Cerebrospinal fluid dynamics coupled to the global circulation in holistic setting: Mathematical models, numerical methods and applications.

This paper presents a mathematical model of the global, arterio-venous circulation in the entire human body, coupled to a refined description of the cerebrospinal fluid (CSF) dynamics in the craniospinal cavity. The present model represents a substantially revised version of the original Müller-Toro mathematical model. It includes one-dimensional (1D), non-linear systems of partial differential equations for 323 major blood vessels and 85 zero-dimensional, differential-algebraic systems for the remaining components.

Modeling Loss of Microvascular Wall Homeostasis during Glycocalyx Deterioration and Hypertension that Impacts Plasma Filtration and Solute Exchange.

The fiber matrix of the surface glycocalyx layer internally coating the endothelial cells and plugging the intercellular clefts is crucial for microvascular wall homeostasis. Disruption of the glycocalyx is found in clinical conditions characterized by microvascular and endothelial dysfunction such as atherosclerosis, diabetes mellitus, chronic renal failure and cerebrovascular disease. Shedding of its components may also occur during oxidative stress and systemic inflammatory states including septis.