相关论文: Analysis of a diffuse interface model of multispec…

Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…

We consider two minimal mathematical models for cancer dynamics and self-adaptation. We aim to capture the interplay between the rapid progression of cancer growth and the possibility to leverage and enhance self-adaptive defense mechanisms…

In recent years, there has been a spike in the interest in multi-phase tissue growth models. Depending on the type of tissue, the velocity is linked to the pressure through Stoke's law, Brinkman's law or Darcy's law. While each of these…

Predictive modeling of the evolutionary dynamics of cancer is a challenge issue in computational cancer biology. In this paper, we propose a general mathematical model framework for the evolutionary dynamics of cancer with plasticity and…

The spread of metastases is a crucial process in which some questions remain unanswered. In this work, we focus on tumor cells circulating in the bloodstream, the so-called Circulating Tumor Cells (CTCs). Our aim is to characterize their…

In most classical approaches of computational geophysics for seismic wave propagation problems, complex surface topography is either accounted for by boundary-fitted unstructured meshes, or, where possible, by mapping the complex…

We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…

We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain…

In this work, we consider a certain multilayered (thick layer) wave--(thin layer) wave--heat (fluid) interactive PDE system. Such coupled PDE systems have been used in the literature to describe the blood transport process in mammalian…

We investigate avascular tumour growth as a two-phase process consisting of cells and liquid. Based on the one-dimensional continuum moving-boundary model formulated by (Byrne, King, McElwain, Preziosi, Applied Mathematics Letters, 2003,…

We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…

We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin film production by…

We introduce a nonisothermal phase-field system of Caginalp type that describes tumor growth under hyperthermia. The model couples a possibly viscous Cahn-Hilliard equation, governing the evolution of the healthy and tumor phases, with an…

We present a robust computational framework for Hele-Shaw tumor growth with necrotic cores, a problem identified as the incompressible limit of the Porous Media Equation. Simulating this system presents a fundamental challenge: while the…

We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation…

Known as one of the hallmarks of cancer [30], cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease.…

In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow…

A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…

We analyze a phase field model for tumor growth consisting of a Cahn-Hilliard-Brinkman system, ruling the evolution of the tumor mass, coupled with an advection-reaction-diffusion equation for a chemical species acting as a nutrient. The…

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [{\em Phys. Rev.} {\bf A 45}, R8309 (1992)]. The evolution equations for the mean heigth and the roughness are reached in a simple…