Assessing haemorrhage-critical values of cerebral blood flow by modelling biomechanical stresses on capillaries in the immature brain.

The development of intraventricular haemorrhages (IVH) in preterm newborns is triggered by a disruption of the vessels responsible for cerebral microcirculation. Analysis of the stresses exerted on vessel walls enables the identification of the critical values of cerebral blood flow (CBF) associated with the development of IVH in preterm infants. The purpose of the present study is the estimation of these critical CBF values using the biomechanical stresses obtained by the finite element modelling of immature brain capillaries. The properties of the endothelial cells and basement membranes employed were selected on the basis of published nanoindentation measurements using atomic force microscopes. The forces acting on individual capillaries were derived with a mathematical model that accounts for the peculiarities of microvascularity in the immature brain. Calculations were based on clinical measurements obtained from 254 preterm infants with the gestational age ranging from 23 to 30 weeks, with and without diagnosis of IVH. No distinction between the affected and control groups with the gestational age of 23 to 26 weeks was possible. For infants with the gestational age of 27 to 30 weeks, the CBF value of 17.03 ml/100 g/min was determined as the critical upper value, above which the likelihood of IVH increases.

Nonstationary Model of Oxygen Transport in Brain Tissue.

The paper addresses the mathematical study of a nonstationary continuum model describing oxygen propagation in cerebral substance. The model allows to estimate the rate of oxygen saturation and stabilization of oxygen concentration in relatively large parts of cerebral tissue. A theoretical and numerical analysis of the model is performed. The unique solvability of the underlying initial-boundary value problem for a system of coupled nonlinear parabolic equations is proved. In the numerical experiment, the tissue oxygen saturation after hypoxia is analyzed for the case when a sufficient amount of oxygen begins to flow into the capillary network. A fast stabilization of the tissue oxygen concentration is demonstrated. The reliability of the results of the numerical simulation is discussed.

Assessing key clinical parameters before and after intraventricular hemorrhage in very preterm infants.

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 pCO2 in 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 pCO2 and 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.

Accounting for Tube Hematocrit in Modeling of Blood Flow in Cerebral Capillary Networks.

The aim of this paper consists in the derivation of an analytic formula for the hydraulic resistance of capillaries, taking into account the tube hematocrit level. The consistency of the derived formula is verified using Finite Element simulations. Such an effective formula allows for assigning resistances, depending on the hematocrit level, to the edges of networks modeling biological capillary systems, which extends our earlier models of blood flow through large capillary networks. Numerical simulations conducted for large capillary networks with random topologies demonstrate the importance of accounting for the hematocrit level for obtaining consistent results.

Extended model of impaired cerebral autoregulation in preterm infants: Heuristic feedback control.

Cerebral autoregulation is the ability to keep almost constant cerebral blood flow (CBF) for some range of changing the mean arterial pressure (MAP). In preterm infants, this range is usually very small, even absent, and a passive (linear) dependence of CBF on MAP is observed. Also, variations of the partial CO2 pressure and intracranial/venous pressure result in fluctuations of CBF. The absence of cerebral autoregulation may be a cause of intracranial hemorrhages due to instability of cerebral blood vessels, especially in the so-called germinal matrix which exists in a developing brain from 22 to 32 weeks of gestation. In the current paper, a mathematical model of impaired cerebral autoregulation is extended compared with previous works of the authors, and a heuristic feedback control that is able to keep deviations from a nominal CBF within a reasonable range is proposed. Viability theory is used to prove that this control can successfully work against a wide range of disturbances.

Postnatal Paraclinical Parameters Associated to Occurrence of Intracerebral Hemorrhage in Preterm Infants.

Intracerebral hemorrhage (ICH) is the most frequent complication in postnatal development of preterm infants. The purpose of the present work is the statistical evaluation of seven standard paraclinical parameters and their association to the development of ICH. Clinical records of 265 preterm infants with gestational age (GA) 23 to 30 weeks were analyzed. According to ICH status, patients were divided into control (without ICH) and affected (with ICH) groups. Mean values of paraclinical parameters at each week of gestation were compared. Different ICH grades, periods before and after ICH were considered separately. Lower hematocrit, SaO2, and pH were statistically significant for preterm infants with 23 to 30 weeks GA and diagnosis of ICH relative to infants without ICH. Additionally, for preterm infants with 27 to 30 weeks GA, higher C-reactive protein, as well as lower values of thrombocytes were associated with the occurrence of ICH. Preterm infants with 23 to 26 weeks GA showed C-reactive protein values similar to those in the group without ICH and lower levels of thrombocytes after bleeding. Significant differences in paraclinical parameters between preterm infants with and without ICH may constitute useful indicators for closer clinical observation of preterm infants at risk of ICH.

Modeling Cerebral Blood Flow Dependence on Carbon Dioxide and Mean Arterial Blood Pressure in the Immature Brain With Accounting for the Germinal Matrix.

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 (pCO 2 ) 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 pCO 2 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 pCO 2 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 pCO 2 and the equivalent values obtained in experimental studies was shown.

Direct modeling of blood flow through the vascular network of the germinal matrix.

A premature birth, before completion of the 32nd pregnancy week, increases the risk of cerebral hemorrhage. The cause of brain bleeding is very often the germinal matrix of the immature brain. The germinal matrix consists of richly vascularized neuroepithelial cells and is located over the lower part of the head of the caudate nucleus. By 32-36 gestation weeks, the germinal matrix essentially disappears so that its hemorrhage is a disease of premature infants. The aim of this paper consists in developing a model of the brain vascular network and computing the pressure distribution in the germinal matrix, particularly near arterioles and venules, where cerebral hemorrhage may occur. Capillary networks consisting of several millions of vessels are directly simulated in the present study.

Mathematical modelling of cerebral blood circulation and cerebral autoregulation: towards preventing intracranial hemorrhages in preterm newborns.

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.