Mathematical considerations for modeling cerebral blood flow autoregulation to systemic arterial pressure.

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Abstract
The shape of the autoregulation curve for cerebral blood flow (CBF) vs. pressure is depicted in a variety of ways to fit experimentally derived data. However, there is no general empirical description to reproduce CBF changes resulting from systemic arterial pressure variations that is consistent with the reported data. We analyzed previously reported experimental data used to construct autoregulation curves. To improve on existing portrayals of the fitting of the observed data, a compartmental model was developed for synthesis of the autoregulation curve. The resistive arterial and arteriolar network was simplified as an autoregulation device (ARD), which consists of four compartments in series controlling CBF. Each compartment consists of a group of identical 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 experimental data. The lower and upper limits of autoregulation (LLA and ULA) 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 predicted 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 with respect to the LLA, ULA, and average slopes of the autoregulation curve below LLA and above ULA.