Linear and nonlinear system identification of autonomic heart-rate modulation

Digital Cardiovascular Biomarker Responses to Transcutaneous Cervical Vagus Nerve Stimulation: State-Space Modeling, Prediction, and Simulation

Background

Transcutaneous cervical vagus nerve stimulation (tcVNS) is a promising alternative to implantable stimulation of the vagus nerve. With demonstrated potential in myriad applications, ranging from systemic inflammation reduction to traumatic stress attenuation, closed-loop tcVNS during periods of risk could improve treatment efficacy and reduce ineffective delivery. However, achieving this requires a deeper understanding of biomarker changes over time.

Objective

The aim of the present study was to reveal the dynamics of relevant cardiovascular biomarkers, extracted from wearable sensing modalities, in response to tcVNS.

Methods

Twenty-four human subjects were recruited for a randomized double-blind clinical trial, for whom electrocardiography and photoplethysmography were used to measure heart rate and photoplethysmogram amplitude responses to tcVNS, respectively. Modeling these responses in state-space, we (1) compared the biomarkers in terms of their predictability and active vs sham differentiation, (2) studied the latency between stimulation onset and measurable effects, and (3) visualized the true and model-simulated biomarker responses to tcVNS.

Results

The models accurately predicted future heart rate and photoplethysmogram amplitude values with root mean square errors of approximately one-fifth the standard deviations of the data. Moreover, (1) the photoplethysmogram amplitude showed superior predictability (P=.03) and active vs sham separation compared to heart rate; (2) a consistent delay of greater than 5 seconds was found between tcVNS onset and cardiovascular effects; and (3) dynamic characteristics differentiated responses to tcVNS from the sham stimulation.

Conclusions

This work furthers the state of the art by modeling pertinent biomarker responses to tcVNS. Through subsequent analysis, we discovered three key findings with implications related to (1) wearable sensing devices for bioelectronic medicine, (2) the dominant mechanism of action for tcVNS-induced effects on cardiovascular physiology, and (3) the existence of dynamic biomarker signatures that can be leveraged when titrating therapy in closed loop.

Trial Registration

ClinicalTrials.gov NCT02992899; https://clinicaltrials.gov/ct2/show/NCT02992899

International Registered Report Identifier (IRRID)

RR2-10.1016/j.brs.2019.08.002

CRSIDLab: A Toolbox for Multivariate Autonomic Nervous System Analysis Using Cardiorespiratory Identification

This paper presents the Cardiorespiratory System Identification Lab (CRSIDLab), a MATLAB-based software tool for multivariate autonomic nervous system (ANS) evaluation through heart rate variability (HRV) analysis and cardiorespiratory system identification. Based on a graphical user interface, CRSIDLab provides a complete set of tools including pre-processing cardiorespiratory data (electrocardiogram, continuous blood pressure, airflow, and instantaneous lung volume), power spectral density estimation, and multivariable cardiorespiratory system model identification. Parametrized multivariate models can assess both HRV and baroreflex sensitivity (BRS) by considering the causal relationship from respiration to heart rate (or its reciprocal, R-to-R interval - RRI) and from systolic blood pressure to RRI, for instance. The impulse response, estimated from the model, is used as a mathematical tool to effectively open the inherently closed-loop nature of the cardiorespiratory system, allowing the investigation of the dynamic response between pairs of cardiorespiratory variables. This system modeling approach provides information on gain and temporal behavior regarding dynamics, such as the baroreflex, complementing traditional HRV, and BRS indices. The toolbox is presented and used to investigate autonomic function in sleep apnea. The results show that, while traditional HRV indices were unable to differentiate between apneic and non-apneic subjects, the autonomic descriptors obtained from the multivariate system identification techniques were able to show vagal impairment in apneic compared to non-apneic subjects. Thus, CRSIDLab can help promote the use of cardiorespiratory system identification as a potentially more sensitive measure of ANS activity than classical HRV analysis.

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.

Extraction of response waveforms of heartbeat and blood pressure to swallowing. Using mixed signal processing of time domain and respiratory phase domain

BACKGROUND

Evaluating the accurate responses of the cardiovascular system to external stimuli is important for a deeper understanding of cardiovascular homeostasis. However, the responses should be distorted by the conventional time domain analysis when a frequency of the effect of external stimuli matches that of intrinsic fluctuations.

OBJECTIVES

The purpose of this study is to propose a mixed signal processing of time domain and respiratory phase domain to extract the response waveforms of heartbeat and blood pressure (BP) to external stimuli and to clarify the physiological mechanisms of swallowing effects on the cardiovascular system.

METHODS

Measurements were conducted on 12 healthy humans in the sitting and standing positions, with each subject requested to swallow every 30 s between expiration and inspiration. Waveforms of respiratory sinus arrhythmia (RSA) and respiratory-related BP variations were extracted as functions of the respiratory phase. Then, respiratory effects were subtracted from response waveforms with reference to the respiratory phase in the time domain.

RESULTS

As a result, swallowing induced tachycardia, which peaked within 3 s and recovered within 8 s. Tachycardia was greater in the sitting position than during standing. Furthermore, systolic BP and pulse pressure immediately decreased and diastolic BP increased coincident with the occurrence of tachycardia. Subsequently, systolic BP and pulse pressure recovered faster than the R-R interval.

CONCLUSIONS

We conclude that swallowing-induced tachycardia arises largely from the decrease of vagal activity and the baroreflex would yield fast oscillatory responses in recovery.

Point process modeling of interbreath interval: a new approach for the assessment of instability of breathing in neonates

Interbreath interval (IBI), the time interval between breaths, is an important measure used to analyze irregular breathing patterns in neonates. The discrete bursts of neural activity generate the IBI time series, which exhibits stochastic as well as deterministic dynamics. To quantify the irregularity of breathing, we propose a point process model of IBI using a comprehensive stochastic dynamic modeling framework. The IBIs of immature breathing patterns exhibit a long tail distribution and within a point process model, we have considered the lognormal distribution to represent the stochastic IBI characteristics. An autoregressive (AR) function is embedded within the model to capture the short-term IBI dynamics including abrupt IBI prolongations related to sporadic and periodic apneas that are common in neonates. We tested the utility of our paradigm for depicting the respiratory dynamics in neonatal rats and in preterm infants. Kolmogorov-Smirnov (KS) and independence tests reveal that the model accurately tracks the dynamic characteristics of the signals. In preterm infants, our model-derived indices of IBI instability strongly correlate with clinically derived indices of maturation. Our results validate a new class of algorithms, based on the point process theory, for defining instantaneous measures of breathing irregularity in neonates.

Identification of sympathetic and parasympathetic nerves function in cardiovascular regulation using ANFIS approximation

OBJECTIVE

In this paper a new nonlinear system identification approach is developed for dynamical quantification of cardiovascular regulation. This approach is specifically focused on the identification of the heart rate (HR) baroreflex mechanism. The principal objective of this paper is to improve the model accuracy in the estimation of HR by proposing a modified nonlinear model.

METHODS AND MATERIAL

The proposed HR baroreflex model is based on inherent features of the autonomic nervous system for which we develop an adaptive neuro-fuzzy inference system (ANFIS) structure. This method allows incorporation of physiological understandings about the sympathetic and parasympathetic nerves through the selection of appropriate membership functions in the ANFIS structure. The required data for system modeling are collected from the publicly available PhysioNet database.

RESULTS

The results agree with the natural characteristics and physiological understanding of the cardiovascular regulatory system, such as delay in the parasympathetic function, durability in the function of sympathetic nerves and the correlation between the HR and the ABP signals. They also show significant improvements in HR prediction in terms of the normalized root mean square error (NRMSE) in comparison with other reported methods. We achieved to 0.191 in mean NRMSE in prediction of HR in this paper which is about 20% better than the best reported result in other researches.

CONCLUSION

We have shown that for cardiovascular system regulation, our proposed nonlinear model is more accurate than other recently developed methods. Accurate HR baroreflex modeling enables clinicians to have more reliable information for their patients.

Mutual nonlinear prediction of cardiovascular variability series: comparison between exogenous and autoregressive exogenous models

A model-based approach to perform mutual nonlinear prediction of short cardiovascular variability series is presented. The approach is based on identifying exogenous (X) and autoregressive exogenous (ARX) models by K-nearest neighbors local linear approximation, and estimates the predictability of a series given the other as the squared correlation between original and predicted values of the series. The method was first tested on simulations reproducing different types of interaction between non-identical Henon maps, and then applied to heart rate (HR) and blood pressure (BP) variability series measured in healthy subjects at rest and after head-up tilt. Simulations showed that different coupling conditions were always detected by the X model but not by the ARX model. The comparison between X and ARX models suggested the presence of oscillatory sources determining the regularity of HR and BP dynamics independently of their closed-loop mutual regulation. The transition from supine to upright position was associated with an enhancement of the HR and BP mutual regulation, compatible with the activation of the sympathetic nervous system induced by tilt.

Closed-loop nonlinear system identification via the vector optimal parameter search algorithm: application to heart rate baroreflex control

The vector optimal parameter search (VOPS) and the constrained optimal parameter search (COPS) are recently developed algorithms for closed-loop linear system identification. We extend both algorithms to be applicable to a closed-loop nonlinear system, which is characterized by a vector nonlinear autoregressive model. Monte Carlo simulations of nonlinear closed-loop systems were performed to compare the performance of the VOPS to the widely utilized vector least squares (VLS), the COPS and the total least squares (TLS) approaches. The relative error and linear transfer functions are computed to determine the accuracy of each method. The comparative results show that both the VOPS and COPS algorithms provide far superior parameter estimates than does the VLS for all simulation examples considered. The TLS provides better estimates than the VOPS, COPS and VLS when there is only observation noise present in the data. However, the performance of the TLS degrades considerably when the data are corrupted by dynamic noise. The clinical applicability of the two extended methods is examined by applying them to a classical physiological closed-loop system, the heart rate baroreflex. It was found that while both control and blockade of parasympathetic system conditions are dominated by linear dynamics, more nonlinearity was observed in the latter. This observation is statistically supported by the calculation of the mutual information of the data and their surrogates.

System identification: a multi-signal approach for probing neural cardiovascular regulation

Short-term, beat-to-beat cardiovascular variability reflects the dynamic interplay between ongoing perturbations to the circulation and the compensatory response of neurally mediated regulatory mechanisms. This physiologic information may be deciphered from the subtle, beat-to-beat variations by using digital signal processing techniques. While single signal analysis techniques (e.g., power spectral analysis) may be employed to quantify the variability itself, the multi-signal approach of system identification permits the dynamic characterization of the neural regulatory mechanisms responsible for coupling the variability between signals. In this review, we provide an overview of applications of system identification to beat-to-beat variability for the quantitative characterization of cardiovascular regulatory mechanisms. After briefly summarizing the history of the field and basic principles, we take a didactic approach to describe the practice of system identification in the context of probing neural cardiovascular regulation. We then review studies in the literature over the past two decades that have applied system identification for characterizing the dynamical properties of the sinoatrial node, respiratory sinus arrhythmia, and the baroreflex control of sympathetic nerve activity, heart rate and total peripheral resistance. Based on this literature review, we conclude by advocating specific methods of practice and that future research should focus on nonlinear and time-varying behaviors, validation of identification methods, and less understood neural regulatory mechanisms. Ultimately, we hope that this review stimulates such future investigations by both new and experienced system identification researchers.

Short-term cardiovascular oscillations in man: measuring and modelling the physiologies

Research into cardiovascular variabilities intersects both human physiology and quantitative modelling. This is because respiratory and Mayer wave (or 10 s) cardiovascular oscillations represent the integrated control of a system through both autonomic branches by systemic haemodynamic changes within a fluid-filled, physical system. However, our current precise measurement of short-term cardiovascular fluctuations does not necessarily mean we have an adequate understanding of them. Empirical observation suggests that both respiratory and Mayer wave fluctuations derive from mutable autonomic and haemodynamic inputs. Evidence strongly suggests that respiratory sinus arrhythmia both contributes to and buffers respiratory arterial pressure fluctuations. Moreover, even though virtual abolition of all R-R interval variability by cholinergic blockade suggests that parasympathetic stimulation is essential for expression of these variabilities, respiratory sinus arrhythmia does not always reflect a purely vagal phenomenon. The arterial baroreflex has been cited as the mechanism for both respiratory and Mayer wave frequency fluctuations. However, data suggest that both cardiac vagal and vascular sympathetic fluctuations at these frequencies are independent of baroreflex mechanisms and, in fact, contribute to pressure fluctuations. Results from cardiovascular modelling can suggest possible sources for these rhythms. For example, modelling originally suggested low frequency cardiovascular rhythms derived from intrinsic delays in baroreceptor control, and experimental evidence subsequently corroborated this possibility. However, the complex stochastic relations between and variabilities in these rhythms indicate no single mechanism is responsible. If future study of cardiovascular variabilities is to move beyond qualitative suggestions of determinants to quantitative elucidation of critical physical mechanisms, both experimental design and model construction will have to be more trenchant.

A model for the genesis of arterial pressure Mayer waves from heart rate and sympathetic activity

Both theoretic models and cross-spectral analyses suggest that an oscillating sympathetic nervous outflow generates the low-frequency arterial pressure fluctuations termed Mayer waves. Fluctuations in heart rate also have been suggested to relate closely to Mayer waves, but empiric models have not assessed the joint causative influences of heart rate and sympathetic activity. Therefore, we constructed a model based simply upon the hemodynamic equation derived from Ohm's Law. With this model, we determined time relations and relative contributions of heart rate and sympathetic activity to the genesis of arterial pressure Mayer waves. We assessed data from eight healthy young volunteers in the basal state and in a high sympathetic state known to produce concurrent increases in sympathetic nervous outflow and Mayer wave amplitude. We fit the Mayer waves (0.05-0.20 Hz) in mean arterial pressure by the weighted sum of leading oscillations in heart rate and sympathetic nerve activity. This model of our data showed heart rate oscillations leading by 2-3.75 s were responsible for almost half of the variance in arterial pressure (basal R2 = 0.435 +/- 0.140, high sympathetic R2= 0.438 +/- 0.180). Surprisingly, sympathetic activity (lead 0-5 s) contributed only modestly to the explained variance in Mayer waves during either sympathetic state (basal: delta R2 = 0.046 +/- 0.026; heightened: delta R2 = 0.085 +/- 0.036). Thus, it appears that heart rate oscillations contribute to Mayer waves in a simple linear fashion, whereas sympathetic fluctuations contribute little to Mayer waves in this way. Although these results do not exclude an important vascular sympathetic role, they do suggest that additional factors, such as sympathetic transduction into vascular resistance, modulate its influence.

Automatic ectopic beat elimination in short-term heart rate variability measurement

Our studies deal with fully automatic measurement of heart rate variability (HRV) in short term electrocardiograms. Presently, all existing HRV analysis programs require user intervention for ectopic beat identification, especially of supraventricular ectopic beats (SVE). This makes the HRV measurement in large, e.g. epidemiological studies problematic. In this paper, we present a fully automatic algorithm for the discrimination of the ventricular (VE) and SVE ectopic beats from the normal QRS complexes suited for a reliable HRV analysis. The QRS identification is based on the template matching method. The ectopic beats are identified based on several morphological and timing properties of the electrocardiogram (ECG) signal. The method incorporates several approaches and makes HRV analysis of large numbers of electrocardiograms feasible. It uses the template matching for the basic morphology check of the QRS complex and the P-wave, the timing information to avoid unnecessary ectopic beat checks and to adjust thresholds and it also looks for a special QRS morphology, which is common in VEs. We used a testing set of 69 electrocardiograms selected from a large number of recordings. The selected ECGs contained abnormalities including ectopic beats, right branch bundle block, respiratory arrhythmia, blocked atrial extrasystole, high amplitude and wide T-waves. The evaluation of our method showed a specificity of 0.99, supraventricular ectopic beat sensitivity of 0.99 and ventricular ectopic beat sensitivity of 0.98.

Radial basis function neural networks for the characterization of heart rate variability dynamics

This study introduces new neural network based methods for the assessment of the dynamics of the heart rate variability (HRV) signal. The heart rate regulation is assessed as a dynamical system operating in chaotic regimes. Radial-basis function (RBF) networks are applied as a tool for learning and predicting the HRV dynamics. HRV signals are analyzed from normal subjects before and after pharmacological autonomic nervous system (ANS) blockade and from diabetic patients with dysfunctional ANS. The heart rate of normal subjects presents notable predictability. The prediction error is minimized, in fewer degrees of freedom, in the case of diabetic patients. However, for the case of pharmacological ANS blockade, although correlation dimension approaches indicate significant reduction in complexity, the RBF networks fail to reconstruct adequately the underlying dynamics. The transient attributes of the HRV dynamics under the pharmacological disturbance is elucidated as the explanation for the prediction inability.