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Impaired cerebral autoregulation leads to fluctuations in cerebral blood flow, which can be especially dangerous for immature brain of preterm newborns. In this paper, two mathematical models of cerebral autoregulation are discussed. The first one is an enhancement of a vascular model proposed by Piechnik et al. We extend this model by adding a polynomial dependence of the vascular radius on the arterial blood pressure and adjusting the polynomial coefficients to experimental data to gain the autoregulation behavior. Moreover, the inclusion of a Preisach hysteresis operator, simulating a hysteretic dependence of the cerebral blood flow on the arterial pressure, is tested. The second model couples the blood vessel system model by Piechnik et al. with an ordinary differential equation model of cerebral autoregulation by Ursino and Lodi. An optimal control setting is proposed for a simplified variant of this coupled model. The objective of the control is the maintenance of the autoregulatory function for a wider range of the arterial pressure. The control can be interpreted as the effect of a medicament changing the cerebral blood flow by, for example, dilation of blood vessels. Advanced numerical methods developed by the authors are applied for the numerical treatment of the control problem.

The Stokes formula for the resistance force exerted on a sphere moving with constant velocity in a fluid is extended to the case of micropolar fluids. A non-homogeneous boundary condition for the micro-rotation vector is used: the micro-rotation on the boundary of the sphere is assumed proportional to the rotation rate of the velocity field on the boundary.

Intraventricular hemorrhage (IVH) is one of the most critical complications in the development of preterm infants. The likelihood of IVH is strongly associated with disturbances in cerebral blood flow (CBF) and with microvascular fragility in the germinal matrix (GM). The CBF value and its reactivity to changes in arterial carbon dioxide pressure (pCO2) and mean arterial blood pressure (MABP) are relevant indicators in the clinical assessment of preterm infants. The objective of the present study is mathematical modeling of the influence of pCO2 and MABP on CBF in immature brain, based on clinical data collected from 265 preterm infants with 23–30 gestational weeks. The model was adapted to the peculiarities of immature brain by taking into account the morphological characteristics of the GM capillary network and vascular reactivity, according to gestational and postnatal age. An analysis of model based values of CBF and its reactivity to changes in MABP and pCO2 was performed separately for each gestational week and for the first two days of life both for preterm infants with and without IVH. The developed model for the estimation of CBF was validated against equivalent experimental measurements taken from the literature. A good agreement between the estimated values of CBF, as well as its reaction on changes in MABP and pCO2 and the equivalent values obtained in experimental studies was shown.

We study both theoretically and experimentally the nonlinear interaction between an intense surface acoustic wave and a two-dimensional electron plasma in semiconductor-piezocrystal hybrid structures. The experiments on hybrid systems exhibit strongly nonlinear acousto-electric effects. The plasma turns into moving electron stripes, the acousto-electric current reaches its maximum, and the sound absorption strongly decreases. To describe the nonlinear phenomena, we develop a coupled-amplitude method for a two-dimensional system in the strongly nonlinear regime of interaction. At low electron densities the absorption coefficient decreases with increasing sound intensity, whereas at high electron density the absorption coefficient is not a monotonous function of the sound intensity. High-harmonic generation coefficients as a function of the sound intensity have a nontrivial behavior.Theory and experiment are found to be in a good agreement. *

In this study, the Cauchy problem for the Laplace equation in a multiply connected region was solved. Solving this problem was replaced by solving the Poisson equation in a simply connected region with an unknown source function different from zero in the adjoined region. To determine the power of the sources, a convergent iterative process has been developed based on polyharmonic functions, including the tests on the effect of the polyharmonic function order on the solution accuracy.