A robust method for detection of linear and nonlinear interactions: application to renal blood flow dynamics

We have developed a method that can identify switching dynamics in time series, termed the improved annealed competition of experts (IACE) algorithm. In this paper, we extend the approach and use it for detection of linear and nonlinear interactions, by employing histograms showing the frequency of switching modes obtained from the IACE, then examining time-frequency spectra. This extended approach is termed Histogram of improved annealed competition of experts-time frequency (HIACE-TF). The hypothesis is that frequent switching dynamics in HIACE-TF results are due to interactions between different dynamic components. To validate this assertion, we used both simulation examples as well as application to renal blood flow data. We compared simulation results to a time-phase bispectrum (TPB) approach, which can also be used to detect time-varying quadratic phase coupling between various components. We found that the HIACE-TF approach is more accurate than the TPB in detecting interactions, and remains accurate for signal-to-noise ratios as low as 15 dB. With all 10 data sets, comprised of volumetric renal blood flow data, we also validated the feasibility of the HIACE-TF approach in detecting nonlinear interactions between the two mechanisms responsible for renal autoregulation. Further validation of the HIACE-TF approach was achieved by comparing it to a realistic mathematical model that has the capability to generate either the presence or the absence of nonlinear interactions between two renal autoregulatory mechanisms.