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

Abstract

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.

Theoretical model of blood flow autoregulation: roles of myogenic, shear-dependent, and metabolic responses

“…Liao and Kuo (20) considered the effects of only myogenic and shear-dependent responses in an empirically based model. Ursino and Lodi (34) and Cornelissen (4) employed pressure-, flow-, and metabolic-dependent responses in their respective models of cerebral and skeletal muscle tissues; however, these three responses were not present in all of the resistance vessels. For example, in the latter model, vascular segments responded to either pressure and shear stress or metabolic state depending on their position in the vascular tree.…”

A comprehensive cerebrovascular simulation model for teaching and research

“…The mathematical relationships between cerebral perfusion pressure (CPP), intracranial pressure (ICP) and cerebral blood flow (CBF) as well as the autoregulatory control of these quantities by the normal brain, have been well described [1]. However, the alterations occurring in these quantities in pathological conditions, and their complex non-linear relations are difficult to be understood in simple qualitative terms, and these have not yet been described in a single comprehensive model.…”

The role of oxygen in cerebrovascular control: a mathematical analysis

“…The model of intracranial hemodynamics and cerebrospinal fluid circulation is the same as in previous studies [2,3]. Hence, it is not described again for briefness.…”

“…1 describes the action of mechanisms, which do not depend on CO 2 and O 2 directly. According to previous studies [2,3], we assumed that large and medium pial arteries (first segment) are mainly controlled by a pressure-dependent mechanism, which causes vasodilation during a decrease in cerebral perfusion pressure. Conversely, small pial arteries (second segment) are controlled by a flow-dependent mechanism, which vasodilates when CBF is reduced below normal.…”

“…In previous years we formulated a mathematical model of cerebrovascular regulation and intracranial dynamics in men, able to account for several results of clinical relevance [2,3]. In this model, however, the effect of oxygen in the control of cerebral vessels was not explicitly considered.…”