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1.
Entropy (Basel) ; 26(4)2024 Mar 28.
Article En | MEDLINE | ID: mdl-38667850

BACKGROUND: Early detection of atrial fibrillation (AF) is essential to prevent stroke and other cardiac and embolic complications. We compared the diagnostic properties for AF detection of the percentage of successive RR interval differences greater than or equal to 30 ms or 3.25% of the previous RR interval (pRR30 and pRR3.25%, respectively), and asymmetric entropy descriptors of RR intervals. Previously, both pRR30 and pRR3.25% outperformed many other heart rate variability (HRV) parameters in distinguishing AF from sinus rhythm (SR) in 60 s electrocardiograms (ECGs). METHODS: The 60 s segments with RR intervals were extracted from the publicly available Physionet Long-Term Atrial Fibrillation Database (84 recording, 24 h Holter ECG). There were 31,753 60 s segments of AF and 32,073 60 s segments of SR. The diagnostic properties of all parameters were analysed with receiver operator curve analysis, a confusion matrix and logistic regression. The best model with pRR30, pRR3.25% and total entropic features (H) had the largest area under the curve (AUC)-0.98 compared to 0.959 for pRR30-and 0.972 for pRR3.25%. However, the differences in AUC between pRR30 and pRR3.25% alone and the combined model were negligible from a practical point of view. Moreover, combining pRR30 and pRR3.25% with H significantly increased the number of false-negative cases by more than threefold. CONCLUSIONS: Asymmetric entropy has some potential in differentiating AF from SR in the 60 s RR interval time series, but the addition of these parameters does not seem to make a relevant difference compared to pRR30 and especially pRR3.25%.

2.
J Clin Med ; 12(23)2023 Dec 02.
Article En | MEDLINE | ID: mdl-38068524

Heart rate asymmetry reflects the different contributions of heart rate (HR) decelerations and accelerations to heart rate variability (HRV). We examined the contribution of monotonic runs of HR accelerations and decelerations to the asymmetric properties of the HR microstructure in the 48 h electrocardiograms (ECGs) of healthy adults (n = 101, 47 males, average age of 39 years) and analysed sex differences in the HR microstructure. The HR microstructure was asymmetric for runs of most lengths, except for sequences of two consecutive decelerations (DR2s) or accelerations (AR2s). Women had a higher prevalence of AR2s than men but fewer runs in the range of 4 to 11 consecutive accelerations (AR4-AR11s) and 5 to 11 consecutive decelerations (DR5-DR11s). The longest runs consisted of 47 consecutive accelerations (AR47s) and 27 consecutive decelerations (DR27s). More DR3s than AR3s and more DR4s than AR4s reveal a crossing of HR microstructure asymmetry. In conclusion, more acceleration than deceleration runs demonstrate that the HR microstructure was asymmetric in the 48 h ECGs. This phenomenon was present in both sexes but was more pronounced in men. For shorter runs of 3 and 4 consecutive heartbeats, there was a crossing of HR microstructure asymmetry, with more deceleration than acceleration runs.

3.
J Clin Med ; 12(18)2023 Sep 10.
Article En | MEDLINE | ID: mdl-37762826

Flow-mediated skin fluorescence (FMSF) at 460 nm is a non-invasive method for assessing dynamic changes in the reduced form of nicotinamide adenine dinucleotide (NADH) and microcirculation in forearm skin under varying conditions of tissue perfusion. Typically, fluorescence increases during ischaemia, but atypical cases show a temporary signal decrease instead of a constant increase. This study aimed to explore the clinical implications of atypical FMSF patterns in patients with newly diagnosed untreated hypertension. NADH fluorescence and pulse wave analysis were performed on 65 patients. Differences in peripheral and arterial pulse pressure profiles were examined based on FMSF curve courses. Patients with atypical curve courses had significantly (p < 0.05 or lower for all) higher heart rate, peripheral and central diastolic pressure, tension time index, central rate pressure product, shorter diastole duration, and reservoir pressure-time integral. Hypertensive patients with atypical FMSF signals had less advantageous blood pressure profiles. Although the underlying factors causing these symptoms are unknown, the atypical FMSF pattern may reflect increased sympathetic stimulation and vascular resistance. The visual assessment of the FMSF curve may have important clinical implications that deserve further investigation.

4.
Behav Pharmacol ; 34(5): 287-298, 2023 08 01.
Article En | MEDLINE | ID: mdl-37401397

Women experience greater difficulties in quitting smoking than men, though the hormonal factors contributing to this sex difference remain to be clarified. The current study aimed to examine menstrual cycle effects on smoking cue-induced cravings as well as examine dynamic reproductive hormone change as a potential mediator underlying any cycle effects observed. Twenty-one women who smoke underwent two laboratory sessions - one in the mid-follicular phase and the other in the late luteal phase - involving an in-vivo smoking cue task, administered before and after exposure to a psychosocial laboratory stressor. Heart rate variability (HRV) and subjective smoking cravings were assessed in response to the cue task. The degree of change in the urinary metabolites of estradiol and progesterone from 2 days before to the day of each laboratory session was measured. Results revealed that both before and following exposure to psychosocial stress, highly nicotine-dependent women exhibited smaller cue-induced increases in HRV relative to the follicular phase. In contrast, less nicotine-dependent women exhibit an increase in HRV in both menstrual cycle phases. Results furthermore suggest that menstrual cycle effects seen in highly nicotine-dependent women are driven by the decline in estradiol and progesterone occurring in the late luteal phase. Though limited by a small sample size, this study suggests that withdrawal from reproductive hormones in the late luteal phase may alter highly nicotine-dependent women's physiological response to smoking cues, which may reflect greater difficulty resisting temptation. These findings may provide some insight regarding women's greater difficulty in maintaining abstinence after quitting smoking.


Cues , Nicotine , Female , Humans , Male , Heart Rate , Nicotine/pharmacology , Progesterone/pharmacology , Craving , Menstrual Cycle/physiology , Luteal Phase/physiology , Luteal Phase/psychology , Follicular Phase/psychology , Estradiol/pharmacology , Smoking
5.
J Clin Med ; 12(3)2023 Jan 28.
Article En | MEDLINE | ID: mdl-36769655

Aldosterone regulates hemodynamics, including blood pressure (BP), and is involved in the development and progression of cardiovascular diseases, including systolic heart failure (HF). While exercise intolerance is typical for HF, neither BP nor heart rate (HR) have specific characteristics in HF patients. This study compares BP and HR profiles during and after standardized exercise between patients with systolic HF with either lower or higher aldosterone concentrations. We measured BP and HR in 306 ambulatory adults with systolic HF (left ventricular ejection fraction (LVEF) <50%) during and after a 6 min walk test (6MWT). All patients underwent a resting transthoracic echocardiography, and venous blood samples were collected for biochemical analyses. The patients were also divided into tertiles of serum aldosterone concentration: T1 (<106 pg/mL), T2 (106 and 263 pg/mL) and T3 (>263 pg/mL), respectively. Individuals from T1 and T2 were combined into T1-T2 as the reference group for comparisons with patients from T3. The individuals from T3 had significantly lower systolic, mean and diastolic BPs at rest, at the end and at 1 and 3 min post-6MWT recovery, as well as a more dilated left atrium and right ventricle alongside a higher concentration of N-terminal pro-B-type natriuretic peptide (NT-proBNP). Higher serum aldosterone concentration in HF patients with an LVEF < 50% is associated with a lower 6MWT BP but not an HR profile.

6.
J Clin Med ; 12(3)2023 Feb 02.
Article En | MEDLINE | ID: mdl-36769841

Heart rate asymmetry (HRA) is a physiological phenomenon characterized by an unequal contribution of heart rate decelerations and accelerations to different heart rate variability (HRV) features. While HRA has been demonstrated in adults' ECGs of different duration, a similar investigation in healthy children has not been conducted. This study investigated the variance- and number-based HRA features in 96 healthy children (50 girls and 46 boys, aged 3-18 years) using 24-h ECGs. Additionally, we studied sex differences in HRA. To quantify HRA, variance-based and relative contributions of heart rate decelerations to short-term (C1d), long-term (C2d), and total (CTd) HRV, and the number of all heartbeats (Nd) were computed. Heart rate decelerations contributed more to C1d, but less to C2d and CTd, and were less frequent than heart rate accelerations. Short-term HRA was better expressed in boys. The majority of children (93.7%) had short-term HRA, 88.5% had long-term HRA, 88.5% had total HRA, and 99.0% had more accelerations than decelerations. No sex differences were observed for the rate of various HRA features. Heart rate asymmetry is a common phenomenon in healthy children, as observed in 24-h ECGs. Our findings can be used as reference data for future clinical studies on HRA in children.

7.
J Clin Med ; 12(3)2023 Feb 03.
Article En | MEDLINE | ID: mdl-36769867

Heart rate asymmetry (HRA) reflects different contributions of heart rate (HR) decelerations and accelerations to heart rate variability (HRV). In this study, we examined various properties of HRA, including its compensation and HRV, in 48-h electrocardiogram (ECG) recordings in healthy adults. Furthermore, we compared sex differences in parameters used to quantify HRA and HRV. Variance-based and relative HRA and HRV parameters were computed for Holter ECG recordings lasting up to 48 h in 101 healthy volunteers. The median age of the subjects was 39 years, with 47 of them being men. The prevalence of all forms of HRA was statistically different from randomness (p < 0.0001). Specifically, HR decelerations contributed >50% (C1d) to short-term HRA in 98.02% of subjects, while HR decelerations contributed <50% to long-term HRA in 89.11% of recordings and to total HRA in 88.12% of recordings. Additionally, decelerations accounted for <50% of all changing heartbeats (Porta's index) in 74.26% of subjects, and HRA compensation was present in 88.12% of volunteers. Our findings suggest that various HRA features are present in most healthy adults. While men had more pronounced HRA expression, the prevalence of short-, long-term, and total HRA and its compensation was similar in both sexes. For HRV, values of variance-based indices were higher in men than in women, but no differences were found for relative measures. In conclusion, our study references HRA and HRV for longer ECG recordings of up to 48 h, which have become increasingly important in clinical ECG monitoring. The findings can help understand and compare the characteristics of HRA and HRV in patients with different diseases.

8.
J Clin Med ; 12(4)2023 Feb 04.
Article En | MEDLINE | ID: mdl-36835783

The reduced form of nicotinamide adenine dinucleotide (NADH) is crucial in cellular metabolism. During hypoxia, NADH accumulation results from anaerobic cytoplasmic glycolysis and impaired mitochondrial function. This study aimed to compare the dynamic changes in the 460-nm forearm skin fluorescence, which reflects cellular NADH content, during transient ischaemia between healthy individuals and patients with newly diagnosed, untreated essential hypertension (HA). Sixteen healthy volunteers and sixty-five patients with HA underwent non-invasive measurement of forearm skin NADH content using the Flow Mediated Skin Fluorescence (FMSF) method at rest and during a 100-s transient ischaemia induced by inflation of the brachial cuff. The fluorescent signal was sampled at 25 Hz. All samples were normalised to the end of the ischaemic phase, which is the most stable phase of the whole recording. Slope values of 1 s linear regressions were determined for every 25-sample neighbouring set. The 1-s slopes in the early phase of skin ischaemia, indicating quicker hypoxia-induced NADH accumulation in skin, were significantly higher in patients with HA than in healthy individuals. These findings suggest that some protecting mechanisms postponing the early consequences of early cellular hypoxia and premature NADH accumulation during skin ischaemia are impaired in patients with untreated HA. Further studies are needed to investigate this phenomenon.

9.
J Clin Med ; 12(4)2023 Feb 07.
Article En | MEDLINE | ID: mdl-36835864

The electrical depolarization of the heart passes through various structures of the cardiac conduction system, which modify its conduction to different extents. In this study, we investigated the relationship between the atrioventricular conduction time (AV interval) and its contributors, the atrioventricular node (AVN) and the His-Purkinje system (HPS), as represented by the AH and HV intervals, respectively. We also compared sex differences in these intervals and their relations. Resting intracardiac tracings lasting 5 min were obtained from 64 patients (33 women) during an invasive electrophysiological study. The aforementioned intervals were measured for all consecutive beats. The mean AH interval was 85.9 ms, HV 43.7 ms, and AV 129.6 ms. Men had longer AH (80.0 vs. 65.9 ms), HV (38.4 vs. 35.3 ms), and AV intervals (124.7 vs. 108.5 ms) than women. The AV intervals were linearly correlated with AH intervals in all patients (r2 = 0.65). No significant correlation was found between AV and HV intervals in all patients (r2 = 0.05). There were no sex differences in these associations. Our results suggest that the atrioventricular conduction time depends mainly on the conduction through the AVN and less on the HPS. These relations are similar in both sexes, although men had longer conduction times through the AVN, HPS, and total atrioventricular conduction time.

10.
Life (Basel) ; 12(9)2022 Sep 08.
Article En | MEDLINE | ID: mdl-36143435

Current methods to diagnose concussions are subjective and difficult to confirm. A variety of physiological biomarkers have been reported, but with conflicting results. This study assessed heart rate variability (HRV), spontaneous baroreflex sensitivity (BRS), and systolic blood pressure variability (BPV) in concussed athletes. The assessment consisted of a 5-min seated rest followed by a 5-min (0.1 Hz) controlled breathing protocol. Thirty participants completed baseline assessments. The protocol was repeated during the post-injury acute phase (days one to five). Total (p = 0.02) and low-frequency (p = 0.009) BPV spectral power were significantly decreased during the acute phase of concussion. BRS down-sequence (p = 0.036) and up-sequence (p = 0.05) were significantly increased in the acute phase of concussion, with a trend towards an increased BRS pooled (p = 0.06). Significant decreases in HRV were also found. Acute concussion resulted in altered BRS and BPV dynamics compared to baseline. These findings highlight objective physiological parameters that could aid concussion diagnosis and return-to-play protocols.

11.
Pol Arch Intern Med ; 132(10)2022 10 21.
Article En | MEDLINE | ID: mdl-35916461

INTRODUCTION: Brain­derived neurotrophic factor (BDNF) is decreased in heart failure (HF), but whether serum BDNF concentration is related to the severity of HF with reduced left ventricular (LV) ejection fraction (LVEF) below 50% is uncertain. OBJECTIVES: We aimed to compare cardiac structure and function in ambulatory and clinically stable patients with HF and LVEF below 50% for lower and higher BDNF serum concentrations. PATIENTS AND METHODS: A total of 361 ambulatory patients with a compensated HF and LVEF below 50% underwent cardiac evaluation and measurement of serum BDNF and N­terminal pro-B­type natriuretic peptide (NT­proBNP). Patients from the lower (below median) and higher (equal to or above median) BDNF serum concentration groups were compared by analysis of covariance (ANCOVA) adjusted for age, sex, body mass index, resting heart rate, and systolic blood pressure. RESULTS: The patients were at a median age of 63.8 (interquartile range [IQR], 57.7-71.5) years and had a median LVEF of 31.0% (IQR, 23.0-37.4). Individuals with lower BDNF (<23.5 ng/ml) had significantly (P ≤0.05) more dilated right and left atria both before and after emptying, larger right ventricular end-diastolic diameter, LV end-systolic diameter, lower tricuspid annulus plane systolic excursion, shorter pulmonary acceleration time, higher mitral E to A waves ratio and mitral E wave to tissue Doppler e' wave ratio, and higher concentration of NT­proBNP. CONCLUSIONS: HF patients with LVEF below 50% and lower serum BDNF concentration present more advanced cardiac remodeling and dysfunction than individuals with higher BDNF. Potential mechanisms and clinical consequences of these findings require further investigation.


Heart Failure, Systolic , Heart Failure , Ventricular Dysfunction, Left , Humans , Middle Aged , Aged , Natriuretic Peptide, Brain , Brain-Derived Neurotrophic Factor , Prognosis
12.
Curr Res Physiol ; 5: 240-245, 2022.
Article En | MEDLINE | ID: mdl-35756694

External stressors such as alcohol, caffeine, and vigorous exercise are known to alter cellular homeostasis, affecting the autonomic nervous system (ANS) and overall physiological function. However, little direct evidence exists quantifying the impact of these external stressors on physiological testing. We assessed the impact of the above-listed stressors on spontaneous baroreflex sensitivity (BRS), heart rate variability (HRV), heart rate asymmetry (HRA), and systolic blood pressure variability (BPV). Seventeen male university varsity American-style football athletes completed two identical assessments on separate days, once presenting with one or more stressors (recent intake of caffeine, alcohol, or exercise participation; contraindicated assessment) and another with no stressors present (repeat assessment). Both assessments were conducted within one week and at the same time of day. The testing protocol consisted of 5-min of rest followed by 5-min of a squat-stand maneuver (0.05 Hz). Continuous beat-to-beat blood pressure and electrocardiogram measurements were collected and allowed for calculations of BRS, HRV, HRA, and BPV. Significant decreases (p < 0.05) in HRV and HRA metrics (SDNN, SD2, SDNNd, SDNNa, SD2a, SD2d), HRV total power, and BRS-up sequence were found during the contraindicated assessment in comparison to the repeat assessment. When assessing those with exercise as their only stressor, high-frequency HRV and BRS-pooled were significantly decreased and increased, respectively, during the contraindicated assessment. Pre-season physiological baseline testing in sport is becoming increasingly prevalent and thus must consider external stressors to ascertain accurate and reliable data. This data confirms the need for stringent and standardized guidelines for pre-participation baseline physiological testing.

13.
Cardiol Res Pract ; 2022: 6159883, 2022.
Article En | MEDLINE | ID: mdl-35402043

Background: Some antihypertensive medications alter cellular energy production, presumably by modification of the mitochondrial function. In vivo studies of such effects are challenging in humans. We applied a noninvasive forearm skin measurement of the 460-nm fluorescence specific for the reduced form of nicotinamide adenine dinucleotide (NADH) to study the 6-week effects of four different antihypertensive medications on mitochondrial function using the Flow-Mediated Skin Fluorescence (FMSF). Methods: In a prospective open-label study, we compared the long-term effects of a 6-week treatment with either amlodipine (5 mg), perindopril (5 mg), nebivolol (5 mg), or metoprolol (50 mg) on the dynamic flow-mediated changes in the skin NADH content in 76 patients (29 women) with untreated primary arterial hypertension (HA). Patients underwent 24-hour ambulatory blood pressure monitoring. To study mitochondrial function, the FMSF was measured at rest, during 100-second ischemia and postischemic reperfusion. The control group consisted of 18 healthy people (7 women). Results: There were no significant differences in the FMSF parameters between the control and the study group before medication. After the 6-week treatment, all drugs similarly reduced blood pressure. Neither amlodipine, perindopril, nor nebivolol changed the flow-mediated 460-nm skin fluorescence significantly. However, metoprolol raised this fluorescence at rest, during ischemia and reperfusion (P at most <0.05), indicating an increase in the total NADH skin content. Conclusion: Amlodipine, perindopril, and nebivolol appear neutral for the skin NADH content during the 6-week antihypertensive treatment. Similar treatment with metoprolol increased skin NADH at rest, during ischemia and reperfusion, probably due to an effect on microcirculation and altered mitochondrial function. Explanation of the potential mechanisms behind metoprolol influence on the skin NADH metabolism requires further investigation.

14.
Can J Physiol Pharmacol ; 100(2): 192-196, 2022 Feb.
Article En | MEDLINE | ID: mdl-34597522

Cannabidiol (CBD) can exert neuroprotective effects without being intoxicating, and in combination with Δ9-tetrahydrocannabinol (THC) CBD has shown to protect against THC psychosis. Acute concussion and post-concussion syndrome (PCS) can result in autonomic dysfunction in heart rate variability (HRV), but less information is available on blood pressure variability (BPV). Furthermore, the effects of phytocannabinoids on HRV and BPV in PCS are unknown. The purpose of this study was to observe the influence of daily administration of CBD or a combination of CBD and THC on HRV and BPV parameters in four female PCS participants. Participants completed a seated 5-min rest followed by six breaths-per-minute paced breathing protocol. Data was collected prior to phytocannabinoid intake and continued over 54 to 70 days. High frequency systolic BPV parameter increased every assessment period, unless altered due to external circumstances and symptoms. HRV parameters showed less consistent and varying responses. These results suggest that CBD can help to improve the altered autonomic dysfunction in those with PCS, and that responses to the drug administration was individualized. Double blinded, randomized controlled trials with greater sample sizes are required to better understand the influences of the varying dosages on human physiology and in PCS.


Autonomic Nervous System Diseases/drug therapy , Blood Pressure/drug effects , Cannabidiol/pharmacology , Heart Rate/drug effects , Neuroprotective Agents , Phytotherapy , Post-Concussion Syndrome/drug therapy , Post-Concussion Syndrome/physiopathology , Adult , Autonomic Nervous System Diseases/etiology , Autonomic Nervous System Diseases/physiopathology , Cannabidiol/administration & dosage , Cannabidiol/therapeutic use , Female , Humans , Middle Aged , Post-Concussion Syndrome/complications
15.
J Clin Med ; 12(1)2022 Dec 22.
Article En | MEDLINE | ID: mdl-36614900

Exercise tolerance is limited in obesity and improves after weight reduction; therefore, we mutually compared the relative changes in exercise capacity variables during cardiopulmonary exercise tests (CPET) in a 12 kg sheer weight reduction model. Twenty healthy male runners underwent two CPETs: CPET1 with the actual body weight, which determined the anaerobic threshold (AT) and respiratory compensation point (RCP); and CPET2 during which the participants wore a +12 kg vest and ran at the AT speed set during the CPET1. Running after body weight reduction shifted the CPET parameters from the high-mixed aerobic-anaerobic (RCP) to the aerobic zone (AT), but these relative changes were not mutually similar. The most beneficial changes were found for breathing mechanics parameters (range 12-28%), followed by cardiovascular function (6-7%), gas exchange (5-6%), and the smallest for the respiratory exchange ratio (5%) representing the energy metabolism during exercise. There was no correlation between the extent of the relative body weight change (median value ~15%) and the changes in CPET parameters. Weight reduction improves exercise capacity and tolerance. However, the observed relative changes are not related to the magnitude of the body change nor comparable between various parameters characterizing the pulmonary and cardiovascular systems and energy metabolism.

16.
Entropy (Basel) ; 23(9)2021 Sep 14.
Article En | MEDLINE | ID: mdl-34573835

We apply tree-based classification algorithms, namely the classification trees, with the use of the rpart algorithm, random forests and XGBoost methods to detect mood disorder in a group of 2508 lower secondary school students. The dataset presents many challenges, the most important of which is many missing data as well as the being heavily unbalanced (there are few severe mood disorder cases). We find that all algorithms are specific, but only the rpart algorithm is sensitive; i.e., it is able to detect cases of real cases mood disorder. The conclusion of this paper is that this is caused by the fact that the rpart algorithm uses the surrogate variables to handle missing data. The most important social-studies-related result is that the adolescents' relationships with their parents are the single most important factor in developing mood disorders-far more important than other factors, such as the socio-economic status or school success.

17.
Br J Clin Pharmacol ; 87(11): 4283-4292, 2021 11.
Article En | MEDLINE | ID: mdl-33792076

AIMS: Transient ischaemia and reperfusion (TIAR) induce early ischaemic preconditioning (IPC) in different tissues and organs, including the skin. IPC protects tissues by modifying the mitochondrial function and decreasing the amount of the reduced form of nicotinamide adenine dinucleotide (NADH). Skin 460-nm autofluorescence is proportional to the NADH content and can be non-invasively measured during TIAR. We propose a non-invasive in vivo human model of skin IPC for studying the effects of repeated TIARs on the NADH content. METHODS: Fifty-one apparently healthy volunteers (36 women) underwent three 100-second forearm ischaemia episodes induced by inflation of brachial pressure cuff to the pressure of 60 mmHg above systolic blood pressure, followed by 500-second long reperfusion episodes. Changes in skin NADH content were measured using 460-nm fluorescence before and during each of the three TIARs. RESULTS: The first two TIARs caused a significant reduction in the skin NADH content before (P = .0065) and during the third ischaemia (P = .0011) and reperfusion (P = .0003) up to 3.0%. During the third TIAR, the increase in skin NADH was 20% lower than during the first ischaemia (P = .0474). CONCLUSIONS: The measurement of the 460-nm fluorescence during repeated TIARs allows for a non-invasive in vivo investigation of human skin IPC. Although IPC reduces the overall NADH skin content, the most noticeable NADH reduction appears during ischaemia after earlier TIARs. Studying the skin model of IPC may provide new avenues for in vivo physiological, clinical and pharmacological research on mitochondrial metabolism.


Ischemic Preconditioning , Female , Forearm , Humans , Ischemia
20.
Entropy (Basel) ; 22(6)2020 Jun 21.
Article En | MEDLINE | ID: mdl-33286466

Relative consistency is a notion related to entropic parameters, most notably to Approximate Entropy and Sample Entropy. It is a central characteristic assumed for e.g., biomedical and economic time series, since it allows the comparison between different time series at a single value of the threshold parameter r. There is no formal proof for this property, yet it is generally accepted that it is true. Relative consistency in both Approximate Entropy and Sample entropy was first tested with the M I X process. In the seminal paper by Richman and Moorman, it was shown that Approximate Entropy lacked the property for cases in which Sample Entropy did not. In the present paper, we show that relative consistency is not preserved for M I X processes if enough noise is added, yet it is preserved for another process for which we define a sum of a sinusoidal and a stochastic element, no matter how much noise is present. The analysis presented in this paper is only possible because of the existence of the very fast NCM algorithm for calculating correlation sums and thus also Sample Entropy.

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