Tube law parametrization using in vitro data for one-dimensional blood flow in arteries and veins: TUBE LAW PARAMETRIZATION IN ARTERIES AND VEINS.

The deformability of blood vessels in one-dimensional blood flow models is typically described through a pressure-area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena.

An anatomically detailed arterial-venous network model. Cerebral and coronary circulation.

In recent years, several works have addressed the problem of modeling blood flow phenomena in veins, as a response to increasing interest in modeling pathological conditions occurring in the venous network and their connection with the rest of the circulatory system. In this context, one-dimensional models have proven to be extremely efficient in delivering predictions in agreement with observations. Pursuing the increase of anatomical accuracy and its connection to physiological principles in haemodynamics simulations, the main aim of this work is to describe a novel closed-loop Anatomically-Detailed Arterial-Venous Network (ADAVN) model.

Modeling essential hypertension with a closed-loop mathematical model for the entire human circulation.

Arterial hypertension, defined as an increase in systemic arterial pressure, is a major risk factor for the development of diseases affecting the cardiovascular system. Every year, 9.4 million deaths worldwide are caused by complications arising from hypertension.

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.

A Computational Model for the Dynamics of Cerebrospinal Fluid in the Spinal Subarachnoid Space.

Global models for the dynamics of coupled fluid compartments of the central nervous system (CNS) require simplified representations of the individual components which are both accurate and computationally efficient. This paper presents a one-dimensional model for computing the flow of cerebrospinal fluid (CSF) within the spinal subarachnoid space (SSAS) under the simplifying assumption that it consists of two coaxial tubes representing the spinal cord and the dura. A rigorous analysis of the first-order nonlinear system demonstrates that the system is elliptic-hyperbolic, and hence ill-posed, for some values of parameters, being hyperbolic otherwise.

A one-dimensional mathematical model of collecting lymphatics coupled with an electro-fluid-mechanical contraction model and valve dynamics.

We propose a one-dimensional model for collecting lymphatics coupled with a novel Electro-Fluid-Mechanical Contraction (EFMC) model for dynamical contractions, based on a modified FitzHugh-Nagumo model for action potentials. The one-dimensional model for a deformable lymphatic vessel is a nonlinear system of hyperbolic Partial Differential Equations (PDEs). The EFMC model combines the electrical activity of lymphangions (action potentials) with fluid-mechanical feedback (circumferential stretch of the lymphatic wall and wall shear stress) and lymphatic vessel wall contractions.

Intracranial Fluid Dynamics Changes in Idiopathic Intracranial Hypertension: Pre and Post Therapy.

Objective: Idiopathic Intracranial Hypertension (IIH) is a condition of unknown etiology frequently associated with dural sinus stenosis. There is emerging evidence that venous sinus stenting is an effective treatment. We use phase contrast cine MRI to observe changes in flow dynamics of multiple intracranial fluids and their response to different treatments in a patient with IIH.

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.

The Oscillating Component of the Internal Jugular Vein Flow: The Overlooked Element of Cerebral Circulation.

The jugular venous pulse (JVP) provides valuable information about cardiac haemodynamics and filling pressures and is an indirect estimate of the central venous pressure (CVP). Recently it has been proven that JVP can be obtained by measuring the cross-sectional area (CSA) of the IJV on each sonogram of an ultrasound B-mode sonogram sequence. It has also been proven that during its pulsation the IJV is distended and hence that the pressure gradient drives the IJV haemodynamics.

Impact of Jugular Vein Valve Function on Cerebral Venous Haemodynamics.

We quantify the effect of internal-jugular vein function on intracranial venous haemodynamics, with particular attention paid to venous reflux and intracranial venous hypertension. Haemodynamics in the head and neck is quantified by computing the velocity, flow and pressure fields, and vessel cross-sectional area in all major arteries and veins. For the computations we use a global, closed-loop multi-scale mathematical model for the entire human circulation, recently developed by the first two authors.

Enhanced global mathematical model for studying cerebral venous blood flow.

Here we extend the global, closed-loop, mathematical model for the cardiovascular system in Müller and Toro (2014) to account for fundamental mechanisms affecting cerebral venous haemodynamics: the interaction between intracranial pressure and cerebral vasculature and the Starling-resistor like behaviour of intracranial veins. Computational results are compared with flow measurements obtained from Magnetic Resonance Imaging (MRI), showing overall satisfactory agreement. The role played by each model component in shaping cerebral venous flow waveforms is investigated.

Computational haemodynamics in stenotic internal jugular veins.

An association of stenotic internal jugular veins (IJVs) to anomalous cerebral venous hemodynamics and Multiple Sclerosis has been recently hypothesized. In this work, we set up a computational framework to assess the relevance of IJV stenoses through numerical simulation, combining medical imaging, patient-specific data and a mathematical model for venous occlusions. Coupling a three-dimensional description of blood flow in IJVs with a reduced one-dimensional model for major intracranial veins, we are able to model different anatomical configurations, an aspect of importance to understand the impact of IJV stenosis in intracranial venous haemodynamics.

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

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.

Well-balanced high-order solver for blood flow in networks of vessels with variable properties.

We present a well-balanced, high-order non-linear numerical scheme for solving a hyperbolic system that models one-dimensional flow in blood vessels with variable mechanical and geometrical properties along their length. Using a suitable set of test problems with exact solution, we rigorously assess the performance of the scheme. In particular, we assess the well-balanced property and the effective order of accuracy through an empirical convergence rate study.

Semi-implicit numerical modeling of axially symmetric flows in compliant arterial systems.

Blood flow in arterial systems is described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the viscoelasticity of the arterial walls. These equations are simplified by assuming cylindrical geometry, axially symmetric flow, and hydrostatic equilibrium in the radial direction. In this paper, an efficient semi-implicit method is formulated in such a fashion that numerical stability is obtained at a minimal computational cost.