相关论文: On a mathematical model for tissue regeneration
In this paper we address some modelling issues related to biological growth. Our treatment is based on a recently-proposed, general formulation for growth within the context of Mixture Theory (Journal of the Mechanics and Physics of Solids,…
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of…
This paper is concerned with the well-posedness and large-time behavior of a two dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis. We first transform the system via a Cole-Hopf type transformation…
In this paper, we propose a new model of chemotaxis motivated by ant trail pattern formation, formulated as a coupled parabolic-parabolic local PDE system, for the population density and the chemical field. The main novelty lies in the…
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…
Models of tissue growth are now well established, in particular in relation to their applications to cancer. They describe the dynamics of cells subject to motion resulting from a pressure gradient generated by the death and birth of cells,…
A new class of micromechanically motivated chain network models for soft biological tissues is presented. On the microlevel, it is based on the statistics of long chain molecules. A wormlike chain model is applied to capture the behavior of…
In this paper, we introduce and study one-dimensional models for the behavior of pedestrians in a narrow street or corridor. We begin at the microscopic level by formulating a stochastic cellular automata model with explicit rules for…
In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in a multiscale tissue. The classical effectiveness factor model is used to formulate…
Modern spatial microscopy has provided developmental biology with powerful research tools. However, the recent significant technological breakthroughs have inevitably led to technical "bottlenecks" for the application of the new procedures…
We present a multiagent-based model that captures the interactions between different types of cells with their microenvironment, and enables the analysis of the emergent global behavior during tissue regeneration and tumor development.…
We study the dynamics of a seeding experiment where a fibrous scaffold material is colonized by two types of cell populations. The specific application that we have in mind is related to the idea of meniscus tissue regeneration. In order to…
Throughout developmental biology and ecology, transport can be driven by nonlocal interactions. Examples include cells that migrate based on contact with pseudopodia extended from other cells, and animals that move based on their vision of…
We propose two approaches to a model deduction for Buruli ulcer spread in a tissue, prove global existence of solutions to the obtained macroscopic cross-diffusion PDE-ODE systems, and perform numerical simulations to illustrate the…
We consider a diffuse interface model for tumor growth recently proposed in [Y. Chen, S.M. Wise, V.B. Shenoy, J.S. Lowengrub, A stable scheme for a nonlinear, multiphase tumor growth model with an elastic membrane, Int. J. Numer. Methods…
While tumor dynamic modeling has been widely applied to support the development of oncology drugs, there remains a need to increase predictivity, enable personalized therapy, and improve decision-making. We propose the use of Tumor Dynamic…
In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a couple of non-linear telegraph equation and a parabolic equation. Proposed strategy…
The paper introduces a PDE model for the growth of a tree stem or a vine. The equations describe the elongation due to cell growth, and the response to gravity and to external obstacles. An additional term accounts for the tendency of a…
The reaction-diffusion models have been extensively applied to explain the mechanism of pattern formations in early embryogenesis based on geometrically confined microtissues consisting of human pluripotent stem cells. Recently, mechanical…
In this work we upscale a prototypical kinetic transport equation which models a cell population moving in a fibrous environment with a chemo- or haptotactic signal influencing both the direction and the magnitude of the cell velocity. The…