Cerebral autoregulation in healthy humans was studied using a novel methodology adapted from Bendat nonlinear analysis technique. A computer simulation of a high-pass filter in parallel with a cubic nonlinearity followed by a low-pass filter was analyzed. A linear system transfer function analysis showed an incorrect estimate of the gain, cut-off frequency, and phase of the high-pass filter. By contrast, using our nonlinear systems identification, yielded the correct gain, cut-off frequency, and phase of the linear system, and accurately quantified the nonlinear system and following low-pass filter. Adding the nonlinear and linear coherence function indicated a complete description of the system. Cerebral blood flow velocity and arterial pressure were measured in six data sets. Application of the linear and nonlinear systems identification techniques to the data showed a high-pass filter, like the linear transfer function, but the gain was smaller. The phase was similar between the two techniques. The linear coherence was low for frequencies below 0.1 Hz but improved by including a nonlinear term. The linear + nonlinear coherence was approximately 0.9 across the frequency bandwidth, indicating an improved description over the linear system analysis of the cerebral autoregulation system.
Keywords: Autoregulation; Nonlinear coherence; Nonlinear systems identification; Quadratic with sign; Transcranial doppler.