A global multiscale mathematical model for the human circulation with emphasis on the venous system

Abstract

We present a global, closed-loop, multiscale mathematical model for the human circulation including the arterial system, the venous system, the heart, the pulmonary circulation and the microcirculation. A distinctive feature of our model is the detailed description of the venous system, particularly for intracranial and extracranial veins. Medium to large vessels are described by one-dimensional hyperbolic systems while the rest of the components are described by zero-dimensional models represented by differential-algebraic equations. Robust, high-order accurate numerical methodology is implemented for solving the hyperbolic equations, which are adopted from a recent reformulation that includes variable material properties. Because of the large intersubject variability of the venous system, we perform a patient-specific characterization of major veins of the head and neck using MRI data. Computational results are carefully validated using published data for the arterial system and most regions of the venous system. For head and neck veins, validation is carried out through a detailed comparison of simulation results against patient-specific phase-contrast MRI flow quantification data. A merit of our model is its global, closed-loop character; the imposition of highly artificial boundary conditions is avoided. Applications in mind include a vast range of medical conditions. Of particular interest is the study of some neurodegenerative diseases, whose venous haemodynamic connection has recently been identified by medical researchers.

Geometric multiscale modeling of the cardiovascular system, between theory and practice

“…Alternatively, a high-order finite volume scheme is presented in [129] and a space-time finite element method is proposed in [204]. Recently, a series of benchmark test cases with an increasing degree of complexity is presented in [35] to compare different numerical schemes.…”

“…Muller and E.F. Toro, 2014 [129] In this work, the authors study the entire cardiovascular system, with a particular attention to the vein system of the head and neck. The final aim is the study of neurovascular diseases linked to the venous vasculature of the head and neck.…”

Methods of Blood Flow Modelling

“…Qualitative analysis of physical experiments confirms that p(A) function should be a monotone S-like curve. Such curve describes satisfactorily both circular and elliptic cross-section states [27,58,92,104]. In practice, S-like pressure-to-area dependence is often approximated by an analytical function.…”

“…Such approach does not result in the closed blood circulation model. In order to design the closed 1D network model, some authors suggest heart filling conditions at the junctions with pulmonary vein and vena cava as well as heart outflow conditions at the junctions with aorta and pulmonary artery through a lumped parameter model [1,51,75,92,122,124]. Alternative heart-vascular network coupling is discussed in [144].…”

ADER schemes and high order coupling on networks of hyperbolic conservation laws

“…Networks of hyperbolic conservation laws occur in many applications such as the human circulatory system [1,2,3,4], gas pipelines [5,6,7], water [8,9,10,11] and road networks [12,13]. For all these applications accurate and stable numerical methods are needed.…”