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An analytical framework for efficient and precision-controlled Monte Carlo simulation of heterogeneous targeted alpha therapy microdosimetry.

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Title: An analytical framework for efficient and precision-controlled Monte Carlo simulation of heterogeneous targeted alpha therapy microdosimetry.
Authors: Zhu J; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China., Cao S; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China., Li X; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China., Qi Y; Division of Ionizing Radiation Metrology, National Institute of Metrology, Beijing, China., Chen Z; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China.
Source: Medical physics [Med Phys] 2026 Aug; Vol. 53 (8), pp. e70598.
Publication Type: Journal Article
Language: English
Journal Info: Publisher: John Wiley and Sons, Inc Country of Publication: United States NLM ID: 0425746 Publication Model: Print Cited Medium: Internet ISSN: 2473-4209 (Electronic) Linking ISSN: 00942405 NLM ISO Abbreviation: Med Phys Subsets: MEDLINE
Imprint Name(s): Publication: 2017- : Hoboken, NJ : John Wiley and Sons, Inc.
Original Publication: Lancaster, Pa., Published for the American Assn. of Physicists in Medicine by the American Institute of Physics.
MeSH Terms: Alpha Particles*/therapeutic use , Radiometry*/methods , Monte Carlo Method*
Abstract: Background: Dosimetric studies of targeted alpha therapy (TAT) show that microscopic heterogeneity in geometry and source distribution strongly affects dose-effect relationships, underscoring the potential of microdosimetry. While Monte Carlo (MC) simulation is the gold standard for dose assessment, its application to TAT microdosimetry remains methodologically challenging and computationally inefficient. This necessitates a systematic and implementable methodology for microdosimetric simulation and analysis.
Purpose: This study aimed to establish a quantitative MC simulation framework for TAT microdosimetry, in which heterogeneous conditions are analytically processed and Type A standard uncertainty of derived microdosimetric quantities can be estimated.
Methods: (1) Elementary-source events were defined under arbitrary microscopic conditions, and the raw moments of single-event microdosimetric quantities scored via MC simulation were identified for each event. The heterogeneous microdosimetric environments were modeled as weighted mixtures of elementary events. (2) Analytical error propagation was derived to explicitly quantify the standard error (SE) of mixture quantities. This enables, for the first time, a trace-back mechanism to identify error-dominating source components for optimized resource allocation. (3) A long-range radiation correction for INLINEMATH -emitting nuclides was developed to bridge microscopic energy deposition with macroscopic absorbed dose, enabling the acquisition of reliable results under affordable computational resources.
Results: A Geant4-based application implemented the framework in heterogeneous microscopic models. The validation against repeated direct sampling demonstrated consistency between the mixture framework and conventional repeated direct simulation. Subsequently, the MC SE of single-event dose-mean specific energy was adopted as the convergence criterion for simulation. Long-range radiation effects were effectively compensated, relaxing spatial-extent requirements for TAT MC geometries. The source-mixture scheme allowed reuse of elementary microdosimetric data, supporting efficient factor analysis for diverse heterogeneous conditions. Coupled with cell-line parameters and the non-Poisson-corrected microdosimetric kinetic model, the analytic results yielded dose-response characteristics consistent with prior studies of TAT.
Conclusions: The framework enables trace-back variance analysis and microdosimetry-compatible variance reduction. This enables precision-controlled MC microdosimetry in TAT, and supports flexible analysis of heterogeneity factors and reliable microdosimetric assessment.
(© 2026 American Association of Physicists in Medicine.)
References: J Transl Med. 2023 Feb 24;21(1):144. (PMID: 36829143)
Int J Radiat Oncol Biol Phys. 2025 Nov 1;123(3):656-668. (PMID: 40550428)
Radiat Res. 2020 Oct 2;194(4):403-410. (PMID: 33045091)
Phys Med Biol. 2022 Apr 20;67(9):. (PMID: 35316802)
J Nucl Med. 2024 Feb 1;65(2):245-251. (PMID: 38124163)
Cancer Biother Radiopharm. 2007 Jun;22(3):387-92. (PMID: 17651044)
Phys Med Biol. 2024 Feb 05;69(4):. (PMID: 38211313)
J ICRU. 2014 Apr;14(1):79-98. (PMID: 27789600)
Radiat Res. 2003 Jul;160(1):61-9. (PMID: 12816524)
Med Phys. 2025 Jul;52(7):e17917. (PMID: 40665591)
J Nucl Med Technol. 2024 Jun 5;52(2):74-85. (PMID: 38839128)
Sci Rep. 2025 Aug 14;15(1):29807. (PMID: 40813872)
Eur Urol Oncol. 2025 Aug;8(4):1150-1164. (PMID: 40579287)
Phys Med Biol. 2010 Nov 21;55(22):6721-37. (PMID: 21030747)
EJNMMI Phys. 2025 Mar 27;12(1):28. (PMID: 40140233)
Radiat Oncol. 2018 May 16;13(1):96. (PMID: 29769103)
Grant Information: BB2140000022 Open Fund of Shanxi Provincial Key Laboratory for Translational Nuclear Medicine and Precision Protection; 2408085MA013 Natural Science Foundation of Anhui Province
Contributed Indexing: Keywords: Monte Carlo method; microdosimetry; microscopic heterogeneity; relative biological effectiveness; targeted alpha therapy
Entry Date(s): Date Created: 20260722 Date Completed: 20260722 Latest Revision: 20260813
Update Code: 20260814
PubMed Central ID: PMC13389354
DOI: 10.1002/mp.70598
PMID: 42482461
Database: MEDLINE
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  Data: An analytical framework for efficient and precision-controlled Monte Carlo simulation of heterogeneous targeted alpha therapy microdosimetry.
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  Data: <searchLink fieldCode="AU" term="%22Zhu+J%22">Zhu J</searchLink>; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China.<br /><searchLink fieldCode="AU" term="%22Cao+S%22">Cao S</searchLink>; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China.<br /><searchLink fieldCode="AU" term="%22Li+X%22">Li X</searchLink>; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China.<br /><searchLink fieldCode="AU" term="%22Qi+Y%22">Qi Y</searchLink>; Division of Ionizing Radiation Metrology, National Institute of Metrology, Beijing, China.<br /><searchLink fieldCode="AU" term="%22Chen+Z%22">Chen Z</searchLink>; School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, China.
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  Data: <i>Publication</i>: 2017- : Hoboken, NJ : John Wiley and Sons, Inc.<br /><i>Original Publication</i>: Lancaster, Pa., Published for the American Assn. of Physicists in Medicine by the American Institute of Physics.
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  Data: <searchLink fieldCode="MM" term="%22Alpha+Particles%22">Alpha Particles*</searchLink>/<searchLink fieldCode="MM" term="%22Alpha+Particles+therapeutic+use%22">therapeutic use</searchLink> <br /><searchLink fieldCode="MM" term="%22Radiometry%22">Radiometry*</searchLink>/<searchLink fieldCode="MM" term="%22Radiometry+methods%22">methods</searchLink> <br /><searchLink fieldCode="MM" term="%22Monte+Carlo+Method%22">Monte Carlo Method*</searchLink>
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  Data: Background: Dosimetric studies of targeted alpha therapy (TAT) show that microscopic heterogeneity in geometry and source distribution strongly affects dose-effect relationships, underscoring the potential of microdosimetry. While Monte Carlo (MC) simulation is the gold standard for dose assessment, its application to TAT microdosimetry remains methodologically challenging and computationally inefficient. This necessitates a systematic and implementable methodology for microdosimetric simulation and analysis.<br />Purpose: This study aimed to establish a quantitative MC simulation framework for TAT microdosimetry, in which heterogeneous conditions are analytically processed and Type A standard uncertainty of derived microdosimetric quantities can be estimated.<br />Methods: (1) Elementary-source events were defined under arbitrary microscopic conditions, and the raw moments of single-event microdosimetric quantities scored via MC simulation were identified for each event. The heterogeneous microdosimetric environments were modeled as weighted mixtures of elementary events. (2) Analytical error propagation was derived to explicitly quantify the standard error (SE) of mixture quantities. This enables, for the first time, a trace-back mechanism to identify error-dominating source components for optimized resource allocation. (3) A long-range radiation correction for INLINEMATH -emitting nuclides was developed to bridge microscopic energy deposition with macroscopic absorbed dose, enabling the acquisition of reliable results under affordable computational resources.<br />Results: A Geant4-based application implemented the framework in heterogeneous microscopic models. The validation against repeated direct sampling demonstrated consistency between the mixture framework and conventional repeated direct simulation. Subsequently, the MC SE of single-event dose-mean specific energy was adopted as the convergence criterion for simulation. Long-range radiation effects were effectively compensated, relaxing spatial-extent requirements for TAT MC geometries. The source-mixture scheme allowed reuse of elementary microdosimetric data, supporting efficient factor analysis for diverse heterogeneous conditions. Coupled with cell-line parameters and the non-Poisson-corrected microdosimetric kinetic model, the analytic results yielded dose-response characteristics consistent with prior studies of TAT.<br />Conclusions: The framework enables trace-back variance analysis and microdosimetry-compatible variance reduction. This enables precision-controlled MC microdosimetry in TAT, and supports flexible analysis of heterogeneity factors and reliable microdosimetric assessment.<br /> (© 2026 American Association of Physicists in Medicine.)
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  Data: J Transl Med. 2023 Feb 24;21(1):144. (PMID: <searchLink fieldCode="PM" term="%2236829143%22">36829143)</searchLink><br />Int J Radiat Oncol Biol Phys. 2025 Nov 1;123(3):656-668. (PMID: <searchLink fieldCode="PM" term="%2240550428%22">40550428)</searchLink><br />Radiat Res. 2020 Oct 2;194(4):403-410. (PMID: <searchLink fieldCode="PM" term="%2233045091%22">33045091)</searchLink><br />Phys Med Biol. 2022 Apr 20;67(9):. (PMID: <searchLink fieldCode="PM" term="%2235316802%22">35316802)</searchLink><br />J Nucl Med. 2024 Feb 1;65(2):245-251. (PMID: <searchLink fieldCode="PM" term="%2238124163%22">38124163)</searchLink><br />Cancer Biother Radiopharm. 2007 Jun;22(3):387-92. (PMID: <searchLink fieldCode="PM" term="%2217651044%22">17651044)</searchLink><br />Phys Med Biol. 2024 Feb 05;69(4):. (PMID: <searchLink fieldCode="PM" term="%2238211313%22">38211313)</searchLink><br />J ICRU. 2014 Apr;14(1):79-98. (PMID: <searchLink fieldCode="PM" term="%2227789600%22">27789600)</searchLink><br />Radiat Res. 2003 Jul;160(1):61-9. (PMID: <searchLink fieldCode="PM" term="%2212816524%22">12816524)</searchLink><br />Med Phys. 2025 Jul;52(7):e17917. (PMID: <searchLink fieldCode="PM" term="%2240665591%22">40665591)</searchLink><br />J Nucl Med Technol. 2024 Jun 5;52(2):74-85. (PMID: <searchLink fieldCode="PM" term="%2238839128%22">38839128)</searchLink><br />Sci Rep. 2025 Aug 14;15(1):29807. (PMID: <searchLink fieldCode="PM" term="%2240813872%22">40813872)</searchLink><br />Eur Urol Oncol. 2025 Aug;8(4):1150-1164. (PMID: <searchLink fieldCode="PM" term="%2240579287%22">40579287)</searchLink><br />Phys Med Biol. 2010 Nov 21;55(22):6721-37. (PMID: <searchLink fieldCode="PM" term="%2221030747%22">21030747)</searchLink><br />EJNMMI Phys. 2025 Mar 27;12(1):28. (PMID: <searchLink fieldCode="PM" term="%2240140233%22">40140233)</searchLink><br />Radiat Oncol. 2018 May 16;13(1):96. (PMID: <searchLink fieldCode="PM" term="%2229769103%22">29769103)</searchLink>
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  Data: BB2140000022 Open Fund of Shanxi Provincial Key Laboratory for Translational Nuclear Medicine and Precision Protection; 2408085MA013 Natural Science Foundation of Anhui Province
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  Data: <i>Keywords: </i>Monte Carlo method; microdosimetry; microscopic heterogeneity; relative biological effectiveness; targeted alpha therapy
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