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Tumor-immune interactions are central to cancer progression and treatment outcomes. In this study, we present a stochastic agent-based model that integrates cellular heterogeneity, spatial cell-cell interactions, and drug resistance…
We formulate a cell-scale model for the degradation of the extra-cellular matrix by membrane-bound and soluble matrix degrading enzymes produced by cancer cells. Based on the microscopic model and using tools from the theory of…
We present and analyze new multi-species phase-field mathematical models of tumor growth and ECM invasion. The local and nonlocal mathematical models describe the evolution of volume fractions of tumor cells, viable cells (proliferative and…
We consider a non homogeneous Gompertz diffusion process whose parameters are modified by generally time-dependent exogenous factors included in the infinitesimal moments. The proposed model is able to describe tumor dynamics under the…
Tumor growth is associated with cell invasion and mass-effect, which are traditionally formulated by mathematical models, namely reaction-diffusion equations and biomechanics. Such models can be personalized based on clinical measurements…
Radiotherapy treatment planning often relies on time-consuming, trial-and-error adjustments that heavily depend on the expertise of specialists, while existing deep learning methods face limitations in generalization, prediction accuracy,…
Cancer cells are widely known to be protected from apoptosis, which is a major hurdle to successful anti-cancer therapy. Over-expression of several anti-apoptotic proteins, or mutations in pro-apoptotic factors, has been recognized to…
Starting from a two-scale description involving receptor binding dynamics and a kinetic transport equation for the evolution of the cell density function under velocity reorientations, we deduce macroscopic models for glioma invasion…
Simulations of biophysical systems inevitably include steps that correspond to time integrations of ordinary differential equations. These equations are often related to enzyme action in the synthesis and destruction of molecular species,…
We introduce a model for the mass transfer of molecular activators and inhibitors in two media separated by an interface, and study its interaction with the deformations exhibited by the two-layer skin tissue where they occur. The…
Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
We deal with a small enough tumor section to consider it homogeneous, such that populations of lymphocytes and cancer cells are independent of spatial coordinates. A stochastic model based in one step processes is developed to take into…
Early assessment of tumor therapeutic response is an important topic in precision medicine to optimize personalized treatment regimens and reduce unnecessary toxicity, cost, and delay. Although diffusion MRI (dMRI) has shown potential to…
In this article, we present a multispecies reaction-advection-diffusion partial differential equation (PDE) coupled with linear elasticity for modeling tumor growth. The model aims to capture the phenomenological features of glioblastoma…
In this paper, we present a model based on a local thermodynamic equilibrium, weakly ionized plasma-mixture model used for medical and technical applications in etching processes. We consider a simplified model based on the Maxwell-Stefan…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
A novel numerical technique has been proposed to solve a two-phase tumour growth model in one spatial dimension without needing to account for the boundary dynamics explicitly. The equivalence to the standard definition of a weak solution…
Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on numerous biochemical and physical properties of cancer cells, adipocytes,…
Glioblastoma Multiforme is a malignant brain tumor with poor prognosis. There have been numerous attempts to model the invasion of tumorous glioma cells via partial differential equations in the form of advection-diffusion-reaction…