Comparison of Fast Fourier Transform and Autoregressive Spectral Analysis for the Study of Heart Rate Variability in Diabetic Patients

International Journal of Cardiology 104 (2005) 307–313 www.elsevier.com/locate/ijcard

Comparison of fast Fourier transform and autoregressive spectral analysis for the study of heart rate variability in diabetic patients

Denis ChemlaT, Jacques Young, Fabio Badilini, Pierre Maison-Blanche, He´le`ne Affres, Yves Lecarpentier, Philippe Chanson

Service de Physiologie Cardio-Respiratoire and Service d’Endocrinologie, Centre Hospitalo-Universitaire de Biceˆtre, Assistance Publique-Hopitaux de Paris, Universite´ Paris Sud 11, 78 rue du Ge´ne´ral Leclerc, 94 275 Le Kremlin Biceˆtre, France Unite´ Propre de l’Enseignement Supe´rieur 2705, Universite´ Paris-Sud 11, 92 141 Clamart, France

Received 8 June 2004; received in revised form 13 September 2004; accepted 7 December 2004 Available online 21 February 2005

Abstract

Introduction: Impaired heart rate variability (HRV) is associated with poor outcome in diabetic patients. The present prospective study compared spectral components of HRV obtained by either fast Fourier transform (FFT) or autoregressive (AR) analyses in diabetic patients. Methods: Thirty patients (49F12 years; 11 F/19 M; 60% with insulin-dependent type 1 diabetes) underwent 24-h ambulatory electrocardiographic recordings which comprised a 10-min resting period at the onset (n=30) and end (n=12) of the monitoring. Spectral analysis was applied to 5-min sequences at rest, and the total power and power spectra integrated over the very low (VLF), low (LF), and high (HF) frequency bands were obtained. Results: Fifteen patients had moderately depressed HRV and two patients had highly depressed HRV (standard deviation of the RR intervals over 24-hb100 ms and b50 ms, respectively). Both raw data and ln-transformed data were significantly different between FFT and AR. All spectra component were obtained in each patient using FFT. Using AR, the LF/HF ratio could not be estimated or was zero in 4 and 11 patients, respectively. The AR results were more sensitive than FFT results to minor changes (F5%) in the timing of the onset of analysis. The day-to-day reproducibility of FFT was better than that of AR. Finally, using FFT, the LF/HF ratio, LFnu, and HFnu were essentially redundant (nu=normalized units). Conclusions: The spectral components of short-term HRV calculated by using the FFT and AR methods were not interchangeable and FFT analysis must be preferred in diabetic patients. D 2005 Elsevier Ireland Ltd. All rights reserved.

Keywords: Heart rate; Autonomic tone; Autonomic neuropathy

1. Introduction The critical evaluation of HRV tests is therefore important if one considers: i) the high incidence of diabetes in the Cardiovascular autonomic neuropathy is a complication normal population; ii) the high incidence (~20%) of of diabetes which results from damage to the autonomic abnormal cardiovascular autonomic function in diabetes; nerve fibers that innervate the heart and blood vessels, thus and iii) the association between impaired HRVand increased leading to decreased heart rate variability (HRV) and risk of life-threatening cardiovascular events in these abnormal blood pressure control. Indexes of HRV are useful patients [7,16,35]. to detect the early impairment in autonomic tone at a time Two HRV methods are most often applied, namely when dysautonomia is not yet clinically patent [6,15,35]. bedside tests and the 24-h ambulatory electrocardiogram. The complete battery of classic autonomic tests is of great value but is long to perform and requires good cooperation T Corresponding author. Tel.: +331 45 21 25 63; fax: +331 45 21 37 78. from the patient, and it only examines short-term HRV in E-mail address: [email protected] (D. Chemla). the time-domain [16]. As the 24-h ambulatory ECG

0167-5273/$ - see front matter D 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.ijcard.2004.12.018 308 D. Chemla et al. / International Journal of Cardiology 104 (2005) 307–313 examines both short-term and long-term HRV in both the ous system status were assessed by a physician unaware time- and frequency-domain, this simple and sensitive after the HRV results. Sixteen patients had peripheral method is increasingly used in diabetic patients [5]. The neuropathy and four patients had clinical signs of recommendation to use standardized duration of recordings dysautonomia. for HRV assessment has been proposed to enable comparisons of research studies [34]. The 24-h standard 2.2. Data acquisition and analysis deviation of normal RR intervals (SDNN) provides a simple and sensitive scale of cardiovascular risk, while the Ambulatory electrocardiographic recordings were spectral analysis of HRV over 5 min helps to quantify the acquired with a dual-lead analog Holter recorder (SEER, sympathovagal balance alterations which play an important Marquette-Helige, GE Medical Systems, Velizy, France). role in the pathophysiology and prognosis of the disease Holter was positioned in the morning. A 10-min resting [23,25,34]. period was performed at the onset of the recording period In the frequency-domain, HRV is described as the sum of in all patients. In a subset of twelve patients, a 10-min elementary oscillatory components defined by their fre- resting period was also performed at the end of the quency and amplitude (power). Physiological mechanisms recording period in order to test the day-to-day reprodu- responsible for power components cannot be considered cibility of the measurements. Patients were instructed to stationary during the 24-h period, and short-term analyses behave in a normal manner during 24 h. Analog data were under controlled conditions are therefore recommended (i.e., digitized at 200 Hz and edited by a cardiologist on a Mars 5 min at rest) [34]. Two spectral methods can be used, 8000 Laser Holter station (Marquette-Helige, GE Medical namely the fast Fourier transform (FFT) [2] and the Systems, Velizy, France). The validation procedure con- autoregressive (AR) methods [19,25,28]. Spectral frequency sisted of beat labeling and tagging of noisy regions. Both components are either integrals of power spectrum density ECG raw data and annotation were transferred to a over specific bands (FFT) or components automatically personal computer for dedicated HRV analysis [3,4].In determined by autoregressive algorithms (AR). As recently an attempt to rule out the hypothesis that potential pointed out, a study comparing the two methods is differences between FFT and AR results would be due to important for the proper interpretation of spectral data in technical limitations or specific features of the Holter terms of physiologic and pathologic processes [22], and recordings, only sinus rhythm, high-quality recordings previous studies have compared the two methods in healthy were selected for entering the final analysis. Exclusion subjects [3,29] and in hypertensives [4]. In diabetic patients, criteria related to recording characteristics included: noisy both the FFT method [8–11,20,21,36] and the AR method regions with absence of at least one good quality lead [6,7,13,31,32] have been used, but up to now no study has (n=11), N2% ectopic beats or ectopic beats occurring compared the results of the two methods. during the 10-min resting period (n=9), a duration b24 h The aim of the present study was to compare short-term (n=1), previously unrecognized atrioventricular block spectral HRV measurements obtained by FFT and AR (n=1), and movements during the resting period (n=1). methods in diabetic patients. We tested whether or not the two methods provide interchangeable estimates of spectral 2.3. Heart rate and heart rate variability HRV in diabetic patients. Time- and frequency-domain HRV variables were calculated as previously described [3,4].Time-domain 2. Material and methods variables included: mean sinus heart rate (HR), average RR interval (NN), standard deviation of the RR intervals 2.1. Study population (SDNN), percentage of normal consecutive RR intervals differing by N50 ms (pNN-50), and root mean of squared The subjects included in this prospective study were successive differences (RMSSD). From a theoretical point diabetic patients hospitalized in our diabetes care unit. of view, spectral analysis requires rigorous stationary Informed consent was obtained for each patient and the conditions which are unknown to biology and medical study protocol conformed to the ethical guidelines of the science [23]. Short-term analyses under controlled condi- 1975 Declaration of Helsinki as reflected in a priori tions are therefore recommended, and it is now admitted that approval by the Institution’s human research committee. the analysis of 5-min resting ECG offers a reasonable, Patients with known cardiovascular diseases or rhythm practical compromise [22,34]. Editing of the tachograms disturbances were excluded from the study and all patients may also help eliminate the runs with step changes of major were free of any cardiovascular medication. Thirty trends in the tachogram [23,34], as performed in the present diabetic subjects aged 49F12 years, 19 men and 11 study. The FFT power spectra were calculated with the women, 18 with insulin-dependent type 1 diabetes and 12 method of average periodogram, also called the Walch with non-insulin dependent type 2 diabetes, were recruited periodogram, as previously described [3,4] and recommen- consecutively. Neurological status and autonomous nerv- ded [34]. The AR power spectra were obtained as D. Chemla et al. / International Journal of Cardiology 104 (2005) 307–313 309

Table 1 reference T0 period, namely T0À15 sec, T0 and T0+15 Time domain heart rate variability parameters at rest over a 5-min period sec. Coefficient of variation was calculated as [(S.D./ (n=30) mean)Â100]. The measurements at onset and end of the F Mean S.D. Range recording (n=12) were compared using paired t test and NN (ms) 822F127 600–1120 calculation of the mean bias. A P valueb0.05 was F SDNN (ms) 31 24 5–125 considered statistically significant. pNN-50 (%) 6F13 0–53 RMSSD (ms) 25F27 6–145 NN: normal RR intervals. SDNN: standard deviation of the RR intervals. pNN-50: percentage of normal consecutive RR intervals differing byN50 3. Results ms. RMSSD: root mean of squared successive differences. The results of the time-domain analysis at baseline are given on Table 1. Using published 24-h SDNN cutoffs of previously described [3,4]. In brief, identification of the moderately depressed HRV (50 to 100 ms) and highly model was achieved with a recursive Levinson–Durbin depressed HRV (b50 ms) [34], 15 patients (50%) had algorithm for the determination of model parameters [19] moderately depressed HRV and 2 patients (7%) had highly and Akaike criterion for the choice of model order [1]. The depressed HRV (Fig. 1). The FFT and AR results obtained frequency-domain variables included the total power (TP) during the 5-min resting period at the onset of the recording spectrum (0 to 0.4 Hz) and the power spectra integrated over are given on Table 2. With the exception of HF, frequency- very low frequency (VLF, 0 to 0.04 Hz), low-frequency (LF, domain variables were not interchangeable when FFT and 0.04 to 0.15 Hz), and high-frequency (HF, 0.15 to 0.4 Hz) AR methods were compared. Major differences were bands. observed between FFT and AR mean results and the mean It is widely believed that i) the HF power reflects vagal bias was huge for each frequency-domain variable but HF modulation of the heart rate; ii) both the LF power and the (Table 2). Similar results were obtained when log-trans- LF/HF ratio reflect a complex interplay between sympa- formed values were considered. thetic and parasympathetic modulation of heart rate; and iii) All spectral components were obtained in each patient the physiological meaning of the VLF power assessed from using the FFT method. Conversely, using the AR method, short-term recordings (~5 min) is less defined and its there were several null or missing values for LF and HF. In interpretation is not recommended when discussing power twelve patients, the power spectra integrated over the low- spectra density results [34]. In the present study, the LF/HF frequency band was null, thus resulting in a null LF/HF ratio was used to quantify the sympathovagal balance, as ratio. In one patient, the power spectra integrated over the previously proposed [23–26,28,34], although it must be high-frequency band was null such that it was not possible noted that there is still an active debate about the exact physiological meaning of LF, HF, and the LF/HF ratio SD-NN (msec) [14,15,22,27]. Measurements of LF and HF components were made in 200 2 absolute values of power (ms ) and in normalized units (nu, 180 in %) which represent the relative value of each power component in proportion to the total power minus VLF 160 component. Finally, log-transformed values were also 140 calculated to normalize the distribution. 120

2.4. Statistical analysis 100

Data are presented as meansFS.D. Time-domain 80 parameters were calculated over the 24-h period. Both 60 time-domain and frequency-domain parameters were also calculated over 5 min during the resting periods 40 performed at the onset and end of the recordings. At the baseline, differences between FFT and AR methods were 20 studied i) by using paired t test; ii) by calculating the 0 mean bias [100Â(ARÀFFT)/(AR+FFT)/2]. The influence 500 600 700 800 900 1000 1100 of mild changes in the onset of the analysis was tested by mean N-N (msec) varying by 5% (15 msec) the onset of analysis. We Fig. 1. Individual values for 24-h-mean NN and 24-h SDNN in the study studied the first 5-min resting period at the onset of the population (n=30). 15 patients had moderately depressed heart rate monitoring (n=30). We studied three overlapping 5-min variability and 2 patients had highly depressed heart rate variability (24-h resting periods spaced out F15 sec apart from the SDNN ranging from 50 to 100 ms and b50 ms, respectively). 310 D. Chemla et al. / International Journal of Cardiology 104 (2005) 307–313

Table 2 Table 4 Comparison between fast Fourier transform (FFT) and autoregressive (AR) Day-to-day reproducibility of fast Fourier Transform (FFT) and autore- methods at baseline gressive (AR) variables (n=12) FFT AR P value Onset of the End of the P value Mean bias F TP (ms2) 958F1589 1270F2201 0.05 24-h recording 24-h recording % S.D. VLF (ms2)113F217 442F490 0.0002 NN (msec) 783F113 770F155 0.63 2F11 LF (ms2) 364F439 222F428 0.05 SDNN (msec) 30F31 21F11 0.31 17F41 HF (ms2) 348F1113 485F1579 0.18 LF/HF (–) using 3.50F3.17 3.04F2.09 0.53 2F74 ln-TP 5.98F1.43 6.30F1.35 0.0001 FFT method ln-VLF 4.64F1.46 5.40F1.41 0.0001 LF/HF (–) using 0.96F1.67 2.72F3.80 0.20 102F105 ln-LF 5.50F1.04 5.02F1.54 0.0103 AR method F F ln-HF 4.35 1.75 4.54 1.72 0.0001 NN: normal RR intervals. SDNN: standard deviation of the RR intervals. F F LFnu (%) 61 22 32 32 0.0001 LF: low-frequency band. HF: high-frequency band. HFnu (%) 31F18 54F26 0.0001 LF/HF (–) 3.20F2.57 1.12F1.60 0.0003 Values are meansFS.D. FFT: fast Fourier transform method. AR: autoregressive method. TP: total power. VLF: very-low frequency band. 92% of the variability of SDNN, while LF and the LF/HF LF: low-frequency band. HF: high-frequency band. nu: normalized units. ratio had not significant additional value. In a subset of 12 patients, the 5-min recordings were analyzed both at onset and end of the Holter. The day-to-day to calculate the LF/HF ratio. It was not possible to compute reproducibility was good for time-domain variables (mean any value for LF in one patient, for HF in one patient and bias ranging from 2% to 17%), was mild-to-moderate for for both HF and LF in one patient. Similar results were frequency-domain FFT variables (mean bias ranging from obtained when various fixed model order values were 2% to 39%), while reproducibility was poor for frequency- imposed. When only the patients with a complete data-set domain AR variables (mean bias ranging from À27% to were considered (i.e., with non-zero LF, HF, and LF/HF 102%). The LF/HF ratio obtained by using the FFT method values using the AR method; n=15), same results as those appeared more reproducible than that obtained by using the observed in the overall population were obtained when FFT AR method (Table 4). and AR were compared. At baseline, using the FFT method, the sum of the LF F When the onset of analysis was modified by 5%, the 5- and HF spectral components was b80% of the total power min time-domain variables of HRV appeared stable, as minus VLF difference in only two patients (50% and 64%, attested to by the low coefficient of variation of NN respectively), thus indicating a significant spectral compo- F F F (0.2 0.1%), SDNN (3 5%), pNN50 (5 7%), and nent N0.40 Hz. In the remaining 28/30 patients, the sum of F RMSSD (3 6%). The 5-min frequency-domain FFT the LF and HF spectral components encompassed for variables were also poorly modified (Table 3). Conversely, 94F5% of the total power minus VLF difference. As a using the AR method, both LF the LF/HF ratio appeared result, LFnu, HFnu, and the LF/HF ratio were essentially extremely sensitive to initial conditions of the analysis, as redundant in these patients (Fig. 2). attested to by their 47% and 44% coefficient of variation, respectively (Table 3). Over the first 5-min resting period, the SDNN was HFnu (%) positively related to FFT indices, especially TP, as expected 100 (R=0.94; Pb0.001). The SDNN was also related to HF (R=0.81) and LF (R=0.80; each Pb0.001) but no the LF/HF 90 ratio. Using multivariate analysis, TP and HF explained 80

Table 3 60 Short-term stability of frequency-domain heart rate variability parameters at rest using the moving average analysis 50 FFT AR P value 40 Cvar-TP (%) 8F57F9 0.38 30 Cvar-VLF (%) 13F11 13F15 0.76 Cvar-LF (%) 10F647F55 0.0044 20 Cvar-HF (%) 5F36F6 0.49 Cvar-(LF/HF) (%) 10F544F55 0.0115 10 Stability was tested at rest by analyzing three overlapping 5-min periods 0 spaced out F15 sec apart from the reference T0 period (TÀ15 sec; T0; 0 2 4 6 8 10 12 T+15 sec; see Methods). Coefficients of variation (Cvar) are expressed as LF / HF percentages and meanFS.D. values are given. FFT: fast Fourier transform method. AR: autoregressive method. Fig. 2. Relationship between HFnu (%) and the LF/HF ratio. D. Chemla et al. / International Journal of Cardiology 104 (2005) 307–313 311

4. Discussion have a higher reproducibility of spectral indices than healthy subjects [18,29,33] although conflicting results have been Impaired heart rate variability is associated with poor published in diabetic subjects [9,17,30]. In our study outcome in diabetic patients, and the ambulatory electro- involving 57% patients with moderately-to-highly depressed cardiogram is increasingly used to precisely quantify the HRV, the day-to-day reproducibility of 5-min time-domain HRVof diabetic patients in the time- and frequency-domain. HRV indices was good, the day-to-day reproducibility of Given the high incidence of diabetes and the high incidence FFT was moderate, and that of AR was weak. Importantly, of abnormal cardiovascular autonomic function in diabetes, FFT was less sensitive than AR to minor changes in the it is important to critically evaluate the two spectral methods timing of onset of the analysis. currently used. The present prospective study indicated that Overall, our results confirmed in diabetic patients that the the fast Fourier transform and autoregressive analyses two methods were not interchangeable and indicated that the provide significantly different estimates of heart rate AR analysis may be unreliable in these patients. Indeed, we variability in resting diabetic patients. The spectral compo- feel that the unusually high frequency of zero- or missing- nents of HRV calculated by using the two methods were not values, the low day-to-day reproducibility and marked interchangeable and the FFT analysis must be preferred to sensitivity to small changes in the onset of analysis make AR for the following reasons: i) all spectra components it impossible to recommend the current use of the AR were obtained in each patient using FFT while numerous method in diabetic patients. Consistently, the uncertainty of null or missing values were obtained using the AR method; the AR estimates has been previously pointed out in a ii) the AR results were more sensitive than FFT results to theoretical study concluding that one must be careful in minor changes (F5%) in the timing of the onset of analysis; assigning pathophysiological origins to specific features of iii) the day-to-day reproducibility of FFT was better than the AR spectral components [12]. that of AR. Finally, by applying FFT over a 5-min resting Because the AR analysis is one of the methods currently period, the LF/HF ratio and LFnu and HFnu (nu=normal- used to quantify HRV in numerous diseased populations ized units) were essentially redundant in diabetic patients. including diabetic patients, the reasons explaining our Significant differences between raw powers obtained by results must be discussed. From a theoretical point of view, using FFT and AR analyses have been reported in healthy the uncertainty of AR estimates appears related to the [3] and hypertensive [4] subjects. Differences in quantitative method per se rather than to the cardiovascular field of results are explained by the mode of spectrum integration of application, as the weakness of the AR analysis is not each spectral approach [3,4,29]. The present study extends specific to heart rate data [12]. The role of model order and these findings to diabetic patients at rest, in whom the low- phase dependency must be discussed. In our study, the and high-frequency components obtained by the two percentage of missing AR data did not decrease by methods as well as their ratio (LF/HF) may have a different increasing the model order. The phase dependency of AR physiological interpretation. Spectral data were analyzed results [12,19] may be involved, as suggested by the strong over a 5-min resting period, as recommended [22,34]. All influence of small changes in the onset of analysis on the spectra components were obtained in each patient using results in our study. Differences in the way the power within FFT, such that it was always possible to calculate the LF/HF a band is computed may also be involved (tail effect), as ratio. In hypertensive subjects, we have previously reported previously proposed by Badilini et al. [3]. Indeed, with FFT, the possibility of missing LF and HF data using the AR the power is calculated by integration of the spectrum method [4]. Consistently, using the AR method in diabetics, between the band lower and upper limits. Conversely, with it was not possible to calculate the LF/HF ratio in four AR, the criteria of assignment are based on the central patients given the lack of LF and HF spectral components. frequency value of a well-defined oscillatory pattern, such a Furthermore,theLF/HFwaszeroinelevenpatients. peak being not always observed. Furthermore, when two Overall, a zero- or missing-value for the LF/HF ratio was neighboring components are considered, the tails of each found in 50% patients. Although controversial [14,27], this component could be assigned to one or another band ratio is currently used to precisely quantify the so-called depending on the method used [3]. Other limitations related sympathovagal balance [24–26,28]. In both the entire study to more complex mathematical characteristics of the AR population and the 15 patients with complete data-set, the method may be also involved [3,4,12,19,29]. LF/HF ratio significantly differed between the AR and FFT Although the FFT method must be preferred, we also methods, thus also confirming previous studies on healthy observed moderate day-to-day reproducibility and moderate [29] and hypertensive subjects [4]. sensitivity to the timing of onset of the analysis for FFT The reproducibility of short-term frequency-domain spectra. As a result, our study suggests that FFT data must HRV measurements has been questioned. In normal be interpreted with caution and in light of other indices subjects, Pitzalis et al. have shown that both FFT and AR quantifying the sympathovagal balance, namely time- spectra were poorly reproducible when evaluated from domain HRV indices. Indeed, although time-domain and short-term recordings in eighteen normal volunteers [29].It FFT frequency-domain indices of HRV were strongly has been suggested that patients with decreased HRV may related, only time-domain indices exhibited excellent day- 312 D. 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