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Time-Variant, Frequency-Selective, Linear and Nonlinear Analysis of Heart Rate Variability in Children With Temporal Lobe Epilepsy Karin Schiecke*, Matthias Wacker, Diana Piper, Franz Benninger, Martha Feucht, and Herbert Witte, Member, IEEE
Abstract—The major aim of our study is to demonstrate that a concerted combination of time-variant, frequency-selective, linear and nonlinear analysis approaches can be beneficially used for the analysis of heart rate variability (HRV) in epileptic patients to reveal premonitory information regarding an imminent seizure and to provide more information on the mechanisms leading to changes of the autonomic nervous system. The quest is to demonstrate that the combined approach gains new insights into specific short-term patterns in HRV during preictal, ictal, and postictal periods in epileptic children. The continuous Morlet-wavelet transform was used to explore the time-frequency characteristics of the HRV using spectrogram, phase-locking, band-power and quadratic phase coupling analyses. These results are completed by time-variant characteristics derived from a signal-adaptive approach. Advanced empirical mode decomposition was utilized to separate out certain HRV components, in particular blood-pressure-related Mayer waves (≈0.1 Hz) and respiratory sinus arrhythmia (≈0.3 Hz). Their time-variant nonlinear predictability was analyzed using local estimations of the largest Lyapunov exponent (point prediction error). Approximately 80–100 s before the seizure onset timing and coordination of both HRV components can be observed. A higher degree of synchronization is found and with it a higher predictability of the HRV. All investigated linear and nonlinear analyses contribute with a specific importance to these results. Index Terms—Epilepsy, heart rate variability (HRV), nonlinear analysis, signal-adaptive decomposition, time-frequency analysis.
Manuscript received April 26, 2013; revised January 28, 2014; accepted February 3, 2014. Date of publication February 20, 2014; date of current version May 15, 2014. This work was supported in part by the DFG under Grant Wi 1166/10-2 and partly by Wi 1166/9-2/Wi 1166/12-1 (EMD analysis) and in part by the Romanian Ministry of Labour, Family and Social Protection through the Financial Agreement POSDRU/107/1.5/S/76903 (D. Piper). Asterisk indicates corresponding author. ∗ K. Schiecke is with the Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital, Friedrich Schiller University Jena, Jena 07740, Germany (e-mail:
[email protected]). M. Wacker and H. Witte are with the Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital, Friedrich Schiller University Jena, Jena 07740, Germany (e-mail:
[email protected];
[email protected]). D. Piper is with the Department of Applied Electronics and Information Engineering, Politehnica University of Bucharest, Bucharest 060042, Romania (e-mail:
[email protected]). F. Benninger and M. Feucht are with the Epilepsy Monitoring Unit, Department of Child and Adolescent Neuropsychiatry, University Hospital Vienna, Wien 1090, Austria (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/TBME.2014.2307481
NOMENCLATURE CEMD
Complete ensemble empirical mode decomposition with adaptive noise. ECG Electrocardiogram. EEG Electroencephalogram. EEMD Ensemble empirical mode decomposition. EMD Empirical mode decomposition. FFT Fast Fourier transform. HF High frequency. HFP (HFPN ) Time course of the HF power (normalized HFPN ) derived from PS. Time course of the HF power derived from HFPP L PSP L . HR Heart rate. HRV Heart rate variability. IMF Intrinsic mode function. LF Low frequency. LFP (LFPN ) Time course of the LF power (normalized LFPN ) derived from PS. Time course of the LF power derived from LFPP L PSP L . LPFES Low-pass filtered event series. mBA Mean biamplitude in the ROI. mBC Mean bicoherence in the ROI. MWT Continuous Morlet wavelet transform. PLI Phase-locking index. PPE Point prediction error. PR Time course of the power ratio. PS Power spectrogram (time-variant power spectrum). Power spectrogram; phase locked. PSP L QPC Quadratic phase coupling. QRS Q-, R-, and S −ECG-waves. ROI Region of interest. RSA Respiratory sinus arrhythmia. SUDEP Sudden unexpected death in epileptic patients. TLE Temporal lobe epilepsy. I. INTRODUCTION HE analysis of heart rate variability (HRV) is frequently used for insight into cardiovascular regulatory mechanisms controlled by the autonomic nervous system in human health and disease. HRV analysis in epilepsy is carried out with two major clinical objectives. One important aim is to reveal
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SCHIECKE et al.: TIME-VARIANT, FREQUENCY-SELECTIVE, LINEAR AND NONLINEAR ANALYSIS OF HEART RATE VARIABILITY
the causes for the sudden unexpected death in epileptic patients [1], [2]. Here, the autonomic instability of the patients, in particular, the impaired baroreflex function [3], is a major focus. Another framework with regard to epilepsy in which the HRV analysis is involved is automatic seizure prediction and detection [4]. Reviews concerning cardiac changes and autonomic alteration in epilepsy have been provided by Jansen and Lagae [5] and Sevcencu and Struijk [6]. Delamont and Walker [7] compiled the results for the analysis of preictal autonomic changes. A first metaanalysis investigating HRV in epilepsy was recently published [8]. The preictal, ictal, and postictal HRV courses have been investigated by using time- and/or frequency-domain features. Features of the time–frequency domain have received much less attention. This is also true for HRV analysis in general (for an overview see [9]). Delamont and Walker [7] reported that a good time resolution is needed to identify any potentially short-duration changes that may be occurring preictally. Nonlinear HRV analyses are frequently applied also in epileptic patients. Nonlinear parameters have shown a better reliability across repeated measurements in comparison to linear parameters. However, the methods are usually time-invariant (for stationary signals) and not frequency-selective. As a rule, the estimation of most nonlinear indices requires stationarity over minutes and their physiological meaning is less clear than linear indices [10]. The major aim of our study is to demonstrate that a concerted combination of time-variant, frequency-selective, linear and nonlinear analysis approaches can be beneficially used for HRV analysis in epileptic patients to reveal premonitory information regarding an imminent seizure and to provide more information on the mechanisms leading to changes of the autonomic nervous system. Each of these approaches is optimally suited in order to quantify certain signal characteristics, i.e., each is specialized to extract a specific type of information from the HRV. We will show that our analysis strategy reveals new insights into the specific timing and grouping characteristics of HRV rhythms before, during and after an epileptic seizure. Two rhythms are of particular interest: The HRV-related Traube–Hering– Mayer waves (Mayer waves) in the low-frequency (LF) range 0.04–0.15 Hz and the high-frequency (HF) range 0.15–0.4 Hz, in which respiratory sinus arrhythmia (RSA) occurs. Our working hypothesis is that phase properties of and between HRV components react sensitively before an EEG epileptic seizure occurs. This hypothesis is based on our findings with regard to patterns characteristic of EEG burst activity which are accompanied by strong phase coupling reactions in HRV [11]. We used HRV data derived from a previous clinical study in which HRV abnormalities in children and adolescents with temporal lobe epilepsy (TLE) were investigated [12]. The continuous Morlet-wavelet transform (MWT) is used as basis algorithms to compute frequency-selective time courses of both linear [power courses, phase-locking index (PLI)] and nonlinear indices (time-variant biamplitude and bicoherence). MWT offers the possibility of time-variant and frequency-selective investigations which can be interpreted in context to classical parameters of HR analysis [13]. Such time-variant HRV analyses in epileptic patients are very rare. Novak et al. [14] performed
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a time frequency HRV analysis (Wigner–Ville distribution) of adult patients with TLE and they extracted two frequency bands, a nonrespiratory and a respiratory band. The authors concluded that “time-frequency analysis revealed that autonomic activation hallmarks clinical seizure onset for several minutes.” However, Wigner–Ville distribution does not provide instantaneous phase information which we have utilized for our phase analyses. Kerem and Geva [15] have not found differences in mean group LF power, HF power and PR in preictal period compared with the period just before it. They investigated HRV records of TLE patients. Additionally, complete ensemble empirical mode decomposition with adaptive noise (CEMD) [16] is used to compute signal components [intrinsic mode functions (IMFs)] which are analyzed by the time-variant point prediction error (PPE) [17], which is a local estimation of the largest Lyapunov exponent. In this way, complementary amplitude-dependent as well as amplitude-independent linear and nonlinear characteristics of the heart rate (HR) signal can be analyzed in a time-variant, frequency-selective mode. Empirical mode decomposition (EMD) operates as a filter bank by remaining nonlinearity of the components. EMD was used in nonlinear HRV analysis [10], [18]. EMD as well as EMD-based approaches like Hilbert–Huang transform were successfully adapted for the assessment of cardiovascular autonomic control [19] and for analysis of HRV in cardiac health [20]. A problem of EMD procedure is the occurrence of “mode mixing.” Mode mixing corresponds to the alternative presence of several components of the signal of interest on the same IMF [21] and is frequently caused by the intermittency of segments with different signal properties, in particular different frequency characteristics. Advanced approaches like ensemble empirical mode decomposition (EEMD) and CEMD solve the problem of mode-mixing and provide a better spectral separation of the modes. Therefore, the combined application of CEMD and PPE to HR is the logical consequence. A comparison of different EMD-based methods and multivariate EMD in the analysis of EEG for the depth of anesthesia—in this approach, the nonlinear sample entropy was used—can be found in [22]. Using our approach of combined linear and nonlinear methods, profiles of timing and grouping characteristics for both rhythmic HRV components starting 5 min before and lasting 5 min after the seizure onset can be observed. These methodological results should be seen as a starting point for further studies including not only HRV but other vegetative parameters as well as EEG. II. DATA MATERIAL AND SUBJECTS Presurgical evaluation was performed at the Vienna pediatric epilepsy center following a standard protocol. EEG was recorded referentially from gold disc electrodes placed according to the extended 10–20 system with additional temporal electrodes. One-channel ECG was recorded from an electrode placed under the left clavicle. EEG and ECG data were recorded referentially against CPZ , filtered (1–70 Hz), converted from analog to digital (sampling frequency 256 Hz, 12 bit), and
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stored digitally for further data analysis. Video recordings of each seizure were reviewed to classify seizure type. Complex partial seizures were included, but not auras or generalized tonicclonic seizures. Seizure onset and termination in the EEG were determined independently by two neurologists experienced in the field of epilepsy and clinical electrophysiology (coauthor Prof. Martha Feucht and another physician of the Epilepsy Monitoring Unit, University Hospital Vienna, Austria). In case of different annotations, the results were discussed between both reviewers. EEG and ECG recordings including 10 min epochs (5 min before (preictal state) and 5 min after the seizure onset (seizure and postictal state)) were stored for each seizure. QRS detection was performed after band-pass filtering (10–50 Hz) and interpolation by cubic splines (interpolated sampling frequency 1024 Hz) to detect the time point of the maximum amplitude of each R-wave and the resulting series of events was used for the HR computation. The low-pass filtered event series (LPFES) was computed by applying the French– Holden algorithm [23]. The final HRV representation was obtained from the LPFES via multiplication with the sampling rate and with 60 beats per minute (bpm) and down sampled to 8 Hz. An artifact rejection was performed manually to minimize the influence of false QRS triggering. The HR data were analyzed in a previous study (visual analysis of heart rate) and the results were published by Mayer et al. [12]. From the group of 20 patients only those were selected who had at least one seizure with a recording time of 10 min (at least 5 min before and after seizure onset). Four children were added to the patients group to achieve comparable numbers of male/female patients and right/left focused seizures as in [12]. This resulted in a group of 18 children who had one seizure recording of at least 10 min (K = 18 seizures; median age 9 years 4 months, range 6 years 6 months to 18 years 0 months; median seizure length 88 s, range 52–177 s). All results were achieved by grand mean analysis over 18 seizures (=18 children). III. METHODS A. Analysis Framework The entire analysis framework is represented in Fig. 1 and consists of two complementary processing strands: the time– frequency MWT-based analysis and the signal-adaptive EMDbased analysis. In a first strand, we used the MWT characterized by a frequency-dependent time–frequency resolution for the computation of time-varying power spectrogram (PS) and the phase-locked power spectrogram (PSP L ) which is able to depict phase-locking (=time-locking) characteristics of the HRV components. The time-varying PSP L captures clusters of repetitive waves of HRV components, i.e., the timing and the grouping of their occurrence, by using a phase-remaining averaging. The repetitive occurrence of waves results in high values of the PSP L . This is an advantage in comparison to the PS which maps the power without consideration of phase locking. In addition, MWT is used for the computation of time-varying measures of band power derived from PS as well as PSP L in frequency
Fig. 1. Design of processing scheme. MWT as well as EMD-based strands of analysis are depicted.
ranges (LF and HF) which are chosen according to the standards of the task force “heart rate variability” [13]. The PLI based on MWT was used to identify time ranges in which the phase-locking characteristics are significant. This thresholding (α = 10%) is carried out by using the Rayleigh test. To study the time-variant coupling between HRV components, a time-variant bispectrum estimation was applied by which the time-variant quadratic phase coupling (QPC) between two HRV components can be detected and quantified. QPC is a nonlinear coupling phenomenon and we developed several time-variant bispectral approaches to analyze HRV [24], [25]. Our QPC implementation is based on MWT. In a second strand, the CEMD as an advanced EMD-based method was applied to HRV. The CEMD is a time-variant, signal-adaptive method which can be used for the analysis of nonstationary, nonlinear signals. It provides monocomponent signals (IMFs) by preserving nonlinear properties within the signals. The IMFs can be interpreted with regards to contents (physically, physiologically, etc.) and their band-pass distances (midfrequency) can be approximately described by a dyadic scaling [26]. The approximately dyadic distances of the IMFs’ pass-band midfrequencies agree rather well with frequency distances which are of interest in the analysis of HRV [13]. Accordingly, the IMFs can be seen as individually and adaptively filtered HRV components and thus the CEMD as the frequencyselective method. Finally, the PPE was estimated both with and without component selection via CEMD. The nonlinear PPEs characterize the time course of the predictability and with it the stability of the signal components.
B. Morlet Transform and Derived Time-Variant Parameters The mother wavelet of the MWT was adapted so that the sigma parameter of its Gaussian envelope equals one cycle for every frequency. The time-frequency resolution of the MWT is frequency-dependent. Higher frequencies lead to a better time
SCHIECKE et al.: TIME-VARIANT, FREQUENCY-SELECTIVE, LINEAR AND NONLINEAR ANALYSIS OF HEART RATE VARIABILITY
resolution to the disadvantage of frequency resolution (concrete time- and frequency resolution values: see Section IV-D). The frequency-dependent complex analytic signal y k (t, fn ) of the HRV (xk (t)) is computed using MWT (see [27]), where k (k = 1,. . . , K) designates the seizure recordings of our children (K = 18). The time-variant power spectrum P S k (t, fn ) and phase ϕk (t, fn ) can be calculated on the basis of the complex analytic signal for each recording k by 2 PSk (t, fn ) = y k (t, fn ) (1) and ϕk (t, fn ) = arg y k (t, fn ) .
(2)
By ensemble averaging the representative time-variant power spectrum (spectrogram) PS can be estimated PS (t, fn ) =
K 2 1 k y (t, fn ) . K
(3)
k =1
The time-variant PS quantifies the averaged spectral characteristics of our 18 recordings of the HRV in a time-frequency map representation. The ensemble averaging of the complex valued analytic signal leads to the estimation of the phase-locked power spectrogram PSP L 2 K 1 k PSP L (t, fn ) = y (t, fn ) . (4) K k =1
This procedure results in a phase-preserving average of the complex spectra of the 18 recordings of the HRV before calculating the spectrogram. Time-variant phase locking describes the stability of the phase ϕk (t, fn ) (decrease of phase jitter) of the frequency component fn for all 18 signal realizations at time point t. In this way, systematic phase-locked spectral components can be separated from phase “noise” [28]. From the PSk (t, fn ) according to (1) and from PSP L (t, fn ) according to (4) the mean band power for each sampling point was computed for the frequency bands 0.04–0.15 Hz (LF) and 0.15–0.4 Hz (HF). In this way, time-variant power courses (LFP—low frequency power, HFP—high frequency power) were computed (grand mean of 18 children). The band limits correspond with those which have been recommended for HRV analysis by the task force “heart rate variability” [13]. The LF and HF courses were normalized by LFPN = LFP/ (LFP + HFP) and HFPN = HFP/ (LFP + HFP). Additionally, the time course of the power ratio PR = LFPN /HFPN = LFP/HFP was used as a parameter. These abbreviations are expanded by the index “–PL” when the power parameters are derived from PSP L . The LFPN and LFPN -P L parameters can be seen as indicators for sympathetic and vagal modulation, whereas the HFPN and HFPN -P L parameters can be considered mainly (but not only) as parameters for respiratory vagal activity. The power ratios are computed as parameters of the sympathico-vagal balance. The phase-locking effect can be analyzed either by including the amplitude information (amplitude-dependent) using the
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time-variant phase-locked spectrogram PSP L (t, fn ) or by excluding the amplitude information (amplitude independent) using the phase-locking index PLI (t, fn ). The PLI is defined by K 1 k (5) PLI (t, fn ) = exp jϕ (t, fn ) . K k =1
The PLI represents the circular statistics for instantaneous phases for a certain set of trials (K = 18 recordings) and ranges between zero and one [29]. Additionally, the time-variant QPC between the frequency bands given above can be computed using time-variant biamplitude and bicoherence. QPC is a phase effect, that occurs, e.g., in the presence of amplitude modulations. If three rhythmic frequency components fm , fn , and fn + fm exist (fn fm ) and their phases are of the same type (ϕ (t, fn + fm ) = ϕ (t, fn ) + ϕ (t, fm )), then high biamplitude and bicoherence values indicate a QPC between fm and fn , i.e., a trace in the time-variant bispectral representation(s) at the coordinates fm , fn can be obtained. In the case of amplitude modulation, fm is the frequency of the modulating component (Mayer waves), fn is the frequency (carrier frequency) of the modulated component (RSA), and fn + fm is the frequency of the upper side band. Additionally, a second trace in the bispectral representation occurs at the coordinates fm , fn − fm because both components and a component of the combination frequency fm + (fn − fm ) = fn (=RSA) are present. For each seizure (k = 1,. . .,K), the following triple product can be calculated for every frequency pair (fm , fn ) and at each point in time B k (t, fm , fn ) = y k (t, fm) · y k (t, fn) · y k ∗ (t, fm +fn ) . (6) Here, ·∗ denotes the complex conjugate. The ensemble averaging of B k (t, fm , fn ) yields an estimation of the time-variant ˆ (t, fm , fn ). bispectrum B The time-variant bispectrum depends on the amplitudes of the frequency components (fm , fn , fn + fm ). For detecting phase couplings, the estimation of the time-variant bicoherence is used as an amplitude independent measure ˆ (t, fm , fn ) Γ
ˆ B (t, fm , fn ) = . k 2 1 k (t, f ) · y k (t, f )|2 · |y (t, f + f )| |y m n m n K (7)
To reduce the three dimensions of the time-variant bispectral measures resulting from (6) and (7) the mean biamplitude (mBA) and the mean bicoherence (mBC) were computed in regions of interest (ROI) F1 × F2 according to ˆ (t, fm , fn ) ˆ (t) = mean mean B mB F1
F2
ˆ (t, fm , fn ) . ˆ (t) = mean mean Γ mΓ F1
F2
(8)
Regarding to the main rhythms of HRV, we calculated timevariant bispectral measures in two different ROIs. First, we
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investigated QPC between the Mayer wave related LF component and the RSA-related HF component in the HRV, i.e., the ROI1 was set to F1 = [0.075 Hz, 0.15 Hz] and F2 = [0.25 Hz, 0.35 Hz]. Second, QPC between lower LF component and again the RSA-related HF component was analyzed, i.e., the ROI2 was set to F1 = [0.04 Hz, 0.075 Hz] and F2 = [0.25 Hz, 0.35 Hz]. C. Signal-Adaptive HRV Decomposition and the PPE The standard EMD separates the HRV into IMFs. The computation of an IMF by the iterative EMD algorithm [30] can be summarized as follows. 1) Identification of all local extrema. 2) Interpolation (cubic splines) between the maxima and between the minima which provides two envelope courses E (t)m ax and E (t)m in . 3) Calculation of the mean envelope and the difference between the mean envelope and the signal. 4) Iterate on the residuals until the criteria for the IMF is fulfilled. 5) The residuum is used instead of the signal to compute the next IMF. 6) The steps 1– 5 are repeated for each following IMF until the stopping criteria. The EEMD which relies on averaging the modes obtained by EMD applied to several realizations of Gaussian white noise added to the original signals solves the EMD mode mixing problem [31]. The CEMD provides a better spectral separation of the modes by adding a particular noise at each stage of the decomposition [16]. Therefore, we used CEMD to separate the HRV into IMFs. The IMFs of the HRV preserve nonlinear properties thereby allowing the introduction of a new concept, the combination of CEMD of the HRV with a time-dependent nonlinear measure, i.e., with the estimation of the PPE. Based on the approach of Takens [32] a 1-D signal x(t) is transformed into a multidimensional phase space by means of a time delay according to T (t) = {x (t) , x (t − τ ) , . . . , x(t − (De − 1) · τ }
(9)
where τ is the time delay, De is the embedding dimension, and T (t) is the trajectory in the phase space. A time delay of τ = 5 and an embedding dimension of De = 8 were used for our analysis. The false nearest neighbor approach [33] was used to set a sufficient embedding dimension. The time delay was estimated depending on the mutual information [34]. The stability analysis is based on the approach of Wolf et al. [35] for the estimation of the largest Lyapunov exponent, but measures the local exponential divergence of trajectories in the phase space similar to the approach of Gao and Zheng [36] who evaluated moving windows. In our approach, the nearest Euclidean neighbor must be searched for each point on a trajectory in the phase space. Changes in the distance between these points are evaluated after evolving a specific time step by PPE (t) =
D (t + i) fs log2 i D (t)
(10)
where t is the actual time point, D (t) the Euclidian distance to the next neighbor in the phase space at the time point t, D (t + i) the evolved distance at time point t + i, i the evolved time steps, fs the sampling frequency, and PPE(t) is the resulting sequence of locally estimated PPEs. Equation (10) reflects the degree of stability of any time point in relation to its initial condition (for theoretical details see [17]). The averaged time courses of the PPE were calculated. A positive PPE is equivalent to a divergence of neighboring points in the phase space and indicates a low predictability, a negative or vanishing PPE describes a quasi-periodic/periodic process or convergence in the phase space and indicates a high predictability. D. Statistical Measures The noncorrected Rayleigh test was used to create a trigger threshold for the detection of time segments of strong phase locking in a PLI time-frequency map. The null hypothesis is that the phases are uniformly distributed. Under this hypothesis, the PLI tends to zero. The application of the statistical threshold results in binary PLI-maps (0 = below the threshold or 1 = above the threshold). In this study, the significance level was α = 10%. In order to estimate confidence tubes of the mean time courses of the extracted parameters time courses without any particular distribution assumption, a bootstrap approach was used. One thousand bootstrap samples of size 18 (each sample element contains 4800 values/600 s) were drawn by a case resampling with replacement. With it 1000 bootstrap replications of each extracted parameters were computed. Based on these replications, the lower limit (the 2.5% quantile) defined the lower bound, and the upper limit (the 97.5% quantile) defined the upper bound of the confidence tube. Significant differences between extracted parameters at different time points were determined by using the Wilcoxon signed rank test (significance level 0.05). The phase-remaining averaging procedure provides only one mean-value course PSP L (t, fn ). Therefore, statistics are not available. IV. RESULTS A. Ensemble Averaging of the HR Courses In Fig. 2(a) and (b), the HR courses of all 18 seizures as well as the averaged HR course (bold black line) are depicted. Distinctive time points were determined and depicted in the simplified mean HR course [see Fig. 2(c)] and the preictal, ictal, and postictal periods are defined. The colored “bar code” of the sequence of time points was adapted to all other figures to define the distinct time points of our analysis. The averaged HR course [see Fig. 2(c)] is characterized by an approximately constant preictal HR course from 0 to 240 s around 85 bpm. In the following 60 s the HR slowly increases. After the EEG seizure onset (=300 s) the mean HR accelerates within 40 s to the maximum value of 135 bpm (=340 s). Thereafter a fast deceleration can be observed between 340 and 420 s and a slow, approximately linear decrease follows until the end
SCHIECKE et al.: TIME-VARIANT, FREQUENCY-SELECTIVE, LINEAR AND NONLINEAR ANALYSIS OF HEART RATE VARIABILITY
Fig. 2. Presentation of HR courses. In (a) the original and in (b) the centered HR course of all 18 seizures in gray, averaged HR course as a bold black line is depicted. Preictal, ictal, and postictal periods as well as distinctive time points in the HR course of seizure were determined and depicted in a simplified mean HR course [see Fig. 1(c)]. Bold black line determines the EEG seizure onset (300 s; end of preictal, beginning of ictal period), bold dashed black line the end of seizure (390 s; end of ictal, beginning of postictal period). Red line designates the onset of the preonset acceleration (240 s), blue line the maximum of the acceleration and begin of deceleration (340 s), and green line the end of the fast deceleration and begin of recuperation (420 s). The “bar code” of these distinct time points was transferred to Figs. 3–5 and Fig. 7. In (d) a zoom in (100 s before seizure onset) to the averaged HR course (bold black line) and the averaged filtered HR course (bold gray line, 0.1–0.15 Hz) is presented.
of our analysis interval (600 s; 96 bpm), i.e., the value of the averaged preictal HR has not been achieved. Fig. 2(d) depicts a zooming of the averaged HR course during the preictal period (between 200 and 320 s). Starting at 220 s (80 s before seizure onset), the occurrence of a strong Mayer wave related LF component in all investigated seizures is apparent. An increasing LF component occurs in all patients, however, a strong synchronization with regard to the seizure’s onset can be observed in 50% of the seizures. To emphasize this, the HR courses of all seizures were filtered [fast Fourier transform (FFT) filter; 0.1– 0.15 Hz], and the original averaged HR course (bold black line) was overlayed by the averaged filtered HR course (bold gray line). The averaged filtered HR course clearly depicts the start of strong LF components at 220 s. B. Time-Frequency Related PS, PSP L , and PLI Analysis The results of the MWT-analyses depict the interval between 0 and 600 s, where the seizure onset is at 300 s [see Fig. 3(a)]. In Fig. 3(b)–(d), the results of the PS, PSP L , and PLI grand mean analyses (18 seizures) are shown.
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Fig. 3. Grand-mean results (K = 18) of time-frequency related PS, PSP L , and PLI analysis (MWT based). In (a) the centered HR course [see Fig. 2(b)] is shown. In (b) the results of the PS analysis are depicted and overlayed by the averaged filtered HR course [black line; see overlay in Fig. 2(d)], (c) shows the results of the PSP L analysis and (d) the results of the PLI statistics analysis [color bar for (b) and (c): in bpm2 ; color code for (d): significant values in black].
The PS [see Fig. 3(b)] provides a clear separation of the Mayer-wave-related LF (around 0.1 Hz) and the RSA-related HF (around 0.3 Hz) range before the seizure onset (300 s). Both components are distinguishable between 0 to 100 s, become most apparent between 200 and 300 s (100 s before seizure onset) and collapse with the onset of seizure (when normal breathing changed dramatically; occurrence of ictal bradypnea [37]). Additionally, a lower LF component (around 0.05 Hz) is present in parallel to the Mayer wave related LF component. Approximately 90 s after the seizure onset (390 s; median duration of seizures) the LF and HF ranges recur with strong power disturbances (390–480 s) and become less pronounced at the end of our analysis interval (500–600 s). Phase-locked power PSP L [see Fig. 3(c)] is a part of the total power PS and can be observed in a similar time-pattern as PS (but with different characteristics) around 0.05 Hz (lower LF), between 0.1 and 0.2 Hz (Mayer wave related LF and higher) and around 0.3 to 0.4 Hz (RSA related HF and higher). Only the lower LF component and the higher frequencies of the phase-locked Mayer wave related LF as well as higher frequencies of the phase-locked RSA related HF are characterized by significant PLI [see Fig. 3(d)], and
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parison to the mean course of the preictal period. However, the preictal and the postictal courses do not differ significantly. For the normalized LF and HF courses significant differences between the ictal courses and both the pre- and postictal time courses exist. The PR is characterized by a peak before the onset of seizure, i.e., during the interval in which the HR is already accelerating (around 270 s), the PR is increasing due to the dynamics of the LFP increase and the HFP decrease. At the beginning of the postictal period short peaks exist indicating that the sympathico-vagal balance is still not achieved. Thereafter, the stabilization proceeds. The PSP L -based power band courses cannot be quantified statistically [grand mean analysis; see Fig. 4(b)]. However, they can be utilized to detect time segments in which phase locking is dominant. For the LF frequency range an increase of the LFPP L (and LFPN -P L ) occurs before (240 s) and at (300 s) seizure onset as well as at the end of the seizure (390 s). In particular, the HFPN -P L bands show high phase locking during the preictal period and after the ictal period which indicates a strong time locking to the onset of normal breathing. The time course of the PRP L does not show essential differences in comparison to the time course of the PR course. Sharp peaks are a result (caused by division) of temporary low HFPP L values. D. Time-Variant QPC Analysis
Fig. 4. Results (K = 18) of the time-variant band power courses (MWT based). In (a) the mean nonphase-locked (PS) and in (b) the grand-mean phase locked (PSP L ) LF and HF power courses (LFP, HFP, LFPP L , HFPP L ) as well as their normalized values (LFPN , HFPN , LFPN -P L , HFPN -P L ) are shown.
especially the LF component related peaks in the PLI occur more often between 200 and 300 s. C. Time-Variant Band Power Analysis The mean nonphase-locked [PS; see Fig. 4(a)] and phaselocked [PSP L ; see Fig. 4(b)] LF and HF power courses (LFP, HFP, LFPP L , HFPP L ) as well as their normalized values (LFPN , HFPN , LFPN -P L , HFPN -P L ) are depicted as instantaneous parameter courses (black lines) over the whole analysis interval in Fig. 4. Additionally, the time courses of the power ratios PR and PRP L were computed. Significant differences between time segments of the LF band cannot be observed for the whole time range. The HF parameter courses collapse after the seizure onset (when breathing changes dramatically). The HFP values during the seizure differ significantly in comparison to the whole preictal course and differ only partially to the postictal course. The mean postictal HF course shows higher power values and a higher variation (broader confidence tube) in com-
Bispectral analysis was performed on the base of MWT. For PS, PSP L , PLI analysis and band power time courses, the mother wavelet was adapted so that the sigma parameter of its Gaussian envelope equals one cycle for every frequency. The resulting time-frequency resolution is essential to analyze the time pattern of linear activity but inadequate for bispectral analysis (frequency resolution is too low; missing “side bands of frequencies”; for reference see [38]); therefore, the mother wavelet had to be readapted to the situation. We used the standard deviation of the Gauss envelope in the time domain and the standard deviation of the Gauss curve in the frequency domain as measure for the time and frequency resolution [38]. For Fig. 5, the following time and frequency resolutions result for the RSA and the Mayer waves: time/frequency resolution in Fig. 5(a) = 5 s/0.2 Hz for 0.3 Hz (“RSA”) and = 15 s/0.06 Hz for 0.1 Hz (“Mayer waves”); time-/frequency resolution in Fig. 5(b) = 12 s/0.08 Hz for 0.3 Hz (“RSA”) and =36 s/0.02 Hz for 0.1 Hz (“Mayer waves”). The grand mean results of the time-variant mean biamplitude (mBA) and bicoherence (mBC) in the ROI between the Mayer wave related LF (at about 0.1 Hz) and HF range (ROI1 ) as well as between lower LF (at about 0.05 Hz) and HF range (ROI2 ) are depicted in Fig. 5(c) and (d). The time courses provide information about the QPC from two different viewpoints: amplitude-dependent and amplitudeindependent. The mBA and mBC courses depict mainly the same time pattern for both investigated ROIs [see Fig. 5(c) and (d)]. The mBA shows lower values during the preictal period (100–220 s) and rises with a peak at the beginning of the preonset acceleration (240 s) and at seizure onset (300 s). Thereafter the values drop down until end of seizure (300–390 s). The termination of seizures is accompanied by a rise of mBA up
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Fig. 6. FFT-based mean spectra (K = 18) of original HRV and EMD-based components IMF1 and IMF5 –IMF8 . The color code of the different IMFs is shared with Fig. 7.
RSA). These findings indicate that modulation of the RSA by both LF components seems to be the source for the QPC. E. Time-Variant Nonlinear EMD-Based PPE Analysis
Fig. 5. Grand-mean results (K = 18) of the time-variant QPC analysis (MWT based). In (a) the time-frequency related PS with a frequency resolution as in Fig. 3(b) is shown, in (b) the time-frequency related PS with a frequency resolution appropriate for bispectral analysis is presented (color bar for (a) and (b): in bpm2 ). White lines indicate the carrier frequencies (solid) and side frequencies (dashed) for the amplitude modulation of the RSA by the 0.05 Hz wave before and after the seizure, i.e., such a constellation of frequency components most probably causes the high bispectral values in ROI2 . In (c) resulting mBA and in (d) resulting mBC courses are shown for investigated ROI1 : (0.075–0.15 Hz ⇔0.25–0.35 Hz; blue lines) and for ROI2 : (0.04–0.075 Hz ⇔0.25–0.35 Hz; red lines).
to peak at the beginning of the recuperation of averaged HR (420 s) and is followed by a decrease of mBA up to the end of the evaluation period. The amplitude-independent observations of QPC provided by the mBC courses [see Fig. 5(d)] allows similar conclusions with regard to the preictal, ictal as well as the recuperation periods validating the suggestion that the revealed effect of QPC is not caused only by changes of amplitude. Time courses of mBA and mBC increase and decrease is following the patterns of phase-locked components of the LF and HF ranges. This can be understood by means of the spectrogram with higher frequency resolution [see Fig. 5(b)]. With the identification of the carrier frequency (RSA), side frequencies may be determined (e.g., for ROI2 : ≈0.32 ± 0.05 Hz; designation by white lines in Fig. 5(b) before seizure onset). Side frequencies can also be detected at ≈0.32 ± 0.1 Hz (Mayer waves modulate
CEMD was used to decompose the HRV into IMFs. FFTbased spectra of the HRV and IMFs were computed to define the components of interest. The fifth to eighths IMFs agreed rather well with frequency distances which are of interest in the analysis of HRV. First IMF was analyzed as a reference outside the frequencies of interest. FFT-based spectral analyses of the IMFs (see Fig. 6) show that IMF1 is mainly related to “noise,” IMF5 to the HF component (RSA, ≈0.3 Hz), IMF6 to the upper part of the LF component (≈0.15 Hz), IMF7 to the blood pressure related Mayer waves (≈0.1 Hz); and IMF8 to the lower part of the LF component (≈0.05 Hz). In Fig. 7, the averaged PPE time courses as well as confidence tubes are shown for the unprocessed HRV signals (a) and for the five IMFs analyzed (b–f). The averaged PPE of the HRV signals [see Fig. 7(a)] starts to decrease around 250 s [50 s before seizure onset) After seizure onset the PPE further decreases (minima at 320 s; significant difference to all other time points)] indicating that the HRV signal is more stable (tachycardia after the onset and up to the maximum of acceleration of HR during seizure; almost no other frequency components). The mean PPE values of the preictal and the postictal periods show significant differences which indicate an incomplete recuperation process. The PPE values of the postictal period are lower and are characterized by smaller confidence tubes, both indicating a more regular behavior of HRV pattern. The IMF1 -related averaged PPE fluctuates between values of 0.6 to 0.7 indicating the expected poor predictability (“noise”) of the IMF1 over the whole analysis interval [see Fig. 7(b)] and no significant differences between preictal, ictal, and postictal period. The averaged PPE of the remaining IMFs [see Fig. 7(c)–(f)] are all characterized by a better predictability (PPE values of 0.1 to 0.4 for the preictal period). Their predictability starts to increases around 220 s for IMF5 (80 s before seizure
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Fig. 7. Results of time-variant nonlinear PPE analysis (EMD based). Timecourses of the mean PPE and their confidence tubes (95%) are presented (K = 18). Mean PPE was calculated for the original HR signal (a) and for IMF1 and IMF5 –IMF8 (b)–(f).
onset; “RSA”), around 200 s for IMF6 (100 s before seizure onset; “upper LF”), around 220 s for IMF7 (80 s before seizure onset; “Mayer waves”) and around 270 s for IMF8 (30 s before seizure onset; “lower LF”). The minima of the further decrease of the PPE (increase of predictability) and the significant difference to all other time points can be found at 320 s for IMF5 to IMF8 , but time pattern of these processes differ between the IMFs. The significant differences of the mean PPE values of the preictal and the postictal periods indicating the incomplete recuperation process appears (besides the unprocessed HRV signals) only for IMF5 (“RSA”) and IMF7 (“Mayer waves”). V. SUMMARY AND CONCLUSION Our methodological study demonstrates the possibilities and advantages of a combination of time-variant, frequency-selective analysis methods by which specific linear and nonlinear HRV properties can be revealed. MWT-based and EMD-based methods were combined to achieve a better interpretability of acute changes in the HR in the preictal, ictal and postictal period of the seizure.
We did not find premonitory information regarding an imminent seizure by means of time-variant power analysis. The nonlinear bispectral analysis describes the QPC between the LF and HF components and was used, e.g., by Chen et al. [39] in HR analyses. As shown in neonatal heart rate analysis the QPC is caused by an amplitude modulation of the HF components by the LF components (Mayer waves modulate the amplitude of RSA [24]). Thus, the time-variant QPC approach complements linear time-variant frequency-selective analyses. The usefulness of the integration of nonlinear time/frequency-based methods and nonlinear stability/causality-based methods was shown by a combined use of time-variant QPC and PPE analysis to characterize nonlinear properties of the electrocorticogram [17]. The PPE is a local estimation of the largest Lyapunov defining the theoretical nonlinear predictability and thus stability of a signal. The contribution of our approach is to achieve the frequency selectivity of the nonlinear PPE by its application to IMFs being the result of the EMD which separates signal components from the whole signal. By means of our advanced time-variant and frequencyselective processing scheme characteristics of the HR before, during and after TLE seizure in children were investigated and quantified. The epileptic seizure is a time-dependent process and HR analysis of the preictal state may provide information with regard to coupling mechanisms between the involved cortical structures and the autonomic nervous system. A possible goal is to detect HR changes which signal the developing seizure and/or give new physiological insights to the periods before the seizure onset. A result which has been confirmed by many studies is that an increase of the HR precedes the EEG seizure onset by up to about 50 s (mean difference 13.7 s) in 75%–80% of TLE patients [40], this effect is more pronounced in mesial TLE. With regard of the time-consuming EMD-based and time-variant nonlinear methods seizure prediction is not the focus of our approach. We used HR data from a clinical monitoring protocol without any coregistration of respiratory movements, blood pressure and other vegetative parameters. Therefore, the physiological interpretation of our findings is limited. Nevertheless, we have found several new physiological phenomena and we have quantified the dynamics of known effects. Both can be used to develop advanced working hypotheses for more in-depth studies. It could be suggested that the phase-locking characteristics of the LF component, approximately 1 min before onset, is attributed to a transient influence of developing neural seizure activity on the autonomic nervous system. This phase locking leads to a peak in PRP L which suggests for a transient disturbance of the sympathico-vagal balance. The mean HR [see Fig. 1(c)] is characterized by LF waves starting at the time point 150 s and lasting until the seizure onset. This time interval is also characterized by a biamplitude peak which indicates a coordination between LF and HF components (Mayer waves and RSA, [24]). We have described a quasi-rhythmic QPC in the HRV of neonates during quiet sleep [24]. It may be possible that the QPC peak is part of a spontaneous long-term QPC fluctuation. To study this phenomenon in detail, the preictal analysis interval must be extended and respiration as well as blood pressure
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should be recorded simultaneously. Furthermore, these investigations can be complemented by investigations of coordination between HRV and EEG [11]. The phase locking of the HF component shortly before seizure onset and before normal breathing changed can be interpreted as a possible influence of the developing central ictal activity on the brainstem reticular networks. Hypopnea and apnea with oxygen desaturation have been observed with partial seizures [41]. The compensatory respiratory reaction resulting from oxygen desaturation is indirectly indicated by a higher mean HFP (deeper breathing) at slower frequencies before the end of the ictal and during the postictal period. This could minimize the cardiac workload; experimental modeling has shown that the cardiac workload is minimized for RSA-like HR functions, most significantly with slow and deep breathing [42]. The PPE values of the IMF5 of the postictal period [see Fig. 7(c)] remain lower than the values of the preictal state, this perpetuated stability of the RSA points to long-term compensatory mechanisms after the seizure. A causal analysis of these interesting HRV characteristics could only be performed by long-term recordings of cardiovascular–cardiorespiratory parameters. Our methodological investigation demonstrates that the use of advanced HRV analysis methods adds to an improved understanding of how epilepsy affects the autonomic nervous system and may have the potential for a better detection and interpretation of the dynamic influences of the central nervous system on the autonomic nervous system in general. Advanced HRV analysis can be applied to any other time-dependent process with known physiological meaning of different frequency characteristics. Our approach serves as a starting point for further studies including not only HRV but other autonomic parameters. The importance of the investigation of autonomic functions in patients with epilepsy in clinical practice was highlighted recently by a meta analysis of HRV in epilepsy [8]. REFERENCES [1] B. Moseley, L. Bateman, J. J. Millichap, E. Wirrell, and C. P. Panayiotopoulos, “Autonomic epileptic seizures, autonomic effects of seizures, and SUDEP,” Epilepsy Behav., vol. 26, pp. 375–385, 2013. [2] S. Shorvon and T. Tomson, “Sudden unexpected death in epilepsy,” Lancet, vol. 378, pp. 2028–2038, 2011. [3] M. Dutsch, M. J. Hilz, and O. Devinsky, “Impaired baroreflex function in temporal lobe epilepsy,” J. Neurol., vol. 253, pp. 1300–1308, 2006. [4] O. M. Doyle, A. Temko, W. Marnane, G. Lightbody, and G. B. Boylan, “Heart rate based automatic seizure detection in the newborn,” Med. Eng. Phys., vol. 32, pp. 829–839, 2010. [5] K. Jansen and L. Lagae, “Cardiac changes in epilepsy,” Seizure, vol. 19, pp. 455–460, 2010. [6] C. Sevcencu and J. J. Struijk, “Autonomic alterations and cardiac changes in epilepsy,” Epilepsia, vol. 51, pp. 725–737, 2010. [7] R. S. Delamont and M. C. Walker, “Pre-ictal autonomic changes,” Epilepsy Res., vol. 97, pp. 267–272, 2011. [8] P. A. Lotufo, L. Valiengo, I. M. Bensenor, and A. R. Brunoni, “A systematic review and meta-analysis of heart rate variability in epilepsy and antiepileptic drugs,” Epilepsia, vol. 53, pp. 272–282, 2012. [9] U. Rajendra Acharya, K. Paul Joseph, N. Kannathal, C. M. Lim, and J. S. Suri, “Heart rate variability: A review,” Med. Biol. Eng. Comput., vol. 44, pp. 1031–1051, 2006. [10] R. Maestri, G. D. Pinna, A. Porta, R. Balocchi, R. Sassi, M. G. Signorini, M. Dudziak, and G. Raczak, “Assessing nonlinear properties of heart rate variability from short-term recordings: Are these measurements reliable?” Physiol. Meas., vol. 28, pp. 1067–1077, 2007.
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[39] Z. Chen, E. N. Brown, and R. Barbieri, “Characterizing nonlinear heartbeat dynamics within a point process framework,” IEEE Trans. Biomed. Eng., vol. 57, no. 6, pp. 1335–1347, 2010. [40] F. Leutmezer, C. Schernthaner, S. Lurger, K. Potzelberger, and C. Baumgartner, “Electrocardiographic changes at the onset of epileptic seizures,” Epilepsia, vol. 44, pp. 348–354, 2003. [41] A. S. Blum, “Respiratory physiology of seizures,” J. Clin. Neurophysiol., vol. 26, pp. 309–315, 2009. [42] A. Ben-Tal, S. S. Shamailov, and J. F. Paton, “Evaluating the physiological significance of respiratory sinus arrhythmia: looking beyond ventilationperfusion efficiency,” J. Physiol., vol. 590, pp. 1989–2008, Apr. 15, 2012.
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