A Monte Carlo Program Converting Activity Distributions to Absorbed Dose Distributions in a Radionuclide Treatment Planning System

Actu Oncologica Vol. 35, No. 3, pp. 367-312, 1996

A MONTE CARL0 PROGRAM CONVERTING ACTIVITY DISTRIBUTIONS TO ABSORBED DOSE DISTRIBUTIONS IN A RADIONUCLIDE TREATMENT PLANNING SYSTEM

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MAGNUSTAGESSON, MICHAELLJUNGBERGand SVEN-ERIKSTRAND

In systemic radiation therapy, the absorbed dose distribution must be calculated from the individual activity distribution. A computer code has been developed for the conversion of an arbitrary activity distribution to a 3-D absorbed dose distribution. The activity distribution can be described either analytically or as a voxel based distribution, which comes from a SPECT acquisition. Decay points are sampled according to the activity map, and particles (photons and electrons) from the decay are followed through the tissue until they either escape the patient or drop below a cut off energy. To verify the calculated results, the mathematically defined MIRD phantom and unity density spheres have been included in the code. Also other published dosimetry data were used for verification. Absorbed fractions and S-values were calculated. A comparison with simulated data from the code with MIRD data shows good agreement. The S values are within 10-20% of published MIRD S values for most organs. Absorbed fractions for photons and electrons in spheres (masses between 1g and 200 kg) are within 10-15% of those published. Radial absorbed dose distributions in a necrotic tumor show good agreement with published data. The application of the code in a radionuclide therapy dose planning system, based on quantitative SPECT, is discussed.

Treatment planning in external radiation therapy and brachytherapy concerning the absorbed dose in the target region are accurate within 5%. In systemic radiation therapy (SRT), the accuracy depends to a large extent on the biokinetics, sometimes difficult to obtain. An accurate knowledge of the absorbed dose to tumors and to other tissues is important both for safety and optimizing, but also when evaluating the radiobiological effect of the therapy. The absorbed dose to normal tissues may also set a limit to the maximum activity that is possible to administer. Received 20 April 1995. Accepted 29 December 1995. From the Department of Radiation Physics, Lund Unversity Hospital, Lund, Sweden. Correspondence to: Dr Magnus Tagesson, Department o f Radiation Physics, Lund University Hospital, S-22185 Lund, Sweden. Paper presented at the 4th Scandinavian Symposium on Radiolabeled Monoclonal Antibodies in Diagnosis and Therapy of Cancer, January 15- 17, 1995, Lillehammer, Norway.

0 Scandinavian University Press 1996. ISSN 0284-386X

The activity distribution is obtained with scintillation camera imaging. Whole-body planar imaging shows the distribution in 2D. Due to over- and underlying activities accurate quantification is difficult. Errors up to 30% have been reported in studies where conjugate-view attenuation correction methods have been applied (1, 2). We have earlier suggested the use of quantitative SPECT for absorbed dose calculation, if accurate correction for the photon attenuation and the scatter contribution can be made (3, 4). By repetitive SPECT studies over several days, the biokinetics, the absorbed dose-rate and the cumulated absorbed dose can be obtained. The MIRD formalism (5) is today the most used method for calculation of the mean absorbed dose to regions of the human body. Several data with absorbed fractions and S values (6-8) and computer codes with the possibility to include the biokinetics in the calculations (9, 10) have been published. The main limitation using the MIRD is its standardized geometry, not allowing arbitrary activity distributions. This is sufficient for radiation protection pur-

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poses in the diagnostic use of radionuclides where mean values should be. used. In systemic radiation therapy a more flexible code is needed. Even if the basic definition of the S value has no restrictions, the data published in MIRD pamphlet No. 11 (6) are restricted to standardized masses, shapes and locations of the organs, based on ‘Reference Man’, published in ICRP publication No. 23. The S-values have also been calculated for a homogeneous activity distribution in the source organ and all electrons and b-particles are assumed to be locally absorbed. The shape, position and mass of an organ differ from one human to another and radiopharmaceuticals are rarely uniformly distributed in organs. The use in SRT of MIRD S-values may therefore give discrepancies. The absorbed dose calculation in radiation therapy is suggested to be based on information of the individual patient’s organs and tumor localization and size. Different methods for conversion of activity distributions to absorbed dose distributions have been suggested in the literature. The use of analytical dose point kernels (1 1, 12) is a straightforward convolution procedure but has generally the disadvantage of not taking inhomogeneities into account in the calculations. If the convolution procedure is made in the spatial domain, the kernel may, however, be rescaled to correct for the inhomogeneities. Uncertainty in the absorbed dose still occurs in the lung and bone regions because of the differences in photon/electron cross sections and scattering properties for soft, bone and lung tissue. The Monte Carlo technique (see for instance (13)) can be used to overcome these limitations. The method is numerical and solves stochastical problems by sampling from different probability distributions. Applying the method to absorbed dose calculations allows accurate calculations of photon and electron transport over arbitrary boundaries and interfaces. The method also makes it possible to study non-measurable parameters, such as the energy distribution of photons and/or electrons at a certain point-of-interest, and absorbed dose distribution within a volume. The method needs a density map of the patient, which can be obtained from CT or transmission SPECT studies, or from Compton scatter segmentation of the acquired SPECT data. Quantitative SPECT images are used to calculate activity volumes to provide information about the true absorbed dose distribution within the tissue. Its application is, however, limited for small volumes due to the limited spatial resolution of SPECT systems. A CT study can be complementary if alignment between CT and SPECT can be performed. The aim of this work was to develop a Monte Carlo program transforming arbitrary activity distributions to absorbed dose distributions in hetrogenous media and to verify the goodness of the results using the code against standard MIRD and other published dosimetry data.

Material and Methods Phantoms

In the code, phantoms can either be defined mathematically (analytically) or tomographically (see ICRU publication No. 48 for definitions). For mathematical body phantoms, a body surface and organ surfaces need to be defined. For a sphere or an ellipsoid, the outer boundary is defined analytically. A tomographic phantom is obtained by a tomographical methoci (e.g. CT, SPECT or MRI) and consists of voxels with a certain size. The content in the voxels can then reflect some parameter, such as activity or density. Mathematical phantoms. The program can read mathematical phantoms as the MIRD and ORNL (Cristy/Eckerman adult/pediatric phantoms (14)) from ASCII-files. In addition to the standard organs, defined by MIRD and ORNL, extensions have been developed in the code, such as the separation of left and right organs. The skeleton is separted into bone matrix, inactive and active bone marrow. Each skeletal part has its own fractional mass. The densities and atomic composition, given for the two phantoms, are used in the code to make the comparison with published data as accurate as possible. It is also possible to include other regions, making it possible to calculate absorbed fractions and S-values for arbitrary postions, shapes and sizes for organs or other regions, such as tumors. Activity and density maps from quantitative SPECT. When calculating a 3-D absorbed dose distribution from SPECT images, the number of simulated decays are proportional to the count density in each voxel of the SPECT matrix. The densities and their distribution in the volume are defined in the density map file. In the program, densities are allowed within the ranges 0.1-0.5 g / c d for lung tissue, 0.5- 1.2 for soft tissue and 1.2- 1.6 for skeletal tissue. Radiation transport code

For an extensive review of the sampling of a decay point and photon simulations, see (15). Electron simulation. A model for the simulation of electrons (16) based on a fractional energy deposition at each macroscopical step is used in the present code. The total mass stopping power is taken from ICRU publication No. 37 (17). Only CSDA with small energy depositions along the electron track is considered. Delta particles and bremsstrahlung photons are not sampled. An energy dependent Gaussian function, based on mass scattering powers from ICRU publication No. 35 (18) is used to sample the deflection of the electron. If the simulated geometry (analytical phantom or voxel based activity distribution), the dimensions of organslregions or pixels/voxels, are smaller than or in the same order as the electron range, then explicit electron simulation should be performed.

Acta Onco[ogica 35 ( 1996)

Scoring of energy depositions. For the calculation of absorbed fractions and S-values from the analytically described phantoms, the absorbed energy is accumulated to an organ/region-specific vector when the energy absorption point (x , y ,z ) is located within the mathematically described organ or region. The program also stores the absorbed energy distribution in a 3-D absorbed energy matrix, written to a binary output file, either as an absorbed energy or as an absorbed dose distribution.

Program ,features

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CONVERSION OF ACTIVITY DISTRIBUTIONS TO ABSORBED DOSE DISTRIBUTIONS

Input data are the decay scheme, the phantom definition and the interaction coefficients. For the MIRD or the ORNL phantoms, differential photon interaction coefficients and densities for the specific material composition are chosen. For a voxel based activity distribution, the input files include the activity and density maps. General output results are absorbed fractions, S-values, statistics and the number of photon and electron interactions in each organ. Additional data, such as 3-D absorbed dose distributions, photon/electron energy spectra through chosen surfaces and radial absorbed dose distributions, can also be calculated. Below follows a brief description of some of the program features. 1) Input files are available with single monoenergetic photons, electrons or a complete radionuclide decay with a list of photon and electron energies and abundances. Also, energy distributions to sample the emitted particles from are available. Decay schemes were taken from references (19, 20). 2) Bremsstrahlung is not included in the electron simulation. In the present code, however, bremsstrahlung emission can be simulated as a part of the decay, with a complete bremsstrahlung spectrum. This may give inaccurate results at short distances from the decay point, but may give accurate results at distance of several centimeters. In this work, we have so far included spectra for 32Pand 9OY (21). 3) Any elemental composition and density of the tissues/ materials are possible. 4) Calculation of photon and electron energy distributions at various points inside the phantom can be performed. 5) Absorbed fractions and S-values are simulated in mathematical phantoms with the activity either as a point source or homogeneously or nonhomogeneously distributed within a sphere or an organ. The scoring of energy depositions in spherical shells and photon/electron energy spectra can be performed to obtain dose point kernels, radial absorbed dose distributions, etc. 6) In the MIRD phantom, the lung and heart model from MIRD pamplet No. 13 (22) may be used. 7) When simulating the MIRD or ORNL phantoms, lung

and skeleton regions can be regarded as soft tissue. This option is useful when investigating the effects of lungs and skeleton in certain regions of the phantom. 8) A 3-D distribution of the absorbed energy or absorbed dose can be calculated. This could then be used for a dose-volume histogram calculation for the volume of interest.

Verification of the code Photon absorbed fractions and S-values. Absorbed fractions in spheres, with and without backscattering from surrounding media, have been calculated for both point sources and uniformly distributed activity spheres of different radius. Results have been compared with published data (7, 8). When calculating the absorbed fractions for monoenergetic photon sources in spheres or ellipsoids, the phantom either is defined as the activity volume itself (if no surrounding media is present) or as an infinite media. In the latter case, the criteria used to terminate a photon history is given by a predefined cut-off energy for the photons. Electron absorbed fractions and absorbed dose distributions. Absorbed fractions for monoenergetic electrons (0.2 and 4.0 MeV) and beta energy distributions of I3'I and 32P in spheres in an infinite water phantom have been compared with published data (23). A simulation of a tumor with a necrotic center was compared with results by Kwok et al. (24) and Howell et al. (25). The sphere outer radius was 6.6mm and the necrotic radius was 2.2mm. Simulations were done with the beta emitters 90Y,'*P and I3'I and monoenergetic photons with energies 15, 30 and 100 KeV.

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Fig. 1. Absorbed fraction as a function of mass for unity density and 140 KeV spheres. Simulated as a point source (P) of 30 (0) ( 0 )monoenergetic photons with no surrounding media for large spheres and 364 keV (+) monoenergetic photons with surrounding media in smaller ellipsoids (axis ratios 1 :2:4). A uniform distribution ( U ) with surrounding media for 140 keV photons in smaller spheres is also shown (m).Comparison with MIRD pamphlet No. 3 (-) and No. S(---)is made.

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Fig. 2. S-values calculated with the present code (darker grey), compared with corresponding values given in MIRD pamphlet No. 11 for uniformly distributed 13'1 in the liver.

Results and Discussion Absorbed fractions for point sources without surrounding, backscattering media and with a uniformly distributed source with surrounding media were compared with published data (7, 8). Results are shown in Fig. 1. The simulated absorbed fractions show agreement with published data of large spheres ( > 2 kg) without surrounding, backscattering media. The deviations are < 2.5% for 30keV and < 5 % for 140keV photons. The standard deviations of the mean are