A branching process model of heterogeneous DNA damages caused by radiotherapy in in vitro cell cultures.

This paper deals with the dynamic modeling and simulation of cell damage heterogeneity and associated mutant cell phenotypes in the therapeutic responses of cancer cell populations submitted to a radiotherapy session during in vitro assays. Each cell is described by a finite number of phenotypic states with possible transitions between them. The population dynamics is then given by an age-dependent multi-type branching process. From this representation, we obtain formulas for the average size of the global survival population as well as the one of subpopulations associated with 10 mutation phenotypes. The proposed model has been implemented into Matlab© and the numerical results corroborate the ability of the model to reproduce four major types of cell responses: delayed growth, anti-proliferative, cytostatic and cytotoxic.

A Model-Based Pharmacokinetics Characterization Method of Engineered Nanoparticles for Pilot Studies.

Recent developments on engineered multifunctional nanomaterials have opened new perspectives in oncology. But assessment of both quality and safety in nanomedicine requires new methods for their biological characterization. This paper proposes a new model-based approach for the pre-characterization of multifunctional nanomaterials pharmacokinetics in small scale in vivo studies. Two multifunctional nanoparticules, with and without active targeting, designed for photodynamic therapy guided by magnetic resonance imaging are used to exemplify the presented method. It allows to the experimenter to rapidly test and select the most relevant PK model structure planned to be used in the subsequent explanatory studies. We also show that the model parameters estimated from the in vivo responses provide relevant preliminary information about the tumor uptake, the elimination rate and the residual storage. For some parameters, the accuracy of the estimates is accurate enough to compare and draw significant pre-conclusions. A third advantage of this approach is the possibility to optimally refine the in vivo protocol for the subsequent explanatory and confirmatory studies complying with the 3Rs (reduction, refinement, replacement) ethical recommendations. More precisely, we show that the identified model may be used to select the appropriate duration of the MR imaging sessions planned for the subsequent studies. The proposed methodology integrates MRI image processing, continuous-time system identification algorithms and statistical analysis. Except, the choice of the model parameters to be compared and interpreted, most of the processing procedure may be automated to speed up the PK characterization process at an early stage of experimentation.

Tumor growth modeling based on cell and tumor lifespans.

This paper deals with the lifespan modeling of heterogenous tumors treated by radiotherapy. A bi-scale model describing the cell and tumor lifespans by random variables is proposed. First- and second-order moments as well as the cumulative distribution functions and confidence intervals are expressed for the two lifespans with respect to the model parameters. One interesting result is that the mean value of the tumor lifespan can be approached by a logarithmic function of the initial cancer cell number. Moreover, we show that TCP and NTCP, used in radiotherapy to evaluate, optimize and compare treatment plans, can be derived from the tumor lifespan and the surrounding healthy tissue, respectively. Finally, we propose a ROC curve, entitled ECT (Efficiency-Complication Trade-off), suited to the selection by clinicians of the appropriate treatment planning.

Multinomial model-based formulations of TCP and NTCP for radiotherapy treatment planning.

Hit and target models of tumor growth, typically assume that all surviving cells have a constant and homogeneous sensitivity during the radiotherapy period. In this study, we propose a new multinomial model based on a discrete-time Markov chain, able to take into account cell repair, cell damage heterogeneity and cell proliferation. The proposed model relies on the 'Hit paradigm' and 'Target' theory in radiobiology and assumes that a cancer cell contains m targets which must be all deactivated to produce cell death. The surviving cell population is then split up into m categories to introduce the variation of cancer cell radio-sensitivity according to their damage states. New expressions of the Tumor Control Probability (TCP) and Normal Tissue Complication Probability (NTCP) are provided. Moreover, we show that hit and target models may be regarded as particular cases of the multinomial model. Numerical results should permit to keep the efficiency of treatment with a lower total radiation dose then that given by the typical hit models, which allow to decrease side effects.

Phenomenological modeling of tumor diameter growth based on a mixed effects model.

Over the last few years, taking advantage of the linear kinetics of the tumor growth during the steady-state phase, tumor diameter-based rather than tumor volume-based models have been developed for the phenomenological modeling of tumor growth. In this study, we propose a new tumor diameter growth model characterizing early, late and steady-state treatment effects. Model parameters consist of growth rhythms, growth delays and time constants and are meaningful for biologists. Biological experiments provide in vivo longitudinal data. The latter are analyzed using a mixed effects model based on the new diameter growth function, to take into account inter-mouse variability and treatment factors. The relevance of the tumor growth mixed model is firstly assessed by analyzing the effects of three therapeutic strategies for cancer treatment (radiotherapy, concomitant radiochemotherapy and photodynamic therapy) administered on mice. Then, effects of the radiochemotherapy treatment duration are estimated within the mixed model. The results highlight the model suitability for analyzing therapeutic efficiency, comparing treatment responses and optimizing, when used in combination with optimal experiment design, anti-cancer treatment modalities.