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Autoregulation and neurovascular coupling are key mechanisms that modulate myogenic tone (MT) in vessels to regulate cerebral blood flow (CBF) during resting state and periods of increased neural activity, respectively. To determine relative contributions of distinct vascular zones across different cortical depths in CBF regulation, we developed a simplified yet detailed and computationally efficient model of the mouse cerebrovasculature. The model integrates multiple simplifications and generalizations regarding vascular morphology, the hierarchical organization of mural cells, and potentiation/inhibition of MT in vessels. Our analysis showed that autoregulation is the result of the synergy between these factors, but achieving an optimal balance across all cortical depths and throughout the autoregulation range is a complex task. This complexity explains the non-uniformity observed experimentally in capillary blood flow at different cortical depths. In silico simulations of cerebral autoregulation support the idea that the cerebral vasculature does not maintain a plateau of blood flow throughout the autoregulatory range and consists of both flat and sloped phases. We learned that small-diameter vessels with large contractility, such as penetrating arterioles and precapillary arterioles, have major control over intravascular pressure at the entry points of capillaries and play a significant role in CBF regulation. However, temporal alterations in capillary diameter contribute moderately to cerebral autoregulation and minimally to functional hyperemia. In addition, hemodynamic analysis shows that while hemodynamics within capillaries remain relatively stable across all cortical depths throughout the entire autoregulation range, significant variability in hemodynamics can be observed within the first few branch orders of precapillary arterioles or transitional zone vessels. The computationally efficient cerebrovasculature model, proposed in this study, provides a novel framework for analyzing dynamics of the CBF regulation where hemodynamic and vasodynamic interactions are the foundation on which more sophisticated models can be developed. 

Tomography is widely used in medical imaging or industrial non-destructive testing applications. One costly and time consuming operation in any form of tomography is the process of data acquisition where a large number of measurements are made and collected data is used for image reconstruction. Data acquisition can slow down tomography to the point that the scanner cannot catch up with the speed of changes in the medium under test. By optimizing the information content of each measurement, we can reduce the number of measurements needed to achieve the target precision. Development of algorithms to optimize the information content of tomography measurements is the main goal of this article. Here, the dynamics of the medium and tomography measurements are formulated in the form of a Kalman estimation filter. A mathematical algorithm is developed to compute the optimal measurement matrix which minimizes the uncertainty left in the estimation of the distribution the tomography scanner is reconstructing. Results, as presented in the paper, show noticeable improvement is the quality of generated images when the medium is scanned by optimal measurements instead of traditional raster or random scanning protocols. 

In tomography, three-dimensional images of a medium are reconstructed from a set of two-dimensional projections. Each projection is the result of a measurement made by the scanner via radiating some form of energy and collecting the scattered field after interacting with the medium. The information content of these measurements is not equal, and one projection can be more informative than others. By choosing the most informative measurement at every step of scanning, an optimal tomography system can maximize the speed of data acquisition and temporal resolution of acquired images, reducing the operation cost and exposure to possible harmful radiations. The aim of this paper is to introduce mathematical algorithms that can be used to design measurements with optimal information content when imaging static or dynamically evolving objects.