A forward model-based validation of cardiovascular system identification

Orthostatic Stress and Baroreflex Sensitivity: A Window into Autonomic Dysfunction in Lone Paroxysmal Atrial Fibrillation

The abnormal neural control of atria has been considered one of the mechanisms of paroxysmal atrial fibrillation (PAF) pathogenesis. The baroreceptor reflex has an important role in cardiovascular regulation and may serve as an index of autonomic function. This study aimed to analyze the baroreceptor reflex's role in heart rate regulation during upright tilt (HUT) in patients with lone PAF. The study included 68 patients with lone PAF and 34 healthy individuals who underwent baroreflex assessment. Parameters such as baroreflex sensitivity (BRS), number of systolic blood pressure (BP) ramps, and the baroreflex effectiveness index (BEI) were evaluated. The study found that PAF patients had comparable resting BPs and heart rates (HRs) to healthy individuals. However, unlike healthy individuals, PAF patients showed a sustained increase in BP with an upright posture followed by the delayed activation of the baroreceptor function with a blunted HR response and lower BEI values. This indicates a pronounced baroreflex impairment in PAF patients, even at rest. Our data suggest that together with BRS, BEI could be used as a marker of autonomic dysfunction in PAF patients, making it important to further investigate its relationship with AF recurrence after ablation and its involvement in cardiovascular autonomic remodeling.

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

Physiology-Informed Real-Time Mean Arterial Blood Pressure Learning and Prediction for Septic Patients Receiving Norepinephrine

OBJECTIVE

Septic shock is a life-threatening manifestation of infection with a mortality of 20-50% [1]. A catecholamine vasopressor, norepinephrine (NE), is widely used to treat septic shock primarily by increasing blood pressure. For this reason, future blood pressure knowledge is invaluable for properly controlling NE infusion rates in septic patients. However, recent machine learning and data-driven methods often treat the physiological effects of NE as a black box. In this paper, a real-time, physiology-informed human mean arterial blood pressure model for septic shock patients undergoing NE infusion is studied.

METHODS

Our methods combine learning theory, adaptive filter theory, and physiology. We learn least mean square adaptive filters to predict three physiological parameters (heart rate, pulse pressure, and the product of total arterial compliance and arterial resistance) from previous data and previous NE infusion rate. These predictions are combined according to a physiology model to predict future mean arterial blood pressure.

RESULTS

Our model successfully forecasts mean arterial blood pressure on 30 septic patients from two databases. Specifically, we predict mean arterial blood pressure 3.33 minutes to 20 minutes into the future with a root mean square error from 3.56 mmHg to 6.22 mmHg. Additionally, we compare the computational cost of different models and discover a correlation between learned NE response models and a patient's SOFA score.

CONCLUSION

Our approach advances our capability to predict the effects of changing NE infusion rates in septic patients.

SIGNIFICANCE

More accurately predicted MAP can lessen clinicians' workload and reduce error in NE titration.

Reduced Rank Least Squares for Real-Time Short Term Estimation of Mean Arterial Blood Pressure in Septic Patients Receiving Norepinephrine

Norepinephrine (NE), an endogenous catecholamine, is a mainstay treatment for septic shock, which is a life-threatening manifestation of severe infection. NE counteracts the loss in blood pressure associated with septic shock. However, an NE infusion that is too low fails to counteract the blood pressure drop, and an NE infusion that is too high can cause a hypertensive crisis and heart attack. Ideally, the NE infusion rate should maintain a patient’s mean arterial blood pressure (MAP) above 65 mmHg. There are a few data-driven, quantitative models to predict the MAP, and incorporate NE effects. This paper presents a model, driven by intensive care unit (ICU) measurable data and known NE inputs, to predict the future MAP of an ICU patient. We derive a least square estimation model for MAP based on available ICU data, including heart period, NE infusion rate, and respiration wave. We learn the parameters of our model from initial patient data and then use this information to predict future MAP data. We assess our model with data from 12 septic patients. Our model successfully predicts and tracks MAP when the NE infusion rate changes. Specifically, we predict MAP 3 to 20 min in the future with the mean error of less than 4 to 7 mmHg over 12 patients. Conclusion: this new approach creates the potential to advance methods for predicting NE infusion rate in septic patients. Significance: successfully predicted patients’ MAP could reduce catastrophic human error and lessen clinicians’ workload.

Application of Mathematical Modeling for Simulation and Analysis of Hypoplastic Left Heart Syndrome (HLHS) in Pre- and Postsurgery Conditions

This paper is concerned with the mathematical modeling of a severe and common congenital defect called hypoplastic left heart syndrome (HLHS). Surgical approaches are utilized for palliating this heart condition; however, a brain white matter injury called periventricular leukomalacia (PVL) occurs with high prevalence at or around the time of surgery, the exact cause of which is not known presently. Our main goal in this paper is to study the hemodynamic conditions under which HLHS physiology may lead to the occurrence of PVL. A lumped parameter model of the HLHS circulation has been developed integrating diffusion modeling of oxygen and carbon dioxide concentrations in order to study hemodynamic variables such as pressure, flow, and blood gas concentration. Results presented include calculations of blood pressures and flow rates in different parts of the circulation. Simulations also show changes in the ratio of pulmonary to systemic blood flow rates when the sizes of the patent ductus arteriosus and atrial septal defect are varied. These changes lead to unbalanced blood circulations and, when combined with low oxygen and carbon dioxide concentrations in arteries, result in poor oxygen delivery to the brain. We stipulate that PVL occurs as a consequence.

Interactive simulator for e-Learning environments: a teaching software for health care professionals

There is an established tradition of cardiovascular simulation tools, but the application of this kind of technology in the e-Learning arena is a novel approach. This paper presents an e-Learning environment aimed at teaching the interaction of cardiovascular and lung systems to health-care professionals. Heart-lung interaction must be analyzed while assisting patients with severe respiratory problems or with heart failure in intensive care unit. Such patients can be assisted by mechanical ventilatory assistance or by thoracic artificial lung.

“In silico” cardiovascular simulator was experimented during a training course given to graduate students of the School of Specialization in Cardiology at ‘Sapienza’ University in Rome.

The training course employed CARDIOSIM^©: a numerical simulator of the cardiovascular system. Such simulator is able to reproduce pathophysiological conditions of patients affected by cardiovascular and/or lung disease. In order to study the interactions among the cardiovascular system, the natural lung and the thoracic artificial lung (TAL), the numerical model of this device has been implemented. After having reproduced a patient’s pathological condition, TAL model was applied in parallel and hybrid model during the training course.

Results obtained during the training course show that TAL parallel assistance reduces right ventricular end systolic (diastolic) volume, but increases left ventricular end systolic (diastolic) volume. The percentage changes induced by hybrid TAL assistance on haemodynamic variables are lower than those produced by parallel assistance. Only in the case of the mean pulmonary arterial pressure, there is a percentage reduction which, in case of hybrid assistance, is greater (about 40%) than in case of parallel assistance (20-30%).

At the end of the course, a short questionnaire was submitted to students in order to assess the quality of the course. The feedback obtained was positive, showing good results with respect to the degree of students’ learning and the ease of use of the software simulator.

Short-term variability of blood pressure: effects of lower-body negative pressure and long-duration bed rest

Mild lower-body negative pressure (LBNP) has been utilized to selectively unload cardiopulmonary baroreceptors, but there is evidence that arterial baroreceptors can be transiently unloaded after the onset of mild LBNP. In this paper, a black box mathematical model for the prediction of diastolic blood pressure (DBP) variability from multiple inputs (systolic blood pressure, R-R interval duration, and central venous pressure) was applied to interpret the dynamics of blood pressure maintenance under the challenge of LBNP and in long-duration, head-down bed rest (HDBR). Hemodynamic recordings from seven participants in the WISE (Women's International Space Simulation for Exploration) Study collected during an experiment of incremental LBNP (−10 mmHg, −20 mmHg, −30 mmHg) were analyzed before and on day 50 of a 60-day-long HDBR campaign. Autoregressive spectral analysis focused on low-frequency (LF, ∼0.1 Hz) oscillations of DBP, which are related to fluctuations in vascular resistance due to sympathetic and baroreflex regulation of vasomotor tone. The arterial baroreflex-related component explained 49 ± 13% of LF variability of DBP in spontaneous conditions, and 89 ± 9% ( P < 0.05) on day 50 of HDBR, while the cardiopulmonary baroreflex component explained 17 ± 9% and 12 ± 4%, respectively. The arterial baroreflex-related variability was significantly increased in bed rest also for LBNP equal to −20 and −30 mmHg. The proposed technique provided a model interpretation of the proportional effect of arterial baroreflex vs. cardiopulmonary baroreflex-mediated components of blood pressure control and showed that arterial baroreflex was the main player in the mediation of DBP variability. Data during bed rest suggested that cardiopulmonary baroreflex-related effects are blunted and that blood pressure maintenance in the presence of an orthostatic stimulus relies mostly on arterial control.

Simulation of Eisenmenger syndrome with ventricular septal defect using equivalent electronic system

BACKGROUND

In this study, we aim to investigate the simulation of the cardiovascular system using an electronic circuit model under normal and pathological conditions, especially the Eisenmenger syndrome.

METHODS AND RESULTS

The Eisenmenger syndrome includes a congenital communication between the systemic and pulmonary circulation, with resultant pulmonary arterial hypertension and right-to-left reversal of flow through the defect. When pulmonary vascular resistance exceeds systemic vascular resistance, it results in hypoxaemia and cyanosis. The Westkessel model including Resistor-Inductance-Capacitance pi-segments was chosen in order to simulate both systemic and pulmonary circulation. The left and right heart are represented by trapezoidal shape stiffness for better simulation results. The Eisenmenger syndrome is simulated using a resistance (septal resistance) connected between the left ventricle and right ventricle points of the model. Matlab® is used for the model implementation. In this model, although there is a remarkable increase in the pulmonary artery pressure and right ventricle pressure, left ventricle pressure, aortic pressure, aortic flow, and pulmonary compliance decrease in the Eisenmenger syndrome. In addition, left-to-right septal flow reversed in these diseases.

CONCLUSION

Our model is effective and available for simulating normal cardiac conditions and cardiovascular diseases, especially the Eisenmenger syndrome.

Patient specific identification of the cardiac driver function in a cardiovascular system model

The cardiac muscle activation or driver function, is a major determinant of cardiovascular dynamics, and is often approximated by the ratio of the left ventricle pressure to the left ventricle volume. In an intensive care unit, the left ventricle pressure is usually never measured, and the left ventricle volume is only measured occasionally by echocardiography, so is not available real-time. This paper develops a method for identifying the driver function based on correlates with geometrical features in the aortic pressure waveform. The method is included in an overall cardiovascular modelling approach, and is clinically validated on a porcine model of pulmonary embolism. For validation a comparison is done between the optimized parameters for a baseline model, which uses the direct measurements of the left ventricle pressure and volume, and the optimized parameters from the approximated driver function. The parameters do not significantly change between the two approaches thus showing that the patient specific approach to identifying the driver function is valid, and has potential clinically.

A cycle-averaged model of hypoplastic left heart syndrome (HLHS)

This paper is concerned with computational modeling of a severe congenital defect called Hypoplastic left heart syndrome (HLHS) that is the most common cardiac malformation with the highest likelihood of deaths in newborns. A lumped parameter model of the HLHS circulation has been developed to study the hemodynamic variables in the various sections of the cardio-pulmonary circulation system. We applied a short-term, cycle-averaging operation to the differential equations of the HLHS model to obtain the cycle-averaged model. Study has been carried out to analyze the variation of blood flow rate in different parts due to parameter changes. Results show that the developed model, could bring a good insight into understanding of the HLHS disease.

Age-dependent cardiopulmonary interaction during airway obstruction: a simulation model

Inspiratory fall in arterial blood pressure (Pa) during airway obstruction was ascribed to ventricular interdependence, afterload, and transmission of intrathoracic pressure swings. We have shown this effect significantly reduced in the elderly, but the underlying reasons remain unclear. Here we compare the results of inspiratory loading in young and older subjects with a mathematical model that simulated beat-by-beat fluctuations in cardiopulmonary variables. By increasing arterial and left ventricular elastance parameters in the older group, simulations strongly correlated with the experimental Pa and identified a linear increase of left ventricular transmural pressures with negative intrathoracic pressure that was nearly 38% larger than that in the younger group. The apparent perfusion preservation by less Pa decline with obstruction in the elderly could be misleading, since it reflects an increased afterload and diastolic dysfunction.

Mathematical modelling and electrical analog equivalent of the human cardiovascular system

The objective of this study is to develop a model of the cardiovascular system capable of simulating the normal operation of the systemic and pulmonary circulation, starts from aorta, and follows by upper and lower extremities vessels, finally ends with pulmonary veins. The model consists of a closed loop lumped elements with 43 compartments representing the cardiovascular system. The model parameters have been extracted from the literature. Using MATLAB software, the mathematical model has been simulated for the cardiovascular system. Each compartment includes a Resistor-Inductor-Capacitor (RLC) segment. The normal cardiovascular operation is characterised by the pressure-volume curves in different parts of the system. Model verification is performed by comparing the simulation results with the clinical observation reported in the literature. The described model is a useful tool in studying the physiology of cardiovascular system, and the related diseases. Also, it could be a great tool to investigate the effects of the pathologies of the cardiovascular system.

Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

Lumped parameter approaches for modelling the cardiovascular system typically have many parameters of which a significant percentage are often not identifiable from limited data sets. Hence, significant parts of the model are required to be simulated with little overall effect on the accuracy of data fitting, as well as dramatically increasing the complexity of parameter identification. This separates sub-structures of more complex cardiovascular system models to create uniquely identifiable simplified models that are one to one with the measurements. In addition, a new concept of parameter identification is presented where the changes in the parameters are treated as an actuation force into a feed back control system, and the reference output is taken to be steady state values of measured volume and pressure. The major advantage of the method is that when it converges, it must be at the global minimum so that the solution that best fits the data is always found. By utilizing continuous information from the arterial/pulmonary pressure waveforms and the end-diastolic time, it is shown that potentially, the ventricle volume is not required in the data set, which was a requirement in earlier published work. The simplified models can also act as a bridge to identifying more sophisticated cardiac models, by providing an initial set of patient specific parameters that can reveal trends and interactions in the data over time. The goal is to apply the simplified models to retrospective data on groups of patients to help characterize population trends or un-modelled dynamics within known bounds. These trends can assist in improved prediction of patient responses to cardiac disturbance and therapy intervention with potentially smaller and less invasive data sets. In this way a more complex model that takes into account individual patient variation can be developed, and applied to the improvement of cardiovascular management in critical care.

A cerebrovascular response model for functional neuroimaging including dynamic cerebral autoregulation

Functional neuroimaging techniques such as functional magnetic resonance imaging (fMRI) and near-infrared spectroscopy (NIRS) can be used to isolate an evoked response to a stimulus from significant background physiological fluctuations. Data analysis approaches typically use averaging or linear regression to remove this physiological baseline with varying degrees of success. Biophysical model-based analysis of the functional hemodynamic response has also been advanced previously with the Balloon and Windkessel models. In the present work, a biophysical model of systemic and cerebral circulation and gas exchange is applied to resting state NIRS neuroimaging data from 10 human subjects. The model further includes dynamic cerebral autoregulation, which modulates the cerebral arteriole compliance to control cerebral blood flow. This biophysical model allows for prediction, from noninvasive blood pressure measurements, of the background hemodynamic fluctuations in the systemic and cerebral circulations. Significantly higher correlations with the NIRS data were found using the biophysical model predictions compared to blood pressure regression and compared to transfer function analysis (multifactor ANOVA, p<0.0001). This finding supports the further development and use of biophysical models for removing baseline activity in functional neuroimaging analysis. Future extensions of this work could model changes in cerebrovascular physiology that occur during development, aging, and disease.

Inferential framework for nonstationary dynamics. II. Application to a model of physiological signaling

The problem of how to reconstruct the parameters of a stochastic nonlinear dynamical system when they are time-varying is considered in the context of online decoding of physiological information from neuron signaling activity. To model the spiking of neurons, a set of FitzHugh-Nagumo (FHN) oscillators is used. It is assumed that only a fast dynamical variable can be detected for each neuron, and that the monitored signals are mixed by an unknown measurement matrix. The Bayesian framework introduced in paper I (immediately preceding this paper) is applied both for reconstruction of the model parameters and elements of the measurement matrix, and for inference of the time-varying parameters in the nonstationary system. It is shown that the proposed approach is able to reconstruct unmeasured (hidden) slow variables of the FHN oscillators, to learn to model each individual neuron, and to track continuous, random, and stepwise variations of the control parameter for each neuron in real time.

Estimation of the total peripheral resistance baroreflex impulse response from spontaneous hemodynamic variability

We previously developed a mathematical analysis technique for estimating the static gain values of the arterial total peripheral resistance (TPR) baroreflex (G(A)) and the cardiopulmonary TPR baroreflex (G(C)) from small, spontaneous beat-to-beat fluctuations in arterial blood pressure, cardiac output, and stroke volume. Here, we extended the mathematical analysis so as to also estimate the entire arterial TPR baroreflex impulse response [h(A)(t)] as well as the lumped arterial compliance (AC). The extended technique may therefore provide a linear dynamic characterization of TPR baroreflex systems during normal physiological conditions from potentially noninvasive measurements. We theoretically evaluated the technique with respect to realistic spontaneous hemodynamic variability generated by a cardiovascular simulator with known system properties. Our results showed that the technique reliably estimated h(A)(t) [error = 30.2 +/- 2.6% for the square root of energy (E(A)), 19.7 +/- 1.6% for absolute peak amplitude (P(A)), 37.3 +/- 2.5% for G(A), and 33.1 +/- 4.9% for the overall time constant] and AC (error = 17.6 +/- 4.2%) under various simulator parameter values and reliably tracked changes in G(C). We also experimentally evaluated the technique with respect to spontaneous hemodynamic variability measured from seven conscious dogs before and after chronic arterial baroreceptor denervation. Our results showed that the technique correctly predicted the abolishment of h(A)(t) [E(A) = 1.0 +/- 0.2 to 0.3 +/- 0.1, P(A) = 0.3 +/- 0.1 to 0.1 +/- 0.0 s(-1), and G(A) = -2.1 +/- 0.6 to 0.3 +/- 0.2 (P < 0.05)] and the enhancement of G(C) [-0.7 +/- 0.44 to -1.8 +/- 0.2 (P < 0.05)] following the chronic intervention. Moreover, the technique yielded estimates whose values were consistent with those reported with more invasive and/or experimentally difficult methods.

Model-based cardiac diagnosis of pulmonary embolism

A minimal cardiac model has been shown to accurately capture a wide range of cardiovascular system dynamics commonly seen in the intensive care unit (ICU). However, standard parameter identification methods for this model are highly non-linear and non-convex, hindering real-time clinical application. An integral-based identification method that transforms the problem into a linear, convex problem, has been previously developed, but was only applied on continuous simulated data with random noise. This paper extends the method to handle discrete sets of clinical data, unmodelled dynamics, a significantly reduced data set theta requires only the minimum and maximum values of the pressure in the aorta, pulmonary artery and the volumes in the ventricles. The importance of integrals in the formulation for noise reduction is illustrated by demonstrating instability in the identification using simple derivative-based approaches. The cardiovascular system (CVS) model and parameter identification method are then clinically validated on porcine data for pulmonary embolism. Errors for the identified model are within 10% when re-simulated and compared to clinical data. All identified parameter trends match clinically expected changes. This work represents the first clinical validation of these models, methods and approach to cardiovascular diagnosis in critical care.

Activation detection in diffuse optical imaging by means of the general linear model

Due to its non-invasive nature and low cost, diffuse optical imaging (DOI) is becoming a commonly used technique to assess functional activation in the brain. When imaging with DOI, two major issues arise in the data analysis: (i) the separation of noise of physiological origin and the recovery of the functional response; (ii) the tomographic image reconstruction problem. This paper focuses on the first issue. Although the general linear model (GLM) has been extensively used in functional magnetic resonance imaging (fMRI), DOI has mostly relied on filtering and averaging of raw data to recover brain functional activation. This is mainly due to the high temporal resolution of DOI which implies a new design of the drift basis modelling physiology. In this paper, we provide (i) a filtering method based on cosine functions that is more adapted than standard averaging techniques for DOI specifically; (ii) a new mode-locking technique to recover small signals and locate them temporally with high precision (shift method). Results on real data show the capability of the shift method to retrieve HbR and HbO(2) peak locations.

ADAPTIVE REAL-TIME CARDIAC MRI USING PARADISE: VALIDATION BY THE PHYSIOLOGICALLY IMPROVED NCAT PHANTOM

Patient-Adaptive Reconstruction and Acquisition Dynamic Imaging with Sensitivity Encoding (PARADISE) is a dynamic MR imaging scheme that optimally combines parallel imaging and model-based adaptive acquisition. In this work, we propose the application of PARADISE to real-time cardiac MRI. We introduce a physiologically improved version of a realistic four-dimensional cardiac-torso (NCAT) phantom, which incorporates natural beat-to-beat heart rate and motion variations. Cardiac cine imaging using PARADISE is simulated and its performance is analyzed by virtue of the improved phantom. Results verify the effectiveness of PARADISE for high resolution un-gated real-time cardiac MRI and its superiority over conventional acquisition methods.

Incorporation of myofilament activation mechanics into a lumped model of the human heart

The success and usefulness of lumped cardiovascular models are directly dependent on the physiological fidelity of their formulation. In most existing lumped formulations for the heart, the compliance of the chamber is modeled based on its electrical analog, the capacitor. This has traditionally resulted in the use of a pre-described time-varying stiffness modulus for simulating the cardiac contractions. Unfortunately, such a time-varying stiffness does not include any physiological contractile machinery and thus no dependency on fiber sarcomere length and intracellular calcium concentrations, key mechanisms responsible for proper cardiac function. In this paper a lumped cardiovascular model is presented that is based on the incorporation of detailed myofilament activation for simulating the ventricular calcium binding and cross-bridging mechanism. Upon validation against experimental data, it is shown that the new myofilament activation-based model considerably increases the physiological validity and internal consistency of the cardiovascular simulations in comparison to the traditional variable compliance-based models. It is also shown, through specific case studies, that the present model can serve as a quick response tool for testing various hypotheses concerning the impact of the calcium binding and crossbridge kinetics on the overall performance of the cardiovascular system.

Mechanistic modeling of digoxin distribution kinetics incorporating slow tissue binding

This study aims to develop a mechanistic pharmacokinetic model that accounts for the kinetics of tissue binding in order to evaluate the effect of slow binding of digoxin to skeletal muscular Na(+)/K(+)-ATPase in humans. The approach is based on a minimal circulatory model with a systemic transit time density function that accounts for vascular mixing, transcapillary permeation and extravascular binding of the drug. The model parameters were estimated using previously published disposition data of digoxin in healthy volunteers and physiological distribution volumes taken from the literature. A time constant of the binding process of 34min was estimated indicating that receptor binding and not permeation clearance is the rate-limiting step of the distribution process. Model simulations suggest that up- or downregulation of sodium pumps, typically observed under physiological or pathophysiological conditions, could be detected with this method. The model allows a quantitative prediction of the effect of changes in skeletal muscular sodium pump activity on plasma levels of digoxin.

A weighted-principal component regression method for the identification of physiologic systems

We introduce a system identification method based on weighted-principal component regression (WPCR). This approach aims to identify the dynamics in a linear time-invariant (LTI) model which may represent a resting physiologic system. It tackles the time-domain system identification problem by considering, asymptotically, frequency information inherent in the given data. By including in the model only dominant frequency components of the input signal(s), this method enables construction of candidate models that are specific to the data and facilitates a reduction in parameter estimation error when the signals are colored (as are most physiologic signals). Additionally, this method allows incorporation of preknowledge about the system through a weighting scheme. We present the method in the context of single-input and multi-input single-output systems operating in open-loop and closed-loop. In each scenario, we compare the WPCR method with conventional approaches and approaches that also build data-specific candidate models. Through both simulated and experimental data, we show that the WPCR method enables more accurate identification of the system impulse response function than the other methods when the input signal(s) is colored.

SIMULATION OF THE CARDIOVASCULAR SYSTEM USING EQUIVALENT ELECTRONIC SYSTEM

This paper describes simulation of the cardiovascular system using a complex electronic circuit. In this study we have taken a slightly different approach to the modeling of the system and tried to advance existing electrical models by increasing more segments and parameters. The model consists of 42 segments representing the arterial system. Anatomical and physiological data for circuit parameters have been extracted from medical articles and textbooks. The frequency of heart is 1 Hz and the system operates in steady state condition. Each artery is modeled by one capacitor, resistor and inductor. The left and right ventricles are modeled using AC power suppliers and diodes. The results of the simulation including pressure and volume graphs exhibit operation of the cardiovascular system under normal condition. The results of the simulation have been compared with the relevant experimental observation and are in good agreement with them.

Dynamic physiological modeling for functional diffuse optical tomography

Diffuse optical tomography (DOT) is a noninvasive imaging technology that is sensitive to local concentration changes in oxy- and deoxyhemoglobin. When applied to functional neuroimaging, DOT measures hemodynamics in the scalp and brain that reflect competing metabolic demands and cardiovascular dynamics. The diffuse nature of near-infrared photon migration in tissue and the multitude of physiological systems that affect hemodynamics motivate the use of anatomical and physiological models to improve estimates of the functional hemodynamic response. In this paper, we present a linear state-space model for DOT analysis that models the physiological fluctuations present in the data with either static or dynamic estimation. We demonstrate the approach by using auxiliary measurements of blood pressure variability and heart rate variability as inputs to model the background physiology in DOT data. We evaluate the improvements accorded by modeling this physiology on ten human subjects with simulated functional hemodynamic responses added to the baseline physiology. Adding physiological modeling with a static estimator significantly improved estimates of the simulated functional response, and further significant improvements were achieved with a dynamic Kalman filter estimator (paired t tests, n=10, P<0.05). These results suggest that physiological modeling can improve DOT analysis. The further improvement with the Kalman filter encourages continued research into dynamic linear modeling of the physiology present in DOT. Cardiovascular dynamics also affect the blood-oxygen-dependent (BOLD) signal in functional magnetic resonance imaging (fMRI). This state-space approach to DOT analysis could be extended to BOLD fMRI analysis, multimodal studies and real-time analysis.

Nonlinear statistical modeling and model discovery for cardiorespiratory data

We present a Bayesian dynamical inference method for characterizing cardiorespiratory (CR) dynamics in humans by inverse modeling from blood pressure time-series data. The technique is applicable to a broad range of stochastic dynamical models and can be implemented without severe computational demands. A simple nonlinear dynamical model is found that describes a measured blood pressure time series in the primary frequency band of the CR dynamics. The accuracy of the method is investigated using model-generated data with parameters close to the parameters inferred in the experiment. The connection of the inferred model to a well-known beat-to-beat model of the baroreflex is discussed.

Inference of a nonlinear stochastic model of the cardiorespiratory interaction

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

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.

Very high frequency oscillations in the heart rate and blood pressure of heart transplant patients

The authors studied the recently reported very high frequency (VHF) peaks in the heart rate (HR) and blood pressure (BP) power spectra of heart transplant (HT) patients. These VHF peaks appear at frequencies much higher than the respiratory frequency, in addition to the typical low-frequency and high-frequency peaks. Twenty-five recordings obtained from 13 male HT patients (0.5-65 months following surgery) were compared with recordings from 14 normal male subjects. The ECG, continuous BP and respiration were recorded during 45min of supine rest. Eight recordings from HT patients were excluded owing to arrhythmias. Spectral analysis was performed on all other recordings. VHF peaks were found in the spectra of both BP and HR in nine recordings obtained from six HT patients. In some cases, the power in the VHF peaks was markedly higher than that of the high-frequency peak. No VHF peaks were observed in eight recordings obtained from four HT patients or in recording from any of the normal subjects. No correlation was found between the incidence of VHF peaks and time after transplant. It was proved that the VHF peaks were not artifactual, and their significance within the framework of the theory of communication systems is discussed. The presence of those peaks was attributed to vagal denervation.

Noninvasive identification of the total peripheral resistance baroreflex

We propose two identification algorithms for quantitating the total peripheral resistance (TPR) baroreflex, an important contributor to short-term arterial blood pressure (ABP) regulation. Each algorithm analyzes beat-to-beat fluctuations in ABP and cardiac output, which may both be obtained noninvasively in humans. For a theoretical evaluation, we applied both algorithms to a realistic cardiovascular model. The results contrasted with only one of the algorithms proving to be reliable. This algorithm was able to track changes in the static gains of both the arterial and cardiopulmonary TPR baroreflex. We then applied both algorithms to a preliminary set of human data and obtained contrasting results much like those obtained from the cardiovascular model, thereby making the theoretical evaluation results more meaningful. This study suggests that, with experimental testing, the reliable identification algorithm may provide a powerful, noninvasive means for quantitating the TPR baroreflex. This study also provides an example of the role that models can play in the development and initial evaluation of algorithms aimed at quantitating important physiological mechanisms.