Hypocapnia after traumatic brain injury: how does it affect the time constant of the cerebral circulation?

The time constant of the cerebral arterial bed (“tau”) estimates how fast the blood entering the brain fills the arterial vascular sector. Analogous to an electrical resistor–capacitor circuit, it is expressed as the product of arterial compliance (Ca) and cerebrovascular resistance (CVR). Hypocapnia increases the time constant in healthy volunteers and decreases arterial compliance in head trauma. How the combination of hyocapnia and trauma affects this parameter has yet to be studied. We hypothesized that in TBI patients the intense vasoconstrictive action of hypocapnia would dominate over the decrease in compliance seen after hyperventilation. The predominant vasoconstrictive response would maintain an incoming blood volume in the arterial circulation, thereby lengthening tau. We retrospectively analyzed recordings of intracranial pressure (ICP), arterial blood pressure (ABP), and blood flow velocity (FV) obtained from a cohort of 27 severe TBI patients [(39/30 years (median/IQR), 5 women; admission GCS 6/5 (median/IQR)] studied during a standard clinical CO₂ reactivity test. The reactivity test was performed by means of a 50-min increase in ventilation (20% increase in respiratory minute volume). CVR and Ca were estimated from these recordings, and their product calculated to find the time constant. CVR significantly increased [median CVR pre-hypocapnia/during hypocapnia: 1.05/1.35 mmHg/(cm³/s)]. Ca decreased (median Ca pre-hypocapnia/during hypocapnia: 0.130/0.124 arbitrary units) to statistical significance (p = 0.005). The product of these two parameters resulted in a significant prolongation of the time constant (median tau pre-hypocapnia/during hypocapnia: 0.136 s/0.152 s, p ˂ .001). Overall, the increase in CVR dominated over the decrease in compliance, hence tau was longer. We demonstrate a significant increase in the time constant of the cerebral circulation during hypocapnia after severe TBI, and attribute this to an increase in cerebrovascular resistance which outweighs the decrease in cerebral arterial bed compliance.