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Quantification of the cardiorespiratory and cerebrovascular couplings is a relevant clinical issue given that their changes are considered signs of pathological status. The inherent nonlinearity of mechanisms underlying cardiorespiratory and cerebrovascular links requires nonlinear tools for their reliable evaluation. In the present study we compare two nonlinear methods for the assessment of coupling strength between two time series, namely cross-sample entropy (CSampEn) and k-nearest-neighbor cross-predictability (KNNCP). CSampEn uses a strategy that fixes the pattern length, while KNNCP optimizes the pattern length to maximize cross-predictability. CSampEn and KNNCP were applied to the beat-to-beat series of heart period (HP) and respiration (R) during a controlled breathing protocol with the aim at assessing cardiorespiratory coupling and to the beat-to-beat series of mean cerebral blood flow (MCBF) and mean arterial pressure (MAP) during an orthostatic stressor with the aim at evaluating cerebrovascular coupling. Although both the methods have the possibility to quantify the degree of HP-R and MCBF-MAP association, they exhibited different statistical power and even diverse trends in response to the considered physiological challenges. CSampEn and KNNCP are not interchangeable and should be utilized in association more than in alternative for the quantification of the HP-R and MCBF-MAP coupling strength. Clinical Relevance - This study proves that cross-entropy and cross-predictability might lead to different conclusions about cardiorespiratory and cerebrovascular couplings.

This work proposes an empirical mode decomposition (EMD) method to assess the strength of the interactions between heart period (HP) and systolic arterial pressure (SAP) variability. EMD was exploited to decompose the original series (OR) into its first, and fastest, intrinsic mode function (IMF1) and the residual (RES) computed by subtracting the IMF1 from OR. EMD procedure was applied to both HP and SAP variability series. Then, the cross correlation function (CCF) was computed over OR, IMF1 and RES series derived from HP and SAP variability in 13 healthy subjects (age 27±8 yrs, 5 males) at rest in supine position (REST) and during head-up tilt (TILT). The first CCF maximum at negative time lags and the first CCF minimum at positive time lags were taken respectively as indexes of the coupling along the feedback baroreflex and feedforward mechanical arms of HP-SAP closed-loop control. Results showed that the coupling strength is increased during TILT on both arms and this result holds on REST. At REST the coupling along both arms was stronger when computed over IMF1 because interactions were mainly governed by respiration. This result was not observed during TILT possibly due to the reduced importance of respiration compared to other mechanisms acting at slower time scales. The proposed method allowed the investigation of the strength of HP-SAP variability interactions according to the time scales of the physiological mechanisms.The proposed EMD-based method allows the quantification of the strength of the HP-SAP closed-loop variability interactions according to the different time scales of respiration and slower baroreflex-mediated reflexes.

The coupling and latency between heart period (HP) and systolic arterial pressure (SAP) variability can be investigated along the two arms of the HP-SAP closed loop, namely along the baroreflex feedback from SAP to HP, and along the feedforward pathway from HP to SAP. This study investigates the HP-SAP closed loop variability interactions through cross-correlation function (CCF). Coupling strength and delay between HP and SAP variability series were monitored in 13 subjects prone to develop orthostatic syncope (SYNC, 28±9 yrs, 5 males) and in 13 subjects with no history of postural syncope (noSYNC, age: 27±8 yrs, 5 males). Analysis was carried out at rest in supine position (REST) and during head-up tilt (TILT) at 60 degrees. The null hypothesis of HP-SAP uncoupling was tested through a surrogate analysis associating the HP series of a subject with a SAP sequence of a different one. Results showed that during TILT the coupling strength increased along the baroreflex and latency augmented along the mechanical feedforward pathway exclusively in noSYNC subjects. Finally, closed loop HP-SAP interactions were detected in about one third of subjects and the situation of full uncoupling was rarely found. CCF analysis was found to be a straightforward and easily applicable method to investigate HP-SAP control deserving a direct comparison with more sophisticated signal processing tools assessing causality.