The estimated five global PDMs for the T7–P7 (left panels) and Fp1–F3 (right panels) inputs in connection with P3–O1 (as an output) in the time- (top panels) and frequency-domain (bottom panels).

<p>PDMs, principal dynamic modes.</p

The estimated cubic ANFs for the interictal state of one representative subject of the training data set corresponding to the five global PDMs (shown in Fig 2) for the T7–P7 (upper panels) and Fp1–F3 (bottom panels), along with their best linear fits (red line).

<p>ANFs, associated nonlinear functions; PDMs, principal dynamic modes.</p

The estimated cubic ANFs for the ictal state of one representative subject of the training data set corresponding to the five global PDMs (shown in Fig 2) for the T7–P7 (upper panels) and Fp1–F3 (bottom panels), along with their best linear fits (red line).

<p>ANFs, associated nonlinear functions; PDMs, principal dynamic modes.</p

The ensemble averages of estimated cubic ANFs along with their standard deviation bounds for the T7–P7 (top panels) and Fp1–F3 (bottom panels) for the interictal states of the training data set.

<p>The solid lines represent means and dotted lines represent standard deviation bounds. Coefficients of cubic ANFs were utilized to determine the mean and standard deviation bounds. ANFs, associated nonlinear functions.</p

The ensemble averages of estimated linear gain coefficients (i.e., slopes of best linear lines fitted to cubic ANFs) for the T7–P7 (upper panel) and Fp1–F3 (bottom panel) for interictal and ictal states of the training data set.

<p>No significant changes were found across any ANF of either input for ictal versus interictal states of the training data set (<i>p</i> > 0.05, paired <i>t</i>-test). The error bars represent standard deviation. ANFs, associated nonlinear functions.</p

The ensemble averages of estimated linear gain coefficients (i.e., slopes of best linear lines fitted to cubic ANFs) for the T7–P7 (upper panel) and Fp1–F3 (bottom panel) for interictal and ictal states of the test data set.

<p>No significant changes were found across any ANF of either input for ictal versus interictal states of the test data set (<i>p</i> > 0.05, paired <i>t</i>-test). The error bars represent standard deviation. ANFs, associated nonlinear functions.</p

Non-Linear Characterisation of Cerebral Pressure-Flow Dynamics in Humans

<div><p>Cerebral metabolism is critically dependent on the regulation of cerebral blood flow (CBF), so it would be expected that vascular mechanisms that play a critical role in CBF regulation would be tightly conserved across individuals. However, the relationships between blood pressure (BP) and cerebral blood velocity fluctuations exhibit inter-individual variations consistent with heterogeneity in the integrity of CBF regulating systems. Here we sought to determine the nature and consistency of dynamic cerebral autoregulation (dCA) during the application of oscillatory lower body negative pressure (OLBNP). In 18 volunteers we recorded BP and middle cerebral artery blood flow velocity (MCAv) and examined the relationships between BP and MCAv fluctuations during 0.03, 0.05 and 0.07Hz OLBNP. dCA was characterised using project pursuit regression (PPR) and locally weighted scatterplot smoother (LOWESS) plots. Additionally, we proposed a piecewise regression method to statistically determine the presence of a dCA curve, which was defined as the presence of a restricted autoregulatory plateau shouldered by pressure-passive regions. Results show that LOWESS has similar explanatory power to that of PPR. However, we observed heterogeneous patterns of dynamic BP-MCAv relations with few individuals demonstrating clear evidence of a dCA central plateau. Thus, although BP explains a significant proportion of variance, dCA does not manifest as any single characteristic BP-MCAv function.</p></div

Cross-spectral coherence, gain and phase for 0.23-Hz resampled BP and MCAv during OLBNP.

<p>Values are mean ± SE for OLBNP data. AU, arbitrary units; BP, blood pressure; MCAv, middle cerebral artery blood flow velocity; OLBNP, oscillatory lower body negative pressure.</p><p>* P < 0.05 vs. 0.03Hz</p><p>^† P < 0.05 vs. 0.05Hz for significant differences; one-way repeated measures ANOVA.</p><p>Cross-spectral coherence, gain and phase for 0.23-Hz resampled BP and MCAv during OLBNP.</p