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Coronary heart disease (CHD) caused by hardening of artery walls due to cholesterol known as atherosclerosis is responsible for large number of deaths world-wide. The disease progression is slow, asymptomatic and may lead to sudden cardiac…
A mathematical model of the metabolic process of formation of the hemostasis in a blood-carrying vessel is constructed. As distinct from the earlier developed model of the multienzyme prostacyclin-thromboxane system of blood, this model…
A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields…
Strokes are still one of the leading causes for death after heart diseases and cancer in all over the world. Most strokes happen because an artery that carries blood uphill from the heart to the head gets clogged. Most of the time, as with…
We present a unified mathematical framework for modeling blood and lymph flow in biological vessels, with a particular focus on lymph transport through lymphangions. Starting from first principles, we rigorously derive a system of partial…
The mathematical, four-layer model of the LDL transport across the arterial wall including the sensitivity of the transport coefficients to the wall shear stress (WSS) is studied. In that model the advection-diffusion equations in porous…
Muscular dystrophy (MD) describes generalized progressive muscular weakness due to the wasting of muscle fibers. The progression of the disease is affected by known immunological and mechanical factors, and possibly other unknown…
Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
The maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue's shape must…
In cell extrusion, a cell embedded in an epithelial monolayer loses its apical or basal surface and is subsequently squeezed out of the monolayer by neighboring cells. Cell extrusions occur during apoptosis, epithelial-mesenchymal…
We investigated existence of global weak solutions for a system of chemotaxis type with nonlinear degenerate diffusion, arising in modelling Multiple Sclerosis disease. The model consists of three equations describing the evolution of…
Platelet adhesion and aggregation are essential for primary hemostasis, forming a clot that quickly stops initial bleeding. Despite this critical role, the dynamic interactions of platelet receptors with exposed collagen and von Willebrand…
Liquid-liquid phase separation is important across biology, physics, and materials science. Although usually studied at equilibrium, active components - such as motor proteins, enzymes, and synthetic microswimmers - are increasingly…
In this paper, a class of reaction-diffusion equations for Multiple Sclerosis is presented. These models are derived by means of a diffusive limit starting from a proper kinetic description, taking account of the underlying microscopic…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
Alzheimer's disease (AD) is a prominent, worldwide, age-related neurodegenerative disease that currently has no systemic treatment. Strong evidence suggests that permeable amyloid-beta peptide (Abeta) oligomers, astrogliosis and reactive…
Autophagy is a conserved biological stress response in mammalian cells that is responsible for clearing damaged proteins and organelles from the cytoplasm and recycling their contents via the lysosomal pathway. In cases of mild stress,…
Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging.…
Diffusion is the macroscopic manifestation of disordered molecular motion. Mathematically, diffusion equations are partial differential equations describing the fluid-like large-scale dynamics of parcels of molecules. Spatially…