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Monte Carlo (MC) radiation transport, generally considered to be the most accurate among different methods for voxel\u2010level absorbed dose estimation, can be computationally inefficient for routine clinical use.<\/jats:p><\/jats:sec><jats:sec><jats:title>Purpose<\/jats:title><jats:p>This work demonstrates a recently implemented grid\u2010based linear Boltzmann transport equation (LBTE) solver for fast and accurate voxel\u2010based dosimetry in RPT and SIRT and benchmarks it against MC.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>A deterministic LBTE solver (Acuros MRT) was implemented within a commercial RPT dosimetry package (Velocity 4.1). The LBTE is directly discretized using an adaptive mesh refined grid and then the coupled photon\u2010electron radiation transport is iteratively solved inside specified volumes to estimate radiation doses from both photons and charged particles in heterogeneous media. To evaluate the performance of the LBTE solver for RPT and SIRT applications, <jats:sup>177<\/jats:sup>Lu SPECT\/CT, <jats:sup>90<\/jats:sup>Y PET\/CT, and <jats:sup>131<\/jats:sup>I SPECT\/CT images of phantoms and patients were used. Multiple lesions (2\u20131052\u00a0mL) and normal organs were delineated for each study. Voxel dosimetry was performed with the LBTE solver, dose voxel kernel (DVK) convolution with density correction, and a validated in\u2010house MC code using the same time\u2010integrated activity and density maps as input to the different dose engines. The resulting dose maps, difference maps, and dose\u2010volume\u2010histogram (DVH) metrics were compared, to assess the voxel\u2010level agreement. Evaluation of mean absorbed dose included comparison with structure\u2010level estimates from OLINDA.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In the phantom inserts\/compartments, the LBTE solver versus MC and DVK convolution demonstrated good agreement with mean absorbed dose and DVH metrics agreeing to within 5% except for the D90 and D70 metrics of a very low activity concentration insert of <jats:sup>90<\/jats:sup>Y where the agreement was within 15%. In the patient studies (five patients imaged after <jats:sup>177<\/jats:sup>Lu DOTATATE RPT, five after <jats:sup>90<\/jats:sup>Y SIRT, and two after <jats:sup>131<\/jats:sup>I radioimmunotherapy), in general, there was better agreement between the LBTE solver and MC than between LBTE solver and DVK convolution for mean absorbed dose and voxel\u2010level evaluations. Across all patients for all three radionuclides, for soft tissue structures (kidney, liver, lesions), the mean absorbed dose estimates from the LBTE solver were in good agreement with those from MC (median difference\u00a0&lt;\u00a01%, maximum 9%) and those from DVK (median difference\u00a0&lt;\u00a05%, maximum 9%). The LBTE and OLINDA estimates for mean absorbed dose in kidneys and liver agreed to within 10%, but differences for lesions were larger with a maximum 14% for <jats:sup>177<\/jats:sup>Lu, 23% for <jats:sup>90<\/jats:sup>Y, and 26% for <jats:sup>131<\/jats:sup>I. For bone regions, the agreement in mean absorbed doses between LBTE and both MC and DVK were similar (median\u00a0&lt;\u00a011%, max 11%) while for lung the agreement between LBTE and MC (median\u00a0&lt;\u00a01%, max 8%) was substantially better than between LBTE and DVK (median\u00a0&lt;\u00a016%, max 33%). Voxel level estimates for soft tissue structures also showed good agreement between the LBTE solver and both MC and DVK with a median difference\u00a0&lt;\u00a05% (maximum\u00a0&lt;\u00a013%) for the DVH metrics with all three radionuclides. The largest difference in DVH metrics was for the D90 and D70 metric in lung and bone where the uptake was low. Here, the difference between LBTE and MC had a median value\u00a0&lt;\u00a014% (maximum 23%) for bone and\u00a0&lt;\u00a04% (maximum 37%) for lung, while the corresponding differences between LBTE and DVK were\u00a0&lt;\u00a023% (maximum 31%) and\u00a0&lt;\u00a067% (maximum 313%), respectively. For a typical patient with a matrix size of 166\u00a0\u00d7\u00a0166\u00a0\u00d7\u00a0129 (voxel size 3\u00a0\u00d7\u00a03\u00a0\u00d7\u00a03 mm<jats:sup>3<\/jats:sup>), voxel dosimetry using the LBTE solver was as fast as \u223c2 min on a desktop computer.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusion<\/jats:title><jats:p>Having established good agreement between the LBTE solver and MC for RPT and SIRT applications, the LBTE solver is a viable option for voxel dosimetry that can be faster than MC. Further analysis is being performed to encompass the broad range of radionuclides and conditions encountered clinically.<\/jats:p><\/jats:sec>","DOI":"10.1002\/mp.16996","type":"journal-article","created":{"date-parts":[[2024,3,4]],"date-time":"2024-03-04T12:19:06Z","timestamp":1709554746000},"page":"5604-5617","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Linear Boltzmann equation solver for voxel\u2010level dosimetry in radiopharmaceutical therapy: Comparison with Monte Carlo and kernel convolution"],"prefix":"10.1002","volume":"51","author":[{"given":"Gunjan","family":"Kayal","sequence":"first","affiliation":[{"name":"Department of Radiology University of Michigan  Ann Arbor Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Van","sequence":"additional","affiliation":[{"name":"Department of Radiology University of Michigan  Ann Arbor Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Andl","sequence":"additional","affiliation":[{"name":"Varian Medical Systems  Atlanta Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cheng","family":"Tu","sequence":"additional","affiliation":[{"name":"Varian Medical Systems  Atlanta Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Todd","family":"Wareing","sequence":"additional","affiliation":[{"name":"Varian Medical Systems  Atlanta Georgia USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Scott","family":"Wilderman","sequence":"additional","affiliation":[{"name":"Department of Radiology University of Michigan  Ann Arbor Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Justin","family":"Mikell","sequence":"additional","affiliation":[{"name":"Department of Radiation Oncology Washington University in St. Louis  St. Louis Missouri USA"},{"name":"Department of Radiation Oncology University of Michigan  Ann Arbor Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuni K.","family":"Dewaraja","sequence":"additional","affiliation":[{"name":"Department of Radiology University of Michigan  Ann Arbor Michigan USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2024,3,4]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.2967\/jnumed.121.262977"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.3390\/ph12030114"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1186\/s40658\u2010017\u20100194\u20103"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.2967\/jnumed.108.056036"},{"issue":"6","key":"e_1_2_8_6_1","first-page":"1023","article-title":"OLINDA\/EXM: the second\u2010generation personal computer software for internal dose assessment in nuclear medicine","volume":"46","author":"Stabin MG","year":"2005","journal-title":"J Nucl Med"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.2967\/jnumed.122.264225"},{"issue":"1","key":"e_1_2_8_8_1","first-page":"11S","article-title":"MIRD pamphlet No. 17: the dosimetry of nonuniform activity distributions\u2013radionuclide S values at the voxel level. 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