MATHEMATICAL CONSIDERATIONS FOR MODELING CEREBRAL BLOOD-FLOW AUTOREGULATION TO SYSTEMIC ARTERIAL-PRESSURE

The shape of the autoregulation curve for cerebral blood flow (CBF) vs . pressure is depicted in a variety of ways to fit experimentally deri ved data. However, there is no general empirical description to reprod uce CBF changes resulting from systemic arterial pressure variations t hat is consistent with the reported data. We analyzed previously repor ted experimental data used to construct autoregulation curves. To impr ove on existing portrayals of the fitting of the observed data, a comp artmental model was developed for synthesis of the autoregulation curv e. The resistive arterial and arteriolar network was simplified as an autoregulation device (ARD), which consists of four compartments in se ries controlling CBF. Each compartment consists of a group of identica l vessels in parallel. The response of each vessel category to changes in perfusion pressure was simulated using reported experimental data. The CBF-pressure curve was calculated from the resistance of the ARD. The predicted autoregulation curve was consistent with reported exper imental data. The lower and upper Limits of autoregulation (LLA and UL A) were predicted as 69 and 153 mmHg, respectively. The average value of the slope of the CBF-pressure curve below LLA and beyond ULA was pr edicted as 1.3 and 3.3% change in CBF per mmHg, respectively. Our four -compartment ARD model, which simulated small arteries and arterioles, predicted an autoregulation function similar to experimental data wit h respect to the LLA, ULA, and average slopes of the autoregulation cu rve below LLA and above ULA.