь Absorbed Dose Calculations:
Exposure and the energy absorbed in air, are related, under equilibrium conditions as follows: The mean energy required to produce an ion pair in air is almost constant for all electron energies and has a value of W.,, = 33.85eV/ion - pair (Faiz , 1984)
19 The electronic charge (e = 1.602 X 10"10'" C) then Wair / e is the average energy absorbed per unit charge of ionizationiz n produced. Since 1 eV= 1.6X 1019 JIthe thern
— = 33.35J/C
Thus the mean energy absorbed, d Ё, in producing a charge dQ in air of mass dm is given by
e dE dQ W ai П.14 dm dm e
i.e., absorbed dose in air Dail W
Dstr = X—— Where X is the exposure Since 1R = 2.58 * lO^ (~* I V ft / Kg) = X(R)*2.5S* 10-*(—r-^)*33.85(7/C) л
= 0.873 *10":(——£)*Х(Я) 11.15 R
Н.З.с Depth Dose Distribution:
As the beam is incident on a patient (or a phantom), the absorbed dose in the patient varies with depth. This variation depends on many parameters, e.g. beam energy, depth, field size, distance from the source and beam collimation system. It is essential to establish depth dose variation along the central axis of the beam, in the dose calculation system. Percentojdepth dose is one of the major
15 quantities which have been defined^for this purpose, some others are tissue-air ratio, tissue-phantom ratios arid tissue-maximum ratio.
Percentage Depth Dose: One way of characterizing the central axis dose distribution is to normalize dose at a depth with respect to dose at a reference depth. The quantity percentage depth dose, PDD, sometimes denoted by P, can be defined as the quotient of the
absorbed dose at any depth d to the absorbed dose at a fixed reference depth do, along the central axis of the beam ,fig II.4 Thus
P = -^-X100 11.16 D,
/\ i ! \
•7 %''''<•>. '•*•- Coifinator \ Central Ax»$ ,- -— Surface Щ D /T dO;; \ _„. Phantom • D . d •"•
Fig. 11.4 Percent Depth Dose
Usually, the surface (d0 = 0) is the reference depth for low energy X-rays and orthovoltage (up to about 400 kVp). For high energies the reference depth is taken at the position of the peak (maximum) absorbed dose (d0 = dm). There are a number of parameters affecting the central axis depth dose distribution viz.:
i) Dependence on beam quality and depth: High beam energies have greater penetrating power. Thus, the beam quality affects the percentage depth dose by virtue of an average attenuation coefficient (д . As |i decreases, the beam becomes more penetrating, resulting
16 in a higher percentage depth dose at any given depth beyond the build up region. i-1) Initial Dose Build-up: The percent depth dose decreases with depth beyond the depth of maximum dose. However, there is an initial build-up of dose as the energy increases till the reference point. The region between the surface and the point of maximum dose is called the dose build-up region. The physics of dose build-up may be explained as follows 1 As the high energy photon beam enters the patient or the phantom, high speed electrons are ejected from the surface and the subsequent layers. 2, These electrons deposit their energies a significant distance away from their site of origin. . Because of 1 and 2 above, the electron fluence and hence the absorbed dose increase with the depth till it reaches the maximum. However, the photon energy fluence decreases with depth, as a result, the production of secondary electrons also decreases with depth. A quantity known as kerma, К (Kinetic energy released in the medium) may be defined as (ICRU, 1980)
dm where dE^ is the sum of the initial kinetic energies of all charged ionizing particles (electrons) liberated by the uncharged ionizing particles (photons) in a material of mass dm. This quantity and the term absorbed dose, are used to explain the build-up phenomenon. Kerma has the same unit as dose, i.e., J/Kg which is also called Gray. Since kerma represents the energy transferred from photons to directly ionizing electrons, it is maximum at the surface and decreases with depth due to the decrease in the photon energy fluence, fig II.5. However, the dose reaches a maximum at a depth approximately equal to the range of electrons in the medium as it depends on the electron fluence. Beyond this depth, the dose decreases as kerma continuously decreases, resulting in a decrease of secondary electron production and hence a net decrease in electron fluence. ii) Effect of Field Size and Shape: Field size may be specified either geometrically or dosimetrically. The geometrical field size is defined (Faiz, 1984) as the projection on a plane perpendicular to the beam axis, of the distal end of the collimator as seen from the front center of the source. The dosimetric or the physical field size is the distance intercepted by a given isodose curve on a plane perpendicular to the beam axis at a stated distance from the source
17 For small field size, e g. 0*0 field, the scattered photon to the depth dose is negligibly small, and the depth dose at a point is effectively due to the primary radiation. As the field size increases, the scattered radiation to the
depth dose increases, at large depths than at the depth of Dmax. Hence, the percent depth dose at a specific depth increases with increasing field size. However, the scattering probability decreases with increased energy. This leads to the less pronounced dependence of the field size on the percent depth dose for higher energy beams.
OS £
о Dose о о
/ Buiid- up i о Reckon .
Depth
Fig. 11.5 Schematic plot of absorbed dose and kerma as functions of depth Percent depth dose data for radiotherapy beams are usually tabulated for square fields. A rectangular field may be approximated by an equivalent square or equivalent circle (Hospital Physicists Association, 1978), if they have the same area/perimeter (A/P). The following formulae are useful for quick calculations of the equivalent field parameters for a rectangular field A ab 7~2(a7b) where a is field width and b is the field length. For square fields, since
- A a. P "4 where a is the side of the square.
18 The A/P parameter, as such, does not apply to circular or irregular shaped fields. However, the radii ( r ) of equivalent circles may be obtained by the relationship 4 A
iii) Dependence on source-surface distance (SSD) Photon fluence emitted by a point source of radiation varies inversely as the square of the distance from the source (Faiz, 1984).The source is considered as a point (finite size) at large SSD, i.e. the source dimensions are unimportant in relation to the variation of photon fluence with distance. Thus, assuming primary beam ,the dose rate in free space from such a source .varies inversely as the square of the distance However, collimation or other scattering materials in the beam may cause deviation from the square law. Although the actual dose rate at a point decreases with increased distance from the source ,the percent depth dose (relative dose with respect to a reference point) increases with SSD fig II.6
20 40 60 SO .100 120 140 160 180 200 Distance From Source fig. II.6 Plot of relative dose rate as inverse square law function of distance from a point source. Reference distance - 80 cm The plot shows that the drop in dose rate between two points is much greater at smaller distances from the source than at large distances.
19 CHAPTER HI
Clinical Uses of X-rays
The X-ray therapy has been divided into subcateyorizes, on the basis of beam quality and their use. These are discussed briefly in the following sub-sections.
Ш.1 Contact Therapy:
A "contact" therapy machine operates at potentials of 40 - 50 kV and facilitates irradiation at a very short source (focal spot) to surface distance (SSD). It provides an SSD of 2.0 cm or less. The very low component of the energy spectrum is filtered, by using 0.5 to 1.0 mm thick aluminum filter, since it has a very low penetration. The contact therapy beam produces a very rapidly decreasing depth dose in a tissue, such that if the beam is incident on a patient, the skin surface is maximally irradiated and this is useful for tumors not deeper than 1-2 mm.
Ш.2 Orthovoltage Therapy or "Deep Therapy":
The deep therapy is used for treatment with X-rays produced at potentials ranging from 150 - 500 kV. A half-value layer between 1 - 4 mm Си can be achieved using applicators or added filters . An adjustable diaphragm, consisting of lead plates, permit adjusting field size, such that the SSD is usually set at 50 cm. The maximum dose occurs close to the skin surface, with 90% occurring at about 2 cm depth. By increasing beam filtration and combining two or more beams directed at the tumor from different directions, one can deliver higher dose to deeper tumors. There are several limitations to the use of orthovoltage beam. It is not advised to use it for lesions deeper than 2-3 cm., multiple beams and other techniques are used to keep the skin dose under tolerance limits, but the problem remained an overriding concern in the orthovoltage era. Also orthovoltage beams are unsuitable for the treatment of tumors behind or adjacent to bone, since for low energy beams, absorbed dose in bone is high due to high probability of photoelectic effect.
III.3 Super Voltage Therapy:
X-ray therapy in the range of 500 - 1000 V has been designated as supervoltage therapy. Insulation of the high voltage transformer has been the major problem, but the approach of a new design using resonant transformer solved It. All these previous applications are of an historic importance. Nowadays electron beams from linear accelerators (linacs) are widely used.
20 Ill A Megavoltage Therapy X-rays of energy I NfV or greater is classified as megavoltage beams AJso y- rays beams produced by radionuclides of energy greater than IMeV are also included in this category. The linear accelerator is an example of clinical megavoltage machines.
The Linear Accelerator:
The linear accelerator is a device designed with high frequency electromagnetic waves to accelerate charged particles such as electrons to high energies through a linear tube. This high energy electron beam can be used for treating superficial tumors or can be made to strike a target to produce X-rays for treating deep seated tumors. Radiotherapy accelerators use traveling or stationary electromagnetic waves of frequency in the microwave region ( ~ 3000 megacycle/seconds). The traveling wave structures require a terminating load in order to absorb residual power at the end of the structure, thus preventing a backward reflected wave. The standing wave structures provide maximum reflection of the waves at both ends of the forward and reverse waves giving rise to stationary waves; this design requires installation of a circulator between the power source and the structure to prevent reflection from reaching the power source (Karzmark et al, 1973).Fig.III.1. is a block diagram of a medical linear accelerator.
Accelerator Tube Electron I I I I.I I I I I Treatment Head Gun I 1 I II III I (Straight Beam) Wave Guide / System Bending Magnet
Magnetron Treatment Head Modulator or (Bent Beam) Klystron
Power Supply
Fig. 111.1 A block diagram of typical medical linear accelerator.
A power supply provides DC power to the modulator which includes the pulse forming network and a switching tube. The pulses are delivered to the magnetron and simultaneously to the electron gun. Microwave pulses produced in the magnetron are injected into the accelerator tube via a wave guide system. Electrons produced by an electron gun are also injected into the accelerator structure which consists of a highly evacuated copper tube with its interior divided by copper discs. The electrons with initial energy of about 50 KeV, interact with the electromagnetic field of the
21 microwaves, and gain energy from the sinusoidal electric field by an acceleration process. In the low energy linacs with relatively short accelerator tubes, the electrons are allowed to proceed straight on and strike a target for X-rays production. In the high energy linacs with long accelerator structure the electrons bend through a suitable angle between the accelerator structure and the target by placing the accelerator structure horizontally or at an angle with respect to the horizontal. This is accomplished by the beam transport system consisting of bending magnets, focusing coils and other components (Karzmark et al, 1973).
i) The Li пас X-ray Beam:
Usually linear accelerators have both electron and X-ray treatment capabilities up to the maximum energy of beam available The electron beam is almost monoenergetic before incidence on the patient surface, while the X-ray beam is heterogeneous in energy, and they are designated by million electron volts and megavolts respectively.
ii) Treatment Head:
The treatment head consists of a thick shell of high density shielding material, like lead or tungsten, against leakage'radiation in accordance with radiation protection guide lines. It contains an X-ray target, a scattering foil, a flattening filter, an ion chamber, fixed and movable collimators, and a light localizer system.
Hi) Target and Flattening Filter:
Since linear accelerators produce electrons in the megavoltage range, the X- ray intensity is peaked in the forward direction. A flattening filter made of lead, tungsten, uranium or other materia!s( Podgorsak et al, 1975 ) is inserted in the beam to make the beam intensity uniform across the field.
iv) Ream CoUimation:
The treatment beam is first collimated by a fixed primary collimator located immediately beyond the target or scattering foil. The collimated X-ray beam passes through the flattening filter. While in the electron mode the filter is moved out of the away. Then the beam is incident on the dose monitor chambers which monitor dose rate, integrated dose, and field symmetry. * The beam is further collimated by a movable X-ray collimator, which consists of two pairs of lead or tungsten blocks providing a rectangular opening from 0*0 to the maximum field size of about 40*40 cm2, projected at the standard distance such as 100 cm from the X-ray source. The field size is provided by light localizing system in the treatment head. Since electrons scatter readily in air, their collimation systems vary from those of X-ray mode, such that the beam collimation must be achieved close to the skin surface of the patient. The scattering of electrons from the collimator surfaces will
22 affect the dose rate by a factor of 2 or 3 as the collimator is opened to maximum field size . This problem has been solved by attaching an auxiliary collimator for electrons in the form of trimmers extended down to the skin surface. Fig. III.2 a,b show the components of the treatment head.
-Target Moved Aside .Target Scattering Foil
||LPrimary Fixed Collrmator Flattening Fitter Flattening Fitter Moved Aside •~—• Ion Chambers 'Zz ion Chambers — Movable CoWmator f~X-rey СоШта tor
i— Cone
Fig. 111.2 Components of treatment header, (a) X-ray therapy mode, (b) electron therapy mode.
V) Gantry: Linear accelerators are, nowadays, constructed so that the source of radiation can rotate about a horizontal axis. The collimator axis moves in a vertical plane, as the gantry rotates, its intersection with the axis of rotation of the gantry is known as the isocenter. Beams are directed from different directions but intersect at the same point, the isocenter, placed inside the patient. Non isocentric units are not flexible, although they are mechanically simpler, more reliable, and less expensive.
Ш.5 Cobalt-60 Unit:
Radionuclides such as radium -226, cesium -137 and cobalt -60 have been used as sources of y-rays in teletherapy . 60Co is the most suitable for external beam radiotherapy ,because it has gotten greater radiation output per Curie and higher average photon energy. The ft0Co is produced by irradiating ordinary stable "Co with neutrons in a reactor. The nuclear reaction can be represented by 59Co(n,y)60Co. The60Co source, usually in the form of solid cylinder, disc or pallets, is contained inside a stainless steel capsule and sealed by welding. This capsule is placed into another steel capsule which is again sealed by welding. The double welding is necessary to prevent any leakage of radioactive material. The 60Co source decays to 60Ni with the emission of P particles and two photons per disintegration (Faiz, 1984). The p particles are absorbed in the cobalt
23 metal and the stainless steel capsules resulting in the emission of bremsstrahlung X- rays and a small amount of characteristic X-rays. However these X-rays of energy around 0 1 MeV are strongly attenuated in the material of the source and the capsule. The primary у radiation may interact with the source, the surrounding capsule, the source housing, and the collimator system, producing lower energy у rays. Electrons may be produced during these interactions and constitute what is usually referred to as the electron contamination of the photon beam. The scattered components of the beam contribute significantly (10%) to the total intensity of the beam (Cormack et al, 1958). A typical teletherapy 60Co source is a cylinder of diameter ranging from 1.0 to 2.0 cm. and is positioned in the cobalt unit with its circular end facing the patient.
24 CHAPTER IV
RADIATION DETECTORS AND EXPOSURE MEASUREMENTS
IV. 1 Radiation Detectors:
The basic principle of detection is the conversion of the photon energy in the form of a measurable energy The following are the basic types of radiation detectors.
IV.la Calorimetric:
Calorimetry is a basic method of determing energy absorbed (absorbed dose) in a medium which appears as heat energy while a small fraction may appear in other forms of energy. The increase in temperature is related to the energy absorbed per unit mass. If a small volume of the medium is thermally isolated from the remainder, the absorcd dose (D) is given by
dEh dE, dm dm where dEh is the energy appearing as heat in the absorber of mass dm and dEs is the , energy due to other changes (Laughlin et al, 1967, Gunn, 1976). The small temperature rise can be measured by thermistors, semiconductors which show a large change in electrical resistance with small change in temperature.
IV.l.b Chemical:
The absorbed energy may produce a chemical change, if this change is quantified, it can be used as a measure of absorbed dose. There are many systems of chemical detection. An example of these is:
i) Oxidation / Reduction Technique:
The Fricke-doscmeter is considered to be the most developed system. It consists of 1 mmol/liter ferrous sulphate, I mmol/liter NaCl, and 0.4 mol/liter sulphuric acid. NaCl is used in the solution to counteract the 2effects of organic impurities. Wjjien the solution is irradiated, the ferrous ions, Fe , are oxidized to ferric ions, Fe which can be determined by spectrophotometry of which shows absorption peaks in the ultraviolet light at wavelengths of 224 and 304 nm (ICRU Report, 1969). The number of molecules oxidized per 100 eV of energy absorbed is known as the G-value. Thus if the yield of ferric ions can be determined, the energy absorbed
25 can be calculated when the G-value is known. A drawback is that only doses greater than 30Gy can be measured with reasonable accuracy.
ii) Film:
This is a radiographic film consisting of a transparent film base coated with an emulsion containing very small crystals of silverbromide. When the film is exposed to ionizing radiation a chemical change takes place within the exposed crystals to form what is referred to as a latent image. When the film is developed, the affected crystals are reduced to small grains of silver. The unaffected granules are removed by using fixing solution, leaving a clear film in their place, while the unaffected metallic silver causes darkening of the film. Thus; the degree of blackening of an area on the film gives the amount of silver deposited and, consequently, gives the energy absorbed. Densitometers are used to determine the degree of blackening by determining the optical density ,OD, which is defined as
OD = log~ IV.2
Where 1° is the amount of light collected without the film and I, is the amount of the light transmitted through the film. This method is useful for checking radiation fields and obtaining quick qualitative patterns of radiation distribution.
IV. 1.с Solid State Methods:
There are two types of solid state dosimeters: integrating type e.g. thermoluminescent crystals and electrical conductivity ones e.g. semiconductor junction. i) THERMOLUMINESCENCEDetectors:
Thermoluminescence Dosimetry, TLD, is one of the available solid - state systems for dosimetry of ionizing radiation. When a crystal, exhibiting the phenomenon of thermoluminescene, is irradiated, a fraction of the absorbed energy is stored in the crystal lattice. If the material is heated, the trapped energy can be recovered as visible light. If the electron in the trap requires energy to get out of the trap and fall to the valence band, the emission of light in this case is called phosphorescence (delayed fluorescence) If the energy is instantaneously emitted due to this transition then the phenomenon is called fluorescence (Wyckoff, 1983). The energy released as visible light can be measured by a photomultiplier tube that converts light into an electrical current. Then the current is amplified and measured by a recorder, for example. Examples of TLD is lithiumflouride which is most extensively studied and used in clinical dosimetry.
26 ii) Semiconductor Detectors: Solids are classified as semiconductors according to their electrical conductivity. In semiconductors electrons cannot move at low temperatures under any voltage, however, electrons can move at moderate voltages as the temperature increases. As temperature increases (by heating, absorption of radiation, or collision with an energetic charged particle) some electrons in the full valence and deeper lying bands may acquire enough energy to cross over to the empty conduction band, with a probability
where Eg is the energy gap, К is the Boltzmann constant and T is the absolute temperature. The electrons can move freely under the influence of an electric field, leaving holes behind moving in the opposite direction to the electrons. In times of the order of I0"12s, the interaction between electrons and holes makes the electrons to concentrate at the bottom of the lowest lying unoccupied (conduction) band, while the holes concentrate near the top of the highest full (valence) band. A mutlistep process occurs and more and more electrons-holes are generated, therefore, the average energy necessary for creation of one electron-hole pair will be much larger than the energy
gap Eg(Nicholas, 1983). In the absence of an electric field, the final step of the de-excitation process is the recombination of the electrons and holes and the return of the crystal to its neutral state. Impurities are introduced to create new donor or acceptor states and to obtain extra electrons and holes which increase the conductivity of the material (Nicholas, 1983). Introduction of an impurity (doping) will result in donor atoms having a large number of electrons and small number of holes (e.g. doping of As5+ in Si4 crystal) and this is called n-type semiconductor. Also doping may result in acceptor atoms having large number of holes and small number of electrons (e.g. doping of Ga3* in Si ' crystal) and is called p-type semiconductor. Now, if p-type and n-type are joined together, electrons and holes move because of two reasons . Both electrons and holes will move from areas of high concentration (diffusion). Electrons diffuse from n to p types, while holes diffuse in opposite direction. . Under influence of electrical field, electrons and holes will move in opposite directions. As a result of diffusion, equilibrium of electrons and holes is produced and the n-type region will be positively charged, while the p-type region will be negatively charged; considering that originally p- and n- types semiconductors were electrically neutral. After equilibrium, a potential difference V° of the order of 0.5 V exists between the two regions, constituting the p-n junction.
If an external voltage Vexl is applied with positive pole connected to the n-side, the total potential across the junction becomes V°+ Vb,fig.IV.l. This is called reverse bias. Application of a negative potential on the n-side have the opposite effect. The total potential difference will be V°- Vb. This is called forward bias.
27 - 4 — — 4 — 4- 4- + I * — 4- -f — 4 4 + - + - 4 — 4 • •* - 4 «• 4 - - - 4-4- :;i
L i _L
(ft)
Fig. IV. 1 (a) A p-n junction without external voltage, (b) A p-n junction with reversed voltage.
The operation of a semiconductor detector is based on the properties of p-n junction with reverse bias. Incident radiation produces electron - hole pairs upon the junction as it passes through it. Electrons and holes are swept away under the influence of the electric field and, the charge collected produces a pulse that can be recorded Hi) Scintillation:
Scintillators are materials (solids, liquids or gases) that produce sparks or scintillation of visible light when ionizing radiation passes through them. The achieved scintillation's light falls on a photosensitive material producing electrons which can be amplified using a photomultiplier tube. We can divide scintillators into three groups . Inorganic scintillators. . Organic scintillators. . Gaseous scintillators. As an example the inorganic scintillator is briefly described.
The Inorganic Scintillator:
In a crystal, the allowed energy states widen into bands, while the electronic energy states of an atom are discrete energy levels , fig IV.2
28 Conduction bend (normally empty)
Exclfon bend
states of ectivotor center с
Ground state of activator center
Velence band (normally full)
Other forbidden end allowed energy bands
Fig. IV.2 Allowed and forbidden energy bands of a crystal.
In the ground state, the valance band (upper most allowed band) is completely filled with electrons, whereas the conduction band (the next allowed band) is empty. Incident photons on a crystal may cause the valence electron to get enough energy to escape to the conduction band, where it is free to move in the lattice leaving a hole behind, which can also move. Sometimes, the energy is not sufficient to raise the electron to the conduction band. However, the electron is elevated to a thin band, called exciton band, with upper level coinciding with the lower level of the conduction band. The electron remains electrostatically bound to the hole in the valence band. The electron-hole pair formed is called an exciton. Also, due to crystal imperfections or impurities, energy states may be created between valence and conduction bands. Particularly important are the states created by the activator atoms such as thallium. The activator may be elevated to an excited state by a photon absorption, capture of an exciton or successive capture of an electron and hole. If transition of the impurity to the ground state is allowed, it will result in the emission of a photon . Then a scintillation is said to occur, if the photon's wavelength is in the visible part of the electromagnetic spectrum
IV.l.d Gas-Filled Detectors: Gas-filled detectors operate by utilizing the ionization produced by radiation as it passes through a gas.
29 Л detector consists of two electrodes to which a certain potential is applied. The space between the electrodes is filled with gas. As ionizing radiation, passing through the space, dissipates part of or all it's energy by generating electron-ion pairs. This pair moves under the influence of the electric field, inducing current, that can be measured Such type of detectors is called current or integrating chamber. However if the charge produced by the radiation is transformed into a pulse, this type of detectors is called a pulse chamber. For most gases the average energy required to produce an electron-ion pair is about 30 eV. A typical gas detector has a capacitance of 50 pF, and the charge will be collected in a time of the order of 1 fjs (Nicholas, 1983). If the high voltage applied to the detector is steadily increased, the charge collected per unit time changes as shov.n in fig.fV.3 which is divided into five regions
ТЕ
Fig. IV.3 The relationship between voltage applied to the counter and charge collected.
Region I
As the voltage increases from zero volts, the electrical field and the carriers (electron-ion) movement will increase. The recombination rate will decrease up to the point where it becomes zero at V^V,. Region I is called the recombination region. No detector operates in this region, because a slight change in the voltage will change the signal.
Region II
The recombination rate is almost zero and so the charge collected stays fairly constant despite the change in the voltage. This region is called ionization region. Ionization chambers operate in this region, such that the output signal is proportional
30 to the particle energy dissipated. _ , _ ; - -••• . -•.''" ••• - • • ...Since the signal from an ionization chamber is usually not large. The voltage applied is less that 1000 V.
Region III
The primary changes acquire enough kinetic energy leading to charge multiplication in this region. The gas multiplication factor, i.e. the ratio of the total ionization produced divided by the primary ionization, is for a given voltage, independent of the primary ionization. Thus the output of the counter is proportional to the primary ionization. This region is called the proportional region, and proportional detectors operate in it. The voltage applied ranges between 800 and 2000 V.
Region IV
In this region the electrical field inside the detector is so strong that a single electron-ion pair, generated, is enough to initiate an avalanche of electron-ion pairs. This region is cal'ied Geiger-Muller (GM) region. GM counters are used in this region. They provide a strong signal and can be used with any kind of ionizing radiation. It provides information only about the number of particles, since its signal is independent of the particle type and energy. The voltage applied to GM counters ranges from 1000 to 3000 V.
Region V
If the applied voltage is raised beyond the value V1V, a single ionizing event initiates a continuous discharge in the gas, and the device is not a detector anymore.
IV.2 Exposure measurements:
In this subsection the different instruments for exposure measurements are discussed.
IV.2.a Free-Air Ionization Chamber:
The free air or standard ionization chamber is an instrument employed in the measurement of exposure. Generally, it is used only for the calibration of secondary instruments designed for field use. A free air chamber is represented schematically in fig IV.4 An X-ray beam , originating from a focal spot S, is defined by the diaphragm D and passes centrally between a pair of parallel plates. A high voltage (100 V) is applied between the plates. The ionization is measured for a length L. the lines of force are made straight and perpendicular to the collector by a guard ring G
The exposure Xp (Faiz ,1984) at the center of the volume specified (Point P) is
'~ pA,L 2.58*10"
31 Where AQ is the charge collected in Coulombs p is the density (kg/m ) of air. A,, is the cross-sectional area (m') of the beam at point P. L(m) is the length of the collecting volume.
Collecting Volume -Lead-Lined \ Box
X-ray Beam
Diaphragm
Guard Wires Collecting Guard Electrode Electrode To Electrometer
Fig IV.4 A schematic diagram of free-air chamber.
A few corrections are usuafly applied for accurate measurements with free-air ionization chamber: . Correction for air attention. . Correction for recombination of ions. . Correction for effects of temperature, pressure and humidity on the density of air. . Correction for ionization produced by scattered photons.
Also there is an upper limit (at about 3 MeV) on the photon energy above which the exposure can not be accurately measured. As the photon energy increases, the range of the electrons liberated in air increases rapidly. This necessitates an increase in the separation of the plates to maintain electronic equilibrium, but too large separation creates a problem of non-uniform electric field and greater ion recombination. Although this can be solved by using air at high pressures, other problems regarding the correction factors and reduction in the efficiency of ion collection still remain.
32 IV.2.b Thimble Chambers:
A thimble chamber is one of the field instruments which is calibrated by free- air ionization chambers. The principle of the thimble chamber is illustrated in fig. IV.5a,b.
Air Shell Solid Air Shell
Air Cavity Air Cavity A В Thimble Wall Insulator Central Electrode
Air Cavity
Fig. IV.5 Schematic diagram illiistratmg the nature of the "thimble" ionization chamber.
In fig. IV.5.a, a spherical volume of air is shown with an air cavity at the center. Suppose this sphere of air is irradiated uniformly with a photon beam and suppose the distance between the outer sphere and the inner cavity is equal to the maximum range of electrons generated in air (so all electrons can deposite their energy inside the region), then, if the number of electrons entering the cavity is the same as that leaving it, electronic equilibrium exists. If we are able to measure the ionization charge produced in the cavity then by knowing the mass of air inside the cavity, we can calculate the exposure at the center of the cavity. The air wall, in fig. IV.5.a, is compressed into a solid shell, fig. IV.5. b, which is air equivalent and it's thickness is such that the electronic equilibrium occurs inside the cavity. In practice, the thimble chamber is constructed with wall thickness of 1 mm or less, for electronic equilibrium, since the density of the solid wall is much greater than that of free air. This thickness is supplemented with close-fitting caps of plastic to bring the total wall thickness up to that needed for electronic equilibrium when high energy photons are used.
33 The chamber construction is shown in fig. IV 5 c.
The inner surface of the thimble wall forms one electrode as it is coated by a special material to make it electrically conducting while the rod of low atomic number, such as aluminum, held insulated in the center forms the other electrode. A suitable voltage is applied between the two electrodes to collect the ions produced in the air cavity. If the energy spectrum of electrons liberated in the thimble wall is similar to that in air, then the thimble chamber is air equivalent. Furthermore the effective atomic number of the wall material and the central electrode must be such that the system as a whole behaves like a free-air chamber. Generally the atomic number of the wall (graphite and Backbite) is a little less than that of air. It is closer to that of carbon ( Z = 6 ) this gives rise to less ionization which is compensated for by the high atomic number of the central electrode.
i) Chamber Calibration:
If all requirements to measure exposure using thimble chambers are satisfied, then the exposure, X, is given by X-S-X- IV.4 pv A Where Q is the ionization charge liberated in the cavity of density p and volume v, A is the fraction of energy fluence transmitted through the air equivalent wall of equilibrium thickness. The factor A is slightly less than 1.00 and is used to calculate the exposure for the energy fluence that would exist at the point of measurement in the absence of the chamber. Thimble chambers are always calibrated against a free-air chamber , since it is difficult to construct a thimble chamber that is exactly air equivalent and to determine the chamber volume directly. AJthough adequate wall thickness is necessary to achieve electronic equilibrium, the wall produces some attenuation of the photon flux (Faiz, 1984). it) Desirable Chamber Characteristics:
For exposure measurements, the ion chamber should have the following characteristics:-
1- There should be minimal dependence of sensitivity on photon energy, variation in sensitivity or exposure calibration factor over a wide rangeof photon energies. 2- Since the sensitivity (charge measured per Roentgen) is directly proportional to the chamber sensitive volume, there should be suitable volume to allow measurements for the expected ranges. 3- There should be minimal variation in sensitivity with the direction of incident radiation. 4- The stem leakage, recorded ionization produced anywhere other than its sensitive volume, should be minimal.
34 5- The chamber should be calibrated against a standard e!ectrometer(described below) 6- The voltage and the electric field strength must be such that minimal ion recombination occurs.
IV.2.C Practical Thimble Chambers:
i) Condenser chambers:
A condenser chamber is a thimble ionization chamber connected to a condenser. In this chamber the central electrode is connected to a conducting layer of carbon coated on the inside of a hollow Polystyrene insulator (Faiz, 1984). The outer metal shield and the inner conducting layer with an insulator in
between constitute an electrical condenser Cc. The central wire and the thimble inner conducting surface form another one Q. Thus, the total capacitance С between the central electrode and the outer metal is
С = Cc + Ct FV.5 When the chamber is fully charged, the potential difference between the central electrode and the wall is 400 V. When the chamber is exposed to radiation there will be a reduction in charge on the electrodes proportional to the exposure. The ions produced within the hollow portion of the stem will recombine since they arc in a field free region.
i-1) Chamber Sensitivity
The sensitivity is the voltage drop per unit exposure. If air is assumed to be at 0 °C temperature , 760 mmHg pressure and density 1.29 Kg/m^, and the fraction of the energy fluence, A, equals 1, then the charge, Q, collected in a chamber with volume v, and exposure X is Q = X{R) *(2.58 • 10 dC/ Kg^) * \.29(KgI m ) * v(m}) The sensitivity is then
If the chamber is connected to an electrometer of capacitance Ce, then the sensitivity is V 3.33X10^ х'-сГсГ
L 2) Stem Effect:
Measurable ionization in the body of the stem and ionization of the air between the end of the chamber and the metal cap are two causes for stem effect.
35 The chamber reading will depend upon the length of the stem in the beam, if the ionization in the stem is measured by the chamber. Thus a correction will be necessary for lengths different from that used for the initial calibration of the chamber. The first mentioned stem leakage is minimized by a metal cap which fits over the end of the chamber and covers up the central electrode, although it may cause stem leakage if it does not fit properly over the chamber end, since charge can be collected in the air adjacent to the end of the electrode.
ii) Farmer Chamber: While condenser chambers have dosimetric problems, Farmer chambers are stable and reliable secondary standards for X and gamma-rays of all energies in the therapeutic range.
PTCFE 3.5 mm Graphite ,^
Fig. IV.6 Farmer graphite/aluminum chamber.
This chamber is shown schematically in fig.IV.6. The thimble waJl is made of pure graphite and the central electrode is of pure aluminum, the insulator consists of Polytrichlorofluorcthylene, and the collecting volume is nominally О.бсс (Aird et aJ, 1972). This chamber is connected to the Baldwin Farmer substandard dosimeter.
1.Ю о Measured «3 with Cap Absorption Co о To
15 О _L .01 .03 .3 1.0 3.0 10.0 H.V.L. mm Cu
Fig. IV.7 Energy response of the chamber shown in Fig. IV.6.
36 Fig.IV.7 shows the relative energy response of the chamber as a function of beam half-value layer (the thickness of a material which if introduced in the pass of the beam reduces the exposure rate by one half) It is found that the total stem leakage of this chamber is 0.4 % when irradiated with 4 MV X-rays with the whole stem in the beam(Faiz, 1984).
IV.2.d Electrometers:
These are devices for charging the chamber and measuring its charge. There are two different types of such devices. One should be detached from the chamber during exposure and then reattached to measure the charge. The other remains connected during exposure. The general principles of dosimetry systems (chambers and electrometers) are shown in fig. IV.8. The instrument can be operated either in the integrated mode or the rate mode. •
С
7
Fig. IV.8 Schematic circuit diagram of a dosimetry system.
Jn the integrated mode, the central electrode of the chamber is connected to one plate of the condenser while the chamber wall is connected through high battery to the other plate of the condenser. As the chamber is irradiated charges begin to
37 accumulate in the condenser. At the end, a charge Q is accumulated and a voltage V is generated across the condenser given by V = Q/C IV.8 Where С is the condenser capacitance. In the rate mode, if the condenser is replaced by a resistance R, a voltage V = IR is generaled across the resistance when the ionization current 1 flows through the circuit due to irradiation of the chamber. In both cases the charge liberated and current are very small. Complex electronics circuitry is used to measure them accurately and hence the exposure is calculated
38 CHAPTER V
Experimental Set Up And Handling Technique
In this chapter the measurement of the absorbed dose in a phantom and the dose calculation parameters are discussed. Measurements of the isodose curves as well as the factors effecting them are outlined. The phantom used is standard IAEA calibration one with the following dimensions cross-section 300 mm * 300 mm, depth 300 mm, with two windows, wall thickness 15 mm, window thickness 100 mm and volume 20 liter of distilled water.
V.I Environmental Conditions:
If the ion chamber is not sealed, its response is affected by air temperature, pressure and relative humidity. The density or the mass of air, in the chamber volume, will increase as the temperature decreases or pressure increases. Since exposure is given by the ionization charge collected per unit mass of air, the chamber reading for a given exposure will increase as the temperature decreases or the pressure increases. Standard laboratories calibrate chambers under the conditions present at the time of calibration. These conditions are then converted to specific atmospheric conditions, namely, 760 mmHg pressure and 20 °C temperature. The correction, Cy.p, for conditions other than the above reference condition can be calculated as
,760 % 273 + t. сг.л = (—)*(^т-) ( 293 ) v.i Where P is the pressure in mmHg and t is temperature in °C. For extreme accuracy, a correction may also be made for relative humidity. This correction is due to differences in electron densities and energy needed to produce an ion pair for air vs. water vapor. Suppose the vapor pressure is P _ , mmHg; then the correction factor, Ст.р.н for temperature, pressure and relative humidity is given by (Faiz, 1984) 760 273 -•- / С * •—- V2 TPH~ P-0.23SP, 293 The correction for relative humidity is usually less than 1 % and can be neglected in most situations.
V.2 Measurement Of Exposure:
Exposure in units of roentgen can be measured with a thimble chamber having an exposure calibration factor, Nc, traceable to a Primary Calibration Dosimetry Lab.(PCDL) e.g. the National Physics Laboratory (NPL), for a given quality of radiation.
39 Suppose a reading M is obtained for a given exposure. This can be converici into roentgcns (Faiz , 1984) as
X = M . Nc CrP Cs Csl V.3
Where CT.p is the correction for temperature and pressure, Cs is the correction for losi
of ionization due to recombination, and Ся is the stem leakage correction. Th< quantity X given by the above equation is the exposure that would be expected in fre< air at the point of measurement in the absence of the chamber. For low energy radiation, the thimble chambers are calibrated and usec without a build-up cap. For high energies, a Lucite build-up is used unless the chamber wall is already thick enough to provide electronic equilibrium. In either case
the correction to zero wall thickness is inherent in the chamber calibration factor Nc.
V.3 Phantoms:
Phantom are tissue equivalent materials usually large enough in volume to provide full scatter conditions for a given beam. Water phantoms are usually used for measuring basic dose distribution, since it is closely approximates the radiation absorption and scattering properties of muscle and other soft tissues, and it is also universally available with reproducible radiation properties. Solid dry water equivalent phantoms(same effective atomic number, number of electrons per gram and mass density) have been developed as substitutes for water, since it is not always possible to put radiation detectors in water.
The electron density pe of a material may be calculated from its mass density p „ and its atomic composition according to the formula (Faiz, 1984) as
P, Pm, | V.4 Where
N, is Avogadro's number, a, is the fraction by weight of the i* element of atomic number Z, and atomic weight Aj.
V.4 Measurement oflsodose Curves:
Isodose curves are lines passing through points of equal dose. They are usually drawn at regular intervals of absorbed dose and are expressed as a percentage of the dose at a reference point. A family of isodose curves forms an isodose chart. An ion chamber is the most reliable method for measuring isodose charts, because of its relatively flat energy response and precision. Others are solid state detectors or radicgraphic films. Water is the most used medium for ionometeric measurements. The chamber can be made waterproof by a thin plastic sleeve which covers the chamber as well as the portion of the cable immersed in the water.
40 The ionization chamber used for isodose measurements should be small(0.1- О.Зсс). It is recommended that the sensitive volume be less than 15 mm long and have an inside diameter of 5 mm or less, so that the measurements can be made in regions of high dose gradient, i.e., near the edges of the beam. Energy independence of the • chamber is another important requirement. Since the X-ray beam spectrum changes with position in the phantom, due to scatter, the energy response of the chamber should be as flat as possible. V.5 Parameters oflsodose Curves:
Single beam isodose distribution is affected by some parameters. Beam quality, source size, beam collimation, field size, source-surface distance (SSD) and the source- diaphragm distance (SDD) are among these parameters.
V.5.a Beam Quality:
Since the central axis depth dose distribution depends on the beam energy, the depth of a given isodose curve increases with beam quality. Low energy beams result in greater scatter of the beam, which causes a bulge out of the isodose curve outside the field. Physical penumbra ,the region at the edge of a radiation beam over which the dose rate changes rapidly as a function of distance from the beam axis, depends on the beam quality as illustrated in fig V. 1
Fig. V.1 Diagram for calculating geometric penumbra.
41 The isodose curves outside the primary beam (e.g. 10% and 20%) are extended in the case of orthovoltage radiation, whereas the scatter outside the field is minimized due to forward scattering and becomes more pronounced for collimation than energy, in megavolts beams.
V.5.b Source Size, SSD, and SDD-the Penumbra Effect:
* The physical penumbra (DE) at depth d is given by (SSD + d- SDD) '~$~ SDD
Where s is the source diameter and d is any depth from the surface of a patient.
Thus, it is clear that the three parameters, in the above equation, affect the shape of the isodose curves, Fig.V.2. In addition, the SSD affects the depth of the isodose curves. Usually the dose measurements for isodose curves are obtained below the first 2cm from the surface ,at steps of 5cm. This is to avoid the build up region and errors in the measurements due to near points of approximately equal dose.
V.5.C CoHimation and Flattening:
The term collimation is used to designate the collimator blocks that give shape and size to the beam and also the flattening filter as well as other absorbers or scatter£»~s in the beam between the target and the patient. The function of the flattening filter is to make the beam (megavolt X-ray beams) intensity distribution relatively uniform across the field i.e.'flat". Therefore, the filter is thicker in the middle and tapers off toward the edges. Furthermore changes in the distribution of radiation scatter ,as the depth increases, result in changes in flatness. Beam flatness is usually specified at 10 cm depth with the maximum limits set at the depth of maximum dose. This degree of flatness should extend over the central area bounded by at least 80% of the field dimensions at the specified depth or 1 cm from the edge of the field.
V.5.d Field Size: ?•
The determination of appropriate field size must always be made dosimetrically rather than geometrically. In other words, a certain isodose curve (e.g. 90%) enclosing the treatment volume should be the guide in choosing a field size.
42 ,' '*•••
! i K;-•-.....:: -•>'i i '
A \
I В
о I • С I '-.
Fig. V.2 Isodose curve. Depending upon the source size, collimation and design of the filter, the isodose curves for small field sizes tend to be bell-shaped. As the field size becomes larger, the isodose curvature for 60Co increases unless the beam is flattened by a flattening filter. The reason for this effect is the progressive reduction in scatter radiation, with increasing distance from the central axis as well as the obliquity of the primary rays. V.6 Data Handling:
Before the measurers 1 out the dosimeters are calibrated. An ionization chamber type N.L -:ч >trial number 164,a timer type N.E 2546,a
43 dosimeter type N.E 2560/NPL, serial number 130 and thermometers type 5807,5805 are used for this purpose. The chamber has a decay factor of 1.4915. The pressure at the time of measurement was 760 torr. The measured average temperature was 19.51" С The measured average dosimeter reading was 17.816. The corrected dosimeter reading was found to be 27.74. The percentage deviation of the corrected reading from standard reading was found to be 0.62. Another calibration was carried out for another chamber of the same type but different serial number (072) and the percentage deviation was found to be 0.21. This chamber is used in combination with an X-ray Linac. The field sizes used are 6*6 and 12*12 cm: The SSD was 100cm. Dose rates are measured forej,i»o2ocm depths in the vertical central axis using a water phantom Whereas along the horizontal axis dose rate profiles were measured at depths 5,)*, 15 cm. for field sizes 6*6 and 12*12 cm2 and the same SSD.
44 CHAPTER VI
RESULTS AND DISCUSSIONS
In this chapter the experimental results obtained are displayed in both tabular and graphical forms. The percentage central axis dose is discussed as well as the horizontal axis. The isodose curve obtained are discussed and compared to standard ones.
VI.I Percentage central axis depth dose:
Table 1 shows the doses for the 6*6 and 12*12 cm2, as a function of depth, whereas figs VI 1,2 are the dose distributions versus depth for the respective fields. As can be seen the percent depth dose decreases with depth beyond the depth of maximum dose However there is an initial build up dose This dose represents the build up region. The results are in good agreement with previous findings (Hospital Physicist's Association 1978). Further an attempt is made to represent the curve by the following equation (Omer, 1994): 7 .... . -004551ч--5 IL %Depthdose = 13(l - 0.8
VI.2 Profiles:
Tables 2,3 are the measured doses for the fields 6*6 and 12* 12 cm2, at depths
5/ fOv15 cm for varying points along the width of the water phantom. In the tables, for «reft field and depth, the first column gives the positions of the detector with respect to the middle point (assumed to be the zero) of the phantom. The second column gives the readings of the detector. The third column is the calculated percentage dose relative to the maximum measured dose. Figs. VI.3-4 are the dose profiles for the two fields. As can be seen the profile widens with increasing depth. This is due to the secondary scatter and the penumbra effect. Figs VI.5-10 are the percentage dose profiles for the fields and depths mentioned. For each field and depth the width of the profiles for the percentage doses, in increments of 10, are calculated and tabulated in table 4. These widths are then used to plot the decrement lines (Dawson, 1976). The dose at any depth is greatest on the central axis of the beam and generally decreases towards the edges of the beam. The decrement lines are usually taken relative to the dose on the central axis, for example the 90% decrement line represents 90% of the dose of the central axis. The decrement lines for each field size are plotted
45 Measured Percent Cfntral Axis Dose Depth (cm) Field size 6*6 Field size 12*12 0 63.5 675 0.6 95 5 96 1 995 100 16 99 99.5 975 98.5 93 95 I 88.5 91 с 84 87 6 81 83 7 75 79.5 8 71 76 9 67 72 10 63 68.5 11 59.5 65 12 56 62 13 53 58.5 14 49.5 55.5 •15 -47 52.5 16 44 50 17 41.5 47 18 39 44.5 19 37 42.5
Table I
Precentage dose of cental axis tor 6*6
100 90 * 8° V 70 о 60 50 40 8 30 20 10 0 10 12 14 16 18 20 Depth (cm) Fig. VI. 1
46 Percentage dose tor central axis of fletd si» 12*12
100 ; 90 • ВО • •
«, 60 t г sol I «: 20 ' 10 J 0 •-- 0 10 12 16 18 20 Depth (cm)
Fig. VI.2 Dose Profiles for 6*6 field size Dose at 5 cmJqAk. Dose at lOcmi?(ft Dose at 15 cm Position Dose Position Dose % Position Dose % -3.8 13 6 17 11 -4.4 12 10 -36 16 8 -3.8 22 14 -4.2 14 12 -3.4 23 11 -3.6 33 21 и 18 15 -3 2 38 18 -3.4 55 35 -3.8 24 20 -j 67 32 -3.2 87 55 -3.6 38 32 -2.8 111 53 _- 118 74 -3.4 59 50 -2.6 167 80 -2 156 98 -3.2 82 69 -2.4 195 94 -1 159 100 99 83 -2.2 196 94 0 159 100 -2.8 108 91 -2 202j 97 1 1581 99 -2.6 112 94 -1 208 100 2 156 98 -2.4 114 96 0 208 100 2.2 154 97 -2.2 116 97 1 208 100 2.4 152 96 -2 117 98 2 206 99 2.6 148 93 -1 119 100 2.2 205 99 2.8 140 88 0 119 100 2.3 203 98 3 122 77 1 118 99 2.5 200 96 3.2 94 59 2 116 97 2.7 194 93 3.4 60 38 2.2 115 97 2.9 180 87 3.6 35 22 2.4 112 94 3.1 152 73 3.8 23 14 2.6 109 92 3.3 108 52 4 17 11 2.8 101 85 3.5 63 30 4.2 14 9 3.2 65 55 3.7 35 17 4.4 13 8 3.4 42 35 3.9 21 10 3.6 27 23 4.1 16 8 3.8 19 16 4.3 13 6 4 15 13 4.2 13 11
Table 2
47 Dose Profiles for 12 4 2 field size Dose at 5 em<^tV\ Dose at 10 спкЦэй* Dose at 15 em oeptV» Position Dose %bose Position Dose %Dosc Position Dose %be>s -i 19 8 -5. 15 8 -7 12 87 - 23 100 -5.2 16 92 -6.8 126 91 232 100 -5 170 94 -6.6 128 93 -' 232 100 -i 178 99 -6.4 130 94 23 100 -'. 179 99 -6.2 13 95 - 23 100 179 99 -6 133 96 0 23 100 - 180 100 -5 136 99 230 99 180 100 .i 136 99 _' 32 230 99 180 100 137 99 231 100 • 180 100 -2 138 100 1 231 100 4 179 99 -1 138 100 В 5 227 98 с 178 99 0 138 100 5.2 225 97 6 177 98 1 137 99 IJ 5.4 222 96 6.2 172 96 z 136 99 5.6 221 95 6.4 170 94 J 136 99 5.8 204 88 6.6 168 93 4 134 97 6 178 77 - 6.8 165 92 5 130 94 6.2 133 57 7 158 88 5.2 129 93 6.4 83 36 7.2 143 79 5.4 127 92 6.6 47 20 7.4 118 66 5.6 123 89 7 23 10 7.6 83 46 5.8 117 85 7.2 19 8 7.7 53 29 6 106 77 7.4 17 7 7.8 ?5 19 6.2 86 62 7.6 16 7 8 23 13 6.4 62 45 8.2 21 12 6.6 42 30 6.8 30 22 7 24 17 7.2 21 15 7.4 19 14 7.6 18 131 7.8 17 12| Table 3 48 in figs VI 11.12. Each line is plotted, for the specific point of the percentage dose, from the three widths corresponding to the mentioned depths. Width (cm) for 6*6 Width (cm) 12*12 Dose 10 15 •; --• 5 10 15 98% 1 62 1 56 1.44 5.54 5.52 5.28 90% 264 2 66 2.78 5.86 6.12 6.20 80% 2 82 2.96 3.00 6.07 640 6.56 70% 2.94 3.08 3.13 621 6.56 6.72 60% 3.02 3.20 3.24 6.32 6.64 6.84 50% 3.10 3.28 3.36 639 6.76 6.96 40% 3.20 3.38 3.47 6.50 6.84 7.08 30% 3.30 3.50 3.60 6.6'. 696 724 20% 3 44 3 66 3.78 6.75 708 7.52 10% 3.72 4.08 4.38 7.14 7.84 8.96 Table 4 VI.3 The Isodose Curves: The decrement lines can be used manually to develop the isodose curves. To plot these curves the following procedure is followed: In fig. VI. 11, for example, the decrement lines are plotted in terms of the width and the depths mentioned. The axis on which depths are plotted is also the central axis. The dose on the central axis, for any depth, can be found from the program output in the appendix. If, X0, is the dose taken, then the X90 value, which is equal to X0, on the 90% decrement line corresponds to a value, in the central axis , given by X = X90* 100/90 VI. 1 where X is the value on the central axis at the same depth as X90 in the 90% decrement line. Now the corresponding depth is read from the table. This denotes the position of the point of the dose, X90, in the 90% decrement line. In the same manner the depths positions for other decrement lines for the same dose are obtained and the isodose curve representing the X0 dose is plotted. Then other values for the dose are taken and the procedure is repeated until the isodose chart is completed (Faiz, 1984). However, to simplify the plotting of the isodose charts, the following method is adopted here. The method is based on the assumption that if the decrement lines are extended, they converge and meet at the source which is considered to be a point source. Fig.VI. 13 represents the source, the surface with different depths and some decrement lines meeting at the source. It can be shown that the take-off angle is nearly constant for given depths and decrement line widths as in : tan(a)= x/(100+y) VI.2 where x is the width and у is the depth. The SSD=100 cm. 49 Source (S) 100 cm О « Depth Fig. V1.13 Table 5 gives the values for the take-off angle for the two fields with the respective depths and widths. As can be seen that the value for the take-off angle is almost constant which justifies the assumption. Then it is possible to represent the decrement lines by the following equation : x = A*Y VI.3 where A is the tangent of the take-off angle and Y=l00+y. ftve<-cxAes For Bot:WF>d Table 5 Now, using equation VI. 1, the depth for any field and %dose can be found. Once the depth is known the width can be computed from equation VI.3. In this work the computations are done for the 6*6 and 12*12 fields Tables 6 and 7 are established manually for calculating the depths, corresponding to each percentage dose value, at various decrement lines, using equation VI 2 and the data in the appendix. Further, the calculated depths are used to calculate the relative widths and then both, the depths and widths are tabulated in tables 8 and 9. The isodose curves are then developed as in figs. VI. 14, 15 where each %dose value is represented by a point (width, depth) in the plane. The points of equal %dose values were then joined. 50 As can be seen from the charts the low dose curves are a bit displaced. This because of more scattering associated with the low dose Usually the dose decreases with increasing depth, therefore low %doses are found in deeper depths near the central axis. Usually the phantoms used in radio-therapy have dimensions that resemble those of a human body in particular the thickness and this why low isodose curves are not plotted Comparison of the isodose curves obtained with those used in the Isotope and Radiation Center, Khartoum Hospital, figs.VI.16,17 shows that the agreement is eood. Depth for a certain percentage dose at various decrement lines 6*6 96% 90% 80% 70% 60% Lines % Dose Depth % Dose Depth % Dose Depth % Dose Depth % Dose Depth at at at at at Central Central Central Central Central Axis Axis Axis Axis Axis 96% 100 91.84 81.63 71.43 61 22 90% 100 1.13 88.89 3.89 77.7X 6.44 66.67 8.87 80% 100 1 13 87.5 4.15 75 7.05 70% 1П0 1.13 85.71 4.44 60% 100 113 50% 40% 30% 20% 10% 50% 40% 30% 20% 10% % Dose Depth % Dose Depth % Dose Depth % Dose Depth % Dose Depth at at at at at Central Central Central Central Central Axis Axis Axis Axis Axis 96% 51.02 40.82 30.61 20.41 10.2 90% 55.56 11.96 44 44 15.93 33.33 22.22 11.11 «0% 62.5 9.93J 50 13.96 37.5 18.95 25 12.5 70% 71.43 7.96 57.14 11.6 42.86 16.25 2857 14.29 60% 8.133 4.95 66.67 8.87 50 13 96 33.33 16.67 50% 100 1 13 80 6 11 60 10.69 40 17.6 20 40% 100 1.13 75 709 50 13.96 25 30% 100 1 13 66.67 8.87 33.33 20% 100 1.13 50 13.96 10% 100 1.13 Table 6 51 Depth Гог я certain percentage dose at various decrement lines 12*12 96% 90% 80% 70% 60% Lines % Dose Depth % Dose Depth % Dose Depth % Dose Depth % Dose Depth at at at at at Central Central Central Central Central Axis Axis Axis Axis Axis 96% 100 1.7 93.75 3.6 83.33 5.9 72.92 8.4 62.5 11.4 90% 100 1.7 88.89 4.6 77.78 7.2 66.67 10.2 80% 100 1.7 87.5 4.9 75 7.9 70% 100 1.7 85.7^ 5.3 60% 100 1.7 50% 40% 30% 20% 10% 50% 40% 30% 20% 10% % Dose Depth % Dose Depth % Dose Depth % Dose Depth % Dose Depth at at at at at Centra) Central Central Central Central Axis Axis Axis Axis Axis Lines 52 0« 15 41 67 19.3 31.25 24.8 20X3 32.7 10.42 96% 55 56 1.4.7 44.44 18 33.33 23.6 22.22 31.4 11.11 90% 62.5 114 50 15.7 37.5 21.3 25 29.1 12.5 80% 71 43 88 57.14 13.2 42 86 18.7 28.57 26.6 14.29 70% 83.33 59 66.67 10.2 50 15.7 33.33 23.6 16.67 60% 100 1.7 80 6.7 60 12.2 40 20 20 33.4 50% 100 1.7 75 7.9 50 15.7 25 29.1 40% 100 1.7 66.67 10.2 33.33 23.6 30% 100 1.7 50 15.7 20% 100 1.7 to% Table 7 52 Position of points according to relative decrements lines 6*6 ! 100% 98% 90% i ! 80% Width j Depth Width ; Depth I Width | Depth | Width ! Depth 100°/c 3! 1.7 0 1.1'! ()! 3.9! ()! 5.9 - 98% i 1.43 1."' 1.4!Я 3.5! 1.4Si! 5.6 90% J 2.4<>; 1.7! 255 ! 4. 80% i I ! 2.71 ! 1.7 70% ... I 60% - i 50% j 40% I "I 4 30% 1 j 20% 1 i i 10% 1 I "1 i ! 70% | ! 60% ! 50% ! | 40% j Width j Depth ! Width i Depth Width I Depth : Width ! Depth 100% j о | 8.2! 0! 10.9 0| 14! 0! 17.9 98% i 1.52i 7.9! 1.55! 10.6 1.61 13.7! 1.65 17.6 90% j 2.6l[ 6.4! 2.67! 9.1 "' 12.2! 2.84 16.1 80% i 2.78] 4.4; 2.85! 2.93 10.2! 3.03 14 70% I 2.82 1 1.7! 2.91| 4.8 2.99 7.9! 31 11.8 60% j ! 2.92! 1.71 3.02 5.2! 3.13 9.1 50% I 3 1.7! 3.13 6 40% i "1 ! 3.1! 1.7 30% r } 4 \ 20% IZZ 10% 1 30% 20% ! 10% i Width Depth I Width ! Depth f Width ! Depth ! I 100% oi 22.8! oi 29.8! Oi 98% 1.721 22.5^ 1.82! 29.5 90% 2.96J 21! 3.14! 28 80% 19! 3.35! 26 70% 3.24i 16.7! 3.43!• 23;7T ! 60% 3.27 141 3.47! 21! 3.82: 33! | 50% 3.27 10.9: 3.48! 17.9 3.83! 29.8! ! 40% 3.26 7! 3.47! 14 3.84i 26! | 30% i 3.21 1.7! 3.43! 8.8 3.81! 211 i •*•-• •«• •• 20% j 10%T T Table 8 53 Position of points according to relative decrements lines/4*$2- 100% 96% ; 90% I 1 80% j Width Depth Width ! Depth 1 Width : Depth i Width ! Depth 100% ! 0 j r! 0: 3.1 ! о 4/ H 0: 6.6 96% ! 2.52 1."'1 2.57 3( >! 2.63! 5.9 90% ! 2.8 l.'i ': 2.88: 4.6 80% ! 2.93! 1.7 70% 60% 50% 40% 30% : l i 20% j i ! 10% ' | 70% I 60% 1 L..sq% ] ! 40% | Width Depth Width I Depth Width ! Depth I Width ; Depth 100% oi 92 0! 12.2 0! 15.7 1 0! 20 96% 2.69: 8.4 2.76! 11.4 2.85! 15! 2.96! 19.3 90% 2.95: 7.2 3.04! 10.2 13.7 : 3.25! 18 80% 3.03i 4.9 3.11! 7.9 • m 11.4 3.34! 15.7 70% 3! 1.7 3.11! 5.3 3.21! 8.8 3.341 13.2 60% 3.05: 1.7 3.18! 5.9 3.31; 10.2 50% i 3.1! 1.7 325! 6.7 40% i 3.15! 1.7 \. -t 30% j 20% i 10% 1 30% 20% i i 10% j Width i Depth ! Width j Depth Width i Depth ! 100% : 0 25.6! o\ 33.4! 0; 96% 3.11 24.8! 3.29! 32.7! 90% 3.41S 23.6! 3.62! 31.4 80% 3.5 21.3! 3.72! 29. Ц 1 70% Щ. 18.7! 3.74! 26.6 ! 60% i 3.47J 15.7! 3.71! 23.6 j I 50% I 3.42! 12.2! 3.66! 20 4.07! 33.4! 40% i .„ 3.34] 7.9i 3.58! 15.7i 3.99: 29.11 30% i 3.21 1.7! 3.47! 10.2 3.9! 23.6! 20% | 3.29! 1.7 3.74'[ 15.71 10% ! 3.681 17! Table 9 54 Dose Distribution For Three Different Depths (Field Size 6*6) 250 - • -- At Depth 5 cm '< •- At Depth 10 cm __-•• » • Щ- | • At Depth 15 cm • 200 • L <:- а !->-о- о О •-• -»__ 100 50 -5 -3 -2 -1 0 1 Position (cm) Fig. VI.3 Dose Distribution For Three Different Depths (Field Size 12*12) 250 ; I »-— *- ...... 200 ~~c o~—с f • о- -П-- 150 | • •— - • <0 if) о • ----- At Depth 5 cm О Q -° At Depth 10 cm 100 [ • At Depth 15 cm I..... 50 •••'•w 1 I I 1 o—b- •- --f -10 -8 -6 -4 -2 0 2 10 Position (cm) Dose Profile at 5 cm (Field size 6X6 cm) 100- i 90 30 t -70- 60— a» / (A 50 О a 40 I 30 20 I y 10 j !•- •o-l -4 -3 -2 -1 0 1 Position Dose Profile at 10 cm (Field size 6X6 cm) 100 90 80 —70 60 <л 50 ^ О 00 a 40 r 30 ;• . _ . 1. 20 i 10 : | о 1 »- -3 -2 -1 0 1 Position Dose Profile 15 cm (Field size 6X6 cm) 100 •- 90 80 70 60 -•- 4) м 50- VO О Q 40 30 20 • 10 0 -5 -4 -3 -2 -1 0 Position Dose Profile at 5 cm (Field size 12X12 cm) -_ ш 100 -90 \ 80 70 Ф ел 60 ON О О О - 40 — 30 20 IV ~^ " ~~~~ ' ~~ " • • 0 ^ t — -8 -4 -2 0 4 Position Dose Profile at 10 cm (Field size 12X12 cm) • -- • 100 -y 90 j •-/- ! I 80 r 70 cn i,_ _, U) -50 о О •40- 30 20 10 г - 0 i - i-- -8 -6 -2 0 2 4 10 Position Dose Profile at 15 cm (Field size 12X12 cm) .-.г-- -• - 100 * -.*-_.-... -~- ,.-• . „,; " -. ... 1 •- - --- "• •• 80 -V ...... ' 70 ; U .70,- - - r— -60- - -•- 40 • \ \ -- -- 30 ; - • - * • ' ^ - / 20 i • - \ .-• _ _ 4Л. j. l__ . I .__ .. I . . . L . _^ A 1- I __ I -10 -8-6-4-2 0 2 4 6 Position Decrement Lines for 6X6 cm 4.5 : ' .._—, '"" "~~ " _ ._.,, -•• 98 3.5 *- _-- -"•• . - - •"— — --• ; "'_—•-"""" • II' - л • с-— go I rv—~~\~ „ " " - ••-л -~~~.~~. ~~~'. --"-" '•- - * з I L-.-TL-:-.:. -••-_--_;:;-. - .-t-z^~--:_:-i.i_—-.:.:..:•::..-:..• ; so — -- ••""'••- | 70 — -c] i E 2.5 О ; —t— 50 5 2 ; ! —• 40 щ _. _ _ _ _ : 1.5 - ~ ""~ -• -^--- 30 20 1 • ; -10 0.5 - } 0 5 10 15 Depth cm O00OOOOOOOOO I i M -s i 0> • • -u- CO N ,<• 0) •i-l • 4- i I E ( i и I i vo X м Ф и Э и ? •! i ,. 0) и о тз i i о ! I и m о I I L х_^.. о см 8 (ШЭ) 64 Decrement Lines for 12X12 cm 4.50 4.00 3.50 •-- 96 '-£•-. - ••:••- 90 - • • • П 300 -П • 80 • 70 E 2.50 о £ " 01) A-- 50 5 2.00 • 40 1.50 •' 30 1.00 - 20 -- . ..- 10 0.50 - 0.00 10 15 Depth cm О о с^ о о ^ о 0 с о г 0(0000000000 т ф N •1-1 СП •о f-t ф •н 4-1 е и 1Л c\i ^» Е и О И 0) и> а и 01 м о •о о и I ' I : j— .i ! , f -— о ю «л о ю О «Л о го о см со см (шо) 66 67 ^* 68 CHAPTER VII CONCLUSIONS AND SUGGESTIONS The earlier chapters of this dissertation deal with the physics of x-rays namely their production, interaction, how they are absorbed. Further the units and the definitions adopted in x-rays are given Further the use of x-rays in radiotherapy is detailed and the techniques whereby x-rays were detected and measured are given. The last chapter deals with the results obtained, their description and analysis. The basic findings of the work is the development of an empirical equation to describe the percentage central axis dose for any depth and field A computer in Turbo Pascal is also written. The horizontal axis dose and the decrement are also found. Further, the isodose curves for two field are plotted. The plotting is based on a simple equation. The isodose curves were compared to standard ones and the agreement was found to be good. It is suggested that a computer program should be written for the calculation and plotting of the isodose curves for all fields. 69 Appendix I. Computer Program Listing. program dose (input.output), const mindepth = 1; maxdepth = 35; delta = 0.1; var depth,dose6,dosel2:real, begin depth := mindepth; writeln(' Depth Dose 6X6 Dose 12X12'); while depth < maxdepth do begin dose6 := 113*(1 - 0.8*exp(-2*depth))*exp((-0.0455*(l + (1.65/6))*depth)); dosel2 := 113*(1 - 0.8*exp(-2*depth))*exp((-0.0455*(l +(1.65/12)) *depth));; writeln(depth:10:3,dose6:10:3,dosel2:10:3); depth := depth + delta; end; end. II. Computer Program Output. Depth Dose 6X6 Dose 12X12 Depth Dose 6X6 Dose 12X12 Depth Dose 6X6 Dose li 1 95.086 95.683 12.2 55.681 60.097 23.5 28.907 3 1.1 96.617 97.284 12.3 55.359 59.787 23.6 28.74 3 12 97.752 98.488 12.4 55038 59.478 23.7 28.574 3 1.3 98.565 99.37 12.5 54.72 59.171 23.8 28.409 4 99.117 99.989 12.6 54.404 58.866 23.9 28.244 .5 99.457 100.395 12.7 54.089 58.562 24 28.081 .6 99.625 100627 12.8 53.776 58.26 24.1 27.918 3 .7 99.654 100.72 12.9 53.465 57.959 24.2 27.757 3 8 99.57 100.698 13 53.156 57.66 24.3 27.596 3 .9 99.395 100.584 13.1 52.848 57.362 24.4 27.437 3 2 99 147 100.395 13.2 52.543 57.066 24.5 27.278 3 2 1 98 839 100.146 13.3 52.239 56.771 24.6 27.12 3 22 98.484 99.848 13.4 51.936 56.478 24.7 26.963 3 2.3 98.09 99.512 13.5 51.636 56.187 24.8 26.807 3 2.4 97.666 99.143 13.6 51.337 55.897 24.9 26.652 3 2.5 97218 98.75 13.7 51.04 55.608 25 26.498 3 2.6 96.75 98.337 13.8 50.745 55.321 25.1 26.345 3 2.7 96.268 97.908 13.9 50.452 55.035 25.2 26.192 3 2.8 95.774 97.466 14 50.16 54.751 25.3 26.041 3 70 2 9 95 271 97.015 14 1 49.87 54 469 25.4 25 89 30.349 3 94.762 96.557 14.2 49581 54 187 25.5 25.741 30.193 3 1 94.247 96.093 14.3 49.294 53.908 25.6 25.592 30037 3 2 93 73 95 625 14.4 49.009 53.629 25.7 25 444 29.882 ; i 93 21 95.155 14.5 48.726 53.353 25.8 25.296; 29 "28 3 i\ 92.68У 94.682 146 48 444 53.0" 2* 9 ' 25 15 29.5 "4 - ^ 92.168 94 209 14" 48 164 52.803 26 25 00 29.421] •\ 91 64" 93.735 14 47.885 52.531 26. 24.8 29 2" 3. 91.127 93.261 14. 47.608 52259 26. 24.71 29.119 3. 90.608 92.78 1 47.333 51.9 26. 24.57 28.968 3 90.09 9231 15. 47.059 51.72 26. 24.43 28.819 4 89.574 91.84 15. 46.787 51.45 26. 24.2 28.67 4. 89 06 91.375 15. 46.516 51.18 26 24.14 28.522 4. 88549 90.907 15. 46.247 50.924 26. 24.0 28.375 4.. 88.04 90 44 15. 45.979 50.661 26. 23.87 28.228 4.4 87.533 89.976 15.6 45.713 50.4 26. 23.73 28.082 4. 87.028 89.513 15. 45.449 50.14 2 23.59 27.937 4/ 86 526 89.053 15 8 45.186 49.881 27. 23.45 27.793 4.7 86.027 88.594 15.9 44.925 49.623 27.2 23.323 27.65 4 8 85.53 88.138 16 44.665 49.367 27.3 23.188 27.507 49 85.037 87 684 16 44.407 49.112 27.4 23.054 27.365 84.545 87.232 16- 44 15 48.859 27. 22.92 27.224 5. 84.057 86.782 16.. 43.894 48.607 27.6 22.788 27.083 5 ^ 83 57 86315 164 43 64 4H.3S6 27.7 226.4 26.9-П 5.3 83.088 85.889 ? 16.5 43.388 48.106 27.8 22.525 26.804 54 82.608 85.446 16.6 43.137 47.858 27.9 22.395 26.666 5.5 82.13 85.005 16.7 42.887 47.611 28 22.265 26.528 5.6 81.655 84.567 16.8 42639 47.365 28. 22.137 26.391 5.7 81.183 84.13 16.9 42.393 47.12 28.2 22.009 26.255 58 80.714 83.696 17 42.147 46.877 28.3 21.881 26.12 5.9 80.247 83.264 17.1 41.904 46635 28.4 21.755 25 985 6 79.783 82.835 17.2 41.661 46.394 28.5 21.629 25.851 6.1 79.321 82.407 17.3 41.42 46.155 28.6 21.504 25.717 6.2 78.863 81.982 17.4 41.181 45.917 28.7 21.379 25.5Я4 6.3 78.406 81.559 17.5 40.943 45 68 28.8 21.256 25.452 6.4 77.953 81.138 17.6 40.706 45.444 28.9 21.133 25.321 6.5 77.502 80.719 17.7 40.47 45.209 29 21.011 25.19 66 77.054 80.302 17.8 40.236 44.976 29.1 20.889 25.06 6.7 76.608 79.888 17.9 40.003 44.744 29.2 20.768 24.931 68 76.165 79.475 18 39.772 44.513 29.3 20.648 24.802 69 75.724 79.065 18.1 39.542 44.283 29.4 20.529 24.674 7 75.286 78.657 18.2 39.313 44.054 29.5 20.41 24.547 7 1 74.851 78.251 18.3 39.086 43.827 29.6 20.292 24.42 7.2 74.418 77.847 18.4 3886 43.601 29.7 20.174 24.294 7.3 73.988 77.445 18.5 38.635 43.376 29.8 20.058 24.169 7.4 73.56 77.045 18.6 38.411 43.152 29.9 19.942 24.044 7.5 73.134 76.647 18.7 38.189 42.929 30 19.826 23.92 7.6 72.711 76.252 18.8 37.968 42.707 30.1 19.712 23.796 7.7 72.29 75J858 18.9 37.749 42.487 30.2 19.598 23.67? 78 71.872 75.467 19 37.53 42.268 30.3 19.484 23.551 7.9 71.457 75.077 19.1 37.313 42.049 30.4 19.372 23.4? 8 71.043 74.689 19.2 37.097 41 832 30.5 19.26 23.309 71 к 7063 74.304 19. 36.88 41.61 30. 19.14?t 23.188 8 70.22 73.92 19 36 66 41.40 30 19.03"' 23 069 8 69.81 73.539 19. 36.45 41.18 30. 18.92 22949 8 6941 73.159 19. 36.24 40.97 30. 1881 22.831 8 69.01 72.781 19. 36.03 40.76 3 18.70 22.713 8. 6861 72.406 19. 35.82 40.55 31. 18.60 22.596 8 68 21 72.032 19. 35.62 40.34 31. 18.49 22.479 8 67.82 71.66 2 35.41 40.13 31. 18.38 22.363 8 67.42 71.29 20. 35.2 39.92 31. 18.2 22.248 67.03 70.922 20. 35.00 39.72 31 18.17 22.133 9. 66.65 70.556 20. 34.80 39.51 31. 18.06 22.019 9 66.26 70.192 20. 34.60 39.31 31. 17.96 21.905 9 65.88 69 829 20. 34.40 39.11 31. 17.8 21.792 9.4 65.50 69.469 20. 34.204 38.908 31. 17.75 21.679 9.. 65.12 69.11 20. 34.006 38.708 3 17.654 21.568 96 64.746 68.754 20.8 33.809 38.508 32. 17.552 21.456 9.7 64.37 68.399 20.9 33.613 38.309 32.2 17.45 21.345 98 63.999 68 045 21 33.419 38.111 32.3 17.35 21.235 9.9 63.629 67.694 21.1 33.226 37.914 32.4 17.249 21.126 10 63.26 67.345 .21.2 33.034 37.719 32.5 17.15 21.017 10.1 62.895 66.997 21.3 32.842 37.524 32.6 17.051 20.908 10.2 62.531 66.65 1 21.4 32.652 37.33 32.7 16952 20.8 10.3 62 169 66.307 21.5 32.464 37.138 32.8 16.854 20.693 10.4 61.81 65.965 21.6 32.276 36.946 32.9 16.756 20.586 10.5 61.452 65624 21.7 32.089 36.755 33 16.659 20.48 10.6 61.097 65.286 21.8 31.903 36.565 33.1 16.563 20.374 10.7 60.743 64.949 21.9 31.719 36.377 33.2 16.467 20.269 10.8 60.392 64.613 22 31.535 36.189 33.3 16.372 20.164 10.9 60.042 64 28 22.1 31.353 36.002 33.4 16.277 20.06 11 59.695 63.948 22.2 31.172 35.816 33.5 16.183 19.956 1.1 59.35 63.618 22.3 30.991 35.631 33.6 16.09 19.853 1.2 59.007 63.289 22.4 30.812 35.447 33.7 15.996 19.751 1.3 58.665 62.963 22.5 30.634 35.264 33.8 15.904 19.649 14 58.326 62.638 22.6 30.457 35.082 33.9 15.812 19.548 115 57.988 62.314 22.7 30 281 34.901 34 15.72 19.447 1.6 57.653 61.993 22.8 30.105 34.721 34.1 15.63 19.346 1.7 57.32 61.673 22.9 29.931 34.542 34.2 15.539 19.246 1.8 56.988 61.354 23 29.758 34.363 34.3 15.449 19.147 1.9 56.658 61.038 23.1 29.586 34.186 34.4 15.36 19.048 12 56.331 60.722 23.2 29.415 34.01 34.5 15271 18.95 12.1 56.005 60.409 23.3 29.245 33.834 34.6 15.183 18.852 23.4 29.075 33.659 34.7 15.095 18.755 34.8 15.008 18.658 34.9 14.921 18.562 72 REFERENCES Aird E. 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