Related papers: A mathematical model for fluid-glucose-albumin tra…
This chapter reviews the differential geometry-based solvation and electrolyte transport for biomolecular solvation that have been developed over the past decade. A key component of these methods is the differential geometry of surfaces…
Fluid mechanical peristaltic transport through esophagus has been of concern in the paper. A mathematical model has been developed with an aim to study the peristaltic transport of a rheological fluid for arbitrary wave shapes and tube…
We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon…
Using well-known mathematical foundations of the elasticity theory, a mathematical model for two solutes transport in a poroelastic material (soft tissue is a typical example) is suggested. It is assumed that molecules of essentially…
Background and objective: Diabetes is one of the four leading causes of death worldwide, necessitating daily blood glucose monitoring. While sweat offers a promising non-invasive alternative for glucose monitoring, its application remains…
Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article blood is treated as an…
The contribution deals with the mathematical modelling of fluid flow in porous media, in particular water flow in soils, with the aim of describing the competition between transport and diffusion. The analysis is based on a mathematical…
We consider a situation commonly encountered in microfluidics: two streams of miscible liquids are brought at a junction to flow side by side within a microchannel, allowing solutes to diffuse from one stream to the other and possibly…
The relationship between the spatiotemporal distribution of oxygen transport and blood flow dynamics, accounting for the motion and deformation of individual red blood cells (RBCs), is of fundamental importance for understanding…
Peristaltic pumping is hypothesized to drive fluid transport in several physiological systems, including cerebrospinal fluid flow through cerebral perivascular spaces (PVSs). Cerebral PVSs are unique in the context of peristaltic pumping…
Flow of cerebrospinal fluid in perivascular spaces is a key mechanism underlying brain transport and clearance. In this paper, we present a mathematical and numerical formalism for reduced models of pulsatile viscous fluid flow in networks…
We develop a physiologically-based lattice model for the transport and metabolism of drugs in the functional unit of the liver, called the lobule. In contrast to earlier studies, we have emphasized the dominant role of convection in…
We derive a reduced model of solute transport in blood based on the center manifold theory. The derivation is carried out on a convection diffusion equation with general axial and radial velocity profiles in a blood vessel of varying cross…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
A mathematical model for the poroelastic materials (PEM) with the variable volume is developed in multidimensional case. Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
Starting from full-dimensional models of solute transport, we derive and analyze multi-dimensional models of time-dependent convection, diffusion, and exchange in and around pulsating vascular and perivascular networks. These models are…
Objective: The design of an Artificial Pancreas (AP) to regulate blood glucose levels requires reliable control methods. Model Predictive Control has emerged as a promising approach for glycemia control. However, model--based control…
Numerical model of the peripheral circulation and dynamical model of the large vessels and the heart are discussed in this paper. They combined together into the global model of blood circulation. Some results of numerical simulations…
A review of non-diffusive transport in fluids and plasmas is presented. In the fluid context, non-diffusive chaotic transport by Rossby waves in zonal flows is studied following a Lagrangian approach. In the plasma physics context the…