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

System Identification and Mathematical Modeling of A Piezoelectric Actuator through A Practical Three-Stage Mechanism

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper, we developed a full analytical model and a simple system identification (SI) method of a piezoelectric actuator, which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, is described extensively. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results. Some of the most well-known forms of system identification are shown briefly, while a new and simple algorithm is described systematically and verified by the model. The main advantage of this work is to provide a solid background and domain knowledge of modelling and system identification methods for further investigations in the field of piezoelectric actuators. Due to their simplicity, both the model and the system identification method can be easily modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in applying a simple system identification algorithm while using the system-level approach for piezoelectric actuators. Lastly, this review work is concluded and some recommendations for researchers working in this area are presented.

Multiscale partial information decomposition of dynamic processes with short and long-range correlations: theory and application to cardiovascular control

OBJECTIVE

In this work, an analytical framework for the multiscale analysis of multivariate Gaussian processes is presented, whereby the computation of Partial Information Decomposition measures is achieved accounting for the simultaneous presence of short-term dynamics and long-range correlations.

APPROACH

We consider physiological time series mapping the activity of the cardiac, vascular and respiratory systems in the field of Network Physiology. In this context, the multiscale representation of transfer entropy within the network of interactions among Systolic arterial pressure (S), respiration (R) and heart period (H), as well as the decomposition into unique, redundant and synergistic contributions, is obtained using a Vector AutoRegressive Fractionally Integrated (VARFI) framework for Gaussian processes. This novel approach allows to quantify the directed information flow accounting for the simultaneous presence of short-term dynamics and long-range correlations among the analyzed processes. Additionally, it provides analytical expressions for the computation of the information measures, by exploiting the theory of state space models. The approach is first illustrated in simulated VARFI processes and then applied to H, S and R time series measured in healthy subjects monitored at rest and during mental and postural stress.

MAIN RESULTS

We demonstrate the ability of the VARFI modeling approach to account for the coexistence of short-term and long-range correlations in the study of multivariate processes. Physiologically, we show that postural stress induces larger redundant and synergistic effects from S and R to H at short time scales, while mental stress induces larger information transfer from S to H at longer time scales, thus evidencing the different nature of the two stressors.

SIGNIFICANCE

The proposed methodology allows to extract useful information about the dependence of the information transfer on the balance between short-term and long-range correlations in coupled dynamical systems, which cannot be observed using standard methods that do not consider long-range correlations.

Review on System Identification and Mathematical Modeling of Flapping Wing Micro-Aerial Vehicles

This paper presents a thorough review on the system identification techniques applied to flapping wing micro air vehicles (FWMAVs). The main advantage of this work is to provide a solid background and domain knowledge of system identification for further investigations in the field of FWMAVs. In the system identification context, the flapping wing systems are first categorized into tailed and tailless MAVs. The most recent developments related to such systems are reported. The system identification techniques used for FWMAVs can be classified into time-response based identification, frequency-response based identification, and the computational fluid-dynamics based computation. In the system identification scenario, least mean square estimation is used for a beetle mimicking system recognition. In the end, this review work is concluded and some recommendations for the researchers working in this area are presented.

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

Transfer Entropy Modeling of Newborn Cardiorespiratory Regulation

This study investigates the complex interplay between the cardiac and respiratory systems in 268 healthy neonates born between 35 and 40 weeks of gestation. The aim is to provide a comprehensive description of the developing cardiorespiratory information transfer mechanisms as a function of gestational age (GA). This report proposes an extension of the traditional Transfer Entropy measure (TE), which employs multiple lagged versions of the time series of the intervals between two successive R waves of the QRS signal on the electrocardiogram (RR series) and respiration time series (RESP). The method aims to quantify the instantaneous and delayed effects between the two processes within a fine-grained time scale. Firstly, lagged TE was validated on a simulated dataset. Subsequently, lagged TE was employed on newborn cardiorespiratory data. Results indicate a progressive increase in information transfer as a function of gestational age, as well as significant differences in terms of instantaneous and delayed interactions between the cardiac and the respiratory system when comparing the two TE directionalities (RR→RESP vs. RESP→RR). The proposed investigation addresses the role of the different autonomic nervous system (ANS) branches involved in the cardiorespiratory system, since the sympathetic and parasympathetic branches operate at different time scales. Our results allow to infer that the two TE directionalities are uniquely and differently modulated by both branches of the ANS. TE adds an original quantitative tool to understanding cardiorespiratory imbalance in early infancy.

Strength and Latency of the HP-SAP Closed Loop Variability Interactions in Subjects Prone to Develop Postural Syncope

The coupling and latency between heart period (HP) and systolic arterial pressure (SAP) variability can be investigated along the two arms of the HP-SAP closed loop, namely along the baroreflex feedback from SAP to HP, and along the feedforward pathway from HP to SAP. This study investigates the HP-SAP closed loop variability interactions through cross-correlation function (CCF). Coupling strength and delay between HP and SAP variability series were monitored in 13 subjects prone to develop orthostatic syncope (SYNC, 28±9 yrs, 5 males) and in 13 subjects with no history of postural syncope (noSYNC, age: 27±8 yrs, 5 males). Analysis was carried out at rest in supine position (REST) and during head-up tilt (TILT) at 60 degrees. The null hypothesis of HP-SAP uncoupling was tested through a surrogate analysis associating the HP series of a subject with a SAP sequence of a different one. Results showed that during TILT the coupling strength increased along the baroreflex and latency augmented along the mechanical feedforward pathway exclusively in noSYNC subjects. Finally, closed loop HP-SAP interactions were detected in about one third of subjects and the situation of full uncoupling was rarely found. CCF analysis was found to be a straightforward and easily applicable method to investigate HP-SAP control deserving a direct comparison with more sophisticated signal processing tools assessing causality.

Comparison of Causal and Non-causal Strategies for the Assessment of Baroreflex Sensitivity in Predicting Acute Kidney Dysfunction After Coronary Artery Bypass Grafting

Coronary artery bypass graft (CABG) surgery may lead to postoperative complications such as the acute kidney dysfunction (AKD), identified as any post-intervention increase of serum creatinine level. Cardiovascular control reflexes like the baroreflex can play a role in the AKD development. The aim of this study is to test whether baroreflex sensitivity (BRS) estimates derived from non-causal and causal approaches applied to spontaneous systolic arterial pressure (SAP) and heart period (HP) fluctuations can help in identifying subjects at risk of developing AKD after CABG and which BRS estimates provide the best performance. Electrocardiogram and invasive arterial pressure were acquired from 129 subjects (67 ± 10 years, 112 males) before (PRE) and after (POST) general anesthesia induction with propofol and remifentanil. Subjects were divided into AKDs (n = 29) or no AKDs (noAKDs, n = 100) according to the AKD development after CABG. The non-causal approach assesses the transfer function from the HP-SAP cross-spectrum in the low frequency (LF, 0.04–0.15 Hz) band. BRS was estimated according to three strategies: (i) sampling of the transfer function gain at the maximum of the HP-SAP squared coherence in the LF band; (ii) averaging of the transfer function gain in the LF band; (iii) sampling of the transfer function gain at the weighted central frequency of the spectral components of the SAP series dropping in the LF band. The causal approach separated the two arms of cardiovascular control (i.e., from SAP to HP and vice versa) and accounted for the confounding influences of respiration via system identification and modeling techniques. The causal approach provided a direct estimate of the gain from SAP to HP by observing the HP response to a simulated SAP rise from the identified model structure. Results show that BRS was significantly lower in AKDs than noAKDs during POST regardless of the strategy adopted for its computation. Moreover, all the BRS estimates during POST remained associated with AKD even after correction for demographic and clinical factors. Non-causal and causal BRS estimates exhibited similar performances. Baroreflex impairment is associated with post-CABG AKD and both non-causal and causal methods can be exploited to improve risk stratification of AKD after CABG.

CHF Detection with LSTM Neural Network

Heart rate variability has been proven to be an effective prediction of risk of heart failure. The tradition method required manual feature extraction, thus may lead to potential error. In order to improve the robustness, a deep learning method based on long short-term memory has been presented in this paper. Three RR interval length (N) for detection are used. Without pre-processing, this method obtain 82.47%, 85.13% and 84.91% accuracy for N=50 (average time length is 37. 8s), N=100 (average time length is 73. 9s), N=500 (average time length is 369. 5s), respectively. This method makes it possible to detect CHF through intelligent hardware or mobile application.

A mathematical modelling analysis of the response of blood pressure and heart rate to submaximal exercise

Objective: According to Golden ratio (GR) and Fibonacci sequence, models of the organisation of various structures can be encountered in biology, medicine, architecture and engineering. Recent studies indicate that GR can be highlighted in the organisation and physiological functioning of the cardiovascular system. The aim of this study was to investigate the cardiovascular homeostasis during rest and exercise testing by determining the GR validity at the dynamic level of systolic and diastolic blood pressure (SBP, DBP) and heart rate (HR) values. Methods and Results: We used data obtained from a cardiovascular testing of a group of 236 young healthy subjects (mean age of 19.35 ± 1.92 years). We realised a double assessment of subjects (HR and BP), at rest and immediately after a six minutes submaximal exercise test (Astrand and Rhyming protocol). The investigated group showed a normal cardiovascular reactivity in subjects. GR harmonic rhythm can be identified in the correlation of hemodynamic parameters of HR and SBP, respectively of SBP and DBP, at rest. The differences between means of the ratios (SBP/HR and SBP/DBP), at rest and after effort, were statistically significant (p < .001), with a large effect size. Conclusions: We confirm that the rest state determines the harmonisation of SBP and HR, respectively, of SBP and DBP values, both ratios being very close to GR value. From the perspective of these cardiovascular parameters, the human body is designed to function in the harmonic regime at rest and to temporarily get out of synchronisation during exercise.

Sickle Cell Disease Subjects Have a Distinct Abnormal Autonomic Phenotype Characterized by Peripheral Vasoconstriction With Blunted Cardiac Response to Head-Up Tilt

In sickle cell disease (SCD), prolonged capillary transit times, resulting from reduced peripheral blood flow, increase the likelihood of rigid red cells entrapment in the microvasculature, predisposing to vaso-occlusive crisis. Since changes in peripheral flow are mediated by the autonomic nervous system (ANS), we tested the hypothesis that the cardiac and peripheral vascular responses to head-up tilt (HUT) are abnormal in SCD. Heart rate, respiration, non-invasive continuous blood pressure and finger photoplethysmogram (PPG) were monitored before, during, and after HUT in SCD, anemic controls and healthy subjects. Percent increase in heart rate from baseline was used to quantify cardiac ANS response, while percent decrease in PPG amplitude represented degree of peripheral vasoconstriction. After employing cluster analysis to determine threshold levels, the HUT responses were classified into four phenotypes: (CP) increased heart rate and peripheral vasoconstriction; (C) increased heart rate only; (P) peripheral vasoconstriction only; and (ST) subthreshold cardiac and peripheral vascular responses. Multinomial logistic regression (MLR) was used to relate these phenotypic responses to various parameters representing blood properties and baseline cardiovascular activity. The most common phenotypic response, CP, was found in 82% of non-SCD subjects, including those with chronic anemia. In contrast, 70% of SCD subjects responded abnormally to HUT: C-phenotype = 22%, P-phenotype = 37%, or ST-phenotype = 11%. MLR revealed that the HUT phenotypes were significantly associated with baseline cardiac parasympathetic activity, baseline peripheral vascular variability, hemoglobin level and SCD diagnosis. Low parasympathetic activity at baseline dramatically increased the probability of belonging to the P-phenotype in SCD subjects, even after adjusting for hemoglobin level, suggesting a characteristic autonomic dysfunction that is independent of anemia. Further analysis using a mathematical model of heart rate variability revealed that the low parasympathetic activity in P-phenotype SCD subjects was due to impaired respiratory-cardiac coupling rather than reduced cardiac baroreflex sensitivity. By having strong peripheral vasoconstriction without compensatory cardiac responses, P-phenotype subjects may be at increased risk for vaso-occlusive crisis. The classification of autonomic phenotypes based on HUT response may have potential use for guiding therapeutic interventions to alleviate the risk of adverse outcomes in SCD.

Towards understanding the complexity of cardiovascular oscillations: Insights from information theory

Cardiovascular complexity is a feature of healthy physiological regulation, which stems from the simultaneous activity of several cardiovascular reflexes and other non-reflex physiological mechanisms. It is manifested in the rich dynamics characterizing the spontaneous heart rate and blood pressure variability (HRV and BPV). The present study faces the challenge of disclosing the origin of short-term HRV and BPV from the statistical perspective offered by information theory. To dissect the physiological mechanisms giving rise to cardiovascular complexity in different conditions, measures of predictive information, information storage, information transfer and information modification were applied to the beat-to-beat variability of heart period (HP), systolic arterial pressure (SAP) and respiratory volume signal recorded non-invasively in 61 healthy young subjects at supine rest and during head-up tilt (HUT) and mental arithmetics (MA). Information decomposition enabled to assess simultaneously several expected and newly inferred physiological phenomena, including: (i) the decreased complexity of HP during HUT and the increased complexity of SAP during MA; (ii) the suppressed cardiorespiratory information transfer, related to weakened respiratory sinus arrhythmia, under both challenges; (iii) the altered balance of the information transferred along the two arms of the cardiovascular loop during HUT, with larger baroreflex involvement and smaller feedforward mechanical effects; and (iv) an increased importance of direct respiratory effects on SAP during HUT, and on both HP and SAP during MA. We demonstrate that a decomposition of the information contained in cardiovascular oscillations can reveal subtle changes in system dynamics and improve our understanding of the complexity changes during physiological challenges.

Multiscale Entropy Analysis of the Differential RR Interval Time Series Signal and Its Application in Detecting Congestive Heart Failure

Cardiovascular systems essentially have multiscale control mechanisms. Multiscale entropy (MSE) analysis permits the dynamic characterization of the cardiovascular time series for both short-term and long-term processes, and thus can be more illuminating. The traditional MSE analysis for heart rate variability (HRV) is performed on the original RR interval time series (named as MSE_RR). In this study, we proposed an MSE analysis for the differential RR interval time series signal, named as MSE_dRR. The motivation of using the differential RR interval time series signal is that this signal has a direct link with the inherent non-linear property of electrical rhythm of the heart. The effectiveness of the MSE_RR and MSE_dRR were tested and compared on the long-term MIT-Boston’s Beth Israel Hospital (MIT-BIH) 54 normal sinus rhythm (NSR) and 29 congestive heart failure (CHF) RR interval recordings, aiming to explore which one is better for distinguishing the CHF patients from the NSR subjects. Four RR interval length for analysis were used ( N = 500 , N = 1000 , N = 2000 and N = 5000 ). The results showed that MSE_RR did not report significant differences between the NSR and CHF groups at several scales for each RR segment length type (Scales 7, 8 and 10 for N = 500 , Scales 3 and 10 for N = 1000 , Scales 2 and 3 for both N = 2000 and N = 5000 ). However, the new MSE_dRR gave significant separation for the two groups for all RR segment length types except N = 500 at Scales 9 and 10. The area under curve (AUC) values from the receiver operating characteristic (ROC) curve were used to further quantify the performances. The mean AUC of the new MSE_dRR from Scales 1–10 are 79.5%, 83.1%, 83.5% and 83.1% for N = 500 , N = 1000 , N = 2000 and N = 5000 , respectively, whereas the mean AUC of MSE_RR are only 68.6%, 69.8%, 69.6% and 67.1%, respectively. The five-fold cross validation support vector machine (SVM) classifier reports the classification Accuracy ( A c c ) of MSE_RR as 73.5%, 75.9% and 74.6% for N = 1000 , N = 2000 and N = 5000 , respectively, while for the new MSE_dRR analysis accuracy was 85.5%, 85.6% and 85.6%. Different biosignal editing methods (direct deletion and interpolation) did not change the analytical results. In summary, this study demonstrated that compared with MSE_RR, MSE_dRR reports better statistical stability and better discrimination ability for the NSR and CHF groups.

A Model-Based Machine Learning Approach to Probing Autonomic Regulation From Nonstationary Vital-Sign Time Series

Physiological variables, such as heart rate (HR), blood pressure (BP) and respiration (RESP), are tightly regulated and coupled under healthy conditions, and a break-down in the coupling has been associated with aging and disease. We present an approach that incorporates physiological modeling within a switching linear dynamical systems (SLDS) framework to assess the various functional components of the autonomic regulation through transfer function analysis of nonstationary multivariate time series of vital signs. We validate our proposed SLDS-based transfer function analysis technique in automatically capturing 1) changes in baroreflex gain due to postural changes in a tilt-table study including ten subjects, and 2) the effect of aging on the autonomic control using HR/RESP recordings from 40 healthy adults. Next, using HR/BP time series of more than 450 adult ICU patients, we show that our technique can be used to reveal coupling changes associated with severe sepsis (AUC = 0.74, sensitivity = 0.74, specificity = 0.60). Our findings indicate that reduced HR/BP coupling is significantly associated with severe sepsis even after adjusting for clinical interventions (P  0.001). These results demonstrate the utility of our approach in phenotyping complex vital-sign dynamics, and in providing mechanistic hypotheses in terms of break-down of autoregulatory systems under healthy and disease conditions.

Nonlinear identification of the total baroreflex arc: higher-order nonlinearity

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). The nonlinear dynamics of this system were recently characterized. First, Gaussian white noise CSP stimulation was employed in open-loop conditions in normotensive and hypertensive rats with sectioned vagal and aortic depressor nerves. Nonparametric system identification was then applied to measured CSP and AP to establish a second-order nonlinear Uryson model. The aim in this study was to assess the importance of higher-order nonlinear dynamics via development and evaluation of a third-order nonlinear model of the total arc using the same experimental data. Third-order Volterra and Uryson models were developed by employing nonparametric and parametric identification methods. The R² values between the AP predicted by the best third-order Volterra model and measured AP in response to Gaussian white noise CSP not utilized in developing the model were 0.69 ± 0.03 and 0.70 ± 0.03 for normotensive and hypertensive rats, respectively. The analogous R² values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R² values were not statistically different from the corresponding values for the previously established second-order Uryson model, which were both 0.71 ± 0.03 (P > 0.1). Furthermore, none of the third-order models predicted well-known nonlinear behaviors including thresholding and saturation better than the second-order Uryson model. Additional experiments suggested that the unexplained AP variance was partly due to higher brain center activity. In conclusion, the second-order Uryson model sufficed to represent the sympathetically mediated total arc under the employed experimental conditions.

Conditional Self-Entropy and Conditional Joint Transfer Entropy in Heart Period Variability during Graded Postural Challenge

Self-entropy (SE) and transfer entropy (TE) are widely utilized in biomedical signal processing to assess the information stored into a system and transferred from a source to a destination respectively. The study proposes a more specific definition of the SE, namely the conditional SE (CSE), and a more flexible definition of the TE based on joint TE (JTE), namely the conditional JTE (CJTE), for the analysis of information dynamics in multivariate time series. In a protocol evoking a gradual sympathetic activation and vagal withdrawal proportional to the magnitude of the orthostatic stimulus, such as the graded head-up tilt, we extracted the beat-to-beat spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiratory activity (R) in 19 healthy subjects and we computed SE of HP, CSE of HP given SAP and R, JTE from SAP and R to HP, CJTE from SAP and R to HP given SAP and CJTE from SAP and R to HP given R. CSE of HP given SAP and R was significantly smaller than SE of HP and increased progressively with the amplitude of the stimulus, thus suggesting that dynamics internal to HP and unrelated to SAP and R, possibly linked to sympathetic activation evoked by head-up tilt, might play a role during the orthostatic challenge. While JTE from SAP and R to HP was independent of tilt table angle, CJTE from SAP and R to HP given R and from SAP and R to HP given SAP showed opposite trends with tilt table inclination, thus suggesting that the importance of the cardiac baroreflex increases and the relevance of the cardiopulmonary pathway decreases during head-up tilt. The study demonstrates the high specificity of CSE and the high flexibility of CJTE over real data and proves that they are particularly helpful in disentangling physiological mechanisms and in assessing their different contributions to the overall cardiovascular regulation.

Cardiovascular control in women with fibromyalgia syndrome: do causal methods provide nonredundant information compared with more traditional approaches?

The cardiovascular autonomic control and the baroreflex sensitivity (BRS) have been widely studied in fibromyalgia syndrome (FMS) patients through the computation of linear indices of spontaneous heart period (HP) and systolic arterial pressure (SAP) variabilities. However, there are many methodological difficulties regarding the quantification of BRS by the traditional indices especially in relation to the issue of causality. This difficulty has been directly tackled via a model-based approach describing the closed-loop HP-SAP interactions and the exogenous influences of respiration. Therefore, we aimed to assess whether the BRS assessed by the model-based causal closed-loop approach during supine and active standing in patients with FMS could provide complementary information to those obtained by traditional indices based on time and frequency domains. The findings of this study revealed that, at difference with the traditional methods to quantify BRS, the causality analysis applied to the HP, SAP, and respiratory series, through the model-based closed-loop approach, detected lower BRS in supine position, as well as a blunted response to the orthostatic stimulus in patients with FMS compared with healthy control subjects. Also, the strength of the causal relation from SAP to HP (i.e., along the cardiac baroreflex) increased during the active standing only in the control subjects. The model-based closed-loop approach proved to provide important complementary information about the cardiovascular autonomic control in patients with FMS.

Stimulation of the cardiopulmonary baroreflex enhances ventricular contractility in awake dogs: a mathematical analysis study

The cardiopulmonary baroreflex responds to an increase in central venous pressure (CVP) by decreasing total peripheral resistance and increasing heart rate (HR) in dogs. However, the direction of ventricular contractility change is not well understood. The aim was to elucidate the cardiopulmonary baroreflex control of ventricular contractility during normal physiological conditions via a mathematical analysis. Spontaneous beat-to-beat fluctuations in maximal ventricular elastance (Emax), which is perhaps the best available index of ventricular contractility, CVP, arterial blood pressure (ABP), and HR were measured from awake dogs at rest before and after β-adrenergic receptor blockade. An autoregressive exogenous input model was employed to jointly identify the three causal transfer functions relating beat-to-beat fluctuations in CVP to Emax (CVP → Emax), which characterizes the cardiopulmonary baroreflex control of ventricular contractility, ABP to Emax, which characterizes the arterial baroreflex control of ventricular contractility, and HR to Emax, which characterizes the force-frequency relation. The CVP → Emax transfer function showed a static gain of 0.037 ± 0.010 ml(-1) (different from zero; P < 0.05) and an overall time constant of 3.2 ± 1.2 s. Hence, Emax would increase and reach steady state in ∼16 s in response to a step increase in CVP, without any change to ABP or HR, due to the cardiopulmonary baroreflex. Following β-adrenergic receptor blockade, the CVP → Emax transfer function showed a static gain of 0.0007 ± 0.0113 ml(-1) (different from control; P < 0.10). Hence, Emax would change little in steady state in response to a step increase in CVP. Stimulation of the cardiopulmonary baroreflex increases ventricular contractility through β-adrenergic receptor system mediation.

Effect of age on complexity and causality of the cardiovascular control: comparison between model-based and model-free approaches

The proposed approach evaluates complexity of the cardiovascular control and causality among cardiovascular regulatory mechanisms from spontaneous variability of heart period (HP), systolic arterial pressure (SAP) and respiration (RESP). It relies on construction of a multivariate embedding space, optimization of the embedding dimension and a procedure allowing the selection of the components most suitable to form the multivariate embedding space. Moreover, it allows the comparison between linear model-based (MB) and nonlinear model-free (MF) techniques and between MF approaches exploiting local predictability (LP) and conditional entropy (CE). The framework was applied to study age-related modifications of complexity and causality in healthy humans in supine resting (REST) and during standing (STAND). We found that: 1) MF approaches are more efficient than the MB method when nonlinear components are present, while the reverse situation holds in presence of high dimensional embedding spaces; 2) the CE method is the least powerful in detecting age-related trends; 3) the association of HP complexity on age suggests an impairment of cardiac regulation and response to STAND; 4) the relation of SAP complexity on age indicates a gradual increase of sympathetic activity and a reduced responsiveness of vasomotor control to STAND; 5) the association from SAP to HP on age during STAND reveals a progressive inefficiency of baroreflex; 6) the reduced connection from HP to SAP with age might be linked to the progressive exploitation of Frank-Starling mechanism at REST and to the progressive increase of peripheral resistances during STAND; 7) at REST the diminished association from RESP to HP with age suggests a vagal withdrawal and a gradual uncoupling between respiratory activity and heart; 8) the weakened connection from RESP to SAP with age might be related to the progressive increase of left ventricular thickness and vascular stiffness and to the gradual decrease of respiratory sinus arrhythmia.

Cross time-frequency analysis for combining information of several sources: application to estimation of spontaneous respiratory rate from photoplethysmography

A methodology that combines information from several nonstationary biological signals is presented. This methodology is based on time-frequency coherence, that quantifies the similarity of two signals in the time-frequency domain. A cross time-frequency analysis method, based on quadratic time-frequency distribution, has been used for combining information of several nonstationary biomedical signals. In order to evaluate this methodology, the respiratory rate from the photoplethysmographic (PPG) signal is estimated. The respiration provokes simultaneous changes in the pulse interval, amplitude, and width of the PPG signal. This suggests that the combination of information from these sources will improve the accuracy of the estimation of the respiratory rate. Another target of this paper is to implement an algorithm which provides a robust estimation. Therefore, respiratory rate was estimated only in those intervals where the features extracted from the PPG signals are linearly coupled. In 38 spontaneous breathing subjects, among which 7 were characterized by a respiratory rate lower than 0.15 Hz, this methodology provided accurate estimates, with the median error {0.00; 0.98} mHz ({0.00; 0.31}%) and the interquartile range error {4.88; 6.59} mHz ({1.60; 1.92}%). The estimation error of the presented methodology was largely lower than the estimation error obtained without combining different PPG features related to respiration.

Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis

We analyse cardiovascular time series with the aim of performing early prediction of preeclampsia (PE), a pregnancy-specific disorder causing maternal and foetal morbidity and mortality. The analysis is made using a novel approach, namely the ε-recurrence networks applied to a phase space constructed by means of the time series of the variabilities of the heart rate and the blood pressure (systolic and diastolic). All the possible coupling structures among these variables are considered for the analysis. Network measures such as average path length, mean coreness, global clustering coefficient and scale-local transitivity dimension are computed and constitute the parameters for the subsequent quadratic discriminant analysis. This allows us to predict PE with a sensitivity of 91.7 per cent and a specificity of 68.1 per cent, thus validating the use of this method for classifying healthy and preeclamptic patients.

Cardiac output is not a significant source of low frequency mean arterial pressure variability

Spontaneous mean arterial pressure (MAP) variability may be mainly due to fluctuations in cardiac output (CO) and total peripheral resistance (TPR). While high frequency (HF ∼ 0.25 Hz) oscillations in MAP are ultimately driven by respiration, the source of low frequency (LF ∼ 0.1 Hz) fluctuations has not been fully elucidated. It is known that CO buffers these oscillations, but there is no evidence on its potential role in also generating them. The main goal was to determine whether CO is a source of LF variability in MAP. Six dogs were chronically instrumented to obtain beat-to-beat measurements of CO and MAP while the dogs were fully awake and at rest. A causal dynamic model was identified to relate the fluctuations in CO to MAP. The model was then used to predict the MAP fluctuations from the CO fluctuations. The CO fluctuations were able to predict about 70% of the MAP oscillations in the HF band but showed no predictive value in the LF band. Hence, respiration induces CO fluctuations in the HF band that, in turn, cause MAP oscillations, while TPR fluctuations appear to be the dominant mediator of LF fluctuations of MAP. CO is not a significant source of these oscillations, and it may only be responsible for dampening them, likely through the baroreflex.

Assessment of the dynamic interactions between heart rate and arterial pressure by the cross time-frequency analysis

In this study, a framework for the characterization of the dynamic interactions between RR variability (RRV) and systolic arterial pressure variability (SAPV) is proposed. The methodology accounts for the intrinsic non-stationarity of the cardiovascular system and includes the assessment of both the strength and the prevalent direction of local coupling. The smoothed pseudo-Wigner-Ville distribution (SPWVD) is used to estimate the time-frequency (TF) power, coherence, and phase-difference spectra with fine TF resolution. The interactions between the signals are quantified by time-varying indices, including the local coupling, phase differences, time delay, and baroreflex sensitivity (BRS). Every index is extracted from a specific TF region, localized by combining information from the different spectra. In 14 healthy subjects, a head-up tilt provoked an abrupt decrease in the cardiovascular coupling; a rapid change in the phase difference (from 0.37 ± 0.23 to -0.27 ± 0.22 rad) and time delay (from 0.26 ± 0.14 to -0.16 ± 0.16 s) in the high-frequency band; and a decrease in the BRS (from 23.72 ± 7.66 to 6.92 ± 2.51 ms mmHg(-1)). In the low-frequency range, during a head-up tilt, restoration of the baseline level of cardiovascular coupling took about 2 min and SAPV preceded RRV by about 0.85 s during the whole test. The analysis of the Eurobavar data set, which includes subjects with intact as well as impaired baroreflex, showed that the presented methodology represents an improved TF generalization of traditional time-invariant methodologies and can reveal dysfunctions in subjects with baroreflex impairment. Additionally, the results also suggest the use of non-stationary signal-processing techniques to analyze signals recorded under conditions that are usually supposed to be stationary.

Time-variant partial directed coherence in analysis of the cardiovascular system. A methodological study

Time-variant partial directed coherence (tvPDC) is used for the first time in a multivariate analysis of heart rate variability (HRV), respiratory movements (RMs) and (systolic) arterial blood pressure. It is shown that respiration-related HRV components which also occur at other frequencies besides the RM frequency (= respiratory sinus arrhythmia, RSA) can be identified. These additional components are known to be an effect of the 'half-the-mean-heart-rate-dilemma' ('cardiac aliasing' CA). These CA components may contaminate the entire frequency range of HRV and can lead to misinterpretation of the RSA analysis. TvPDC analysis of simulated and clinical data (full-term neonates and sedated patients) reveals these contamination effects and, in addition, the respiration-related CA components can be separated from the RSA component and the Traube-Hering-Mayer wave. It can be concluded that tvPDC can be beneficially applied to avoid misinterpretations in HRV analyses as well as to quantify partial correlative interaction properties between RM and RSA.

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.

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.

Predicting acute hypotensive episodes based on HR baroreflex model estimation

A new method to predict acute hypotensive episodes (AHE) is proposed in this paper. The AHE is defined as any period of 30 min or more during which at least 90% of mean arterial pressure (MAP) measurements are below 60 mmHg. Since arterial pressure has a direct correlation with heart rate through heart rate (HR) baroreflex and cardiovascular systems, any changes in MAP, directly affect HR and vice versa. Predicting HR using our developed model, the periods in which HR drops to the values less than 40 beat/min are detected. The demonstrated AHE data for twenty patients are picked to validate the proposed algorithm. Results show that the proposed method could truly predict occurrence of the AHE in 17 out of 20 cases analyzed. Results show reliable accuracy in predicting AHE in these patients.

Assessment of cardiovascular regulation through irreversibility analysis of heart period variability: a 24 hours Holter study in healthy and chronic heart failure populations

We propose an approach based on time reversibility analysis to characterize the cardiovascular regulation and its nonlinearities as derived from 24 hours Holter recordings of heart period variability in a healthy population (n=12, age: median=43 years, range=34-55 years) and in a pathological group of age-matched chronic heart failure (CHF) patients (n=13, primarily in NYHA class II, age: median=37 years, range=33-56 years, ejection fraction: median=25%, range=13-30%). Two indices capable of detecting nonlinear irreversible dynamics according to different strategies of phase-space reconstruction (i.e. a fixed two-dimensional phase-space reconstruction and an optimal selection of the embedding dimension, respectively) are tested and compared with a more traditional nonlinear index based on local nonlinear prediction. Results showed that nonlinear dynamics owing to time irreversibility at short time scales are significantly present during daytime in healthy subjects, more frequently present in the CHF population and less frequently during night-time in both groups, thus suggesting their link with a dominant sympathetic regulation and/or with a vagal withdrawal. On the contrary, nonlinear dynamics owing to time irreversibility at longer, dominant time scales were insignificantly present in both groups. During daytime in the healthy population, irreversibility was mostly due to the presence of asymmetric patterns characterized by bradycardic runs shorter than tachycardic ones. Nonlinear dynamics produced by mechanisms different from those inducing temporal irreversibility were significantly detectable in both groups and more frequently during night-time. The present study proposes a method to distinguish different types of nonlinearities and assess their contribution over different temporal scales. Results confirm the usefulness of this method even when applied in uncontrolled experimental conditions such as those during 24 hours Holter recordings.

Modelling and disentangling physiological mechanisms: linear and nonlinear identification techniques for analysis of cardiovascular regulation

Cardiovascular (CV) regulation is the result of a number of very complex control interactions. As computational power increases and new methods for collecting experimental data emerge, the potential for exploring these interactions through modelling increases as does the potential for clinical application of such models. Understanding these interactions requires the application of a diverse set of modelling techniques. Several recent mathematical modelling techniques will be described in this review paper. Starting from Granger's causality, the problem of closed-loop identification is recalled. The main aspects of linear identification and of grey-box modelling tailored to CV regulation analysis are summarized as well as basic concepts and trends for nonlinear extensions. Sensitivity analysis is presented and discussed as a potent tool for model validation and refinement. The integration of methods and models is fostered for a further physiological comprehension and for the development of more potent and robust diagnostic tools.

Methods for improving simulations of biological systems: systemic computation and fractal proteins

Modelling and simulation are becoming essential for new fields such as synthetic biology. Perhaps the most important aspect of modelling is to follow a clear design methodology that will help to highlight unwanted deficiencies. The use of tools designed to aid the modelling process can be of benefit in many situations. In this paper, the modelling approach called systemic computation (SC) is introduced. SC is an interaction-based language, which enables individual-based expression and modelling of biological systems, and the interactions between them. SC permits a precise description of a hypothetical mechanism to be written using an intuitive graph-based or a calculus-based notation. The same description can then be directly run as a simulation, merging the hypothetical mechanism and the simulation into the same entity. However, even when using well-designed modelling tools to produce good models, the best model is not always the most accurate one. Frequently, computational constraints or lack of data make it infeasible to model an aspect of biology. Simplification may provide one way forward, but with inevitable consequences of decreased accuracy. Instead of attempting to replace an element with a simpler approximation, it is sometimes possible to substitute the element with a different but functionally similar component. In the second part of this paper, this modelling approach is described and its advantages are summarized using an exemplar: the fractal protein model. Finally, the paper ends with a discussion of good biological modelling practice by presenting lessons learned from the use of SC and the fractal protein model.

Design and Subspace System Identification of an Ex Vivo Vascular Perfusion System

Numerical algorithms for subspace system identification (N4SID) are a powerful tool for generating the state space (SS) representation of any system. The purpose of this work was to use N4SID to generate SS models of the flowrate and pressure generation within an ex vivo vascular perfusion system (EVPS). Accurate SS models were generated and converted to transfer functions (TFs) to be used for proportional integral and derivative (PID) controller design. By prescribing the pressure and flowrate inputs to the pumping components within the EVPS and measuring the resulting pressure and flowrate in the system,_four TFs were estimated;_two for a flowrate controller (HRP,f and HRPP,f) and two for a pressure controller (HRP,p and HRPP,p). In each controller,_one TF represents a roller pump (HRP,f and HRP,p),_and the other represents a roller pump and piston in series (HRPP,f and HRPP,p). Experiments to generate the four TFs were repeated five times (N=5) from which average TFs were calculated. The average model fits, computed as the percentage of the output variation (to_the_prescribed_inputs) reproduced by the model, were 94.93±1.05% for HRP,p, 81.29±0.20% for HRPP,p, 94.45±0.73% for HRP,f, and 77.12±0.36% for HRPP,f. The simulated step, impulse, and frequency responses indicate that the EVPS is a stable system and can respond to signals containing power of up to 70_Hz.

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.

Mutual nonlinear prediction as a tool to evaluate coupling strength and directionality in bivariate time series: comparison among different strategies based on k nearest neighbors

We compare the different existing strategies of mutual nonlinear prediction regarding their ability to assess the coupling strength and directionality of the interactions in bivariate time series. Under the common framework of k -nearest neighbor local linear prediction, we test three approaches based on cross prediction, mixed prediction, and predictability improvement. The measures of interdependence provided by these approaches are first evaluated on short realizations of bivariate time series generated by coupled Henon models, investigating also the effects of noise. The usefulness of the three mutual nonlinear prediction schemes is then assessed in a common physiological application during known conditions of interaction-i.e., the analysis of the interdependence between heart rate and arterial pressure variability in healthy humans during supine resting and passive head-up tilting. Based on both simulation results and physiological interpretability of cardiovascular results, we conclude that cross prediction is valuable to quantify the coupling strength and predictability improvement to elicit directionality of the interactions in short and noisy bivariate time series.

Selective quantification of the cardiac sympathetic and parasympathetic nervous systems by multisignal analysis of cardiorespiratory variability

Heart rate (HR) power spectral indexes are limited as measures of the cardiac autonomic nervous systems (CANS) in that they neither offer an effective marker of the β-sympathetic nervous system (SNS) due to its overlap with the parasympathetic nervous system (PNS) in the low-frequency (LF) band nor afford specific measures of the CANS due to input contributions to HR [e.g., arterial blood pressure (ABP) and instantaneous lung volume (ILV)]. We derived new PNS and SNS indexes by multisignal analysis of cardiorespiratory variability. The basic idea was to identify the autonomically mediated transfer functions relating fluctuations in ILV to HR (ILV→HR) and fluctuations in ABP to HR (ABP→HR) so as to eliminate the input contributions to HR and then separate each estimated transfer function in the time domain into PNS and SNS indexes using physiological knowledge. We evaluated these indexes with respect to selective pharmacological autonomic nervous blockade in 14 humans. Our results showed that the PNS index derived from the ABP→HR transfer function was correctly decreased after vagal and double (vagal + β-sympathetic) blockade ( P < 0.01) and did not change after β-sympathetic blockade, whereas the SNS index derived from the same transfer function was correctly reduced after β-sympathetic blockade in the standing posture and double blockade ( P < 0.05) and remained the same after vagal blockade. However, this SNS index did not significantly decrease after β-sympathetic blockade in the supine posture. Overall, these predictions were better than those provided by the traditional high-frequency (HF) power, LF-to-HF ratio, and normalized LF power of HR variability.