A human cardiopulmonary system model applied to the analysis of the Valsalva maneuver

Investigation into the two-way interaction of coronary flow and heart function in coronary artery disease predicted by a computational model of autoregulation of coronary flow

This study presents a closed-loop computational model to investigate the interplay between heart function, coronary flow, and systemic circulation during exercise, with a specific focus on the impact of coronary artery stenosis. The model incorporates a lumped representation of the heart, main arteries, and coronary arteries, establishing a closed circulatory system. The simulation investigates the autoregulation of coronary flow in response to myocardial oxygen demands during physical exercise by incorporating sympathetic and parasympathetic functions. This study establishes a closed supply-demand loop and investigates the effect of coronary flow deficiency on heart function and systemic circulation in coronary artery diseases during exercise. In coronary artery diseases with low stenosis, heart function and systemic flow resemble those of a healthy person. However, as stenosis intensifies with physical exercise, an additional regulatory mechanism (reg2) is activated. This mechanism adjusts coronary flow by reducing myocardial contractility (E) and increasing heart rate (HR) while maintaining cardiac output (CO). The study results indicate that, at the highest exercise intensity for a healthy individual (HR = 150), the value of E increases from 6 to 8.65mmHg/ml. Meanwhile, for a patient with 85 % coronary artery stenosis in the same exercise intensity, the HR increases to 200, and the value of E decreases to 3.45mmHg/ml. The results also demonstrate that the initiation of the (reg2) mechanism at rest occurs at 83 % stenosis, while at the highest exercise intensity, this mechanism commences at 67 % stenosis.

An analytic method to investigate hemodynamics of the cardiovascular system - single ventricular system

Based on the lumped parameter model (LPM) of the cardiovascular system, an analytic method is developed to derive its hemodynamics theoretically. As soon as the LPM (a series of differential equations) is solved, the hemodynamics would be obtained immediately. However, because of time-varying ventricular elastance and high order, it is difficult to solve analytically. Through simplifying the LPM, the original biventricular system with continuously varying elastance becomes a single ventricular system with discrete elastance which keeps constant during the systolic or diastolic phase. As a consequence, the original time-varying and high-order system becomes a time-invariant and first-order system during each phase. From the analytic solutions of the simplified system, a set of algebraic equations is carried out. Then the hemodynamics are obtained from the solutions of the algebraic equations. The nature of the algebraic equations is an integral form of the differential equations. A connection between the equations and PV loop is established. All of these equations are deduced based on the idealization of replacing the continuous elastance with the discrete elastance. However, there exist algebraic equations, that can be derived directly from volume conservation, still hold for the case of continuous elastance. As a preliminary application, the method is utilized to deduce the hemodynamics of left heart failure (LHF). The results show that the theoretical hemodynamics of LHF are coincident with simulated results. The analytic method can be generalized to investigate biventricular system. A program for developing a more general framework is presented in the last part.

A variable heart rate multi-compartmental coupled model of the cardiovascular and respiratory systems

Current mathematical models of the cardiovascular system that are based on systems of ordinary differential equations are limited in their ability to mimic important features of measured patient data, such as variable heart rates (HR). Such limitations present a significant obstacle in the use of such models for clinical decision-making, as it is the variations in vital signs such as HR and systolic and diastolic blood pressure that are monitored and recorded in typical critical care bedside monitoring systems. In this paper, novel extensions to well-established multi-compartmental models of the cardiovascular and respiratory systems are proposed that permit the simulation of variable HR. Furthermore, a correction to current models is also proposed to stabilize the respiratory behaviour and enable realistic simulation of vital signs over the longer time scales required for clinical management. The results of the extended model developed here show better agreement with measured bio-signals, and these extensions provide an important first step towards estimating model parameters from patient data, using methods such as neural ordinary differential equations. The approach presented is generalizable to many other similar multi-compartmental models of the cardiovascular and respiratory systems.

Study of the Relationship between Pulmonary Artery Pressure and Heart Valve Vibration Sound Based on Mock Loop

The vibration of the heart valves' closure is an important component of the heart sound and contains important information about the mechanical activity of a heart. Stenosis of the distal pulmonary artery can lead to pulmonary hypertension (PH). Therefore, in this paper, the relationship between the vibration sound of heart valves and the pulmonary artery blood pressure was investigated to contribute to the noninvasive detection of PH. In this paper, a lumped parameter circuit platform of pulmonary circulation was first set to guide the establishment of a mock loop of circulation. By adjusting the distal vascular resistance of the pulmonary artery, six different pulmonary arterial pressure states were achieved. In the experiment, pulmonary artery blood pressure, right ventricular blood pressure, and the vibration sound of the pulmonary valve and tricuspid valve were measured synchronously. Features of the time domain and frequency domain of two valves' vibration sound were extracted. By conducting a significance analysis of the inter-group features, it was found that the amplitude, energy and frequency features of vibration sounds changed significantly. Finally, the continuously varied pulmonary arterial blood pressure and valves' vibration sound were obtained by continuously adjusting the resistance of the distal pulmonary artery. A backward propagation neural network and deep learning model were used, respectively, to estimate the features of pulmonary arterial blood pressure, pulmonary artery systolic blood pressure, the maximum rising rate of pulmonary artery blood pressure and the maximum falling rate of pulmonary artery blood pressure by the vibration sound of the pulmonary and tricuspid valves. The results showed that the pulmonary artery pressure parameters can be well estimated by valve vibration sounds.

The Role of Transcranial Doppler in Detecting Patent Foramen Ovale

Air embolic signals detected in the intracranial arteries using transcranial Doppler after intravenous injection of agitated saline bubbles indicate right-to-left cardiac shunting. They prove that emboli from venous sites can bypass the lungs and flow to the intracranial arteries. The Valsalva maneuver immediately after an intravenous injection of agitated saline bubbles helps the air bubbles pass through the shunt. If the air embolic signal appears in the intracranial arteries without the Valsalva maneuver, the shunting is highly significant to the etiology of embolism. Transcranial Doppler to detect air embolic signals after intravenous injection of agitated saline bubbles may not be mandatory to diagnose and treat patent foramen ovale; however, as with echocardiography, transcranial Doppler is considered a noninvasive, convenient, and low-cost investigation. The test should be helpful to confirm the significance of the corresponding patent foramen ovale.

A Novel Strategy to Fit and Validate Physiological Models: A Case Study of a Cardiorespiratory Model for Simulation of Incremental Aerobic Exercise

Applying complex mathematical models of physiological systems is challenging due to the large number of parameters. Identifying these parameters through experimentation is difficult, and although procedures for fitting and validating models are reported, no integrated strategy exists. Additionally, the complexity of optimization is generally neglected when the number of experimental observations is restricted, obtaining multiple solutions or results without physiological justification. This work proposes a fitting and validation strategy for physiological models with many parameters under various populations, stimuli, and experimental conditions. A cardiorespiratory system model is used as a case study, and the strategy, model, computational implementation, and data analysis are described. Using optimized parameter values, model simulations are compared to those obtained using nominal values, with experimental data as a reference. Overall, a reduction in prediction error is achieved compared to that reported for model building. Furthermore, the behavior and accuracy of all the predictions in the steady state were improved. The results validate the fitted model and provide evidence of the proposed strategy's usefulness.

Proposed cardio-pulmonary model to investigate the effects of COVID-19 on the cardiovascular system

In this paper, we propose a new mathematical model of cardiovascular system coupled with a respiratory system to study the effects of COVID-19 on global blood circulation parameters using the lumped parameters model. We use the fourth-order Runge-Kutta method for solving the sets of equations of motion. We validate our model by showing that the simulated flows in pulmonary and aortic valves corroborate, respectively, the results established by Smith et al. [IFAC Proceedings Volumes, 39 (2006) 453-458]. Then we examine the effects of the new coronavirus (covid-19) on the cardiopulmonary system through the impact of the high respiratory frequency and the variation of the alveoli volume. To achieve this aim, we propose a new exponential law for the time varying of the pulmonary resistance. It appears that when the respiratory frequency grows, the delay between the systemic artery flow and the flow in the pulmonary artery diminishes. Therefore, the efficiency of the cardiac pump is reduced. Moreover, our results also show that variations of the alveoli volume cause the increment of the pleural pressure in the vascular cavities that induces an exponential growth of the pulmonary resistance. Furthermore, this growth of the pulmonary resistance provokes the augmentation of pressure in some organs and its reduction in others. We found that patient with covid-19 having a prior history of cardiovascular diseases is exposed to a severe case of inflammation/damage of certain organs than those with no history of cardiovascular disease.

Development and validation of a mathematical model to simulate human cardiovascular and respiratory responses to battlefield trauma

Mathematical models of human cardiovascular and respiratory systems provide a viable alternative to generate synthetic data to train artificial intelligence (AI) clinical decision-support systems and assess closed-loop control technologies, for military medical applications. However, existing models are either complex, standalone systems that lack the interface to other applications or fail to capture the essential features of the physiological responses to the major causes of battlefield trauma (i.e., hemorrhage and airway compromise). To address these limitations, we developed the cardio-respiratory (CR) model by expanding and integrating two previously published models of the cardiovascular and respiratory systems. We compared the vital signs predicted by the CR model with those from three models, using experimental data from 27 subjects in five studies, involving hemorrhage, fluid resuscitation, and respiratory perturbations. Overall, the CR model yielded relatively small root mean square errors (RMSEs) for mean arterial pressure (MAP; 20.88 mm Hg), end-tidal CO₂ (ETCO₂ ; 3.50 mm Hg), O₂ saturation (SpO₂ ; 3.40%), and arterial O₂ pressure (PaO₂ ; 10.06 mm Hg), but a relatively large RMSE for heart rate (HR; 70.23 beats/min). In addition, the RMSEs for the CR model were 3% to 10% smaller than the three other models for HR, 11% to 15% for ETCO₂ , 0% to 33% for SpO₂ , and 10% to 64% for PaO₂ , while they were similar for MAP. In conclusion, the CR model balances simplicity and accuracy, while qualitatively and quantitatively capturing human physiological responses to battlefield trauma, supporting its use to train and assess emerging AI and control systems.

Mechanical Interaction of the Pericardium and Cardiac Function in the Normal and Hypertensive Rat Heart

The pericardium is a thin connective tissue membrane that surrounds the heart and is an integral regulatory component of cardiopulmonary performance. Pathological growth and remodeling of the right ventricle (RV) stemming from structural heart diseases are thought to include a significant role of the pericardium, but its exact role remains unclear. The objective of this study was to investigate potential biomechanical adaptations of the pericardium in response to pulmonary hypertension and their effects on heart behavior. Integrated computational-experimental modeling of the heart offers a robust platform to achieve this objective. We built upon our recently developed high-fidelity finite-element models of healthy and hypertensive rodent hearts via addition of the pericardial sac. In-silico experiments were performed to investigate changes in pericardium reserve elasticity and their effects on cardiac function in hypertensive hearts. Our results suggest that contractile forces would need to increase in the RV and decrease in the left ventricle (LV) in the hypertensive heart to compensate for reductions in pericardium reserve elasticity. The discrepancies between chamber responses to pericardium addition result, in part, from differences in the impact of pericardium on the RV and LV preload. We further demonstrated the capability of our platform to predict the effect of pericardiectomy on heart function. Consistent with previous results, the effect of pericardiectomy on the chamber pressure-volume loop was the largest in the hypertensive RV. These insights are expected to motivate further computational investigations of the effect of pericardiectomy on cardiac function which remains an important factor in surgical planning of constrictive pericarditis and coronary artery bypass grafting.

In Vivo Validation of a Cardiovascular Simulation Model in Pigs

Many computer simulation models of the cardiovascular system, of varying complexity and objectives, have been proposed in physiological science. Every model needs to be parameterized and evaluated individually. We conducted a porcine animal model to parameterize and evaluate a computer simulation model, recently proposed by our group. The results of an animal model, on thirteen healthy pigs, were used to generate consistent parameterization data for the full heart computer simulation model. To evaluate the simulation model, differences between the resulting simulation output and original animal data were analysed. The input parameters of the animal model, used to individualize the computer simulation, showed high interindividual variability (range of coefficient of variation: 10.1–84.5%), which was well-reflected by the resulting haemodynamic output parameters of the simulation (range of coefficient of variation: 12.6–45.7%). The overall bias between the animal and simulation model was low (mean: −3.24%, range: from −26.5 to 20.1%). The simulation model used in this study was able to adapt to the high physiological variability in the animal model. Possible reasons for the remaining differences between the animal and simulation model might be a static measurement error, unconsidered inaccuracies within the model, or unconsidered physiological interactions.

Systems analysis of the mechanisms governing the cardiovascular response to changes in posture and in peripheral demand during exercise

Blood flows and pressures throughout the human cardiovascular system are regulated in response to various dynamic perturbations, such as changes to peripheral demands in exercise, rapid changes in posture, or loss of blood from hemorrhage, via the coordinated action of the heart, the vasculature, and autonomic reflexes. To assess how the systemic and pulmonary arterial and venous circulation, the heart, and the baroreflex work together to effect the whole-body responses to these perturbations, we integrated an anatomically-based large-vessel arterial tree model with the TriSeg heart model, models capturing nonlinear characteristics of the large and small veins, and baroreflex-mediated regulation of vascular tone and cardiac chronotropy and inotropy. The model was identified by matching data from the Valsalva maneuver (VM), exercise, and head-up tilt (HUT). Thirty-one parameters were optimized using a custom parameter-fitting tool chain, resulting in an unique, high-fidelity whole-body human cardiovascular systems model. Because the model captures the effects of exercise and posture changes, it can be used to simulate numerous clinical assessments, such as HUT, the VM, and cardiopulmonary exercise stress testing. The model can also be applied as a framework for representing and simulating individual patients and pathologies. Moreover, it can serve as a framework for integrating multi-scale organ-level models, such as for the heart or the kidneys, into a whole-body model. Here, the model is used to analyze the relative importance of chronotropic, inotropic, and peripheral vascular contributions to the whole-body cardiovascular response to exercise. It is predicted that in normal physiological conditions chronotropy and inotropy make roughly equal contributions to increasing cardiac output and cardiac power output during exercise. Under upright exercise conditions, the nonlinear pressure-volume relationship of the large veins and sympathetic-mediated venous vasoconstriction are both required to maintain preload to achieve physiological exercise levels. The developed modeling framework is built using the open Modelica modeling language and is freely distributed.

Modeling patient-specific desaturation patterns in sleep apnea

OBJECTIVE

The physiological mechanisms involved in cardio-respiratory responses to sleep apnea events are not yet fully elucidated. A model-based approach is proposed to analyse the acute desaturation response to obstructive apneas.

METHODS

An integrated model of cardio-respiratory interactions was proposed and parameters were identified, using an evolutionary algorithm, on a database composed of 107 obstructive apneas acquired from 10 patients (HYPNOS clinical study). Unsupervised clustering was applied to the identified parameters in order to characterize the phenotype of each response to obstructive apneas.

RESULTS

A close match was observed between simulated oxygen saturation (SaO2) and experimental SaO2 in all identifications (median RMSE = 1.3892%). Two clusters of parameters, associated with different dynamics related to sleep apnea and periodic breathing were obtained.

CONCLUSION AND SIGNIFICANCE

The proposed patient and event-specific model-based analysis provides understanding on specific desaturation patterns, consequent to apnea events, with potential applications for personalized diagnosis and treatment.

Parametric Analysis of an Integrated Model of Cardio-respiratory Interactions in Adults in the Context of Obstructive Sleep Apnea

An original integrated model of cardio-respiratory interactions is presented in this paper with the objective of studying the acute physiological responses evoked by obstructive sleep apnea events in adults. A comprehensive sensitivity analysis of the model is proposed during the simulation of a 20 s obstructive apnea episode using the Morris' screening method and local sensitivity analysis. The more relevant parameters are related to the following mechanisms of the physiology: (i) the fraction of oxygen in inspired air, (ii) metabolic rates (oxygen consumption rate, CO₂ production rate); (iii) chemoreflex (gains and time constants) (iv) respiratory mechanics (lung compliance and unstressed volume of air in the alveoli). These results highlight significant physiological variables that may be particularly useful for the development of novel diagnostic and therapeutic strategies, integrating a virtual patient approach.

Can party balloons replace autoinflation balloons to treat glue ear? A technical comparison

Background

Autoinflation balloons are used to treat patients with otitis media with effusion (OME) to help avoid surgery.

Aim

To compare the ability of party balloons with Otovent balloons to produce sufficient pressure for a Valsalva manoeuvre.

Design & setting

Pressure testing was used to determine the number of times each balloon could produce pressures sufficient for a Valsalva manoeuvre. Subsequently, Otovent balloons were compared with spherical party balloons in a pilot clinical trial of 12 healthy adults.

Method

Each balloon was inflated 20 times and the maximum pressure was recorded. Three balloons of each type were tested to 50 inflations to assess pressures over persistent use.

Results

Otovent balloons’ mean inflation pressure was 93 mmHg (95% confidence interval [CI] = 89 to 97 mmHg) on first inflation, dropping to 83 mmHg (95% CI = 80 to 86 mmHg) after 20 inflations. Two types of spherical party balloon required mean inflation pressures of 84 mmHg (95% CI = 77 to 90 mmHg) and 108 mmHg (95% CI = 97 to 119 mmHg) on first inflation, dropping to 74 mmHg (95% CI = 68 to 81 mmHg) and 83 mmHg (95% CI = 77 to 88 mmHg) after 20 inflations. In the pilot trial, there was no difference between the ability of Otovent and spherical balloons (χ² = 0.24, P = 0.89) to produce the sensation of a Valsalva manoeuvre.

Conclusion

Otovent balloons can be used more than the 20 times quoted by the manufacturer. The two spherical balloons produced similar pressures to Otovent balloons, indicating potentially the same clinical effect. The pilot study suggests a potential use of spherical party balloons instead of Otovent balloons as a cost-efficient treatment.

Global sensitivity analysis informed model reduction and selection applied to a Valsalva maneuver model

In this study, we develop a methodology for model reduction and selection informed by global sensitivity analysis (GSA) methods. We apply these techniques to a control model that takes systolic blood pressure and thoracic tissue pressure data as inputs and predicts heart rate in response to the Valsalva maneuver (VM). The study compares four GSA methods based on Sobol' indices (SIs) quantifying the parameter influence on the difference between the model output and the heart rate data. The GSA methods include standard scalar SIs determining the average parameter influence over the time interval studied and three time-varying methods analyzing how parameter influence changes over time. The time-varying methods include a new technique, termed limited-memory SIs, predicting parameter influence using a moving window approach. Using the limited-memory SIs, we perform model reduction and selection to analyze the necessity of modeling both the aortic and carotid baroreceptor regions in response to the VM. We compare the original model to systematically reduced models including (i) the aortic and carotid regions, (ii) the aortic region only, and (iii) the carotid region only. Model selection is done quantitatively using the Akaike and Bayesian Information Criteria and qualitatively by comparing the neurological predictions. Results show that it is necessary to incorporate both the aortic and carotid regions to model the VM.

Integrative Computational Models of Lung Structure-Function Interactions

Anatomically based integrative models of the lung and their interaction with other key components of the respiratory system provide unique capabilities for investigating both normal and abnormal lung function. There is substantial regional variability in both structure and function within the normal lung, yet it remains capable of relatively efficient gas exchange by providing close matching of air delivery (ventilation) and blood delivery (perfusion) to regions of gas exchange tissue from the scale of the whole organ to the smallest continuous gas exchange units. This is despite remarkably different mechanisms of air and blood delivery, different fluid properties, and unique scale-dependent anatomical structures through which the blood and air are transported. This inherent heterogeneity can be exacerbated in the presence of disease or when the body is under stress. Current computational power and data availability allow for the construction of sophisticated data-driven integrative models that can mimic respiratory system structure, function, and response to intervention. Computational models do not have the same technical and ethical issues that can limit experimental studies and biomedical imaging, and if they are solidly grounded in physiology and physics they facilitate investigation of the underlying interaction between mechanisms that determine respiratory function and dysfunction, and to estimate otherwise difficult-to-access measures. © 2021 American Physiological Society. Compr Physiol 11:1501-1530, 2021.

An integrated mathematical model of the cardiovascular and respiratory response to exercise: model-building and comparison with reported models

The use of physiological models in medicine allows the evaluation of new hypotheses, development of diagnosis and clinical treatment applications, and development of training and medical education tools, as well as medical device design. Although several mathematical models of physiological systems have been presented in the literature, few of them are able to predict the human cardiorespiratory response under physical exercise stimulus adequately. This paper aims to present the building and comparison of an integrated cardiorespiratory model focused on the prediction of the healthy human response under rest and aerobic exercise. The model comprises cardiovascular circulation, respiratory mechanics, and gas exchange system, as well as cardiovascular and respiratory controllers. Every system is based on previously reported physiological models and incorporates reported mechanisms related to the aerobic exercise dynamics. Experimental data of 30 healthy male volunteers undergoing a cardiopulmonary exercise test and simulated data from two of the most current and complete cardiorespiratory models were used to evaluate the performance of the presented model. Experimental design, processing, and exploratory analysis are described in detail. The simulation results were compared against the experimental data in steady state and in transient regime. The predictions of the proposed model closely mimic the experimental data, showing in overall the lowest prediction error (10.35%), the lowest settling times for cardiovascular and respiratory variables, and in general the fastest and similar responses in transient regime. These results suggest that the proposed model is suitable to predict the cardiorespiratory response of healthy adult humans under rest and aerobic exercise conditions.NEW & NOTEWORTHY This paper presents a new cardiorespiratory model focused on the prediction of the healthy human response under rest and aerobic dynamic exercise conditions. Simulation results of cardiorespiratory variables are compared against experimental data and two of the most current and complete cardiorespiratory models.

Heart-Lung Interactions During Mechanical Ventilation: Analysis via a Cardiopulmonary Simulation Model

Heart-lung interaction mechanisms are generally not well understood. Mechanical ventilation, for example, accentuates such interactions and could compromise cardiac activity. Thereby, assessment of ventilation-induced changes in cardiac function is considered an unmet clinical need. We believe that mathematical models of the human cardiopulmonary system can provide invaluable insights into such cardiorespiratory interactions. In this article, we aim to use a mathematical model to explain heart-lung interaction phenomena and provide physiologic hypotheses to certain contradictory experimental observations during mechanical ventilation. To accomplish this task, we highlight three model components that play a crucial role in heart-lung interactions: 1) pericardial membrane, 2) interventricular septum, and 3) pulmonary circulation that enables pulmonary capillary compression due to lung inflation. Evaluation of the model’s response under simulated ventilation scenarios shows good agreement with experimental data from the literature. A sensitivity analysis is also presented to evaluate the relative impact of the model’s highlighted components on the cyclic ventilation-induced changes in cardiac function.

In silico study of airway/lung mechanics in normal human breathing

The airway/lung mechanics is usually represented with nonlinear 0-D models based on a pneumatic-electrical analogy. The aim of this work is to provide a detailed description of the human respiratory mechanics in healthy and diseased conditions. The model used for this purpose employs some known constitutive functions of the main components of the respiratory system. We give a detailed mathematical description of these functions and subsequently derive additional key ones. We are interested not only in the main output such as airflow at the mouth or alveolar pressure and volume, but also in other quantities such as resistance and pressure drop across each element of the system and even recoil and compliance of the chest wall. Pathological conditions are simulated by altering the parameters of the constitutive functions. Results show that increased upper airway resistance induces airflow reduction with concomitant narrowing of volume and pressure ranges without affecting lung compliance. Instead, increased elastic recoil leads to low volumes and decreased lung compliance. The model could be used in the study of the interaction between respiratory and cardiovascular systems in pathophysiological conditions.

Model-Based Weaning Tests for VA-ECLS Therapy

Venoarterial extracorporeal life support (VA-ECLS) is used in ICUs (intensive care units) for the most extreme presentations of acute and severe cardiogenic shock, and one of the main issues the clinicians have to deal with is the weaning from VA-ECLS. In this study, a patient-specific model of the cardiovascular system connected to a VA-ECLS is built to improve the understanding of this complex system. Pig experiments are performed to validate the model, and the results are quite promising since the mean difference between experimental data and simulation is smaller than 5% for all the hemodynamic quantities. It is also a major objective of this paper to provide a proof-of-concept analysis that model-based approaches could improve the weaning strategy for VA-ECLS therapy.

Analysis of Cleveland Clinic continuous-flow total artificial heart performance using the Virtual Mock Loop: Comparison with an in vivo study

The Virtual Mock Loop (VML) is a mathematical model designed to simulate mechanism of the human cardiovascular system interacting with mechanical circulatory support devices. Here, we aimed to mimic the hemodynamic performance of Cleveland Clinic's self-regulating continuous-flow total artificial heart (CFTAH) via VML and evaluate the accuracy of the VML compared with an in vivo acute animal study. The VML reproduced 124 hemodynamic conditions from three acute in vivo experiments in calves. Systemic/pulmonary vascular resistances, pump rotational speed, pulsatility, and pulse rate were set for the VML from in vivo data. We compared outputs (pump flow, left and right pump pressure rises, and atrial pressure difference) between the two systems. The pump performance curves all fell in the designed range. There was a strong correlation between the VML and the in vivo study in the left pump flow (r2 = 0.84) and pressure rise (r2 = 0.80), and a moderate correlation in right pressure rise (r2 = 0.52) and atrial pressure difference (r2 = 0.59). Although there is room for improvement in simulating right-sided pump performance of self-regulating CFTAH, the VML acceptably simulated the hemodynamics observed in an in vivo study. These results indicate that pump flow and pressure rise can be estimated from vascular resistances and pump settings.

A Full-Body Model of Burn Pathophysiology and Treatment Using the BioGears Engine

We have created a model of systemic burn pathophysiology by incorporating a mathematical model of acute inflammation within the BioGears Engine. This model produces outputs consistent with burns of varying severities and leverages existing BioGears functionality to simulate the effect of treatment on virtual patient outcome. The model performs well for standard resuscitation scenarios and we thus expect it to be useful for educational and training purposes.

Lumped-Parameter Circuit Platform for Simulating Typical Cases of Pulmonary Hypertensions from Point of Hemodynamics

Pulmonary hypertension (PH) presents unusual hemodynamic states characterized by abnormal high blood pressure in pulmonary artery. The objective of this study is to simulate how the hemodynamics develops in typical PH cases without treatment. A lumped-parameter circuit platform of human circulation system is set up to simulate hemodynamic abnormalities of PH in different etiologies and pathogenesis. Four typical cases are considered, which are distal pulmonary artery stenosis, left ventricular diastolic dysfunction, ventricular septal defect, and mitral stenosis. The authors propose regulation laws for chambers and vessels to adapt the abnormal hemodynamic conditions for each PH case. The occurrence and development of each PH case are simulated over time using the lumped-parameter circuit platform. The blood pressure, blood flow, pressure-volume relations for chambers and vessels are numerically calculated for each case of PH progression. The model results could be a quite helpful to understand the hemodynamic mechanism of typical PHs. Graphical Abstract.

Persistent instability in a nonhomogeneous delay differential equation system of the Valsalva maneuver

Delay differential equations are widely used in mathematical modeling to describe physical and biological systems, often inducing oscillatory behavior. In physiological systems, this instability may signify (i) an attempt to return to homeostasis or (ii) system dysfunction. In this study, we analyze a nonlinear, nonautonomous, nonhomogeneous open-loop neurological control model describing the autonomic nervous system response to the Valsalva maneuver (VM). We reduce this model from 5 to 2 states (predicting sympathetic tone and heart rate) and categorize the stability properties of the reduced model using a two-parameter bifurcation analysis of the sympathetic delay (D_s) and time-scale (τ_s). Stability regions in the D_sτ_s-plane for this nonhomogeneous system and its homogeneous analog are classified numerically and analytically, identifying transcritical and Hopf bifurcations. Results show that the Hopf bifurcation remains for both the homogeneous and nonhomogeneous systems, while the nonhomogeneous system stabilizes the transition at the transcritical bifurcation. This analysis was compared with results from blood pressure and heart rate data from three subjects performing the VM: a control subject exhibiting sink behavior, a control subject exhibiting stable focus behavior, and a patient with postural orthostatic tachycardia syndrome (POTS) also exhibiting stable focus behavior. Results suggest that instability caused from overactive sympathetic signaling may result in autonomic dysfunction.

A chair based ballistocardiogram time interval measurement with cardiovascular provocations

The objective of this study was to measure ballistocardiogram (BCG) based time intervals and compare them with systolic blood pressure values. Electrocardiogram (ECG) and BCG signals of six subjects sitting in a chair were measured with a ferroelectret film sensor. Time intervals between ECG R peak and BCG I and J waves were calculated to obtain RJ, RI and IJ intervals. The time intervals were modified with two cardiovascular provocations, controlled breathing and Valsalva maneuver. The controlled breathing changed all the time intervals (RJ, RI and IJ) whereas the Valsalva maneuver mainly caused variations in the RJ and RI intervals. The calculated time intervals were compared with reference arterial blood pressure values. Correlation coefficients of r = -0.61 and r = -0.78 were found between the RJ and RI time intervals and systolic blood pressure during Valsalva maneuver, respectively.

Multiscale Computational Analysis of Right Ventricular Mechanoenergetics

Right ventricular (RV) failure, which occurs in the setting of pressure overload, is characterized by abnormalities in mechanical and energetic function. The effects of these cell- and tissue-level changes on organ-level RV function are unknown. The primary aim of this study was to investigate the effects of myofiber mechanics and mitochondrial energetics on organ-level RV function in the context of pressure overload using a multiscale model of the cardiovascular system. The model integrates the mitochondria-generated metabolite concentrations that drive intracellular actin-myosin cross-bridging and extracellular myocardial tissue mechanics in a biventricular heart model coupled with simple lumped parameter circulations. Three types of pressure overload were simulated and compared to experimental results. The computational model was able to capture a wide range of cardiovascular physiology and pathophysiology from mild RV dysfunction to RV failure. Our results confirm that, in response to pressure overload alone, the RV is able to maintain cardiac output (CO) and predict that alterations in either RV active myofiber mechanics or RV metabolite concentrations are necessary to decrease CO.

Influence of nasal CPAP on cardiorespiratory control in healthy neonate

The present study aimed to further unravel the effects of nasal continuous positive airway pressure (nCPAP) on the cardiovascular and respiratory systems in the neonatal period. Six-hour polysomnographic recordings were first performed in seven healthy newborn lambs, aged 2-3 days, without and with nCPAP application at 6 cmH₂O (nCPAP-6), in randomized order. The effects of nCPAP-6 on heart rate variability, respiratory rate variability, and cardiorespiratory interrelations were analyzed using a semiautomatic signal processing approach applied to ECG and respiration recordings. Thereafter, a cardiorespiratory mathematical model was adapted to the experimental conditions to gain further physiological interpretation and to simulate higher nCPAP levels (8 and 10 cmH₂O). Results from the signal processing approach suggest that nCPAP-6 applied in newborns with healthy lungs: 1) increases heart rate and decreases the time and frequency domain indices of heart rate variability, especially those representing parasympathetic activity, while increasing the complexity of the RR-interval time series; 2) prolongs the respiratory cycle and expiration duration and decreases respiratory rate variability; and 3) slightly impairs cardiorespiratory interrelations. Model-based analysis revealed that nCPAP-6 increases the heart rate and decreases respiratory sinus arrhythmia amplitude, in association with a reduced parasympathetic efferent activity. These results were accentuated when simulating an increased CPAP level. Overall, our results provide a further understanding of the effects of nCPAP in neonates, in the absence of lung disease.NEW & NOTEWORTHY Application of nasal continuous positive airway pressure (CPAP) at 6 cmH₂O, a level very frequently used in newborns, alters heart and respiratory rate variability, as well as cardiorespiratory interrelations in a full-term newborn model without lung disease. Moreover, whereas nasal CPAP at 6 cmH₂O decreases parasympathetic efferent activity, there is no change in sympathetic efferent activity.

A model-based analysis of autonomic nervous function in response to the Valsalva maneuver

The Valsalva maneuver (VM) is a diagnostic protocol examining sympathetic and parasympathetic activity in patients with autonomic dysfunction (AD) impacting cardiovascular control. Because direct measurement of these signals is costly and invasive, AD is typically assessed indirectly by analyzing heart rate and blood pressure response patterns. This study introduces a mathematical model that can predict sympathetic and parasympathetic dynamics. Our model-based analysis includes two control mechanisms: respiratory sinus arrhythmia (RSA) and the baroreceptor reflex (baroreflex). The RSA submodel integrates an electrocardiogram-derived respiratory signal with intrathoracic pressure, and the baroreflex submodel differentiates aortic and carotid baroreceptor regions. Patient-specific afferent and efferent signals are determined for 34 control subjects and 5 AD patients, estimating parameters fitting the model output to heart rate data. Results show that inclusion of RSA and distinguishing aortic/carotid regions are necessary to model the heart rate response to the VM. Comparing control subjects to patients shows that RSA and baroreflex responses are significantly diminished. This study compares estimated parameter values from the model-based predictions to indices used in clinical practice. Three indices are computed to determine adrenergic function from the slope of the systolic blood pressure in phase II [α (a new index)], the baroreceptor sensitivity (β), and the Valsalva ratio (γ). Results show that these indices can distinguish between normal and abnormal states, but model-based analysis is needed to differentiate pathological signals. In summary, the model simulates various VM responses and, by combining indices and model predictions, we study the pathologies for 5 AD patients.NEW & NOTEWORTHY We introduce a patient-specific model analyzing heart rate and blood pressure during a Valsalva maneuver (VM). The model predicts autonomic function incorporating the baroreflex and respiratory sinus arrhythmia (RSA) control mechanisms. We introduce a novel index (α) characterizing sympathetic activity, which can distinguish control and abnormal patients. However, we assert that modeling and parameter estimation are necessary to explain pathologies. Finally, we show that aortic baroreceptors contribute significantly to the VM and RSA affects early VM.

A Chest-Laminated Ultrathin and Stretchable E-Tattoo for the Measurement of Electrocardiogram, Seismocardiogram, and Cardiac Time Intervals

Seismocardiography (SCG) is a measure of chest vibration associated with heartbeats. While skin soft electronic tattoos (e-tattoos) have been widely reported for electrocardiogram (ECG) sensing, wearable SCG sensors are still based on either rigid accelerometers or non-stretchable piezoelectric membranes. This work reports an ultrathin and stretchable SCG sensing e-tattoo based on the filamentary serpentine mesh of 28-µm-thick piezoelectric polymer, polyvinylidene fluoride (PVDF). 3D digital image correlation (DIC) is used to map chest vibration to identify the best location to mount the e-tattoo and to investigate the effects of substrate stiffness. As piezoelectric sensors easily suffer from motion artifacts, motion artifacts are effectively reduced by performing subtraction between a pair of identical SCG tattoos placed adjacent to each other. Integrating the soft SCG sensor with a pair of soft gold electrodes on a single e-tattoo platform forms a soft electro-mechano-acoustic cardiovascular (EMAC) sensing tattoo, which can perform synchronous ECG and SCG measurements and extract various cardiac time intervals including systolic time interval (STI). Using the EMAC tattoo, strong correlations between STI and the systolic/diastolic blood pressures, are found, which may provide a simple way to estimate blood pressure continuously and noninvasively using one chest-mounted e-tattoo.

Construction of lumped-parameter cardiovascular models using the CellML language

Lumped-parameter models are widely used by cardiovascular researchers in the analysis of the circulatory dynamics. However, portability and model exchange have always been a problem, with different researchers implement the model differently. To improve the situation, in this study, a group of lumped-parameter cardiovascular system models with different levels of complexity have been implemented using the CellML mark-up language. The models have been curated and made publicly available in the CellML model repository, and the purpose of this paper is to provide further technical details to support the usage of these models by the research community. The developed models are validated and tested under the OpenCell environment as part of the curation process. Simulation results agree well with typical published data on cardiovascular system response.

Preliminary evaluation of a predictive controller for a rotary blood pump based on pulmonary oxygen gas exchange

Physiological control of rotary blood pumps is becoming increasingly necessary for clinical use. In this study, the mean oxygen partial pressure in the upper airway was first quantitatively evaluated as a control objective for a rotary blood pump. A model-free predictive controller was designed based on this control objective. Then, the quantitative evaluation of the controller was implemented with a rotary blood pump model on a complete cardiovascular model incorporated with airway mechanics and gas exchange models. The results show that the controller maintained a mean oxygen partial pressure at a normal and constant level of 138 mmHg in the left heart failure condition and restored basic haemodynamics of blood circulation. A left ventricular contractility recovery condition was also replicated to assess the response of the controller, and a stable result was obtained. This study indicates the potential use of the oxygen partial pressure index during pulmonary gas exchange when developing a multi-objective physiological controller for rotary blood pumps.

Open Source Pharmacokinetic/Pharmacodynamic Framework: Tutorial on the BioGears Engine

BioGears is an open-source, lumped parameter, full-body human physiology engine. Its purpose is to provide realistic and comprehensive simulations for medical training, research, and education. BioGears incorporates a physiologically based pharmacokinetic/pharmacodynamic (PK/PD) model that is designed to be applicable to a diversity of drug classes and patients and is extensible to future drugs. In addition, BioGears also supports drug interactions with various patient insults and interventions allowing for a realistic research framework and accurate dose-patient responses. This tutorial will demonstrate how the generic BioGears PK/PD model can be extended to a new substance for prediction of drug administration outcomes.

Effects on the pulmonary hemodynamics and gas exchange with a speed modulated right ventricular assist rotary blood pump: a numerical study

Rotary blood pumps (RBPs) are the newest generation of ventricular assist devices. Although their continuous flow characteristics have been accepted widely, more and more research has focused on the pulsatile modulation of RBPs in an attempt to provide better perfusion. In this study, we investigated the effects of an axial RBP serving as the right ventricular assist device on pulmonary hemodynamics and gas exchange using a numerical method with a complete cardiovascular model along with airway mechanics and a gas exchange model. The RBP runs in both constant speed and synchronized pulsatile modes using speed modulation. Hemodynamics and airway O₂ and CO₂ partial pressures were obtained under normal physiological conditions, and right ventricle failure conditions with or without RBP. Our results showed that the pulsatile mode of the RBP could support right ventricular assist to restore most hemodynamics. Using speed modulation, both pulmonary arterial pressure and flow pulsatility were increased, while there was only very little effect on alveolar O₂ and CO₂ partial pressures. This study could provide basic insight into the influence of pulmonary hemodynamics and gas exchange with speed modulated right ventricular assist RBPs, which is concerned when designing their pulsatile control methods.

Simulated Performance of the Cleveland Clinic Continuous-Flow Total Artificial Heart Using the Virtual Mock Loop

Our new Virtual Mock Loop (VML) is a mathematical model designed to simulate the human cardiovascular system and gauge performance of mechanical circulatory support devices. We aimed to mimic the hemodynamic performance of Cleveland Clinic's self-regulating continuous-flow total artificial heart (CFTAH) via VML and evaluate VML's accuracy versus bench data from our standard mock circulatory loop. The VML reproduced 23 hemodynamic conditions. Systemic/pulmonary vascular resistances and pump rotational speed were set for VML from bench test data. We compared outputs (pump flow, left/right pump pressure rise, normalized pump performance, and atrial pressure difference) of the two methods. Data from pump flow and left pump pressure rise were similar, but right pump pressure rise slightly differed. Left pump normalized pump performance curves were similar. Right pump VML results were within the same performance range indicated by bench tests. The plots of atrial pressure differences of VML versus bench-test data were similar, but slightly differed in the midrange of systemic/pulmonary gradients. Virtual Mock Loop successfully reproduced results from our mock circulatory loop of CFTAH test conditions. The CFTAH's self-regulation feature of right pump performance was also calculated effectively. We foresee using versions of the VML for training, simulating physiologic cardiac conditions, and patient monitoring.

An object-oriented computational model to study cardiopulmonary hemodynamic interactions in humans

BACKGROUND AND OBJECTIVE

This work introduces an object-oriented computational model to study cardiopulmonary interactions in humans.

METHODS

Modeling was performed in object-oriented programing language Matlab Simscape, where model components are connected with each other through physical connections. Constitutive and phenomenological equations of model elements are implemented based on their non-linear pressure-volume or pressure-flow relationship. The model includes more than 30 physiological compartments, which belong either to the cardiovascular or respiratory system. The model considers non-linear behaviors of veins, pulmonary capillaries, collapsible airways, alveoli, and the chest wall. Model parameters were derisved based on literature values. Model validation was performed by comparing simulation results with clinical and animal data reported in literature.

RESULTS

The model is able to provide quantitative values of alveolar, pleural, interstitial, aortic and ventricular pressures, as well as heart and lung volumes during spontaneous breathing and mechanical ventilation. Results of baseline simulation demonstrate the consistency of the assigned parameters. Simulation results during mechanical ventilation with PEEP trials can be directly compared with animal and clinical data given in literature.

CONCLUSIONS

Object-oriented programming languages can be used to model interconnected systems including model non-linearities. The model provides a useful tool to investigate cardiopulmonary activity during spontaneous breathing and mechanical ventilation.

Multiscale systems biology of trauma-induced coagulopathy

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

Mathematical modelling of cardiovascular response to the Valsalva manoeuvre

The Valsalva manoeuvre (VM) used for clinical autonomic testing results in a complex cardiovascular response with a concomitant action of several regulatory mechanisms whose nonlinear interactions are difficult to analyse without the aid of a mathematical model. The article presents a new non-pulsatile compartmental model of the human cardiovascular system with a variable intrathoracic pressure enabling the simulation of the haemodynamic response to the VM. The model is based on physiological data and includes three baroreflex mechanisms acting on heart rate, systemic resistance and venous unstressed volume. New nonlinear functions have been proposed to model cardiac output dependence on preload and afterload. Following the individual fitting of some parameters with a clear physiological meaning, the model is able to fit clinical data from patients with both typical and abnormal haemodynamic response to the VM. The sensitivity analysis showed that the model is most sensitive to the parameters describing the vascular pressure-volume relationships (the maximal volume of systemic veins and the relative level of vascular compliance). The use of nonlinear pressure-volume relationships for systemic veins proved crucial for the accurate modelling of the VM. On the contrary, the introduction of aroreflex time delays did not change significantly the haemodynamic response to the manoeuvre. The model can be a useful tool for aiding the interpretation of patient's response to the VM and provides a framework for analysing the interactions between the cardiovascular system and autonomic regulatory mechanisms.

Effects of septum and pericardium on heart-lung interactions in a cardiopulmonary simulation model

Mechanical heart-lung interactions are often overlooked in clinical settings. However, their impact on cardiac function can be quite significant. Mechanistic physiology-based models can provide invaluable insights into such cardiorespiratory interactions, which occur not only under external mechanical ventilatory support but in normal physiology as well. In this work, we focus on the cardiac component of a previously developed mathematical model of the human cardiopulmonary system, aiming to improve the model's response to the intrathoracic pressure variations that are associated with the respiratory cycle. Interventricular septum and pericardial membrane are integrated into the existing model. Their effect on the overall cardiac response is explained by means of comparison against simulation results from the original model as well as experimental data from literature.

Periodic ventilation: Consequences for the bodily CO2 stores and gas exchange efficiency

Using a mathematical model of CO2 transport, we investigated the underlying cause of why and to what extent periodic ventilation is less efficient for CO2 excretion/elimination compared to continuous/tidal ventilation leading to elevated CO2 stores unless mean alveolar minute ventilation () is elevated. The model predicts that the reduced efficiency of periodic ventilation is intrinsic to the sequential arrangement and differences in the relative storage capacities (product of size and CO2 capacitance coefficient) of the lungs, blood and tissues that leads to predominant blood and tissue storage during apnoeic periods. Consequently, overall CO2 transport becomes more prone to perfusion and diffusion limitation during periodic ventilation. At constant cardiac output (Q.) inefficiency will increase with the apnoeic duration (tap) concomitant with increasing blood and tissues CO2 storage and with the relative time spent apnoeic (tap/tcyc) due to increasing V.A/Q. mismatch. Conversely, temporal variation of Q. to better match V.A can reduce inefficiency radically. Thus such adjustment in blood flow is necessary for efficient CO2 elimination in periodic ventilation.

Autonomous control of cardiovascular reactivity in patients with episodic and chronic forms of migraine

BACKGROUND

The autonomous cardiovascular control can contribute to progression of migraine. However, current data on cardiovascular reactivity in migraine, especially severe forms, are essentially contradictory. The main aim of this study was to compare the autonomous regulation of circulation in patients with episodic and chronic migraine and healthy subjects.

METHODS

Seventy three migraine patients (mean age 35 ± 10) including episodic migraine (51 patients, 4-14 headache days/months) and chronic migraine (22 patients, ≥15 headache days/month) along with age-match control (71 healthy voluntaries) were examined. The autonomic regulation of circulation was examined with the tilt-table test, a deep breathing and Valsalva Maneuver, handgrip test, cold-stress vasoconstriction, arterial baroreflex and blood pressure variability.

RESULTS

The changes in heart rate induced by deep breathing, Valsalva Maneuver, and blood pressure in tilt-table test in patients with migraine did not differ from the control group. In contrast, the values of cold-stress-vasoconstriction forearm blood-flow reactivity (p <0.001), the increase in diastolic blood pressure in handgrip test (p <0.001), mean blood pressure in the late stage of the second phase of Valsalva Maneuver (p <0.001) and blood pressure variability (p <0.005) were all higher in patients with migraine than in the control group.

CONCLUSION

Thus, both episodic and chronic migraine are associated with significant disturbances in autonomous control resulting in enhanced vascular reactivity whereas the cardiac regulation remains largely unchanged.

An integrated mathematical model of the human cardiopulmonary system: model validation under hypercapnia and hypoxia

A novel integrated physiological model of the interactions between the cardiovascular and respiratory systems has been in development for the past few years. The model has hundreds of parameters and variables representing the physical and physiological properties of the human cardiopulmonary system. It can simulate many dynamic states and scenarios. The description of the model and the results in normal resting conditions were presented in a companion paper (Albanese A, Cheng L, Ursino M, Chbat NW. Am J Physiol Heart Circ Physiol 310: 2016; doi:10.1152/ajpheart.00230.2014), where model predictions were compared against average population data from literature. However, it is also essential to test the model in abnormal or pathological conditions to prove its consistency. Hence, in this paper, we concentrate on testing the cardiopulmonary model under hypercapnic and hypoxic conditions, by comparing model's outputs to population-averaged cardiorespiratory data reported in the literature. The utility of this comprehensive model is demonstrated by testing the internal consistency of the simulated responses of a significant number of cardiovascular variables (heart rate, arterial pressure, and cardiac output) and respiratory variables (tidal volume, respiratory rate, minute ventilation, alveolar O2 and CO2 partial pressures) over a wide range of perturbations and conditions; namely, hypercapnia at 3–7% CO2 levels and hypoxia at 7–9% O2 levels with controlled CO2 (isocapnic hypoxia) and without controlled CO2 (hypocapnic hypoxia). Finally, a sensitivity analysis is performed to analyze the role of the main cardiorespiratory control mechanisms triggered by hypercapnia and hypoxia.

An integrated mathematical model of the human cardiopulmonary system: model development

Several cardiovascular and pulmonary models have been proposed in the last few decades. However, very few have addressed the interactions between these two systems. Our group has developed an integrated cardiopulmonary model (CP Model) that mathematically describes the interactions between the cardiovascular and respiratory systems, along with their main short-term control mechanisms. The model has been compared with human and animal data taken from published literature. Due to the volume of the work, the paper is divided in two parts. The present paper is on model development and normophysiology, whereas the second is on the model's validation on hypoxic and hypercapnic conditions. The CP Model incorporates cardiovascular circulation, respiratory mechanics, tissue and alveolar gas exchange, as well as short-term neural control mechanisms acting on both the cardiovascular and the respiratory functions. The model is able to simulate physiological variables typically observed in adult humans under normal and pathological conditions and to explain the underlying mechanisms and dynamics.

Recursive identification of an arterial baroreflex model for the evaluation of cardiovascular autonomic modulation

The evaluation of the time-varying vagal and sympathetic contributions to heart rate remains a challenging task because the observability of the baroreflex is generally limited and the time-varying properties are difficult to take into account, especially in non-stationnary conditions. The objective is to propose a model-based approach to estimate the autonomic modulation during a pharmacological challenge. A recursive parameter identification method is proposed and applied to a mathematical model of the baroreflex, in order to estimate the time-varying vagal and sympathetic contributions to heart rate modulation during autonomic maneuvers. The model-based method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictor drugs, on normal conditions and under beta-blockers, so as to quantify the effect of the pharmacological sympathetic blockade on the estimated parameters. After parameter identification, results show a close match between experimental and simulated signals for the five lambs, as the mean relative root mean squared error is equal to 0.0026 (± 0.003). The error, between simulated and experimental signals, is significantly reduced compared to a batch identification of parameters. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and, as expected, it was possible to observe an alteration of the sympathetic response under beta-blockers. The simulated vagal modulation illustrates a response similar to traditional heart rate variability markers during the pharmacological maneuver. The model-based method, proposed in the paper, highlights the advantages of using a recursive identification method for the estimation of vagal and sympathetic modulation.

A model-based approach for the evaluation of vagal and sympathetic activities in a newborn lamb

This paper proposes a baroreflex model and a recursive identification method to estimate the time-varying vagal and sympathetic contributions to heart rate variability during autonomic maneuvers. The baroreflex model includes baroreceptors, cardiovascular control center, parasympathetic and sympathetic pathways. The gains of the global afferent sympathetic and vagal pathways are identified recursively. The method has been validated on data from newborn lambs, which have been acquired during the application of an autonomic maneuver, without medication and under beta-blockers. Results show a close match between experimental and simulated signals under both conditions. The vagal and sympathetic contributions have been simulated and, as expected, it is possible to observe different baroreflex responses under beta-blockers compared to baseline conditions.

Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: new insights from mathematical modeling

A minimal model for the neural control of heart rate (HR) has been developed with the aim of better understanding respiratory sinus arrhythmia (RSA)--a modulation of HR at the frequency of breathing. This model consists of two differential equations and is integrated into a previously-published model of gas exchange. The heart period is assumed to be affected primarily by the parasympathetic signal, with the sympathetic signal taken as a parameter in the model. We include the baroreflex, mechanical stretch-receptor feedback from the lungs, and central modulation of the cardiac vagal tone by the respiratory drive. Our model mimics a range of experimental observations and provides several new insights. Most notably, the model mimics the growth in the amplitude of RSA with decreasing respiratory frequency up to 7 breaths per minute (for humans). Our model then mimics the decrease in the amplitude of RSA at frequencies below 7 breaths per minute and predicts that this decrease is due to the baroreflex (we show this both numerically and analytically with a linear baroreflex). Another new prediction of the model is that the gating of the baroreflex leads to the dependency of RSA on mean vagal tone. The new model was also used to test two previously-suggested hypotheses regarding the physiological function of RSA and supports the hypothesis that RSA minimizes the work done by the heart while maintaining physiological levels of arterial CO2. These and other new insights the model provides extend our understanding of the integrative nature of vagal control of the heart.

Model-Based Comparison of the Normal and Fontan Circulatory Systems

Background:

Every year, approximately 1,000 Fontan operations are performed in the United States. Transplant-free, 30-year survival is only 50%. Although some performance characteristics may be universal among Fontan survivors, others may be patient specific and tunable; in either case, a quantitatively rigorous understanding of the Fontan circulatory arrangement would facilitate improvements in patient surveillance and management.

Methods:

To create a computational model of a normal two-year-old and a two-year-old patient with hypoplastic left heart syndrome (HLHS) following staged surgical palliations, we extensively modified the lumped parameter model developed by Clark, a multicompartment model of both pulmonary and systemic circulations.

Results:

With appropriately scaled parameter values, we achieved a maximum relative error (against target values for clinically realistic hemodynamic variables for the normal two-year-old) of 2.8% and an average relative error of 0.9%. Employing the model of a Fontan operation, we achieved a maximum relative error of 2.0% and the average relative error of 0.8%.

Conclusions:

Even with >200 model parameters, once we identified an acceptable set of values for the normal, only 12 required modification in order to attain clinically plausible hemodynamics in the HLHS after Fontan. When placed within the broad context of our extensive model, the impact on cardiac output of the resistance of the total cavopulmonary connection is found to be significantly affected by ventricular elastance and to be much lower in the two-year-old than in patients with markedly lower end-diastolic elastance (higher end-diastolic compliance).

Why is ABI effective in detecting vascular stenosis? Investigation based on multibranch hemodynamic model

The ankle-brachial index (ABI), defined as the ratio of systolic pressure in the ankle arteries and that in the brachial artery, was a useful noninvasive method to detect arterial stenoses. There had been a lot of researches about clinical regularities of ABI; however, mechanism studies were less addressed. For the purpose of a better understanding of the correlation between vascular stenoses and ABI, a computational model for simulating blood pressure and flow propagation in various arterial stenosis circumstances was developed with a detailed compartmental description of the heart and main arteries. Particular attention was paid to the analysis of effects of vascular stenoses in different large-sized arteries on ABI in theory. Moreover, the variation of ABI during the increase of the stenosis severity was also studied. Results showed that stenoses in lower limb arteries, as well as, brachial artery, caused different variations of blood pressure in ankle and brachial arteries, resulting in a significant change of ABI. Furthermore, the variation of ABI became faster when the severity of the stenosis increased, validating that ABI was more sensitive to severe stenoses than to mild/moderate ones. All these in findings revealed the reason why ABI was an effective index for detecting stenoses, especially in lower limb arteries.