Figure: Schematic representation of realistic microvascular network sample. The vasculature network is represented by a graph, a collection of nodes and an ensemble of edges that connect pairs of nodes on which the endfeet are placed. Between 2 black circles, sections (where bifurcation start or end) are represented, while between 2 orange dashes, segment is highlighted. Equations to compute blood flow and pressure are solved at each time point and each vessels radii under different boundary conditions. The blood pressure is computed on each node of the vasculature, while the flow is computed on each edge.
Mathematical models of cerebral microcirculation are widely used in order to run hemodynamic simulations. These models imply to combine biophysical principles with data from medical imaging. For instance, data from synchrotron radiation based X-ray tomographic microscopy data of rat somatosensory cortex was used in Reichold (2009). These models have increasingly become an obvious field of research for cerebral circulation to get the whole NGV ensemble working together. This would enable a better understanding of the anatomical principles and geometric constraint, a better prediction of cerebral blood flow, a better characterization of metabolites exchanges from and to tissues, and this could deepen our knowledge of the mechanisms involved in the blood flow control.
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Mathematical framework of the blood-flow model and Simulation of blood flow and blood pressure
Stochastic simulation of endfeet activity
Figure: Model calibration: in this model we have 2 parameters, sigma and kappa for every vessels. Kappa stands for speed of reversion to the RS, while square sigma stands for the variance of the noise. On the left, sample path of a Reflected OU process with T = 1, kappa = 5 and sigma = 4. On the right: comparison of the asymptotic OU and ROU distributions. We simulated 5000 ROU paths and created an histogram with the values of XT at T = 1.