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The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Background: This study evaluated the effects of stroke on regulation of cerebral blood flow in response to fluctuations in systemic blood pressure (BP). The autoregulatory dynamics are difficult to assess because of the nonstationarity and nonlinearity of the component signals. Methods: We studied 15 normotensive, 20 hypertensive and 15 minor stroke subjects (48.0 ± 1.3 years). BP and blood flow velocities (BFV) from middle cerebral arteries (MCA) were measured during the Valsalva maneuver (VM) using transcranial Doppler ultrasound. Results: A new technique, multimodal pressure-flow analysis (MMPF), was implemented to analyze these short, nonstationary signals. MMPF analysis decomposes complex BP and BFV signals into multiple empirical modes, representing their instantaneous frequency-amplitude modulation. The empirical mode corresponding to the VM BP profile was used to construct the continuous phase diagram and to identify the minimum and maximum values from the residual BP (BPR) and BFV (BFVR) signals. The BP-BFV phase shift was calculated as the difference between the phase corresponding to the BPR and BFVR minimum (maximum) values. BP-BFV phase shifts were significantly different between groups. In the normotensive group, the BFVR minimum and maximum preceded the BPR minimum and maximum, respectively, leading to large positive values of BP-BFV shifts. Conclusion: In the stroke and hypertensive groups, the resulting BP-BFV phase shift was significantly smaller compared to the normotensive group. A standard auto-regulation index did not differentiate the groups. The MMPF method enables evaluation of autoregulatory dynamics based on instantaneous BP-BFV phase analysis. Regulation of BP-BFV dynamics is altered with hypertension and after stroke, rendering blood flow dependent on blood pressure. [ABSTRACT FROM AUTHOR]