The autonomic regulation is non-invasively estimated from heart rate variability (HRV). Many methods utilized to assess autonomic regulation require stationarity of HRV recordings. However, non-stationarities are frequently present even during well-controlled experiments, thus potentially biasing HRV indices. The aim of our study is to quantify the potential bias of spectral, symbolic and entropy HRV indices due to non-stationarities. We analyzed HRV series recorded in healthy subjects during uncontrolled daily life activities typical of 24 h Holter recordings and during predetermined levels of robotic-assisted treadmill-based physical exercise. A stationarity test checking the stability of the mean and variance over short HRV series (about 300 cardiac beats) was utilized to distinguish stationary periods from non-stationary ones. Spectral, symbolic and entropy indices evaluated solely over stationary periods were contrasted with those derived from all the HRV segments. When indices were calculated solely over stationary series, we found that (i) during both uncontrolled daily life activities and controlled physical exercise, the entropy-based complexity indices were significantly larger; (ii) during uncontrolled daily life activities, the spectral and symbolic indices linked to sympathetic modulation were significantly smaller and those associated with vagal modulation were significantly larger; (iii) while during uncontrolled daily life activities, the variance of spectral, symbolic and entropy rate indices was significantly larger, during controlled physical exercise, it was smaller. The study suggests that non-stationarities increase the likelihood to overestimate the contribution of sympathetic control and affect the power of statistical tests utilized to discriminate conditions and/or groups.

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

In physiological conditions, heart period (HP) affects systolic arterial pressure (SAP) through diastolic runoff and Starling's law, but, the reverse relation also holds as a result of the continuous action of baroreflex control. The prevailing mechanism sets the dominant temporal direction in the HP-SAP interactions (i.e., causality). We exploited cross-conditional entropy to assess HP-SAP causality. A traditional approach based on phases was applied for comparison. The ability of the approach to detect the lack of causal link from SAP to HP was assessed on 8 short-term (STHT) and 11 long-term heart transplant (LTHT) recipients (i.e., less than and more than 2 yr after transplantation, respectively). In addition, spontaneous HP and SAP variabilities were extracted from 17 healthy humans (ages 21–36 yr, median age 29 yr; 9 females) at rest and during graded head-up tilt. The tilt table inclinations ranged from 15 to 75° and were changed in steps of 15°. All subjects underwent recordings at every step in random order. The approach detected the lack of causal relation from SAP to HP in STHT recipients and the gradual restoration of the causal link from SAP to HP with time after transplantation in the LTHT recipients. The head-up tilt protocol induced the progressive shift from the prevalent causal direction from HP to SAP to the reverse causality (i.e., from SAP to HP) with tilt table inclination in healthy subjects. Transformation of phases into time shifts and comparison with baroreflex latency supported this conclusion. The proposed approach is highly efficient because it does not require the knowledge of baroreflex latency. The dependence of causality on tilt table inclination suggests that “spontaneous” baroreflex sensitivity estimated using noncausal methods (e.g., spectral and cross-spectral approaches) is more reliable at the highest tilt table inclinations.

This study was designed to demonstrate the need of accounting for respiration (R) when causality between heart period (HP) and systolic arterial pressure (SAP) is under scrutiny. Simulations generated according to a bivariate autoregressive closed-loop model were utilized to assess how causality changes as a function of the model parameters. An exogenous (X) signal was added to the bivariate autoregressive closed-loop model to evaluate the bias on causality induced when the X source was disregarded. Causality was assessed in the time domain according to a predictability improvement approach (i.e., Granger causality). HP and SAP variability series were recorded with R in 19 healthy subjects during spontaneous and controlled breathing at 10, 15, and 20 breaths/min. Simulations proved the importance of accounting for X signals. During spontaneous breathing, assessing causality without taking into consideration R leads to a significantly larger percentage of closed-loop interactions and a smaller fraction of unidirectional causality from HP to SAP. This finding was confirmed during paced breathing and it was independent of the breathing rate. These results suggest that the role of baroreflex cannot be correctly assessed without accounting for R.

Cardiac baroreflex is a fundamental component of the cardiovascular control. The continuous assessment of baroreflex sensitivity (BRS) from spontaneous heart period (HP) and systolic arterial pressure (SAP) variations during general anesthesia provides relevant information about cardiovascular regulation in physiological conditions. Unfortunately, several difficulties including unknown HP-SAP causal relations, negligible SAP changes, small BRS values, and confounding influences due to mechanical ventilation prevent BRS monitoring from HP and SAP variabilities during general anesthesia. We applied a model-based causal closed-loop approach aiming at BRS assessment during propofol anesthesia in 34 patients undergoing coronary artery bypass graft (CABG) surgery. We found the following: 1) traditional time and frequency domain approaches (i.e., baroreflex sequence, cross-correlation, spectral, and transfer function techniques) exhibited irremediable methodological limitations preventing the assessment of the BRS decrease during propofol anesthesia; 2) Granger causality approach proved that the methodological caveats were linked to the decreased presence of bidirectional closed-loop HP-SAP interactions and to the increased incidence of the HP-SAP uncoupling; 3) our model-based closed-loop approach detected the significant BRS decrease during propofol anesthesia as a likely result of accounting for the influences of mechanical ventilation and causal HP-SAP interactions; and 4) the model-based closed-loop approach found also a diminished gain of the relation from HP to SAP linked to vasodilatation and reduced ventricular contractility during propofol anesthesia. The proposed model-based causal closed-loop approach is more effective than traditional approaches in monitoring cardiovascular control during propofol anesthesia and indicates an overall depression of the HP-SAP closed-loop regulation.