Decomposing the complexity of heart-rate variability by the multifractal-multiscale approach to detrended fluctuation analysis: an application to low-level spinal cord injury

Prediction of mortality in intensive care unit with short-term heart rate variability: Machine learning-based analysis of the MIMIC-III database

BACKGROUND

Prognosis prediction in the intensive care unit (ICU) traditionally relied on physiological scoring systems based on clinical indicators at admission. Electrocardiogram (ECG) provides easily accessible information, with heart rate variability (HRV) derived from ECG showing prognostic value. However, few studies have conducted a comprehensive analysis of HRV-based prognostic model against established standards, which limits the application of HRV's prognostic value in clinical settings. This study aims to evaluate the utility of HRV in predicting mortality in the ICU. Additionally, we analyzed the applicability and interpretability of the HRV-integrated clinical model and identified the HRV factors that are most significant for patient prognosis.

METHODS

A total of 2838 patients from the MIMIC-III database were retrospectively included in this study. These patients were randomly divided into training and testing sets at a 4:1 ratio. We collected 86 HRV indicators from patients' lead II ECG readings between 0.5h and 2h before the time of death in the ICU of deceased patients or time of discharge from the ICU of alive patients, in addition to 9 clinical parameters upon admission. Subsequently, machine learning models were developed by algorithms including logistic regression (LR), Random Forest (RF), Adaptive Boosting (Adaboost), Gradient Boost (GB), eXtreme Gradient Boosting (XGB), and Light GBM (LGB) algorithms. An ensemble model that integrated these six algorithms, along with a deep neural network model, was also explored. The ten most important variables were identified using the Shapley method. Subsequently, an HRV-modified clinical scoring system was constructed through recursive feature elimination.

RESULTS

The study demonstrated that the integrated model, utilizing both clinical and HRV features, outperformed the model based solely on clinical information in XGB, LGB and LR algorithms (p = 0.005-0.03). The ensemble model exhibited the best performance (AUROC = 0.878), followed closely by XGB algorithm (AUROC = 0.869). Both of these models significantly outperformed the APS III scoring system (AUROC = 0.765). Notably, this improvement is not dependent on a specific disease but rather on the timing of ECG recordings that are closer to clinical endpoints. For parameter analysis, Shapley's method identified MSEn, SD1SD2, DFAα1, and DFAα2 as key HRV features in predicting mortality. These variables also showed significant differences in univariate analysis across patients with different clinical outcomes (p < 0.0001). Additionally, regardless of machine learning, the additive scoring system incorporating HRV showed a significant enhancement in prognostic ability compared to traditional physiological scores APS III (p = 0.02).

CONCLUSIONS

The integration of HRV features into mortality prediction models has been shown to enhance predictive performances in ICU. This enhancement is not limited to specific machine learning models or diseases but is influenced by the timing of HRV measurement relative to clinical endpoints. HRV features, when combined with other clinical parameters, offer high interpretability and significant prognostic value. Furthermore, incorporating HRV into traditional ICU scoring systems can lead to improved predictive performance.

Entropy-Based Multifractal Testing of Heart Rate Variability during Cognitive-Autonomic Interplay

Entropy-based and fractal-based metrics derived from heart rate variability (HRV) have enriched the way cardiovascular dynamics can be described in terms of complexity. The most commonly used multifractal testing, a method using q moments to explore a range of fractal scaling in small-sized and large-sized fluctuations, is based on detrended fluctuation analysis, which examines the power-law relationship of standard deviation with the timescale in the measured signal. A more direct testing of a multifractal structure exists based on the Shannon entropy of bin (signal subparts) proportion. This work aims to reanalyze HRV during cognitive tasks to obtain new markers of HRV complexity provided by entropy-based multifractal spectra using the method proposed by Chhabra and Jensen in 1989. Inter-beat interval durations (RR) time series were obtained in 28 students comparatively in baseline (viewing a video) and during three cognitive tasks: Stroop color and word task, stop-signal, and go/no-go. The new HRV estimators were extracted from the f/α singularity spectrum of the RR magnitude increment series, established from q-weighted stable (log-log linear) power laws, namely: (i) the whole spectrum width (MF) calculated as αmax - αmin; the specific width representing large-sized fluctuations (MFlarge) calculated as α0 - αq+; and small-sized fluctuations (MFsmall) calculated as αq- - α0. As the main results, cardiovascular dynamics during Stroop had a specific MF signature while MFlarge was rather specific to go/no-go. The way these new HRV markers could represent different aspects of a complete picture of the cognitive-autonomic interplay is discussed, based on previously used entropy- and fractal-based markers, and the introduction of distribution entropy (DistEn), as a marker recently associated specifically with complexity in the cardiovascular control.

Sample, Fuzzy and Distribution Entropies of Heart Rate Variability: What Do They Tell Us on Cardiovascular Complexity?

Distribution Entropy (DistEn) has been introduced as an alternative to Sample Entropy (SampEn) to assess the heart rate variability (HRV) on much shorter series without the arbitrary definition of distance thresholds. However, DistEn, considered a measure of cardiovascular complexity, differs substantially from SampEn or Fuzzy Entropy (FuzzyEn), both measures of HRV randomness. This work aims to compare DistEn, SampEn, and FuzzyEn analyzing postural changes (expected to modify the HRV randomness through a sympatho/vagal shift without affecting the cardiovascular complexity) and low-level spinal cord injuries (SCI, whose impaired integrative regulation may alter the system complexity without affecting the HRV spectrum). We recorded RR intervals in able-bodied (AB) and SCI participants in supine and sitting postures, evaluating DistEn, SampEn, and FuzzyEn over 512 beats. The significance of "case" (AB vs. SCI) and "posture" (supine vs. sitting) was assessed by longitudinal analysis. Multiscale DistEn (mDE), SampEn (mSE), and FuzzyEn (mFE) compared postures and cases at each scale between 2 and 20 beats. Unlike SampEn and FuzzyEn, DistEn is affected by the spinal lesion but not by the postural sympatho/vagal shift. The multiscale approach shows differences between AB and SCI sitting participants at the largest mFE scales and between postures in AB participants at the shortest mSE scales. Thus, our results support the hypothesis that DistEn measures cardiovascular complexity while SampEn/FuzzyEn measure HRV randomness, highlighting that together these methods integrate the information each of them provides.

Multiscale assessment of the degree of multifractality for physiological time series

Recent advancements in detrended fluctuation analysis (DFA) allow evaluating multifractal coefficients scale-by-scale, a promising approach for assessing the complexity of biomedical signals. The multifractality degree is typically quantified by the singularity spectrum width (W_SS), a method that is critically unstable in multiscale applications. Thus, we aim to propose a robust multiscale index of multifractality, compare it with W_SS and illustrate its performance on real biosignals. The proposed index is the cumulative function of squared increments between consecutive DFA coefficients at each scale n: α_CF(n). We compared it with W_SS calculated scale-by-scale considering monofractal/monoscale, monofractal/multiscale, multifractal/monoscale and multifractal/multiscale random processes. The two indices provided qualitatively similar descriptions of multifractality, but α_CF(n) differentiated better the multifractal components from artefacts due to crossovers or detrending overfitting. Applied on 24 h heart rate recordings of 14 participants, the singularity spectrum failed to always satisfy the concavity requirement for providing meaningful W_SS, while α_CF(n) demonstrated a statistically significant heart rate multifractality at night in the scale ranges 16-100 and 256-680 s. Furthermore, α_CF(n) did not reject the hypothesis of monofractality at daytime, coherently with previous reports of lower nonlinearity and monoscale multifractality during the day. Thus, α_CF(n) appears a robust index of multiscale multifractality that is useful for quantifying complexity alterations of physiological series. This article is part of the theme issue 'Advanced computation in cardiovascular physiology: new challenges and opportunities'.

Sex Differences in Heart Rate Nonlinearity by Multifractal Multiscale Detrended Fluctuation Analysis

Recent developments of detrended fluctuation analysis (DFA) provide multifractal/multiscale (MFMS) descriptions of the heart rate self-similarity, a promising approach to cardiovascular complexity. However, it is unclear whether the MFMS DFA may also describe the nonlinear components of heart rate variability. Our aim is to define MFMS DFA indices for quantifying the short-term and long-term degree of the heart-rate nonlinearity and to apply these indices to detect possible sex-related differences.We recorded the inter-beat-interval (IBI) series in 42 male and in 42 female healthy participants sitting at rest for about 2 hours. For each series j, we generated 100 phase-randomized surrogate series. We applied the MFMS DFA to estimate the self-similarity coefficients α over scales τ between 8 and 512 s and moment orders q between -5 and +5, obtaining coefficients for the original series, α^O,j (q, τ), and for each surrogate, α^i,j (q, τ) with 1≤i≤100. We first evaluated π^j(q, τ), percentile of α^i,j (q, τ) distribution in which was α^O,j (q, τ). Then we calculated the percentages of scales where π^j(q, τ) was <5% for 8≤τ≤16 s (short-term nonlinearity index NL₁(q)) and for 16≤τ≤512 s (long-term nonlinearity index NL₂(q)). We found that NL₁(q) was generally greater than 50% at all q≥0 but q=2 (i.e., moment order of the monofractal DFA), while at q<0 it was high in males only, with significant sex differences at q=-1 and q=-2. Results indicate that the multifractal DFA may highlight nonlinear heart-rate components at the short scales that are not revealed by the traditional monofractal DFA and that appear related to gender differences.Clinical Relevance- This supports the use of MFMS DFA to integrate the linear information from traditional spectral methods of heart rate variability in clinical studies aimed at improving the stratification of the cardiovascular risk.

Day and Night Changes of Cardiovascular Complexity: A Multi-Fractal Multi-Scale Analysis

Recently, a multifractal-multiscale approach to detrended fluctuation analysis (DFA) was proposed to evaluate the cardiovascular fractal dynamics providing a surface of self-similarity coefficients α(q,τ), function of the scale τ, and moment order q. We hypothesize that this versatile DFA approach may reflect the cardiocirculatory adaptations in complexity and nonlinearity occurring during the day/night cycle. Our aim is, therefore, to quantify how α(q, τ) surfaces of cardiovascular series differ between daytime and night-time. We estimated α(q,τ) with -5 ≤ q ≤ 5 and 8 ≤ τ ≤ 2048 s for heart rate and blood pressure beat-to-beat series over periods of few hours during daytime wake and night-time sleep in 14 healthy participants. From the α(q,τ) surfaces, we estimated short-term (<16 s) and long-term (from 16 to 512 s) multifractal coefficients. Generating phase-shuffled surrogate series, we evaluated short-term and long-term indices of nonlinearity for each q. We found a long-term night/day modulation of α(q,τ) between 128 and 256 s affecting heart rate and blood pressure similarly, and multifractal short-term modulations at q < 0 for the heart rate and at q > 0 for the blood pressure. Consistent nonlinearity appeared at the shorter scales at night excluding q = 2. Long-term circadian modulations of the heart rate DFA were previously associated with the cardiac vulnerability period and our results may improve the risk stratification indicating the more relevant α(q,τ) area reflecting this rhythm. Furthermore, nonlinear components in the nocturnal α(q,τ) at q ≠ 2 suggest that DFA may effectively integrate the linear spectral information with complexity-domain information, possibly improving the monitoring of cardiac interventions and protocols of rehabilitation medicine.