Stable approximation schemes for solving Hamilton–Jacobi–Bellman–Isaacs equations in $R^n$ are proposed. The efficiency of numerical procedures based on such approximations is demonstrated by solving several differential games in two, three, and four dimensions.

Intracerebral hemorrhage in preterm infants is a major cause of brain damage and cerebral palsy. The pathogenesis of cerebral hemorrhage is multifactorial. Among the risk factors are impaired cerebral autoregulation, infections, and coagulation disorders. Machine learning methods allow the identification of combinations of clinical factors to best differentiate preterm infants with intra-cerebral bleeding and the development of models for patients at risk of cerebral hemorrhage. In the current study, a Random Forest approach is applied to develop such models for extremely and very preterm infants (23–30 weeks gestation) based on data collected from a cohort of 229 individuals. The constructed models exhibit good prediction accuracy and might be used in clinical practice to reduce the risk of cerebral bleeding in prematurity.

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.

Intraventricular cerebral hemorrhage (IVH) is one of the most severe complications of premature birth, potentially leading to lifelong disability. The purpose of this paper is the assessment of the evolution of three of the most relevant parameters, before and after IVH: mean arterial pressure (MAP), arterial carbon dioxide pressure (pCO₂), and cerebral blood flow (CBF). Clinical records of 254 preterm infants with a gestational age of 23–30 weeks, with and without a diagnosis of IVH, were reviewed for MAP and arterial pCO₂in the period up to 7 days before and 3 days after IVH or during the first 10 days of life in cases without IVH.Conclusion: A statistically significant increase in pCO₂and decrease in MAP in patients with IVH compared with those without were detected. Both the mean values and the mean absolute deviations of CBF were computed in this study, and the latter was significantly higher than in control group. High deviations of CBF, as well as hypercapnia and hypotension, are likely to contribute to the rupture of cerebral blood vessels in preterm infants, and consequently, to the development of IVH. What is Known:•The origin of IVH is multifactorial, but mean arterial pressure, carbon dioxide partial pressure, and cerebral blood flow are recognized as the most important parameters.• In premature infants, the autoregulation mechanisms are still underdeveloped and cannot compensate for cerebral blood flow fluctuations. What is New:•The numerical simulation of CBF is shown to be a promising approach that may be useful in the care of preterm infants.• The mean values of CBF before and after IVH in the affected group were similar to those in the control group, but the mean absolute deviations of CBF in the affected group before and after IVH were significantly higher than that in the control group.