Section: New Results

Cancer

Long-term treatment effects in chronic myeloid leukemia

We propose and analyze in [12] a simplified version of a partial differential equation (PDE) model for chronic myeloid leukemia (CML) derived from an agent-based model proposed by Roeder et al. in [38]. This model describes the proliferation and differentiation of leukemic stem cells in the bone marrow and the effect of the drug Imatinib on these cells. We first simplify the PDE model by noting that most of the dynamics occurs in a subspace of the original 2D state space. Then we determine the dominant eigenvalue of the corresponding linearized system that controls the long-term behavior of solutions. We mathematically show a non-monotonous dependence of the dominant eigenvalue with respect to treatment dose, with the existence of a unique minimal negative eigen-value. In terms of CML treatment, this shows that there is a unique dose that maximizes the decay rate of the CML tumor load over long time scales. Moreover this unique dose is lower than the dose that maximizes the initial tumor load decay. Numerical simulations of the full model confirm that this phenomenon is not an artifact of the simplification. Therefore, while optimal asymptotic dosage might not be the best one at short time scales, our results raise interesting perspectives in terms of strategies for achieving and improving long-term deep response.

A model of interaction between the immune system and cancer cells in chronic myelogenous leukemia

We describe in [11] a simple model for the interaction between leukemic cells and the autologous immune response in chronic phase chronic myelogenous leukemia (CML). This model is a simplified version of the model we proposed in 2015 ( [34]). Our simplification is based on the observation that certain key characteristics of the dynamics of CML can be captured with a three compartments model: two for the leukemic cells (stem cells and mature cells) and one for the immune response. We characterize the existence of steady states and their stability for generic forms of immunosuppres-sive effects of leukemic cells. We provide a complete co-dimension one bifurcation analysis. Our results show how clinical response to tyrosine kinase inhibitors treatment is compatible with the existence of a stable low-disease, treatment-free steady state.

A hybrid computation model to describe the progression of multiple myeloma and its intra-clonal heterogeneity

Multiple myeloma (MM) is a genetically complex hematological cancer that is characterized by proliferation of malignant plasma cells in the bone marrow. MM evolves from the clonal premalignant disorder monoclonal gammopathy of unknown significance (MGUS) by sequential genetic changes involving many different genes, resulting in dysregulated growth of multiple clones of plasma cells. The migration, survival, and proliferation of these clones require the direct and indirect interactions with the non-hematopoietic cells of the bone marrow. We develop in [14], a hybrid discrete-continuous model of MM development from the MGUS stage. The discrete aspect of the model is observed at the cellular level: cells are represented as individual objects which move, interact, divide, and die by apoptosis. Each of these actions is regulated by intracellular and extracellular processes as described by continuous models. The hybrid model consists of the following submodels that have been simplified from the much more complex state of evolving MM: cell motion due to chemotaxis, intracellular regulation of plasma cells, extracellular regulation in the bone marrow, and acquisition of mutations upon cell division. By extending a previous, simpler model in which the extracellular matrix was considered to be uniformly distributed, the new hybrid model provides a more accurate description in which cytokines are produced by the marrow microenvironment and consumed by the myeloma cells. The complex multiple genetic changes in MM cells and the numerous cell-cell and cytokine-mediated interactions between myeloma cells and their marrow microenviroment are simplified in the model such that four related but evolving MM clones can be studied as they compete for dominance in the setting of intraclonal heterogeneity.

Fast and binary assay for predicting radiosensitivity based on the nucleoshuttling of ATM protein: development, validation and performances

The societal and clinical impact of post-radiotherapy adverse tissue events (AE) has highlighted the need of molecular parameters to predict individual radiosensitivity. Recent studies have stressed the role of the phosphorylated forms of the ATM protein (pATM) and its nucleoshuttling in response to radiation. The statistical performance of the pATM immunofluorescence assay to predict AE is promising. However, immunofluorescence requires a time-consuming amplification of cells. The purpose of the study in [24] was to develop a predictive assay based on the ELISA technique that renders faster the previous approach. Materials and methods This study was performed on 30 skin fibroblasts from 9 radioresistant and 21 AE patients. Patients were divided in 2 groups, radioresistant (toxicity grade$<2$) and radiosensitive (toxicity grade $\ge 2$). The quantity of nuclear pATM molecules was assessed by ELISA method at 10 min and 1 h after 2 Gy and compared to pATM immunofluorescence data. Results The pATM ELISA data were found in quantitative agreement with the immunofluorescence ones. A ROC analysis was applied first to two data sets (a training ($n=14$) and a validating ($n=16$) one) and thereafter to the whole data with a 2-fold cross-validation method. The assay showed an AUC value higher than $0.8$, a sensitivity of $0.8$ and a specificity ranging from $0.75$ and 1, which strongly document the predictive power of the pATM ELISA assay. Conclusion This study showed that the assessment of nuclear pATM quantity after 2 Gy via ELISA technique can be the basis of a predictive assay with the highest statistical performance among the available predictive approaches.