Linear and non-linear measures applied to heart rate variability (HRV)  can be used to quantify modulation of the sympathetic and parasympathetic branches of the autonomic nervous system. RR signals were obtained from the ECG recorded during five Maintenance of Wakefulness (MWT) and Multiple Sleep Latency (MSLT) tests alternated throughout the day from patients suffering sleep disturbance.
Two different end-points were considered: Study A, excessive daytime sleepiness (EDS) versus without daytime sleepiness (WDS); Study B, Pre-CPAP versus Post-CP AP (continuous positive airway pressure therapy) in EDS. Measures obtained from spectral analysis (PSD), time-frequency representation (TFR), auto-correntropy (ACORR) and auto-mutual-information function (AMIF) were applied to describe autonomic nervous system activity and RR regularity. Statistical differences between EDS and WDS groups were found in MSLT events.
During MSLT, the parasympathetic activity and RR regularity in EDS were affected by CPAP therapy. Non-linear measures obtained from EDS in Post-CPAP differed from Pre-CPAP (p-value<0.05) and tended to be similar to WDS.Peer ReviewedPostprint (published version

Caminal Magrans, Pere

Clarià Sancho, Francesc

Embid, Cristina

Guaita, Marc

Melia, Umberto Sergio Pio

Salamero, Manuel

Santamaria, J.

Vallverdú Ferrer, Montserrat

Vilaseca, Isabel

English

Linear and non-linear measures applied to heart rate variability (HRV)  can be used to quantify modulation of the sympathetic and parasympathetic branches of the autonomic nervous system. RR signals were obtained from the ECG recorded during five Maintenance of Wakefulness (MWT) and Multiple Sleep Latency (MSLT) tests alternated throughout the day from patients suffering sleep disturbance.

Two different end-points were considered: Study A, excessive daytime sleepiness (EDS) versus without daytime sleepiness (WDS); Study B, Pre-CPAP versus Post-CP AP (continuous positive airway pressure therapy) in EDS. Measures obtained from spectral analysis (PSD), time-frequency representation (TFR), auto-correntropy (ACORR) and auto-mutual-information function (AMIF) were applied to describe autonomic nervous system activity and RR regularity. Statistical differences between EDS and WDS groups were found in MSLT events.

During MSLT, the parasympathetic activity and RR regularity in EDS were affected by CPAP therapy. Non-linear measures obtained from EDS in Post-CPAP differed from Pre-CPAP (p-value<0.05) and tended to be similar to WDS.Peer Reviewe

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Non-linear dynamic analysis of RR signals in patients with and without excessive daytime sleepiness

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Non-Linear Dynamic Analysis of RR Signals in Patients with and without Excessive Daytime Sleepiness Umberto Melia!, Marc Guaita2, Montserrat Vallverdu1, Francese Claria3, Pere Caminal!, Cristina Embid2, Isabel Vilaseca2, Manel Salamero2, Joan Santamaria2 !Dept. ESAII, CREB, Universitat Politecnica de Catalunya, CIBER-BBN, Barcelona, Spain 2 MSD Unit, Hospital Clinic de Barcelona, IDIBAPS, Barcelona, Spain 3 Dept. lIE, Lleida University, Spain Abstract Linear and non-linear measures applied to heart rate variability (HRV) can be used to quantifY modulation of the sympathetic and parasympathetic branches of the autonomic nervous system. RR signals were obtained from the ECG recorded during five Maintenance of Wakefulness (MWT) and Multiple Sleep Latency (MSLT) tests alternated throughout the day from patients suffering sleep disturbance. Two different end-points were considered: Study A, excessive daytime sleepiness (EDS) versus without daytime sleepiness (WDS); Study B, Pre-CPAP versus Post-CP AP (continuous positive airway pressure therapy) in EDS. Measures obtained from spectral analysis (PSD), time-frequency representation (TFR), auto-correntropy (ACORR) and auto-mutual-information function (AMIF) were applied to describe autonomic nervous system activity and RR regularity. Statistical differences between EDS and WDS groups were found in MSLT events. During MSLT, the parasympathetic activity and RR regularity in EDS were affected by CP AP therapy. Non-linear measures obtained from EDS in Post-CPAP differed from Pre-CPAP (p-value<0.05) and tended to be similar to WDS. 1. Introduction Sleep-related breathing disorders are common causes of excessive daytime sleepiness, a socially and clinically relevant problem. An excessive daytime sleepiness (EDS) is a symptom that can have many different causes, not only sleep deprivation. Mechanisms responsible for daytime sleepiness are still largely unknown. EDS, with subjects falling asleep at unusual times of the day and during activities where vigilance is required, represents a troublesome symptom in patients with sleep­related breathing disorders (SRBD) [1,2]. Moreover, the reduced cognitive perfonnance reported in patients with SRBD may not only depend on their typical nocturnal intermittent hypoxia, but may also be related to EDS [3]. ISSN 2325-8861 449 The pathogenesis of EDS in SRBD is still ill defmed. In this context, SRBD may affect autonomic modulation of the cardiovascular system, by interfering with autonomic influences responsible for cardiovascular regulation, leading to a kind of autonomic arousal [4,5]. A previous study [1] has shown that the phasic and tonic autonomic changes induced by SRBD might represent sensItive additional markers of the concomitant perturbation of sleep quality and, thus, of the occurrence of daytime sleepiness in patients with SRBD. Among various symptoms associated with this condition, the most prevalent is EDS. In the present work, linear and nonlinear signal processing techniques were applied to RR series for the assessment of drowsiness in patients suffering sleep disturbance who undergoing the maintenance of wakefulness test (MWT) and multiple sleep latency test (MSL T). In the clinical practice, the MSL T and MWT are frequently used to measure the time elapsed from the start of a daytime nap period to the first signs of sleep, called sleep latency [6-9]. Measures based on time-frequency representation (TFR) and power spectral analysis (PSD) were applied to RR series in awaking state in order to quantify modulation of the sympathetic and parasympathetic branches of the autonomic nervous system. Auto-mutual information function (AMIF) and auto-correntropy (ACORR) were used to describe the complexity and regularity of the RR time series. Finally, statistical analysis was perfonned in order to characterize patients with excessive daytime sleepiness (EDS) and without daytime sleepiness (WDS). Furthermore, the patients of the EDS group were analyzed before and after the CPAP (continuous positive airway pressure) therapy. 2. Materials and methods 2.1. Analyzed database and preprocessing The analyzed database belongs to the Multidisciplinary Computing in Cardiology 2013; 40:449-452. Sleep Disorders Unit of the Hospital Clinic (Barcelona, Spain). This database contains data recorded from 40 patients: EDS group, 20 patients with excessive somnolence (MWT < 20 min and MSL T < 8 min); WDS group, 20 patients without somnolence (MWT > 20 min and MSL T > 8 min). RR series (interval between consecutive heartbeats) were obtained from the ECG recorded during five MWT and five MSL T alternated throughout the day. The MSL T and MWT consisted of a series of five nap opportunities during the day beginning approximately two hours after morning awakening. The MSL T measures the propensity for falling asleep in a comfortable situation, lying in bed in a dark and quiet room, with explicit permission to fall asleep. The MWT assesses resistance to fall asleep. Subjects were sitting in a bed and were instructed to stay awake. RR series were filtered by replacing artifacts or ectopic beats if deviate more than a 15% tolerance of the mean value of the previous twenty beats. These unevenly sampled signals were processed using cubic spline interpolation and sampled at 4 Hz. For each MWT and MSL T test, a sequence of 180 s of time series RR(t) in the awaking state was selected 30 s after test started. Windows belonging to tests in which the patient fell asleep in less than 180 s were not included in this study. 2.2. Spectral analysis TFR based on Choi-Williams distribution (CWD) is calculated by convoluting the Wigner distribution (WD) and the Choi-Williams (CW) exponential, [10]. The functions, instantaneous power (IP) and instantaneous frequency (IF), were obtained from CWDRR(t,f), and the spectrum was divided into the characteristic frequency bands of the RR(t): VLF, <0.04 Hz; LF, 0.04-0.15 Hz; HF, 0.15-0.4 Hz; TB, total­frequency band. IP was calculated as the area under the curve of the CWDRR(t,f) at each instant. In each of the considered bands, this value was normalized by the total power. IF was defined as the mean frequency of the spectrum at each instant [11]. The mean value (m) was calculated on the TFR functions along the time. Also the known frequency domain analysis based on the power spectral density (PSD) using Yule-Walker AR method was applied. The maximum order of the AR model was fixed to 20th. The normalized powers LF and HF and the rate LF/HF were calculated [12]. 2.3. Auto-mutual information and Auto-correntropy function AMIF is a metric to estimate both linear and nonlinear dependences between two time series [13,14], XI and XI+r' It can be regarded as a nonlinear equivalent of the correlation 450 function. AMIF is calculated by the distribution of the probability amplitudes of XI =RR(t) and XI+r =RR(t+r), and the joint probability of these time series, based on Shannon entropy. � ( P{Xt,XtH} ) (1) AMIF_ShCr) = L P{Xt,xtH}log2 P{xtlP{Xt+r} Xt,Xt+T Probabilities and joint probabilities were computed on the basis of a quantization in 5 bits. This function describes how the infonnation of a signal (AMIF value at r=O) decreases over a prediction time intervals (AMIF values at r>O). Increasing information loss is related to decreasing predictability, and increasing complexity of the signal [15]. AMIF was also defmed from Renyi entropy as in (2). 1 � pq{Xt,XtH} (2) AMIF_ReqCr) = q _ 110g2 L pq-l{xtlPq-1{XtH} Xt,Xt+T In this work, AMIF was calculated using a discrete time delay 0::;r::;100 samples for different values of the control parameter of Renyi entropy: q = {O.l, 0.2, 0.5, 2, 3, 5, 10, 30, 50, 100} and q� 1 using (4). AMIF was nonnalized by its maximum value that corresponds to FO. ACORR is a similarity measure of signals that generalizes the autocorrelation function to nonlinear spaces. N � 1 L 1 (RR(t)-RR(t-r))2 VCr) = - --e 20'2 N t=l ../21[(5 (3) where (J is the size of the kernel detennined in this study by Silverman's rule [16] of density estimation. AMIF and ACORR were applied to RR(t) time series (TB) and to RR(t) filtered in the frequency bands: VLF, <0.04 Hz; LF, 0.04-0.15 Hz; HF, 0.15-0.4 Hz. Several measures were defined on the AMIF and ACORR along the time delay r: m, mean value; maxL, first relative maximum; min, absolute minimum; FD, first derivative. 2.4. Statistical analysis Two different end-points have been considered: Study A, comparing excessive somnolence (EDS) versus without somnolence (WDS) groups; Study B, comparing pre­CPAP versus Post-CPAP therapy in a subgroup of 10 EDS patients. For both studies, measures obtained from each MWT (MWTl, MWT2, MWT3, MWT4, MWT5) and MSLT (MSLTl, MSLT2, MSLT3, MSLT4, MSLT5) were independently analyzed. A non-parametric test, U of Mann-Whitney test, was applied and a significance level p-value <0.05 was taken into account. Measures that satisfy this condition were considered for building the discriminant function. The leaving-one-out method was perfonned as validation method. 3. Results and discussions 3.1. Study A The present study has permitted to characterize EDS and WDS groups only during MSL T with statistically significant difference. Table 1 shows the linear and non­linear measures which were able to classify both studied groups. The TFR measure mIP(HF) that describes the autonomic parasympathetic nervous system activity (HF band) have presented higher values in EDS group than WDS group, with p-value=O.003 in MSLT3. EDS group presented a higher (p-value<O.05) heart rate variability (stdRR) during MSL Tl and MSL T4. Table 1. Study A: Linear and non-linear measures able to statistically differentiate between WDS and EDS groups. Measures p-value WDS EDS WDS EDS ('Yo) ('Yo) (mean+ std) (mean+ std) stdRR (ms) MSLTI 0.041 75 MSL T4 <0.0005 85 LF norm (n.u.) MSLTS 0.047 60 MSLTJ 0.003 95 mAMfF RedTB) MSL T3 <0.0005 90 MSL T4 <0.0005 90 MSLTS 0.008 90 maxLAMlF ReOl(VLF) MSLT3 0.0025 90 MSLT4 <0.0005 75 mAMfF SheLF) MSLT3 0.0023 90 MSLTS 0.0033 80 mAMlF Re,(HF) MSLTI <0.0005 100 MSLT3 <0.0005 90 maxLACORR(TB) MSLTI 0.027 80 MSLT2 0.006 90 MSLT3 0.008 65 MSLT4 <0.0005 85 MSLTS 0.002 80 60 39.1±3.37 51.2±5.55 75 27.5±1.84 44.7±3.32 80 36.0±2.5 29.7±1.7 60 6.49±0.54I 12.5+ 1.87 75 0.250±0.012 0.323±0.015 75 0.225±0.007 0.288±0.012 60 0.227±0.005 0.271±0.013 80 0.381±0.013 0.466±0.019 75 0.352±0.0 13 0.431±0.015 75 0.344±0.015 0.416±0.014 65 0.317±0.008 0.376±0.015 70 0.371±0.004 0.406±0.008 70 0.387±0.009 0.436±0.01l 60 0.287±0.0 14 0.338±0.0 17 65 0.306±0.012 0.371±0.018 75 0.314±0.016 0.363±0.014 80 0.303±0.012 0.389±0.014 60 0.299±0.012 0.361±0.0 17 The non-linear measures that describe the regularity of the RR(t) have evidenced more regularity behavior in EDS group than WDS group, with p-value<O.05 for all MSL T tests. Observing the results, it can be noted that RR(t) in VLF, LF and HF bands has similar regularity behavior when the groups are compared (p-value<O.005), this means higher values of maxL and m in EDS group. Figure 1 shows the evolution of the mean value of mAMIF_Reo.2 and maxLACORR with respect to MWT and MSL T. As it can be seen in figure 1, the non-linear 451 measures present more changes between MWT and MSL T in EDS group than WDS group. However, the values of these measures in EDS group during MWT tend to be similar to those of WDS group, presenting a non­significant statistical level. 0.42 0.4 --:- 0.38 :0 � rr 0.36 0: � 0.34 � E 0.32 0.3 0.28 0.26 �-:----:-----:-----;:-----c-----c=--c----:c----;c-----;:---i 5 f S f g f 5 f $ � � � 1 � 1 � 1 � 1 (b) Figure 1. Study A. Mean value and standard error: (a) mAMIF _ Reo 2; (b) maxLACORR. 3.2. Study B The best results of the Pre-CP AP and Post-CPAP study are shown in Table 2. Only non-linear measures, AMIF and ACORR, were able to describe the Pre-CP AP and Post-CPAP therapy. The evolution of non-linear variables was similar in the first part of the day (from MWTl to MWT3 and from MSL Tl to MSL T3), however the statistical differences were presented during the last part of the day, after lunch time (MWT4, MWT5, MSLT4 and MSL T5), as it can be seen in figure 2. Particularly, it can be observed a more regularity behavior in Pre-CPAP than Post-CPAP during MSLT4 and MSLT5. In this way, measures that describe the regularity of RR(t) in EDS group were affected by CPAP therapy, and they assumed values similar to those of WDS group in Study A. Table 2. Study B: Non-linear measures able to statistically differentiate between Pre- and Post-CP AP in EDS group. Measures p-value Pre (%) maxLAMIF ReOl(VLF) MSLT4 0.0379 70 mAMIF SheLF) MSLT5 0.038 maxLACORR(TB) MSLT4 0.038 MSLT5 0.026 0.46 0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.46 0.44 0.42 0.4 0.38 0.36 0.34 0.32 0.3 70 70 70 Post Pre Post (mean+ std) (%) (mean+ std) 85 0.451±0.0 16 0.378±0.0 13 85 85 70 (a) (b) 0.439±0.0 12 0.359±0.0 14 0.418±0.013 0.336±0.014 0.436±0.0 16 0.352±0.0 13 Figure 2. Study B. Mean value and standard error: (a) mAMIF_Sh(LF); (b) maxLACORR(TB). 4. Conclusions Autonomic parasympathetic and sympathetic nervous system activity and the regularity of the RR(t) were described by measures of TFR, AMIF and ACORR in two groups of patients in awake state. Statistical differences between EDS group and WDS group were found in MSL T events. Measures that describe the parasympathetic nervous system activity and regularity behavior of RR(t) were found to have higher values in EDS group during MSLT. Comparing Pre-CPAP and Post-CPAP therapy, statistical differences were found using measures of AMIF 452 and ACORR in MSLT4 and MSLT5. Acknowledgment This work was supported within the framework of the CICYT grant TEC2010-20886, the FIS PI07/0318 to MS (co-financed by FEDER) and the Research Fellowship Grant FPU AP2009-0858 from the Spanish Government. CIBER of BBN is an initiative of lSClI1. References [I] Lombardi C, Parati G, Cortelli P, Provini F, Vetrugno R, Plazzi G, Vignatelli 1. Daytime sleepiness and neural cardiac modulation in sleeprelated breathing disorders. J of sleep research 2008;17 (3 ):263-270. [2] Cassel W, Ploch T, Becker C, Dugnus D, Peter J, Handvon WP. Risk of traffic accidents in patients with sleep-disordered breathing: reduction with nasal CPAP. Eur Respir J 1996;9:2606-2611. [3] Sateia MJ. Neuropsychological impairment and quality of life in obstructive sleep apnea. Clin. 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Non-linear dynamic analysis of RR signals in patients with and without excessive daytime sleepiness

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