Multiscale Integration Of Receptor-Ligand Dynamics Into Discrete And Continuous Tumor Growth Models With Application To Tyrosine Kinase Inhibitor Treatment

The epidermal growth factor (EGF) receptor cascade plays a crucial role in the survival and proliferation of tumor cells. Tyrosine kinase inhibitors (TKIs) are a class of drugs that inhibit epidermal growth factor receptors (EGFRs), thereby preventing the downstream signal transduction. Despite their importance, models that link spatial receptor dynamics to tumor growth remain scarce. Further, TKIs act through selective mechanisms, inhibiting active, inactive, or all receptor states, which poses a challenge to traditional modeling approaches. We propose to numerically study two mathematical models incorporating receptor-dynamics into cancer models to describe the impact of EGFR overexpression and TKIs. The first is a 3D multiscale model that was previously introduced to study the impact of EGFR overexpression. We refine this model by (i) modeling intracellular dynamics using a simple ordinary differential equation to speed up computations, (ii) improve the accuracy of the model by applying coarse-graining, and (iii) incorporating the effect of erlotinib, a TKI treatment, using an appropriate pharmacokinetics-pharmacodynamics model. Numerical simulations show the existence of a threshold for EGF concentration which limits tumor growth. Next, we validate the model against experimental data for the action of erlotinib and apply it to predict the evolution of the tumor under treatment. Additionally, we develop for the first time a continuous framework that stratifies tumor cells based on the number of active receptors. This approach provides a flexible way of integrating ligand-receptor dynamics - including association, dissociation and affinity - into continuous tumor growth models. We validate the model using numerical simulations for EGF-dependent tumor growth obtained using the multiscale model. Then, we use it to study the distribution of cells across active receptor states during the different stages of tumor evolution. This model will be extended to incorporate the action of TKIs and elucidate the conditions promoting the action of TKIs that bind to active, inactive, and all receptors.