On the validity of the state space correspondence strategy based on k-nearest neighbor cross-predictability in assessing directionality in stochastic systems: Application to cardiorespiratory coupling estimation.

We tested the validity of the state space correspondence (SSC) strategy based on k-nearest neighbor cross-predictability (KNNCP) to assess the directionality of coupling in stochastic nonlinear bivariate autoregressive (NBAR) processes. The approach was applied to assess closed-loop cardiorespiratory interactions between heart period (HP) variability and respiration (R) during a controlled respiration (CR) protocol in 19 healthy humans (aged from 27 to 35 yrs, 11 females) and during active standing (STAND) in 25 athletes (aged from 20 to 40 yrs, all men) and 25 non-athletes (aged from 20 to 40 yrs, all men). Over simulated NBAR processes, we found that (i) the SSC approach can detect the correct causal relationship as the direction leads to better KNNCP from the past of the driver to the future state of the target and (ii) simulations suggest that the ability of the method is preserved in any condition of complexity of the interacting series. Over CR and STAND protocols, we found that (a) slowing the breathing rate increases the strength of the causal relationship in both temporal directions in a balanced modality; (b) STAND is more powerful in modulating the coupling strength on the pathway from HP to R; (c) regardless of protocol and experimental condition, the strength of the link from HP to R is stronger than that from R to HP; (d) significant causal relationships in both temporal directions are found regardless of the level of complexity of HP variability and R. The SSC strategy is useful to disentangle closed-loop cardiorespiratory interactions.

Changes of the cardiac baroreflex bandwidth during postural challenges.

Baroreflex is commonly typified from heart period (HP) and systolic arterial pressure (SAP) spontaneous variations in the frequency domain mainly by estimating its sensitivity. However, an informative parameter linked to the rapidity of the HP response to SAP changes, such as the baroreflex bandwidth, remains unquantified. We propose a model-based parametric approach for estimating the baroreflex bandwidth from the impulse response function (IRF) of the HP-SAP transfer function (TF). The approach accounts explicitly for the action of mechanisms modifying HP regardless of SAP changes. The method was tested during graded baroreceptor unloading induced by head-up tilt (HUT) at 15°, 30°, 45°, 60°, and 75° (T15, T30, T45, T60, and T75) in 17 healthy individuals (age: 21-36 yr; 9 females and 8 males) and during baroreceptor loading obtained via head-down tilt (HDT) at -25° in 13 healthy men (age: 41-71 yr). The bandwidth was estimated as the decay constant of the monoexponential IRF fitting. The method was robust because the monoexponential fitting described adequately the HP dynamics following an impulse of SAP. We observed that 1) baroreflex bandwidth is reduced during graded HUT and this narrowing is accompanied by the reduction of the bandwidth of mechanisms that modify HP regardless of SAP changes and 2) baroreflex bandwidth is not affected by HDT but that of SAP-unrelated mechanisms becomes wider. This study provides a method for estimating a baroreflex feature that provides different information compared with the more usual baroreflex sensitivity while accounting explicitly for the action of mechanisms changing HP irrespective of SAP.

Comparison of discretization strategies for the model-free information-theoretic assessment of short-term physiological interactions.

This work presents a comparison between different approaches for the model-free estimation of information-theoretic measures of the dynamic coupling between short realizations of random processes. The measures considered are the mutual information rate (MIR) between two random processes X and Y and the terms of its decomposition evidencing either the individual entropy rates of X and Y and their joint entropy rate, or the transfer entropies from X to Y and from Y to X and the instantaneous information shared by X and Y. All measures are estimated through discretization of the random variables forming the processes, performed either via uniform quantization (binning approach) or rank ordering (permutation approach). The binning and permutation approaches are compared on simulations of two coupled non-identical Hènon systems and on three datasets, including short realizations of cardiorespiratory (CR, heart period and respiration flow), cardiovascular (CV, heart period and systolic arterial pressure), and cerebrovascular (CB, mean arterial pressure and cerebral blood flow velocity) measured in different physiological conditions, i.e., spontaneous vs paced breathing or supine vs upright positions. Our results show that, with careful selection of the estimation parameters (i.e., the embedding dimension and the number of quantization levels for the binning approach), meaningful patterns of the MIR and of its components can be achieved in the analyzed systems. On physiological time series, we found that paced breathing at slow breathing rates induces less complex and more coupled CR dynamics, while postural stress leads to unbalancing of CV interactions with prevalent baroreflex coupling and to less complex pressure dynamics with preserved CB interactions. These results are better highlighted by the permutation approach, thanks to its more parsimonious representation of the discretized dynamic patterns, which allows one to explore interactions with longer memory while limiting the curse of dimensionality.

On the Different Abilities of Cross-Sample Entropy and K-Nearest-Neighbor Cross-Unpredictability in Assessing Dynamic Cardiorespiratory and Cerebrovascular Interactions.

Nonlinear markers of coupling strength are often utilized to typify cardiorespiratory and cerebrovascular regulations. The computation of these indices requires techniques describing nonlinear interactions between respiration (R) and heart period (HP) and between mean arterial pressure (MAP) and mean cerebral blood velocity (MCBv). We compared two model-free methods for the assessment of dynamic HP-R and MCBv-MAP interactions, namely the cross-sample entropy (CSampEn) and k-nearest-neighbor cross-unpredictability (KNNCUP). Comparison was carried out first over simulations generated by linear and nonlinear unidirectional causal, bidirectional linear causal, and lag-zero linear noncausal models, and then over experimental data acquired from 19 subjects at supine rest during spontaneous breathing and controlled respiration at 10, 15, and 20 breaths·minute-1 as well as from 13 subjects at supine rest and during 60° head-up tilt. Linear markers were computed for comparison. We found that: (i) over simulations, CSampEn and KNNCUP exhibit different abilities in evaluating coupling strength; (ii) KNNCUP is more reliable than CSampEn when interactions occur according to a causal structure, while performances are similar in noncausal models; (iii) in healthy subjects, KNNCUP is more powerful in characterizing cardiorespiratory and cerebrovascular variability interactions than CSampEn and linear markers. We recommend KNNCUP for quantifying cardiorespiratory and cerebrovascular coupling.

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.

Information decomposition in the frequency domain: a new framework to study cardiovascular and cardiorespiratory oscillations.

While cross-spectral and information-theoretic approaches are widely used for the multivariate analysis of physiological time series, their combined utilization is far less developed in the literature. This study introduces a framework for the spectral decomposition of multivariate information measures, which provides frequency-specific quantifications of the information shared between a target and two source time series and of its expansion into amounts related to how the sources contribute to the target dynamics with unique, redundant and synergistic information. The framework is illustrated in simulations of linearly interacting stochastic processes, showing how it allows us to retrieve amounts of information shared by the processes within specific frequency bands which are otherwise not detectable by time-domain information measures, as well as coupling features which are not detectable by spectral measures. Then, it is applied to the time series of heart period, systolic and diastolic arterial pressure and respiration variability measured in healthy subjects monitored in the resting supine position and during head-up tilt. We show that the spectral measures of unique, redundant and synergistic information shared by these variability series, integrated within specific frequency bands of physiological interest and reflect the mechanisms of short-term regulation of cardiovascular and cardiorespiratory oscillations and their alterations induced by the postural stress. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Optimizing phase variability threshold for automated synchrogram analysis of cardiorespiratory interactions in amateur cyclists.

We propose a procedure suitable for automated synchrogram analysis for setting the threshold below which phase variability between two marker event series is of such a negligible amount that the null hypothesis of phase desynchronization can be rejected. The procedure exploits the principle of maximizing the likelihood of detecting phase synchronization epochs and it is grounded on a surrogate data approach testing the null hypothesis of phase uncoupling. The approach was applied to assess cardiorespiratory phase interactions between heartbeat and inspiratory onset in amateur cyclists before and after 11-week inspiratory muscle training (IMT) at different intensities and compared to a more traditional approach to set phase variability threshold. The proposed procedure was able to detect the decrease in cardiorespiratory phase locking strength during vagal withdrawal induced by the modification of posture from supine to standing. IMT had very limited effects on cardiorespiratory phase synchronization strength and this result held regardless of the training intensity. In amateur athletes training, the inspiratory muscles did not limit the decrease in cardiorespiratory phase synchronization observed in the upright position as a likely consequence of the modest impact of this respiratory exercise, regardless of its intensity, on cardiac vagal control. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Complexity of Knee Extensor Torque: Effect of Aging and Contraction Intensity.

ABSTRACT: Fiogbé, E, Vassimon-Barroso, V, Catai, AM, de Melo, RC, Quitério, RJ, Porta, A, and Takahashi, ACdM. Complexity of knee extensor torque: effect of aging and contraction intensity. J Strength Cond Res 35(4): 1050-1057, 2021-Assessing the knee extensors' torque complexity in older adults is relevant because these muscles are among the most involved in functional daily activities. This study aimed to investigate the effects of aging and isometric contraction intensity on knee extensor torque complexity. Eight young (24 ± 2.8 years) and 13 old adults (63 ± 2.8 years) performed 3 maximal (maximum voluntary contraction [MVC], duration = 10 seconds) and submaximal isometric contractions (SICs, targeted at 15, 30, and 40% of MVC, respectively) of knee extensors. Torque signals were sampled continuously, and the metrics of variability and complexity were calculated basing on the SIC torque data. The coefficient of variation (CV) was used to quantify the torque variability. The torque complexity was determined by calculating the corrected approximate entropy (CApEn) and sample entropy (SampEn) and its normalized versions (NCApEn and NSampEn). Young subjects produced greater isometric torque than older adults, and the CV was similar between both groups except at the highest force level (40% MVC) where young subjects' value was higher. The major novel finding of this investigation was that although the knee extensor torque complexity is reduced in older adults, its relationship with contraction intensity is similar to young subjects. This means that despite the age-related decrease of the interactions between the components of the neuromuscular system, the organization of force control remains preserved in older adults, at least up to just below the force midrange.

Is pelvic floor muscle training able to alter the response of cardiovascular autonomic modulation and provide a possible cardiovascular benefit to pregnant women?

AIMS: To evaluate the acute and chronic effect of an exercise protocol of pelvic floor muscles (PFMs) contraction on the heart period (HP) and systolic arterial pressure (SAP) variabilities and baroreflex sensitivity (BRS) at rest in pregnant women; and to evaluate if this progressive exercise protocol was well-tolerated by the pregnant women studied. METHODS: We evaluated 48 women at 18 weeks of pregnancy by vaginal palpation, vaginal manometry, and cardiopulmonary exercise test. They were divided in control (CG; 31.75 ± 3.91 years) and training groups (TG; 30.71 ± 3.94 years). At 19 and 36 weeks of pregnancy, electrocardiogram and noninvasive peripheral SAP data were collected at rest before and after 10 PFM contractions. TG performed PFMT from the 20th to the 36th week. HP and SAP variabilities were analyzed by spectral and symbolic analysis. The baroreflex was evaluated by cross-spectral analysis between the HP and SAP series. RESULTS: The groups did not differ in relation to VO2 , HP and SAP variabilities, and BRS at the beginning of the protocol. TG increased the endurance of the PFM after training. PFM contraction did not change the HP and SAP variabilities, and BRS at the 18th week. After the training, the TG presented lower SAP mean, lower BF of SAP variability, and higher BRS than CG. CONCLUSIONS: Acute PFM contractions did not alter HP and SAP variabilities and BRS, but PFMT resulted in a lower SAP mean and higher BRS in trained pregnant when compared to the untrained.

Complexity analysis of heart rate variability in chronic obstructive pulmonary disease: relationship with severity and symptoms.

PURPOSE: Chronic obstructive pulmonary disease (COPD) negatively impacts autonomic control of the heart rate, as assessed by time and frequency domains of heart rate variability (HRV) analysis. However, it is unknown whether symbolic dynamic analysis may identify cardiac autonomic impairment, and whether such nonlinear indices may be associated with disease severity, prognostic markers, perceived dyspnea and functional capacity in patients with COPD. The current study assessed cardiac autonomic modulation by symbolic analysis of HRV in patients with COPD compared with healthy controls. METHODS: We recruited 54 COPD patients and 20 healthy controls. The interval between two successive R-wave peaks was calculated in the resting supine position. HRV was analyzed using symbolic markers and Shannon entropy (SE). The six-minute walk test (6MWT) was applied in a 30-m corridor. RESULTS: We found a lower 6MWT distance in patients with COPD compared with healthy controls (p < 0.05). We found increased SE and decreased percentage of no variation patterns (0V%) in COPD patients compared with the control group (p = 0.001). Significant correlations were found between the percentage of one variation pattern (1V%) and the Medical Research Council dyspnea scale (r = 0.38, p = 0.01), BODE index (r = 0.38, p = 0.01), forced expiratory volume in the first second (FEV1) [L] (r = -0.44, p = 0.003) and FEV1 [%] (r = -0.35, p = 0.02). It was found that SE was inversely associated with 0V% (r = -0.87, p < 0.0001). CONCLUSION: COPD patients present with depressed sympathetic modulation of HR and higher SE compared with healthy controls. This increased irregularity was inversely associated with 0V%. These results suggested that COPD patients seem to have a cardiac control shifted towards a parasympathetic predominance compared with controls. Symbolic dynamic and complexity index of HRV are related to disease severity, symptoms and functional impairment in these patients.

Acute effect of photobiomodulation using light-emitting diodes (LEDs) on baroreflex sensitivity during and after constant loading exercise in patients with type 2 diabetes mellitus.

To evaluate the photobiomodulation (PBM) effect on the cardiovascular autonomic control, analyzed by baroreflex sensitivity (sequence method), during constant load exercise and recovery in diabetic men, we evaluated 11 men with type 2 diabetes (DM2) (40-64 years). The constant workload exercise protocol (TECC) was performed on two different days, 14 days apart from each other, to guarantee PBM washout period. After PBM by light-emitting diode (LED) irradiation (150 J or 300 J or placebo), 10 min of rest (REST) was performed. After this period, the volunteer was positioned on a cycloergometer to start the test (1-min rest, 3-min free-load heating, 6-min constant workload-EXERCISE, 6-min free-load cool-down, 1-min rest) followed by a sitting period of 10 min (RECOVERY). The constant workload corresponded to 80%VO2GET (gas exchange threshold) identified by a previous cardiopulmonary exercise test (CPET). PBM was applied in continuous mode, contact technique, bilaterally, on both femoral quadriceps and gastrocnemius muscle groups. The electrocardiogram R-R intervals (BioAmp FE132) and the peripheral pulse pressure signals (Finometer PRO) were collected continuously throughout the protocol. Stable sequences of 256 points were chosen at REST, EXERCISE, and RECOVERY. The baroreflex sensitivity (BRS) was computed in time domain according to the sequence method (αseq). The comparison between therapies (150 J/300 J/placebo) and condition (REST, EXERCISE, and RECOVERY) was performed using the ANOVA two-way repeated measures test. There was no interaction between therapy and conditions during the TECC. There was only the condition effect (p < 0.001), showing that the behavior of αseq was similar regardless of the therapy. Photobiomodulation with 150 J or 300 J applied previously to a moderate-intensity TECC in DM2 was not able to promote cardiovascular autonomic control changes leading to an improvement in BRS.

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.

Effects of inspiratory muscle-training intensity on cardiovascular control in amateur cyclists.

Chronic effects of inspiratory muscle training (IMT) on autonomic function and baroreflex regulation are poorly studied. This study aims at evaluating chronic effects of different IMT intensities on cardiovascular control in amateur cyclists. A longitudinal, randomized, controlled blind study was performed on 30 recreational male cyclists undergoing IMT for 11 wk. Participants were randomly allocated into sham-trained group (SHAM, n = 9), trained group at 60% of the maximal inspiratory pressure (MIP60, n = 10), and trained group at critical inspiratory pressure (CIP, n = 11). Electrocardiogram, finger arterial pressure, and respiratory movements were recorded before (PRE) and after (POST) training at rest in supine position (REST) and during active standing (STAND). From the beat-to-beat series of heart period (HP) and systolic arterial pressure (SAP), we computed time domain markers, frequency domain indexes in the low frequency (0.04-0.15 Hz) and high frequency (HF, 0.15-0.4 Hz) bands, an entropy-based complexity index (CI), and baroreflex markers estimated from spontaneous HP-SAP sequences. Compared with SHAM, the positive effect of MIP60 over the HP series led to the HF power increase during REST (PRE: 521.2 ± 447.5 ms2; POST: 1,161 ± 878.9 ms2) and the CI rise during STAND (PRE: 0.82 ± 0.18; POST: 0.97 ± 0.13). Conversely, the negative effect of CIP took the form of the decreased HP mean during STAND (PRE: 791 ± 71 ms; POST: 737 ± 95 ms). No effect of IMT was visible over SAP and baroreflex markers. These findings suggest that moderate-intensity IMT might be beneficial when the goal is to limit cardiac sympathetic hyperactivity at REST and/or in response to STAND.

Cardiac baroreflex hysteresis is one of the determinants of the heart period variability asymmetry.

In heart period (HP) variability (HPV) recordings the percentage of negative HP variations tends to be greater than that of positive ones and this pattern is referred to as HPV asymmetry (HPVA). HPVA has been studied in several experimental conditions in healthy and pathological populations, but its origin is unclear. The baroreflex (BR) exhibits an asymmetric behavior as well given that it reacts more importantly to positive than negative arterial pressure (AP) variations. We tested the hypothesis that the BR asymmetry (BRA) is a HPVA determinant over spontaneous fluctuations of HP and systolic AP (SAP). We studied 100 healthy subjects (age from 21 to 70 yr, 54 men) comprising 20 subjects in each age decade. Electrocardiogram and noninvasive AP were recorded for 15 min at rest in supine position (REST) and during active standing (STAND). The HPVA was evaluated via Porta's index and Guzik's index, while the BRA was assessed as the difference, and normalized difference, between BR sensitivities computed over positive and negative SAP variations via the sequence method applied to HP and SAP variability. HPVA significantly increased during STAND and decreased progressively with age. BRA was not significantly detected both at REST and during STAND. However, we found a significant positive association between BRA and HPVA markers during STAND persisting even within the age groups. This study supports the use of HPVA indexes as descriptors of BRA and identified a challenge soliciting the BR response like STAND to maximize the association between HPVA and BRA markers.

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.

Refined Multiscale Entropy Using Fuzzy Metrics: Validation and Application to Nociception Assessment.

The refined multiscale entropy (RMSE) approach is commonly applied to assess complexity as a function of the time scale. RMSE is normally based on the computation of sample entropy (SampEn) estimating complexity as conditional entropy. However, SampEn is dependent on the length and standard deviation of the data. Recently, fuzzy entropy (FuzEn) has been proposed, including several refinements, as an alternative to counteract these limitations. In this work, FuzEn, translated FuzEn (TFuzEn), translated-reflected FuzEn (TRFuzEn), inherent FuzEn (IFuzEn), and inherent translated FuzEn (ITFuzEn) were exploited as entropy-based measures in the computation of RMSE and their performance was compared to that of SampEn. FuzEn metrics were applied to synthetic time series of different lengths to evaluate the consistency of the different approaches. In addition, electroencephalograms of patients under sedation-analgesia procedure were analyzed based on the patient's response after the application of painful stimulation, such as nail bed compression or endoscopy tube insertion. Significant differences in FuzEn metrics were observed over simulations and real data as a function of the data length and the pain responses. Findings indicated that FuzEn, when exploited in RMSE applications, showed similar behavior to SampEn in long series, but its consistency was better than that of SampEn in short series both over simulations and real data. Conversely, its variants should be utilized with more caution, especially whether processes exhibit an important deterministic component and/or in nociception prediction at long scales.

Paced Breathing Increases the Redundancy of Cardiorespiratory Control in Healthy Individuals and Chronic Heart Failure Patients.

Synergy and redundancy are concepts that suggest, respectively, adaptability and fault tolerance of systems with complex behavior. This study computes redundancy/synergy in bivariate systems formed by a target X and a driver Y according to the predictive information decomposition approach and partial information decomposition framework based on the minimal mutual information principle. The two approaches assess the redundancy/synergy of past of X and Y in reducing the uncertainty of the current state of X. The methods were applied to evaluate the interactions between heart and respiration in healthy young subjects (n = 19) during controlled breathing at 10, 15 and 20 breaths/minute and in two groups of chronic heart failure patients during paced respiration at 6 (n = 9) and 15 (n = 20) breaths/minutes from spontaneous beat-to-beat fluctuations of heart period and respiratory signal. Both methods suggested that slowing respiratory rate below the spontaneous frequency increases redundancy of cardiorespiratory control in both healthy and pathological groups, thus possibly improving fault tolerance of the cardiorespiratory control. The two methods provide markers complementary to respiratory sinus arrhythmia and the strength of the linear coupling between heart period variability and respiration in describing the physiology of the cardiorespiratory reflex suitable to be exploited in various pathophysiological settings.

Assessing multiscale complexity of short heart rate variability series through a model-based linear approach.

We propose a multiscale complexity (MSC) method assessing irregularity in assigned frequency bands and being appropriate for analyzing the short time series. It is grounded on the identification of the coefficients of an autoregressive model, on the computation of the mean position of the poles generating the components of the power spectral density in an assigned frequency band, and on the assessment of its distance from the unit circle in the complex plane. The MSC method was tested on simulations and applied to the short heart period (HP) variability series recorded during graded head-up tilt in 17 subjects (age from 21 to 54 years, median = 28 years, 7 females) and during paced breathing protocols in 19 subjects (age from 27 to 35 years, median = 31 years, 11 females) to assess the contribution of time scales typical of the cardiac autonomic control, namely in low frequency (LF, from 0.04 to 0.15 Hz) and high frequency (HF, from 0.15 to 0.5 Hz) bands to the complexity of the cardiac regulation. The proposed MSC technique was compared to a traditional model-free multiscale method grounded on information theory, i.e., multiscale entropy (MSE). The approach suggests that the reduction of HP variability complexity observed during graded head-up tilt is due to a regularization of the HP fluctuations in LF band via a possible intervention of sympathetic control and the decrement of HP variability complexity observed during slow breathing is the result of the regularization of the HP variations in both LF and HF bands, thus implying the action of physiological mechanisms working at time scales even different from that of respiration. MSE did not distinguish experimental conditions at time scales larger than 1. Over a short time series MSC allows a more insightful association between cardiac control complexity and physiological mechanisms modulating cardiac rhythm compared to a more traditional tool such as MSE.

Pulse photoplethysmographic amplitude and heart rate variability during laparoscopic cholecystectomy: A prospective observational study.

BACKGROUND: Surgical stress affects the autonomic nervous system by increasing sympathetic outflow. One method of monitoring sympathetic activity is pulse photoplethysmographic analysis. From this two indices can be derived - autonomic nervous system state (ANSS) and ANSS index (ANSSi). It has recently been claimed that these indices can be used to measure sympathetic activity in anaesthetised patients, but their validity has not yet been demonstrated. OBJECTIVE: To measure changes in pulse photoplethysmographic indices and determine any agreement with autonomic nervous system modulation of the cardiovascular system in healthy study participants during surgery under general anaesthesia. DESIGN: Prospective observational study. SETTING: Single-centre study based at a tertiary care centre in Milan, Italy. PATIENTS: Healthy patients undergoing general anaesthesia for elective laparoscopic cholecystectomy. INTERVENTIONS: ANSS, ANSSi, and heart rate variability (HRV) were analysed at three main times: baseline, after induction of general anaesthesia, and after pneumoperitoneum insufflation. MAIN OUTCOME MEASURES: The magnitude of changes in photoplethysmographic and HRV indices was measured. The agreement between pulse photoplethysmographic and HRV-derived indices was assessed by Bland-Altman plots. RESULTS: In total, 52 patients were enrolled and their data analysed. Both pulse photoplethysmographic and HRV indices changed during the study phases. An agreement was found between ANSSi and low frequency spectral components of HRV [bias 10.2nu, 95% confidence interval (CI) -13 to 33.4], high frequency spectral components of HRV (bias 6.1 nu, 95% CI -16.3 to 28.6), and low frequency/high frequency ratio (bias 16.1nu, 95% CI -1.4 to 33.5). The agreement was weaker between ANSSI and HRV indices. CONCLUSION: The study endorses the use of pulse photoplethysmographic indices ANSS and ANSSi as surrogates to estimate changes of autonomic modulation of the cardiovascular system in healthy adults during surgery under general anaesthesia.Orcid ID: orcid.org/0000-0002-9616-803X.

Calibrated variability of muscle sympathetic nerve activity during graded head-up tilt in humans and its link with noradrenaline data and cardiovascular rhythms.

Muscle sympathetic nerve activity (MSNA) variability is traditionally computed through a low-pass filtering procedure that requires normalization. We proposed a new beat-to-beat MSNA variability computation that preserves dimensionality typical of an integrated neural discharge (i.e., bursts per unit of time). The calibrated MSNA (cMSNA) variability technique is contrasted with the traditional uncalibrated MSNA (ucMSNA) version. The powers of cMSNA and ucMSNA variabilities in the low-frequency (LF, from 0.04 to 0.15 Hz) band were computed with those of the heart period (HP) of systolic and diastolic arterial pressure (SAP and DAP, respectively) in seven healthy subjects (age, 20-28 years; median, 22 years; 5 women) during a graded head-up tilt. Subjects were sequentially tilted at 0°, 20°, 30°, 40°, and 60° table inclinations. The LF powers of ucMSNA and HP variabilities were expressed in normalized units (LFnu), whereas all remaining spectral markers were expressed in absolute units. We found that 1) the LF power of cMSNA variability was positively correlated with tilt angle, whereas the LFnu power of the ucMSNA series was uncorrelated; 2) the LF power of cMSNA variability was correlated with LF powers of SAP and DAP, LFnu power of HP and noradrenaline concentration, whereas the relationship of the LFnu power of ucMSNA variability to LF powers of SAP and DAP was weaker and that to LFnu power of HP was absent; and 3) the stronger relationship of cMSNA variability to SAP and DAP spectral markers compared with the ucMSNA series was confirmed individually. The cMSNA variability appears to be more suitable in describing sympathetic control in humans than traditional ucMSNA variability.