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

Information sensitivity functions to assess parameter information gain and identifiability of dynamical systems

A new class of functions, called the ‘information sensitivity functions’ (ISFs), which quantify the information gain about the parameters through the measurements/observables of a dynamical system are presented. These functions can be easily computed through classical sensitivity functions alone and are based on Bayesian and information-theoretic approaches. While marginal information gain is quantified by decrease in differential entropy, correlations between arbitrary sets of parameters are assessed through mutual information. For individual parameters, these information gains are also presented as marginal posterior variances, and, to assess the effect of correlations, as conditional variances when other parameters are given. The easy to interpret ISFs can be used to (a) identify time intervals or regions in dynamical system behaviour where information about the parameters is concentrated; (b) assess the effect of measurement noise on the information gain for the parameters; (c) assess whether sufficient information in an experimental protocol (input, measurements and their frequency) is available to identify the parameters; (d) assess correlation in the posterior distribution of the parameters to identify the sets of parameters that are likely to be indistinguishable; and (e) assess identifiability problems for particular sets of parameters.

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.

Credibility Evidence for Computational Patient Models Used in the Development of Physiological Closed-Loop Controlled Devices for Critical Care Medicine

Physiological closed-loop controlled medical devices automatically adjust therapy delivered to a patient to adjust a measured physiological variable. In critical care scenarios, these types of devices could automate, for example, fluid resuscitation, drug delivery, mechanical ventilation, and/or anesthesia and sedation. Evidence from simulations using computational models of physiological systems can play a crucial role in the development of physiological closed-loop controlled devices; but the utility of this evidence will depend on the credibility of the computational model used. Computational models of physiological systems can be complex with numerous non-linearities, time-varying properties, and unknown parameters, which leads to challenges in model assessment. Given the wide range of potential uses of computational patient models in the design and evaluation of physiological closed-loop controlled systems, and the varying risks associated with the diverse uses, the specific model as well as the necessary evidence to make a model credible for a use case may vary. In this review, we examine the various uses of computational patient models in the design and evaluation of critical care physiological closed-loop controlled systems (e.g., hemodynamic stability, mechanical ventilation, anesthetic delivery) as well as the types of evidence (e.g., verification, validation, and uncertainty quantification activities) presented to support the model for that use. We then examine and discuss how a credibility assessment framework (American Society of Mechanical Engineers Verification and Validation Subcommittee, V&V 40 Verification and Validation in Computational Modeling of Medical Devices) for medical devices can be applied to computational patient models used to test physiological closed-loop controlled systems.

A Mathematical Model of dP/dt Max for the Evaluation of the Dynamic Control of Heart Contractility in Septic Shock

OBJECTIVE

Septic shock (SS) patients often show elevated heart rate (HR) despite resuscitation, and this condition is considered an early manifestation of myocardial dysfunction due to an impairment of autonomic nervous system (ANS). We aimed at proposing a mathematical model to assess the autonomic control of ventricular contractility (VC) and HR to track changes in heart functionality during an experimental animal model of SS and resuscitation.

METHODS

SS was induced in six adult swine by polymicrobial peritonitis. We analyzed the beat-to-beat variability of the maximum positive time derivative of left ventricular pressure (dP/dt max), heart period (HP), and aortic blood pressure (ABP). We identified the transfer functions relating fluctuations in ABP and HP to dP/dt max to characterize the static and dynamic properties of the arterial baroreflex and the force-frequency relation mechanisms, respectively. Standard indices of autonomic dysfunction have also been considered as HR variability (HRV) and baroreflex sensitivity (BRS).

RESULTS

During baseline, the baroreflex is predominant in controlling VC with a gain value of -5.8 (-7.5,-3) s^-1, compared to -1.2 (-1.9,-0.5) mmHg/s ms^-1 of the force-frequency autoregulation. During shock, both mechanisms increase their extent in VC control (higher gains and slightly faster dynamics for the baroreflex). After resuscitation, the physiological control of VC is not restored and all the animals still exhibit high HR and reduced HRV and BRS.

CONCLUSION

A condition of cardiovascular inefficiency is persistent after resuscitation and this could be due to autonomic dysfunction.

SIGNIFICANCE

The ANS in SS is crucial to restore homeostasis. Our model could be used to evaluate the efficacy of treatments on VC and related control mechanisms.

Lower Body Negative Pressure: Physiological Effects, Applications, and Implementation

This review presents lower body negative pressure (LBNP) as a unique tool to investigate the physiology of integrated systemic compensatory responses to altered hemodynamic patterns during conditions of central hypovolemia in humans. An early review published in Physiological Reviews over 40 yr ago (Wolthuis et al. Physiol Rev 54: 566-595, 1974) focused on the use of LBNP as a tool to study effects of central hypovolemia, while more than a decade ago a review appeared that focused on LBNP as a model of hemorrhagic shock (Cooke et al. J Appl Physiol (1985) 96: 1249-1261, 2004). Since then there has been a great deal of new research that has applied LBNP to investigate complex physiological responses to a variety of challenges including orthostasis, hemorrhage, and other important stressors seen in humans such as microgravity encountered during spaceflight. The LBNP stimulus has provided novel insights into the physiology underlying areas such as intolerance to reduced central blood volume, sex differences concerning blood pressure regulation, autonomic dysfunctions, adaptations to exercise training, and effects of space flight. Furthermore, approaching cardiovascular assessment using prediction models for orthostatic capacity in healthy populations, derived from LBNP tolerance protocols, has provided important insights into the mechanisms of orthostatic hypotension and central hypovolemia, especially in some patient populations as well as in healthy subjects. This review also presents a concise discussion of mathematical modeling regarding compensatory responses induced by LBNP. Given the diverse applications of LBNP, it is to be expected that new and innovative applications of LBNP will be developed to explore the complex physiological mechanisms that underline health and disease.

Measures of sympathetic and parasympathetic autonomic outflow from heartbeat dynamics

Reliable and effective noninvasive measures of sympathetic and parasympathetic peripheral outflow are of crucial importance in cardiovascular physiology. Although many techniques have been proposed to take up this long-lasting challenge, none has proposed a satisfying discrimination of the dynamics of the two separate branches. Spectral analysis of heart rate variability is the most currently used technique for such assessment. Despite its widespread use, it has been demonstrated that the subdivision in the low-frequency (LF) and high-frequency (HF) bands does not fully reflect separate influences of the sympathetic and parasympathetic branches, respectively, mainly due to their simultaneous action in the LF. Two novel heartbeat-derived autonomic measures, the sympathetic activity index (SAI) and parasympathetic activity index (PAI), are proposed to separately assess the time-varying autonomic nervous system synergic functions. Their efficacy is validated in landmark autonomic maneuvers generally employed in clinical settings. The novel measures move beyond the classical frequency domain paradigm through identification of a set of coefficients associated with a proper combination of Laguerre base functions. The resulting measures were compared with the traditional LF and HF power. A total of 236 ECG recordings were analyzed for validation, including autonomic outflow changes elicited by procedures of different nature and temporal variation, such as postural changes, lower body negative pressure, and handgrip tests. The proposed SAI-PAI measures consistently outperform traditional frequency-domain indexes in tracking expected instantaneous autonomic variations, both vagal and sympathetic, and may aid clinical decision making, showing reduced intersubject variability and physiologically plausible dynamics. NEW & NOTEWORTHY While it is possible to obtain reliable estimates of parasympathetic activity from the ECG, a satisfying method to disentangle the sympathetic component from HRV has not been proposed yet. To overcome this long-lasting limitation, we propose two novel HRV-based indexes, the sympathetic and parasympathetic activity indexes.

A methodological paradigm for patient-specific multi-scale CFD simulations: from clinical measurements to parameter estimates for individual analysis

A new framework for estimation of lumped (for instance, Windkessel) model parameters from uncertain clinical measurements is presented. The ultimate aim is to perform patient-specific haemodynamic analysis. This framework is based on sensitivity analysis tools and the sequential estimation approach of the unscented Kalman filter. Sensitivity analysis and parameter estimation are performed in lumped parameter models, which act as reduced order surrogates of the 3D domain for haemodynamic analysis. While the goal of sensitivity analysis is to assess potential identifiability problems, the unscented Kalman filter estimation leads to parameter estimates based on clinical measurements and modelling assumptions. An application of such analysis and parameter estimation methodology is demonstrated for synthetic and real data. Equality constraints on various physiological parameters are enforced. Since the accuracy of the Windkessel parameter estimates depends on the lumped parameter representativeness, the latter is iteratively improved by running few 3D simulations while simultaneously improving the former. Such a method is applied on a patient-specific aortic coarctation case. Less than 3% and 9% errors between the clinically measured quantities and 3D simulation results for rest and stress are obtained, respectively. Knowledge on how these Windkessel parameters change from rest to stress can thus be learned by such an approach. Lastly, it is demonstrated that the proposed approach is capable of dealing with a wide variety of measurements and cases where the pressure and flow clinical measurements are not taken simultaneously.

A practical approach to parameter estimation applied to model predicting heart rate regulation

Mathematical models have long been used for prediction of dynamics in biological systems. Recently, several efforts have been made to render these models patient specific. One way to do so is to employ techniques to estimate parameters that enable model based prediction of observed quantities. Knowledge of variation in parameters within and between groups of subjects have potential to provide insight into biological function. Often it is not possible to estimate all parameters in a given model, in particular if the model is complex and the data is sparse. However, it may be possible to estimate a subset of model parameters reducing the complexity of the problem. In this study, we compare three methods that allow identification of parameter subsets that can be estimated given a model and a set of data. These methods will be used to estimate patient specific parameters in a model predicting baroreceptor feedback regulation of heart rate during head-up tilt. The three methods include: structured analysis of the correlation matrix, analysis via singular value decomposition followed by QR factorization, and identification of the subspace closest to the one spanned by eigenvectors of the model Hessian. Results showed that all three methods facilitate identification of a parameter subset. The "best" subset was obtained using the structured correlation method, though this method was also the most computationally intensive. Subsets obtained using the other two methods were easier to compute, but analysis revealed that the final subsets contained correlated parameters. In conclusion, to avoid lengthy computations, these three methods may be combined for efficient identification of parameter subsets.

Space physiology IV: mathematical modeling of the cardiovascular system in space exploration

Mathematical modeling represents an important tool for analyzing cardiovascular function during spaceflight. This review describes how modeling of the cardiovascular system can contribute to space life science research and illustrates this process via modeling efforts to study postflight orthostatic intolerance (POI), a key issue for spaceflight. Examining this application also provides a context for considering broader applications of modeling techniques to the challenges of bioastronautics. POI, which affects a large fraction of astronauts in stand tests upon return to Earth, presents as dizziness, fainting and other symptoms, which can diminish crew performance and cause safety hazards. POI on the Moon or Mars could be more critical. In the field of bioastronautics, POI has been the dominant application of cardiovascular modeling for more than a decade, and a number of mechanisms for POI have been investigated. Modeling approaches include computational models with a range of incorporated factors and hemodynamic sophistication, and also physical models tested in parabolic and orbital flight. Mathematical methods such as parameter sensitivity analysis can help identify key system mechanisms. In the case of POI, this could lead to more effective countermeasures. Validation is a persistent issue in modeling efforts, and key considerations and needs for experimental data to synergistically improve understanding of cardiovascular responses are outlined. Future directions in cardiovascular modeling include subject-specific assessment of system status, as well as research on integrated physiological responses, leading, for instance, to assessment of subject-specific susceptibility to POI or effects of cardiovascular alterations on muscular, vision and cognitive function.

Short-term complexity indexes of heart period and systolic arterial pressure variabilities provide complementary information

It is unclear whether the complexity of the variability of the systolic arterial pressure (SAP) provides complementary information to that of the heart period (HP). The complexity of HP and SAP variabilities was assessed from short beat-to-beat recordings (i.e., 256 cardiac beats). The evaluation was made during a pharmacological protocol that induced vagal blockade with atropine or a sympathetic blockade (beta-adrenergic blockade with propranolol or central sympathetic blockade with clonidine) alone or in combination, during a graded head-up tilt, and in patients with Parkinson's disease (PD) without orthostatic hypotension undergoing orthostatic challenge. Complexity was quantified according to the mean square prediction error (MSPE) derived from univariate autoregressive (AR) and multivariate AR (MAR) models. We found that: 1) MSPEMAR did not provide additional information to that of MSPEAR; 2) SAP variability was less complex than that of HP; 3) because HP complexity was reduced by either vagal blockade or vagal withdrawal induced by head-up tilt and was unaffected by beta-adrenergic blockade, HP was under vagal control; 4) because SAP complexity was increased by central sympathetic blockade and was unmodified by either vagal blockade or vagal withdrawal induced by head-up tilt, SAP was under sympathetic control; 5) SAP complexity was increased in patients with PD; and 6) during orthostatic challenge, the complexity of both HP and SAP variabilities in patients with PD remained high, thus indicating both vagal and sympathetic impairments. Complexity indexes derived from short HP and SAP beat-to-beat series provide complementary information and are helpful in detecting early autonomic dysfunction in patients with PD well before circulatory symptoms become noticeable.

Maximizing information from space data resources: a case for expanding integration across research disciplines

Regulatory systems are affected in space by exposure to weightlessness, high-energy radiation or other spaceflight-induced changes. The impact of spaceflight occurs across multiple scales and systems. Exploring such interactions and interdependencies via an integrative approach provides new opportunities for elucidating these complex responses. This paper argues the case for increased emphasis on integration, systematically archiving, and the coordination of past, present and future space and ground-based analogue experiments. We also discuss possible mechanisms for such integration across disciplines and missions. This article then introduces several discipline-specific reviews that show how such integration can be implemented. Areas explored include: adaptation of the central nervous system to space; cerebral autoregulation and weightlessness; modelling of the cardiovascular system in space exploration; human metabolic response to spaceflight; and exercise, artificial gravity, and physiologic countermeasures for spaceflight. In summary, spaceflight physiology research needs a conceptual framework that extends problem solving beyond disciplinary barriers. Administrative commitment and a high degree of cooperation among investigators are needed to further such a process. Well-designed interdisciplinary research can expand opportunities for broad interpretation of results across multiple physiological systems, which may have applications on Earth.

Autonomic mediation of the interdependence between variability signals of heart rate and blood pressure in the lizard Gallotia galloti

Autonomic nervous system (ANS) involvement in the mediation of the synchronization between beat-to-beat RR interval variability (RRIV) and systolic blood pressure variability (SBPV) signals of the lizard Gallotia galloti (Oudart, 1839) was investigated through linear and nonlinear time series analysis methods in a pharmacological blockade context. The ANS blockers used were atropine, prazosin, and propranolol. The interdependence between the signals was quantified by means of the magnitude-squared coherence (MSC), which measures amplitude and phase linear synchronization; the phase lag index (PLI), which evaluates the phase synchronization; and the index L, which quantifies the generalized linear and nonlinear synchronization. Atropine decreased the PLI in the low-frequency (LF: 0.01–0.05 Hz) range; prazosin decreased the MSC in the medium-frequency (MF: 0.06–0.15 Hz) range; and propranolol did not alter any of the interdependence measures. It is suggested that (i) the cholinoceptor activity mediates the phase cardiovascular synchronization in the LF range; (ii) the α1-adrenoceptor activity mediates the amplitude and phase linear cardiovascular synchronization in the MF range; and (iii) the β-adrenoceptor activity plays no role in mediating any dynamics of cardiovascular synchronization in the studied frequency range. When comparing these results with those in mammals, a lesser overall autonomic involvement in the mediation of the studied cardiovascular interdependences is seen in reptiles.

Teaching fluid shifts during orthostasis using a classic paper by Foux et al

Hypovolemic and orthostatic challenge can be simulated in humans by the application of lower body negative pressure (LBNP), because this perturbation leads to peripheral blood pooling and, consequently, central hypovolemia. The classic paper by Foux and colleagues clearly shows the effects of orthostasis simulated by LBNP on fluid shifts and homeostatic mechanisms. The carefully carried out experiments reported in this paper show the interplay between different physiological control systems to ensure blood pressure regulation, failure of which could lead to critical decreases in cerebral blood flow and syncope. Here, a teaching seminar for graduate students is described that is designed in the context of this paper and aimed at allowing students to learn how Foux and colleagues have advanced this field by addressing important aspects of blood regulation. This seminar is also designed to put their research into perspective by including important components of LBNP testing and protocols developed in subsequent research in the field. Learning about comprehensive protocols and carefully controlled studies can reduce confounding variables and allow for an optimal analysis and elucidation of the physiological responses that are being investigated. Finally, in collaboration with researchers in mathematical modeling, in the future, we will incorporate the concepts of applicable mathematical models into our curriculum.

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

This paper considers the outcome of a formal sensitivity analysis on a series of epidemic model structures developed to study the population level effects of maternal antibodies. The analysis is used to compare the potential influence of maternally acquired immunity on various age and time domain observations of infection and serology, with and without seasonality. The results of the analysis indicate that time series observations are largely insensitive to variations in the average duration of this protection, and that age related empirical data are likely to be most appropriate for estimating these characteristics.

Modeling the cardiovascular-respiratory control system: data, model analysis, and parameter estimation

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

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.

Baroreflex contribution to blood pressure and heart rate oscillations: time scales, time-variant characteristics and nonlinearities

The aim of this paper is to highlight the aspects of the baroreflex control of the cardiovascular system that could be relevant to the analysis and modelling of cardiovascular oscillations and regulation. In particular, complex and/or controversial issues of the baroreflex control are addressed on the basis of results obtained in previous studies by others as well as by our group. Attention has been focused on time-variant and nonlinear characteristics of the baroreflex function and on the influence of this physiological mechanism on different frequency regions of blood pressure and heart rate spectra.