A bond graph model of the cardiovascular system

Model-based assessment of cardiopulmonary autonomic regulation in paced deep breathing

Autonomic dysfunction can lead to many physical and psychological diseases. The assessment of autonomic regulation plays an important role in the prevention, diagnosis, and treatment of these diseases. A physiopathological mathematical model for cardiopulmonary autonomic regulation, namely Respiratory-Autonomic-Sinus (RSA) regulation Model, is proposed in this study. A series of differential equations are used to simulate the whole process of RSA phenomenon. Based on this model, with respiration signal and ECG signal simultaneously acquired in paced deep breathing scenario, we manage to obtain the cardiopulmonary autonomic regulation parameters (CARP), including the sensitivity of respiratory-sympathetic nerves and respiratory-parasympathetic nerves, the time delay of sympathetic, the sensitivity of norepinephrine and acetylcholine receptor, as well as cardiac remodeling factor by optimization algorithm. An experimental study has been conducted in healthy subjects, along with subjects with hypertension and coronary heart disease. CARP obtained in the experiment have shown their clinical significance.

A computational model of contributors to pulmonary hypertensive disease: impacts of whole lung and focal disease distributions

Pulmonary hypertension has multiple etiologies and so can be difficult to diagnose, prognose, and treat. Diagnosis is typically made via invasive hemodynamic measurements in the main pulmonary artery and is based on observed elevation of mean pulmonary artery pressure. This static mean pressure enables diagnosis, but does not easily allow assessment of the severity of pulmonary hypertension, nor the etiology of the disease, which may impact treatment. Assessment of the dynamic properties of pressure and flow data obtained from catheterization potentially allows more meaningful assessment of the strain on the right heart and may help to distinguish between disease phenotypes. However, mechanistic understanding of how the distribution of disease in the lung leading to pulmonary hypertension impacts the dynamics of blood flow in the main pulmonary artery and/or the pulmonary capillaries is lacking. We present a computational model of the pulmonary vasculature, parameterized to characteristic features of pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension to help understand how the two conditions differ in terms of pulmonary vascular response to disease. Our model incorporates key features known to contribute to pulmonary vascular function in health and disease, including anatomical structure and multiple contributions from gravity. The model suggests that dynamic measurements obtained from catheterization potentially distinguish between distal and proximal vasculopathy typical of pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension. However, the model suggests a non-linear relationship between these data and vascular structural changes typical of pulmonary arterial hypertension and chronic thromboembolic pulmonary hypertension which may impede analysis of these metrics to distinguish between cohorts.

Meeting the multiscale challenge: representing physiology processes over ApiNATOMY circuits using bond graphs

We introduce, and provide examples of, the application of the bond graph formalism to explicitly represent biophysical processes between and within modular biological compartments in ApiNATOMY. In particular, we focus on modelling scenarios from acid-base physiology to link distinct process modalities as bond graphs over an ApiNATOMY circuit of multiscale compartments. The embedding of bond graphs onto ApiNATOMY compartments provides a semantically and mathematically explicit basis for the coherent representation, integration and visualisation of multiscale physiology processes together with the compartmental topology of those biological structures that convey these processes.

Cardiorespiratory Model-Based Data-Driven Approach for Sleep Apnea Detection

Obstructive sleep apnea (OSA) is a chronic sleep disorder affecting millions of people worldwide. Individuals with OSA are rarely aware of the condition and are often left untreated, which can lead to some serious health problems. Nowadays, several low-cost wearable health sensors are available that can be used to conveniently and noninvasively collect a wide range of physiological signals. In this paper, we propose a new framework for OSA detection in which we combine the wearable sensor measurement signals with the mathematical models of the cardiorespiratory system. Vector-valued Gaussian processes (GPs) are adopted to model the physiological variations among different individuals. The GP covariance is constructed using the sum of separable kernel functions, and the GP hyperparameters are estimated by maximizing the marginal likelihood function. A likelihood ratio test is proposed to detect OSA using the widely available heart rate and peripheral oxygen saturation (SpO ) measurement signals. We conduct experiments on both synthetic and real data to show the effectiveness of the proposed OSA detection framework compared to purely data-driven approaches.

Recursive Model Identification for the Evaluation of Baroreflex Sensitivity

A method for the recursive identification of physiological models of the cardiovascular baroreflex is proposed and applied to the time-varying analysis of vagal and sympathetic activities. The proposed method was evaluated with data from five newborn lambs, which were acquired during injection of vasodilator and vasoconstrictors and the results show a close match between experimental and simulated signals. The model-based estimation of vagal and sympathetic contributions were consistent with physiological knowledge and the obtained estimators of vagal and sympathetic activities were compared to traditional markers associated with baroreflex sensitivity. High correlations were observed between traditional markers and model-based indices.

Requirements for the formal representation of pathophysiology mechanisms by clinicians

Knowledge of multiscale mechanisms in pathophysiology is the bedrock of clinical practice. If quantitative methods, predicting patient-specific behaviour of these pathophysiology mechanisms, are to be brought to bear on clinical decision-making, the Human Physiome community and Clinical community must share a common computational blueprint for pathophysiology mechanisms. A number of obstacles stand in the way of this sharing-not least the technical and operational challenges that must be overcome to ensure that (i) the explicit biological meanings of the Physiome's quantitative methods to represent mechanisms are open to articulation, verification and study by clinicians, and that (ii) clinicians are given the tools and training to explicitly express disease manifestations in direct contribution to modelling. To this end, the Physiome and Clinical communities must co-develop a common computational toolkit, based on this blueprint, to bridge the representation of knowledge of pathophysiology mechanisms (a) that is implicitly depicted in electronic health records and the literature, with (b) that found in mathematical models explicitly describing mechanisms. In particular, this paper makes use of a step-wise description of a specific disease mechanism as a means to elicit the requirements of representing pathophysiological meaning explicitly. The computational blueprint developed from these requirements addresses the Clinical community goals to (i) organize and manage healthcare resources in terms of relevant disease-related knowledge of mechanisms and (ii) train the next generation of physicians in the application of quantitative methods relevant to their research and practice.

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.

Blood clot simulation model by using the Bond-Graph technique

The World Health Organization estimates that 17 million people die of cardiovascular disease, particularly heart attacks and strokes, every year. Most strokes are caused by a blood clot that occludes an artery in the cerebral circulation and the process concerning the removal of this obstruction involves catheterisation. The fundamental object of the presented study consists in determining and optimizing the necessary simulation model corresponding with the blood clot zone to be implemented jointly with other Mechanical Thrombectomy Device simulation models, which have become more widely used during the last decade. To do so, a multidomain technique is used to better explain the different aspects of the attachment to the artery wall and between the existing platelets, it being possible to obtain the mathematical equations that define the full model. For a better understanding, a consecutive approximation to the definitive model will be presented, analyzing the different problems found during the study. The final presented model considers an elastic characterization of the blood clot composition and the possibility of obtaining a consecutive detachment process from the artery wall. In conclusion, the presented model contains the necessary behaviour laws to be implemented in future blood clot simulation models.

Graphical simulation environments for modelling and simulation of integrative physiology

Guyton's original integrative physiology model was a milestone in integrative physiology, combining significant physiological knowledge with an engineering perspective to develop a computational diagrammatic model. It is still used in research and teaching, with a small number of variants on the model also in circulation. However, though new research has added significantly to the knowledge represented by Guyton's model, and significant advances have been made in computing and simulation software, an accepted common platform to integrate this new knowledge has not emerged. This paper discusses the issues in the selection of a suitable platform, together with a number of current possibilities, and suggests a graphical computing environment for modelling and simulation. By way of example, a validated version of Guyton's 1992 model, implemented in the ubiquitous Simulink environment, is presented which provides a hierarchical representation amenable to extension and suitable for teaching and research uses. It is designed to appeal to the biomedical engineer and physiologist alike.

A multiformalism and multiresolution modelling environment: application to the cardiovascular system and its regulation

The role of modelling and simulation in the systemic analysis of living systems is now clearly established. Emerging disciplines, such as systems biology, and worldwide research actions, such as the Physiome Project or the Virtual Physiological Human, are based on an intensive use of modelling and simulation methodologies and tools. One of the key aspects in this context is to perform an efficient integration of various models representing different biological or physiological functions, at different resolutions, spanning through different scales. This paper presents a multiformalism modelling and simulation environment (M2SL) that has been conceived to ease model integration. A given model is represented as a set of coupled and atomic model components that may be based on different mathematical formalisms with heterogeneous structural and dynamical properties. A co-simulation approach is used to solve these hybrid systems. The pioneering model of the overall regulation of the cardiovascular system proposed by Guyton and co-workers in 1972 has been implemented under M2SL and a pulsatile ventricular model based on a time-varying elastance has been integrated in a multi-resolution approach. Simulations reproducing physiological conditions and using different coupling methods show the benefits of the proposed environment.

A tissue-level electromechanical model of the left ventricle: application to the analysis of intraventricular pressure

The ventricular pressure profile is characteristic of the cardiac contraction progress and is useful to evaluate the cardiac performance. In this contribution, a tissue-level electromechanical model of the left ventricle is proposed, to assist the interpretation of left ventricular pressure waveforms. The left ventricle has been modeled as an ellipsoid composed of twelve mechano-hydraulic sub-systems. The asynchronous contraction of these twelve myocardial segments has been represented in order to reproduce a realistic pressure profiles. To take into account the different energy domains involved, the tissue-level scale and to facilitate the building of a modular model, multiple formalisms have been used: Bond Graph formalism for the mechano-hydraulic aspects and cellular automata for the electrical activation. An experimental protocol has been defined to acquire ventricular pressure signals from three pigs, with different afterload conditions. Evolutionary Algorithms have been used to identify the model parameters in order to minimize the error between experimental and simulated ventricular pressure signals. Simulation results show that the model is able to reproduce experimental ventricular pressure. In addition, electro-mechanical activation times have been determined in the identification process. For example, the maximum electrical activation time is reached, respectively, 96.5, 139.3 and 131.5 ms for the first, second, and third pigs. These preliminary results are encouraging for the application of the model on non-invasive data like ECG, arterial pressure or myocardial strain.

SAPHIR: a physiome core model of body fluid homeostasis and blood pressure regulation

We present the current state of the development of the SAPHIR project (a Systems Approach for PHysiological Integration of Renal, cardiac and respiratory function). The aim is to provide an open-source multi-resolution modelling environment that will permit, at a practical level, a plug-and-play construction of integrated systems models using lumped-parameter components at the organ/tissue level while also allowing focus on cellular- or molecular-level detailed sub-models embedded in the larger core model. Thus, an in silico exploration of gene-to-organ-to-organism scenarios will be possible, while keeping computation time manageable. As a first prototype implementation in this environment, we describe a core model of human physiology targeting the short- and long-term regulation of blood pressure, body fluids and homeostasis of the major solutes. In tandem with the development of the core models, the project involves database implementation and ontology development.

The role of the autonomic nervous system in hypertension: a bond graph model study

A bond graph model of the cardiovascular system with embedded autonomic nervous regulation was developed for a better understanding of the role of the autonomic nervous system (ANS) in hypertension. The model is described by a pump model of the heart and a detailed representation of the head and neck, pulmonary, coronary, abdomen and extremity circulation. It responds to sympathetic and parasympathetic activities by modifying systemic peripheral vascular resistance, heart rate, ventricular end-systolic elastance and venous unstressed volumes. The impairment of ANS is represented by an elevation of the baroreflex set point. The simulation results show that, compared with normotensive, in hypertension the systolic and diastolic blood pressure (SBP/DBP) rose from 112/77 mmHg to 144/94 mmHg and the left ventricular wall thickness (LVWT) increased from 10 mm to 12.74 mm. In the case that ANS regulation was absent, both the SBP and DBP further increased by 8 mmHg and the LVWT increased to 13.22 mm. The results also demonstrate that when ANS regulation is not severely damaged, e.g. the baroreflex set point is 97 mmHg, it still has an effect in preventing the rapid rise of blood pressure in hypertension; however, with the worsening of ANS regulation, its protective role weakens. The results agree with human physiological and pathological features in hemodynamic parameters and carotid baroreflex function curves, and indicate the role of ANS in blood pressure regulation and heart protection. In conclusion, the present model may provide a valid approach to study the pathophysiological conditions of the cardiovascular system and the mechanism of ANS regulation.

SAPHIR - a multi-scale, multi-resolution modeling environment targeting blood pressure regulation and fluid homeostasis

We present progress on a comprehensive, modular, interactive modeling environment centered on overall regulation of blood pressure and body fluid homeostasis. We call the project SAPHIR, for "a Systems Approach for PHysiological Integration of Renal, cardiac, and respiratory functions". The project uses state-of-the-art multi-scale simulation methods. The basic core model will give succinct input-output (reduced-dimension) descriptions of all relevant organ systems and regulatory processes, and it will be modular, multi-resolution, and extensible, in the sense that detailed submodules of any process(es) can be "plugged-in" to the basic model in order to explore, eg. system-level implications of local perturbations. The goal is to keep the basic core model compact enough to insure fast execution time (in view of eventual use in the clinic) and yet to allow elaborate detailed modules of target tissues or organs in order to focus on the problem area while maintaining the system-level regulatory compensations.

Hardware acceleration for real time simulation of physiological systems

Testing of medical equipment such as pacemaker is a critical task, because any malfunction may cause patient death or serious and long-lasting health consequences. Thus, device behavior under normal functioning conditions as well as under faulty conditions should be tested as thoroughly as possible under the project's budget. This paper presents a real-time digital simulator (DRTS) for possible use in testing of medical devices. The simulator runs a model of a physiological system (an organ or a group of organs) in real time and uses A/D and D/A cards to interface the simulation results to real medical equipment. With this simulator, the tests can be made as thorough as needed without much increase in cost.