相关论文: Adjoint method for a tumor invasion PDE-constraine…
In this paper we present a method for estimating unknown parameter that appear on a non-linear reaction-diffusion model of cancer invasion. This model considers that tumor-induced alteration of micro-enviromental pH provides a mechanism for…
In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death…
In this paper, we consider a mathematical model for the invasion of host tissue by tumour cells in a $d$-dimensional bounded domain, $d\leq 3$. This model consists of a system of differential equations describing the evolution of cancer…
We present a problem-suited numerical method for a particularly challenging cancer invasion model. This model is a multiscale haptotaxis advection-reaction-diffusion system that describes the macroscopic dynamics of two types of cancer…
We present a mathematical analysis of a reaction-diffusion model describing acid-mediated tumor invasion. The model describes the spatial distribution and temporal evolution of tumor cells, normal cells, and excess lactic acid…
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…
The acid-mediated tumor invasion hypothesis proposes that altered glucose metabolism exhibited by the vast majority of tumors leads to increased acid (H+ ion) production which subsequently facilitates tumor invasion [1-3]. The…
We present a numerical scheme for solving a parameter estimation problem for a model of low-grade glioma growth. Our goal is to estimate the spatial distribution of tumor concentration, as well as the magnitude of anisotropic tumor…
In this paper, we present a novel numerical framework for solving a specific biological reaction-diffusion-advection system of cancer growth in three dimensions (3D) using particles of variable mass. We adopt empirical particle measures to…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
We introduce the problem of parameter identification for a coupled nonlocal Cahn-Hilliard-reaction-diffusion PDE system stemming from a recently introduced tumor growth model. The inverse problem of identifying relevant parameters is…
We propose a diffuse interface model to describe tumor as a multicomponent deformable porous medium. We include mechanical effects in the model by coupling the mass balance equations for the tumor species and the nutrient dynamics to a…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
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…
Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…
We develop a linear fully discrete structure-preserving finite element method for a diffuse-interface model of tumour growth. The system couples a Cahn--Hilliard type equation with a nonlinear reaction-diffusion equation for nutrient…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…