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

Abstract

Key points The control of cerebral blood flow in hypoxia, anaemia and hypocapnia is reviewed with an emphasis on the links between cerebral blood flow and possible stimuli. A mathematical model is developed to examine the changes in the partial pressure of oxygen in brain tissue associated with changes in cerebral blood flow regulation produced by carbon dioxide, anaemia and hypoxia. The model demonstrates that hypoxia, anaemia and hypocapnia, alone or in combination, produce varying degrees of cerebral hypoxia, an effect exacerbated when blood flow regulation is impaired. The suitability of brain hypoxia as a common regulator of cerebral blood flow in hypoxia and anaemia was explored, although we failed to find support for this hypothesis. Rather, cerebral blood flow appears to be related to arterial oxygen concentration in both anaemia and hypoxia. Abstract A mathematical model is developed to examine the changes in the partial pressure of oxygen in brain tissue associated with changes in cerebral blood flow regulation produced by carbon dioxide, anaemia and hypoxia. The model simulation assesses the physiological plausibility of some currently hypothesized cerebral blood flow control mechanisms in hypoxia and anaemia, and also examines the impact of anaemia and hypoxia on brain hypoxia. In addition, carbon dioxide is examined for its impact on brain hypoxia in the context of concomitant changes associated with anaemia and hypoxia. The model calculations are based on a single compartment of brain tissue with constant metabolism and perfusion pressure, as well as previously developed equations describing oxygen and carbon dioxide carriage in blood. Experimental data are used to develop the control equations for cerebral blood flow regulation. The interactive model illustrates that there are clear interactions of anaemia, hypoxia and carbon dioxide in the determination of cerebral blood flow and brain tissue oxygen tension. In both anaemia and hypoxia, cerebral blood flow increases to maintain oxygen delivery, with brain hypoxia increasing when cerebral blood flow control mechanisms are impaired. Hypocapnia superimposes its effects, increasing brain hypoxia. Hypoxia, anaemia and hypocapnia, alone or in combination, produce varying degrees of cerebral hypoxia, and this effect is exacerbated when blood flow regulation is degraded by conditions that negatively impact cerebrovascular control. Differences in brain hypoxia in anaemia and hypoxia suggest that brain oxygen tension is not a plausible sensor for cerebral blood flow control.

High-altitude cerebral edema: its own entity or end-stage acute mountain sickness?

“…A detailed discussion is beyond the scope of the current review and leading mechanisms have been detailed elsewhere (47,48). However, an important observation is that arterial oxygen content (CaO 2 ), rather than oxygen tension (PaO 2 ), is considered the primary controller of CBF in response to hypoxemia via a yet undiscovered regulatory pathway governing cerebrovascular tone (24,47).…”

Fail‐safe aspects of oxygen supply

“…The supply of O 2 to the brain is crucial to cerebral health, and CBF is consequently increased when the supply fails to meet requirements (Hoiland et al 2016). A recent article describing the regulation of CBF in arterial hypoxia and anaemia showed that these challenges resulted in markedly different changes in the cerebral tissue O 2 tension, which decreases less in anaemia than in hypoxia as arterial O 2 content falls (Duffin et al 2020). The question arising from this model was formulated in a commentary by Payne (2020): 'Searching for the stimulus controlling brain oxygen supply'; the assumption was the existence of a hypoxia sensor.…”

“…Multiple layers of vascular smooth muscle cells cover the large pial arteries on the surface of the cortex, with penetrating arterioles sheathed in a single layer of vascular smooth muscle cells (Nishimura et al 2007). These vascular smooth muscles control vascular diameter and consequently CBF to (1) maintain a constant CBF in the face of changes in arterial blood pressure (autoregulation) (Tan & Taylor, 2014;Tzeng et al 2014), (2) increase CBF in hypoxia and anaemia (Borzage et al 2016;Duffin et al 2020) and (3) increase local CBF in response to increases in brain activity (neurovascular coupling) (Attwell et al 2011(Attwell et al , 2016Phillips et al 2016). Quite apart from these functions, cerebrovascular smooth muscles respond to changes in arterial carbon dioxide tension, vasodilating in hypercapnia and vasoconstricting in hypocapnia (Battisti-Charbonney et al 2011).…”

“…2016; Duffin et al . 2020) and (3) increase local CBF in response to increases in brain activity (neurovascular coupling) (Attwell et al . 2011, 2016; Phillips et al .…”

Editorial: Imaging Cerebrovascular Reactivity: Physiology, Physics and Therapy

“…(1) autoregulation to maintain flow against supply pressure changes ( Tan and Taylor, 2014;Tzeng et al, 2014), (2) neurovascular coupling to increase flow in active regions (Attwell et al, 2011(Attwell et al, , 2016Phillips et al, 2016), and (3) increased flow during hypoxemia (Duffin et al, 2020).…”