Absorbed fractions in a voxel-based phantom calculated with the MCNP-4B code

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1 Absorbed fractions in a voxel-based phantom calculated with the MCNP-4B code Hélio Yoriyaz and Adimir dos Santos a) Instituto de Pesquisas Energéticas e Nucleares IPEN-CNEN/SP, São Paulo, Brazil Michael G. Stabin Universidade Federal de Pernambuco, Recife, Brazil Roberto Cabezas Instituto de Pesquisas Energéticas e Nucleares IPEN-CNEN/SP, São Paulo, Brazil Received 12 October 1999; accepted for publication 19 April 2000 A new approach for calculating internal dose estimates was developed through the use of a more realistic computational model of the human body. The present technique shows the capability to build a patient-specific phantom with tomography data a voxel-based phantom for the simulation of radiation transport and energy deposition using Monte Carlo methods such as in the MCNP-4B code. MCNP-4B absorbed fractions for photons in the mathematical phantom of Snyder et al. agreed well with reference values. Results obtained through radiation transport simulation in the voxelbased phantom, in general, agreed well with reference values. Considerable discrepancies, however, were found in some cases due to two major causes: differences in the masses between the phantoms and the occurrence of overlap in the voxel-based phantom, which is not considered in the mathematical phantom American Association of Physicists in Medicine. S X Key words: voxel-based phantom, Monte Carlo simulations, internal dosimetry I. INTRODUCTION Recent advances in medical image processing have made possible the use of more accurate patient-specific anatomic data and three-dimensional activity mapping for the development of new dose assessment methods. Particularly, in radioimmunotherapy RIT, data gathered from SPECT or PET images can provide important information related to the spatial distribution of radionuclides administered to patients in diagnosis and therapy. 1 4 Also, patient-specific anatomic information, obtained from CT and MRI images can be used for the construction of voxel-based geometric models of the human body, 5 7 where previously only models using approximate geometric constructs have been available. 8,9 The simulation of radiation transport by Monte Carlo techniques has become an important basic tool for dose calculations, and several program packages are currently available to treat problems in radiation protection and RIT dosimetry Computer capabilities are also improving, with a constant upgrade of information storage capacity and CPU speed affording the ability to solve very complex problems in a reasonable amount of time. In this paper we describe the use of a voxel-based phantom built from a series of CT images taken from Zubal et al. 7 for the calculation of absorbed fractions AFs and specific absorbed fractions SAFs in several internal s through the simulation of radiation transport photons and electrons using the MCNP-4B Monte Carlo code. 13 The results of the numerical simulation were compared to the existing results obtained for the mathematical phantoms of Snyder et al. 8 and Cristy Eckerman, 9 which have been used for many years. II. METHODS AND MATERIALS A. CT-based phantom The computational model of a male human patient is based on the CT images from Zubal et al., which consists of a 3-dimensional array of cubic voxels, 4 mm on each side. Multiple internal s and structures were identified by Zubal et al. and related to an index number for each voxel. The masses of the s are determined as the sum of the volume of the voxels belonging to the respective multiplied by the density of the voxels. Three distinct tissue types are considered: soft tissue, lung, and bone with densities of 1.04, and 1.40 g/cm 3, respectively. Table I shows the masses of several s, with a comparison to those in the Cristy Eckerman mathematical phantom. 9 Some discrepancies have been found in some s which was assumed that in part came from the differences in the anatomy between the phantoms, demonstrating somewhat the variability in mass possible for the same. Moreover, discrepancies as found for spleen, pancreas, adrenals, and kidneys, for instance, alert us to the fact that average s masses like those of the mathematical phantom can differ significantly from the real patient s masses accounting for the fact that this particular patient had some diseases and abnormalities. 14 Yet, these discrepancies are inherent to the available CT images and will not affect the efficiency of the present methodology which uses these 1555 Med. Phys. 27 7, July Õ2000Õ27 7 Õ1555Õ8Õ$ Am. Assoc. Phys. Med. 1555

2 1556 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1556 TABLE I. Selected masses in the voxel-based phantom, with a comparison to corresponding values in the Cristy Eckerman adult male phantom Ref. 8. Organ Cristy Eckerman Mass g Mass g Zubal Numer of voxels Liver Kidneys Lungs Spleen Adrenals Bladder Pancreas Heart CT images as input for the geometric construction of each. On the other hand, differences in volumes affect the final results in dose calculation, so that the image data which affect the volume estimates should be provided as accurately as possible. B. The MCNP-4B Monte Carlo code The MCNP-4B Monte Carlo radiation transport code developed at Los Alamos National Laboratory 13 was employed to perform the calculations in this work. Although originally conceived and utilized for neutron and photon transport problems, it has incorporated the capability of electron transport, and has been used to study many problems in internal and external dose assessment. The code supports a wide variety of scoring options and radiation source modeling. Several variance reduction techniques are also available, allowing performance optimization for a more efficient determination of results. A particular MCNP-4B feature called Repeated Structures has been used for the geometric modeling of this 3-dimensional phantom. The concept of this feature is that generic geometrical shapes can be built based on the repetition of single MCNP cells. Even irregular shapes can be reproduced. In MCNP, cells are the basic tool for the geometric construction for any problem in MCNP and consist of combinations of surfaces. Using the Repeated Structures feature, each cell can be filled with a universe, which can represent a lattice or collection of cells. Each universe has an identification number so that every cell belonging to this universe is associated with this number. Using this procedure, each voxel in the segmented anatomic data is related to a MCNP cell, which is associated with a universe number, which in turn can be the index number of the to which those voxels belong. For example, suppose a geometry constituted by 3 different material regions A, B and C, as shown in Fig. 1 a. Each region is formed by a set of voxels distributed in an irregular pattern. This geometry can be modeled defining 3 MCNP cells each of them corresponding to a voxel belonging to the specific material region. Each of the MCNP cells can be FIG. 1. Example of a generic geometry b composed by single cells a using the Repeated Structures feature. repeated according to the given spatial distribution pattern of voxels to form the entire region and thus forming the whole geometry as can be seen in Fig. 1 b. This is particularly interesting in modeling irregular geometries consisting of a large number of individual volume elements, such as in the case of voxel-based s. Using this MCNP capability, dosimetry problems involving millions of voxels can be treated with reasonable amounts of time and computational memory. The user must also specify for each problem the tallies, or regions in which quantities such as energy, flux, etc. are recorded by MCNP; in our problem, we are interested in absorbed dose energy/g in either individual voxels or groups of voxels within a universe. C. The SCMS software In order to utilize the segmented human anatomy as a computational model for the simulation of radiation transport, an interface program, SCMS, was developed to build the geometric configurations for the phantom using the Repeated Structures feature. The SCMS software creates an archive of geometric information in an appropriate format to be read by the MCNP-4B code. The average energy deposition in each can be calculated by associating the universe number with each index number, so that all voxels belonging to this are associated to the respective universe number. On the other hand, if each voxel of an is associated with an individual universe number, each of the MCNP cells associated with the voxel can be tallied individually. This provides an energy deposition distribution in that, thus allowing the determination of a spatial distribution of doses in regions of interest ROI.

3 1557 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1557 FIG. 2. Segmented anatomies of heart a ; lungs b ; pancreas d and part of the gastrointestinal GI tract c in the Zubal et al. phantom. As an illustration, the segmented anatomies of heart, lungs, pancreas, and part of the gastrointestinal GI tract built by the SCMS program using the CT images provided by Zubal et al. 7 are shown in Fig. 2. D. Calculation of absorbed fractions Although the main interest of the application of voxelbased phantoms is in the development of dose distributions within s and tissues in individual patients, an important side benefit which can be derived is the calculation of average dose estimates and dose conversion factors based on more realistic voxel-based images of real individuals, instead of the mathematical representations of reference individuals that we have used for many years. Thus, in this work, we calculated absorbed fractions AFs and specific absorbed fractions SAFs 8 for whole s within the Zubal et al. phantom, to demonstrate this capability and pave the way for the use of a new generation of more realistic phantoms for use in internal and external dose assessment. Photon and electron sources were assumed to be uniformly distributed within the volume of several source s. Two to three million histories were generally run for most energies, although ten million histories were used in some cases involving low energy source particles, in order to improve the statistics of the final results using the analogous process no variance reduction technique was used. One of the scoring options provided by the MCNP code is the energy deposition tally, which was used in the present calculation. It provides the energy deposited from both photons and electrons, if present, in a cell, in MeV per particle. Energy deposited in all voxels of a target were summed, and this value was divided by the total energy emitted in the source to FIG. 3. Absorbed fractions a AF liver liver and b AF kidneys kidneys in the energy range of 0.01 to 4.0 MeV. obtain the AF; subsequently, the SAF was calculated as the AF divided by the known mass of the target. In order to make a direct comparison of the MCNPproduced SAFs with those of Snyder et al. and of Cristy and Eckerman, the equations given by these authors were used to develop another adult male phantom in MCNP. These phantoms should have all of the same geometric constructs as those of the original phantoms, thus differences between the transport algorithms used by these authors from those in MCNP will not interfere with the interpretation of any differences observed in the results. III. RESULTS AND DISCUSSION A. Absorbed fractions for photons Absorbed fractions AFs for photons in various s of the Zubal et al. segmented phantom were calculated and compared to those reported for the mathematical phantoms of Snyder and Cristy Eckerman. They were also compared to the SAFs provided by Cristy and Eckerman in the original reference. 9 Figure 3 shows the AF liver liver and AF kidneys kidneys values, in the energy range 0.01 to 4.0 MeV. Differences between results obtained in the Zubal et al. phantom from those of Snyder et al. were at a maximum of about 16% and 18%, for liver and kidneys at all energies. Differences in volume and geometric shape directly affect the energy deposition and can explain these discrepancies. MCNP-calculated values in the Snyder et al. phantom

4 1558 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1558 FIG. 4. Absorbed fractions a AF liver kidneys and b AF kidneys liver in the energy range of 0.01 to 4.0 MeV. FIG. 5. Anatomic shapes comparison of liver and kidneys between the Zubal et al. phantom a and the Snyder phantom b. agree to within 3% and 6%, respectively, for liver and kidneys compared to the original tabulated values. 8 The values of AF liver kidneys and AF kidneys liver are shown in Fig. 4. The MCNP results in the Snyder phantom are in good agreement with those of Snyder et al. except at 0.01 MeV, where the reference value for the latter was obtained through extrapolation from higher energies. However, most other AF values for crossirradiation obtained in the segmented phantom are considerably higher than those in the Snyder phantom. The main cause of these differences, however, is likely the occurrence of overlap between s kidneys and liver in the Zubal et al. phantom, which of course exists in reality, but which was not well modeled in mathematical phantoms. This can be observed in Fig. 5. The differences in the AFs are more evident at low energies 0.01 to 0.03 MeV, the results for which are more dependent on the relative distance between s. Also, these curves demonstrate reciprocity, i.e., AF liver kidneys AF kidneys liver. Differences in volumes between the phantoms also contributes to some observed discrepancies. For example, the kidneys volume in the Zubal et al. phantom is almost twice that in the Snyder phantom. This can also be observed in the AFs spleen spleen, Fig. 6. Organ shape also influences the simulation of radiation transport and, consequently, the AF values. Energy deposition in target s occurs due to radiation leaving the source and undergoing interactions in other s. The amount of radiation emitted from the source region depends on the shape of the and the particle energy. For low energies ( 0.05 MeV, the differences are small due to the short range of the particles, but increases as the energy increases. For higher energies 1.5 MeV the differences decreases again, because the majority of the energy emitted is deposited in more distant regions. B. Specific absorbed fractions for photons Specific absorbed fractions SAFs for photons of 0.01, 0.05, 0.1, 0.5, 1.0, 2.0, and 4.0 MeV are shown in Tables II VIII for various source and target combinations. Comparisons with the reference values of Snyder et al. at times show significant discrepancies. However, these discrepancies can usually be attributed to the differences in masses between the phantoms. Although some characteristics of the patient, such as total mass and height, were similar to those of the mathematical phantom of Snyder FIG. 6. Absorbed fraction in the spleen AF spleen spleen in the energy range of 0.01 to 4.0 MeV.

5 1559 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1559 TABLE II. SAF values in g 1. Photon energy of 0.01 MeV. Source Liver Z a 4.91e e e e e-6 S b 5.36e e e e e-7 Kidneys Z 3.25e e e e e-5 S 8.39e e e e e e-6 Lungs Z 1.27e e e S 7.76e e e e e e-7 Pancreas Z 2.13e-7 1.4e e e-4 S 1.47e e e e e e-8 Spleen Z e e e S 7.27e e e e e e-7 Adrenals Z 9.11e e e e-1 S 2.45e e e e e e-2 a Z Zubal et al. phantom. b S Snyder et al. phantom. TABLE III. SAF values in g 1. Photon energy of 0.05 MeV. Source Organ Liver Z 1.42E e e e e e-5 S 1.52e e e e e e-5 Kidneys Z 3.00E e e e e e-4 S 1.95e e e e e e-5 Lungs Z 1.84E e e e e e-5 S 1.45e e e e e e-5 Pancreas Z 3.79E e e e e e-4 S 2.18e e e e e e-5 Spleen Z 4.38E e e e e e-5 S 2.93e e e e e e-5 Adrenals Z 5.97E e e e e e-3 S 2.15e e e e e e-3 TABLE IV. SAF Values in g 1. Photon energy of 0.1 MeV. Source Liver Z 9.01e e e e e e-5 S 9.14e e e e e e-5 Kidneys Z 2.31e e e e e e-5 S 1.58e e e e e e-5 Lungs Z 1.42e e e e e e-5 S 9.92e e e e e e-6 Pancreas Z 2.88e e e e e e-4 S 1.77e e e e e e-5 Spleen Z 5.75e e e e e e-5 S 3.56e e e e e e-5 Adrenals Z 4.31e e e e e e-3 S 1.61e e e e e e-3

6 1560 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1560 TABLE V. SAF values in g 1. Photon energy of 0.5 MeV. Source Liver Z 8.41e e e e e e-5 S 8.85e e e e e e-5 Kidneys Z 1.95e e e e e e-5 S 1.29e e e e e e-5 Lungs Z 1.19e e e e e e-5 S 8.23e e e e e e-6 Pancreas Z 2.34e e e e e e-4 S 1.66e e e e e e-5 Spleen Z 5.19e e e e e e-5 S 3.44e e e e e e-5 Adrenals Z 3.64e e e e e e-3 S 1.68e e e e e e-3 TABLE VI. SAF values in g 1. Photon energy of 1.0 MeV. Source Organ Liver Z 7.58e e e e e e-5 S 8.07e e e e e e-5 Kidneys Z 1.76e e e e e e-5 S 1.18e e e e e e-5 Lungs Z 1.07e e e e e e-6 S 7.90e e e e e e-6 Pancreas Z 2.10e e e e e e-4 S 1.36e e e e e e-5 Spleen Z 4.82e e e e e e-5 S 3.81e e e e e e-5 Adrenals Z 3.31e e e e e e-3 S 1.56e e e e e e-3 TABLE VII. SAF values in g 1. Photon energy of 2.0 MeV. Source Organ Liver Z 6.19e e e e e e-5 S 6.86e e e e e e-5 Kidneys Z 1.49e e e e e e-5 S 1.10e e e e e e-5 Lungs Z 9.17e e e e e e-6 S 6.96e e e e e e-6 Pancreas Z 1.81e e e e e e-4 S 9.99e e e e e e-5 Spleen Z 4.39e e e e e e-6 S 3.14e e e e e e-5 Adrenals Z 2.76e e e e e e-3 S 1.53e e e e e e-3

7 1561 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1561 TABLE VIII. SAF values in g 1. Photon energy of 4.0 MeV. Source Liver Z 4.64e e e e e e-5 S 5.58e e e e e e-5 Kidneys Z 1.23e e e e e e-5 S 8.23e e e e e e-5 Lungs Z 7.58e e e e e e-6 S 5.60e e e e e e-6 Pancreas Z 1.47e e e e e e-5 S 8.75e e e e e e-5 Spleen Z 3.77e e e e e e-5 S 2.14e e e e e e-5 Adrenals Z 2.31e e e e e e-4 S 1.83e e e e e e-3 et al., individual masses are considerably different in many cases. Also, the relative position of s has a strong influence on cross-irradiation calculations. From the results, one can observe that, in general, in cases when the target is different than the source, SAF values in the Zubal phantom s are considerably higher than those of the Snyder et al. phantom. In most cases, this is due to the overlap of s that occurs in the Zubal et al. phantom but not in the Snyder et al. phantom. C. S values for electrons Estimates of S values 15 were derived also for electrons using the MCNP-4B code. Y-90, which has an average electron energy of MeV, was assumed to be distributed uniformly in various source s. Table IX shows the S values in mgy/mbq-s for three source s: liver, kidneys, and lungs. Estimates of S values in the Snyder et al. phantom obtained by the simulation of electron transport using the MCNP-4B code are compared with tabulated values. 15 Values of S liver liver, S kidneys kidneys, and S lungs lungs generated by MCNP for the Snyder et al. phantom were lower by 7%, 2%, and 10%, respectively, than the values given in MIRD 11. These discrepancies demonstrate the errors caused by differences in the methodologies and the assumption that all energy is being locally deposited TABLE IX. S-values in mgy/mbq-s for electrons in different phantoms for a Y-90 source. / methods Source Liver Kidneys Lungs Snyder a 8.25E E E 00 Liver Snyder/MCNP 7.65E E E-09 Zubal/MCNP 7.35E E E-07 Snyder a 0.00E E E 00 Kidneys Snyder/MCNP 7.04E E E-09 Zubal/MCNP 4.65E E E-09 Snyder a 0.00E E E-04 Lungs Snyder/MCNP 3.99E E E-04 Zubal/MCNP 1.73E E E-04 a Reference 15. by electrons, as was adopted in MIRD 11. Speculative calculations using the Zubal phantom revealed that the differences between values generated with and without electron transport result in differences of about 3% and 5%, respectively, for S liver liver and photon source energy of 1.5 MeV and for S spleen liver and photon source energy of 0.03 MeV. Results of the electron transport simulation between the Zubal et al. and Snyder et al. phantoms differed by 4%, 17%, and 42%, respectively, for liver, lungs, and kidneys. In these cases, the main causes of the differences is the differences in masses. Very significant differences were also observed in the cross-irradiation S values, where the differences were sometimes several times higher, as is the case of S liver kidneys and S liver lungs. As mentioned before, the main cause for the magnitude of these discrepancies is due to the overlapping between s that occurs in the Zubal et al. phantom. Thus, we see that this component of the total dose to an, while perhaps small in the final analysis in many cases, traditionally has been underestimated. As the cross dose for this energy is delivered over about a few mm to cm past the overlapping region, one must study the dose distribution, rather than the overall average dose, to properly understand this phenomenon. IV. CONCLUSIONS A new approach for calculating internal dose estimates was developed through the use of a more realistic computational model of the human body. The present technique shows the capability to build a patient-specific phantom with tomography data a voxel-based phantom for the simulation of radiation transport and energy deposition using Monte Carlo methods such as in the MCNP-4B code. The interface program, SCMS, was used to couple the CT images with the input requirements of the MCNP-4B code. MCNP-4B calculated absorbed fractions for photons in the mathematical phantom of Snyder et al. agreed well with reference values. Results obtained through radiation transport simulation in the voxel-based phantom, in general, agreed well with reference values. Considerable discrepancies, however, were found in some cases due to two major causes: differences in the masses between the phantoms and

8 1562 Yoriyaz et al.: Absorbed fractions in a voxel-based phantom 1562 the occurrence of overlap in the voxel-based phantom, which is not considered in the mathematical phantom. This effect was quite evident for cross-irradiation from electrons. These new techniques offer the promise of developing a new generation of more realistic phantoms for internal, as well as external, dose assessment. The principal area of implementation should be in the development of patientspecific dose estimates in internal emitter therapy, such as RIT. However, as new phantoms can be acquired and segmented, they may also be used with the SCMS code and the techniques developed here to derive new SAF values and replace the traditional values used for other applications in internal and external dose assessment, which have been based on mathematical constructs that are not always very representative of real human s. Thus, in addition to improvements in RIT treatment planning for patients, using anatomical phantoms based on individual subject images, more realistic and accurate dose conversion factors like S values may be developed for a new generation of phantoms using the techniques demonstrated here. ACKNOWLEDGMENTS The authors are grateful to the Fundação de Amparo à Pesquisa do Estado de São Paulo FAPESP for providing the computational resources to perform part of the calculations and to prepare the manuscript. a Address for correspondence: Instituto de Pesquisas Energéticas e Nucleares, Cidade Universitária, Caixa Postal 11049, Pinheiros São Paulo Brazil; fax: ; electronic mail: asantos@net.ipen.br 1 A. K. Erdi, Y. E. Erdi, E. D. Yorke, and W. Wessels, Treatment planning for radio-immunotherapy, Phys. Med. Biol. 41, D. R. Fisher, Radiation dosimetry for radioimmunotherapy, Cancer N.Y. 73, E. E. Furhang, C. C. Chui, and G. Sgouros, A Monte Carlo approach to patient-specific dosimetry, Med. Phys. 23, T. Johnson, D. McClure, and S. McCourt, MABDOSE I: Characterization of a general purpose dose estimation code, Med. Phys. 26, K. S. Kolbert, G. Sgouros, A. M. Scott, J. E. Bronstein, R. A. Malane, J. Zhang, H. Kalaigian, S. McNamara, L. Schwartz, and S. M. Larson, Implementation and evaluation of patient-specific three-dimensional internal dosimetry, J. Nucl. Med. 38, P. K. Leichner, N-C. Yang, B. W. Wessels, W. G. Hawkins, S. E. Order, and J. L. Klein, Dosimetry and treatment planning in radioimmunotherapy, Front. Radiat. Ther. Oncol. 24, G. Zubal, C. Harrell, E. Smith, Z. Ratner, G. Gindi, and P. Hoffer, Computerized three-dimensional segmented human anatomy, Math. Phys. 21, V. S. Snyder, M. R. Ford, and G. G. Warner, Estimates of specific absorbed fractions for photon sources uniformly distributed in a heterogeneous phantom, MIRD Pamphlet No. 5 Society of Nuclear Medicine, New York, M. Cristy and K. F. Eckerman, Specific absorbed fractions of energy at various ages from internal photons sources. I. Methods, Oak Ridge National Laboratory Report No. ORNL/NUREG/TM-8381, G. Sgouros, Treatment planning for internal emitter therapy: methods, applications, and clinical implications, in The 6th International Radiopharmaceutical Dosimetry Symposium, edited by A. Stelson, M. Stabin and R. Sparks, Oak Ridge Associated Universities, 1999, pp M. Tagesson, M. Ljungberg, and S-E. Strand, The SIMDOS Monte Carlo code for conversion of activity distributions to absorbed dose and doserate distributions, in Ref. 10, pp A. Liu, L. Williams, G. Lopatin, D. Yamauchi, J. Wong, and A. Raubitschek, A radionuclide therapy treatment planning and dose estimation system, J. Nucl. Med. 40, J. F. Briesmeister, MCNP A general Monte Carlo N-Particle transport code, version 4B, Los Alamos National Laboratory Report, LA M, I. G. Zubal personal communication. 15 W. S. Snyder, M. R. Ford, G. G. Warner, and S. B. Watson, S absorbed dose per unit cumulated activity for selected radionuclides and s, in Ref. 8.