A mathematical model of cerebral blood flow chemical regulation. I. Diffusion processes

1989 ◽  
Vol 36 (2) ◽  
pp. 183-191 ◽  
Author(s):  
M. Ursino ◽  
P. Di Giammarco ◽  
E. Belardinelli
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Diffusion Processes ◽  
Chemical Regulation

Interaction among autoregulation, CO2 reactivity, and intracranial pressure: a mathematical model

1998 ◽  
Vol 274 (5) ◽  
pp. H1715-H1728 ◽  
Author(s):  
Mauro Ursino ◽  
Carlo Alberto Lodi
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Intracranial Pressure ◽  
Nonlinear Interaction ◽  
Cerebral Blood Volume ◽  
Cerebral Hemodynamics ◽  
Pial Arteries ◽  
Arterial Circulation ◽  
Neurosurgical Patients

The relationships among cerebral blood flow, cerebral blood volume, intracranial pressure (ICP), and the action of cerebrovascular regulatory mechanisms (autoregulation and CO2 reactivity) were investigated by means of a mathematical model. The model incorporates the cerebrospinal fluid (CSF) circulation, the intracranial pressure-volume relationship, and cerebral hemodynamics. The latter is based on the following main assumptions: the middle cerebral arteries behave passively following transmural pressure changes; the pial arterial circulation includes two segments (large and small pial arteries) subject to different autoregulation mechanisms; and the venous cerebrovascular bed behaves as a Starling resistor. A new aspect of the model exists in the description of CO2 reactivity in the pial arterial circulation and in the analysis of its nonlinear interaction with autoregulation. Simulation results, obtained at constant ICP using various combinations of mean arterial pressure and CO2 pressure, substantially support data on cerebral blood flow and velocity reported in the physiological literature concerning both the separate effects of CO2 and autoregulation and their nonlinear interaction. Simulations performed in dynamic conditions with varying ICP underline the existence of a significant correlation between ICP dynamics and cerebral hemodynamics in response to CO2 changes. This correlation may significantly increase in pathological subjects with poor intracranial compliance and reduced CSF outflow. In perspective, the model can be used to study ICP and blood velocity time patterns in neurosurgical patients in order to gain a deeper insight into the pathophysiological mechanisms leading to intracranial hypertension and secondary brain damage.

Quantitative assessment of cerebral blood flow using Technetium-99m-hexamethyl-propyleneamine oxime: Part I, design of a mathematical model

1988 ◽  
Vol 2 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Hiroshi Matsuda ◽  
Hiroshi Oba ◽  
Hitoshi Terada ◽  
Shiro Tsuji ◽  
Hisashi Sumiya ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Quantitative Assessment ◽  
Technetium 99M

A mathematical model of cerebral blood flow control in anaemia and hypoxia

2020 ◽  
Vol 598 (4) ◽  
pp. 717-730 ◽  
Author(s):  
James Duffin ◽  
Gregory M.T Hare ◽  
Joseph A. Fisher
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Flow Control ◽  
Blood Flow Control

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

PLoS ONE ◽  
2021 ◽  
Vol 16 (12) ◽  
pp. e0261819
Author(s):  
Irina Sidorenko ◽  
Varvara Turova ◽  
Esther Rieger-Fackeldey ◽  
Ursula Felderhoff-Müser ◽  
Andrey Kovtanyuk ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Preterm Infants ◽  
Blood Viscosity ◽  
Intraventricular Hemorrhage ◽  
Clinical Care ◽  
Diagnostic Tools ◽  
Vessel Resistance

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.

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