Starling forces drive intracranial water exchange during normal and pathological states

Contribution of Direct Cerebral Vascular Transport in Brain Substance Clearance

The accumulation of harmful substances has long been recognized as a likely cause of many neurodegenerative diseases. The two classic brain clearance pathways are cerebrospinal fluid (CSF) and vascular circulation systems. Since the discovery of the glymphatic system, research on the CSF pathway has gained momentum, and impaired CSF clearance has been implicated in virtually all neurodegenerative animal models. However, the contribution of the direct participation of vascular transport across the blood-brain barrier in clearing substances is often ignored in glymphatic papers. Supportive evidence for the direct involvement of parenchymal vasculature in substance clearance is accumulated. First, multiple mechanisms have been proposed for the vascular drainage of exogenous and endogenous substances across the blood-brain barriers. Second, the "traditional" role of arachnoid villi and granulations as the main site for CSF draining into the vasculature system has been questioned. Third, MRI studies using different CSF tracers indicate that parenchymal vasculature directly participates in tracer efflux, consistent with immunohistochemical findings. Here we will review evidence in the literature that supports the direct participation of the parenchymal vascular system in substance clearance, in addition to the CSF clearance pathways.

Sensitivity analysis of a multi-physics model for the vascular microenvironment

The vascular microenvironment is the scale at which microvascular transport, interstitial tissue properties and cell metabolism interact. The vascular microenvironment has been widely studied by means of quantitative approaches, including multi-physics mathematical models as it is a central system for the pathophysiology of many diseases, such as cancer. The microvascular architecture is a key factor for fluid balance and mass transfer in the vascular microenvironment, together with the physical parameters characterizing the vascular wall and the interstitial tissue. The scientific literature of this field has witnessed a long debate about which factor of this multifaceted system is the most relevant. The purpose of this work is to combine the interpretative power of an advanced multi-physics model of the vascular microenvironment with state of the art and robust sensitivity analysis methods, in order to determine the factors that most significantly impact quantities of interest, related in particular to cancer treatment. We are particularly interested in comparing the factors related to the microvascular architecture with the ones affecting the physics of microvascular transport. Ultimately, this work will provide further insight into how the vascular microenvironment affects cancer therapies, such as chemotherapy, radiotherapy or immunotherapy.

Measurement and Modeling of Transport Across the Blood-Brain Barrier

The blood-brain barrier (BBB) is a dynamic regulatory barrier at the interface of blood circulation and the brain parenchyma, which plays a critical role in protecting homeostasis in the central nervous system. However, it also significantly impedes drug delivery to the brain. Understanding the transport across BBB and brain distribution will facilitate the prediction of drug delivery efficiency and the development of new therapies. To date, various methods and models have been developed to study drug transport at the BBB interface, including in vivo brain uptake measurement methods, in vitro BBB models, and mathematic brain vascular models. Since the in vitro BBB models have been extensively reviewed elsewhere, we provide a comprehensive summary of the brain transport mechanisms and the currently available in vivo methods and mathematic models in studying the molecule delivery process at the BBB interface. In particular, we reviewed the emerging in vivo imaging techniques in observing drug transport across the BBB. We discussed the advantages and disadvantages associated with each model to serve as a guide for model selection in studying drug transport across the BBB. In summary, we envision future directions to improve the accuracy of mathematical models, establish noninvasive in vivo measurement techniques, and bridge the preclinical studies with clinical translation by taking the altered BBB physiological conditions into consideration. We believe these are critical in guiding new drug development and precise drug administration in brain disease treatment.

The glymphatic system: Current understanding and modeling

We review theoretical and numerical models of the glymphatic system, which circulates cerebrospinal fluid and interstitial fluid around the brain, facilitating solute transport. Models enable hypothesis development and predictions of transport, with clinical applications including drug delivery, stroke, cardiac arrest, and neurodegenerative disorders like Alzheimer's disease. We sort existing models into broad categories by anatomical function: Perivascular flow, transport in brain parenchyma, interfaces to perivascular spaces, efflux routes, and links to neuronal activity. Needs and opportunities for future work are highlighted wherever possible; new models, expanded models, and novel experiments to inform models could all have tremendous value for advancing the field.

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.

The brain’sglymphatic system:physiological anatomy and clinical perspectives

The recently discovered glymphatic system (GS) ensures the efficient clearance of interstitial fluid and soluble compounds from the central nervous system into cerebrospinal fluid (CSF), which compensates for the lack of conventional lymphatic vessels in the brain parenchyma. This unique anatomical and physiological phenomenon had been unknown until 2012. GS lacks inherent proper vessels Р the current of CSF and interstitial fluid is carried out directly inside the arterial walls (the perivascular pathway) or near the walls of the cerebral arteries and veins (the paravascular pathway). Current biorheological technologies could establish a special role of aquaporin-4 in the filtration of CSF and interstitial fluid. The close link between GS and the CSF circulatory system allows the established views on fluid dynamics within the brain to be reconsidered. The discovery of GS can contribute to our understanding of the pathogenesis of increased intracranial pressure and neurodegenerative diseases, as well as to the elaboration of new therapeutic approaches to their treatment.

Simulations of blood as a suspension predicts a depth dependent hematocrit in the circulation throughout the cerebral cortex

Recent advances in modeling oxygen supply to cortical brain tissue have begun to elucidate the functional mechanisms of neurovascular coupling. While the principal mechanisms of blood flow regulation after neuronal firing are generally known, mechanistic hemodynamic simulations cannot yet pinpoint the exact spatial and temporal coordination between the network of arteries, arterioles, capillaries and veins for the entire brain. Because of the potential significance of blood flow and oxygen supply simulations for illuminating spatiotemporal regulation inside the cortical microanatomy, there is a need to create mathematical models of the entire cerebral circulation with realistic anatomical detail. Our hypothesis is that an anatomically accurate reconstruction of the cerebrocirculatory architecture will inform about possible regulatory mechanisms of the neurovascular interface. In this article, we introduce large-scale networks of the murine cerebral circulation spanning the Circle of Willis, main cerebral arteries connected to the pial network down to the microcirculation in the capillary bed. Several multiscale models were generated from state-of-the-art neuroimaging data. Using a vascular network construction algorithm, the entire circulation of the middle cerebral artery was synthesized. Blood flow simulations indicate a consistent trend of higher hematocrit in deeper cortical layers, while surface layers with shorter vascular path lengths seem to carry comparatively lower red blood cell (RBC) concentrations. Moreover, the variability of RBC flux decreases with cortical depth. These results support the notion that plasma skimming serves a self-regulating function for maintaining uniform oxygen perfusion to neurons irrespective of their location in the blood supply hierarchy. Our computations also demonstrate the practicality of simulating blood flow for large portions of the mouse brain with existing computer resources. The efficient simulation of blood flow throughout the entire middle cerebral artery (MCA) territory is a promising milestone towards the final aim of predicting blood flow patterns for the entire brain.

The brain’s astonishing cognitive capacity depends on the coordination between neurons and the cerebral circulation, a system known as the neurovascular unit. The spatial and temporal coupling between these two networks is the object of intense research. However, the concise anatomical description of the cerebral circulation has so far been intractable. This paper introduces a methodology for the in silico creation of realistic models for the entire cerebral circulation. This innovation incorporates topological data from several neuroimaging modalities covering three lengths scales as input into a computer algorithm, which assembles anatomically accurate circulatory networks. When simulating blood flow as red blood cells suspended in plasma for experimental and synthetic cortical network models, we discovered that red blood cells tend to be more concentrated in deeper layers of the cortex compared to the surface. RBC fluxes are more homogenous in deeper layers. The phenomenon of depth dependent red blood cell supply supports the notion that the intricate architecture of the cortical microcirculation serves a self-regulating function to maintain uniform oxygen perfusion to neurons. We also demonstrate the practicality of predicting blood flow patterns for the entire brain with existing computer power.