A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy

Abstract

Purpose: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. Methods: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131 I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N r : 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to N r À1=2 . From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 lm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. Results: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. Conclusions: The adjusted spherical model p...

Microdosimetry for Targeted Alpha Therapy of Cancer

“…Radiation dose in conventional external radiotherapy is a macroscopic concept. Upon the properties of the short path length alpha emissions and the spatial distribution of the radionuclide relative to the small target volumes, microdosimetry is indispensible for TAT to investigate the physical properties of radiation energy deposition in biological cells [ 11 ].…”

MIRD Pamphlet No. 25: MIRDcell V2.0 Software Tool for Dosimetric Analysis of Biologic Response of Multicellular Populations

“…Accordingly, the absorbed dose delivered to the various cells in the tissue element and their response may differ markedly. Therefore, a combination of voxel-, cellular-, and multicellular-level dosimetry is required to accurately predict biologic response to nonuniform distributions of radioactivity (1,13).…”

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“…Clonegenic survival assays were performed on monolayer suspensions of MDA-MB-468, SQ20B and 231-H2N cells treated with 111 In-EGF and 111 In-Tz (Supplemental Material). For 3-D spheroid survival fraction ( SF ) calculation, the survival probability of an individual cell SP i , follows the linear-quadratic model (LQM) (12); SPi=e−(αDi+βGDi2) with D i the absorbed dose (Gy) of an individual cell, α and β radiosensitivity parameters determined from 137 Cs irradiation (Supplemental Material) and G the Lea-Catcheside factor which accounts for radiation damage repair. Dose was calculated according to the MIRD formulation (27), where D i is taken as the product of accumulated activity à in each cell compartment with its associated S -value, where τ is the target (nucleus) and σ the source (i.e.…”

“…Multicellular tumor spheroids are excellent models of micro-metastasis as they reflect the in vitro 3-D architecture, heterogeneous cell populations, and physiological gradients (9, 10) as well as resistance to therapy of small tumors (11). By coupling experimental data detailing the dose distribution in individual cells and the spatial distribution of the radionuclide within a spheroid with theoretical close-packed 3-D multicellular Monte Carlo (MC) models, radiobiological quantities such as tumor control probability (TCP), that relate the fate of individual cells to a macroscopic outcome, can be calculated (12, 13). To date, only a few studies have attempted to link MC simulations with experimental observation to predict the efficacy of AE-emitters (14–16).…”