Ageing is a major risk factor for many neurological pathologies, but its mechanisms remain unclear. Unlike other tissues, the parenchyma of the central nervous system (CNS) lacks lymphatic vasculature and waste products are removed partly through a paravascular route. (Re)discovery and characterization of meningeal lymphatic vessels has prompted an assessment of their role in waste clearance from the CNS. Here we show that meningeal lymphatic vessels drain macromolecules from the CNS (cerebrospinal and interstitial fluids) into the cervical lymph nodes in mice. Impairment of meningeal lymphatic function slows paravascular influx of macromolecules into the brain and efflux of macromolecules from the interstitial fluid, and induces cognitive impairment in mice. Treatment of aged mice with vascular endothelial growth factor C enhances meningeal lymphatic drainage of macromolecules from the cerebrospinal fluid, improving brain perfusion and learning and memory performance. Disruption of meningeal lymphatic vessels in transgenic mouse models of Alzheimer's disease promotes amyloid-β deposition in the meninges, which resembles human meningeal pathology, and aggravates parenchymal amyloid-β accumulation. Meningeal lymphatic dysfunction may be an aggravating factor in Alzheimer's disease pathology and in age-associated cognitive decline. Thus, augmentation of meningeal lymphatic function might be a promising therapeutic target for preventing or delaying age-associated neurological diseases.

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.

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. The EFMC model is governed by four Ordinary Differential Equations (ODEs) and phenomenologically relies on: (1) environmental calcium influx, (2) stretch-activated calcium influx, and (3) contraction inhibitions induced by wall shear stresses. We carried out a stability analysis of the stationary state of the EFMC model. Contractions turn out to be triggered by the instability of the stationary state. Overall, the EFMC model allows emulating the influence of pressure and wall shear stress on the frequency of contractions observed experimentally. Lymphatic valves are modelled by extending an existing lumped-parameter model for blood vessels. Modern numerical methods are employed for the one-dimensional model (PDEs), for the EFMC model and valve dynamics (ODEs). Adopting the geometrical structure of collecting lymphatics from rat mesentery, we apply the full mathematical model to a carefully selected suite of test problems inspired by experiments. We analysed several indices of a single lymphangion for a wide range of upstream and downstream pressure combinations which included both favourable and adverse pressure gradients. The most influential model parameters were identified by performing two sensitivity analyses for favourable and adverse pressure gradients.

There is increasing interest in understanding the physiology of the extracellular fluid compartments in the central nervous system and their dynamic interaction. Such interest has been in part prompted by a vigorous resurgence of the role of the venous system, the recent discoveries of the meningeal lymphatics, the brain waste removal mechanisms and their potential link to neurological diseases, such as idiopathic intracranial hypertension, Ménière’s disease, migraine, small vessel disease, and most neurodegenerative diseases. The rigid cranial cavity houses several space-competing material compartments: the brain parenchyma (BP) and four extracellular fluids, namely arterial, venous, cerebrospinal fluid (CSF) and interstitial fluid (ISF). During cardiac pulsations, the harmonious, temporal and spatial dynamic interaction of all these fluid compartments and the BP assures a constant intracranial volume at all times, consistent with the Monro-Kellie hypothesis. The dynamic interaction involves high-pressure input of arterial blood during systole and efflux of CSF into the spinal subarachnoid space (SSAS) followed by venous blood exiting directly into the vertebral and internal jugular veins towards the heart and intraventricular CSF displacing caudally towards the SSAS. Arterial pulsatile energy is transmitted to the BP that contributes to the smooth movement of fluids in and out of the brain. Perturbing any of these fluid compartments will alter the entire brain dynamics, potentially increase intracranial pressure, affect perfusion and hamper clearance capacity of metabolic waste. This review of all major extracellular fluid compartments within the brain, advocates a holistic approach to our understanding of the fluid dynamics, rather than focusing on a single compartment when analyzing neurological diseases. This approach may contribute to advance our comprehension of some common neurological disorders, paving the way to newer treatment options.

Introduction: The study examined the behavior of vasculature in conditions of eliminated cardiac function using mathematical modeling. In addition, we addressed the question of whether the stretch-recoil capability of veins, at least in part accounts for the slower response to simulated cardiac arrest. Methods: In the first set of computational experiments, blood flow and pressure patterns in veins and arteries during the first few seconds after cardiac arrest were assessed via a validated multi-scale mathematical model of the whole cardiovascular system, comprising cardiac dynamics, arterial and venous blood flow dynamics, and microcirculation. In the second set of experiments, the effects of stretch-recoil zones of venous vessels with different diameters and velocities on blood velocity and dynamic pressure analyzed using computational fluid dynamics (CFD) modeling. Results: In the first set of experiments, measurement of changes in velocity, dynamic pressure, and fluid flow revealed that the venous system responded to cardiac arrest more slowly compared to the arteries. This disparity might be due to the intrinsic characteristics of the venous system, including stretch-recoil and elastic fiber composition. In the second set of experiments, we attempted to determine the role of the stretch-recoil capability of veins in the slower response to cardiac arrest. During the second set of experiments, we found that this recoil behavior increased dynamic pressure, velocity, and blood flow. The enhancement in dynamic pressure through combining the results from both experiments yielded a 15-40% increase in maximum dynamic pressure due to stretch-recoil, depending on vein diameter under normal conditions. Conclusion: In the situation of cardiac arrest, the vein geometry changes continue, promoting smooth responses of the venous system. Moreover, the importance of such vein behavior in blood displacement may grow as the pressure on the venous side gradually decreases with time. Our experiments suggest that the driving force for venous return is the pressure difference that remains within the venous system after the energy coming from every ventricular systole spent to overcome the resistance created by arterial and capillary systems.

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Ménière’s disease (MD) is a pathology of the inner ear, the symptoms of which include tinnitus, vertigo attacks, fluctuating hearing loss, and nausea. Neither cause nor cure are currently known, though animal experiments suggest that disruption of the inner ear circulation, including venous hypertension and endolymphatic hydrops, to be hallmarks of the disease. Recent evidence for humans suggests a potential link to strictures in the extracranial venous outflow routes. The purpose of the present work is to demonstrate that the inner-ear circulation in humans is disrupted by extracranial venous outflow stricture and to discuss the implications of this finding for MD. The hypothesis linking extracranial venous outflow strictures to the altered dynamics of central nervous system (CNS) fluid compartments is investigated theoretically via a global, closed-loop, multiscale mathematical model for the entire human circulation, interacting with the brain parenchyma and cerebrospinal fluid (CSF). The fluid dynamics model for the full human body includes submodels for the heart, pulmonary circulation, arterial system, microvasculature, venous system and the CSF, with a specially refined description of the inner ear vasculature. We demonstrate that extracranial venous outflow strictures disrupt inner ear circulation, and more generally, alter the dynamics of fluid compartments in the whole CNS. Specifically, as compared to a healthy control, the computational results from our model show that subjects with extracranial outflow venous strictures exhibit: altered inner ear circulation, redirection of flow to collaterals, increased intracranial venous pressure and increased intracranial pressure. Our findings are consistent with recent clinical evidence in humans that links extracranial outflow venous strictures to MD, aid the mechanistic understanding of the underlying features of the disease and lend support to recently proposed biophysically motivated therapies aimed at reducing the overall pressure in the inner ear circulation. More work is required to understand the finer details of the condition, such as the associated dynamics of fluids in the perilymphatic and endolymphatic spaces, so as to incorporate such knowledge into the mathematical models in order to reflect the real physiology more closely.

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