Calibration of the NPTC Range Verifier
Calibration of the NPTC range verifier
Bernard Gottschalk∗
Harvard Cyclotron Laboratory 44 Oxford St., Cambridge, MA 01238, USA January 16, 2001
Abstract The Range Verifier (RV) is a multi-layer Faraday Cup with relatively thick brass plates. The stopping peak of a monoenergetic proton beam is coarsely binned by the RV so that the main signal appears in only three or four channels. We search for the best way to evaluate this spectrum. Fitting the data with various functions—for instance a Gaussian—works reasonably well, but a straightforward two-step computation of the mean x0 is better and much faster. We study the integral and differential lin- earity of this method using runs at many beam energies, each with several different degrader combinations. We then compare RV measurements with interleaved measurements of the range d80 in a Scanditronix (SCX) water tank. The relation between d80 and x0 requires a small quadratic term because range in brass is not exactly proportional to range in water. The calibration function is x x 2 d =0.0618 + 40.3957 0 +0.9117 0 80 35 35 and agrees with theory. The water tank measurements also yield informa- tion about the difference between d80 and d90 and about the accuracy of the Range at Nozzle Entrance (RNE) set by the NPTC treatment control program.
∗This work was performed for Ion Beam Applications s.a. (IBA).
1 Contents
1 Introduction 3 1.1 The Range Verifier ...... 3 1.2ErrorinRVData...... 4 1.3 The Mean Proton Range: r0, d80 and d90 ...... 5 1.4 Equivalent Thicknesses ...... 5
2 Analysis of the RV Spectrum 7 2.1 Converting to Charge, Merging, Correcting for Beam Steering . . 7 2.2 Computing x0 ...... 7 2.2.1 Fitting the Spectrum ...... 7 2.2.2 Obtaining x0 Directly...... 8
3 Results 8 3.1Resolution...... 9 3.2 RNE-based Runs: Integral and Differential Linearity ...... 9 3.3 SCX-based Runs: x0 v. Range in Water ...... 10 3.4 RV Calibration Curve ...... 10 3.5 d80, d90 andRNE...... 11
4 Summary and Acknowledgement 11
2 1 Introduction
Each proton nozzle of the Northeast Proton Therapy Center (NPTC) includes a Range Verifier (RV) built into one set of jaws of the the variable collimator. This report analyzes recent data taken with the X jaws open and the Y jaws closed (that is, intercepting the full beam) and with nominally monochromatic beams (no depth modulation). We mainly address three questions: • What is the best way to evaluate RV range spectra? • What are the integral linearity, differential linearity and resolution? • How well do RV ranges agree with ranges from Bragg peaks? The remainder of this Introduction, however, is devoted to a brief description of the RV and three related issues: the measurement error in RV data; the definition of mean range and the quantities r0, d80 and d90 and finally, the concept of ‘water equivalent’ and of equivalent thicknesses in general.
1.1 The Range Verifier The RV consists of a Multi-Layer Faraday Cup (MLFC) in each of the two opposing downstream (Y ) jaws of the 4-jaw adjustable collimator, which are ≈ 40 cm downstream of the second scatterer and just upstream of the second ionization chamber set. A MLFC is a stack of metal collecting plates (here 2 mm brass) separated from each other and from ground by thin insulating sheets (here 0.025 mm polyethylene, two thicknesses per gap). Each collector goes to a current integrator. The MLFC has two favorable properties that may not be immediately obvious. First, the ejection of electrons from insulators into collectors and vice versa has no net effect because each such electron remains ‘bound’ to the positive ion it left behind and therefore does not contribute to the measured current. Second, protons that stop in insulators attract a mirror charge into the nearest collector, and are therefore counted just as well as protons that stop in collectors. Therefore the MLFC counts only the incident charge and counts all of it, accurately measuring differential fluence v. depth. The distribution of charge in a MLFC after exposure to monoenergetic pro- tons consists (Fig.1) of a continuum and a sharp peak. The continuum comes from the charged decay products (mostly protons) of the inelastic nuclear inter- actions experienced by some of the incident protons. The peak comes from those protons that stop entirely by electromagnetic interactions. The total charge col- lected equals the beam current entering the device, integrated over time. The continuum can be exactly accounted for by appropriate Monte Carlo models of the nuclear interaction [1]. Note especially that Fig.1 does not look like a Bragg peak and is not a Bragg peak. It is a differential stopping curve, rather than a differential energy deposition curve. For that reason the measured mean proton range corresponds to the peak value rather than the distal 80% value, as will be discussed more fully below. For reasons of economy the present RV is a bit more complicated than a simple stack of collectors. Each of the two jaws has 29 brass plates, each roughly equivalent to 1.1 cm of water. To improve the overall range resolution, one of the jaws has an additional half-thickness plate which is passive (not connected to an integrator). Precise range calculations must also take into account the 2 mm aluminum cover plates, the insulating sheets between the brass plates, and the fact that the brass plates may not have exactly the nominal thickness. If we use the rule (Sec. 1.4) that the effective energy in a finely divided stopping
3 stack is 0.52 × the incident energy, we find that the RV is ≈ 0.4% polyethylene by stopping power. When taking data with monochromatic beams, some upstream scatterer should be used to broaden the beam at the RV so as to reduce the fraction grazing the edge of the plates. In the runs presented below we used at least 1 mm of lead (lollipop #4).1 The transverse proton distribution at the RV can be inferred from the ion chambers downstream of it. The vertical distribution is sharp because the Y jaws are closed, whereas the horizontal distribution reflects the width of the ribbon of beam coming through the small gap between the Y jaws (Fig. 9). Near the maximum energy the distribution at the RV has a FWHM of ≈7 cm for a 1 mm lead scatterer, which appears to be adequate to get a clean spectrum in the RV.
1.2 Error in RV Data Because raw RV numbers are usually referred to as ‘counts’ and because of the superficial resemblance between an RV spectrum and a pulse height or Monte Carlo spectrum, there is an erroneous tendency to think of the error of each RV datum as having something to do with the square root of the number. Actually the error is far smaller. Each RV channel represents a charge measurement, not a statistical sample. The error comes from the resolution of the measurement, ∆Q = 10 pC, and is constant, independent of the ‘counts’. This is illustrated by Fig. 2, where a portion of the spectrum is shown for seven runs taken back- to-back. Because the count interval varied a bit (no beam monitor), the spectra have been normalized to the same total charge. Even the funny-looking peak channel (≈ 260 ‘counts’) has an rms spread√ of only 0.6%. If this were a statistical sample the relative error would be 1/ 260 or about 6%! The expected order of magnitude of the error is easily found. A recycling integrator with its counter is equivalent to an analog-to-digital converter having charge resolution ∆Q. The measured charge Q0 always equals ∆Q times an integer e.g. 1.000 nC for 100 counts. Only the counter, not the residual charge, is reset at the beginning of a measurement. The true charge Q that came in during the measurement interval may be nearly ∆Q less than Q0 (if the residual charge was nearly ∆Q) or it may be nearly ∆Q more (if the residual charge was nearly 0). Therefore the measurement error Q − Q0 is uniformly distributed between −∆Q and +∆Q if we assume all values of residual charge are equally likely. The rms error is therefore√ the rms deviation of a square distribution of half-width ∆Q, namely ∆Q/ 3 ≈ 0.6∆Q. Of course it is frequently the case that not all values of residual charge are equally likely. The runs may be taken back-to-back as here, leading to correlations. The measured rms deviation for all active channels in Fig. 2 varies considerably but averages only 0.4∆Q. However, without belaboring the point further we may conclude that the error in any point is at most a fraction of a count. Therefore a hundred counts or so in the peak channel is generally enough for a good measurement. That corresponds to a nanoAmp for a few seconds if the RV intercepts most of the beam. Under those circumstance the overall error in the range determination probably depends more on the algorithm used to find the range than on the number of counts, as will be seen below.
1A ‘lollipop’, so called because of its shape, is one of six lead or three Lexan degraders that may be inserted into the beam just upstream of the range modulator.
4 1.3 The Mean Proton Range: r0, d80 and d90
The distal 80% point d80 and the distal 90% point d90 of the Bragg peak are both relevant to proton radiation therapy, leading to potential confusion and annoyance. In this section we will try to clarify this situation. Referring to the top frame of Fig. 3, the mean projected range r0 of a proton beam is defined as the depth at which the integral fluence curve falls to 50% if we define 100% not at zero depth but at the start of the steep part. Such a curve may be measured by stacking degraders in front of a Faraday cup: the dots represent such a measurement done at HCL. The slow falloff is due to inelastic nuclear interactions. The sharp drop happens when the surviving primary protons finally stop by electromagnetic (EM) interactions. In other words, r0 is defined as the depth by which half the protons have stopped, if we count only those stopping by EM processes. The top frame shows that 2 2 r0 is independent of the falloff width parameter σ = pσ1 + σ0. Here σ1 characterizes the energy spread of the beam and an irreducible minimum σ0 characterizes range straggling, that is, the statistical nature of the stopping process. The middle frame shows what happens if, instead of measuring integral fluence, we use a device—such as a MLFC—which measures the differential fluence. Here the maximum of the peak (very nearly equal to its mean, since the peak is very nearly symmetrical) occurs at r0, independent of the width. The bottom frame shows the Bragg peak: energy deposition v. depth, in- stead of number of protons v. depth. Around 1960 Andy Koehler showed, in the course of deriving the Bragg peak from the fluence distribution, that r0 corresponds to the distal 80% point of the Bragg peak, to wit
d80 = r0 (1)
Later on, that unpublished result was independently confirmed by Berger [2], and it is also respected by Bortfeld’s recent analytical model [3] of the Bragg peak.2 The Bragg curves in Fig. 3 were generated with the Bortfeld model. They have been normalized at the peak to demonstrate that d80 is the only feature of the Bragg peak that stays the same when the energy spread of the beam is changed. By contrast, the quantity d90, that is, the point at which the dose drops to 90% of its prescribed value, is usually taken as the distal point of clinical interest for a spread out Bragg peak. This choice, though well established at HCL and by extension at NPTC, is essentially arbitrary, whereas d80 = r0 is given by the physics of the Bragg peak. Because we wish in this report to make statements that are strictly independent of beam energy spread, we will mostly use d80, showing its relationship to d90 under the conditions of the experiment only at the very end. Looking ahead, however, the entire quantity (d80 −d90) only varies from 0.5 to 1.2 mm over the energy range of clinical interest (Fig. 15), so that its further variation with energy spread under practical conditions is probably quite negligible.
1.4 Equivalent Thicknesses Occasionally in this report we use ‘water equivalence’ or more generally, the thickness of one material equivalent in stopping power to a thickness of some other material. If millimeter accuracy is required, this needs to be done with some care.
2 A second useful property of d80 is that the width of the Bragg peak at the 80% point is a good choice for the stepsize of a range modulator.
5 Fig. 4 shows the range-energy relation for lead, brass, Lexan and water, materials commonly used in proton radiation therapy.3 The curves are not quite straight on a log-log plot (the range-energy relationship is not exactly a power law) nor are they quite parallel. The stopping power ratio of two materials (ratio of slopes of the range-energy curves) is not quite independent of energy, especially if the two materials are far apart in the Periodic Table. Suppose a proton beam of energy T passes through a thin foil (thickness ∆x1) of material 1. A foil of material 2 is said to be equivalent if its thickness ∆x2 is such that the energy loss of the beam is the same in each foil:
S2(T ) ρ2 ∆x2 = S1(T ) ρ1 ∆x1 (2) where we have written S for the mass stopping power
1 dE S ≡− (3) ρ dx T and ρ stands for density. There is no ambiguity: S is to be evaluated at T , and because the foils are thin T does not change much. However the result may depend upon energy. The predicted water equivalent of 1 cm of Lexan is 1.143 cm at 200 MeV and 1.144 cm at 70 MeV. However, the water equivalent of 0.62 cm of lead (the thickness of second scatterer S2) is 3.556 cm at 200 MeV and 3.355 cm at 70 MeV. The 2 mm difference is just enough to be troublesome. To avoid problems of this sort our computer programs deal directly with ranges and avoid equivalent thicknesses as much as possible. However, this is impractical for the RV itself, a stack of thick brass plates separated by thin polyethylene sheets. In checking whether our measurements agree with theory we would like to treat it as being all brass. While stopping, the protons encounter brass and polyethylene insulator at all energies from the incident energy down to zero. What energy should we use to find the average stopping power ratio of polyethylene to brass? The answer, as can be shown numerically with the aid of range-energy tables, is 0.52 × the incident energy. For any two materials we find
R2 S1 = (4) R S 1 T 2 0.52T where R stands for mean projected range in g/cm2. If we have a stack of equal plates of brass, each of B g/cm2, separated by equal sheets of polyethylene each 2 of P g/cm we find that the average brass equivalent
3Throughout this report we use ICRU49 [4] for everything except brass where we use Janni [5].
6 2 Analysis of the RV Spectrum 2.1 Converting to Charge, Merging, Correcting for Beam Steering The first step is to convert the raw data to nCoul by multiplying by 0.01. The recycling integrator charge quantum is 10 pCoul ±0.2% for all integrators, so we do not need an array of calibration constants. The next step is to merge the data from the upper and lower jaws, creating a combined spectrum in which the numbers are plotted alternately. Based on this spectrum we define the mean range of protons in plates. Protons that stop in the first plate of the non-shifted jaw are said to have an average range of 0.5 plate and plotted accordingly. Protons stopping in the first plate of the shifted jaw have a mean range of 1.0 plate, and so on. Once the spectra have been merged one may see an odd/even effect in the numbers, especially obvious in the continuum, because more beam stops in the upper jaw than in the lower or vice versa. Before taking data it is best to adjust the vertical steering so this imbalance is only a few percent. The residual imbalance is then corrected in software. If QU , QL represent the total charge collected by the upper and lower jaws, we compute the overall asymmetry A ≡ (QU − QL)/(QU + QL) and then correct channel by channel for A.
2.2 Computing x0 The main goal of the analysis was to determine the mean of the EM stopping peak x0 as accurately as possible, testing each procedure for resolution and integral and differential linearity. x0 is expressed in plates. Only at the very end of the analysis, when we check whether x0 measured under each set of conditions conforms to our expectations, do we need secondary information such as the actual thickness of each brass plate, the thickness of the cover plate, and so forth. Because the merged spectrum represents the effect of coarsely binning some underlying fluence v. depth distribution F (x) which is presumably continuous, our first attempts at extracting x0 consisted of assuming various forms for F (x), adjusting the parameters of F to fit the observed binned data and then identi- fying the x0 of the fitted F . We briefly describe these studies for the record. However, in the end a very much simpler procedure, namely a two-step direct computation of the mean of the merged peak, proved to be better.
2.2.1 Fitting the Spectrum It is known that F (x) ≈ G(x) namely the Gaussian function
2 Q − 1 x−x0 G(x) ≡ √ e 2 σ (6) 2πσ which is normalized so the total charge in the peak is Q. The relation
b Q b − x a − x Z G(x) dx = Erf √ 0 − Erf √ 0 (7) a 2 2 σ 2 σ allows us to compute the charge in a bin running from x = a to x = b. Fig. 5 shows one of the better Gaussian fits. The filled and hollow squares represent data from the two jaws. The crosses represent the fitted charge in each bin. The underlying Gaussian has also been drawn, though its relationship to the data points is a bit obscure because the spectrum is merged. For instance, the data
7 point at 10.5 represents the integral of the curve from 10 to 11, not from 10.25 to 10.75 as might be thought. Reasonably good fits are obtained for most of the data taken, and the best measure of x0 is obviously the x0 of the Gaussian. When the deviations from theory using the Gaussian turned out to be fairly large, we tried two other forms to improve the fit in the region leading up to the peak. First, we tried a Gaussian on a polynomial background. However, the fitting procedure would only support a linear background. That is, when we used more than two coefficients in the polynomial, all of the background coeffi- cients developed a large scatter from fit to fit. And when x0 was obtained from the Gaussian with linear background, the deviation from theory was actually somewhat worse than before. Finally, reasoning that the background, which comes from inelastic and near- elastic nuclear interactions, is not really well represented by a polynomial, we approximated F (x)bye raised to a polynomial in x, of which G(x) is a special case. In that case there is no simple formula for the bin counts analogous to Eq. 7, and one must integrate numerically. Also, there is no obvious choice for x0, so we used the maximum of the fitted F . Again, many spectra were fit and the fits were reasonably good, but the deviations from theory were still larger. The fitting method was not discarded lightly. The procedure was automated so that scores of merged spectra were fit with each of the three hypotheses, and the entire analysis described below was carried through in each case. Eventually, though, it turned out that the deviation plots using any of the fits were worse than those obtained using the simple computation to be described next. Only the best one (the simple Gaussian) will be shown later as an example (Fig. 14).
2.2.2 Obtaining x0 Directly The direct two-step computation is very simple. First, we search for the four contiguous points in the merged spectrum that have the most counts. We com- pute the mean value of x for these channels using the usual formula. Using that mean as a center, we define a new range of full-width three channels and recompute the mean, where, since the limits of the new range do not coincide with channel boundaries, we adjust the counts in split bins pro rata. The ‘four’ (an integer) and the ‘three’ (a continuous variable) were optimized to minimize the deviations described below, but the optimum, particularly for the ‘three’, is fairly broad. The first step already gives decent results, but in a few cases minute changes in repeated runs cause the range to jump by one channel, with a corresponding jump in the result. The second step largely cures that. The code and execution time are both vastly shorter for this method than for fitting.
3 Results
Data-taking runs at NPTC fell into three categories: • A run designed to test the resolution of the RV, that is, to find directly how small a change in degrader could be detected. • Runs at various beam energies with various combinations of lollipops to test the integral and differential linearity of x0. For the determination of beam energy these runs relied entirely on the nominal ‘Range at Nozzle Entrance’ (RNE) set by the treatment control program.
8 • A smaller set of runs where the beam was measured, as near simulta- neously as possible, both in the RV and in a Scanditronix (SCX) water tank at isocenter.4
3.1 Resolution This test was done to see whether the RV could detect a very small change in degrader. The box containing the lollipops and range modulators was taken out of the beam. A 1.55 mm lead scatterer was taped to IC1 to broaden the beam at the RV and a set of back-to-back measurements of a few seconds each was recorded. A 0.025 mm lead foil was added and more data were taken. Finally the extra lead was removed and a third set taken. The results are shown in Fig. 6 where the shift in x0 due to the extra lead is seen clearly. There are indications of beam energy drift in the third set. Note however that the entire y range of the graph is 0.1 plate or ≈ 1mmH2O! If the shift in x0 is converted to H2O equivalent, with its standard deviation taken from the scatter in the data sets, we obtain 0.119 ±0.015 mm H2O, in fair agreement with the 0.144 mm H2O equivalent expected for 0.025 mm lead. The fourth data set in Fig. 6 was taken with a vertical beam (the first three were horizontal), and shows that the energy change with gantry angle was negligible at least this time.
3.2 RNE-based Runs: Integral and Differential Linearity Several evening’s worth of data were taken at different settings of RNE, each with several different lollipop combinations. (Previously a program LOLLIES had been written to find the water equivalent of every combination of the nine degraders, so as to allow us to space the data evenly.) Fig. 7 (207 entries superimposed) summarizes the results. Many of the dots represent multiple measurements. The x axis represents predicted d80—mean proton range—at isocenter. More specifically, for each point we take the nominal RNE, apply a small correction based on subsequent SCX measurements (Sec. 3.3), and then deduct the range lost in IC’s, air, and whatever else was in the beam to obtain range at isocenter. One evening the second scatterer S2 was inadvertently left in and this has also been corrected using the known thickness of S2. The y axis (upper frame) represents the raw data with a quadratic fit. The lower frame shows the deviations from the fit. The maximum deviation is less than 0.1 plate and the rms deviation is 0.030 plate. Though not contemptible, this is significantly more than will be found below for the SCX-based runs. To try to account for some of it, we investigated some of the more extreme cases in detail. Four of these are marked in Fig. 7 and displayed in more detail in the next two figures. Fig. 8 shows the RV spectra, of which three show evidence of beam scraping. Even the normal one, #104, has an anomaly in the 12th plate due to leakage current in an integrator, but this clearly did not affect x0. #74 has a fully resolved subsidiary peak which shows that a few protons are passing cleanly through some unintended degrader. #82 shows a broadening of the primary peak; some protons are losing just a little more energy than they should. Finally #110 shows a small but definite shoulder under the peak. This one is somewhat disturbing because Fig. 9 shows that the beam was apparently well steered whereas for the previous two it was not. A survey of all 107 distinct configurations in Fig. 7 found evidence of beam scraping in 16%. We conclude that at least three effects contribute to the scatter
4A second set, with the beam vertical, has not been included. These measurements were considered less reliable because of evaporation during the run as well as the meniscus effect.
9 in Fig. 7: data were taken on three separate occasions, the RNE correction is probably not perfect and finally, the beam scraped in some cases. Nevertheless, the integral and differential linearity look good.
3.3 SCX-based Runs: x0 v. Range in Water The final run combined RV measurements (Fig. 10) with nearly simultaneous measurements in the SCX water tank (Fig. 11). For good measure the RV spectra show the Gaussian fits without background (crosses) but except for Fig. 14 we obtained x0 from the two-step direct computation as stated earlier. Fig. 12 is a first look at the results. Here the x axis represents measured d80 from the Bragg peaks, using a wall correction with three terms: a) the 5 actual wall, 1.5 cm of Lucite , using the H2O equivalent ratio 1.150 from HCL measurements, b) a 1 cm gap deliberately left between the wall and the Markus IC and c) the 1 mm H2O equivalent protection cap of the Markus IC [6]. The circles represent measured x0 from the two-step calculation. The crosses represent a theoretical calculation of x0: assuming measured d80 is correct, one can by correcting for air find the proton energy just entering the RV cover plate and then, using the known thicknesses of the cover plate, the brass plates and the insulator find the expected x0. Doing this we find that we need one adjustable parameter to get decent agreement: the brass plates must be assumed to have 1.0287× their nominal thickness. This 3% effect could well be due to the plates actually being thicker than nominal, being of the same magnitude as was found for a copper MLFC whose plates were individually weighed and measured [1]. On the other hand it could be at least partly due to the range-energy table for brass being wrong relative to water. The deviation plot (lower frame) shows that the linear fit is not quite good enough. Experiment and theory both demand a quadratic term of about the same magnitude. On a moment’s reflection, we are not surprised. Range in brass is nearly but not exactly proportional to range in water because the stopping power ratios depend slightly on energy. The final calibration curve is shown in Fig. 13 where we use a quadratic. As before, we fit the experimental points, but one can see that the deviations of experiment and theory from the same curve are of the same magnitude and much smaller than before. The rms deviation of the experimental points from the fit is 0.013 plates (about 0.14 mm H2O equivalent). As promised, we also show (Fig. 14) the best result from the fitting technique, obtained with a simple Gaussian and no background. The curve is a quadratic fit to the data. This far more difficult technique is not as good as the two-step direct computation of x0.
3.4 RV Calibration Curve With some scaling to make the coefficients more comprehensible the curve in Fig. 13 can be written
d d 2 x = − 0.0515 + 30.3107 80 − 0.5575 80 (8) 0 35 35
As we already know, the quadratic coefficient is small but significant. Its error (not given here) is less than one tenth of its magnitude. At times, we may need the inverse relation. This can of course be gotten from the quadratic formula, but there are large cancellations because of the
5The SCX specifications erroneously say 1 cm.
10 dominant linear term. By expanding the square root in the quadratic formula we can recover a quadratic form for d80(x0) but it is easier and somewhat more accurate to simply reverse the roles of x0 and d80 in the analysis program and re-fit, obtaining
x x 2 d =0.0618 + 40.3957 0 +0.9117 0 (9) 80 35 35
3.5 d80, d90 and RNE
We can use our water tank data to look at the difference between d80 and d90 and to come up with a correction to the nominal Range at Nozzle Entrance (RNE). This is all summarized in Fig. 15, which of course has nothing to do with the RV. The x axis is simply nominal RNE. The full circles represent d80,ent−(nominal RNE), where d80,ent stands for the measured mean proton range at isocenter, corrected back to nozzle entrance by accounting for air, IC’s, and lollipop #4. It is seen that whatever procedure the control system was using for RNE on 24NOV00 was quite accurate. The error is less than ±1mmH2O if, as we should, we define ‘range’ as d80. The fitted curve is the correction that was applied to nominal RNE in Fig. 7. The open circles show d90 translated to nozzle entrance the same way d80 was. The conversion from d80 to d90 is the difference between the two curves and ranges from 0.5 to 1.2 mm H2O over the clinical range of interest. It will vary somewhat with energy spread.
4 Summary and Acknowledgement
The RV was originally intended as a device of rather poor resolution designed to detect major problems with the depth-dose. The present report shows that, au contraire, it is capable of considerable accuracy, on the order of 0.15 mm H2O equivalent at all clinically interesting energies. In the course of these studies it also carried out its mission for the first time, detecting both the inadvertent presence of S2 and the fact that the beam was occasionally scraping. The latter should be taken as a warning shot. It is disturbing that in a set of runs taken with some care there was evidence of beam scraping 16% of the time. We do not yet have a comprehensive picture of the beam trajectory at standard tunes as a function of energy and gantry angle, or of the transverse clearance of the beam at each object. When the beam is properly steered on S2 as is required for a uniform dose, it may sometimes not completely miss the lollipop frames, the neighboring modulator track or some other obstacle. Therefore one would like to use the RV as a diagnostic before treating by closing the collimator and taking a small sample. After such a check, the short-term stability of the magnets would allow one to proceed with confidence. (In the runs that did show beam scraping, the RV spectrum remained the same for sample after sample.) Unfortunately, to do this at present the X jaws must be open, and the Y jaws do not close completely. Therefore the RV test would deliver a small but highly non-uniform proton dose to the patient. If the X and Y jaws were swapped and furthermore, if the X jaws had ridges or in some other way stopped the protons completely, one would have a very sensitive and useful diagnostic. The small additional neutron dose to the patient would be justified by the improved quality control. This modification should be discussed. We are indebted to Yves Jongen, Adrian Van Meerbeeck, Jim Bailey, and others for helping take the data.
11 References
[1] B. Gottschalk, R. Platais and H. Paganetti, ‘Nuclear interactions of 160 MeV protons stopping in copper: a test of Monte Carlo nuclear models,’ Med. Phys. 26 (12) (1999) 2597–2601 [2] M. Berger, ‘Penetration of proton beams through water: I. Depth-dose distributions, spectra and LET distribution,’ report NISTIR 5226, U.S. Natl. Inst. of Standards and Technology, Gaithersburg, MD 20899 (1993) [3] T. Bortfeld, ‘An analytical approximation of the Bragg curve for therapeu- tic proton beams,’ Med. Phys. 24 (12) (1997) 2024-2033 [4] Berger et al., ‘Stopping powers and ranges for protons and alpha particles,’ International Commission on Radiation Units and Measurements (ICRU) report 49 (1993) [5] J.F. Janni, ‘Proton range-energy tables, 1 KeV–10 GeV, Part 1. Com- pounds,’ Atomic Data and Nuclear Data Tables 27 (1982) [6] Instruction Manual for Markus Chamber type 23343, PTW New York, 2437 Grand Avenue, Bellmore, NY 11710
List of Figures
1 Raw RV data, merged and corrected for beam centering...... 13 2 Portion of an RV spectrum showing seven back-to-back data sam- ples...... 13 3 Fluence, differential fluence and dose as a function of depth for proton beams of a given range and different energy spreads, il- lustrating r0 = d80...... 14 4 The range-energy relation for three common materials...... 14 5 Gaussian fit to an RV spectrum...... 15 6 RV resolution: effect of 0.12 mm water equivalent of lead. . . . . 15 7 Measurements with various combinations of incident beam ener- gies and lollipops. Upper frame: mean plate number x0 v. d80 at isocenter predicted from range at nozzle entrance. The dots are data and the line is a quadratic fit. Lower frame: scatter about the fit, with a few cases marked for later discussion...... 16 8 RV spectra for the cases marked in Fig. 7 ...... 17 9 Transverse distributions for the cases marked in Fig. 7 ...... 17 10 RV spectra corresponding to Fig. 11 ...... 18 11 Bragg curves obtained with the Scanditronix water tank...... 18 12 Upper frame: mean plate number x0 v. d80 measured at isocen- ter. The line is a linear fit. Dots: measured data. Crosses: theoretical prediction. The theory has a single parameter, the effective brass plate thickness, which has been adjusted for the best overall fit. Lower frame: scatter from the linear fit...... 19 13 Same as Fig. 12, but the line is a quadratic fit. This is the final calibration curve...... 19 14 Same as Fig. 13, but the Gaussian fit method was used for x0..20 15 Corrections to RNE, the control system’s Range at Nozzle En- trance in force on 24NOV00. The upper curve (a quadratic fit to the data) should be used to obtain d80,ent, the lower to obtain d90,ent...... 20
12 Figure 1: Raw RV data, merged and corrected for beam centering.
Figure 2: Portion of an RV spectrum showing seven back-to-back data samples.
13 Figure 3: Fluence, differential fluence and dose as a function of depth for proton beams of a given range and different energy spreads, illustrating r0 = d80.
Figure 4: The range-energy relation for three common materials.
14 Figure 5: Gaussian fit to an RV spectrum.
Figure 6: RV resolution: effect of 0.12 mm water equivalent of lead.
15 Figure 7: Measurements with various combinations of incident beam energies and lollipops. Upper frame: mean plate number x0 v. d80 at isocenter predicted from range at nozzle entrance. The dots are data and the line is a quadratic fit. Lower frame: scatter about the fit, with a few cases marked for later discussion.
16 Figure 8: RV spectra for the cases marked in Fig. 7
Figure 9: Transverse distributions for the cases marked in Fig. 7
17 Figure 10: RV spectra corresponding to Fig. 11
Figure 11: Bragg curves obtained with the Scanditronix water tank.
18 Figure 12: Upper frame: mean plate number x0 v. d80 measured at isocenter. The line is a linear fit. Dots: measured data. Crosses: theoretical prediction. The theory has a single parameter, the effective brass plate thickness, which has been adjusted for the best overall fit. Lower frame: scatter from the linear fit.
Figure 13: Same as Fig. 12, but the line is a quadratic fit. This is the final calibration curve.
19 Figure 14: Same as Fig. 13, but the Gaussian fit method was used for x0.
Figure 15: Corrections to RNE, the control system’s Range at Nozzle Entrance in force on 24NOV00. The upper curve (a quadratic fit to the data) should be used to obtain d80,ent, the lower to obtain d90,ent.
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