Modified permutation-entropy analysis of heartbeat dynamics

Comparing different approaches to compute Permutation Entropy with coarse time series

Biomedical signals carry important information about the behaviour of the living systems under study. A proper processing of these signals in principle enhances their physiological and clinical information. Analysis of variations in the instantaneous heart rate time series using the beat to-beat RR intervals (the RR tachogram) is known as heart rate variability (HRV) analysis. Sample entropy (SampEn), refined version of approximate entropy (ApEn), is a nonlinear complexity measure used to quantify the irregularity of a RR interval time series without biasing. An increase in SampEn is an indicator of increases in complexity. Linear HRV parameters are very sensitive to ECG sampling frequency and low sampling frequency may result in clinically misinterpretation of HRV. In this study consequences of errors in SampEn based HRV induced by ECG sampling frequency have been investigated. The error induced in SampEn based HRV was found to be a function of ECG sampling frequency and RR interval data length. The relative error in SampEn was approximately 3.5%.for medium and long term data (N=500, 1000 respectively) and less than 2% for short term data (N=200) at low ECG sampling frequency of 125 Hz with respect to reference values at 2000 Hz. Therefore the SampEn based HRV indices computed from RR interval time series with low ECG sampling should be regarded with caution. The finding of this study can be partly used as a reference for the optimal ECG sampling frequency for the SampEn-based HRV assessment.

Obstructive sleep apnea (OSA) is a common disorder which can cause periodic fluctuations in heart rate. To diagnose sleep apnea, some studies analyze electrocardiogram (ECG) signals by adopting chaos-based analysis. This research is going to specifically focus on whether it is possible to use chaos-based analysis of heart rate variability (HRV) signals rather than using chaotic analysis of ECG signals to diagnose OSA. While conventional studies mostly use chaos-based analysis of ECG signals to detect OSA, here, we apply correlation dimension (CD) as a chaotic index to analyze HRV data in OSA patients. For this purpose, 17 patients with OSA and 9 healthy individuals referred to a sleep clinic in Isfahan/Iran are studied, and their HRV time series were extracted from 1-h ECG signals recorded overnight. The preliminary step to calculate CD is phase-space reconstruction of the system based on HRV time series. Corresponding parameters, including embedding dimension and lag time, are estimated optimally using enhanced related methods, and then CD is calculated using Grassberger–Procaccia algorithm. Moreover, to evaluate our results, detrended fluctuation analysis (DFA), one of the well-known nonlinear methods in HRV analysis to detect OSA, is also applied to our data and the result is compared with those obtained from CD analysis of HRV. CD index with P < 0.005 indicates a significant difference in nonlinear dynamics of HRV signals detected from OSA patients and healthy individuals.

Shannon Entropy is the preeminent tool for measuring the level of uncertainty (and conversely, information content) in a random variable. In the field of communications, entropy can be used to express the information content of given signals (represented as time series) by considering random variables which sample from specified subsequences. In this paper, we will discuss how an entropy variant, the \textit{permutation entropy} can be used to study and classify radio frequency signals in a noisy environment. The permutation entropy is the entropy of the random variable which samples occurrences of permutation patterns from time series given a fixed window length, making it a function of the distribution of permutation patterns. Since the permutation entropy is a function of the relative order of data, it is (global) amplitude agnostic and thus allows for comparison between signals at different scales. This article is intended to describe a permutation patterns approach to a data driven problem in radio frequency communications research, and includes a primer on all non-permutation pattern specific background. An empirical analysis of the methods herein on radio frequency data is included. No prior knowledge of signals analysis is assumed, and permutation pattern specific notation will be included. This article serves as a self-contained introduction to the relationship between permutation patterns, entropy, and signals analysis for studying radio frequency signals and includes results on a classification task.

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.

BackgroundIt has been shown that linear and non-linear heart rate variability (HRV) metrics are suitable to assess workload of anesthetists administering anesthesia. In pre-hospital emergency care, these parameters have not yet been evaluated. We hypothesized that heart rate (HR) and HRV metrics discriminate between differing workload levels of an emergency physician.MethodsElectrocardiograms were obtained from 13 emergency physicians. Mean HR, ten linear and seven non-linear HRV metrics were analyzed. For each sortie, four different levels of workload were defined. Mixed-effects models and the area under the receiver operating characteristics curve (AUC) were used to test and quantify the HR and HRV metrics’ ability to discriminate between levels of workload. This was conducted for mean HR and each HRV metric as well as for groups of metrics (time domain vs. frequency domain vs. non-linear metrics).ResultsThe non-linear HRV metric Permutation entropy (PeEn) discriminated best between the time before the alarm and primary patient care (AUC = 0.998, 1st rank of 18 HRV metrics). In contrast, AUC of the mean HR was low (0.558, 17th rank). In the multivariable approach, the non-linear HRV metrics provided a higher AUC (0.998) compared to the frequency domain (0.677) and to the time domain metrics (0.680).ConclusionNon-linear heart rate metrics and, specifically, PeEn provided good validity for the assessment of different levels of a physician’s workload in the setting of pre-hospital emergency care. In contradiction to earlier findings, the physicians’ mean HR was not a valid marker of workload.

Improved analysis of heart rate variability by methods of nonlinear dynamics

The complexity of a system recorded in time series data can be measured statistically using permutation entropy (PE). The state of a system (e.g. regular, chaotic, random, etc.) that underlies the appearance of variations in time series can be determined with PE. Since volcanoes are considered as the complex dynamical system controlled by interactions of many processes. Permutation entropy can be applied to study the system mechanism of volcano. We utilized PE to study system mechanism of Kelud volcano in 2007 dome-forming eruption period, from 3 (KWH; KLD; UMBK) seismic stations with different distances from the crater lake. Then, we want to compare the results. The result of study shows that the PE pattern for each station is different. The unique PE pattern that can be used as an eruption precursor is only shown at KWH and KLD stations. This pattern began to appear 2.7 days before the eruption on 3 November 2007. Data from UMBK station doesn’t show unique PE pattern. The factors such as sensor distance from magmatic activity center, size, and type of eruption probably influenced the final PE result. Using PE as the addition to volcano monitoring can maximize efforts in mitigation activities.

In this paper the permutation entropy (PE) obtained from heart rate variability (HRV) is analyzed in a statistical model. In this model we also integrate other feature extraction techniques, the cepstrum coefficients derived from the same HRV and a set of band powers obtained from the electrocardiogram derived respiratory (EDR) signal. The aim of the model is detecting obstructive sleep apnea (OSA) events. For this purpose, we apply two statistical classification methods: Logistic Regression (LR) and Quadratic Discriminant Analysis (QDA). For testing the models we use seventy ECG recordings from the Physionet database which are divided into equal-size learning and testing sets. Both sets consist of 35 recordings, each containing a single ECG signal. In our experiments we have found that the features extracted from the EDR signal present a sensitivity of 65.6% and specificity of 87.7% (auc = 85) in the LR classifier, and sensitivity of 59.4% and specificity of 90.3% (auc = 83.9) in the QDA classifier. The HRV-based cepstrum coefficients present a sensitivity of 63.8% and specificity of 89.2% (auc = 86) in the LR classifier, and sensitivity of 67.2% and specificity of 86.8% (auc = 86.9) in the QDA. Subsequent tests show that the contribution of the permutation entropy increases the performance of the classifiers, implying that the complexity of RR interval time series play an important role in the breathing pauses detection. Particularly, when all features are jointly used, the quantification task reaches a sensitivity of 71.9% and specificity of 92.1% (auc = 90.3) for LR. Similarly, for QDA the sensitivity is 75.1% and the specificity is 90.5% (auc = 91.7).

Heart rate variability (HRV) is the physiological phenomenon of variation in the time interval between heartbeats. It is measured by the variation in the beat-to-beat interval and/or RR variability (where R is a point corresponding to the peak of the QRS complex of the ECG wave and RR is the interval between successive Rs) and other components extracted from these. HRV is a field of research interest in pathophysiology (in general) and cancer prognosis (more specifically). Adolescents with adrenal tumor or craniopharyngioma were investigated, herein. Αutonomic nervous system recordings were performed with Task Force® Monitor (gold standard of the Task Force of the European Society of Cardiology and the North American Society of Electrophysiology). The RR interval (RRI) time series calculations were performed with the MatLab® computational environment and included the estimation of fractal dimension and Lyapunov exponent. Fractal dimensions were calculated by estimating N and R, where N represents the number of "squares" needed for a fractal shape to be completed and their respective "square size" R. By definition, if the first derivative of d ln N/d ln R remains constant for a space of R, this is the fractal dimension of the shape, in the present case of the time series trajectory. We found that RRI manifested different fractal dynamics, thus, a complex pattern of progression in these two morbid entities, suggesting the need for further investigation in ANS contribution to tumor pathophysiology.

Heart rate variability (HRV) provides both linear and nonlinear autonomic proxies that can be informative of health status in fibromyalgia (FM), where sympatho-vagal abnormalities are common. This retrospective observational study aims to: 1. detect differences in correlation dimension (D2) between FM patients and healthy controls (HCs); 2. correlate D2 with standard HRV parameters; 3. correlate the degree of HRV changes using a global composite parameter called HRV grade, derived from three linear indices (SDNN = intervals between normal sinus beats; RMSSD = mean square of successive differences; total power), with FM clinical outcomes; 4. correlate all linear and nonlinear HRV parameters with clinical variables in patients. N = 85 patients were considered for the analysis and compared to 35 healthy subjects. According to standard diagnostic protocol, they underwent a systematic HRV protocol with a 5-min paced breathing task. Disease duration, pain intensity, mood, sleep, fatigue, and quality of life were assessed. Non-parametric tests for independent samples and pairwise correlations were performed using JMP (all p < 0.001). Mann-Whitney U found a significant difference in D2 values between FM patients and HCs (p < 0.001). In patients, D2 was associated with all HRV standard indices (all p < 0.001) and FM impairment (FIQ = -0.4567; p < 0.001). HRV grade was also associated with FM impairment (FIQ = 0.5058; p < 0.001). Combining different HRV measurements may help understand the correlates of autonomic dysregulation in FM. Specifically, clinical protocols could benefit from the inclusion and validation of D2 and HRV parameters to target FM severity and related dysautonomia.

The complexity of time series can be quantitatively measured using Permutation Entropy (PE). PE has recently been introduced as a potential tool in eruption forecasting by applying it to the seismic time series. Examples of successful applications are the eruptions at Strokkur Geyser, Iceland, the 1996 eruption of Gj&amp;#225;lp, Iceland, and the eruptions of Shinmoedake volcano, Japan, in 2011, 2017, and 2018. While PE is able to show temporal changes prior to an eruption, these features are not always prominent. To improve this method, we calculate PE not only for the amplitudes of the seismic signals but also for the seismic instantaneous phases, called Phase Permutation Entropy (PPE). To understand the difference between PE and PPE, we performed synthetic tests by creating several synthetic waveforms using different numbers of sin wave superposition. We used more wave superposition with different frequencies to create complex waves containing broader frequency spectrum, while less superposition is used to create simpler waves containing narrower frequency spectrum. PE and PPE values are both low for simple waves and high for complex waves, but their absolute values differ, which might contain valuable information. The gap, dP = PE-PPE, is found to be smaller for complex waves compared to the more simple waves.&amp;#160; We then calculated PE and PPE for seismic data recorded from January 2014 to December 2015, which covered the eruption period of Holuhraun in Iceland. During the time of quiescence, both PE and PPE exhibit a long period variation which seems to be seasonal. Calculating dP weakens the long period noise and generates a more stable baseline.&amp;#160; We observe that the temporal variation of dP started to decrease below the baseline after 24 May 2014, indicating that the ground motion got more complex. An abrupt drop of dP to its lowest level was observed on 16 August 2014, when the dyke started to propagate from Bardarbunga to Holuhraun. While dP increases after the onset of eruption on 29 and 31August 2014, there is no prominent feature between the dyke propagation and the onset of the eruptions.&amp;#160; During the eruption period, dP stays lower than the background dP, indicating a higher ground motion complexity compared to the quiescence time. After January 2015, the gradual increase of dP back to the baseline level is clearly observed, showing the method&amp;#8217;s potential to foresee the end of the eruption.

Distribution entropy (DistEn) is a recently developed measure of complexity that is used to analyse heart rate variability (HRV) data. Its calculation requires two input parameters—the embedding dimension m, and the number of bins M which replaces the tolerance parameter r that is used by the existing approximation entropy (ApEn) and sample entropy (SampEn) measures. The performance of DistEn can also be affected by the data length N. In our previous studies, we have analyzed stability and performance of DistEn with respect to one parameter (m or M) or combination of two parameters (N and M). However, impact of varying all the three input parameters on DistEn is not yet studied. Since DistEn is predominantly aimed at analysing short length heart rate variability (HRV) signal, it is important to comprehensively study the stability, consistency and performance of the measure using multiple case studies. In this study, we examined the impact of changing input parameters on DistEn for synthetic and physiological signals. We also compared the variations of DistEn and performance in distinguishing physiological (Elderly from Young) and pathological (Healthy from Arrhythmia) conditions with ApEn and SampEn. The results showed that DistEn values are minimally affected by the variations of input parameters compared to ApEn and SampEn. DistEn also showed the most consistent and the best performance in differentiating physiological and pathological conditions with various of input parameters among reported complexity measures. In conclusion, DistEn is found to be the best measure for analysing short length HRV time series.

In fetal surveillance, fetal heart rate changes are assessed using cardiotocography (CTG). Standard procedures used in the quantification of heart rate variability (HRV) are seldom applied as CTG does not deliver beat interval durations with the same accuracy as the electrocardiogram (ECG). Thus little is known about the interdependency of standard HRV measures prenatally. Using fetal magnetocardiography (FMCG: the magnetic equivalent of the fetal ECG), we investigated standard HRV measures in a homogenous group of 20 healthy fetuses. Ten HRV measures were analyzed in 60 five-minute RR interval time series derived from FMCG acquisitions (16th-40th week of gestation). Using regression analysis, we found a clear dependency on gestational age and mean RR interval for measures from the time and frequency domains as well as for a measure for complexity. Correlation analysis revealed a strong interdependency of the measures, in particular within the specific domains. An adequate description of fetal HRV may be achieved using the standard deviation from the time domain, the high frequency band (0.15-0.40 Hz) from the frequency domain and approximate entropy as a complexity measure. The results indicate that different characteristics of fetal HRV are embedded in the different domains.

1 Anu Muraja‐Murro, 1 Ari Pääkkönen, 2 Leena Jutila, 2 Reetta Kälviäinen, 3 Arto Immonen, 1 Sara Määttä, and 1 Esa Mervaala ( 1 Clinical Neurophysiology, Kuopio University Hospital, University of Kuopio, Kuopio, Finland ; 2 Neurology, Kuopio University Hospital, University of Kuopio, Kuopio, Finland ; and 3 Neurosurgery, Kuopio University Hospital, University of Kuopio, Kuopio, Finland ) Rationale: Mismatch‐negativity (MMN) is an auditory event‐related potential (ERP) produced by a deviant stimuli that occurs infrequenty among standard stimuli. MMN is thought to reflect the activation of an automatic change‐detector system that compares new auditory input with a short‐term memory trace generated by the previous auditory stimuli. MMN in human has been demonstrated from several cortical sites, but not to our knowledge from hippocampus or amygdala. This is surprising, given that these limbic structures are so essential for learning and memory functions. We could obtain MMN from these temporomesial structures using intracranial electrodes in adult patients undergoing presurgical evaluation for epilepsy surgery. Methods: 4 adults with intractable temporal lobe seizures (age 32–48 years) had each 2–4 stereotactically implanted 6‐contact depth‐electrodes at amygdalo‐hippocampal complex. The electrodes were implanted via lateral approach and their exact anatomical localizations were confirmed by MRI and CT in situ. After the post hoc anatomical localization of the depth‐electrodes, the presence of MMN could be studied from 6 hippocampi and 5 amygdalas (i.e., the electrode tips were exactly within amygdalo‐hippocampal complex). The most mesial depth‐electrode contacts were chosen for the MMN analysis with the MMN latency range of 120–250 ms, as well as with the P300 range of 250–500 ms. We analyzed possible statistically significant differences between the ERPs to deviant and standard tones. Results: A definite MMN within 120–250 ms latency range could be recorded from 4/6 hippocampi and 3/5 amygdalas. MMN was also detected within 250–500 ms latency range in 3/6 hippocampi and 2/5 amygdalas, respectively. In only one patient the hippocampal MMN resembled typical scalp‐recorded MMN. In all, the MMN decreased from the deepest contacts towards the cortex, suggesting a local maximum of MMN at the amygdalo‐hippocampal complex. Conclusions: Our data implicates that a local and early (120–500 ms post‐stimuli) automatic electrophysiological change‐detector system exists within the amygdalo‐hippocampal complex. This data is the first to demonstrate that also these temporomesial structures are activated and involved in mismatch detection, and is in line with recent sensory mismatch fMRI studies. Other sensory stimuli might also produce MMN in the same structures, possibly thus revealing a common function for hippocampus and amygdala in early sensory stimulus detection. 1 Tobias Loddenkemper, 2 Gabriel Moeddel, 1 Elia M. Pestana, 1 Deepak K. Lachhwani, 1 Ajay Gupta, 1 Prakash Kotagal, and 1 Elaine Wyllie ( 1 Department of Epilepsy and Sleep Disorder, The Cleveland Clinic Foundation, Cleveland, OH ; and 2 Department of Neurology, Universitaetsklinikum Muenster, Muenster, Westfalen, Germany ) Rationale: The intracarotid amobarbital test (IAT) is part of the presurgical workup of patients scheduled for epilepsy surgery to determine language and memory lateralization. Most information on results and complications are derived from adults. Little is known about children undergoing IAT. Difficulties arise from anxiety, need for barbiturate dosage adjustment, and impaired baseline memory in children with mental retardation [4]. The goal of this study was 1) to describe language lateralization in children with epilepsy and 2) to outline complications during IAT. Methods: 126 consecutive pediatric IAT performed at the Cleveland Clinic Foundation during a seven year period were reviewed. Results: 44 patients were age 5–12 years, 82 were age 13–18. 102 were right‐handed. Amobarbital (n = 96, average dose: 100 +‐ 25 mg) or Methohexital (n = 30, average dose 5 +‐ 1 mg) was injected into the left (n = 18), right (n = 13), or both (n = 95) ICA. Language was localized in 95 patients (75.4%): 75 [78.9%] were left, 6 [6.3%] were right, 14 [14.7%] bilateral language dominant. Neurological complications included prolonged lethargy impairing language and memory evaluation in 4 patients. Four children had a seizure after injection. Additionally, valid data could not be obtained due to fear or agitation in three children age 5–9 years. No lasting neurological deficits were seen. General complications included shortness of breath after contrast injection in one boy. One girl presented with fever of 38.5 C the night after the procedure complaining of groin pain. No other major complications were seen. Conclusions: This is one of the largest pediatric IAT series studied so far. The data on language lateralization agree with those previously reported [1, 2, 3]. The IAT in children is an invasive test with a potential for complications, as in adults, occuring in 10 out of 126 patients [7.9%]. Our series highlights the need for refinement and further development of novel methods to establish language lateralization in children during the evaluation for epilepsy surgery. REFERENCES 1. Loring D et al : . Neuropsychologia 28/8 ( 1990 ): 831 – 938 . 2. Mateer CA , Dodrill CB : . Hum Neurobiol 2 ( 1983 ): 135 – 142 3. Strauss E , Wada J : . Cortex 19 ( 1983 ): 165 – 177 ). 4. Szabo CA , Wyllie E : . Epilepsy Res 15 () ( 1993 ): 239 – 246 1 Eija Ronkainen, 1 Juha T. Korpelainen, 2 Heikki V. Huikuri, 1 Vilho V. Myllylä, and 1 Jouko I.T. Isojärvi ( 1 Department of Neurology, University of Oulu, Oulu, Finland ; and 2 Department of Internal Medicine, Division of Cardiology, University of Oulu, Oulu, Finland ) Rationale: To prospectively evaluate changes in interictal heart rate (HR) variability in patients with temporal lobe epilepsy (TLE) after 4 years follow‐up. Methods: A 24‐hour ECG recording was obtained at baseline and four years after first record