Validation of a Multiscale Computational Model Using a Mock Circulatory Loop to Simulate Cardiogenic Shock.

The objectives of this study are to characterize the hemodynamics of cardiogenic shock (CS) through a computational model validated using a mock circulatory loop (MCL) and to perform sensitivity analysis and uncertainty propagation studies after the American Society of Mechanical Engineers (ASME) Validation and Verification (V&V) guidelines. The uncertainties in cardiac cycle time ( ), total resistance ( ), and total volume ( ) were quantified in the MCL and propagated in the computational model. Both models were used to quantify the pressure in the left atrium, aorta (Ao), and left ventricle (LV), along with the flow through the aortic valve, reaching a good agreement. The results suggest that 1) is the main source of uncertainty in the variables under study, 2) showed its greatest impact on the uncertainty of Ao hemodynamics, and 3) mostly affected the uncertainty of LV pressure and Ao flow at the late-systolic phase. Comparison of uncertainty levels in the computational and experimental results was used to infer the presence of additional contributing factors that were not captured and propagated during a first analysis. Future work will expand upon this study to analyze the impact of mechanical circulatory support devices, such as ventricular assist devices, under CS conditions.

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. 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.

Function of arteries and veins in conditions of simulated cardiac arrest.

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.

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. In addition, the system cannot be written in conservation-law form, and thus, an appropriate numerical approach is required, namely the path conservative approach. The designed computational algorithm is shown to be second-order accurate in both space and time, capable of handling strongly nonlinear discontinuities, and a method of coupling it with an unsteady inflow condition is presented. Such an approach is sufficiently rapid to be integrated into a global, closed-loop model for computing the dynamics of coupled fluid compartments of the CNS.

Publisher Correction: Functional aspects of meningeal lymphatics in ageing and Alzheimer's disease.

Change history: In this Article, Extended Data Fig. 9 was appearing as Fig. 2 in the HTML, and in Fig. 2, the panel labels 'n' and 'o' overlapped the figure; these errors have been corrected online.

Functional aspects of meningeal lymphatics in ageing and Alzheimer's disease.

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-ß deposition in the meninges, which resembles human meningeal pathology, and aggravates parenchymal amyloid-ß 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.

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. 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.

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. METHODS: We quantified the following parameters at the level of the aqueduct of Sylvius and the cervical C2C3: Cerebrospinal Fluid (CSF), arterial and venous flow; CSF velocity amplitude; artero-venous delay (AVD); artero-CSF delay and percentage of venous outflow normalized to total arterial inflow (tIJV/tA). Analyses were run before Lumbar Puncture (LP) (A), after LP (B), after medical therapy (C) and after venous stent placements deployed at two separate times (D and E). RESULTS: AVD and tIJV/tA improved only after CSF removal and after stent placements. CSF velocity amplitude remained elevated. Arterial flow profile showed a dramatic reduction after LP with improvement in mean venous flow. This report is the first to demonstrate interactive changes in intracranial fluid dynamics that occur before and after different therapeutic interventions in IIH. CONCLUSION: The data provide valuable information regarding changes in different fluid compartments suggesting a profound redistribution of pressures along fluid compartments after different treatments. We discuss how increased intracranial venous blood could be "tumoral" in IIH and facilitating its outflow could be therapeutic.