Modelling of subarachnoid space width changes in apnoea resulting as a function of blood flow parameters

During apnoea, the pial artery is subjected to two opposite physiological processes: vasoconstriction due to elevated blood pressure and vasorelaxation driven by rising pH in the brain parenchyma. We hypothesized that the pial artery response to apnoea may vary, depending on which process dominate. Apnoea experiments were performed in a group of 19 healthy, non-smoking volunteers (9 men and 10 women). The following parameters were obtained for further analysis: blood pressure, the cardiac (from 0.5 to 5.0Hz) and slow (<0.5Hz) components of subarachnoid space width, heart rate, mean cerebral blood flow velocity in the internal carotid artery, pulsatility and resistivity index, internal carotid artery diameter, blood oxygen saturation and end-tidal carbon dioxide. The experiment consisted of three apnoeas, sequentially: 30s, 60s and maximal apnoea. The breath-hold was separated for 5minute rest. The control process is sophisticated, involving internal cross-couplings and cross-dependences. The aim of work was to find a mathematical dependence between data. Unexpectedly, the modelling revealed two different reactions, on the same experimental procedure. As a consequence, there are two subsets of cardiac subarachnoid space width responses to breath-hold in humans. A positive cardiac subarachnoid space width change to apnoea depends on changes in heart rate and cerebral blood flow velocity. A negative cardiac subarachnoid space width change to apnoea is driven by heart rate, mean arterial pressure and pulsatility index changes. The described above two different reactions to experimental breath-hold provides new insights into our understanding of the complex mechanisms governing the adaptation to apnoea in humans. We proposed a mathematical methodology that can be used in further clinical research.