相关论文: Bifurcation for a free boundary problem modeling a…

We argue that nucleation of brittle cracks in initially flawless soft elastic solids is preceded by a nonlinear elastic instability, which cannot be captured without accounting for geometrical precise description of finite elastic…

In this paper we study a nonlinear free boundary problem on the radial growth of a two-layer solid tumor with a quiescent core. The tumor surface and its inner interface separating the proliferating cells and the quiescent cells are both…

The link between atherosclerosis and blood flow-induced haemodynamic luminal shear stresses is well established. However, this understanding has not been translated into clinical practice because of the interdependent effects of the complex…

This paper investigates the existence of periodic solutions in blood flow propagating through vessels with free boundary conditions via the bifurcation theory. It is rigorously proved that a local $C^1$-curve of small-amplitude periodic…

Coronary anatomy governs local haemodynamics associated with atherosclerotic development, progression and ultimately adverse clinical outcomes. However, lack of large sample size studies and methods to link adverse haemodynamics to…

We study dynamics emergent from a two-dimensional reaction--diffusion process modelled via a finite lattice dynamical system, as well as an analogous PDE system, involving spatially nonlocal interactions. These models govern the evolution…

This paper is concerned with a multi-dimensional free boundary problem modeling the growth of a tumor with two species of cells: proliferating cells and quiescent cells. This free boundary problem has a unique radial stationary solution. By…

Smooth muscle cells (SMCs) play a fundamental role in the development of atherosclerotic plaques. They ingest lipids in a similar way to monocyte-derived macrophages (MDMs) in the plaque. This can stimulate SMCs to undergo a phenotypic…

A mathematical model of atherosclerosis of a blood vessel is advanced with regard for the entry of low-density lipoproteins (LDLs) into blood. For the first time, the influence of cytokines on the inflammation of a blood vessel at the…

Detection of non-calcified plaques in the coronary tree is a challenging problem due to the nature of comprising substances. Hard plaques are easily discernible in CTA data cloud due to apparent bright behaviour, therefore many approaches…

Cellular differentiation in a developping organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emenating from its environment. Depending on the…

We present a direct numerical method for the solution of an optimal control problem controlling the growth of LDL, HDL and plaque. The optimal control problem is constrained with a system of coupled nonlinear free and mixed boundary partial…

The Raman spectrum of microscopic droplets of lipid material on the lumen of the aorta of an apolipoprotein E knock-out mouse were reported in the proceedings of an SPIE conference. Based on the absence of the carbonyl band in the spectrum,…

The impact of cell segregation and margination in blood disorders on microcirculatory hemodynamics within bifurcated vessels are physiologically significant, yet poorly understood. This study presents a comprehensive computational…

In this paper, we present a mathematical and numerical model for blood solidification and its rupture in stenosed arteries. The interaction between the blood flow and an existing stenosis in the arterial wall is modeled as a three…

A numerical study of laminar flow through symmetric and slightly asymmetric sudden expansion, of expansion ratio 1:3, in channels with increasing cross section, is carried out using two different approaches - Conventional CFD and Lattice…

For a 2-D coupled PDE-ODE bulk-cell model, we investigate symmetry-breaking bifurcations that can emerge when two bulk diffusing species are coupled to two-component nonlinear intracellular reactions that are restricted to occur only within…

We investigate, both experimentally and theoretically, the bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled either as a smooth or as border-collision period-doubling bifurcation. Using a new…

Atherosclerosis is a major cardiovascular complication of diseases associated with elevated oxidative stress such as type 2 diabetes and metabolic syndrome. In these situations, low density lipoproteins (LDL) undergo oxidation. Oxidized LDL…

In modeling the inflammatory response to a lesion in an artery wall, there are a number of chemotactic mechanisms going on within the wall layer that lead to an arterial plaque. We introduce a rather reduced model of these dynamic…