On the Relevance of Computing a Local Version of Sample Entropy in Cardiovascular Control Analysis

Enhancing cardiovascular monitoring: a non-linear model for characterizing RR interval fluctuations in exercise and recovery

This work aimed to develop and validate a novel non-linear model to characterize RR interval (RRi) time-dependent fluctuations throughout a rest-exercise-recovery protocol, offering a more precise and physiologically relevant representation of cardiac autonomic responses than traditional HRV metrics or linear approaches. Using data from a cohort of 272 elderly participants, the model employs logistic functions to capture the non-stationary and transient nature of RRi time-dependent fluctuations, with parameter estimation achieved via Hamiltonian Monte Carlo. Sobol sensitivity analysis identified baseline RRi (α) and recovery proportion (c) as the primary drivers of variability, underscoring their critical roles in autonomic regulation and resilience. Validation against real-world RRi data demonstrated robust model performance (R2 = 0.868, CI95%[0.834, 0.895] and Root Mean Square Error [RMSE] = 32.6 ms, CI95%[30.01, 35.77]), accurately reflecting autonomic recovery and exercise-induced fluctuations. By advancing real-time cardiovascular assessments, this framework holds significant potential for clinical applications in rehabilitation and cardiovascular monitoring in athletic contexts to optimize performance and recovery. These findings highlight the model's ability to provide precise, physiologically relevant assessments of autonomic function, paving the way for its use in personalized health monitoring and performance optimization across diverse populations.

Characterization of cardiorespiratory coupling via a variability-based multi-method approach: Application to postural orthostatic tachycardia syndrome

There are several mechanisms responsible for the dynamical link between heart period (HP) and respiration (R), usually referred to as cardiorespiratory coupling (CRC). Historically, diverse signal processing techniques have been employed to study CRC from the spontaneous fluctuations of HP and respiration (R). The proposed tools differ in terms of rationale and implementation, capturing diverse aspects of CRC. In this review, we classify the existing methods and stress differences with the aim of proposing a variability-based multi-method approach to CRC evaluation. Ten methodologies for CRC estimation, namely, power spectral decomposition, traditional and causal squared coherence,\;information transfer, cross-conditional entropy, mixed prediction, Shannon entropy of the latency between heartbeat and inspiratory/expiratory onset, conditional entropy of the phase dynamics, synchrogram-based analysis, pulse-respiration quotient, and joint symbolic dynamics, are considered. The ability of these techniques was exemplified over recordings acquired from patients suffering from postural orthostatic tachycardia syndrome (POTS) and healthy controls. Analyses were performed at rest in the supine position (REST) and during head-up tilt (HUT). Although most of the methods indicated that at REST, the CRC was lower in POTS patients and decreased more evidently during HUT in POTS, peculiar differences stressed the complementary value of the approaches. The multiple perspectives provided by the variability-based multi-method approach to CRC evaluation help the characterization of a pathological state and/or the quantification of the effect of a postural challenge. The present work stresses the need for the application of multiple methods to derive a more complete evaluation of the CRC in humans.

Investigating autonomic nervous system dysfunction among patients with post-COVID condition and prolonged cardiovascular symptoms

Heart Rate Variability (HRV) and arterial pressure (AP) variability and their responses to head-up tilt test (HUTT) were investigated in Post-COVID-19 syndrome (PCS) patients reporting tachycardia and/or postural hypotension. Besides tachycardia, PCS patients also showed attenuation of the following HRV parameters: RMSSD [square root of the mean of the sum of the squares of differences between adjacent normal-to-normal (NN) intervals] from statistical measures; the power of RR (beat-to-beat interval) spectra at HF (high frequency) from the linear method spectral analysis; occurrence of 2UV (two unlike variation) pattern of RR from the nonlinear method symbolic analysis; and the new family of statistics named sample entropy, when compared to control subjects. Basal AP and LF (low frequency) power of systolic AP were similar between PCS patients and control subjects, while 0 V (zero variation) patterns of AP from the nonlinear method symbolic analysis were exacerbated in PCS patients. Despite tachycardia and a decrease in RMSSD, no parameter of HRV changed during HUTT in PCS patients compared to control subjects. PCS patients reassessed after 6 months showed higher HF power of RR spectra and a higher percentage of 2UV pattern of RR. Moreover, the reassessed PCS patients showed a lower occurrence of 0 V patterns of AP, while the HUTT elicited HR (heart rate) and AP responses identical to control subjects. The HRV and AP variability suggest an autonomic dysfunction with sympathetic predominance in PCS patients. In contrast, the lack of responses of HRV and AP variability indices during HUTT indicates a marked impairment of autonomic control. Of note, the reassessment of PCS patients showed that the noxious effect of COVID-19 on autonomic control tended to fade over time.

Application of Multiscale Sample Entropy in Assessing Effects of Exercise Training on Skin Blood Flow Oscillations in People with Spinal Cord Injury

Spinal cord injury (SCI) causes a disruption of autonomic nervous regulation to the cardiovascular system, leading to various cardiovascular and microvascular diseases. Exercise training is an effective intervention for reducing risk for microvascular diseases in healthy people. However, the effectiveness of exercise training on improving microvascular function in people with SCI is largely unknown. The purpose of this study was to compare blood flow oscillations in people with spinal cord injury and different physical activity levels to determine if such a lifestyle might influence skin blood flow. A total of 37 participants were recruited for this study, including 12 athletes with SCI (ASCI), 9 participants with SCI and a sedentary lifestyle (SSCI), and 16 healthy able-bodied controls (AB). Sacral skin blood flow (SBF) in response to local heating at 42 °C for 50 min was measured using laser Doppler flowmetry. The degree of the regularity of blood flow oscillations (BFOs) was quantified using a multiscale entropy approach. The results showed that BFO was significantly more irregular in ASCI and AB compared to SSCI during the maximal vasodilation period. Our results also demonstrate that the difference in the regularity of BFOs between original SBF signal and phase-randomized surrogate time series was larger in ASCI and AB compared to SSCI. Our findings indicate that SCI causes a loss of complexity of BFOs and exercise training may improve complexity in people with SCI. This study demonstrates that multiscale entropy is a sensitive method for detecting differences between different categories of people with SCI and might be able to detect effects of exercise training related to skin blood flow.

A fast sample entropy for pulse rate variability analysis

Sample entropy is an effective nonlinear index for analyzing pulse rate variability (PRV) signal, but it has problems with a large amount of calculation and time consumption. Therefore, this study proposes a fast sample entropy calculation method to analyze the PRV signal according to the microprocessor process of data updating and the principle of sample entropy. The simulated data and PRV signal are employed as experimental data to verify the accuracy and time consumption of the proposed method. The experimental results on simulated data display that the proposed improved sample entropy can improve the operation rate of the entropy value by a maximum of 47.6 times and an average of 28.6 times and keep the entropy value unchanged. Experimental results on PRV signal display that the proposed improved sample entropy has great potential in the real-time processing of physiological signals, which can increase approximately 35 times.

Utility of sample entropy from intraoperative cerebral NIRS oximetry data in the diagnosis of postoperative cognitive improvement

Background: Appropriate monitoring and early recognition of postoperative cognitive improvement (POCI) are essential. Near-infrared spectroscopy (NIRS) showed the predictive potential of POCI. Non-linear dynamical analysis is a powerful approach for understanding intraoperative regional cerebral oxygen saturation (rSO₂).

Objective: We hypothesized that the sample entropy (SampEn) value of intraoperative rSO₂ has the potential to predict POCI.

Methods: This retrospective cohort study was conducted from June 2019 and December 2020 in a tertiary hospital in Beijing, China. A total of 126 consecutive patients who underwent carotid endarterectomy (CEA) were screened. 57 patients were included in this analysis. The primary outcome was the diagnostic accuracy of rSO₂ for the prediction of POCI.

Results: 33 patients (57.9%) developed POCI on postoperative day. The SampEn values of rSO₂ were significantly higher in the POCI group (p < 0.05). SampEn remained an independent predictor of POCI in multivariate analysis. The area under the ROC curve (AUC) value of SampEn of rSO₂ for POCI were 0.706 (95% CI, 0.569–0.843; p = 0.008). Addition of preoperative MoCA assessment and blood pressure-lowering treatment increased the AUC to 0.808 (95% CI, 0.697–0.919; p < 0.001).

Conclusions: The SampEn value of rSO₂ showed promise as a predictor of POCI. Non-linear analysis could be used as a supplementary method for intraoperative physiological signals.

Evolution of Heart Rate Complexity Indices in the Early Detection of Neonatal Sepsis

Despite advances in prenatal health care, neonatal sepsis remains a major cause of neonatal mortality. Early diagnosis and adequate treatment are essential to reduce morbidity and mortality related to this disease. In this paper, we propose a new method to detect neonatal sepsis based on heart rate (HR) complexity measures (entropy and compression indices) that takes into consideration neonatal gestational age. First, the percentile curves were computed for all the complexity indices using data from 118 control neonates. Eight indices were computed: the sample entropy (SampEn) and three indices to quantify the multiscale entropy (MSE) curve - the sum, the slope, and the product of the previous two - and the compression ratio (CR), using the bzip2 compressor, as well as the same three indices but related to the multiscale compression (MSC) curve. Then, the corresponding percentile was estimated for 23 sepsis neonates. Results show a significant decrease in the entropy indices SampEn and MSEsum and in the MSCslope a day before the detection of sepsis by the clinicians. The indices CR and MSCsum increased before the antibiotic take. These results imply that sepsis causes a random, uncorrelated pattern on the HR signal. Future studies should include a bigger data set to calculate a compound index comprising information of other physiological signals. Clinical Relevance - Prompt and accurate diagnosis of neona-tal sepsis is essential for the successful clinical management of neonates and significantly reduce morbidity and mortality. Complexity measures applied to the HR time series appear to detect sepsis in neonates starting one day before the clinical detection.

The autonomic balance of heart rhythm complexity after renal artery denervation: insight from entropy of entropy and average entropy analysis

Background

The current method to evaluate the autonomic balance after renal denervation (RDN) relies on heart rate variability (HRV). However, parameters of HRV were not always predictive of response to RDN. Therefore, the complexity and disorder of heart rhythm, measured by entropy of entropy (EoE) and average entropy (AE), have been used to analyze autonomic dysfunction. This study evaluated the dynamic changes in autonomic status after RDN via EoE and AE analysis.

Methods

Five patients were prospectively enrolled in the Global SYMPLICITY Registry from 2020 to 2021. 24-h Holter and ambulatory blood pressure monitoring (ABPM) was performed at baseline and 3 months after RDN procedures. The autonomic status was analyzed using the entropy-based AE and EoE analysis and the conventional HRV-based low frequency (LF), high frequency (HF), and LF/HF.

Results

After RDN, the ABPM of all patients showed a significant reduction in blood pressure (BP) and heart rate. Only AE and HF values of all patients had consistent changes after RDN (p < 0.05). The spearman rank-order correlation coefficient of AE vs. HF was 0.86, but AE had a lower coefficient of variation than HF.

Conclusions

Monitoring the AE and EoE analysis could be an alternative to interpreting autonomic status. In addition, a relative change of autonomic tone, especially an increasing parasympathetic activity, could restore autonomic balance after RDN.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12938-022-00999-4.

Entropy Could Quantify Brain Activation Induced by Mechanical Impedance-Restrained Active Arm Motion: A Functional NIRS Study

Brain activation has been used to understand brain-level events associated with cognitive tasks or physical tasks. As a quantitative measure for brain activation, we propose entropy in place of signal amplitude and beta value, which are widely used, but sometimes criticized for their limitations and shortcomings as such measures. To investigate the relevance of our proposition, we provided 22 subjects with physical stimuli through elbow extension-flexion motions by using our exoskeleton robot, measured brain activation in terms of entropy, signal amplitude, and beta value; and compared entropy with the other two. The results show that entropy is superior, in that its change appeared in limited, well established, motor areas, while signal amplitude and beta value changes appeared in a widespread fashion, contradicting the modularity theory. Entropy can predict increase in brain activation with task duration, while the other two cannot. When stimuli shifted from the rest state to the task state, entropy exhibited a similar increase as the other two did. Although entropy showed only a part of the phenomenon induced by task strength, it showed superiority by showing a decrease in brain activation that the other two did not show. Moreover, entropy was capable of identifying the physiologically important location.

Fifty years of Shannon information theory in assessing the accuracy and agreement of diagnostic tests

Since 1948, Shannon theoretic methods for modeling information have found a wide range of applications in several areas where information plays a key role, which goes well beyond the original scopes for which they have been conceived, namely data compression and error correction over a noisy channel. Among other uses, these methods have been applied in the broad field of medical diagnostics since the 1970s, to quantify diagnostic information, to evaluate diagnostic test performance, but also to be used as technical tools in image processing and registration. This review illustrates the main contributions in assessing the accuracy of diagnostic tests and the agreement between raters, focusing on diagnostic test performance measurements and paired agreement evaluation. This work also presents a recent unified, coherent, and hopefully, final information-theoretical approach to deal with the flows of information involved among the patient, the diagnostic test performed to appraise the state of disease, and the raters who are checking the test results. The approach is assessed by considering two case studies: the first one is related to evaluating extra-prostatic cancers; the second concerns the quality of rapid tests for COVID-19 detection.

Research on control method of upper limb exoskeleton based on mixed perception model

As one of the research hotspots in the field of rehabilitation robotics, the upper limb exoskeleton robot has been widely used in the field of rehabilitation. However, the existing methods cannot comprehensively and accurately reflect the motion state of patients, which may lead to overtraining and secondary injury of patients in the process of rehabilitation training. In this paper, an upper limb exoskeleton control method based on mixed perception model of motion intention and intensity is proposed, which is based on the 6 degree-of-freedom upper limb rehabilitation exoskeleton in the laboratory. First, the kinematic information and heart rate information in the rehabilitation process of patients are collected, corresponding to patients’ motion intention and motion intensity, and fused to obtain the mixed perception vector. Second, the motion perception model based on long short-term memory neural network is established to realize the prediction of upper limb motion trajectory of patients and compared with back-propagation neural network to prove its effectiveness. Finally, the control system is built, and both offline and online test of the control method proposed are implemented. The experimental results show that the method can achieve comprehensive motion state perception of patients, realize real-time and accurate prediction trajectory according to human motion intention and intensity. The average prediction accuracy is 95.3%, and predicted joint angle error is less than 5 degrees. Therefore, the control method based on mixed perception model has good robustness and universality, which provides a new method for the active control of upper limb exoskeleton.

Monitoring the Evolution of Asynchrony between Mean Arterial Pressure and Mean Cerebral Blood Flow via Cross-Entropy Methods

Cerebrovascular control is carried out by multiple nonlinear mechanisms imposing a certain degree of coupling between mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). We explored the ability of two nonlinear tools in the information domain, namely cross-approximate entropy (CApEn) and cross-sample entropy (CSampEn), to assess the degree of asynchrony between the spontaneous fluctuations of MAP and MCBF. CApEn and CSampEn were computed as a function of the translation time. The analysis was carried out in 23 subjects undergoing recordings at rest in supine position (REST) and during active standing (STAND), before and after surgical aortic valve replacement (SAVR). We found that at REST the degree of asynchrony raised, and the rate of increase in asynchrony with the translation time decreased after SAVR. These results are likely the consequence of the limited variability of MAP observed after surgery at REST, more than the consequence of a modified cerebrovascular control, given that the observed differences disappeared during STAND. CApEn and CSampEn can be utilized fruitfully in the context of the evaluation of cerebrovascular control via the noninvasive acquisition of the spontaneous MAP and MCBF variability.

The Value of Heart Rhythm Complexity in Identifying High-Risk Pulmonary Hypertension Patients

Pulmonary hypertension (PH) is a fatal disease—even with state-of-the-art medical treatment. Non-invasive clinical tools for risk stratification are still lacking. The aim of this study was to investigate the clinical utility of heart rhythm complexity in risk stratification for PH patients. We prospectively enrolled 54 PH patients, including 20 high-risk patients (group A; defined as WHO functional class IV or class III with severely compromised hemodynamics), and 34 low-risk patients (group B). Both linear and non-linear heart rate variability (HRV) variables, including detrended fluctuation analysis (DFA) and multiscale entropy (MSE), were analyzed. In linear and non-linear HRV analysis, low frequency and high frequency ratio, DFAα1, MSE slope 5, scale 5, and area 6–20 were significantly lower in group A. Among all HRV variables, MSE scale 5 (AUC: 0.758) had the best predictive power to discriminate the two groups. In multivariable analysis, MSE scale 5 (p = 0.010) was the only significantly predictor of severe PH in all HRV variables. In conclusion, the patients with severe PH had worse heart rhythm complexity. MSE parameters, especially scale 5, can help to identify high-risk PH patients.

Entropy and Multifractal-Multiscale Indices of Heart Rate Time Series to Evaluate Intricate Cognitive-Autonomic Interactions

Recent research has clarified the existence of a networked system involving a cortical and subcortical circuitry regulating both cognition and cardiac autonomic control, which is dynamically organized as a function of cognitive demand. The main interactions span multiple temporal and spatial scales and are extensively governed by nonlinear processes. Hence, entropy and (multi)fractality in heart period time series are suitable to capture emergent behavior of the cognitive-autonomic network coordination. This study investigated how entropy and multifractal-multiscale analyses could depict specific cognitive-autonomic architectures reflected in the heart rate dynamics when students performed selective inhibition tasks. The participants (N=37) completed cognitive interference (Stroop color and word task), action cancellation (stop-signal) and action restraint (go/no-go) tasks, compared to watching a neutral movie as baseline. Entropy and fractal markers (respectively, the refined composite multiscale entropy and multifractal-multiscale detrended fluctuation analysis) outperformed other time-domain and frequency-domain markers of the heart rate variability in distinguishing cognitive tasks. Crucially, the entropy increased selectively during cognitive interference and the multifractality increased during action cancellation. An interpretative hypothesis is that cognitive interference elicited a greater richness in interactive processes that form the central autonomic network while action cancellation, which is achieved via biasing a sensorimotor network, could lead to a scale-specific heightening of multifractal behavior.

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.

A Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy and Its Application to Multivariate Signal of Rotating Machinery

In the fault monitoring of rotating machinery, the vibration signal of the bearing and gear in a complex operating environment has poor stationarity and high noise. How to accurately and efficiently identify various fault categories is a major challenge in rotary fault diagnosis. Most of the existing methods only analyze the single channel vibration signal and do not comprehensively consider the multi-channel vibration signal. Therefore, this paper presents Refined Composite Multivariate Multiscale Fluctuation Dispersion Entropy (RCMMFDE), a method which extracts the recognition information of multi-channel signals with different scale factors, and the refined composite analysis ensures the recognition stability. The simulation results show that this method has the characteristics of low sensitivity to signal length and strong anti-noise ability. At the same time, combined with Joint Mutual Information Maximisation (JMIM) and support vector machine (SVM), RCMMFDE-JMIM-SVM fault diagnosis method has been proposed. This method uses RCMMFDE to extract the state characteristics of the multiple vibration signals of the rotary machine, and then uses the JMIM method to extract the sensitive characteristics. Finally, different states of the rotary machine are classified by SVM. The validity of the method is verified by the composite gear fault data set and bearing fault data set. The diagnostic accuracy of the method is 99.25% and 100.00%. The experimental results show that RCMMFDE-JMIM-SVM can effectively recognize multiple signals.

Non-linear heart rate dynamics during and after three controlled exercise intensities in healthy men

We aimed to analyse the complexity and fractal nature of heartbeat during constant exercise, at three different intensities, and recovery.Fourteen healthy men underwent 4 separate sessions. The first session was an incremental treadmill test to determine ventilatory thresholds (VT1 and VT2) and maximal aerobic speed (MAS). Each subject ran at VT1 and VT2 speeds and MAS (second, third and fourth day). The duration of VT1 and VT2 loads were selected in such a way that the product intensity-duration (training load) was the same. Sample Entropy (SampEn) and slope of Detrended Fluctuation Analysis (DFA α1) were measured during the whole session.DFA α1 declines with exercise, being less in the VT1 trial than in the other two.SampEn shows no significant change during exercise. The three tests induce the same decline in SampEn, but at the highest intensity (MAS) tends to decline during the exercise itself, whereas at lower intensities (VT1, VT2) the decline is delayed (10 min of recovery). Subsequently, SampEn at VT1 gradually recovers, whereas at VT2 and MAS it remains stable during recovery.In conclusion, exercise produces a loss of heartbeat complexity, but not fractal nature, during recovery and it depends on intensity.

Are Strategies Favoring Pattern Matching a Viable Way to Improve Complexity Estimation Based on Sample Entropy?

It has been suggested that a viable strategy to improve complexity estimation based on the assessment of pattern similarity is to increase the pattern matching rate without enlarging the series length. We tested this hypothesis over short simulations of nonlinear deterministic and linear stochastic dynamics affected by various noise amounts. Several transformations featuring a different ability to increase the pattern matching rate were tested and compared to the usual strategy adopted in sample entropy (SampEn) computation. The approaches were applied to evaluate the complexity of short-term cardiac and vascular controls from the beat-to-beat variability of heart period (HP) and systolic arterial pressure (SAP) in 12 Parkinson disease patients and 12 age- and gender-matched healthy subjects at supine resting and during head-up tilt. Over simulations, the strategies estimated a larger complexity over nonlinear deterministic signals and a greater regularity over linear stochastic series or deterministic dynamics importantly contaminated by noise. Over short HP and SAP series the techniques did not produce any practical advantage, with an unvaried ability to discriminate groups and experimental conditions compared to the traditional SampEn. Procedures designed to artificially increase the number of matches are of no methodological and practical value when applied to assess complexity indexes.

Neural Decoding of Multi-Modal Imagery Behavior Focusing on Temporal Complexity

Mental imagery behaviors of various modalities include visual, auditory, and motor behaviors. Their alterations are pathologically involved in various psychiatric disorders. Results of earlier studies suggest that imagery behaviors are correlated with the modulated activities of the respective modality-specific regions and the additional activities of supramodal imagery-related regions. Additionally, despite the availability of complexity analysis in the neuroimaging field, it has not been used for neural decoding approaches. Therefore, we sought to characterize neural oscillation related to multimodal imagery through complexity-based neural decoding. For this study, we modified existing complexity measures to characterize the time evolution of temporal complexity. We took magnetoencephalography (MEG) data of eight healthy subjects as they performed multimodal imagery and non-imagery tasks. The MEG data were decomposed into amplitude and phase of sub-band frequencies by Hilbert-Huang transform. Subsequently, we calculated the complexity values of each reconstructed time series, along with raw data and band power for comparison, and applied these results as inputs to decode visual perception (VP), visual imagery (VI), motor execution (ME), and motor imagery (MI) functions. Consequently, intra-subject decoding with the complexity yielded a characteristic sensitivity map for each task with high decoding accuracy. The map is inverted in the occipital regions between VP and VI and in the central regions between ME and MI. Additionally, replacement of the labels into two classes as imagery and non-imagery also yielded better classification performance and characteristic sensitivity with the complexity. It is particularly interesting that some subjects showed characteristic sensitivities not only in modality-specific regions, but also in supramodal regions. These analyses indicate that two-class and four-class classifications each provided better performance when using complexity than when using raw data or band power as input. When inter-subject decoding was used with the same model, characteristic sensitivity maps were also obtained, although their decoding performance was lower. Results of this study underscore the availability of complexity measures in neural decoding approaches and suggest the possibility of a modality-independent imagery-related mechanism. The use of time evolution of temporal complexity in neural decoding might extend our knowledge of the neural bases of hierarchical functions in the human brain.

Comparison of methods for the assessment of nonlinearity in short-term heart rate variability under different physiopathological states

Despite the widespread diffusion of nonlinear methods for heart rate variability (HRV) analysis, the presence and the extent to which nonlinear dynamics contribute to short-term HRV are still controversial. This work aims at testing the hypothesis that different types of nonlinearity can be observed in HRV depending on the method adopted and on the physiopathological state. Two entropy-based measures of time series complexity (normalized complexity index, NCI) and regularity (information storage, IS), and a measure quantifying deviations from linear correlations in a time series (Gaussian linear contrast, GLC), are applied to short HRV recordings obtained in young (Y) and old (O) healthy subjects and in myocardial infarction (MI) patients monitored in the resting supine position and in the upright position reached through head-up tilt. The method of surrogate data is employed to detect the presence and quantify the contribution of nonlinear dynamics to HRV. We find that the three measures differ both in their variations across groups and conditions and in the percentage and strength of nonlinear HRV dynamics. NCI and IS displayed opposite variations, suggesting more complex dynamics in O and MI compared to Y and less complex dynamics during tilt. The strength of nonlinear dynamics is reduced by tilt using all measures in Y, while only GLC detects a significant strengthening of such dynamics in MI. A large percentage of detected nonlinear dynamics is revealed only by the IS measure in the Y group at rest, with a decrease in O and MI and during T, while NCI and GLC detect lower percentages in all groups and conditions. While these results suggest that distinct dynamic structures may lie beneath short-term HRV in different physiological states and pathological conditions, the strong dependence on the measure adopted and on their implementation suggests that physiological interpretations should be provided with caution.

Short-term multiscale complexity analysis of cardiovascular variability improves low cardiac output syndrome risk stratification after coronary artery bypass grafting

BACKGROUND

Low cardiac output syndrome (LCOS) is a myocardial dysfunction leading to systemic hypoperfusion, favored by particular conditions of the autonomic nervous system. LCOS is one of the adverse events that might occur after cardiac surgery.

OBJECTIVE

The aim is to test the hypothesis that short-term multiscale complexity (MSC) analysis of heart period (HP) and systolic arterial pressure (SAP) variability series in the frequency bands typical of cardiovascular control could be fruitfully exploited in identifying subjects at risk of developing LCOS after coronary artery bypass graft (CABG).

APPROACH

HP and SAP beat-to-beat series were derived from electrocardiogram (ECG) and invasive arterial pressure (AP) signal acquired in 128 patients scheduled for CABG before (PRE) and after (POST) the induction of general anesthesia with propofol and remifentanil. Subjects were labeled as LCOS (n  =  14) and noLCOS (n  =  114) according to the LCOS development. MSC markers were calculated as the complement to 1 of the modulus of the average position of the poles dropping in the low-frequency (LF, 0.04-0.15 Hz) and high-frequency (HF, 0.15-0.5 Hz) bands as derived from the autoregressive model of HP and SAP series. Traditional time and frequency domain indexes were also calculated.

MAIN RESULTS

Traditional parameters were able to assess the depression of the cardiovascular regulation induced by general anesthesia, but showed weak performances in differentiating LCOS and noLCOS groups. Conversely, HP complexity in LF band and SAP complexity in HF band assessed during POST remained associated with LCOS even after entering a multivariate logistic regression model adjusted for clinical and demographic factors.

SIGNIFICANCE

The MSC approach can be fruitfully applied to improve risk stratification for LCOS after CABG likely because MSC markers describe the dysfunction of the sympathetic control and the impairment of the mechanical properties of the heart in the LCOS group.