相关论文: A Damage-Driven Model for Duchenne Muscular Dystro…
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions.…
We present a new class of models for assessing the cell dynamics characterising muscular dystrophies. The proposed approach comprises a system of integro-differential equations for the statistical distributions, over a large patient cohort,…
A Darcy-Cahn-Hilliard model coupled with damage is developed to describe multiphase-flow and fluid-driven fracturing in porous media. The model is motivated by recent experimental observations in Hele-Shaw cells of the fluid-driven…
We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…
In this paper, we propose a new workflow to analyze macrophage motion during wound healing. These immune cells are attracted to the wound after an injury and they move showing both directional and random motion. Thus, first, we smooth the…
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 propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
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…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly…
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…
We formulate a Hele-Shaw type free boundary problem for a tumor growing under the combined effects of pressure forces, cell multiplication and active motion, the latter being the novelty of the present paper. This new ingredient is…
The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…
In this paper, we derive a new chemotaxis model with degenerate diffusion and density-dependent chemotactic sensitivity, and we provide a more realistic description of cell migration process for its early and late stages. Different from the…
We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able…
We propose a data-driven constitutive framework for anisotropic damage mechanics based on the second-order damage tensor approach for both compressible and incompressible materials. The formulation is thermodynamically consistent and…
Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from…
Medical conditions due to acute cell injury, such as stroke and heart attack, are of tremendous impact and have attracted huge amounts of research effort. The biomedical research that seeks cures for these conditions has been dominated by a…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…