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

Area of Science:

• Physiology
• Biomedical Engineering
• Computational Fluid Dynamics

Background:

• Existing models of human circulation and cerebrospinal fluid (CSF) dynamics have limitations.
• A comprehensive, integrated model is needed to accurately simulate physiological processes.

Purpose of the Study:

• To present a revised and enhanced mathematical model of global arterio-venous circulation coupled with CSF dynamics.
• To investigate the myogenic mechanism of cerebral blood regulation and the impact of vascular properties.

Main Methods:

• Development of a 1D non-linear system of partial differential equations for major blood vessels and differential-algebraic systems for other components.
• Approximation of parabolic systems using hyperbolic systems with stiff source terms and a relaxation approach.
• Numerical solution using the Arbitrary DERivative Riemann problem finite volume framework with well-balanced formulation and local time stepping.

Main Results:

• The model incorporates refined vasculature for the brainstem, cerebellum, and inner ear, and viscoelastic properties for all blood vessels.
• Validation against published data and MRI measurements confirms model accuracy.
• Simulations demonstrate the relationship between transverse sinus stenoses and Idiopathic Intracranial Hypertension, and extra-cranial venous strictures and Ménière's disease.

Conclusions:

• The coupled circulation-CSF model provides a robust platform for studying cerebrovascular and neurological disorders.
• The model's applications highlight its potential for understanding conditions like Idiopathic Intracranial Hypertension and Ménière's disease.