A nonlinear model of cardiac autonomic control in obstructive sleep apnea syndrome

Unanticipated evolution of cardio-respiratory interactions with cognitive load during a Go-NoGo shooting task in virtual reality

The cardiovascular system interacts continuously with the respiratory system to maintain the vital balance of oxygen and carbon dioxide in our body. The interplay between the sympathetic and parasympathetic branches of the autonomic nervous system regulates the aforesaid involuntary functions. This study analyzes the dynamics of the cardio-respiratory (CR) interactions using RR Intervals (RRI), Systolic Blood Pressure (SBP), and Respiration signals after first-order differencing to make them stationary. It investigates their variation with cognitive load induced by a virtual reality (VR) based Go-NoGo shooting task with low and high levels of task difficulty. We use Pearson's correlation-based linear and mutual information-based nonlinear measures of association to indicate the reduction in RRI-SBP and RRI-Respiration interactions with cognitive load. However, no linear correlation difference was observed in SBP-Respiration interactions with cognitive load, but their mutual information increased. A couple of open-loop autoregressive models with exogenous input (ARX) are estimated using RRI and SBP, and one closed-loop ARX model is estimated using RRI, SBP, and Respiration. The impulse responses (IRs) are derived for each input-output pair, and a reduction in the positive and negative peak amplitude of all the IRs is observed with cognitive load. Some novel parameters are derived by representing the IR as a double exponential curve with cosine modulation and show significant differences with cognitive load compared to other measures, especially for the IR between SBP and Respiration.

A comprehensive evaluation of linear and non-linear HRV parameters between paced breathing and stressful mental state

Background

Heart rate variability (HRV) is a crucial metric that provides valuable insight into the balance between relaxation and stress. Previous research has shown that most HRV parameters improve during periods of mental relaxation, while decreasing during tasks involving cognitive workload. Although a comprehensive analysis of both linear and non-linear HRV parameters has been carried out in existing literature, there still exists a need for further research in this area. Additionally, limited knowledge exists regarding how specific interventions may influence the interpretation of these parameters and how the different parameters correlate under different interventions. This study aims to address these gaps by conducting a thorough comparison of different linear and non-linear HRV parameters under mentally relaxed versus stressful states.

Methodology

Participants were randomly and equally divided among two between-subjects groups: relaxed-stress (RS) (N = 22) and stress-relaxed (SR) (N = 22). In the RS group, a paced breathing task was given for 5 min to create relaxation, and was followed by a 5-min time-based mental calculation task to create stress. In the SR group, the order of the stress and relaxed tasks was reversed. There was a washout period of 15 min after the first task in both groups.

Results

Of the 37 HRV parameters, 33 differed significantly between the two interventions. The majority of the parameters exhibited an improving and degrading tendency of HRV parameters in the relaxed and stressed states, respectively. The correlation of the majority of HRV parameters decreases during stress, while prominent time domain and geometric domain parameters stand out in the correlation.

Conclusion

Overall, HRV parameters can be reliably used to assess a person's relaxed and stressed mental states during paced breathing and mental arithmetic task respectively. Furthermore, non-linear HRV parameters provide accurate estimators of the mental state, in addition to the commonly used linear parameters.

A Nonlinear Effective Connectivity Measure Based on Granger Causality and Volterra Series

Estimating effective connectivity, especially in brain networks, is an important topic to find out the brain functions. Various effective connectivity measures are presented, but they have drawbacks, including bivariate structure, the problem in detecting nonlinear interactions, and high computational cost. In this paper, we have proposed a novel multivariate effective connectivity measure based on a hierarchical realization of the Volterra series model and Granger causality concept, namely hierarchical Volterra Granger causality (HVGC). HVGC is a multivariate connectivity measure that can detect linear and nonlinear causal effects. The performance of HVGC is compared with Granger causality index (GCI), conditional Granger causality index (CGCI), transfer entropy (TE), phase transfer entropy (Phase TE), and partial transfer entropy (Partial TE) in simulated and physiological datasets. In addition to accuracy, specificity, and sensitivity, the Matthews correlation coefficient (MCC) is used to evaluate the connectivity estimation in simulated datasets. Furthermore influence of different SNRs is investigated on the estimated connectivity. The obtained results show that HVGC with a minimum MCC of 0.76 performs well in the detection of both linear and nonlinear interactions in simulated data. HVGC is also applied to a physiological dataset that was cardiorespiratory interaction signals recorded during sleep from a patient suffering from sleep apnea. The results of this dataset also demonstrate the capability of the proposed method in the detection of causal interactions. Applying HVGC on the simulated fMRI dataset led to a high MCC of 0.78. Moreover, the results indicate that HVGC has slight changes in different SNRs. The results indicate that HVGC can estimate the causal effects of a linear and nonlinear system with a low computational cost and it is slightly affected by noise.

Sleep-disordered breathing and self-reported general health status in Thai patients

Background: Sleep-disordered breathing (SDB) has been a rapidly increasing health problem in Thai. Its effect on quality of life of Thai patients has not been adequately addressed. Objective: Determine the relationship between SDB and self-reported general health status in Thai patients. Materials and methods: A descriptive and cross-sectional study was used. Two hundred and sixtyeight patients (195 men and 73 women, age: 16-82 years) are recruited from King Chulalongkorn Memorial Hospital between January 2006 and December 2007. A health profile was obtained by self-administered questionnaire. SDB severity was assessed using an attended single-night comprehensive polysomnography. Results: SDB was not directly associated with the general health status. Presence of excessive daytime sleepiness, which was the major symptom of obstructive sleep apnea, was associated with a decrease in all domains of Short Form 36. Age, sex, and body mass index were also related to a lower physical function. Hypertension and excessive daytime sleepiness were associated with the severity of SDB. Conclusion: SDB is indirectly related to a lower general health status, and this relationship is of clinical significance.

Attenuation of vagal modulation with aging: Univariate and bivariate analysis of HRV

The aging process leads to diverse changes in the human organism, including in autonomic system modulation. In this study, we calculated indices of HRV in frequency (power spectral density, PSD) and time (the impulse response (IR) method) domains, using data from healthy young and elderly volunteers (Fantasia database from Physionet). The results obtained showed that aging leads to an attenuation of vagal modulation of elderly individuals when compared to young volunteers.

Nonlinear Dynamics Forecasting of Obstructive Sleep Apnea Onsets

Recent advances in sensor technologies and predictive analytics are fueling the growth in point-of-care (POC) therapies for obstructive sleep apnea (OSA) and other sleep disorders. The effectiveness of POC therapies can be enhanced by providing personalized and real-time prediction of OSA episode onsets. Previous attempts at OSA prediction are limited to capturing the nonlinear, nonstationary dynamics of the underlying physiological processes. This paper reports an investigation into heart rate dynamics aiming to predict in real time the onsets of OSA episode before the clinical symptoms appear. A prognosis method based on a nonparametric statistical Dirichlet-Process Mixture-Gaussian-Process (DPMG) model to estimate the transition from normal states to an anomalous (apnea) state is utilized to estimate the remaining time until the onset of an impending OSA episode. The approach was tested using three datasets including (1) 20 records from 14 OSA subjects in benchmark ECG apnea databases (Physionet.org), (2) records of 10 OSA patients from the University of Dublin OSA database and (3) records of eight subjects from previous work. Validation tests suggest that the model can be used to track the time until the onset of an OSA episode with the likelihood of correctly predicting apnea onset in 1 min to 5 mins ahead is 83.6 ± 9.3%, 80 ± 8.1%, 76.2 ± 13.3%, 66.9 ± 15.4%, and 61.1 ± 16.7%, respectively. The present prognosis approach can be integrated with wearable devices, enhancing proactive treatment of OSA and real-time wearable sensor-based of sleep disorders.

Model-Derived Markers of Autonomic Cardiovascular Dysfunction in Sleep-Disordered Breathing

Evidence indicates that sleep-disordered breathing leads to elevated sympathetic tone and impaired vagal activity, promoting hypertension and cardiometabolic disease. Low-cost but accurate monitoring of autonomic function is useful for the aggressive management of sleep apnea. This article reviews the development and application of multivariate dynamic biophysical models that enable the causal dependencies among respiration, blood pressure, heart rate variability, and peripheral vascular resistance to be quantified. The markers derived from these models can be used in conjunction with heart rate variability to increase the sensitivity with which abnormalities in autonomic cardiovascular control are detected in subjects with sleep-disordered breathing.

A Nonlinear Causality Estimator Based on Non-Parametric Multiplicative Regression

Causal prediction has become a popular tool for neuroscience applications, as it allows the study of relationships between different brain areas during rest, cognitive tasks or brain disorders. We propose a nonparametric approach for the estimation of nonlinear causal prediction for multivariate time series. In the proposed estimator, C NPMR , Autoregressive modeling is replaced by Nonparametric Multiplicative Regression (NPMR). NPMR quantifies interactions between a response variable (effect) and a set of predictor variables (cause); here, we modified NPMR for model prediction. We also demonstrate how a particular measure, the sensitivity Q, could be used to reveal the structure of the underlying causal relationships. We apply C NPMR on artificial data with known ground truth (5 datasets), as well as physiological data (2 datasets). C NPMR correctly identifies both linear and nonlinear causal connections that are present in the artificial data, as well as physiologically relevant connectivity in the real data, and does not seem to be affected by filtering. The Sensitivity measure also provides useful information about the latent connectivity.The proposed estimator addresses many of the limitations of linear Granger causality and other nonlinear causality estimators. C NPMR is compared with pairwise and conditional Granger causality (linear) and Kernel-Granger causality (nonlinear). The proposed estimator can be applied to pairwise or multivariate estimations without any modifications to the main method. Its nonpametric nature, its ability to capture nonlinear relationships and its robustness to filtering make it appealing for a number of applications.

Estimating the baroreflex and respiratory modulation of peripheral vascular resistance

The peripheral vascular resistance (RPV) control is known to be largely sympathetically-mediated; thus assessment of the RPV control would allow us to infer valuable information regarding sympathetic nervous activity. The linear and 2nd-order nonlinear minimal models were used to capture the influences of blood pressure (baroreflex) and respiration (respiratory-coupling) on fluctuations of RPV. To validate the minimal models, they were applied on the "data" generated by the simulation model developed in our previous study. This study demonstrated that the linear minimal model was able to recover the "true" (simulated) kernels. The nonlinear model was able to detect the increase in nonlinearity in the system. The system gains derived from the estimated kernels showed strong relationship with the simulation gains, suggesting that the system gains could be employed as potential biomarkers of autonomic function. These results also showed that the nonlinear model had sufficient sensitivity to detect the difference in autonomic reactivity between subjects with mild and severe metabolic syndrome and obstructive sleep apnea syndrome exposed to orthostatic stress.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Effect of repetitive end-inspiration breath holding on very short-term heart rate variability in healthy humans

Very short-term heart rate variability (HRV) is thought to reflect dynamic changes in autonomic nervous activity, which is helpful in understanding the role of autonomic nervous function (ANF) in the mechanisms underlying apnea-induced cardiac arrhythmias. The goal of this study was to investigate the effect of repetitive end-inspiration breath holding on very short-term HRV. A total of 32 young healthy participants took part in the experiments. Three trials were performed, each involving seven repetitive end-inspiration breath holding and a 30 s recovery period between breath holding. Durations of breath holding in the three trials were 1:2:3. The study first evaluated the effect of analyzed data lengths on the stability of HRV indices and determined three HRV indices suitable for very short-term analysis. The results showed that in most cases, during breath holding, the square root of the mean squared differences of successive normal RR intervals (rMSSD) was significantly lower, but normalized units of the power in the low frequency band ranging from 0.04 to 0.15 Hz (nLF) and LF/high frequency (HF) were significantly higher than those during corresponding durations under the normal breathing conditions. On the contrary, during recovery after breath holding, rMSSD was significantly higher but nLF and LF/HF were lower than normal. Moreover, the durations of breath holding had no significant influence on the variations of LF/HF. In addition, as participants repeated the breath holding, HRV indices varied non-linearly. HRV changes may indicate sympathetic activation during breath holding and parasympathetic activation during recovery after breath holding. In conjunction with the existing physiological interpretation based on changes in heart rate, the results may imply that breath holding leads to both cardiac sympathetic and parasympathetic activation simultaneously, which may be a possible pathogenic factor of apnea-induced arrhythmias.

Revealing real-time emotional responses: a personalized assessment based on heartbeat dynamics

Emotion recognition through computational modeling and analysis of physiological signals has been widely investigated in the last decade. Most of the proposed emotion recognition systems require relatively long-time series of multivariate records and do not provide accurate real-time characterizations using short-time series. To overcome these limitations, we propose a novel personalized probabilistic framework able to characterize the emotional state of a subject through the analysis of heartbeat dynamics exclusively. The study includes thirty subjects presented with a set of standardized images gathered from the international affective picture system, alternating levels of arousal and valence. Due to the intrinsic nonlinearity and nonstationarity of the RR interval series, a specific point-process model was devised for instantaneous identification considering autoregressive nonlinearities up to the third-order according to the Wiener-Volterra representation, thus tracking very fast stimulus-response changes. Features from the instantaneous spectrum and bispectrum, as well as the dominant Lyapunov exponent, were extracted and considered as input features to a support vector machine for classification. Results, estimating emotions each 10 seconds, achieve an overall accuracy in recognizing four emotional states based on the circumplex model of affect of 79.29%, with 79.15% on the valence axis, and 83.55% on the arousal axis.

Sleep-related changes in autonomic control in obstructive sleep apnea: a model-based perspective

This paper reviews our current understanding of the long-term effects of obstructive sleep apnea (OSA) on cardiovascular autonomic function in humans, focusing directly on the knowledge derived from noninvasive measurements of heart rate, beat-to-beat blood pressure (BP), and respiration during wakefulness and sleep. While heart rate variability (HRV) as a means of autonomic assessment has become ubiquitous, there are serious limitations with the conventional time-domain and spectral methods of analysis. These shortcomings can be overcome with the application of a multivariate mathematical model that incorporates BP, respiration and other external factors as physiological sources of HRV. Using this approach, we have found that: (a) both respiratory-cardiac coupling and baroreflex dynamics are impaired in OSA; (b) continuous positive airway pressure therapy partially restores autonomic function; (c) baroreflex gain, which increases during sleep in normals, remains unchanged or decreases in OSA subjects; and (d) the autonomic changes that accompany transient arousal from NREM sleep in normals are largely absent in patients with OSA.

Changes in the heart rate variability in patients with obstructive sleep apnea and its response to acute CPAP treatment

Introduction

Obstructive Sleep Apnea (OSA) is a major risk factor for cardiovascular disease. The goal of this study was to demonstrate whether the use of CPAP produces significant changes in the heart rate or in the heart rate variability of patients with OSA in the first night of treatment and whether gender and obesity play a role in these differences.

Methods

Single-center transversal study including patients with severe OSA corrected with CPAP. Only patients with total correction after CPAP were included. Patients underwent two sleep studies on consecutive nights: the first night a basal study, and the second with CPAP. We also analyzed the heart rate changes and their relationship with CPAP treatment, sleep stages, sex and body mass index. Twenty-minute segments of the ECG were selected from the sleep periods of REM, no-REM and awake. Heart rate (HR) and heart rate variability (HRV) were studied by comparing the R-R interval in the different conditions. We also compared samples from the basal study and CPAP nights.

Results

39 patients (15 females, 24 males) were studied. The mean age was 50.67 years old, the mean AHI was 48.54, and mean body mass index was 33.41 kg/m² (31.83 males, 35.95 females). Our results showed that HRV (SDNN) decreased after the use of CPAP during the first night of treatment, especially in non-REM sleep. Gender and obesity did not have any influence on our results.

Conclusions

These findings support that cardiac variability improves as an acute effect, independently of gender or weight, in the first night of CPAP use in severe OSA patients, supporting the idea of continuous use and emphasizing that noncompliance of CPAP treatment should be avoided even if it is just once.

Dynamic assessment of baroreflex control of heart rate during induction of propofol anesthesia using a point process method

In this article, we present a point process method to assess dynamic baroreflex sensitivity (BRS) by estimating the baroreflex gain as focal component of a simplified closed-loop model of the cardiovascular system. Specifically, an inverse Gaussian probability distribution is used to model the heartbeat interval, whereas the instantaneous mean is identified by linear and bilinear bivariate regressions on both the previous R-R intervals (RR) and blood pressure (BP) beat-to-beat measures. The instantaneous baroreflex gain is estimated as the feedback branch of the loop with a point-process filter, while the RR-->BP feedforward transfer function representing heart contractility and vasculature effects is simultaneously estimated by a recursive least-squares filter. These two closed-loop gains provide a direct assessment of baroreflex control of heart rate (HR). In addition, the dynamic coherence, cross bispectrum, and their power ratio can also be estimated. All statistical indices provide a valuable quantitative assessment of the interaction between heartbeat dynamics and hemodynamics. To illustrate the application, we have applied the proposed point process model to experimental recordings from 11 healthy subjects in order to monitor cardiovascular regulation under propofol anesthesia. We present quantitative results during transient periods, as well as statistical analyses on steady-state epochs before and after propofol administration. Our findings validate the ability of the algorithm to provide a reliable and fast-tracking assessment of BRS, and show a clear overall reduction in baroreflex gain from the baseline period to the start of propofol anesthesia, confirming that instantaneous evaluation of arterial baroreflex control of HR may yield important implications in clinical practice, particularly during anesthesia and in postoperative care.

Characterizing nonlinear heartbeat dynamics within a point process framework

Human heartbeat intervals are known to have nonlinear and nonstationary dynamics. In this paper, we propose a model of R-R interval dynamics based on a nonlinear Volterra-Wiener expansion within a point process framework. Inclusion of second-order nonlinearities into the heartbeat model allows us to estimate instantaneous heart rate (HR) and heart rate variability (HRV) indexes, as well as the dynamic bispectrum characterizing higher order statistics of the nonstationary non-gaussian time series. The proposed point process probability heartbeat interval model was tested with synthetic simulations and two experimental heartbeat interval datasets. Results show that our model is useful in characterizing and tracking the inherent nonlinearity of heartbeat dynamics. As a feature, the fine temporal resolution allows us to compute instantaneous nonlinearity indexes, thus sidestepping the uneven spacing problem. In comparison to other nonlinear modeling approaches, the point process probability model is useful in revealing nonlinear heartbeat dynamics at a fine timescale and with only short duration recordings.

Model-based assessment of cardiovascular autonomic control in children with obstructive sleep apnea

STUDY OBJECTIVES

To quantitatively assess daytime autonomic cardiovascular control in pediatric subjects with and without obstructive sleep apnea syndrome (OSAS).

DESIGN

Respiration, R-R intervals, and noninvasive continuous blood pressure were monitored in awake subjects in the supine and standing postures, as well as during cold face stimulation.

SETTING

Sleep disorders laboratory in a hospital setting.

PARTICIPANTS

Ten pediatric patients (age 11.4 +/- 3.6 years) with moderate to severe OSAS (obstructive apnea-hypopnea index = 21.0 +/- 6.6/1 h) before treatment and 10 age-matched normal control subjects (age 11.5 +/- 3.7 years).

MEASUREMENTS AND RESULTS

Spectral analysis of heart rate variability revealed that high-frequency power was similar and the ratio of low- to high-frequency power was lower in subjects with OSAS vs control subjects. The closed-loop minimal model allowed heart rate variability to be partitioned into a component mediated by respiratory-cardiac coupling and a baroreflex component, whereas blood pressure variability was assumed to result from the direct effects of respiration and fluctuations in cardiac output. Baroreflex gain was lower in subjects with OSAS vs control subjects. Under orthostatic stress, respiratory-cardiac coupling gain decreased in both subject groups, but baroreflex gain decreased only in controls. The model was extended to incorporate time-varying parameter changes for analysis of the data collected during cold face stimulation: cardiac output gain increased in controls but remained unchanged in OSAS.

CONCLUSIONS

Our findings suggest that vagal modulation of the heart remains relatively normal in pediatric subjects with OSAS. However, baseline cardiovascular sympathetic activity is elevated, and reactivity to autonomic challenges is impaired.

Investigation of obstructive sleep apnea using nonlinear mode interactions in nonstationary snore signals

Acoustic studies on snoring sounds have recently drawn attention as a potential alternative to polysomnography in the diagnosis of obstructive sleep apnea (OSA). This paper investigates the feasibility of using nonlinear coupling between frequency modes in snore signals via wavelet bicoherence (WBC) analysis for screening of OSA. Two novel markers (PF1 and PSF), which are frequency modes with high nonlinear coupling strength in their respective WBC spectrum, are proposed to differentiate between apneic and benign snores in same- or both-gender snorers. Snoring sounds were recorded from 40 subjects (30 apneic and 10 benign) by a hanging microphone, and subsequently preprocessed within a wavelet transform domain. Forty inspiratory snores (30 as training and 10 as test data) from each subject were examined. Results demonstrate that nonlinear mode interactions in apneic snores are less self-coupled and usually occupy higher and wider frequency ranges than that of benign snores. PF1 and PSF are indicative of apneic and benign snores (p < 0.0001), with optimal thresholds of PF1 = 285 Hz and PSF = 492 Hz (for both genders combined), as well as sensitivity and specificity values between 85.0 and 90.7%, respectively, outperforming the conventional diagnostic indicator (spectral peak frequency, PF = 243-275 Hz, sensitivity = 77.7-79.7%, specificity = 72.0-78.0%, p < 0.0001). Relationships between apnea-hypopnea index and the proposed markers could likely take the functional form of exponential or power. Perspectives on nonlinear dynamics analysis of snore signals are promising for further research and development of a reliable and inexpensive diagnostic tool for OSA.

Multivariate decomposition of arterial blood pressure variability for the assessment of arterial control of circulation

In order to analyze the information carried by arterial blood pressure (ABP) variability, a multivariate parametric model of interactions involving systolic ABP (SAP), diastolic ABP (DAP), pulse pressure (PP), heart period (HP), and respiration is proposed. The model defines SAP as sum of the preceding DAP and PP values; DAP model accounts for arterial baroreflex, diastolic runoff; PP reflects changes in stroke volume related to respiration and HP, afterload; equation residuals reveal other vascular and cardiac output modulations. The model was applied to data from nine young volunteers (aged 29 +/- 6 years) during supine cycling at 10%, 20%, and 30% of their maximum effort. Significant basal values and changes across the epochs of the experiment were found in all hemodynamic parameters describing fast, beat-by-beat responses; in SAP and PP total power, DAP low- and high-frequency power (LF, HF), PP very low frequency (VLF), and LF and HF power. A primary role of vascular control through DAP and PP was emphasized by the considered feedbacks and the model residuals. The model proved to be able to assess beat-by-beat cardiovascular interactions and offer a comprehensive view of arterial tree control.

Fully automated deconvolution method for on-line analysis of time-resolved fluorescence spectroscopy data based on an iterative Laguerre expansion technique

Time-resolved fluorescence spectroscopy (TRFS) is a powerful analytical tool for quantifying the biochemical composition of organic and inorganic materials. The potential of TRFS for tissue diagnosis has been recently demonstrated. To facilitate the translation of TRFS to the clinical arena, algorithms for online TRFS data analysis are essential. A fast model-free TRFS deconvolution algorithm based on the Laguerre expansion method has previously been introduced. One limitation of this method, however, is the need to heuristically select two parameters that are crucial for the accurate estimation of the fluorescence decay: the Laguerre parameter alpha and the expansion order. Here, a new implementation of the Laguerre deconvolution method is introduced, in which a nonlinear least-square optimization of the Laguerre parameter alpha is performed, and the optimal expansion order is selected based on a minimum description length criterion (MDL). In addition, estimation of the zero-time delay between the recorded instrument response and fluorescence decay is also performed based on normalized mean square error criterion (NMSE). The method is validated on experimental data from fluorescence lifetime standards, endogenous tissue fluorophores, and human tissue. The proposed automated Laguerre deconvolution method will facilitate online applications of TRFS, such as real-time clinical tissue diagnosis.

Multimodal signal processing for the analysis of cardiovascular variability

Cardiovascular (CV) variability as a primary vital sign carrying information about CV regulation systems is reviewed by pointing out the role of the main rhythms and the various control and functional systems involved. The high complexity of the addressed phenomena fosters a multimodal approach that relies on data analysis models and deals with the ongoing interactions of many signals at a time. The importance of closed-loop identification and causal analysis is remarked upon and basic properties, application conditions and methods are recalled. The need of further integration of CV signals relevant to peripheral and systemic haemodynamics, respiratory mechanics, neural afferent and efferent pathways is also stressed.

Kernel method for nonlinear granger causality

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Modeling of autonomic control in sleep-disordered breathing

There is ample evidence to support the notion that chronic exposure to repetitive episodes of interrupted breathing during sleep can lead to systemic hypertension, heart failure, myocardial infarction and stroke. Recent studies have suggested that abnormal autonomic control may be the common factor linking sleep-disordered breathing (SDB) to these cardiovascular diseases. We have developed a closed-loop minimal model that enables the delineation of the major physiological mechanisms responsible for changes in autonomic system function in SDB, and also forms the basis for a noninvasive technique that enables the early detection of cardiovascular control abnormalities. The model is "minimal" in the sense that all its parameters can be estimated through analysis of the data measured noninvasively from a single experimental procedure. Parameter estimation is enhanced by broadening the frequency content of the subject's ventilatory pattern, either through voluntary control of breathing or involuntary control using ventilator assistance. Although the original form of the model is linear and time-invariant, extensions of the model include the incorporation of nonlinear dynamics in the autonomic control of heart rate, and allowing the transfer functions of the model components to assume time-varying characteristics. The various versions of the model have been applied to different populations of subjects with SDB under different conditions (e.g. supine wakefulness, orthostatic stress, sleep). Our cumulative findings suggest that the minimal model approach provides a more sensitive means of detecting abnormalities in autonomic cardiovascular control in SDB, compared to univariate analysis of heart rate variability or blood pressure variability.