A comprehensive approach to the mathematical modeling of mass transport in biological systems: Fundamental concepts and models

Abstract Multiscale mathematical modeling of transport phenomena across different levels of biological systems, such as cells, capillaries, tissues, and organs, has been increasingly helpful in describing how interactions among these systems lead to their function and dysfunction. The development of models across these scales is based on knowledge from various fields, such as engineering, physiology, and biophysics, and it requires significant collaboration among scientists from the relevant areas. Therefore, a unified framework to describe the fundamental principles and unite the established models could support this growing research community. In this regard, the present work deals with the essential terminology required to understand and model biological transport mechanisms, as well as to compile currently available models. An inclusive mathematical framework for models of mass transport mechanisms in different tissue compartments, including cells, capillaries, and gland ducts, is developed, with a primary focus on the mechanisms of membrane-mediated transporters such as channels, uniporters, symporters, pumps, and antiporters. The main objective of this study is to provide a comprehensive tool to facilitate the analysis of biological mass transport mechanisms and substantially decrease the time taken to find the appropriate model for a study.