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.     

Mitral valve dynamics in structural and fluid–structure interaction models

Modelling and simulation of heart valves is a challenging biomechanical problem due to anatomical variability, pulsatile physiological pressure loads and 3D anisotropic material behaviour. Current valvular models based on the finite element method can be divided into: those that do model the interaction between the blood and the valve (fluid–structure interaction or ‘wet’ models) and those that do not (structural models or ‘dry’ models).Here an anatomically sized model of the mitral valve has been used to compare the difference between structural and fluid–structure interaction techniques in two separately simulated scenarios: valve closure and a cardiac cycle. Using fluid–structure interaction, the valve has been modelled separately in a straight tubular volume and in a U-shaped ventricular volume, in order to analyse the difference in the coupled fluid and structural dynamics between the two geometries.The results of the structural and fluid–structure interaction models have shown that the stress distribution in the closure simulation is similar in all the models, but the magnitude and closed configuration differ. In the cardiac cycle simulation significant differences in the valvular dynamics were found between the structural and fluid–structure interaction models due to difference in applied pressure loads. Comparison of the fluid domains of the fluid–structure interaction models have shown that the ventricular geometry generates slower fluid velocity with increased vorticity compared to the tubular geometry.In conclusion, structural heart valve models are suitable for simulation of static configurations (opened or closed valves), but in order to simulate full dynamic behaviour fluid–structure interaction models are required.     

Simulation study of the cardiovascular functional status in hypertensive situation

An extended cardiovascular model was established based on our previous work to study the consequences of physiological or pathological changes to the homeostatic functions of the cardiovascular system. To study hemodynamic changes in hypertensive situations, the impacts of cardiovascular parameter variations (peripheral vascular resistance, arterial vessel wall stiffness and baroreflex gain) upon hemodynamics and the short-term regulation of the cardiovascular system were investigated. For the purpose of analyzing baroregulation function, the short-term regulation of arterial pressure in response to moderate dynamic exercise for normotensive and hypertensive cases was studied through computer simulation and clinical experiments. The simulation results agree well with clinical data. The results of this work suggest that the model presented in this paper provides a useful tool to investigate the functional status of cardiovascular system in normal or pathological conditions.     

In vivo validation of a fluid dynamics model of mitral valve M-mode echocardiogram

A fluid dynamics model of mitral valve motion during diastolic filling of the left heart is described. Given a pulsed Doppler velocity pattern in the mitral annulus, the radius of circular mitral orifice, the length of leaflets and the end-systolic left ventricular volume, the numerical model predicts the time course of the mitral leaflets during diastole: the mitral valve M-mode echocardiogram. Results obtained by computer simulation have been validated with in vivo data. It is shown that mitral valve flow is essentially a fluid dynamics process of floating mitral valve leaflets with blood flow due to the atrioventricular pressure gradient. In addition, a partial opening of the mitral valve as the initial boundary condition is required to simulate the overshooting of the leaflets during early peak filling. Some back flow is a condition for perfect closing of the native mitral valve. The higher the unsteady character of mitral flow, the less efficient is the opening and closing processes of the mitral valve.     

Design considerations and quantitative assessment for the development of percutaneous mitral valve stent

Percutaneous heart valve replacement is gaining popularity, as more positive reports of satisfactory early clinical experiences are published. However this technique is mostly used for the replacement of pulmonary and aortic valves and less often for the repair and replacement of atrioventricular valves mainly due to their anatomical complexity. While the challenges posed by the complexity of the mitral annulus anatomy cannot be mitigated, it is possible to design mitral stents that could offer good anchorage and support to the valve prosthesis. This paper describes four new Nitinol based mitral valve designs with specific features intended to address migration and paravalvular leaks associated with mitral valve designs. The paper also describes maximum possible crimpability assessment of these mitral stent designs using a crimpability index formulation based on the various stent design parameters. The actual crimpability of the designs was further evaluated using finite element analysis (FEA). Furthermore, fatigue modeling and analysis was also done on these designs. One of the models was then coated with polytetrafluoroethylene (PTFE) with leaflets sutured and put to: (i) leaflet functional tests to check for proper coaptation of the leaflet and regurgitation leakages on a phantom model and (ii) anchorage test where the stented valve was deployed in an explanted pig heart. Simulations results showed that all the stents designs could be crimped to 18F without mechanical failure. Leaflet functional test results showed that the valve leaflets in the fabricated stented valve coapted properly and the regurgitation leakage being within acceptable limits. Deployment of the stented valve in the explanted heart showed that it anchors well in the mitral annulus. Based on these promising results of the one design tested, the other stent models proposed here were also considered to be promising for percutaneous replacement of mitral valves for the treatment of mitral regurgitation, by virtue of their key features as well as effective crimping. These models will be fabricated and put to all the aforementioned tests before being taken for animal trials.     

Studying the dynamics of autonomic activity during emotional experience

Recent theories emphasize the dynamic aspects of emotions. However, the physiological measures and the methodological approaches that can capture the dynamics of emotions are underdeveloped. In the current study, we investigated whether moment‐to‐moment changes in autonomic nervous system (ANS) activity are reliably associated with the unfolding of emotional experience. We obtained cardiovascular and electrodermal signals from participants while they viewed emotional movies. We found that the ANS signals were temporally aligned across individuals, indicating a reliable stimulus‐driven response. The degree of response reliability was associated with the emotional time line of the movie. Finally, individual differences in ANS response reliability were strongly correlated with the subjective emotional responses. The current research offers a methodological approach for studying physiological responses during dynamic emotional situations.     

Clinically relevant computer model of cardiac rhythm and pacemaker/heart interaction

A computer simulation model of cardiac rhythm disturbances and of the heart/pacemaker interaction has been created and implemented on a NORD-100 minicomputer. The model incorporates important properties including cycle length dependence of the refractory periods of different parts of the heart and of the atrioventricular nodal conduction speed. Computational experiments produce an explicit timetable of polarisation changes, a simulated one-channel electrocardiographic record and a pacemaker marker channel. The simulation program is written infortran and uses discrete event simulation techniques. The heart is modelled using instances of nine simulation process prototypes. The paper presents and discusses several examples in the form of simulated electrocardiographic records and the results show that the model is clinically relevant. Included in the examples are the modelling of rhythm disturbances, pacemaker actions, pacing for tachycardia prophylaxis and atrioventricular nodal conduction disorders.     

Three-dimensional model system of valvulogenesis.

Valvular defects are among the most common and deleterious of all cardiac malformations. The early cardiac cushions are located in the atrioventricular (AV) canal of the embryonic heart. These cushions contain cells that are the primordia of the cardiac valves and membranous septa. Significant progress has been made in delineating the molecular mechanisms that regulate the early steps of cushion formation; however, little is known about how these cushions differentiate into valve leaflets. Here, a new three-dimensional collagen tube culturing system was tested for its ability to sustain the development and maturation of the AV cushion anlagen. We report that AV cushion tissues grown within the collagen tube scaffold recapitulate aspects of AV valve development both at the molecular and morphological levels. Furthermore, our results indicate that valve leaflet formation in the tube model is dependent on the presence of cardiac myocytes.     

An Experimentally Derived Stress Resultant Shell Model for Heart Valve Dynamic Simulations

In order to achieve a more realistic and accurate computational simulation of native and bioprosthetic heart valve dynamics, a finite shell element model was developed. Experimentally derived and uncoupled in-plane and bending behaviors were implemented into a fully nonlinear stress resultant shell element. Validation studies compared the planar biaxial extension and three-point bending simulations to the experimental data and demonstrated excellent fidelity. Dynamic simulations of a pericardial bioprosthetic heart valve with the developed shell element model showed significant differences in the deformation characteristics compared to the simulation with an assumed isotropic bending model. The new finite shell element model developed in the present study can also incorporate various types of constitutive models and is expected to help us to understand the complex dynamics of native and bioprosthetic heart valve function in physiological and pathological conditions.     

Computational Study of the Dynamics of a Bileaflet Mechanical Heart Valve in the Mitral Position

A computational study of the flow-structure interaction of a bileaflet mechanical heart valve in the mitral position is presented. Flow in a simple model of the left ventricle is simulated using an immersed boundary method, and the dynamics of the valve leaflets are solved in a fully-coupled manner with the flow. Simulations are conducted for two distinct valve orientations and multiple valve hinge locations, and the performance of the valve is compared in terms of metrics associated with leaflet motion, mitral regurgitation, and mechanical energy losses through the valve. Results indicate that a bileaflet mechanical heart valve with a more centrally located hinge, and implanted in the anatomical orientation provides the best overall performance. The fluid and leaflet dynamics, as well as the clinical implications underlying these findings are discussed.     

Mathematical modeling of cardiovascular system dynamics using a lumped parameter method

This work reviews the main aspects of cardiovascular system dynamics with an emphasis on modeling hemodynamic characteristics by the use of a lumped parameter approach. The methodological and physiological aspects of the circulation dynamics are summarized with the help of existing mathematical models. The main characteristics of the hemodynamic elements, such as the heart and arterial and venous systems, are first described. Distributed models of an arterial network are introduced, and their characteristics are compared with those of lumped parameter models. We also discuss the nonlinear characteristics of the pressure-volume relationship in veins. Then the control pathways that participate in feedback mechanisms (baroreceptors and cardiopulmonary receptors) are described to explain the interaction between hemodynamics and autonomic nerve control in the circulation. Based on a set-point model, the computational aspects of reflex control are explained.     

心血管循环系统建模和仿真研究中的功率键合图方法

提出心血管循环系统的血流动力学功率键合图模型，应用状态空间方法和计算机仿真技术，对一个简化的心血管循环系统模型进行了仿真研究，所得仿真数据同基本的生理规律具有较好的符合性，证明了功率键合图这种系统动力学建模方法在循环系统仿真中具有良好的可行性和有效性，为心血管系统的计算机仿真提供一种直观和统一的建模方法进行了有益的尝试和探索。     

Aberrant twinning (diprosopus) associated with anencephaly

A case of Monocephalus diprosopus, associated with craniorachischisis and duplication of most of the foregut derivates is presented. The major part of the cardiovascular system remained single but the heart exhibited severe defects, including a complete persistent atrioventricular canal, transposition of the great arteries and atresia of the pulmonary valve. This report further supports the hypothesis that certain types of incomplete twinning and neural tube defects may be caused by a single teratogenic mechanism.     

左心循环系统的建模与仿真

将左心模型与四元件的动脉系统Windkessel模型耦合,构成左心-动脉系统交互的左心循环系统模型.模型包括左心房、左心室、二尖瓣、动脉辩和动脉系统,实现了对左心循环系统的血流动力学模拟.应用状态空间法和SIMULINK框图模型法两种技术和MATLAB工具,进行了数学建模和数值计算,具有模型直观、容易实现、方便调节参数等优点.应用这一仿真模型,可以对左心室容积、血压及主动脉血压和血流等进行动态模拟.仿真结果与生理实际情况相符.     

Numerical Modeling of Hemodynamics with Pulsatile Impeller Pump Support

There is significant interest in the development and application of variable speed impeller-pump type ventricular assist devices designed to generate pulsatile blood flow. However, no study has so far been carried out to investigate the systemic cardiovascular response to various aspects of pump motion. In this article, a numerical model is constructed for the simulation of the cardiovascular response in the heart failure condition under representative cases of pulsatile impeller pump support. The native cardiovascular model is based on a previously validated model, and the impeller pump is modeled by directly fitting the pressure–flow curves that describe the pump characteristics. The model developed is applied to study circulatory dynamics under different degrees of phase shift and pulsation ratio in the pump motion profile. The characteristic variables are discussed as criteria for the evaluation of system response for comparison of the pulsatile flows. Simulation results show that a constant pump speed is the most efficient work mode for the rotary pump, and with the application of either a phase shift of 75% and a pulsation ratio of 0.5, or a phase shift of 42% and a pulsation ratio of 0.55, it is possible to generate arterial pulse pressure with the maximal magnitude of about 28 mmHg. However, this is achieved at the cost of reduced cardiac output and pump efficiency.     

Atrioventricular canal malformation interpreted as secondary to reduced compression upon the developing heart.

This study was undertaken to evaluate the nature and pathogenesis of malformations of the atrioventricular canal in relation to normal cardiogenesis. Serial histologic sections of normal human embryos and fetuses were made, from which three-dimensional images were reconstructed to show the relationship between the developing heart and its surrounding structures, and the course of development of the atrial septum and atrioventricular valves. Based on these reconstructions and on examination of the hearts of 59 patients with atrioventricular canal malformations, it is suggested that the spectrum of atrioventricular malformations may arise as a result of reduced compression of the developing atria by surrounding structures during embryonic Stages 13 through 18. Comparison of hearts with atrioventricular canal defects with normal embryos indicated that the malformations may be classified as primitive canals, complete canals, or partial canals, corresponding to failure of completion of normal development in Stages 14 through 18. In primitive canal the atrial septum was absent or had only a portion of septum primum. In complete canal both atrial septums were present, but the atrioventricular valve material was not subdivided and the four chambers were in communication. In partial canal, the atrioventricular valve was divided, but atrial and ventricular septal defects and valve clefts were present in varying degrees of severity. It is proposed that the spectrum of cardiac abnormalities which constitutes atrioventricular canal malformations may be understood as arising from varying degrees of lack of normal compression of the developing heart by surrounding structures. (Am J Pathol 95.579-598, 1979)     

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.     

The structure of the atrioventricular conducting system in the avian heart

The atrioventricular conduction system in three avian species has been studied by light and electron microscopy. A morphologically definable atrioventricular node was not found in any of these. The atrioventricular bundle is a well-defined structure, the proximal portion of which is in direct continuity with the atrioventricular ring, located in the arterial sheet of the muscular valve of the right atrioventricular opening. In the zone of transition between atrioventricular ring and bundle the compactness of the bundle is loosened, but the fibers do not establish continuity with the atrial fibers. The ring consists of Purkinje-like fibers, 10–15 μm in diameter, and (peripherally) small 3–5-μm-diameter junctional fibers which are in continuity with the common atrial fibers. In the muscular atrioventricular valve the fibers of the ring are insulated from the ventricular myocardium by a connective tissue sheet of the annulus fibrosus. It is suggested that in the avian heart the atrioventricular ring may fulfill a role similar to that of the atrioventricular node of mammals.     

Mathematical Modeling of Flow-Generated Forces in an In Vitro System of Cardiac Valve Development

Heart valve defects are the most common cardiac defects. Therefore, defining the mechanisms of cardiac valve development is critical to our understanding and treatment of these disorders. At early stages of embryonic cardiac development, the heart begins as a simple tube that then becomes constricted into separate atrial and ventricular regions by the formation of small, mound-like structures, called atrioventricular (AV) cushions. As valve development continues, these mounds fuse and then elongate into valve leaflets. A longstanding hypothesis proposes that blood flow-generated shear stress and pressure are critical in shaping the cushions into leaflets. Here we show results from a two-dimensional mathematical model that simulates the forces created by blood flow present in a developing chick heart and in our in vitro, tubular model system. The model was then used to predict flow patterns and the resulting forces in the in vitro system. The model indicated that forces associated with shear stress and pressure have comparable orders of magnitude and collectively produce a rotational profile around the cushion in the direction of flow and leaflet growth. Further, it was concluded that the replication of these forces on a cushion implanted in our tubular in vitro system is possible. Overall, the two-dimensional, mathematical model provides insight into the forces that occur during early cardiac valve elongation.