Multiscale computational analysis of the steady fluid flow through a lymph node.

Lymph Nodes (LNs) are crucial to the immune and lymphatic systems, filtering harmful substances and regulating lymph transport. LNs consist of a lymphoid compartment (LC) that forms a porous bulk region, and a subcapsular sinus (SCS), which is a free-fluid region. Mathematical and mechanical challenges arise in understanding lymph flow dynamics.

Multiscale homogenization for dual porosity time-dependent Darcy-Brinkman/Darcy coupling and its application to the lymph node.

We study the coupling between time-dependent Darcy-Brinkman and the Darcy equations at the subjected to inhomogeneous body forces and initial conditions to describe a double porosity problem. We derive the homogenized governing equations for this problem using the asymptotic homogenization technique, and as macroscopic results, we obtain a coupling between two Darcy equations, one of which with memory effects, with mass exchange between phases. The memory effects are a consequence of considering the time dependence in the Darcy-Brinkman equation, and they allow us to study in more detail the role of time in the problem under consideration.

A Mathematical Description of the Flow in a Spherical Lymph Node.

The motion of the lymph has a very important role in the immune system, and it is influenced by the porosity of the lymph nodes: more than 90% takes the peripheral path without entering the lymphoid compartment. In this paper, we construct a mathematical model of a lymph node assumed to have a spherical geometry, where the subcapsular sinus is a thin spherical shell near the external wall of the lymph node and the core is a porous material describing the lymphoid compartment. For the mathematical formulation, we assume incompressibility and we use Stokes together with Darcy-Brinkman equation for the flow of the lymph.

Predicting Ageing: On the Mathematical Modelization of Ageing Muscle Tissue.

The ageing of biological tissues can be accelerated by many factors, mainly of physiological and nutritional nature. In the case of skeletal muscle tissue, one of the main consequences of ageing is a progressive loss of muscle mass and a worsening of the quality of muscle tissue, termed "sarcopenia". The correlation between the deterioration of muscle tissue and what we usually refer to as the "lifestyle", although being the subject of several studies, up to now has been considered only from a clinical and a statistical viewpoint.

Topological nonconnectivity threshold in long-range spin systems.

We demonstrate the existence of a topological disconnection threshold, recently found by Borgonovi [J. Stat. Phys.