Nonlinear dynamics of cardiovascular ageing

Exercise training in older adults, what effects on muscle oxygenation? A systematic review

AIM

To determine the effects of different modality of exercise training programs on muscle oxygenation in older adults.

METHODS

Relevant articles were searched in PubMed, Web of Science, Science Direct and Scopus, using the keywords: "Aged" AND "Muscle oxygenation" AND (Exercise OR "Exercise therapy" OR "Exercise Movement Techniques" OR Hydrotherapy), without limitation concerning the publication date. To be included in the full analysis, the study had to be a randomized controlled trial in which older adults participants (mean age: 65 years at least) were submitted to an exercise-training program and muscle oxygenation assessment.

RESULTS

The searches resulted in 1238 articles from which 7 met all the inclusion criteria. The trials involved 370 older adults (68.7±1.7years), healthy and with peripheral arterial disease. Studies included resistance and endurance exercises as well as walking sessions. Training sessions were 2-6 time per week, lasted 3-24 months and with different training intensity throughout studies. After a long-term resistance training, healthy older adults showed enhanced muscle oxygen extraction capacity, regulation of vessels and vascular endothelium function; endurance training is reported to improve microvascular blood flow and matching of oxygen delivery to oxygen utilization, muscle oxidative capacity and muscle saturation, and walking sessions results in better muscle oxygen availability and muscle oxygen extraction capacity in older adults with peripheral arterial disease.

CONCLUSIONS

This review supports the fact that depending on the clinical status of the participants and the modality, exercise training improves different aspects of the muscle oxygenation in older adults.

Acute hypoxia diminishes the relationship between blood pressure and subarachnoid space width oscillations at the human cardiac frequency

Background

Acute hypoxia exerts strong effects on the cardiovascular system. Heart-generated pulsatile cerebrospinal fluid motion is recognised as a key factor ensuring brain homeostasis. We aimed to assess changes in heart-generated coupling between blood pressure (BP) and subarachnoid space width (SAS) oscillations during hypoxic exposure.

Methods

Twenty participants were subjected to a controlled decrease in oxygen saturation (SaO₂ = 80%) for five minutes. BP and heart rate (HR) were measured using continuous finger-pulse photoplethysmography, oxyhaemoglobin saturation with an ear-clip sensor, end-tidal CO₂ with a gas analyser, and cerebral blood flow velocity (CBFV), pulsatility and resistive indices with Doppler ultrasound. Changes in SAS were recorded with a recently-developed method called near-infrared transillumination/backscattering sounding. Wavelet transform analysis was used to assess the relationship between BP and SAS oscillations.

Results

Gradual increases in systolic, diastolic BP and HR were observed immediately after the initiation of hypoxic challenge (at fifth minute +20.1%, +10.2%, +16.5% vs. baseline, respectively; all P<0.01), whereas SAS remained intact (P = NS). Concurrently, the CBFV was stable throughout the procedure, with the only increase observed in the last two minutes of deoxygenation (at the fifth minute +6.8% vs. baseline, P<0.05). The cardiac contribution to the relationship between BP and SAS oscillations diminished immediately after exposure to hypoxia (at the fifth minute, right hemisphere -27.7% and left hemisphere -26.3% vs. baseline; both P<0.05). Wavelet phase coherence did not change throughout the experiment (P = NS).

Conclusions

Cerebral haemodynamics seem to be relatively stable during short exposure to normobaric hypoxia. Hypoxia attenuates heart-generated BP SAS coupling.

Functional connectivity analysis using fNIRS in healthy subjects during prolonged simulated driving

Noninvasive and accurate assessment of driving fatigue in relation to brain activity during long-term driving can contribute to traffic safety and accident prevention. This study evaluated functional connectivity (FC) in relevant brain regions. Synergistic mechanisms in different brain regions were detected by a novel simulator, which combined semi-immersive virtual reality technology and functional near-infrared spectroscopy. Each subject was instructed to complete driving tasks coupled with a mental calculation task. Wavelet coherence (WCO) and wavelet phase coherence (WPCO) were calculated and assessed in frequency intervals (I) 0.6-2 and (II) 0.145-0.6Hz as global connectivity measures; (III) 0.052-0.145, (IV) 0.021-0.052, (V) 0.0095-0.021 and (VI) 0.005-0.0095Hz as FC. WCO and WPCO revealed the strength and synchronization of cerebral connectivity, respectively. Significantly low WCO levels were found in intervals I and III in prefrontal cortex (PFC) and IV in motor cortex (MC) at the end of the driving task. Furthermore, significantly low WPCO were found in intervals I, and III in PFC and interval IV in MC. Experimental findings suggested that progressive mental fatigue adversely influences the cognitive function in the PFC and the cooperative mechanism between the PFC and MC.

Effects of Sleep Deprivation on Phase Synchronization as Assessed by Wavelet Phase Coherence Analysis of Prefrontal Tissue Oxyhemoglobin Signals

Purpose

To reveal the physiological mechanism of the decline in cognitive function after sleep deprivation, a within-subject study was performed to assess sleep deprivation effects on phase synchronization, as revealed by wavelet phase coherence (WPCO) analysis of prefrontal tissue oxyhemoglobin signals.

Materials and Methods

Twenty subjects (10 male and 10 female, 25.5 ± 3.5 years old) were recruited to participate in two tests: one without sleep deprivation (group A) and the other with 24 h of sleep deprivation (group B). Before the test, each subject underwent a subjective evaluation using visual analog scales. A cognitive task was performed by judging three random numbers. Continuous recordings of the near-infrared spectroscopy (NIRS) signals were obtained from both the left and right prefrontal lobes during rest, task, and post-task periods. The WPCO of cerebral Delta [HbO₂] signals were analyzed for these three periods for both groups A and B.

Results

Six frequency intervals were defined: I: 0.6–2 Hz (cardiac activity), II: 0.145–0.6 Hz (respiratory activity), III: 0.052–0.145 Hz (myogenic activity), IV: 0.021–0.052 Hz (neurogenic activity), V: 0.0095–0.021 Hz (nitric oxide related endothelial activity) and VI: 0.005–0.0095 Hz (non-nitric oxide related endothelial activity). WPCO in intervals III (F = 5.955, p = 0.02) and V (F = 4.7, p = 0.037) was significantly lower in group B than in group A at rest. During the task period, WPCO in intervals III (F = 5.175, p = 0.029) and IV (F = 4.585, p = 0.039) was significantly lower in group B compared with group A. In the post-task recovery period, the WPCO in interval III (F = 6.125, p = 0.02) was significantly lower in group B compared with group A. Reaction time was significantly prolonged, and the accuracy rate and F₁ score both declined after sleep deprivation.

Conclusions

The decline in WPCO after sleep deprivation indicates reduced phase synchronization between left and right prefrontal oxyhemoglobin oscillations, which may contribute to the diminished cognitive function.

Kölliker-Fuse nuclei regulate respiratory rhythm variability via a gain-control mechanism

Respiration varies from breath to breath. On the millisecond timescale of spiking, neuronal circuits exhibit variability due to the stochastic properties of ion channels and synapses. Does this fast, microscopic source of variability contribute to the slower, macroscopic variability of the respiratory period? To address this question, we modeled a stochastic oscillator with forcing; then, we tested its predictions experimentally for the respiratory rhythm generated by the in situ perfused preparation during vagal nerve stimulation (VNS). Our simulations identified a relationship among the gain of the input, entrainment strength, and rhythm variability. Specifically, at high gain, the periodic input entrained the oscillator and reduced variability, whereas at low gain, the noise interacted with the input, causing events known as "phase slips", which increased variability on a slow timescale. Experimentally, the in situ preparation behaved like the low-gain model: VNS entrained respiration but exhibited phase slips that increased rhythm variability. Next, we used bilateral muscimol microinjections in discrete respiratory compartments to identify areas involved in VNS gain control. Suppression of activity in the nucleus tractus solitarii occluded both entrainment and amplification of rhythm variability by VNS, confirming that these effects were due to the activation of the Hering-Breuer reflex. Suppressing activity of the Kölliker-Fuse nuclei (KFn) enhanced entrainment and reduced rhythm variability during VNS, consistent with the predictions of the high-gain model. Together, the model and experiments suggest that the KFn regulates respiratory rhythm variability via a gain control mechanism.

Early differential diagnosis of the severity of acute pancreatitis

There is a great need for early verification of the severity of acute pancreatitis (AP). The early stage of pathogenesis of AP is characterized by endothelial dysfunction which could be determined by wavelet analysis of skin temperature (WAST) technique. The aim is to investigate whether the dysregulation of microvascular tone caused by endothelial dysfunction and detected by WAST can be a significant indicator in early differential diagnosis of AP severity. The WAST performed in the frequency range of 0.0095-0.02 Hz during the contralateral cold test. Forty nine patients with AP aged 19-65 participated in this study. The control group included 12 healthy volunteers aged 20-65. Dysregulation of vascular tone during the contralateral cold test was observed in all patients with AP. The basal amplitudes of skin temperature oscillations in patients with AP were much lower than in healthy volunteers and progressively decreased as the disease severity increased. In patients with mild and moderate AP only the vasodilator component is destroyed, but vasoconstriction still operates. In patients with severe AP both mechanisms of endothelial vascular tone regulation are destroyed. Patients with AP have abnormal microvascular reactions related to the endothelial mechanism of vascular tone regulation. Based on the initial values of amplitudes and the indices of vasoconstriction and postcold vasodilatation, the WAST method makes it possible to evaluate two related but different characteristics of the endothelial dysfunction in patients with AP on admission which can be a significant indicator in early differential diagnosis of AP severity.

Wavelet coherence analysis of cerebral oxygenation signals measured by near-infrared spectroscopy in sailors: an exploratory, experimental study

OBJECTIVE

The objective of this study was to assess the effects of long-term offshore work on cerebral oxygenation oscillations in sailors based on the wavelet phase coherence (WPCO) of near-infrared spectroscopy (NIRS) signals.

METHODS

The fatigue severity scale (FSS) was first applied to assess the fatigue level of sailors and age-matched controls. Continuous recordings of NIRS signals were then obtained from the prefrontal lobes in 30 healthy sailors and 30 age-matched controls during the resting state. WPCO between the left and right prefrontal oscillations was analysed and Pearson correlation analysis was used to study the relationship between the FSS and the wavelet amplitude (WA), and between the FSS and the WPCO level.

RESULTS

The periodic oscillations of Delta (HbO₂) signals were identified at six frequency intervals: I (0.6-2 Hz); II (0.145-0.6 Hz); III (0.052-0.145 Hz); IV (0.021-0.052 Hz); V (0.0095-0.021 Hz); and VI (0.005-0.0095 Hz). The WA in intervals I (F=8.823, p=0.004) and III (F=4.729, p=0.034) was significantly lower in sailors than that in the controls. The WPCO values of sailor group were significantly lower in intervals III (F=4.686, p=0.039), IV (F=4.864, p=0.036) and V (F=5.195, p=0.03) than those of the control group. In the sailor group, the WA in interval I (r=-0.799, p<0.01) and in interval III (r=-0.721, p<0.01) exhibited a negative correlation with the FSS. Also, the WPCO exhibited a negative correlation with the FSS in intervals III (r=-0.839, p<0.01), IV (r=-0.765, p<0.01) and V (r=-0.775, p<0.01) in the sailor group.

CONCLUSIONS

The negative correlation between WA and FSS indicates that the lower oscillatory activities might contribute to the development of fatigue. The low WPCO in intervals III, IV and V represents a reduced phase synchronisation of myogenic, neurogenic and endothelial metabolic activities respectively and this may suggest a decline of cognitive function.

Vigilance Task-Related Change in Brain Functional Connectivity as Revealed by Wavelet Phase Coherence Analysis of Near-Infrared Spectroscopy Signals

This study aims to assess the vigilance task-related change in connectivity in healthy adults using wavelet phase coherence (WPCO) analysis of near-infrared spectroscopy signals (NIRS). NIRS is a non-invasive neuroimaging technique for assessing brain activity. Continuous recordings of the NIRS signals were obtained from the prefrontal cortex (PFC) and sensorimotor cortical areas of 20 young healthy adults (24.9 ± 3.3 years) during a 10-min resting state and a 20-min vigilance task state. The vigilance task was used to simulate driving mental load by judging three random numbers (i.e., whether odd numbers). The task was divided into two sessions: the first 10 min (Task t1) and the second 10 min (Task t2). The WPCO of six channel pairs were calculated in five frequency intervals: 0.6–2 Hz (I), 0.145–0.6 Hz (II), 0.052–0.145 Hz (III), 0.021–0.052 Hz (IV), and 0.0095–0.021 Hz (V). The significant WPCO formed global connectivity (GC) maps in intervals I and II and functional connectivity (FC) maps in intervals III to V. Results show that the GC levels in interval I and FC levels in interval III were significantly lower in the Task t2 than in the resting state (p < 0.05), particularly between the left PFC and bilateral sensorimotor regions. Also, the reaction time (RT) shows an increase in Task t2 compared with that in Task t1. However, no significant difference in WPCO was found between Task t1 and resting state. The results showed that the change in FC at the range of 0.6–2 Hz was not attributed to the vigilance task per se, but the interaction effect of vigilance task and time factors. The findings suggest that the decreased attention level might be partly attributed to the reduced GC levels between the left prefrontal region and sensorimotor area. The present results provide a new insight into the vigilance task-related brain activity.

Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states

Altered cellular energy metabolism is a hallmark of many diseases, one notable example being cancer. Here, we focus on the identification of the transition from healthy to abnormal metabolic states. To do this, we study the dynamics of energy production in a cell. Due to the thermodynamic openness of a living cell, the inability to instantaneously match fluctuating supply and demand in energy metabolism results in nonautonomous time-varying oscillatory dynamics. However, such oscillatory dynamics is often neglected and treated as stochastic. Based on experimental evidence of metabolic oscillations, we show that changes in metabolic state can be described robustly by alterations in the chronotaxicity of the corresponding metabolic oscillations, i.e. the ability of an oscillator to resist external perturbations. We also present a method for the identification of chronotaxicity, applicable to general oscillatory signals and, importantly, apply this to real experimental data. Evidence of chronotaxicity was found in glycolytic oscillations in real yeast cells, verifying that chronotaxicity could be used to study transitions between metabolic states.

Posture-related changes in brain functional connectivity as assessed by wavelet phase coherence of NIRS signals in elderly subjects

Postural instability and falls are commonly seen because of aging and motor disabilities. This study aims to assess the posture-related changes in brain functional connectivity by wavelet phase coherence (WPCO) of oxyhemoglobin concentration change (Δ[HbO2]) signals measured through near-infrared spectroscopy (NIRS) in elderly subjects. The NIRS signals were continuously recorded from the prefrontal cortex and sensorimotor cortical areas in 39 healthy elderly subjects and 22 young healthy subjects during 20min resting and 10min standing states. Eight connection types were obtained from the recorded brain areas. The WPCO were calculated in five frequency intervals in each channel pair as follows: I, 0.6-2Hz; II, 0.145-0.6Hz; III, 0.052-0.145Hz; IV, 0.021-0.052Hz; and V, 0.0095-0.021Hz. Results show that posture change and age significantly interacts with the right prefrontal cortex (PFC) and left sensorimotor cortex (SMC) connectivity in interval V (F=5.010, p=0.028). The left and right PFC connectivity in interval I, the left and right SMC connectivity in interval IV, and the connectivity in interval V, including right PFC and right SMC connectivity, left PFC and left SMC connectivity, and right PFC and left SMC connectivity, showed a significant difference between the Group Elderly and Group Young in response to posture change (p<0.05). This study provides new insight into the mechanism of posture control, and results may be useful in assessing the risk of postural instability in aged persons.

Using Modified Sample Entropy to Characterize Aging-Associated Microvascular Dysfunction

Cutaneous microvascular function can be assessed by skin blood flow (SBF) response to thermal stimuli. Usually, the activities of the regulatory mechanisms are quantified by means of spectral analysis of the response. However, spectral measures are unable to characterize the nonlinear dynamics of SBF signal. Sample entropy (SampEn) is a commonly used nonlinear measure of the degree of regularity of time series. However, SampEn value depends on the relationship between the frequency of the studied dynamics and sampling rate. Hence, when time series data are oversampled, SampEn may give misleading results. We modified the definition of SampEn by including a lag between successive data points of the vectors to be compared to address the oversampled issue. The lag could be chosen as the first minimum of the auto mutual information function of the time series. We tested the performance of modified SampEn using simulated signals and SBF data in the young and old groups. The results indicated that modified SampEn yields consistent results for different sampling rates in simulated data, but SampEn cannot. Blood flow data showed a higher degree of regularity during the maximal vasodilation period as compared to the baseline in both groups and a higher degree of regularity in the older group as compared to the young group. Furthermore, our results showed that during the second peak the more regular behavior of blood flow oscillations (BFO) is mainly attributed to enhanced cardiac oscillations. This study suggests that the modified SampEn approach may be useful for assessing microvascular function.

Universal structures of normal and pathological heart rate variability

The circulatory system of living organisms is an autonomous mechanical system softly tuned with the respiratory system, and both developed by evolution as a response to the complex oxygen demand patterns associated with motion. Circulatory health is rooted in adaptability, which entails an inherent variability. Here, we show that a generalized N-dimensional normalized graph representing heart rate variability reveals two universal arrhythmic patterns as specific signatures of health one reflects cardiac adaptability, and the other the cardiac-respiratory rate tuning. In addition, we identify at least three universal arrhythmic profiles whose presences raise in proportional detriment of the two healthy ones in pathological conditions (myocardial infarction; heart failure; and recovery from sudden death). The presence of the identified universal arrhythmic structures together with the position of the centre of mass of the heart rate variability graph provide a unique quantitative assessment of the health-pathology gradient.

Synthesis of polyester urethane urea and fabrication of elastomeric nanofibrous scaffolds for myocardial regeneration

Fabrication of bioactive scaffolds is one of the most promising strategies to reconstruct the infarcted myocardium. In this study, we synthesized polyester urethane urea (PEUU), further blended it with gelatin and fabricated PEUU/G nanofibrous scaffolds. Attenuated total reflectance Fourier transform infrared spectroscopy (ATR-FTIR), differential scanning calorimetry (DSC) and X-ray diffraction were used for the characterization of the synthesized PEUU and properties of nanofibrous scaffolds were evaluated using scanning electron microscopy (SEM), ATR-FTIR, contact angle measurement, biodegradation test, tensile strength analysis and dynamic mechanical analysis (DMA). In vitro biocompatibility studies were performed using cardiomyocytes. DMA analysis showed that the scaffolds could be reshaped with cyclic deformations and might remain stable in the frequencies of the physiological activity of the heart. On the whole, our study suggests that aligned PEUU/G 70:30 nanofibrous scaffolds meet the required specifications for cardiac tissue engineering and could be used as a promising construct for myocardial regeneration.

Reference values for time- and frequency-domain heart rate variability measures

BACKGROUND

The analysis of heart rate variability (HRV) has become an established procedure in recent decades. Because there are no appropriate reference values available, HRV findings can still only be compared within a group or in individuals in longitudinal studies.

OBJECTIVE

The objectives of the present study were to examine a group of healthy subjects of different ages and sexes and to identify reference values for common HRV parameters.

METHODS

Long-term 24-hour electrocardiograms of 695 voluntary subjects were recorded by using a 2-channel Holter system over a period of 24 hours during daily activities.

RESULTS

Reference values for men and women in 10-year age groups were calculated for standard deviation of NN intervals, root mean square of successive differences of NN intervals, standard deviation of the average of all consecutive 5-minute NN intervals, percentage of consecutive NN intervals that deviate from one another by more than 50 ms, low-frequency power normalized unit, high-frequency power normalized unit, low frequency/high frequency ratio, SD1, and SD2. The 5th and 95th percentiles were given for each sex and for the age groups 20-30, 30-40, 40-50, and 50-60 years. We observed a consistent decrease in HRV measures with increasing age as well as a sex dependency of HRV findings.

CONCLUSION

We studied a large group of healthy subjects and identified reference values for commonly used HRV measures for 24-hour ECG measurements. The reference values differed considerably from the values published in 1996 in the Guidelines of the Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology. In the future, steps should be taken to expand the database and define reference values for the age groups under 20 and over 60 years. It would be desirable to obtain reference values for short-term recordings (eg, 5-minute recordings) as well.

Using Skewness and the First-Digit Phenomenon to Identify Dynamical Transitions in Cardiac Models

Disruptions in the normal rhythmic functioning of the heart, termed as arrhythmia, often result from qualitative changes in the excitation dynamics of the organ. The transitions between different types of arrhythmia are accompanied by alterations in the spatiotemporal pattern of electrical activity that can be measured by observing the time-intervals between successive excitations of different regions of the cardiac tissue. Using biophysically detailed models of cardiac activity we show that the distribution of these time-intervals exhibit a systematic change in their skewness during such dynamical transitions. Further, the leading digits of the normalized intervals appear to fit Benford's law better at these transition points. This raises the possibility of using these observations to design a clinical indicator for identifying changes in the nature of arrhythmia. More importantly, our results reveal an intriguing relation between the changing skewness of a distribution and its agreement with Benford's law, both of which have been independently proposed earlier as indicators of regime shift in dynamical systems.

Analysis of the microcirculatory pulse wave: age-related alterations

Morphological analysis of the pulse wave of central blood pressure signal is commonly used for the study of cardiac and vascular properties, but very few attempts were performed for analyzing the peripheral pulse wave of blood flow. In this work, we analyzed this waveform using classical methods, based on the application of FFT, followed by principal components analysis, for assessing the properties of the blood flow. As a sample problem, we evaluated the capability of the proposed method of assessing the alterations correlated with the aging of the vascular system. Results show a good discrimination between the different age groups, confirming the validity of the approach.

Effect of filtering on the classification rate of nonlinear analysis methods applied to uterine EMG signals

Nonlinear time series analysis can provide useful information regarding nonlinear features of biological signals. The effect of filtering on the performance of nonlinear methods is not well-understood. In this work, we investigate the effects of signal filtering on the sensitivity of four nonlinear methods: Time reversibility, Sample Entropy, Lyapunov Exponents and Delay Vector Variance. These methods were applied to uterine EMG signals with the aim of using them to discriminate between pregnancy and labor contractions. The signals were filtered using three different band-pass filters before the application of the methods. Results showed that the sensitivity of some methods such as sample entropy was significantly improved with filtering. On the other hand, filtering had little effect on some other methods such as time reversibility. This study concludes that while filtering increases computation time, it may be necessary for some nonlinear methods particularly those with low sensitivity.

Age-related alterations in phase synchronization of oxyhemoglobin concentration changes in prefrontal tissues as measured by near-infrared spectroscopy signals

The prefrontal cortex plays an important role in planning complex cognitive behavior, personality expression, and decision making. This study aims to assess the phase synchronization of signals of the oxyhemoglobin concentration changes (Δ[HbO2]) in the left and right prefrontal tissues through near-infrared spectroscopy (NIRS) with wavelet phase coherence (WPCO) method. The NIRS signals were continuously recorded from the left and right prefrontal lobes in 43 healthy elderly subjects (age: 69.6 ± 8.4 years) and 40 young healthy subjects (age: 24.5 ± 1.7 years) during the resting state. Phase synchronization between the left and right prefrontal oscillations in six frequency intervals (I, 0.6-2 Hz; II, 0.145-0.6 Hz; III, 0.052-0.145 Hz; IV, 0.021-0.052 Hz; V, 0.0095-0.021 Hz; and VI, 0.005-0.0095 Hz) was analyzed using the WPCO method. The WPCO values of elderly subjects were significantly lower in frequency intervals I (F=7.376, p=0.010) and III (F=6.418, p=0.016) than those of the young subjects. Low phase coherence in intervals I and III indicates reduced synchronization of cardiac activity in the prefrontal area and weakened prefrontal functional connectivity, respectively.

Wavelet analysis of skin perfusion to assess the effects of FREMS therapy before and after occlusive reactive hyperemia

Laser Doppler Fluxmetry is used to evaluate the hemodynamics of skin microcirculation. Laser Doppler signals contain oscillations due to fluctuations of microvascular perfusion. By performing spectral analysis, six frequency intervals from 0.005 to 2 Hz have been identified and assigned to distinct cardiovascular structures: heart, respiration, vascular myocites, sympathetic terminations and endothelial cells (dependent and independent on nitric oxide). Transcutaneous electrical pulses are currently applied to treat several diseases, i.e. neuropathies and chronic painful leg ulcers. Recently, FREMS (Frequency Rhythmic Electrical Modulation System) has been applied to vasculopathic patients, too. In this study Laser Doppler signals of skin microcirculation were measured in five patients with intermittent claudication, before and after the FREMS therapy. Changes in vascular activities were assessed by wavelet transform analysis. Preliminary results demonstrate that FREMS induces alterations in vascular activities.

The discriminatory value of cardiorespiratory interactions in distinguishing awake from anaesthetised states: a randomised observational study

Depth of anaesthesia monitors usually analyse cerebral function with or without other physiological signals; non‐invasive monitoring of the measured cardiorespiratory signals alone would offer a simple, practical alternative. We aimed to investigate whether such signals, analysed with novel, non‐linear dynamic methods, would distinguish between the awake and anaesthetised states. We recorded ECG, respiration, skin temperature, pulse and skin conductivity before and during general anaesthesia in 27 subjects in good cardiovascular health, randomly allocated to receive propofol or sevoflurane. Mean values, variability and dynamic interactions were determined. Respiratory rate (p = 0.0002), skin conductivity (p = 0.03) and skin temperature (p = 0.00006) changed with sevoflurane, and skin temperature (p = 0.0005) with propofol. Pulse transit time increased by 17% with sevoflurane (p = 0.02) and 11% with propofol (p = 0.007). Sevoflurane reduced the wavelet energy of heart (p = 0.0004) and respiratory (p = 0.02) rate variability at all frequencies, whereas propofol decreased only the heart rate variability below 0.021 Hz (p < 0.05). The phase coherence was reduced by both agents at frequencies below 0.145 Hz (p < 0.05), whereas the cardiorespiratory synchronisation time was increased (p < 0.05). A classification analysis based on an optimal set of discriminatory parameters distinguished with 95% success between the awake and anaesthetised states. We suggest that these results can contribute to the design of new monitors of anaesthetic depth based on cardiovascular signals alone.

Shape analysis of the microcirculatory flow wave

The cardiovascular system and its alterations are a crucial aspect of physiology and medicine. Non-invasive assessment of the functional properties of circulation is of considerable interest to clinicians and physiologists. In this work we investigate the possibility of detecting alterations of the flow waveform in microcirculation, using non-invasive measurements based on a laser Doppler flowmeter. As a test case, we focus on the effect of ageing. Skin is warmed up to a fixed temperature (44 °C) during measurement, to increase blood flow. The shape of the perfusion waveform during each heart beat after the flow was stabilized was used to estimate dynamic parameters of the microcirculatory system. Both the wave rise time, defined as the delay between the diastolic minimum and the following systolic maximum, and the oscillation fraction, defined as the normalized difference between the maximum and minimum flow, present significant variation with age.

Frequency-specific functional connectivity revealed by wavelet-based coherence analysis in elderly subjects with cerebral infarction using NIRS method

PURPOSE

Resting-state functional connectivity in subjects with cerebral infarction (CI) was assessed using wavelet-based coherence analysis of near-infrared spectroscopy (NIRS) signals.

METHODS

Continuous recordings of NIRS signals were measured from the prefrontal cortex and sensorimotor cortical areas of 12 subjects with CI (CI group) and 16 healthy subjects (healthy group) during the resting state. The channels in these areas were divided into four connection types: homologous connectivity, frontoposterior connectivity, contralateral connectivity, and homolateral connectivity. Wavelet coherence (WCO) and wavelet phase coherence (WPCO) were calculated in six frequency intervals in each channel pair: I, 0.6-2 Hz; II, 0.145-0.6 Hz; III, 0.052-0.145 Hz; IV, 0.021-0.052 Hz; V, 0.0095-0.021 Hz; and VI, 0.005-0.0095 Hz.

RESULTS

WCO in the six frequency intervals was significant for all channels in the healthy group. By contrast, WCO in frequency intervals II-VI showed weakened connectivity in the CI group, especially in terms of frontoposterior connectivity. WCO was significantly lower in the CI group than in the healthy group in the following connectivities and frequency intervals: front-posterior, IV-VI (p < 0.05); homologous, III-V (p < 0.01); motor-contralateral, III-V (p < 0.05); and motor-homolateral, III-V (p < 0.05). WPCO in frequency intervals III (F = 5.032, p = 0.033) and IV (F = 11.95, p = 0.002) in frontoposterior connectivity, as well as in intervals III-V in homologous, motor-contralateral and motor-homolateral connectivities were significantly lower (p < 0.05) in the CI group than in the healthy group. However, WPCO in interval I showed significantly higher levels in motor-homolateral connectivity in the CI group than in the healthy group (F = 4.241, p = 0.049).

CONCLUSIONS

The authors' results suggest that CI causes a frequency-specific disruption in resting-state connectivity. This may be useful for assessing the effectiveness of functional recovery after CI.

Nonlinear mode decomposition: a noise-robust, adaptive decomposition method

The signals emanating from complex systems are usually composed of a mixture of different oscillations which, for a reliable analysis, should be separated from each other and from the inevitable background of noise. Here we introduce an adaptive decomposition tool-nonlinear mode decomposition (NMD)-which decomposes a given signal into a set of physically meaningful oscillations for any wave form, simultaneously removing the noise. NMD is based on the powerful combination of time-frequency analysis techniques-which, together with the adaptive choice of their parameters, make it extremely noise robust-and surrogate data tests used to identify interdependent oscillations and to distinguish deterministic from random activity. We illustrate the application of NMD to both simulated and real signals and demonstrate its qualitative and quantitative superiority over other approaches, such as (ensemble) empirical mode decomposition, Karhunen-Loève expansion, and independent component analysis. We point out that NMD is likely to be applicable and useful in many different areas of research, such as geophysics, finance, and the life sciences. The necessary matlab codes for running NMD are freely available for download.

Effect of Maximal Apnoea Easy-Going and Struggle Phases on Subarachnoid Width and Pial Artery Pulsation in Elite Breath-Hold Divers

Purpose

The aim of the study was to assess changes in subarachnoid space width (sas-TQ), the marker of intracranial pressure (ICP), pial artery pulsation (cc-TQ) and cardiac contribution to blood pressure (BP), cerebral blood flow velocity (CBFV) and cc-TQ oscillations throughout the maximal breath hold in elite apnoea divers. Non-invasive assessment of sas-TQ and cc-TQ became possible due to recently developed method based on infrared radiation, called near-infrared transillumination/backscattering sounding (NIR-T/BSS).

Methods

The experimental group consisted of seven breath-hold divers (six men). During testing, each participant performed a single maximal end-inspiratory breath hold. Apnoea consisted of the easy-going and struggle phases (characterised by involuntary breathing movements (IBMs)). Heart rate (HR) was determined using a standard ECG. BP was assessed using the photoplethysmography method. SaO₂ was monitored continuously with pulse oximetry. A pneumatic chest belt was used to register thoracic and abdominal movements. Cerebral blood flow velocity (CBFV) was estimated by a 2-MHz transcranial Doppler ultrasonic probe. sas-TQ and cc-TQ were measured using NIR-T/BSS. Wavelet transform analysis was performed to assess cardiac contribution to BP, CBFV and cc-TQ oscillations.

Results

Mean BP and CBFV increased compared to baseline at the end of the easy phase and were further augmented by IBMs. cc-TQ increased compared to baseline at the end of the easy phase and remained stable during the IBMs. HR did not change significantly throughout the apnoea, although a trend toward a decrease during the easy phase and recovery during the IBMs was visible. Amplitudes of BP, CBFV and cc-TQ were augmented. sas-TQ and SaO₂ decreased at the easy phase of apnoea and further decreased during the IBMs.

Conclusions

Apnoea increases intracranial pressure and pial artery pulsation. Pial artery pulsation seems to be stabilised by the IBMs. Cardiac contribution to BP, CBFV and cc-TQ oscillations does not change throughout the apnoea.

Sympathetic Activation Does Not Affect the Cardiac and Respiratory Contribution to the Relationship between Blood Pressure and Pial Artery Pulsation Oscillations in Healthy Subjects

Introduction

Using a novel method called near-infrared transillumination backscattering sounding (NIR-T/BSS) that allows for the non-invasive measurement of pial artery pulsation (cc-TQ) and subarachnoid width (sas-TQ) in humans, we assessed the influence of sympathetic activation on the cardiac and respiratory contribution to blood pressure (BP) cc-TQ oscillations in healthy subjects.

Methods

The pial artery and subarachnoid width response to handgrip (HGT) and cold test (CT) were studied in 20 healthy subjects. The cc-TQ and sas-TQ were measured using NIR-T/BSS; cerebral blood flow velocity (CBFV) was measured using Doppler ultrasound of the left internal carotid artery; heart rate (HR) and beat-to-beat mean BP were recorded using a continuous finger-pulse photoplethysmography; respiratory rate (RR), minute ventilation (MV), end-tidal CO₂ (EtCO2) and end-tidal O₂ (EtO2) were measured using a metabolic and spirometry module of the medical monitoring system. Wavelet transform analysis was used to assess the relationship between BP and cc-TQ oscillations.

Results

HGT evoked an increase in BP (+15.9%; P<0.001), HR (14.7; P<0.001), SaO₂ (+0.5; P<0.001) EtO₂ (+2.1; P<0.05) RR (+9.2%; P = 0.05) and MV (+15.5%; P<0.001), while sas-TQ was diminished (-8.12%; P<0.001), and a clear trend toward cc-TQ decline was observed (-11.0%; NS). CBFV (+2.9%; NS) and EtCO₂ (-0.7; NS) did not change during HGT. CT evoked an increase in BP (+7.4%; P<0.001), sas-TQ (+3.5%; P<0.05) and SaO₂(+0.3%; P<0.05). HR (+2.3%; NS), CBFV (+2.0%; NS), EtO₂ (-0.7%; NS) and EtCO₂ (+0.9%; NS) remained unchanged. A trend toward decreased cc-TQ was observed (-5.1%; NS). The sas-TQ response was biphasic with elevation during the first 40 seconds (+8.8% vs. baseline; P<0.001) and subsequent decline (+4.1% vs. baseline; P<0.05). No change with respect to wavelet coherence and wavelet phase coherence was found between the BP and cc-TQ oscillations.

Conclusions

Short sympathetic activation does not affect the cardiac and respiratory contribution to the relationship between BP—cc-TQ oscillations. HGT and CT display divergent effects on the width of the subarachnoid space, an indirect marker of changes in intracranial pressure.

Low-frequency oscillations in cerebrovascular and cardiovascular hemodynamics: Their interrelationships and the effect of age

The aim of this study was to investigate how the interrelationships between low-frequency oscillations (LFOs) in the cerebral and systemic cardiovascular hemodynamic systems change with aging and systemic hemodynamic perturbation. Seventeen young adult (28.4±3.5years) and seventeen elderly subjects (69.4±8.7years) underwent continuous measurements of arterial blood pressure (ABP), heart rate (HR), and cerebral oxygenation (oxy-hemoglobin, deoxy-hemoglobin, and total hemoglobin) using near-infrared spectroscopy. The LFOs were subdivided into three frequency intervals (FI-1: 0.01-0.02Hz, FI-2: 0.02-0.06Hz, and FI-3: 0.06-0.15Hz) via spectral analysis based on continuous wavelet transform. The amplitudes of the LFOs at these FIs were calculated to examine the effects of aging and head-up tilt (HUT) on cerebral and cardiovascular hemodynamics. Granger causality (GC) was used for analyzing the causal relationships between the LFOs observed in ABP, oxy-hemoglobin, and HR. The amplitudes of the LFOs were generally higher in young adults than in the elderly and increased significantly only in the younger subjects after HUT. GCs in FI-3 oscillations were significantly higher in young subjects compared to older participants in the HUT state. These results indicate that aging dampens systemic and cerebral hemodynamic regulatory mechanisms, and the interrelationships between systemic and cerebral hemodynamics become weaker with age.

Dynamic markers based on blood perfusion fluctuations for selecting skin melanocytic lesions for biopsy

Skin malignant melanoma is a highly angiogenic cancer, necessitating early diagnosis for positive prognosis. The current diagnostic standard of biopsy and histological examination inevitably leads to many unnecessary invasive excisions. Here, we propose a non-invasive method of identification of melanoma based on blood flow dynamics. We consider a wide frequency range from 0.005-2 Hz associated with both local vascular regulation and effects of cardiac pulsation. Combining uniquely the power of oscillations associated with individual physiological processes we obtain a marker which distinguishes between melanoma and atypical nevi with sensitivity of 100% and specificity of 90.9%. The method reveals valuable functional information about the melanoma microenvironment. It also provides the means for simple, accurate, in vivo distinction between malignant melanoma and atypical nevi, and may lead to a substantial reduction in the number of biopsies currently undertaken.

Phase synchronization analysis of prefrontal tissue oxyhemoglobin oscillations in elderly subjects with cerebral infarction

PURPOSE

This study aims to assess the phase relationship of prefrontal tissue oxyhemoglobin oscillations using wavelet phase coherence analysis of cerebral Delta [HbO₂] signals in cerebral infarction (CI) patients during the resting state.

METHODS

Continuous recordings of near-infrared spectroscopy signals were obtained from the left and right prefrontal lobes in 21 subjects with CI (Group CI, age: 76.6 ± 8.5 yr) and 21 healthy elderly subjects (Group Healthy, age: 69.0 ± 7.4 yr) during the resting state. The Group CI was further divide into two groups: CI with hypertension and CI without hypertension. The phase synchronization between left and right prefrontal Delta [HbO₂] oscillations in four frequency intervals (I, 0.6-2 Hz; II, 0.145-0.6 Hz; III, 0.052-0.145 Hz; and IV, 0.021-0.052 Hz) was analyzed using wavelet phase coherence method.

RESULTS

The phase coherences in intervals III and IV were significantly lower in CI with hypertension than in healthy elderly subjects (F = 12.974, p = 0.001 for III and F = 10.073, p = 0.004 for interval IV). The phase coherence of CI without hypertension in interval III was significantly lower than in healthy elderly subjects (F = 9.909, p = 0.004). Also, the phase coherence in interval IV was significantly lower in CI with hypertension than in CI without hypertension (F = 5.665, p = 0.028). Also, the phase agreement in interval IV showed evident difference between Group CI with hypertension and without hypertension.

CONCLUSIONS

The difference in phase characteristics of prefrontal tissue oxyhemoglobin oscillations between the CI patients and healthy elderly indicates altered phase synchronization. Moreover, the CI combined with hypertension would aggravate this process. This study provides new insight into the phase dynamics of cerebral oxygenation and may be useful in assessing the risk for stroke.

Multifractality in heartbeat dynamics in patients undergoing beating-heart myocardial revascularization

BACKGROUND

The multifractal approach of HRV analysis offers new insight into the mechanisms of autonomic modulation of the diseased hearts and has a potential to depict subtle changes in cardiac autonomic nervous control not revealed by conventional linear and non-linear analyses in various conditions like heart failure or stable angina pectoris. The aim of this study was to employ the multifractality approach in cardiac surgery patients and evaluate the multifractality before and after beating-heart myocardial revascularization (off-pump CABG).

METHODS

Twenty-four hour Holter recordings were performed pre- and postoperatively in 60 patients undergoing off-pump CABG. Selected conventional time- and frequency-domain linear HRV indices were calculated from the 24h and 5 min ECG segments, and preselected multifractal parameters τ(q=2), τ(q=3), h_top and Δh were determined for daytime (12:00-18:00) and nighttime (00:00-06:00) periods of the ECG recordings using Ivanov's method. Mean differences over time were tested using paired-samples t-test and exact Wilcoxon matched-pairs test. The results are reported as mean ± SD and median with interquartile range. A p value of <0.05 was considered statistically significant.

RESULTS

All selected conventional linear HRV parameters decreased significantly after off pump CABG (p from <0.001-0.015). Preoperatively, multifractal parameter τ(q=2) was -0.60 ± 0.12 and -0.54 ± 0.12, τ(q=3) -0.52 ± 0.18 and -0.49 ± 0.17, h_top 0.20 ± 0.07 and 0.15 ± 0.07 and Δh 0.31 ± 0.14 and 0.17 ± 0.14 for daytime and nighttime periods, respectively. Postoperatively, τ(q=2) and τ(q=3) were significantly higher for daytime (-0.49 ± 0.15, p<0.001 and -0.43 ± 0.23, p=0.015), whereas h_top and Δh were significantly higher for both daytime and nighttime (0.25 ± 0.07, p<0.001 and 0.19 ± 0.06, p=0.002 for h_top and 0.41 ± 0.20, p=0.003 and 0.31 ± 0.19, p < 0.001 for Δh, respectively). All pre- and postoperative parameters, except τ(q=2) and τ(q=3) preoperatively, were significantly lower for nighttime as compared to daytime periods.

CONCLUSIONS

A significant breakdown of multifractal complexity and anti-correlation behavior with a significant sympathetic overdrive and a concomitant parasympathetic withdrawal occurs after off-pump CABG. The circadian pattern of multifractality regains its day-night variation in the first week after the surgical procedure.

Frequency and temperature dependence of skin bioimpedance during a contralateral cold test

A study of the α- and β-dispersion of skin bioimpedance dependence on temperature and micro-hemodynamics is presented. The vascular tone changes during the cold test are verified by the wavelet-analysis of skin temperature signals obtained simultaneously with impedance measurements. Thirty three normal healthy subjects of 28  ±  7 years old were entered into the study. The tetra-polar electrode system was used to record the resistance and reactance; measurements were carried out at 67 frequencies, in a frequency range from 2 Hz to 50 kHz. It has been found that the impedance decreases with vasodilation and increases with vasoconstriction. The high values of correlation among thermal oscillation amplitudes and Nyquist diagram parameters prove the impedance dependence on blood flow in three frequency bands corresponding to the myogenic, neurogenic and endothelial vascular tone regulation mechanisms. Using an equivalent RC circuit, we obtained the changes in the Nyquist diagram matching the experimental data. The proposed descriptive α-dispersion model can be used to study mechanisms responsible for intercellular interaction.

Ageing of the couplings between cardiac, respiratory and myogenic activity in humans

The balance and functionality of the cardiovascular system are maintained by a network of couplings between the different oscillations involved. We study the effect of ageing on these interactions through the application of wavelet analysis, and by the use of dynamical Bayesian inference to compute coupling functions. The method, applied to phases extracted from microvascular flow recorded by laser Doppler flowmetry (LDF), reveals the coupling functions between oscillations propagated to the smallest vessels. Consistent with earlier work based on analysis of cardiac and respiratory phases obtained from direct measurements, our analysis demonstrates an impairment of the propagated cardio-respiratory coupling with ageing. The coupling weakens despite the increased cardiac component in the LDF with ageing. Our results bring new insight to the effect of ageing on cardiovascular regulation that might help improve the diagnostic potential of LDF monitors.

Cerebral autoregulation in response to posture change in elderly subjects-assessment by wavelet phase coherence analysis of cerebral tissue oxyhemoglobin concentrations and arterial blood pressure signals

This study aims to assess the dynamic cerebral autoregulation (dCA) in response to posture change using wavelet phase coherence (WPCO) of cerebral tissue oxyhemoglobin concentrations (Delta [HbO2]) and arterial blood pressure (ABP) signals in healthy elderly subjects. Continuous recordings of near-infrared spectroscopy (NIRS) and ABP signals were obtained from simultaneous measurements in 16 healthy elderly subjects (age: 68.9±7.1 years) and 19 young subjects (age: 24.9±3.2 years). The phase coherence between Delta [HbO2] and ABP oscillations in six frequency intervals (I, 0.6-2 Hz; II, 0.15-0.6 Hz; III, 0.05-0.15 Hz; IV, 0.02-0.05 Hz, V, 0.0095-0.02 Hz and VI, 0.005-0.0095 Hz) was analyzed using WPCO. The sit-to-stand posture change induces significantly lower WPCO in interval III (F=5.50 p=0.025) in the elderly subjects than in the young subjects. However, the stand-to-sit posture change induces higher WPCO in intervals II (F=5.25 p=0.028) and V (F=6.22 p=0.018) in the elderly subjects than in the young subjects. The difference of WPCO in response to posture change between the elderly and the young subjects indicates an altered CA due to aging. This study provides new insight into the dynamics of CA and may be useful in identifying the risk for dCA processes.

Generalized chronotaxic systems: time-dependent oscillatory dynamics stable under continuous perturbation

Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in Phys. Rev. Lett. 111, 024101 (2013) chronotaxic systems had often been treated as stochastic, inappropriately, and the deterministic component had been ignored. While the previous work addressed the case of the decoupled amplitude and phase dynamics, in this paper we develop a generalized theory of chronotaxic systems where such decoupling is not required. The theory presented is based on the concept of a time-dependent point attractor or a driven steady state and on the contraction theory of dynamical systems. This simplifies the analysis of chronotaxic systems and makes possible the identification of chronotaxic systems with time-varying parameters. All types of chronotaxic dynamics are classified and their properties are discussed using the nonautonomous Poincaré oscillator as an example. We demonstrate that these types differ in their transient dynamics towards a driven steady state and according to their response to external perturbations. Various possible realizations of chronotaxic systems are discussed, including systems with temporal chronotaxicity and interacting chronotaxic systems.

RR interval-respiratory signal waveform modeling in human slow paced and spontaneous breathing

Our aim was to model the dependence of respiratory sinus arrhythmia (RSA) on the respiratory waveform and to elucidate underlying mechanisms of cardiorespiratory coupling. In 30 subjects, RR interval and respiratory signal were recorded during spontaneous and paced (0.1Hz/0.15Hz) breathing and their relationship was modeled by a first order linear differential equation. This model has two parameters: a0 (related to the instantaneous degree of abdominal expansion) and a1 (referring to the speed of abdominal expansion). Assuming that a0 represents slowly adapting pulmonary stretch receptors (SARs) and a1 SARs in coordination with other stretch receptors and central integrative coupling; then pulmonary stretch receptors relaying the instantaneous lung volume are the major factor determining cardiovagal output during inspiration. The model's results depended on breathing frequency with the least error occurring during slow paced breathing. The role of vagal afferent neurons in cardiorespiratory coupling may relate to neurocardiovascular diseases in which weakened coupling among venous return, arterial pressure, heart rate and respiration produces cardiovagal instability.

Wavelet coherence analysis of prefrontal tissue oxyhaemoglobin signals as measured using near-infrared spectroscopy in elderly subjects with cerebral infarction

This study aims to assess the prefrontal functional connectivity using wavelet coherence analysis of cerebral tissue oxyhaemoglobin concentration (Delta [HbO2]) signals in elderly subjects with cerebral infarction (CI) during the resting state. Continuous recordings of near-infrared spectroscopy (NIRS) signals were obtained from the left and right prefrontal lobes in 10 subjects with CI (age: 74.4±9.0years) and 18 healthy elderly subjects (age: 69.9±7.3years) during the resting state. The coherence between left and right prefrontal Delta [HbO2] oscillations in four frequency intervals (I, 0.6-2Hz; II, 0.145-0.6Hz; III, 0.052-0.145Hz and IV, 0.021-0.052Hz) was analyzed using wavelet coherence analysis. In healthy elderly subjects, the Delta [HbO2] oscillations were significantly wavelet coherent in intervals I and III (p<0.05), wavelet phase coherent in intervals from I to IV. In elderly subjects with CI, the left and right Delta [HbO2] oscillations were significantly wavelet coherent and phase coherent in interval I (p<0.05). In elderly subjects with CI, the power and phase coherences were significantly lower in interval III (p<0.01) than in healthy subjects. The difference in wavelet coherence between the healthy elderly and elderly with CI indicates an altered brain functional connectivity in CI patients. This may be useful for assessing the effectiveness of functional recovery following a CI.

Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: new insights from mathematical modeling

A minimal model for the neural control of heart rate (HR) has been developed with the aim of better understanding respiratory sinus arrhythmia (RSA)--a modulation of HR at the frequency of breathing. This model consists of two differential equations and is integrated into a previously-published model of gas exchange. The heart period is assumed to be affected primarily by the parasympathetic signal, with the sympathetic signal taken as a parameter in the model. We include the baroreflex, mechanical stretch-receptor feedback from the lungs, and central modulation of the cardiac vagal tone by the respiratory drive. Our model mimics a range of experimental observations and provides several new insights. Most notably, the model mimics the growth in the amplitude of RSA with decreasing respiratory frequency up to 7 breaths per minute (for humans). Our model then mimics the decrease in the amplitude of RSA at frequencies below 7 breaths per minute and predicts that this decrease is due to the baroreflex (we show this both numerically and analytically with a linear baroreflex). Another new prediction of the model is that the gating of the baroreflex leads to the dependency of RSA on mean vagal tone. The new model was also used to test two previously-suggested hypotheses regarding the physiological function of RSA and supports the hypothesis that RSA minimizes the work done by the heart while maintaining physiological levels of arterial CO2. These and other new insights the model provides extend our understanding of the integrative nature of vagal control of the heart.

Dynamical inference: where phase synchronization and generalized synchronization meet

Synchronization is a widespread phenomenon that occurs among interacting oscillatory systems. It facilitates their temporal coordination and can lead to the emergence of spontaneous order. The detection of synchronization from the time series of such systems is of great importance for the understanding and prediction of their dynamics, and several methods for doing so have been introduced. However, the common case where the interacting systems have time-variable characteristic frequencies and coupling parameters, and may also be subject to continuous external perturbation and noise, still presents a major challenge. Here we apply recent developments in dynamical Bayesian inference to tackle these problems. In particular, we discuss how to detect phase slips and the existence of deterministic coupling from measured data, and we unify the concepts of phase synchronization and general synchronization. Starting from phase or state observables, we present methods for the detection of both phase and generalized synchronization. The consistency and equivalence of phase and generalized synchronization are further demonstrated, by the analysis of time series from analog electronic simulations of coupled nonautonomous van der Pol oscillators. We demonstrate that the detection methods work equally well on numerically simulated chaotic systems. In all the cases considered, we show that dynamical Bayesian inference can clearly identify noise-induced phase slips and distinguish coherence from intrinsic coupling-induced synchronization.

Heart motion uncertainty compensation prediction method for robot assisted beating heart surgery - Master-slave Kalman Filters approach

Robot Assisted Coronary Artery Bypass Graft (CABG) allows the heart keep beating in the surgery by actively eliminating the relative motion between point of interest (POI) on the heart surface and surgical tool. The inherited nonlinear and diverse nature of beating heart motion gives a huge obstacle for the robot to meet the demanding tracking control requirements. In this paper, we novelty propose a Master-slave Kalman Filter based on beating heart motion Nonlinear Adaptive Prediction (NAP) algorithm. In the study, we describe the beating heart motion as the combination of nonlinearity relating mathematics part and uncertainty relating non-mathematics part. Specifically, first, we model the nonlinearity of the heart motion via quadratic modulated sinusoids and estimate it by a Master Kalman Filter. Second, we involve the uncertainty heart motion by adaptively change the covariance of the process noise through the slave Kalman Filter. We conduct comparative experiments to evaluate the proposed approach with four distinguished datasets. The results indicate that the new approach reduces prediction errors by at least 30 μm. Moreover, the new approach performs well in robustness test, in which two kinds of arrhythmia datasets from MIT-BIH arrhythmia database are assessed.

In vivo cardiac phase response curve elucidates human respiratory heart rate variability

Recovering interaction of endogenous rhythms from observations is challenging, especially if a mathematical model explaining the behaviour of the system is unknown. The decisive information for successful reconstruction of the dynamics is the sensitivity of an oscillator to external influences, which is quantified by its phase response curve. Here we present a technique that allows the extraction of the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators--in this case heartbeat and respiration--in its natural environment and under free-running conditions. We use this method to obtain the phase-coupling functions describing cardiorespiratory interactions and the phase response curve of 17 healthy humans. We show for the first time the phase at which the cardiac beat is susceptible to respiratory drive and extract the respiratory-related component of heart rate variability. This non-invasive method for the determination of phase response curves of coupled oscillators may find application in many scientific disciplines.

Wavelet coherence analysis of prefrontal oxygenation signals in elderly subjects with hypertension

This study aims to assess the prefrontal functional connectivity in elderly subjects with hypertension during the resting state using wavelet coherence analysis of changes in prefrontal tissue oxyhaemoglobin concentrations (Δ[HbO2]) signals measured by near-infrared spectroscopy (NIRS). Continuous recordings of NIRS signals were obtained from the left and right prefrontal lobes in 24 elderly subjects with hypertension (age: 70.7 ± 8.4 years) and 26 elderly normotensive subjects (age: 70.6 ± 7.9 years) during the resting state. The coherence between the left and right prefrontal oscillations in four frequency intervals (I, 0.4 Hz to 2 Hz; II, 0.15 Hz to 0.4 Hz; III, 0.05 Hz to 0.15 Hz; and IV, 0.02 Hz to 0.05 Hz) was analyzed using wavelet coherence method. The Δ[HbO2] oscillations showed significant wavelet coherence (WCO) in intervals I and III, and significant wavelet phase coherence (WPCO) in intervals from I to IV. Remarkably, in elderly subjects with hypertension, the WCO and WPCO in interval III were significantly lower in the left and right prefrontal regions than in healthy elderly subjects (p = 0.014 for WCO, p = 0.007 for WPCO). The lower coherence in interval III indicates a decreased synchronization of neural control in the left and right prefrontal regions in elderly subjects with hypertension. This might suggest a weakened brain functional connectivity in the elderly subjects with hypertension.

Wavelet coherence analysis of spontaneous oscillations in cerebral tissue oxyhemoglobin concentrations and arterial blood pressure in elderly subjects

This study aims to assess the relationship between spontaneous oscillations in changes in cerebral tissue oxyhemoglobin concentrations (Delta [HbO2]) and arterial blood pressure (ABP) signals in healthy elderly subjects during the resting state using wavelet coherence analysis. Continuous recordings of near-infrared spectroscopy (NIRS) and ABP signals were obtained from simultaneous measurements in 33 healthy elderly subjects (age: 70.7±7.9 years) and 27 young subjects (age: 25.2±3.7 years) during the resting state. The coherence between Delta [HbO2] and ABP oscillations in six frequency intervals (I, 0.4-2 Hz; II, 0.15-0.4 Hz; III, 0.05-0.15 Hz; IV, 0.02-0.05 Hz, V, 0.005-0.0095 Hz and VI, 0.005-0.0095 Hz) was analyzed using wavelet coherence analysis. In elderly subjects, the Delta [HbO2] and ABP oscillations were significantly wavelet coherent in interval I, and wavelet phase coherent in intervals I, II and IV. The wavelet coherence in interval I was significantly higher (p=0.040), in elderly subjects than in young subjects whereas that in interval V significantly lower (p=0.015). In addition, the wavelet phase coherence in interval IV was significantly higher in elderly subjects than in young subjects (p=0.028). The difference in the wavelet coherence of the elderly subjects and the young subjects indicates an altered cerebral autoregulation caused by aging. This study provides new insight into the dynamics of Delta [HbO2] and ABP oscillations and may be useful in identifying the risk for dynamic cerebral autoregulation processes.

Inverse approach to chronotaxic systems for single-variable time series

Following the development of a new class of self-sustained oscillators with a time-varying but stable frequency, the inverse approach to these systems is now formulated. We show how observed data arranged in a single-variable time series can be used to recognize such systems. This approach makes use of time-frequency domain information using the wavelet transform as well as the recently developed method of Bayesian-based inference. In addition, a set of methods, named phase fluctuation analysis, is introduced to detect the defining properties of the new class of systems by directly analyzing the statistics of the observed perturbations.We apply these methods to numerical examples but also elaborate further on the cardiac system.

Performance analysis of four nonlinearity analysis methods using a model with variable complexity and application to uterine EMG signals

Several measures have been proposed to detect nonlinear characteristics in time series. Results on time series, multiple surrogates and their z-score are used to statistically test for the presence or absence of non-linearity. The z-score itself has sometimes been used as a measure of nonlinearity. The sensitivity of nonlinear methods to the nonlinearity level and their robustness to noise have rarely been evaluated in the past. While surrogates are important tools to rigorously detect nonlinearity, their usefulness for evaluating the level of nonlinearity is not clear. In this paper we investigate the performance of four methods arising from three families that are widely used in non-linearity detection: statistics (time reversibility), predictability (sample entropy, delay vector variance) and chaos theory (Lyapunov exponents). We used sensitivity to increasing complexity and the mean square error (MSE) of Monte Carlo instances for quantitative comparison of their performances. These methods were applied to a Henon nonlinear synthetic model in which we can vary the complexity degree (CD). This was done first by applying the methods directly to the signal and then using the z-score (surrogates) with and without added noise. The methods were then applied to real uterine EMG signals and used to distinguish between pregnancy and labor contraction bursts. The discrimination performances were compared to linear frequency based methods classically used for the same purpose such as mean power frequency (MPF), peak frequency (PF) and median frequency (MF). The results show noticeable difference between different methods, with a clear superiority of some of the nonlinear methods (time reversibility, Lyapunov exponents) over the linear methods. Applying the methods directly to the signals gave better results than using the z-score, except for sample entropy.