Reduced-order modeling and analysis of dynamic cerebral autoregulation via diffusion maps.

Objective.A data-driven technique for parsimonious modeling and analysis of dynamic cerebral autoregulation (DCA) is developed based on the concept of diffusion maps. Specifically, first, a state-space description of DCA dynamics is considered based on arterial blood pressure, cerebral blood flow velocity, and their time derivatives. Next, an eigenvalue analysis of the Markov matrix of a random walk on a graph over the dataset domain yields a low-dimensional representation of the intrinsic dynamics. Further dimension reduction is made possible by accounting only for the two most significant eigenvalues. The value of their ratio indicates whether the underlying system is governed by active or hypoactive dynamics, indicating healthy or impaired DCA function, respectively. We assessed the reliability of the technique by considering healthy individuals and patients with unilateral internal carotid artery (ICA) stenosis or occlusion. We computed the sensitivity of the technique to detect the presumed side-to-side difference in the DCA function of the second group (assuming hypoactive dynamics on the occluded or stenotic side), using McNemar's chi square test. The results were compared with transfer function analysis (TFA). The performance of the two methods was also compared under the assumption of missing data.Main results.Both diffusion maps and TFA suggested a physiological side-to-side difference in the DCA of ICA stenosis or occlusion patients with a sensitivity of 81% and 71%, respectively. Further, both two methods suggested the difference between the occluded or stenotic side and any two sides of the healthy group. However, the diffusion maps captured additional difference between the unoccluded side and the healthy group, that TFA did not. Furthermore, compared to TFA, diffusion maps exhibited superior performance when subject to missing data.Significance.The eigenvalues ratio derived using the diffusion maps technique can be potentially used as a reliable and robust biomarker for assessing how active the intrinsic dynamics of the autoregulation is and for indicating healthy versus impaired DCA function.

Joint time-frequency analysis of dynamic cerebral autoregulation using generalized harmonic wavelets.

OBJECTIVE: To develop a joint time-frequency analysis technique based on generalized harmonic wavelets (GHWs) for dynamic cerebral autoregulation (DCA) performance quantification. APPROACH: We considered two groups of human subjects to develop and validate the method: 55 healthy volunteers and 35 stroke-free subjects with unilateral internal carotid artery stenosis (CAS). We determined the mean and coherence-weighted average of the phase shift (PS) of appropriately defined GHW-based transfer functions, based on data points over the joint time-frequency domain. We compared agreement of standard transfer function analysis (TFA) and GHW analyses in healthy subjects using Bland-Altman plots. We assessed sensitivity of each metric to detect the presumed side-to-side difference in DCA function in CAS subjects (with decreased PS on the occluded side), using McNemar's chi square test to compare each metric to the standard TFA approach. An alternative Morlet wavelet-based approach was also considered. MAIN RESULTS: The GHW and TFA methods exhibited strong agreement in healthy subjects. Among CAS subjects, GHW metrics outperformed TFA and Morlet wavelet-based approaches in identifying expected side-to-side differences: TFA sensitivity was 40.0% (95%CI 23.9-57.9), Morlet 60.0% (95%CI 42.1-76.1), and GHW >70% for both metrics (GHW mean PS sensitivity 74.3, 95%CI 56.7-87.5, p  = 0.0027 versus TFA; GHW coherence-weighted PS sensitivity 71.4, 95%CI 53.7-85.4, p  = 0.0009 versus TFA). SIGNIFICANCE: In comparison to the widely used stationary Fourier transform-based TFA and to Morlet wavelet-based analysis, our data suggest that the GHW-based analysis performs better in identifying DCA asymmetry between the two cerebral hemispheres in patients with high grade unilateral carotid stenosis. Our method may provide enhanced confidence in employing DCA metrics as a sensitive diagnostic tool for detecting impaired DCA function in a variety of pathological settings.