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Uniform depth dose distribution for biological irradiation using negative pions

This content has been downloaded from IOPscience. Please scroll down to see the full text. 1979 Phys. Med. Biol. 24 1243 (http://iopscience.iop.org/0031-9155/24/6/014) View the table of contents for this issue, or go to the journal homepage for more

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PHYS. MED. BIOL.,1979, Vol. 24, NO. 6, 1243-1249.

Printed in Great Britain

Uniform Depth Dose Distribution for Biological Irradiation using Negative Pions GABRIEL K . Y. LAM, PH.D., R. MARK HENKELMAN, PH.D., ROBERT W . HARRISON, RI.SC., LLOYD D. SKARSGARD, PH.D. and BRANKO PALCIC, PH.D. British Columbia Cancer Foundation, and Batho Biomedical Facility, TRIUMF, University of British Columbia, Vancouver, British Columbia V6T 1W5, Canada

Received 7 March 1978, in$nal f o r m 24 A p r i l 1979 ABSTRACT. A simple, flexible techniquehas been developed to generateuniform depth dose profiles for the biomedical pion beam at TRIUXF using dynamic momentum control and linear programming. Either the entrance dose or the irradiation time required for a certain dose over the uniform region can be minimised. The dynamic momentum control can operate automatically under computer control even with a highly unstablebeam. Cell survival profiles have been obtained for this uniform dose distribution using the gelatintechnique.The RBE increases with increasing depth through the uniform dose region.

1. Introduction

The biomedical pion beam channel a t TRIUMF has been in operation since 1975. The channel characteristics and the results of some physical and radiobiological measurementshave been described (Harrison and Lobb 1973, Henkelman, Skarsgard, Lam, Harrison and Palcic 1977, Skarsgard, Henkelman, Lam, Harrison and Palcic 1977). As this channel does not in general produce a beam giving a uniform depth dose profile over an extended depth, as would be required for radiotherapy treatment, a simple systematic t'echnique for providing this profile has been developed. This is based on the dynamic control of the beam momentum and momentum distribution during irradiation. Thebiological effect of this uniform depth dose profile obt'ained in this way has also been studied using CH0 cells with the gelatin technique (Henkelman, Lam, Harrison, Shortt, Poon, Lang, Jaggi, Palcic and Skarsgard 1977). Uniformdepth dose profile The general technique for producing a desired depth dose distribution is to superpose a finite number of beams of differing momenta andtherefore differing range(Larsson 1961, Koehler,Schneider and Sisterton 1975, Liska 1977, Lloyd, Reading, Purrott, Hynes, Spinks and Stephenson 1978). The TRIUMF biomedical beam line has a set of two momentum-defining blades which are operated under computer control for defining the momentum distribution of the irradiation beam (Harrison and Lobb 1973). These blades can be moved during an irradiation in a mode which will be referred to hereafter as dynamic momentumcontrol. As illustratedin fig. 1, by varying the position of the 2.

0031-9155/79/061243+07$01.00

@ 1979 The Institute of Physics

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Gabriel K . Y . Lam et al.

Fig. 1. Depth doseprofile generated by various settings of the momentum-defining blades. -, both blades completely open; - - -, low momentum blade half closed, high momentum blade open; -,high momentum blade closed t o 10% of maximum opening, low momentum blade open; . *, low momentum blade closed to 10% of maximum opening, high momentum blade open.

---

momentum-defining blades, both the width and theaverage depth of the peak dose region can be varied over a range constrained by the channel momentum acceptance which is Aplp = 14% full width a t half maximum. However, by reducing the momentum acceptance, partof the pion flux is removed from the beam and hence the average dose rate over the region of interest decreases. This decrease inoverall dose rate when t'hemomentum-definingbladesare partially closed during an irradiat'ionmust be takeninto consideration in generating uniform depth dose profiles. The practical deliveryof the component dose profiles requires the correct number of pions for each momentum distribution to be delivered. This is complicated by fluctuating beam intensities and requires that the momentumbladepositions be changedinrelation to the monitored beam rather than according to fixed time intervals. Theaddition of anumber of different depth dose profiles to generatea required profile cannot be solved directly, particularly when the input is in the form of discrete empirical measurementswhich are noteasily represented by simple analytic equations. Trial and error solutions can be found but are not necessarily optimal. However, providedthe depthdose data have been measured a t a set of fixed depths, the combination of t'he distribut,ions can be handled conveniently using standard linear programming techniques. 3. Thelinearprogrammingtechnique

The general linear programming problem can the following form (Gass 1969). The objective function y = c,x,+c,x,+

be stated mathematically in

... + C , % ,

(1)

is tot be maximised or minimised subject t o the set of linear constraints on the

Uniform Pion Depth Dose Profile

1245

variables xl,x2,... ,x, such that xj>O, j = l , ...,n

and

a,,x,+a,,x,+

U,,

where

(2)

...+U , , X , ~ b ,

x1+a,, x2+ .. . + a,,,, x , 6 b,

aij,b,, c j ,

i j

...)m = 1, ., .)n are = 1,

constants.

Both equalities and inequalities canbe used in eqn (3). Linear programming problems of this type canbe readily solved using the Simplex method (Dantzig 1951).

Toapplythe linearprogrammingtechniquet'o the uniform depth dose problem, the region over which the dose is to be made uniform is first divided into equal depth intervals such that there are m locations p l , p 2 , ...,p,,,. A set of n depth dose measurements wit'h different momentum distributions is made over these m locations and the data obtained a t location p , for the jth depth dose are designated aij. The unknown variable x j will be the relative contribution of t h e j t h dept'h dose component required to produce the total dose b, a t location p i . The b, values are equal for a uniform dose profile but they may not be the same if non-uniform profiles are required. For our beam line, the measurements of depth dose componentsareobtainedbysettingthe momentum-defining blades a t different positions. A st'andard set is obtained by keeping one blade fixed and progressively closing the other blade. Various parameters canbeoptimisedin the objectivefunction.Forinstance,t'he entrance dose can be minimised and in this case t'he ci values in eqn (1) will be the ent'rance doses for the individualdepth dose distribution.To minimise the overall time for irradiat'ion, the cj values will be the time for obtaining a beam monitor pulse (which will be defined later in t'his section) forthe various momentum-defining blade settings. (3) aresetas However, it is observed that if all the constraintsineqn equalities, the mathematical constraint becomes extremely severe and usually t'here is no solution, because of experimental variation in the measured depth such dose curves. A const'ant bo is therefore introduced into t'he constraints that eqn (3) becomes

Gabriel K . Y . L a m et al.

1246

This effectively requires the summation dose to be between bi +bo and bi - bo instead of being exactly equal to bi. It should be not'ed that this manoeuvre will double t'he number of constraints. TTit'h this modification, it' is observed that solut'ions for uniform dept'h dose profiles are readily available for values of b o b i as small as 0.1%. The introduction of a tolerance term bo is also logical from the practical point of view. bo/bi is a measure of t'he composite dose uniformity. I t does not seem reasonable t'o generate adose profile with uniformit'y better than the statistical uncertainty in the individua'l depth dose measurement's. The input set of depth dose profiles for the linear programming problem is obtained for various sett'ings of the momentum-defining blades using an automatic dose mapping system (Lam, Henkelman and Harrison 1978). The data obtained wjt'h this system are automat'ically normalised with respect to beam intensity using beam monitor puIses from a current integrator which reads a transmissionchamber.Thesolution tothe linearprogrammingproblem minimised ineitherentrance dose or total irradiationtime will be aset of numbers defining the contributions required from each of the various depth dose components. These numbers are then rounded off into a set of reasonable integral numbers which will be the numbers of beam monit~or pulses required of the correspondingsettings of the momentum-definingblade foreach configuration. These numbersandthe momentum-definingblade configurationsaretheninputtothe beam line controlcomputer which setsupa momentum-defining blade cycle and executes the uniform depth dose profile irradiation as shown in fig. 2 . The computer controls the momentum-defining blades by means of a' pulse generator and stepping mot'ors. The position of t'he momentum-defining blades arealso const'antly monitoredby analogue readback from potent'iometers. The tot'al momentum-defining blade movement time in a cycle is typically 5 S. I n order to make this transition time negligible, the Blomedlcal channel Highmomentu beam definlng Programmable blade

Steppmg motor controller

beam deflnlng blade

Stepplng motor controller

pulse generator

Computer

l' I

Analogue readbacK Anolo ue

to dlglta? converter

I

Tronsmlsslon Ionisailon Monltor Current pulses Inregrator current chamber

Preset scalar

I1

Fig. 2. Block diagram for the computer control of the uniform dose irradiation.

Uniform Pion Depth Dose Projile

1247

cycle time was set to be about 10 min so that t,he momentum-defining blades can be assumed to move instantaneously. One of the uniform depth dose profiles generated for the biomedical channel is shown in fig. 3. It is uniform to 0.2y0 over an extent of 6 cm (from depth 19 cm to 25 cm) and is made up of superposing five depth dose profiles, each with a different range distribution, also shown in fig. 3. The individual depth dose measurements were made a t intervals of 5 mm using an ionisation chamber dose profile of 0.5 cm3sensitive volume along the beamaxis.Theuniform has been opt'imised for minimum total irradiation time. The excellent agreement between the calculated profile, as shown in fig. 3, and the measured profile, as shown in fig. 4,indicat'es t'hat the system is working satisfactorily. 1.2 1.0

l

1

._ 9 X

E

I

'

,

\'

\

l

a,

LL

OL

0

30

0 .S 10 15 20 25 30 35 L0 Depth in wa!er ( c d Fig. 3. Generation of a uniform depth Fig. 4. Depth survival curve of CH0 dose profile by addition of various cells obtained with the depth dose depth dose profiles obtained with profile. The depth dose profile is different momentum-defining blade measured experimentally and the settings. -, the individual fluctuation of the data is within the depth dose profiles (measurements width of the line drawn. Peak 5 mm intervals but dose: curve 1, 2.14 gray; curve 2, were made at continuous curves were drawn for 4.66 gray; curve 3, 7.28 gray. clarity) ; - - - -, the partial sums; , the total depth dose profile. 5

10 15 20 25 Depth In water (cm)

35

-

4. Radiobiologicalresults

Depth cell survival profiles were obtained for the above uniform depth dose profile using Chinese hamster ovary cells suspended in a gelatin matrix. The cells were suspended a t 37 'c innutrient mediumcontaining 25% gelatin. This suspension was loaded into long polycarbonate tubes (1.2 cm diameter x 30 cm long), cooled to 0 'C and irradiated under oxygenated conditions with on the beam axis. The cell concentration was the axis of thetube 5 x lo5 cells ml-l. The dose rate at the peak region was approximately 50 rad h-1 with about 35% electron and 10% muon contamination in the pion beam of 180 MeV/c midline momentum.Thepeak doses were measured using an 60Co machine and allowing a correction ionisation chamber calibrated with a

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Gabriel K . Y . L a m et al.

factor of 0.95 for the different TB values and stoppingpowers for pions (Dicello 1975). The results are shown in fig. 4. 5. Discussion and conclusion

A simple technique for generating uniform depth dose profiles for a particle t'herapy beam using dynamic moment'um control and linear programming has beendescribed.The advantages of thistechnique can be summarised as follows : 1. When there is more than one feasible solution to satisfy the dose uniformity requirement, this t'echnique can select the unique solution optilnised in a certain parameter, e.g. minimum entrance dose or maximum average dose rate. No trial and error is involved. 2. The technique is not limited to generating only uniform flat, topped distributions. It can be readily observed that by changing the bi value in eqn (3) any reasonable depth dose profile can be generated. S o changein any hardware is required. 3. The computer execution of the composite dose profile through the use of beam intensit'y monitorpulses enables the system to run automaticallyeven with a pion beam that fluctuates in int'ensity. Theabovelinearprogrammingtechniquecan also be used to generate special depth dose profiles by the dynamic range shifter as well as with our dynamicmomentumcontrol. I n this case,dept'h dose profiles generat'ed by range shifting in discrete steps would be used as input to the linear programming problem and for automatic execution, t'he range shift'er to has be under computer control a's well. The depth cell survival profiles obtained are not flat over t'he uniform dose region for the different doses used. They all decrease towards the deeper end of t'he uniform dose region where the pion stopping density can be shown to be highest (Xordell, Baarli, Sullivanand Zielczynski 1977, Henkelman and Lam 1979), showing an increase in RBE with increase in pion stopping density. This resultindicates that the specification of the dose alone is not adequate to characterise the biological effect of a pion beam. The qua'lity variation of the beam has also to be ta,ken into consideration. This work was supported by t,he British Columbia Cancer Foundat'ion a'nd the Nat'ional Cancer Institute of Canada. The authors wish to thank Nrs. I. Harrison and Mi. B. Douglas for expert technical assistance in conducting the biological experiments and Dr. J. T. Sample and the TRIUMF staff for excellent cooperation.

RESUME Distribution uniforme de dose en profondeur pour irradiation biologique utilisant des mi.sons negatifs v n e technique simple et flexible a et6 mise au point pour engendrer des profils de dose en profondeur uniformes pour le rayon B mesons biomedical Q TRIULIPH en utilisant un contrC% du moment dynamique et m e programmation lineaire. La dose d'entr6e ou le temps d'irradiation nkcessaire Q une certain8 dose sur une region uniforme peut etre r6duit. Le contrek du moment

Uniform Pion Depth Dose Profile

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dynamique peut &re effectui: automatiquement par ordinateur meme avec un rayon hautement instable. Des profils de survie de cellules ont 6 t h obtenus pour cette distribution uniforme de dose en utilisant la technique de la gelatine. L’efficaciti:biologique relative augmente en m6me temps que la profondeur sur tout’e la region de dose uniforme.

ZUSAMMENFASSUNG Einheitliche Tiefendosisverteilung bei der biologischen Bestrahlung mit negativen pi-Mesonen Zur Erzeugung einheitlicher Tiefendosisprofile bei der biomedischen Strahlenbehandlung mit pi-Mesonen wurde eine einfache, anpassungsfahige Methode entwickelt. Bei dieser TRIURIFBehandlungsart kommt eine dynamische Jiomentsteuerungund lineare Programmierung zur Anwendung. Es ist moglich, entweder die Eingangsdosis oder die verlangte Bestrahlungsdauer bei einer bestimmten Dosis innerhalb einer einheitlichen Korperzone zu minimisieren. Die dynamische Momensteuerung kannautomatisch funktionieren,indem ein Steuerkomputer angeschlossen wird. Dies trifft auch dann zu, wenn es sich um einen stark unstabilen Strahl handelt. Mit Hilfe der Gelatine-Methode gelang es, fur diese einheitliche Dosisverteilung Profilbilder zu erhalten, die das uberleben der bestrahlten Zellen kennzeichnen. Mit zunehmenderEindringtiefedurch die einheitliche Dosiszone nimmt auch der RBE, d.h. der radiobiologische Effekt, zu.

REFERENCES DANTZIG,G. B., 1951, A c t i v i t y A m l y s i s of Production and Allocation (Pu’ew York: Wiley). DICELLO,J. F., 1975, i n Proc. Particle Radiation Therapy International Workshop, Key Biscayne, Flu. (Philadelphia: American College of Radiology). GASS, S. I., 1969, Linear Programming, Nethods and Applications, 3rd edn ( X e w York: RlcGraw-Hill).

HARRISOK,R.W., a n d LOBB,D. E., 1973, I E E E T r a n s . N u c l . S c i . , NS-20, 1029. R. M., LAM,K. Y., HARRISON,R. W . , SHORTT,K. R., POOX,M., LASG, H., HEXKELMAN, JAGGI, B. W., PALCIC, B., a n d SKARSGARD,L.D., 1977, T R I C M F External Report TRI-77-2. HENKELMAN, R. M., a n d LAM, G. K. Y., 1978, i n Proc. Gth S y m p . o n Xicrodosimetry (Brussels: CEC) Vol. 1, p. 497. HENKELMAN, R. M., SKARSGARD,L. D.,LAM,G. K. Y., HARRISON, R.W., a n d PALCIC, B., 1977, I n t . J . Radiat. Oncol. Biol. Phys., 2, 123. KOEHLER,A. Rf., SCHNEIDER,R. J., a n d SISTERSOT,J. M., 1975, S u c l . I n s t r u m . J d e t h . , 131, 437. LAM,G. K. Y., HENKELMAT,R. M,, a n d HARRISOX, R. W., 1978, P h y s . M e d . R i o l . 23, , 768. LARSSOX,B., 1961, B r . J . Radiol., 34, 143. LISKA, D. J., 1977, Rev. S c i . I n s t r u m . , 48, 52. LLOYD,D. C., READIXG,D. H., PURROTT, R. J., HYNES,M . A., SPIKKS, TV. S., a n d STEPHENSON, B. D., 1978, B r . J . Radiol., 51, 41. NORDELL,B., BAARLI,J . , SULLIVAN,A. H., a n d ZIELCZYNSEI,M,, 1977, Phys. Med. Biol., 22, 466. L. D.,HENKELMAN, R. M., LAM,G. K. Y., HARRISON, R. W., and PALCIC, B,, SKARSGARD, 1977, in Radiobiological Research and Radiotherapy, STI/PUB/44 (Vienna: IAEA).

Uniform depth dose distribution for biological irradiation using negative pions.

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