The aim of this work was to analyze the cerebral hemodynamics in patients with internal carotid artery (ICA) occlusion during CO2 dynamical tests. The study was performed using an original mathematical model of cerebral hemodynamics. The model includes the circle of Willis, the microvascular circulation in the territories of each cerebral artery, cortical anastomoses, intracranial pressure, the cerebrospinal fluid circulation, the brain venous circulation and two regulation mechanisms: autoregulation and CO2 reactivity. Model predictions are compared with real data obtained on 20 healthy subjects (group A) and 14 patients with unilateral ICA stenosis (group B) during CO2 tests. The percent changes in Doppler middle cerebral artery velocity per mm Hg of CO2 pressure variations (reactivity index, RI) were separately computed during hypocapnia and hypercapnia. In group A, the reactivity index was practically the same in both sides. Patients in group B had a significantly lower CO2 reactivity in the side ipsilateral to the occlusion (hypocapnia RI: 1.06 ± 1.6 vs. 2.3 ± 0.8%/mm Hg; hypercapnia: 0.9 ± 0.8 vs. 2.4 ± 1.0%/mm Hg). Our model can explain these results very well, assuming values for the diameter of the communicating arteries in the range reported in the clinical literature. Moreover, computer simulations suggest that patients with a small diameter of both communicating arteries (as low as 0.4–0.5 mm) exhibit a dramatic fall in CO2 reactivity in the ipsilateral side compared with the contralateral one, with the appearance of paradoxical responses. A decrease in ipsilateral RI reactivity, however, may also depend on the presence of a significant stenosis of the contralateral ICA.

Keywords:
Circle of Willis, Cerebral autoregulation, CO2 reactivity, Mathematical models, Cerebrovascular compensatory reserve
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