Experimentally constrained circuit model of cortical arteriole networks for understanding flow redistribution due to occlusion and neural activation.

Computations are described which estimate flows in all branches of the cortical surface arteriole network from two-photon excited fluorescence (2PEF) microscopy images which provide the network topology and, in selected branches red blood cell (RBC) speeds and lumen diameters. Validation is done by comparing the flow predicted by the model with experimentally measured flows and by comparing the predicted flow redistribution in the network due to single-vessel strokes with experimental observations. The model predicts that tissue is protected from RBC flow decreases caused by multiple occlusions of surface arterioles but not penetrating arterioles. The model can also be used to study flow rerouting due to vessel dilations and constrictions.

A mathematical model relating cortical oxygenated and deoxygenated hemoglobin flows and volumes to neural activity.

OBJECTIVE: To describe a toolkit of components for mathematical models of the relationship between cortical neural activity and space-resolved and time-resolved flows and volumes of oxygenated and deoxygenated hemoglobin motivated by optical intrinsic signal imaging (OISI). APPROACH: Both blood flow and blood volume and both oxygenated and deoxygenated hemoglobin and their interconversion are accounted for. Flow and volume are described by including analogies to both resistive and capacitive electrical circuit elements. Oxygenated and deoxygenated hemoglobin and their interconversion are described by generalization of Kirchhoff's laws based on well-mixed compartments. MAIN RESULTS: Mathematical models built from this toolkit are able to reproduce experimental single-stimulus OISI results that are described in papers from other research groups and are able to describe the response to multiple-stimuli experiments as a sublinear superposition of responses to the individual stimuli. SIGNIFICANCE: The same assembly of tools from the toolkit but with different parameter values is able to describe effects that are considered distinctive, such as the presence or absence of an initial decrease in oxygenated hemoglobin concentration, indicating that the differences might be due to unique parameter values in a subject rather than different fundamental mechanisms.

In vivo two-photon excited fluorescence microscopy reveals cardiac- and respiration-dependent pulsatile blood flow in cortical blood vessels in mice.

Subtle alterations in cerebral blood flow can impact the health and function of brain cells and are linked to cognitive decline and dementia. To understand hemodynamics in the three-dimensional vascular network of the cerebral cortex, we applied two-photon excited fluorescence microscopy to measure the motion of red blood cells (RBCs) in individual microvessels throughout the vascular hierarchy in anesthetized mice. To resolve heartbeat- and respiration-dependent flow dynamics, we simultaneously recorded the electrocardiogram and respiratory waveform. We found that centerline RBC speed decreased with decreasing vessel diameter in arterioles, slowed further through the capillary bed, and then increased with increasing vessel diameter in venules. RBC flow was pulsatile in nearly all cortical vessels, including capillaries and venules. Heartbeat-induced speed modulation decreased through the vascular network, while the delay between heartbeat and the time of maximum speed increased. Capillary tube hematocrit was 0.21 and did not vary with centerline RBC speed or topological position. Spatial RBC flow profiles in surface vessels were blunted compared with a parabola and could be measured at vascular junctions. Finally, we observed a transient decrease in RBC speed in surface vessels before inspiration. In conclusion, we developed an approach to study detailed characteristics of RBC flow in the three-dimensional cortical vasculature, including quantification of fluctuations in centerline RBC speed due to cardiac and respiratory rhythms and flow profile measurements. These methods and the quantitative data on basal cerebral hemodynamics open the door to studies of the normal and diseased-state cerebral microcirculation.

Estimating brain microvascular blood flows from partial two-photon microscopy data by computation with a circuit model.

The cortical microvasculature plays a key role in cortical tissue health by transporting important molecules via blood. Disruptions to blood flow in the microvasculature due to events such as stroke can thus induce damage to the cortex. Recent developments in two-photon microscopy have enabled in vivo imaging of anesthetized rat cortex in three dimensions. The microscopy data provide information about the geometry of the cortical microvasculature, length and diameter of the vessels in the imaged microvasculature network, and blood flow through a subset of those vessels. We demonstrate a model that achieves three goals. First, given a network of interconnected vessels and flow measurements on a subset of those vessels, we can estimate the flows in the remaining vessels. Second, we can determine which and how many vessels should have blood flow measurements taken to provide sufficient information to predict the unmeasured flows. Finally, the model enables us to predict effects of blockages in one or more vessels, indicating which vessels are most important to overall flow in the network.