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

Modeling of Cerebral Blood Flow Autoregulation Using Mathematical Control Theory

A mathematical model of cerebral blood flow in the form of a dynamical system is studied. The cerebral blood flow autoregulation modeling problem is treated as a nonlinear control problem and the potential and applicability of the nonlinear control theory techniques are analyzed in this respect. It is shown that the cerebral hemodynamics model in question is differentially flat. Then, the integrator backstepping approach combined with barrier Lyapunov functions is applied to construct the control laws that recover the cerebral autoregulation performance of a healthy human. Simulation results confirm the good performance and flexibility of the suggested cerebral blood flow autoregulation design. The conducted research should enrich our understanding of the mathematics behind the cerebral blood flow autoregulation mechanisms and medical treatments to compensate for impaired cerebral autoregulation, e.g., in preterm infants.

A Mathematical Model for Blood Flow Accounting for the Hematological Disorders

This paper considers a mathematical model that accounts for the hematological disorders of blood in its flow in human arteries. Blood is described as a Newtonian fluid but with its viscosity as a function of the hematocrit, plasma viscosity, and shape factor of the red blood cells. The artery is modeled as a flexible circular pipe with the blood flow as oscillatory. This model is solved using HAM (Homotopy Analysis Method), an approximate analytical method, and we computed expressions for wall shear stress (WSS) and volumetric flow rate. With the help of publicly available data, blood flow in the human femoral artery for male and female populations aged 19 to 60 and above years is simulated for healthy, anemia, and polycythemia cases. The model projected a significant difference in the mean volumetric flow rates in the conditions mentioned above. Results also indicated that the mean WSS of healthy and anemic populations are not significantly different. However, a significant difference in the mean has been observed in healthy and polycythemic conditions. Furthermore, a 33.3% decrease in hematocrit value from that in the normal range (taken as 0.45) of a healthy population has increased the flow rate by 33.5%. For a value 33.3% above 0.45, there is a decrease of 42.7% in the flow rate.

Mathematical modeling of the hematocrit influence on cerebral blood flow in preterm infants

Premature birth is one of the most important factors increasing the risk for brain damage in newborns. Development of an intraventricular hemorrhage in the immature brain is often triggered by fluctuations of cerebral blood flow (CBF). Therefore, monitoring of CBF becomes an important task in clinical care of preterm infants. Mathematical modeling of CBF can be a complementary tool in addition to diagnostic tools in clinical practice and research. The purpose of the present study is an enhancement of the previously developed mathematical model for CBF by a detailed description of apparent blood viscosity and vessel resistance, accounting for inhomogeneous hematocrit distribution in multiscale blood vessel architectures. The enhanced model is applied to our medical database retrospectively collected from the 254 preterm infants with a gestational age of 23-30 weeks. It is shown that by including clinically measured hematocrit in the mathematical model, apparent blood viscosity, vessel resistance, and hence the CBF are strongly affected. Thus, a statistically significant decrease in hematocrit values observed in the group of preterm infants with intraventricular hemorrhage resulted in a statistically significant increase in calculated CBF values.