Mathematical modeling used to understand vascular remodeling

Abstract

Vascular adaptation to metabolic and hemodynamic signals is a dynamic process defining vascular structure and function. While many components of these reactions, e.g. vascular responses to reduced oxygen or increased shear stress have been investigated in experimentally, exclusive biological approaches have some limitations: long term structural adaptation is difficult to investigate and most experiments are focussed at testing a given cause‐effect hypothesis. Mathematical modelling can complement biological experiments and result in additional insight. For vascular remodeling of vessel diameter and vessel wall mass, a minimal set of relevant signals can be defined including oxygen partial pressure, shear stress and circumferential stress. Using this approach and comparing experimental distributions of diameter and blood flow with model predictions, a number of hypotheses could be derived: A single set of response characteristics governs adaptation of all microvessels. Information transfer along vessels (conduction) is necessary to maintain functionally adequate perfusion. Inadequate distribution of blood and oxygen in tumor microcirculation results from compromised conduction. Spatial heterogeneity of perfusion and demand results from adaptation and topological network heterogeneity. Oxygen sensing for structural adaptation is located in the vascular wall.