Beam localization via 15O activation in proton-radiation therapy

NUCLEAR INSTRUMENTS AND METHODS

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0975) 333-338;

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BEAM LOCALIZATION VIA 1SO ACTIVATION IN PROTON-RADIATION THERAPY* G. W. BENNETT, A. C. G O L D B E R G , G. S. LEVINE, J. G U T H Y and J. BALSAMO

Brookhaven National Laboratory, Upton, New York 11973, U.S.A. and J. O. A R C H A M B E A U

Nassau County Medical Center, East Meadow, New York 11554, U.S.A. Received 7 October 1974 and in revised form 29 January 1975 The importance of beam localization to heavy charged-particle radiation therapy is discussed. The results of the cross section for 150 production by 200 MeV protons on 160 are presented. Using published values for the cross section for this reaction at energies below 150 MeV the dose and event density to be

expected from proton irradiation of a cylindrical tissue-equivalent p h a n t o m are calculated. Applications of this mechanism are discussed for beam localization, and mapping internal body structures of differing density and oxygen content.

1. Introduction

ciency. The direction of the gamma ray must be determined by means of a multi-hole collimator. The effective solid angle of the detector decreases as the square of the resolution. In positron annihilation, the location of both gammas specifies the position of the originating event along the line connecting the detection sites of the two gamma rays. In this case a collimator is not necessary and the effective solid angle of detection is increased enormously. Alpha-particle beams have been used to activate positron-emitting nuclides in vivo, particularly 1~C, and have successfully defined the beam interaction region by means of an off-line positron camera6). Positron activity versus depth has been measured in gelatin exposed to a 100 MeV negative pion beam~). Techniques for mapping the spatial distribution of stopping pions in tissue have been surveyed8). In addition to deexcitation and annihilation gamma rays, pions and protons produce neutrons which are difficult to detect. Pions also generate characteristic X-rays (pi-mesic X-rays) and energetic gamma pairs of small angular separation from neutral-pion decay. Of the five methods discussed, the detection of single gamma rays using a multi-hole collimator was preferred, supplemented, if necessary, by detection of positron annihilation. In the present work, it is demonstrated that the activation of 150 by the interaction of a therapeutic proton beam and oxygen nuclei in tissue, and the detection of the positron annihilation radiation from the 1sO decay provides a beam-location mechanism with reasonable precision and dose. Among the primary advantages of oxygen are its relative abundance in the human body (65%), the short half life of 150 (2 min) and the large cross section for ~50

Intermediate-energy proton beams are presently used for irradiation of the pituitary gland~), and for cancer therapy in the U.S.A.2), Sweden a) and the U.S.S.R.4). These beams can provide a dose distribution which is better confined to the target volume than is possible using conventional high-energy photon irradiations. In particular, the sharply defined range of the proton beam permits a sharp cutoff of the dose at the distal edge of the target volume. The distribution of dose vs depth (Bragg curve) permits sparing of overlying tissue. The integral dose to normal tissue from conventional radiation can be two to five times greater than for proton-radiation therapyS). Unfortunately, this virtue shines in theory but can vanish in clinical applications where tissue density is not uniform. Successful exploitation of radiation therapy using protons or other heavy charged particles (pions, heavy ions) ~equires some means to measure the spatial distribution of the beam in complex tissue. In particular, the axial distribution of the beam must be available, or tissue density in the treatment field must be mapped and compensated for. High-resolution beam localization is made possible by employing the interactions between beam particles and the atomic nuclei of the material traversed by the beam. Proton interactions produce isotropic and independent gamma rays from nuclear deexcitation, and pairs of oppositely directed gamma rays from positron-emitting nuclides generated by the beam. Single gamma rays pose problems in detection effi* Work performed under auspices of the U.S. Atomic Energy Commission.

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BENNETT

production by intermediate-energy protons down to a low threshold energy, 20 MeV. 2. Measurement of 160(p,pn)lSo cross section at 200 MeV Proton therapy beams with maximum energy of about 200 MeV have sufficient range to be most useful in clinical applications. However, the cross section for SO production has not been previously published for incident proton energies between 156 MeV and 360 MeV. We have measured the cross section for the reaction 160(p, pn)1SO, relative to the well-known reaction ~2C(p,pn)l~C, using protons of 200 MeV kinetic energy. Three 1 cm 3 samples of methyl methacrylate (C~H802) were irradiated for short periods (30#s) in the beam from the Brookhaven Proton Linac. Within one minute, 1-3 m m size chips of the samples were placed in a NaI(TI) well counter, and counted at 20-s intervals. A single-channel analyzer was adjusted by means of a 22Na source to detect the double-capture peak from positron annihilation in the well counter. Both ~tC and ~SO are pure positron emitters. The decay rate vs time for one of the samples is shown in fig. 1. Two components were evident, one with a 2-min half life ascribed to ~~O, and the other with a 20-rain half life ascribed to ~~C. Using the mean lives T O = 2.98 minutes (half life = 1 2 4 s ) for 150 and Tc=29.47 rain (half life = 20.4rain) for ~ C , the raw data were fitted to a function of the form: C(t)

=

N o exp +/VB

[-t/To]+#lc exp [-t/Tc] +

exp [ -

time, t, after bombardment, and No and Nc are the initial decay rates for the ~50 and 1~C, respectively. NB and TB are free parameters to account for any other component. The average value of No/#/c was found to be 3.44-0.2. The goodness of fit may be judged from the value of [z2/degrees of freedom] -~, which was 0.97-1.78 for the three samples. The fitted half life for the " b a c k g r o u n d " component was 0.3 minutes, apparently 1°C; the average background rate, NB//Vo, was 1.6. Note that 1~C results from p + t 6 0 reaction as well as from the p + ~ 2 C reaction. The observed ratio ~/o//9c is then related to the appropriate cross sections by: To #lo(nc acc + no aco) a°

Tc Nc no

=

'

where oo

=

o-[160(p,pn)150],

O'cc ~ o-[12C(p,pn)llC], aco - a[leO(p,3p3n)11C] , and, no = 2 and nc = 5 are the relative abundances of the corresponding nuclei in methyl methacrylate. The excitation function for the 12C(p, pn)l~C reaction has been thoroughly investigated because of its value in beam-intensity monitoring9). The cross section has the value ( 3 9 + 2 ) m b at 200 MeV. The cross section @ o = ( 1 1 4 - 1 ) m b for a proton enelgy of 155 MeVI°); aco=(13.64-1.6) mb at 362 and 383 MeV ~x). Choosing a c o = ( 1 2 + 2 ) mb, the 150 cross section at 200 MeV is then: ao = (37.7 4- 3.7) rob.

t/TB],

where C(t) is the experimentally observed decay rate vs .E I 0 E E

et al.

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TIME (MINUTES) IO Fig. 1. D e c a y curve for methyl methacrylate sample irradiated by 200 MeV protons. T h e solid points are experimental data. T h e line t h r o u g h the solid points indicates the c o m p o n e n t with 20.4 m i n half life. T h e open points are obtained by subtracting the 20 rnin constituent leaving a 2 m i n c o m p o n e n t (line t h r o u g h open points).

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function for the reaction

160(13 ,

pn)150.

335

BEAM L O C A L I Z A T I O N VIA 1 5 0 A C T I V A T I O N

This is shown in fig. 2, to compare with the values from Orsay at energies up to 155 MeV, and with the Liverpool results at 362 MeV 11). In addition, a 2 g sample of ground beef muscle, including fat and bone, was irradiated in the 200 MeV beam and counted in the same manner as the acrylic samples. The least-squares fit to these data gave No//~/c = 7.9, NB/No = 0.27, [z2/degrees of freedom] } = 1.16. In this case, the fit was relatively insensitive to the background component with half lives between 0.3 and 1.0 minutes. 3. Beam localization

The range, in cm, of protons in biological material is determined primarily by the density of the material traversed by the beam. Second-order corrections account for the effect of different effective ionization potentials. Bone, the density of which can be as high as 1.85, can shift the location o f the Bragg peak forward (upstream) by an amount about equal to the thickness of overlying bone. Conversely, overlying air volumes in lung or intestine can cause the peak to be shifted downstream by a distance comparable to the axial dimension of the void. An efficient detection apparatus is rather narrowly defined by the characteristics of the chosen nuclide and its emission. The positrons from 150 are emitted isotopically and travel some distance before annihilating at rest with an electron to give a pair of 5l 1 keV g a m m a rays with opposite directions. The axes formed

DETECTOR50 crn DIA

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rl/////I//I/IA/llllllll//d ~"~AXIS OF DETECTORS Fig. 3. Geometry assumed for calculating dose and detected event density. Lines connecting detectors represent positronannihilation gamma rays.

TABLE 1 Composition of the human body. The major elements that compose the human body and their approximate relative amounts are shown. Per cent

Oxygen Carbon Hydrogen Nitrogen Calcium Phosphorus Potassium Sulfur Sodium Chlorine Magnesium Iron Zinc Rubidium Silicon (estimated)

65.0 18.0 10.0 3.0 1.5 1.0 0.35 0.25 0.15 0.15 0.05 0.004 0.0033 0.0017 0.0017

Approximate amount in a 70-kg man (grams) 45 500 12 600 7 000 2 100 1 050 700 245 175 105 105 35 3 2.3 1.2 1.2

by these g a m m a pairs are also isotropic. The g a m m a rays are absorbed in muscle tissue with a mass absorption coefficient of 0.095 c m - 1 . Projection of the photons onto the detector plane by means of pin-hole optics or a multihole collimator reduces the solid angle and thus the net efficiency by many orders of magnitude. "Coincidence-collimation" detection using a positron camera as developed by Anger 12) offers good efficiency, practicality, and resolution. The schematic of the beam localization set up is idealized in fig. 3, a horizontal plane through the patient (phantom), detectors and beam. Each sodium-iodide detector is viewed by an array of photomultiplier tubes. Positron-annihilation events are defined by the simultaneous detection of g a m m a rays in both detectors. The location of each photon in the sodium iodide is determined from the relative pulse heights in the photo-tubes. The site of the annihilation then lies on the line connecting the photon-detection sites in the two crystals. Given sufficient detected events the beam interaction region can be reconstructed. The practicality of this procedure depends on the magnitude of dose necessary to get a " p i c t u r e " of the beam. To calculate the approximate event density and absorbed dose to be expected, a proton beam of I cm 2 cross-sectional area, is assumed to be incident on the 30 cm diam. cylindrical phantom, of unit-density material, constituted as in table ! 13). Two cases are considered, one with a beam of 200 MeV which

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G . W . BENNETT et al.

penetrates 25.5 cm (point B, fig. 3); the second with an energy of 150 MeV where the beam can penetrate just to the center of the p h a n t o m (point C, fig. 3). The number of detected events is N d e t -~- N p r o d

TAE.

where T is the fraction of annihilation photons transmitted through the phantom, A is the fractional solid angle subtended by the detectors, E is the net efficiency of the detectors, and Nprod is the number of 15 0 nuclei produced. Nprod

~

No~xN p.

Here No is the number of oxygen nuclei per c m 3 in 2.55×1022, t7 is the cross section for 150 production (varying with energy and thus depth in the phantom), and x is taken as 1 cm. Np is the number of protons at each depth; for 200 MeV incident beam energy, approximately 40% of the protons are absorbed before they range out. T = e x p ( - u l ) where u = 0 . 0 9 5 c m -~, and I is the sum of the path lengths in tissue for both gammas. The measured photopeak detection efficiency for tissue,

500

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12

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0

4

8 12 16 20 DEPTH,cm OF TISSUE EQUIV.

[

24

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Fig. 4. Dose and detected event density vs depth in the phantom. Incident beam energy is 200 MeV.

511 keV photons in a 1/2" sodium-iodide crystal is 0.1412), but the net efficiency for detecting both gammas is E -- (0.14) 2 -- 0.02. The solid angle of each detector is taken as 1.8 sterad. and thus A = 0.29. The number of protons was chosen so that 300 events per cm of beam path length are detected for the first cm of penetration (point A, fig. 3). The relative dose is available from the Bragg curve, with the absolute normalization of 1.3 x 10 7 protons/ cm 2 = 1 rad at 200 MeV 14). The results are shown in figs. 4 and 5. Note that the m a x i m u m dose is only 20 rads for a peak event late at depth of 110 and 80 detected positron annihilations per cm of beam path length. This result is conservative since the photopeak efficiency was used for the raw detector efficiency. By including Compton-scattered events, the detection efficiency and thus the ratio of event density to dose may increase by as much as a factor of 15, but with some loss in spatial resolution. The number of detected events increases by at least 10% over that shown in the figures when the contribution of carbon activation is included. By integrating the ~50 cross section over the range of the 200 MeV proton beam, it is shown that the total number of annihilation g a m m a pairs produced in tissue is 2.2x 10 -2 per incident proton. This is comparable to the yield for a pion therapy beam, 1.2 x 10-2 per incident pion for all positron emittersT). Typical background rate is 1 event per minute randomly distributed over the detector. Allowing 9 min of beam detection after exposure 95% of the 1SO nuclei will decay, so the anticipated background is a total of nine g a m m a pairs. The peak dose should be compared to the therapeutic dose fraction, typically 200 rads for conventional irradiations. Since the detector solid angle was assumed constant, the data of figs. 4 and 5 indicate the maximum event density for each depth, the density to be expected when the detector axis is at that depth. In practice, the transverse location of the beam at the surface is best detected directly, for example, using a multi-wire proportional chamber. The crucial region is the distal edge of the Bragg peak, so the detector axis should be at or near the expected maxim u m depth of the beam. The axial location of the beam edge can be determined from a computer-generated display similar to figs. 4 and 5. The transverse location can be defined as the region which has the highest volumetric density of event lines formed by the gammadetection points in the two crystals of the positron camera. Three factors affect the accuracy of this technique. First, the energy of the emitted positron is large enough

BEAM LOCALIZATION

(1.7 MeV) that it could travel up to 8 m m f r o m the original oxygen nucleus. However, the mean energy in beta decay is about one third the maximum, and the resulting mean positron range is 2¼ m m in tissue. The rms uncertainty in any of three mutually orthogonal directions is further reduced by a factor o f 1/~/3 to 1.6 mm. Secondly, the threshold energy for the 15 0 activation reaction is 20 MeV, so the last 5 m m o f the p r o t o n range in tissue is not detectable. Finally, scattering can further degrade picture quality. Anger indicates the inherent resolution o f a scintillation camera with ½" thick crystal is 5 m m ; the overall resolution then is of the order o f ¼ cm. 4. D i s c u s s i o n

Clearly the beam characteristics and the nature o f the tissue traversed by the beam directly affect the resulting positron-camera picture. The internal b o d y structure is revealed by this activation technique, particularly the oxygen distribution and gross density variation. The oxygen and, to a lesser extent the carbon density affect the n u m b e r o f positrons generated by the beam; the nature and gross density o f even the overlying tissue 3O0

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VIA 150

337

ACTIVATION TABLE 2

The water a nd oxygen c ont e nt o f various tissues.

Parts analyzed

Skin Skeleton Teeth Striated muscle Brain, spinal cord, nerve trunks Liver Heart e Lungsd Spleen Kidneys Pancreas Alimentary tract Adipose tissues Remaining tissues: liquid solid

% of total wt.

Water content (%)

Oxygen contenta (%)

7.81 14.84 0.06 31.56

64.68 31.81 5.00b 79.52

63.88 31.42 4.94 78.54

2.52 3.41 0.69 4.15 0.19 0.51 0. ! 6 2.07 13.63

7.3.33 71.46 73.69 83.74 78.69 79.47 73.08 79.07 50.09

72.42 70.58 72.78 82.71 77.72 78.49 72.18 78.09 49.47

3.79 13.63

93.33 70.40

92.18 69.53

a Derived from column 3, assuming 90% of oxygen is in the form of water. b Assumed. e Somewhat enlarged. a Somewhat congested.

z

z

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W 0 IE3

12

:______j I 0

4

L

I___

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l

8 12 16 20 DEPTH, cm OF TISSUE EQUIV.

I 24

28

Fig. 5. Dose and detected event density vs depth in the phantom. Incident beam energy is 135 MeV.

determines the fraction of annihilation gammas which are transmitted to the detectors. To study the oxygen and density distributions in the body, the beam should be o f appropriate range (energy), 1 cm in horizontal extent, and a vertical size matched to the field o f interest. The oxygen content and density o f various tissues is indicated in table 2 (adapted f r o m ref. 15). A n air void in the beam path would be quite deficient in oxygen nuclei and would appear " b l a c k " to the positron camera. Muscle tissue would appear brightest because of the high oxygen concentration, but an intervening lateral bone mass can cast a shadow on the detector to reduce this apparent brightness. Bone has a low oxygen content but high density so that the oxygen density m a y be as high as that o f muscle tissue. More p h o t o n absorption occurs, however, even in the absence o f lateral bone. N o t e that the dose is not increased by increasing the transverse beam size if the proton density is unchanged. A large field does cause a reduced solid angle for points off the detector axis. Large detectors are essential for high sensitivity and low dose. Some potential problems with the suggested technique remain to be investigated. The positron-emitting nuclides generated by the beam may be transported via

338

G.W.

B E N N E T T etal.

biological pathways in the body and cause further deterioration in spatial resolution. Neutron contamination in the beam is more penetrating than the protons and can produce a background which will be most detrimental in defining the end of range region of the proton beam. Cellular material contains some elements of low concentration. If their distribution in the body is not uniform, and if these elements have very large activation cross sections, an inaccurate picture of the beam distribution in vivo will result. Preliminary estimates of these effects indicate thay they are small, but some of these effects were observed in the alpha-beam activation experiments at Berkeley6). 5. Conclusion The activation of ~50 in vivo and the use of available positron cameras on-line offer a practical means for defining the interaction region of proton beams in radiation therapy. This method may be used with beams of other strongly interacting particles such as pions, with similar dose and event density. This procedure also produces a type of transverse tomogram which maps the density and oxygen concentration in the body. References 1) R. N. Kjellberg, N. C. Nguyen and B. Kliman, Neuro-Chir.

(Paris) 18 (1972) 235. 2) A. M. Koehler, Cyclotrons-1972, AlP Proc. no. 9 (J. Burgerjon and A. Strathdee, eds.; AlP, New York) p. 586. a) S. Grafman et al., High energy Protons in radiotherapy, recent developments: progress in radiology, Proc. XI Intern. Congress of Radiology (Rome, 1965). 4) V. I. Abazar et al., Report E-5854, Joint Institute for Nuclear Research, Dubna (1971). 5) j. O. Archambeau, G. W. Bennett, G. S. Levine, R. Cowen and A. Akanuma, Radiology 110 (1974) 445. 6) H. D. Maccabee, U. Madhvanath and M. R. Raju, Phys.

Med. Biol. 14 (1969) 213. 7) M. C. Taylor, G. C. Phillips and R. C. Young, Science 169 (1970) 377. 8) j. Sperinde, L. E. Temple, V. Perez-Mendez, A. J. Miller and A. Rindi, Nucl. Instr. and Meth. 97 (1971) 331. 9) j. B. Cumming, Ann. Rev. Nucl. Sci. 13 (1963) 261. 10) L. Valentin, G. Albany, J. P. Cohen and M. Gusakow, Phys. Letters 7 (1963) 163. 11) V. Parikh, Nucl. Phys. 18 (1960) 646. 1~) H. O. Anger, IEEE Trans. Nucl. Sci. NS-13 (1966) 380. 13) B. L. Oser, ed., Hawks' physiological chemistry (McGrawHill, New York, 1965). 14) C. D. Zerby and W. E. Kinney, Nucl. Instr. and Meth. 36 (1965) 125. 15) H. H. Mitchell et al., J. Biol. Chem. 158 (1945) 625. This work gave the composition (water, nitrogen, ether extract, ash, phosphorous, and calcium) of the cadaver of a white male 35 years of age. The oxygen content in table 2 is derived from the water content assuming that 90 % of the oxygen is present in water.