Automated estimation of the logistic curve model of cerebral CO₂ vasomotor reactivity

An automated method is presented to derive the logistic curve model (LCM), to express the simultaneous effects of partial pressure of arterial CO₂ (PaCO₂) on cerebral blood flow (CBF) and cerebral autoregulation, without the need for operator assistance. Measurements of middle cerebral artery blood velocity (MCAv, transcranial Doppler), arterial blood pressure (Finometer) and end-tidal CO₂ (EtCO₂, capnography) were performed in 106 healthy subjects. Hypercapnia was induced with breathing 5% CO₂ and hypocapnia was induced with hyperventilation. Dynamic autoregulation was expressed by the Autoregulation Index (ARI). Confidence limits for the fitting error were obtained with a surrogate bootstrap approach for both MCAv and ARI. An algorithm for the gradual removal of outlier values was implemented to identify optimal number of samples that minimises the fitting error. Induction of hyper- and hypocapnia was demonstrated by the range of EtCO₂ values achieved (28.4 ± 6.0 to 47.7 ± 5.8 mmHg, p < 0.001). LCMs meeting confidence limit requirements were obtained for MCAv (n = 98/106) and ARI (104/106). Females showed an upwards shift of their LCM for MCAv (p = 0.001) compared to males and their ARI model was shifted laterally towards lower values of EtCO₂ (p = 0.0053). Automated identification of the LCM for MCAv and ARI, with rigorous confidence limits of the fitting error is feasible and can identify differences due to biological sex.