Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia

This study develops a lumped cardiovascular–respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO₂ partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO₂ reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO₂ induced challenges. It is difficult to characterize cerebral CO₂ reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO₂ reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO₂ and O₂) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO₂ partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.