| סיכום: | <p>A healthy brain possesses an intrinsic collection of mechanisms, known as dynamic cerebral autoregulation, that allow it to withstand physiological disturbances and maintain a sufficient and continuous supply of blood required to perform its functions. Abnormalities in cerebral autoregulation have been implicated in various disease conditions, including ischaemic stroke, and more recently neurodegenerative diseases such as Alzheimer’s. These protective mechanisms occur predominantly in the microvasculature, the site of exchange between the blood and the brain tissue. However, the microvasculature’s role in diseases is poorly understood, primarily due to the current imaging gap between the scales of clinical imaging (<em>mm</em>) and the microvasculature (<em>μm</em>). Hence, models of blood flow in the microvasculature can play a key role in filling this gap and help achieve a better understanding of cerebrovascular pathologies. These conditions are often linked to structural modifications in the vessel network, alterations in blood flow patterns, as well as impairment in the autoregulatory responses, all of which are changes that the model should be able to address if it were to have any clinical value.</p>
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<p>We use perturbation methods to derive a model of dynamic blood flow and control
in the microvasculature, one that resolves the structure of the individual microvessels in the network, and the autoregulation mechanisms are incorporated via a feedback model that alters the compliance of the individual vessels. We then validate the model and use it to model blood flow in the cortical penetrating vessels, whereas we model the capillary bed of the cortex as a porous medium and geometrically discretise it using a novel finite volume algorithm that ensures numerical accuracy and computational feasibility of the numerical solver. We then appropriately couple the discrete and continuum parts of the networks, giving rise to a single multiscale system that characterises the dynamic pressure and flux variations throughout an MRI voxel-sized network.</p>
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<p>We conduct parameter calibration and sensitivity analyses to ensure an accurate characterisation of the feedback model parameter space. Finally, to demonstrate the utility of the models, we use the constructed networks as <em>in-silico</em> vascular testing beds to explore the biophysical origins and mechanisms behind the hypercapnic response, which remain poorly understood due to the difficulties of investigating the response in a conventional experimental context. Drawing from the available experimental data, we propose a sequence of the signalling events underpinning the hypercapnic response, and use the models to test the hypothesis and provide compelling evidence that strongly corroborates its validity, thereby providing an important addition to our understanding of the blood flow control processes and motivating further <em>in-vivo</em> investigations.</p>
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