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

Abstract

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. Highlights include the myogenic mechanism of cerebral blood regulation; refined vasculature for the inner ear, the brainstem and the cerebellum; and viscoelastic, rather than purely elastic, models for all blood vessels, arterial and venous. The derived 1D parabolic systems of partial differential equations for all major vessels are approximated by hyperbolic systems with stiff source terms following a relaxation approach. A major novelty of this paper is the coupling of the circulation, as described, to a refined description of the CSF dynamics in the craniospinal cavity, following Linninger et al. The numerical solution methodology employed to approximate the hyperbolic non-linear systems of partial differential equations with stiff source terms is based on the Arbitrary DERivative Riemann problem finite volume framework, supplemented with a well-balanced formulation, and a local time stepping procedure. The full model is validated through comparison of computational results against published data and bespoke MRI measurements. Then we present two medical applications: (i) transverse sinus stenoses and their relation to Idiopathic Intracranial Hypertension; and (ii) extra-cranial venous strictures and their impact in the inner ear circulation, and its implications for Ménière's disease.

Real-Time Phase-Contrast MRI to Monitor Cervical Blood and Cerebrospinal Fluid Flow Beat-by-Beat Variability

“…In addition, despite being beyond the scope of this work, it is worth mentioning a potential impact on hemodynamic modelling studies, i.e., the modelling of AF, VF, and CSFF and their interactions in the IC circulation [ 14 , 15 , 16 , 17 , 18 , 19 ]. In this field, moving from the fitting of single gated wave shapes to several sampled ones is expected to highly increase the statistical power of model fitting to be exploited by parametric identification.…”

Influence of interaction of cerebral fluids on ventricular deformation: A mathematical approach

“…The authors hypothesized that the loss of damping capacity of the cisterna magna and the resulting increase in pressure in the wall of the central channel lead to the formation of syrinx in patients with Chiari anomaly. A mathematical model of global arteriovenous circulation in the human body combined with a refined description of CSF dynamics in the craniospinal cavity is presented in [ 15 ]. The main innovation of this study is the connection of blood flow with CSF dynamics in the craniospinal cavity following the ideas presented in [ 8 ].…”

A flux‐vector splitting scheme for the shallow water equations extended to high‐order on unstructured meshes

“…In this article such term is moved to the pressure system. This is justified in the framework of deriving zero‐dimensional models from one‐dimensional models, a popular approach in computational hemodynamics 30‐32 . The zero‐dimensional models derived in this manner keep the advection term of the continuity equation and the advection operator vanishes when the inertial term in the momentum equation in the full system is discarded.…”

“…This is justified in the framework of deriving zero-dimensional models from one-dimensional models, a popular approach in computational hemodynamics. [30][31][32] The zero-dimensional models derived in this manner keep the advection term of the continuity equation and the advection operator vanishes when the inertial term in the momentum equation in the full system is discarded. Moreover, the straight extension of the TV splitting, so good for the Euler equations, does not work well for the shallow water equations, anomaly which is actually remedied by the proposed modification.…”