Mathematical modeling of cerebral capillary blood flow heterogeneity and its effect on brain tissue oxygen levels

Cerebral Small Vessel Disease: a Review of the Pathophysiological Mechanisms

Cerebral small vessel disease (cSVD) refers to the age-dependent pathological processes involving the brain small vessels and leading to vascular cognitive impairment, intracerebral hemorrhage, and acute lacunar ischemic stroke. Despite the significant public health burden of cSVD, disease-specific therapeutics remain unavailable due to the incomplete understanding of the underlying pathophysiological mechanisms. Recent advances in neuroimaging acquisition and processing capabilities as well as findings from cSVD animal models have revealed critical roles of several age-dependent processes in cSVD pathogenesis including arterial stiffness, vascular oxidative stress, low-grade systemic inflammation, gut dysbiosis, and increased salt intake. These factors interact to cause a state of endothelial cell dysfunction impairing cerebral blood flow regulation and breaking the blood brain barrier. Neuroinflammation follows resulting in neuronal injury and cSVD clinical manifestations. Impairment of the cerebral waste clearance through the glymphatic system is another potential process that has been recently highlighted contributing to the cognitive decline. This review details these mechanisms and attempts to explain their complex interactions. In addition, the relevant knowledge gaps in cSVD mechanistic understanding are identified and a systematic approach to future translational and early phase clinical research is proposed in order to reveal new cSVD mechanisms and develop disease-specific therapeutics.

Approaches to vascular network, blood flow, and metabolite distribution modeling in brain tissue

The cardiovascular system plays a key role in the transport of nutrients, ensuring a continuous supply of all cells of the body with the metabolites necessary for life. The blood supply to the brain is carried out by the large arteries located on its surface, which branch into smaller arterioles that penetrate the cerebral cortex and feed the capillary bed, thereby forming an extensive branching network. The formation of blood vessels is carried out via vasculogenesis and angiogenesis, which play an important role in both embryo and adult life. The review presents approaches to modeling various aspects of both the formation of vascular networks and the construction of the formed arterial tree. In addition, a brief description of models that allows one to study the blood flow in various parts of the circulatory system and the spatiotemporal metabolite distribution in brain tissues is given. Experimental study of these issues is not always possible due to both the complexity of the cardiovascular system and the mechanisms through which the perfusion of all body cells is carried out. In this regard, mathematical models are a good tool for studying hemodynamics and can be used in clinical practice to diagnose vascular diseases and assess the need for treatment.

Modeling the response of homogeneous and heterogeneous cerebral capillary networks to local changes in vessel diameters

While microvascular cerebral capillary networks are known to be highly heterogeneous, previous computational models have predicted that heterogeneous cerebral capillary flow patterns result in lower brain tissue partial oxygen pressures. Moreover, as blood flow increases, the flux among capillaries homogenizes. This homogenization of flow is expected to improve the efficiency of oxygenation extraction from the blood. In this work, we use mathematical modeling to explore a possible functional role for the high degree of heterogeneity observed in cerebral capillary networks. Our results suggest that heterogeneity allows for a greater response of tissue oxygen levels to local changes in vessel diameters due to neuronal activation. This result is confirmed for a full 3-dimensional model of capillary networks that includes oxygen diffusion within the tissue region and a reduced model that accounts for changes in capillary blood flow.

Predictive Design and Analysis of Drug Transport by Multiscale Computational Models Under Uncertainty

Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these drug carriers, dosages and treatment schemes will require advanced models that can simulate transport processes across multiple length and time scales from genomic to population levels. In order to address this problem, multiscale modeling efforts that integrate existing discrete and continuum modeling strategies have recently emerged. These multiscale approaches provide a promising direction for bottom-up in silico pipelines of drug design for delivery. However, there are remaining challenges in terms of model parametrization and validation in the presence of variability, introduced by multiple levels of heterogeneities in disease state. Parametrization based on physiologically relevant in vitro data from microphysiological systems as well as widespread adoption of uncertainty quantification and sensitivity analysis will help address these challenges.