Section: New Results

Tumor growth modeling

Participants: R. Keinj, T. Bastogne, P. Vallois.

Up to now, the treatment planning systems used in radiotherapy only use mathematical models to describe the delivery of physical doses of radiation within biological tissues but cannot accurately predict the biological damages caused by such treatments. One important bottleneck is to account for the cell damage heterogeneity in the treated tumor. To this aim we firstly introduced in [51] a stochastic model based on multi-state Markov chains able to describe both treatment damage and cell reparation process.

More recently, we have proposed another model describing the lifespan of heterogenous tumors treated by radiotherapy. It is a bi-scale model in which the cell and tumor lifespans are represented by random variables. 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 (Tumor Control Probability) and NTCP (Normal Tissue Complication Probability), 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 (see [10] ).

One difference between photodynamic therapy (PDT) and radiotherapy (RT) is the irradiation signal (X ray in RT and light beam in PDT). Another one is the treatment planning: 10 to 30 daily sessions of treatment in RT against only one for PDT. To adapt the previous model to PDT, a continuous-time version was developed and proposed in [18] . The model has been implemented into Matlab and numerical simulations have emphasized the effects of the model parameters on the model output.

In the framework of a new collaboration with S. Niclou (NorLux Neuro-Oncology Laboratory, Department of Oncology, Centre de Recherche Public de la Santé, Luxembourg), we have extended our stochastic model of cell damage to describe the phenotypic heterogeneity in brain tumors. Preliminary results have recently been presented in [16] . Cancer stem cell (CSC) hypothesis suggests that tumor progression and recurrence rely on a small subpopulation of cancer cells with stem-like properties. The unresolved question is whether cancer stem cells lead to organisation of intratumoral phenotypic heterogeneity by hierarchical differentiation events or whether they represent one of the transitory phenotypic states. This is crucial not only for our understanding of tumor progression, but also for the successful design of novel therapeutic strategies targeting CSCs. Let us also highlight the fact that those studies are related to a more application oriented research synthesized in [3] , [13] , [21]