Predicting Vessel Diameter Changes to Up-Regulate Biphasic Blood Flow During Activation in Realistic Microvascular Networks

Distal activity patterns shape the spatial specificity of neurovascular coupling

Neurovascular coupling links brain activity to local changes in blood flow, forming the basis for non-invasive brain mapping. Using multiscale imaging, we investigated how vascular activity spatially relates to neuronal activity elicited by single whiskers across different columns and layers of mouse cortex. Here we show that mesoscopic hemodynamic signals quantitatively reflect neuronal activity across space but are composed of a highly heterogeneous pattern of responses across individual vessel segments that is poorly predicted by local neuronal activity. Rather, this heterogeneity is dependent on vessel directionality, specifically in thalamocortical input layer 4, where capillaries respond preferentially to neuronal activity patterns along their downstream perfusion domain. Thus, capillaries fine-tune blood flow based on distant activity and encode laminar-specific activity patterns. These findings imply that vascular anatomy sets a resolution limit on functional imaging signals, where individual blood vessels inaccurately report neuronal activity in their immediate vicinity but, instead, integrate activity patterns along the vascular arbor.

Pressure-Poisson equation in numerical simulation of cerebral arterial circulation and its effect on the electrical conductivity of the brain

BACKGROUND AND OBJECTIVE

This study considers dynamic modeling of the cerebral arterial circulation and reconstructing an atlas for the electrical conductivity of the brain. Electrical conductivity is a governing parameter in several electrophysiological modalities applied in neuroscience, such as electroencephalography (EEG), transcranial electrical stimulation (tES), and electrical impedance tomography (EIT). While high-resolution 7-Tesla (T) Magnetic Resonance Imaging (MRI) data allow for reconstructing the cerebral arteries with a cross-sectional diameter larger than the voxel size, electrical conductivity cannot be directly inferred from MRI data. Brain models of electrophysiology typically associate each brain tissue compartment with a constant electrical conductivity, omitting any dynamic effects of cerebral blood circulation. Incorporating those effects poses the challenge of solving a system of incompressible Navier-Stokes equations (NSEs) in a realistic multi-compartment head model. However, using a simplified circulation model is well-motivated since, on the one hand, the complete system does not always have a numerically stable solution and, on the other hand, the full set of arteries cannot be perfectly reconstructed from the MRI data, meaning that any solution will be approximative.

METHODS

We postulate that circulation in the distinguishable arteries can be estimated via the pressure-Poisson equation (PPE), which is coupled with Fick's law of diffusion for microcirculation. To establish a fluid exchange model between arteries and microarteries, a boundary condition derived from the Hagen-Poisseuille model is applied. The relationship between the estimated volumetric blood concentration and the electrical conductivity of the brain tissue is approximated through Archie's law for fluid flow in porous media.

RESULTS

Through the formulation of the PPE and a set of boundary conditions (BCs) based on the Hagen-Poisseuille model, we obtained an equivalent formulation of the incompressible Stokes equation (SE). Thus, allowing effective blood pressure estimation in cerebral arteries segmented from open 7T MRI data.

CONCLUSIONS

As a result of this research, we developed and built a useful modeling framework that accounts for the effects of dynamic blood flow on a novel MRI-based electrical conductivity atlas. The electrical conductivity perturbation obtained in numerical experiments has an appropriate overall match with previous studies on this subject. Further research to validate these results will be necessary.

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.

Challenges and opportunities of integrating imaging and mathematical modelling to interrogate biological processes

Advances in biological imaging have accelerated our understanding of human physiology in both health and disease. As these advances have developed, the opportunities gained by integrating with cutting-edge mathematical models have become apparent yet remain challenging. Combined imaging-modelling approaches provide unprecedented opportunity to correlate data on tissue architecture and function, across length and time scales, to better understand the mechanisms that underpin fundamental biology and also to inform clinical decisions. Here we discuss the opportunities and challenges of such approaches, providing literature examples across a range of organ systems. Given the breadth of the field we focus on the intersection of continuum modelling and in vivo imaging applied to the vasculature and blood flow, though our rationale and conclusions extend widely. We propose three key research pillars (image acquisition, image processing, mathematical modelling) and present their respective advances as well as future opportunity via better integration. Multidisciplinary efforts that develop imaging and modelling tools concurrently, and share them open-source with the research community, provide exciting opportunity for advancing these fields.

Pericyte Control of Blood Flow Across Microvascular Zones in the Central Nervous System

The vast majority of the brain's vascular length is composed of capillaries, where our understanding of blood flow control remains incomplete. This review synthesizes current knowledge on the control of blood flow across microvascular zones by addressing issues with nomenclature and drawing on new developments from in vivo optical imaging and single-cell transcriptomics. Recent studies have highlighted important distinctions in mural cell morphology, gene expression, and contractile dynamics, which can explain observed differences in response to vasoactive mediators between arteriole, transitional, and capillary zones. Smooth muscle cells of arterioles and ensheathing pericytes of the arteriole-capillary transitional zone control large-scale, rapid changes in blood flow. In contrast, capillary pericytes downstream of the transitional zone act on slower and smaller scales and are involved in establishing resting capillary tone and flow heterogeneity. Many unresolved issues remain, including the vasoactive mediators that activate the different pericyte types in vivo, the role of pericyte-endothelial communication in conducting signals from capillaries to arterioles, and how neurological disease affects these mechanisms.

Origins of 1/f-like tissue oxygenation fluctuations in the murine cortex

The concentration of oxygen in the brain spontaneously fluctuates, and the distribution of power in these fluctuations has a 1/f-like spectra, where the power present at low frequencies of the power spectrum is orders of magnitude higher than at higher frequencies. Though these oscillations have been interpreted as being driven by neural activity, the origin of these 1/f-like oscillations is not well understood. Here, to gain insight of the origin of the 1/f-like oxygen fluctuations, we investigated the dynamics of tissue oxygenation and neural activity in awake behaving mice. We found that oxygen signal recorded from the cortex of mice had 1/f-like spectra. However, band-limited power in the local field potential did not show corresponding 1/f-like fluctuations. When local neural activity was suppressed, the 1/f-like fluctuations in oxygen concentration persisted. Two-photon measurements of erythrocyte spacing fluctuations and mathematical modeling show that stochastic fluctuations in erythrocyte flow could underlie 1/f-like dynamics in oxygenation. These results suggest that the discrete nature of erythrocytes and their irregular flow, rather than fluctuations in neural activity, could drive 1/f-like fluctuations in tissue oxygenation.