A closed-loop model of the canine cardiovascular system that includes ventricular interaction

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.

Optimization framework for patient-specific modeling under uncertainty

Estimating a patient-specific computational model's parameters relies on data that is often unreliable and ill-suited for a deterministic approach. We develop an optimization-based uncertainty quantification framework for probabilistic model tuning that discovers model inputs distributions that generate target output distributions. Probabilistic sampling is performed using a surrogate model for computational efficiency, and a general distribution parameterization is used to describe each input. The approach is tested on seven patient-specific modeling examples using CircAdapt, a cardiovascular circulatory model. Six examples are synthetic, aiming to match the output distributions generated using known reference input data distributions, while the seventh example uses real-world patient data for the output distributions. Our results demonstrate the accurate reproduction of the target output distributions, with a correct recreation of the reference inputs for the six synthetic examples. Our proposed approach is suitable for determining the parameter distributions of patient-specific models with uncertain data and can be used to gain insights into the sensitivity of the model parameters to the measured data.

CARDIOSIM©: The First Italian Software Platform for Simulation of the Cardiovascular System and Mechanical Circulatory and Ventilatory Support

This review is devoted to presenting the history of the CARDIOSIM^© software simulator platform, which was developed in Italy to simulate the human cardiovascular and respiratory systems. The first version of CARDIOSIM^© was developed at the Institute of Biomedical Technologies of the National Research Council in Rome. The first platform version published in 1991 ran on a PC with a disk operating system (MS-DOS) and was developed using the Turbo Basic language. The latest version runs on PC with Microsoft Windows 10 operating system; it is implemented in Visual Basic and C++ languages. The platform has a modular structure consisting of seven different general sections, which can be assembled to reproduce the most important pathophysiological conditions. One or more zero-dimensional (0-D) modules have been implemented in the platform for each section. The different modules can be assembled to reproduce part or the whole circulation according to Starling’s law of the heart. Different mechanical ventilatory and circulatory devices have been implemented in the platform, including thoracic artificial lungs, ECMO, IABPs, pulsatile and continuous right and left ventricular assist devices, biventricular pacemakers and biventricular assist devices. CARDIOSIM^© is used in clinical and educational environments.

Algebraic formulas characterizing an alternative to Guyton's graphical analysis relevant for heart failure

Although Guyton's graphical analysis of cardiac output-venous return has become a ubiquitous tool for explaining how circulatory equilibrium emerges from heart-vascular interactions, this classical model relies on a formula for venous return that contains unphysiological assumptions. Furthermore, Guyton's graphical analysis does not predict pulmonary venous pressure, which is a critical variable for evaluating heart failure patients' risk of pulmonary edema. Therefore, the purpose of the present work was to use a minimal closed-loop mathematical model to develop an alternative to Guyton's analysis. Limitations inherent in Guyton's model were addressed by 1) partitioning the cardiovascular system differently to isolate left ventricular function and lump all blood volumes together, 2) linearizing end-diastolic pressure-volume relationships to obtain algebraic solutions, and 3) treating arterial pressures as constants. This approach yielded three advances. First, variables related to morbidities associated with left ventricular failure were predicted. Second, an algebraic formula predicting left ventricular function was derived in terms of ventricular properties. Third, an algebraic formula predicting flow through the portion of the system isolated from the left ventricle was derived in terms of mechanical properties without neglecting redistribution of blood between systemic and pulmonary circulations. Although complexities were neglected, approximations necessary to obtain algebraic formulas resulted in minimal error, and predicted variables were consistent with reported values.

Particle swarm optimizer for arterial blood flow models

BACKGROUND AND OBJECTIVE

Mathematical modeling and computational simulations of arterial blood flow network can offer an insilico platform for both diagnostics and therapeutic phases of patients that suffer from cardiac diseases. These models are normally complex and involve many unknown parameters. For physiological relevance, these parameters should be optimized using in-vivo human/animal data sets. The main goal of this work is to develop an efficient, yet an accurate optimization algorithm to compute parameters in the arterial blood flow models.

METHODS

The particle swarm optimization (PSO) method is proposed herein for the first time, as an accurate algorithm that applies to computing parameters in the Windkessel type model of blood flow in the arterial system. We begin by defining a 6-element Windkessel (WK6) arterial flow model, which is then implemented and validated using multiple flow rate and aortic pressure measurements obtained from different subjects including dogs, pigs and humans. The parameters in the model are obtained using the PSO technique which minimizes the pressure root mean square (P-RMS) error between the computed and the measured aortic pressure waveform.

RESULTS

Model parameters obtained using the proposed PSO method were able to recover the pressure waveform in the aorta during the cardiac cycle for both healthy and diseased species (animals/humans). The PSO method provides an accurate approach to solve this challenging multi-dimensional parameter identification problem. The results obtained by PSO algorithm was compared with the classical gradient-based, namely the non-linear square fit (NLSF) algorithm.

CONCLUSIONS

The results indicate that the PSO method offers alternative and accurate method to find optimal physiological parameters involved in the Windkessel model for the study of arterial blood flow network. The PSO method has performed better than the NLSF approach as depicted from the P-RMS calculations. Finally, we believe that the PSO method offers a great potential and could be used for many other biomedicine optimization problems.

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.

Cardiovascular Function and Ballistocardiogram: A Relationship Interpreted via Mathematical Modeling

OBJECTIVE

To develop quantitative methods for the clinical interpretation of the ballistocardiogram (BCG).

METHODS

A closed-loop mathematical model of the cardiovascular system is proposed to theoretically simulate the mechanisms generating the BCG signal, which is then compared with the signal acquired via accelerometry on a suspended bed.

RESULTS

Simulated arterial pressure waveforms and ventricular functions are in good qualitative and quantitative agreement with those reported in the clinical literature. Simulated BCG signals exhibit the typical I, J, K, L, M, and N peaks and show good qualitative and quantitative agreement with experimental measurements. Simulated BCG signals associated with reduced contractility and increased stiffness of the left ventricle exhibit different changes that are characteristic of the specific pathological condition.

CONCLUSION

The proposed closed-loop model captures the predominant features of BCG signals and can predict pathological changes on the basis of fundamental mechanisms in cardiovascular physiology.

SIGNIFICANCE

This paper provides a quantitative framework for the clinical interpretation of BCG signals and the optimization of BCG sensing devices. The present paper considers an average human body and can potentially be extended to include variability among individuals.

A hybrid Windkessel-Womersley model for blood flow in arteries

A hybrid Windkessel-Womersley (WK-W) coupled mathematical model for the study of pulsatile blood flow in the arterial system is proposed in this article. The model consists of the Windkessel-type proximal and distal compartments connected by a tube to represent the aorta. The blood flow in the aorta is described by the Womersley solution of the simplified Navier-Stokes equations. In addition, we defined a 6-elements Windkessel model (WK6) in which the blood flow in the connecting tube is modeled by the one-dimensional unsteady Bernoulli equation. Both models have been applied and validated using several aortic pressure and flow rate data acquired from different species such as, humans, dogs and pigs. The results have shown that, both models were able to accurately reconstruct arterial input impedance, however, only the WK-W model was able to calculate the radial distribution of the axial velocity in the aorta and consequently the model predicts the time-varying wall shear stress, and frictional pressure drop during the cardiac cycle more accurately. Additionally, the hybrid WK-W model has the capability to predict the pulsed wave velocity, which is also not possible to obtain when using the classical Windkessel models. Moreover, the values of WK-W model parameters have found to fall in the physiologically realistic range of values, therefore it seems that this hybrid model shows a great potential to be used in clinical practice, as well as in the basic cardiovascular mechanics research.

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.

Simulation as a preoperative planning approach in advanced heart failure patients. A retrospective clinical analysis

BACKGROUND

Modelling and simulation may become clinically applicable tools for detailed evaluation of the cardiovascular system and clinical decision-making to guide therapeutic intervention. Models based on pressure-volume relationship and zero-dimensional representation of the cardiovascular system may be a suitable choice given their simplicity and versatility. This approach has great potential for application in heart failure where the impact of left ventricular assist devices has played a significant role as a bridge to transplant and more recently as a long-term solution for non eligible candidates.

RESULTS

We sought to investigate the value of simulation in the context of three heart failure patients with a view to predict or guide further management. CARDIOSIM^© was the software used for this purpose. The study was based on retrospective analysis of haemodynamic data previously discussed at a multidisciplinary meeting. The outcome of the simulations addressed the value of a more quantitative approach in the clinical decision process.

CONCLUSIONS

Although previous experience, co-morbidities and the risk of potentially fatal complications play a role in clinical decision-making, patient-specific modelling may become a daily approach for selection and optimisation of device-based treatment for heart failure patients. Willingness to adopt this integrated approach may be the key to further progress.

Bridging the gap between measurements and modelling: a cardiovascular functional avatar

Lumped parameter models of the cardiovascular system have the potential to assist researchers and clinicians to better understand cardiovascular function. The value of such models increases when they are subject specific. However, most approaches to personalize lumped parameter models have thus far required invasive measurements or fall short of being subject specific due to a lack of the necessary clinical data. Here, we propose an approach to personalize parameters in a model of the heart and the systemic circulation using exclusively non-invasive measurements. The personalized model is created using flow data from four-dimensional magnetic resonance imaging and cuff pressure measurements in the brachial artery. We term this personalized model the cardiovascular avatar. In our proof-of-concept study, we evaluated the capability of the avatar to reproduce pressures and flows in a group of eight healthy subjects. Both quantitatively and qualitatively, the model-based results agreed well with the pressure and flow measurements obtained in vivo for each subject. This non-invasive and personalized approach can synthesize medical data into clinically relevant indicators of cardiovascular function, and estimate hemodynamic variables that cannot be assessed directly from clinical measurements.

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.

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).

Simulation of left atrial function using a multi-scale model of the cardiovascular system

During a full cardiac cycle, the left atrium successively behaves as a reservoir, a conduit and a pump. This complex behavior makes it unrealistic to apply the time-varying elastance theory to characterize the left atrium, first, because this theory has known limitations, and second, because it is still uncertain whether the load independence hypothesis holds. In this study, we aim to bypass this uncertainty by relying on another kind of mathematical model of the cardiac chambers. In the present work, we describe both the left atrium and the left ventricle with a multi-scale model. The multi-scale property of this model comes from the fact that pressure inside a cardiac chamber is derived from a model of the sarcomere behavior. Macroscopic model parameters are identified from reference dog hemodynamic data. The multi-scale model of the cardiovascular system including the left atrium is then simulated to show that the physiological roles of the left atrium are correctly reproduced. This include a biphasic pressure wave and an eight-shaped pressure-volume loop. We also test the validity of our model in non basal conditions by reproducing a preload reduction experiment by inferior vena cava occlusion with the model. We compute the variation of eight indices before and after this experiment and obtain the same variation as experimentally observed for seven out of the eight indices. In summary, the multi-scale mathematical model presented in this work is able to correctly account for the three roles of the left atrium and also exhibits a realistic left atrial pressure-volume loop. Furthermore, the model has been previously presented and validated for the left ventricle. This makes it a proper alternative to the time-varying elastance theory if the focus is set on precisely representing the left atrial and left ventricular behaviors.

Lumped parameter model of cardiovascular-respiratory interaction

The aim of this work was to develop a lumped parameter model of the cardiovascular system and to couple it with a model of respiratory mechanics. In comparison to existing models, modifications and additions have been implemented to include a model of the upper limb vasculature employing the electrical analogy of hemodynamic variables. The model prediction of respiratory effects on arterial pressure was compared with in vivo invasive measurement of blood pressure in patients. The model indicates that the inherent coupling between the cardiovascular and respiratory systems can be described by mathematical relationships of physiological parameters with robust predictions. With specification of parameters based on individual measurements of cardio-respiratory variables, the model can be used in the clinical setting of intensive care units to predict hemodynamic changes and to optimize ventilation and volume loading strategies.

Understanding the metabolic syndrome: a modeling perspective

The prevalence of obesity is growing at an alarming rate, placing many at risk for developing diabetes, hypertension, sleep apnea, or a combination of disorders known as "metabolic syndrome". The evidence to date suggests that metabolic syndrome results from an imbalance in the mechanisms that link diet, physical activity, glucose-insulin control, and autonomic cardiovascular control. There is also growing recognition that sleep-disordered breathing and other forms of sleep disruption can contribute significantly to autonomic dysfunction and insulin resistance. Chronic sleep deprivation resulting from sleep-disordered breathing or behavioral causes can lead to excessive daytime sleepiness and lethargy, which in turn contribute to increasing obesity. Analysis of this complex dynamic system using a model-based approach can facilitate the delineation of the causal pathways that lead to the emergence of the metabolic syndrome. In this paper, we provide an overview of the main physiological mechanisms associated with obesity and sleep-disordered breathing that are believed to result in metabolic and autonomic dysfunction, and review the models and modeling approaches that are relevant in characterizing the interplay among the multiple factors that underlie the development of the metabolic syndrome.

Virtual ICU and E-learning tools: Scope in critical care medicine in India

Critical care medicine is an important tool for decreasing morbidity and mortality of patients. There is a need to develop effective web content for use of intensivists and related disciplinaries. Use of simulators and production of good quality videos and their uploading on national connectivity can add fillip to the “National Mission of Education” started by the Government of India.

Cardiovascular modeling in pulmonary arterial hypertension: focus on mechanisms and treatment of right heart failure using the CircAdapt model

In recent years, increased understanding of cardiovascular system dynamics has led to the development of mathematical models of the heart and circulation. Models that enable realistic simulation of ventricular mechanics and interactions under a range of conditions have the potential to provide an ideal method with which to investigate the effects of pulmonary arterial hypertension and its treatment on cardiac mechanics and hemodynamics. Such mathematical models have the potential to contribute to a personalized, patient-specific treatment approach and allow more objective diagnostic decision-making, patient monitoring, and assessment of treatment outcome. This review discusses the development of mathematical models of the heart and circulation, with particular reference to the closed-loop CircAdapt model, and how the model performs under both normal and pathophysiological (pulmonary hypertensive) conditions.

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

Background

Valve dysfunction is a common cardiovascular pathology. Despite significant clinical research, there is little formal study of how valve dysfunction affects overall circulatory dynamics. Validated models would offer the ability to better understand these dynamics and thus optimize diagnosis, as well as surgical and other interventions.

Methods

A cardiovascular and circulatory system (CVS) model has already been validated in silico, and in several animal model studies. It accounts for valve dynamics using Heaviside functions to simulate a physiologically accurate "open on pressure, close on flow" law. However, it does not consider real-time valve opening dynamics and therefore does not fully capture valve dysfunction, particularly where the dysfunction involves partial closure. This research describes an updated version of this previous closed-loop CVS model that includes the progressive opening of the mitral valve, and is defined over the full cardiac cycle.

Results

Simulations of the cardiovascular system with healthy mitral valve are performed, and, the global hemodynamic behaviour is studied compared with previously validated results. The error between resulting pressure-volume (PV) loops of already validated CVS model and the new CVS model that includes the progressive opening of the mitral valve is assessed and remains within typical measurement error and variability. Simulations of ischemic mitral insufficiency are also performed. Pressure-Volume loops, transmitral flow evolution and mitral valve aperture area evolution follow reported measurements in shape, amplitude and trends.

Conclusions

The resulting cardiovascular system model including mitral valve dynamics provides a foundation for clinical validation and the study of valvular dysfunction in vivo. The overall models and results could readily be generalised to other cardiac valves.

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

Subject-specific cardiovascular system model-based identification and diagnosis of septic shock with a minimally invasive data set: animal experiments and proof of concept

A cardiovascular system (CVS) model and parameter identification method have previously been validated for identifying different cardiac and circulatory dysfunctions in simulation and using porcine models of pulmonary embolism, hypovolemia with PEEP titrations and induced endotoxic shock. However, these studies required both left and right heart catheters to collect the data required for subject-specific monitoring and diagnosis-a maximally invasive data set in a critical care setting although it does occur in practice. Hence, use of this model-based diagnostic would require significant additional invasive sensors for some subjects, which is unacceptable in some, if not all, cases. The main goal of this study is to prove the concept of using only measurements from one side of the heart (right) in a 'minimal' data set to identify an effective patient-specific model that can capture key clinical trends in endotoxic shock. This research extends existing methods to a reduced and minimal data set requiring only a single catheter and reducing the risk of infection and other complications-a very common, typical situation in critical care patients, particularly after cardiac surgery. The extended methods and assumptions that found it are developed and presented in a case study for the patient-specific parameter identification of pig-specific parameters in an animal model of induced endotoxic shock. This case study is used to define the impact of this minimal data set on the quality and accuracy of the model application for monitoring, detecting and diagnosing septic shock. Six anesthetized healthy pigs weighing 20-30 kg received a 0.5 mg kg(-1) endotoxin infusion over a period of 30 min from T0 to T30. For this research, only right heart measurements were obtained. Errors for the identified model are within 8% when the model is identified from data, re-simulated and then compared to the experimentally measured data, including measurements not used in the identification process for validation. Importantly, all identified parameter trends match physiologically and clinically and experimentally expected changes, indicating that no diagnostic power is lost. This work represents a further with human subjects validation for this model-based approach to cardiovascular diagnosis and therapy guidance in monitoring endotoxic disease states. The results and methods obtained can be readily extended from this case study to the other animal model results presented previously. Overall, these results provide further support for prospective, proof of concept clinical testing with humans.

A computational model of cardiovascular physiology and heart sound generation

A computational model of the cardiovascular system is described which provides a framework for implementing and testing quantitative physiological models of heart sound generation. The lumped-parameter cardiovascular model can be solved for the hemodynamic variables on which the heart sound generation process is built. Parameters of the cardiovascular model can be adjusted to represent various normal and pathological conditions, and the acoustic consequences of those adjustments can be explored. The combined model of the physiology of cardiovascular circulation and heart sound generation has promise for application in teaching, training and algorithm development in computer-aided auscultation of the heart.

Three-wall segment (TriSeg) model describing mechanics and hemodynamics of ventricular interaction

A mathematical model (TriSeg model) of ventricular mechanics incorporating mechanical interaction of the left and right ventricular free walls and the interventricular septum is presented. Global left and right ventricular pump mechanics were related to representative myofiber mechanics in the three ventricular walls, satisfying the principle of conservation of energy. The walls were mechanically coupled satisfying tensile force equilibrium in the junction. Wall sizes and masses were rendered by adaptation to normalize mechanical myofiber load to physiological standard levels. The TriSeg model was implemented in the previously published lumped closed-loop CircAdapt model of heart and circulation. Simulation results of cardiac mechanics and hemodynamics during normal ventricular loading, acute pulmonary hypertension, and chronic pulmonary hypertension (including load adaptation) agreed with clinical data as obtained in healthy volunteers and pulmonary hypertension patients. In chronic pulmonary hypertension, the model predicted right ventricular free wall hypertrophy, increased systolic pulmonary flow acceleration, and increased right ventricular isovolumic contraction and relaxation times. Furthermore, septal curvature decreased linearly with its transmural pressure difference. In conclusion, the TriSeg model enables realistic simulation of ventricular mechanics including interaction between left and right ventricular pump mechanics, dynamics of septal geometry, and myofiber mechanics in the three ventricular walls.

Model-based identification and diagnosis of a porcine model of induced endotoxic shock with hemofiltration

A previously validated cardiovascular system (CVS) model and parameter identification method for cardiac and circulatory disease states are extended and further validated in a porcine model (N=6) of induced endotoxic shock with hemofiltration. Errors for the identified model are within 10% when the model is re-simulated and compared to the clinical data. All identified parameter trends over time in the experiments match clinically expected changes both individually and over the cohort. This work represents a further clinical validation of these model-based cardiovascular diagnosis and therapy guidance methods for use with monitoring endotoxic disease states.

Study of ventricular interaction during pulmonary embolism using clinical identification in a minimum cardiovascular system model

Cardiovascular disturbances are difficult to diagnose and treat because of the large range of possible underlying dysfunctions combined with regulatory reflex mechanisms that can result in conflicting clinical data. Thus, medical professionals often rely on experience and intuition to optimize hemodynamics in the critically ill. This paper combines an existing minimal cardiovascular system model with an extended integral based parameter identification method to track the evolution of induced pulmonary embolism in porcine data. The model accounts for ventricular interaction dynamics and is shown to predict an increase in the right ventricle expansion index and a decrease in septum volume consistent with known physiological response to pulmonary embolism. The full range of hemodynamic responses was captured with mean prediction errors of 4.1% in the pressures and 3.1% in the volumes for 6 sets of clinical data. Pulmonary resistance increased significantly with the onset of embolism in all cases, as expected, with the percentage increase ranging from 89.98% to 261.44% of the initial state. These results are an important first step towards model-based cardiac diagnosis in the Intensive Care Unit.

Subject-specific model estimation of cardiac output and blood volume during hemorrhage

We have developed a novel method for estimating subject-specific hemodynamics during hemorrhage. First, a mathematical model representing a closed-loop circulation and baroreceptor feedback system was parameterized to match the baseline physiology of individual experimental subjects by fitting model results to 1 min of pre-injury data. This automated parameterization process matched pre-injury measurements within 1.4 +/- 1.3% SD. Tuned parameters were then used in similar open-loop models to simulate dynamics post-injury. Cardiac output (CO) estimates were obtained continuously using post-injury measurements of arterial blood pressure (ABP) and heart rate (HR) as inputs to the first open-loop model. Secondarily, total blood volume (TBV) estimates were obtained by summing the blood volumes in all the circulatory segments of a second open-loop model that used measured CO as an additional input. We validated the estimation method by comparing model CO results to flowprobe measurements in 14 pigs. Overall, CO estimates had a Bland-Altman bias of -0.30 l/min with upper and lower limits of agreement 0.80 and -1.40 l/min. The negative bias is likely due to overestimation of the peripheral resistance response to hemorrhage. There was no reference measurement of TBV; however, the estimates appeared reasonable and clearly predicted survival versus death during the post-hemorrhage period. Both open-loop models ran in real time on a computer with a 2.4 GHz processor, and their clinical applicability in emergency care scenarios is discussed.

Hardware-in-the-loop-simulation of the cardiovascular system, with assist device testing application

This paper presents a technique for evaluating the performance of biomedical devices by combining physical (mechanical) testing with a numerical, computerised model of a biological system. This technique is developed for evaluation of a cardiac assist device prior to in vivo trials. This device will wrap around a failing heart and provide physical beating assistance (dynamic cardiac compression). In vitro, the device to be tested is placed around a simulator comprising a mechanical simulation of the beating ventricles. This hardware model interfaces with a computerised (software) model of the cardiovascular system. In real time the software model calculates the effect of the assistance on the cardiovascular system and controls the beating motion of the hardware heart simulator appropriately. The software model of the cardiovascular system can represent ventricles in various stages of heart failure, and/or hardened or congested blood vessels as required. The software displays physiological traces showing the cardiac output, depending on the natural function of the modelled heart together with the physical assist power provided. This system was used to evaluate the effectiveness of control techniques applied to the assist device. Experimental results are presented showing the efficacy of prototype assist on healthy and weakened hearts, and the effect of asynchronous assist.

Simulation of the human cardiovascular system for real-time physical interaction with an assist device

In the development of left ventricular assist devices (LVADs), numerical simulations of the cardiovascular (CV) system have been widely used. Further, electro-hydraulic simulations have been developed to evaluate the performance of a physical LVAD prototype against a numerical model of the CV system. The effects of dynamic cardiac compression (DCC) have been less well modeled. This paper considers the interaction between a DCC device and a closed-loop numerical model of the cardiovascular system, which is specifically developed. The model is operated in realtime, and interfaced to the physical assist device for realistic testing. Assist control strategies are compared: constant pressure DCC, and volume-proportional pressure to simulate cardiomyoplasty. The model shows that applying equal pressure to both ventricles causes inflation of the left ventricle.

A functional cardiovascular model with disorders

This paper introduces a functional model of the cardiovascular system that is capable of describing its behavior in normal as well as pathologic cases. The developed model includes all the main compartments of the circulatory system and also the baroreflex-feedback regulatory mechanism. The model response to the incorporation of two critical cardiovascular disorders namely hypertension and acute congestive heart failure is realistic and within the expected range of the results of the literature experimental data.

A closed-loop model of the ovine cardiovascular system

We develop a closed-loop model of the ovine cardiovascular system, with the long term goal of developing a platform for simulating the hemodynamic efficacy of cardiopulmonary assist devices implanted and tested in this animal. The modeling of the systemic circulation is distributed and divided into subsystem circulations. Nonlinear aspects of the systemic venous system are included, such as the pressure-volume relation (PVR) of the systemic veins. In addition, a lumped model of the neural system controlling blood pressure is incorporated. The complete model provides good approximations to measured data from healthy reclining sheep. Moreover, it can predict the hemodynamic changes that accompany pre-load variation upon standing, and the short-term neurally mediated cardiovascular responses that attend this imposed orthostatic stress. We conclude that the model can serve as a simulation platform for evaluating cardiovascular and pulmonary assist devices.

Hemodynamic analysis and design of a paracorporeal artificial lung device

We have extended our model of the ovine pulmonary circulation to include a model of a paracorporeal artificial lung (AL) and its attachments to the natural pulmonary circulation in two configurations: in series and in parallel. Our model of the natural lung (NL) circulation is first shown to be in agreement with hemodynamic and input impedance data from the open literature. We then study design efficacy of the AL in terms of its housing and attachments. A sensitivity analysis of the modified pulmonary circulation model reveals that there are three key parameters: inlet graft length (IGL) and the compliances of the inlet compliance chamber (CC) and housing of the artificial lung. Based on literature reports, we assume the right ventricle is well-matched to the impedance of the natural pulmonary circulation and adjust the parameters of the modeled AL circuit to achieve the best least-squares fit to natural pulmonary input impedance data. Best-fit parameters produce impedance curves that fit natural impedance well, particularly below 3 Hz, where both compliance and graft length have their largest effects. Of these parameters, the impedance profile is most sensitive to IGL. However, the compliances are important, as well, particularly at low frequencies.

A LabVIEW model incorporating an open-loop arterial impedance and a closed-loop circulatory system

While numerous computer models exist for the circulatory system, many are limited in scope, contain unwanted features or incorporate complex components specific to unique experimental situations. Our purpose was to develop a basic, yet multifaceted, computer model of the left heart and systemic circulation in LabVIEW having universal appeal without sacrificing crucial physiologic features. The program we developed employs Windkessel-type impedance models in several open-loop configurations and a closed-loop model coupling a lumped impedance and ventricular pressure source. The open-loop impedance models demonstrate afterload effects on arbitrary aortic pressure/flow inputs. The closed-loop model catalogs the major circulatory waveforms with changes in afterload, preload, and left heart properties. Our model provides an avenue for expanding the use of the ventricular equations through closed-loop coupling that includes a basic coronary circuit. Tested values used for the afterload components and the effects of afterload parameter changes on various waveforms are consistent with published data. We conclude that this model offers the ability to alter several circulatory factors and digitally catalog the most salient features of the pressure/flow waveforms employing a user-friendly platform. These features make the model a useful instructional tool for students as well as a simple experimental tool for cardiovascular research.

Simulating transient ventricular interaction using a minimal cardiovascular system model

A minimal closed-loop cardiovascular system (CVS) model has been developed that can simulate ventricular interaction due to both direct interaction through the septum and series interaction through the circulation system. The model is used to simulate canine experiments carried out to study the transient response of the left ventricle due to changes in right ventricle pressures and volumes. The model-simulated trends in left and right ventricle pressures and volumes, septum deflection and arterial flow rates are compared with the experimental results. In spite of the limited physiological data available describing the animals, the model is shown to capture all the transient trends in the experimental data. This is the first known example of a physiological model that can capture all these trends. The model is then used to illustrate the separate effects of direct and series interactions independently. This study proves the value of this modelling method to be used in conjunction with experimental data for delineating and understanding the factors that contribute to ventricular dynamics.

Effects of atrial contraction, atrioventricular interaction and heart valve dynamics on human cardiovascular system response

Various simulation models of different complexity have been proposed to model the dynamic response of the human cardiovascular system. In a related paper we proposed an improved numerical model to study the dynamic response of the cardiovascular system, and the pressures, volumes and flow-rates in the four chambers of the heart, which included the effects of atrial contraction, atrioventricular interaction, and heart valve dynamics. This paper investigates the effects of each one of these aspects of the model on the overall dynamic system response. The dynamic response is studied under different situations, with and without including the effect of various features of the model, and these situations are studied and compared among themselves and to detailed aspects of expected healthy-system response. As an important contribution with potential clinical applications, this paper examines the corresponding effects of atrioventricular interaction, and heart valve opening and closing dynamics to the general system dynamic response. This isolation of physical cause-effect relationships is difficult to study with purely experimental methods. The simulation results agree well with results in the open literature. Comparison shows that introduction of these new features greatly improves the simulation accuracy of the effects of a, v and c waves, and in predicting regurgitant valve flow, the dichrotic notch, and E/A velocity ratio.

A concentrated parameter model for the human cardiovascular system including heart valve dynamics and atrioventricular interaction

Numerical modeling of the human cardiovascular system has always been an active research direction since the 19th century. In the past, various simulation models of different complexities were proposed for different research purposes. In this paper, an improved numerical model to study the dynamic function of the human circulation system is proposed. In the development of the mathematical model, the heart chambers are described with a variable elastance model. The systemic and pulmonary loops are described based on the resistance-compliance-inertia concept by considering local effects of flow friction, elasticity of blood vessels and inertia of blood in different segments of the blood vessels. As an advancement from previous models, heart valve dynamics and atrioventricular interaction, including atrial contraction and motion of the annulus fibrosus, are specifically modeled. With these improvements the developed model can predict several important features that were missing in previous numerical models, including regurgitant flow on heart valve closure, the value of E/A velocity ratio in mitral flow, the motion of the annulus fibrosus (called the KG diaphragm pumping action), etc. These features have important clinical meaning and their changes are often related to cardiovascular diseases. Successful simulation of these features enhances the accuracy of simulations of cardiovascular dynamics, and helps in clinical studies of cardiac function.

Adaptation to mechanical load determines shape and properties of heart and circulation: the CircAdapt model

With circulatory pathology, patient-specific simulation of hemodynamics is required to minimize invasiveness for diagnosis, treatment planning, and followup. We investigated the advantages of a smart combination of often already known hemodynamic principles. The CircAdapt model was designed to simulate beat-to-beat dynamics of the four-chamber heart with systemic and pulmonary circulation while incorporating a realistic relation between pressure-volume load and tissue mechanics and adaptation of tissues to mechanical load. Adaptation was modeled by rules, where a locally sensed signal results in a local action of the tissue. The applied rules were as follows: For blood vessel walls, 1) flow shear stress dilates the wall and 2) tensile stress thickens the wall; for myocardial tissue, 3) strain dilates the wall material, 4) larger maximum sarcomere length increases contractility, and 5) contractility increases wall mass. The circulation was composed of active and passive compliances and inertias. A realistic circulation developed by self-structuring through adaptation provided mean levels of systemic pressure and flow. Ability to simulate a wide variety of patient-specific circumstances was demonstrated by application of the same adaptation rules to the conditions of fetal circulation followed by a switch to the newborn circulation around birth. It was concluded that a few adaptation rules, directed to normalize mechanical load of the tissue, were sufficient to develop and maintain a realistic circulation automatically. Adaptation rules appear to be the key to reduce dramatically the number of input parameters for simulating circulation dynamics. The model may be used to simulate circulation pathology and to predict effects of treatment.

Minimal haemodynamic system model including ventricular interaction and valve dynamics

Characterising circulatory dysfunction and choosing a suitable treatment is often difficult and time consuming, and can result in a deterioration in patient condition, or unsuitable therapy choices. A stable minimal model of the human cardiovascular system (CVS) is developed with the ultimate specific aim of assisting medical staff for rapid, on site modelling to assist in diagnosis and treatment. Models found in the literature simulate specific areas of the CVS with limited direct usefulness to medical staff. Others model the full CVS as a closed loop system, but they were found to be very complex, difficult to solve, or unstable. This paper develops a model that uses a minimal number of governing equations with the primary goal of accurately capturing trends in the CVS dynamics in a simple, easily solved, robust model. The model is shown to have long term stability and consistency with non-specific initial conditions as a result. An "open on pressure close on flow" valve law is created to capture the effects of inertia and the resulting dynamics of blood flow through the cardiac valves. An accurate, stable solution is performed using a method that varies the number of states in the model depending on the specific phase of the cardiac cycle, better matching the real physiological conditions. Examples of results include a 9% drop in cardiac output when increasing the thoracic pressure from -4 to 0 mmHg, and an increase in blood pressure from 120/80 to 165/130 mmHg when the systemic resistance is doubled. These results show that the model adequately provides appropriate magnitudes and trends that are in agreement with existing data for a variety of physiologically verified test cases simulating human CVS function.

Velocity profile method for time varying resistance in minimal cardiovascular system models

This paper investigates the fluid dynamics governing arterial flow used in lumped parameter cardiovascular system (CVS) models, particularly near the heart where arteries are large. Assumptions made in applying equations conventionally used in lumped parameter models are investigated, specifically that of constant resistance to flow. The Womersley number is used to show that the effects of time varying resistance must be modelled in the pulsatile flow through the large arteries near the heart. It is shown that the equation commonly used to include inertial effects in fluid flow calculations is inappropriate for including time varying resistance. A method of incorporating time varying resistance into a lumped parameter model is developed that uses the Navier-Stokes equations to track the velocity profile. Tests on a single-chamber model show a 17.5% difference in cardiac output for a single-chamber ventricle model when comparing constant resistance models with the velocity profile tracking method modelling time varying resistance. This increase in precision can be achieved using 20 nodes with only twice the computational time required. The method offers a fluid dynamically and physiologically accurate method of calculating large Womersley number pulsatile fluid flows in large arteries around the heart and valves. The proposed velocity profile tracking method can be easily incorporated into existing lumped parameter CVS models, improving their clinical application by increasing their accuracy.

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

Previous models combining the human cardiovascular and pulmonary systems have not addressed their strong dynamic interaction. They are primarily cardiovascular or pulmonary in their orientation and do not permit a full exploration of how the combined cardiopulmonary system responds to large amplitude forcing (e.g., by the Valsalva maneuver). To address this issue, we developed a new model that represents the important components of the cardiopulmonary system and their coupled interaction. Included in the model are descriptions of atrial and ventricular mechanics, hemodynamics of the systemic and pulmonic circulations, baroreflex control of arterial pressure, airway and lung mechanics, and gas transport at the alveolar-capillary membrane. Parameters of this combined model were adjusted to fit nominal data, yielding accurate and realistic pressure, volume, and flow waveforms. With the same set of parameters, the nominal model predicted the hemodynamic responses to the markedly increased intrathoracic (pleural) pressures during the Valsalva maneuver. In summary, this model accurately represents the cardiopulmonary system and can explain how the heart, lung, and autonomic tone interact during the Valsalva maneuver. It is likely that with further refinement it could describe various physiological states and help investigators to better understand the biophysics of cardiopulmonary disease.