相关论文: On a cross-diffusion hybrid model: Cancer Invasion…
There are many interesting physical processes which involve the generation of high density plasmas in large volumes. However, when modeling these systems numerically, the large densities and volumes present a significant computational…
Motivated by an ongoing collaboration with clinical oncologists and pathologists, we develop a hybrid partial differential equation--ordinary differential equation (PDE--ODE) framework that captures (i) competition between susceptible and…
Cancer is viewed as a multistep process whereby a normal cell is transformed into a cancer cell through the acquisition of mutations. We reduce the complexities of cancer progression to a simple set of underlying rules that govern the…
We consider a two-component reaction-diffusion system that has previously been developed to model invasion of cells into a resident cell population. The system is an idealised version of models of tumour growth in which tumour cells degrade…
With the continuous emergence of molecular and cluster devices or systems, the relationship between the plasmonic properties of multiple clusters and molecular interactions and the properties of the original single cluster or molecule…
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed in [A. Hawkins-Daruud, K.G. van der Zee, J.T. Oden, Numerical simulation of a thermodynamically consistent…
An existence result is proved for a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by Neumann homogeneous boundary conditions and initial conditions.…
Volume-filling cross-diffusion equations for the components of a tissue structure are formally derived from mass conservation laws and force balances for the interphase pressures and viscous drag forces in a multiphase approach. The…
Aberrantly regulated cell motility is a hallmark of cancer cells. A hybrid agent-based model has been developed to investigate the synergistic and antagonistic cell motility-impacting effects of three microenvironment variables…
Drug resistance and metastasis - the major complications in cancer - both entail adaptation of cancer cells to stress, whether a drug or a lethal new environment. Intriguingly, these adaptive processes share similar features that cannot be…
Coupling within-host infection dynamics with population-level transmission remains a major challenge in infectious disease modeling, especially for airborne pathogens with potential to spread indoor. The frequent emergence of such diseases…
We study coupled mass transport in a tumor--microenvironment setting with two motile densities $(S,R)$ and non-motile state switching $(P,A)$. The populations diffuse and undergo chemotactic drift; $(P,A)$ follow pointwise ODE switching. A…
Reaction-diffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agent-based phenomena. The underlying dynamics of these systems occur at the individual…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…
Multicellular tumor spheroids are an important {\it in vitro} model of the pre-vascular phase of solid tumors, for sizes well below the diagnostic limit: therefore a biophysical model of spheroids has the ability to shed light on the…
We investigate the dynamics of cancer initiation in a mathematical model with one driver mutation and several passenger mutations. Our analysis is based on a multi type branching process: We model individual cells which can either divide or…
We propose here a multiscale model for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization. The model accounts for the interplay between the different components of the neoplasm and…
A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumor-induced angiogenesis. Thanks to proper…
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…
Current analysis of tumor proliferation, the most salient prognostic biomarker for invasive breast cancer, is limited to subjective mitosis counting by pathologists in localized regions of tissue images. This study presents the first…