A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics

The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.     

Compression of interventricular septum during right ventricular pressure loading

The interventricular septum, which flattens and inverts in conditions such as pulmonary hypertension, is considered by many to be an unstressed membrane, in that its position is assumed to be determined solely by the transseptal pressure gradient. A two-dimensional finite element model was developed to investigate whether compression and bending moments (behavior incompatible with a membrane) exist in the septum during diastole under abnormal loading, i.e., pulmonary artery (PA) constriction. Hemodynamic and echocardiographic data were obtained in six open-chest anesthetized dogs. For both control and PA constriction, the measured left ventricular and right ventricular pressures were applied to a residually stressed mesh. Adjustments were made to the stiffness and end-bending moments until the deformed and loaded residually stressed mesh matched the observed configuration of the septum. During PA constriction, end-bending moments were required to obtain satisfactory matches but not during control. Furthermore, substantial circumferential compressive stresses developed during PA constriction. Such stresses might impede septal blood flow and provoke the unexplained ischemia observed in some conditions characterized by abnormal septal motion.     

Models of cardiac electromechanics based on individual hearts imaging data Image-based electromechanical models of the heart

Current multi-scale computational models of ventricular electromechanics describe the full process of cardiac contraction on both the micro- and macro- scales including: the depolarization of cardiac cells, the release of calcium from intracellular stores, tension generation by cardiac myofilaments, and mechanical contraction of the whole heart. Such models are used to reveal basic mechanisms of cardiac contraction as well as the mechanisms of cardiac dysfunction in disease conditions. In this paper, we present a methodology to construct finite element electromechanical models of ventricular contraction with anatomically accurate ventricular geometry based on magnetic resonance and diffusion tensor magnetic resonance imaging of the heart. The electromechanical model couples detailed representations of the cardiac cell membrane, cardiac myofilament dynamics, electrical impulse propagation, ventricular contraction, and circulation to simulate the electrical and mechanical activity of the ventricles. The utility of the model is demonstrated in an example simulation of contraction during sinus rhythm using a model of the normal canine ventricles.     

Computational modeling of left heart diastolic function: examination of ventricular dysfunction

A computational model that accounts for blood-tissue interaction under physiological flow conditions was developed and applied to a thin-walled model of the left heart. This model consisted of the left ventricle, left atrium, and pulmonary vein flow. The input functions for the model included the pulmonary vein driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The Immersed Boundary Method was used for the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology, and the fluid mass and momentum conservation equations were solved using Patankar's Semi-Implicit Method for Pressure Linked Equations (SIMPLE). This model was used to examine the flow fields in the left heart under abnormal diastolic conditions of delayed ventricular relaxation, delayed ventricular relaxation with increased ventricular stiffness, and delayed ventricular relaxation with an increased atrial contraction. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions, and to the results from simulations of normal diastolic function in this model [1]. Cases involving impairment of diastolic function were modeled with changes to the input functions for fiber relaxation/contraction of the chambers. The three cases of diastolic dysfunction investigated agreed with the changes in diastolic flow fields seen clinically. The effect of delayed relaxation was to decrease the early filling magnitude, and this decrease was larger when the stiffness of the ventricle was increased. Also, increasing the contraction of the atrium during atrial systole resulted in a higher late filling velocity and atrial pressure. The results show that dysfunction can be modeled by changing the relationships for fiber resting-length and/or stiffness. This provides confidence in future modeling of disease, especially changes to chamber properties to examine the effect of local dysfunction on global flow fields.     

A finite element study relating to the rapid filling phase of the human ventricles

During the rapid diastolic filling phase at rest, the ventricles of the human heart double approximately in volume. In order to investigate whether the ventricular filling pressures measured under physiological conditions can give rise to such an extensive augmentation in ventricular volumes, a finite element model of the human right and left ventricles has been developed, taking into account the nonlinear mechanical behavior and effective compressibility of the myocardial tissue. The results were compared with the filling phase of the human left ventricle as extrapolated from measurements documented in the literature. We arrived at the conclusion that the ventricular pressures measured during the rapid filling phase cannot be the sole cause of the rise of the observed ventricular volumes. We rather advocate the assumption that further dilating mechanisms might be part of ventricular activity thus heralding a multiple function of the ventricular muscle body. A further result indicates that under normal conditions the influence of the viscoelasticity of the tissue should not be disregarded in ventricular mechanics.     

Modelling the left ventricle using rapid prototyping techniques

Biomechanical research of left ventricular function involves the assessment and understanding of both ventricular wall mechanics and deformation and intraventricular flow patterns, as well as how they interact. Experimental research using hydraulic bench models should therefore aim for an as realistic as possible simulation of both. In previous experimental investigations, wall deformation was studied by means of thin-walled passive experimental models, consisting of a silicone membrane in a closed box, which is squeezed passively by an externally connected piston pump. Although the pump function of these models has already been well established, the membrane deformation remains unpredictable and the effect of muscle contraction – and hence natural wall deformation – cannot be simulated. In this study, we propose a new design of an experimental hydraulic left ventricular model in which left ventricular wall deformation can be controlled. We built this model by a combination of rapid prototyping techniques and tested it to demonstrate its wall deformation and pump function. Our experiments show that circumferential and longitudinal contraction can be attained and that this model can generate fairly normal values of pressure and flow.     

OSAHS患者上气道和软腭的流固耦合有限元模型的建立

目的:重建OSAHS患者上气道和软腭的流固耦合有限元模型,研究OSAHS患者上气道及软腭气流动力学特征,为进一步探讨OSAHS的的发病机制奠定基础。方法:对一名中度OSAHS患者的上气道及周围组织进行MRI扫描,将以DICOM格式存储的扫描数据导入Mimics15.0软件中进行预处理,得到上气道和软腭的模型;再利用逆向工程软件Geomagic Studio 2013建立了2 mm气道壁;然后在3-D重建软件NX中,生成气道壁和气道以及软腭之间的组合模型;最后将该组合模型导入ANSYS Workbench13.0软件中,通过网格划分、定义材料属性、设定模型的边界条件操作建立了上气道和软腭的流固耦合有限元模型。结果:利用Mimics、Ansys等软件建立了完整的上气道和软腭的流固耦合有限元模型。共得到气道:2806835单元和529281个节点;气道壁:2304348单元和3487609个节点;软腭:131855单元和204784个节点。结论:本研究建立的上气道及软腭的流固耦合有限元模型符合人体的生物力学特点,为下一步的数值模拟实验提供了一个更真实、可靠的模型。     

Prevention of mesh-dependent damage growth in finite element simulations of crack formation in acrylic bone cement

Peak stress levels predicted in finite element analysis (FEA) usually depend on mesh density, due to singular points in the model. In an earlier study, an FEA algorithm was developed to simulate the damage accumulation process in the cement mantle around total hip replacement (THR) implants. It allows cement crack formation to be predicted, as a function of the local cement stress levels. As the simulation is driven by mesh-dependent peak stresses, predicted crack formation rates are also likely to be mesh dependent. The aim of this study was to evaluate the mesh dependence of the predicted crack formation process, and to present a method to reduce the mesh dependence. Crack-propagation experiments were simulated. Experimental specimens, representing transverse slices of cemented THR reconstructions, were subjected to cyclic torsional loading. Crack development around the corners of the stem was monitored. The experiments were simulated using three meshes with increasing levels of mesh refinement. Crack locations and orientations were accurately predicted, and were virtually independent of the level of mesh refinement. However, the experimental crack propagation rates were overestimated considerably, increasing with mesh refinement. To eliminate the effect of stress singularities around the corners of the stem, a stress averaging algorithm was applied in the simulation. This algorithm redistributed the stresses by weighted spatial averaging. When damage accumulation was computed based on averaged stresses, the crack propagation rates predicted were independent of the level of mesh refinement. The critical distance, a parameter governing the effect of the averaging algorithm, was optimized such that the predicted crack propagation rates accurately corresponded to the experimental ones. These results are important for the validity and standardization of pre-clinical testing methods for orthopaedic implants.     

FSI simulation of asymmetric mitral valve dynamics during diastolic filling

In this article, we present a fluid-structure interaction algorithm accounting for the mutual interaction between two rigid bodies. The algorithm was used to perform a numerical simulation of mitral valve (MV) dynamics during diastolic filling. In numerical simulations of intraventricular flow and MV motion, the asymmetry of the leaflets is often neglected. In this study the MV was rendered as two rigid, asymmetric leaflets. The 2D simulations incorporated the dynamic interaction of blood flow and leaflet motion and an imposed subject-specific, transient left ventricular wall movement obtained from ultrasound recordings. By including the full Jacobian matrix in the algorithm, the speed of the simulation was enhanced by more than 20% compared to using a diagonal Jacobian matrix. Furthermore, our results indicate that important features of the flow field may not be predicted by the use of symmetric leaflets or in the absence of an adequate model for the left atrium.     

Tissue-fluid interface analysis using biphasic finite element method

Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.     

CFD simulation of flow through heart: a perspective review

The heart is an organ which pumps blood around the body by contraction of muscular wall. There is a coupled system in the heart containing the motion of wall and the motion of blood fluid; both motions must be computed simultaneously, which make biological computational fluid dynamics (CFD) difficult. The wall of the heart is not rigid and hence proper boundary conditions are essential for CFD modelling. Fluid-wall interaction is very important for real CFD modelling. There are many assumptions for CFD simulation of the heart that make it far from a real model. A realistic fluid-structure interaction modelling the structure by the finite element method and the fluid flow by CFD use more realistic coupling algorithms. This type of method is very powerful to solve the complex properties of the cardiac structure and the sensitive interaction of fluid and structure. The final goal of heart modelling is to simulate the total heart function by integrating cardiac anatomy, electrical activation, mechanics, metabolism and fluid mechanics together, as in the computational framework.     

A two-phase finite element model of the diastolic left ventricle

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.     

Critical role of cardiac t-tubule system for the maintenance of contractile function revealed by a 3D integrated model of cardiomyocytes

T-tubules in mammalian ventricular myocytes constitute an elaborate system for coupling membrane depolarization with intracellular Ca(2+) signaling to control cardiac contraction. Deletion of t-tubules (detubulation) has been reported in heart diseases, although the complex nature of the cardiac excitation-contraction (E-C) coupling process makes it difficult to experimentally establish causal relationships between detubulation and cardiac dysfunction. Alternatively, numerical simulations incorporating the t-tubule system have been proposed to elucidate its functional role. However, the majority of models treat the subcellular spaces as lumped compartments, and are thus unable to dissect the impact of morphological changes in t-tubules. We developed a 3D finite element model of cardiomyocytes in which subcellular components including t-tubules, myofibrils, sarcoplasmic reticulum, and mitochondria were modeled and realistically arranged. Based on this framework, physiological E-C coupling was simulated by simultaneously solving the reaction-diffusion equation and the mechanical equilibrium for the mathematical models of electrophysiology and contraction distributed among these subcellular components. We then examined the effect of detubulation in this model by comparing with and without the t-tubule system. This model reproduced the Ca(2+) transients and contraction observed in experimental studies, including the response to beta-adrenergic stimulation, and provided detailed information beyond the limits of experimental approaches. In particular, the analysis of sarcomere dynamics revealed that the asynchronous contraction caused by a large detubulated region can lead to impairment of myocyte contractile efficiency. These data clearly demonstrate the importance of the t-tubule system for the maintenance of contractile function.     

Diastolic ventricular aspiration: a mechanism supporting the rapid filling phase of the human ventricles

During the rapid filling phase of the heart cycle, the internal volumes of the two ventricular cavities approximately double, while the intraventricular pressures rise typically only by an amount of less than 1 kPa. Such a small pressure increase cannot be the sole driving mechanism for the large inflow of blood associated with ventricular expansion during this period. Instead, the rapid filling phase is to be interpreted as being mediated primarily by the heart recoiling elastically from its contracted state, causing blood to be aspirated rapidly into the ventricles. In order to study the role of this mechanism, elastic finite element (FE) simulations of ventricular expansion were performed, taking into account the large deformations occurring during this period and the effective compressibility of the myocardium due to intramural fluid flow. Thereby, a realistic three-dimensional geometry derived from magnetic resonance imaging (MRI) measurements of both human ventricles was used. To validate our FE analyses, the results were compared with published measurements relating to the rapid filling phase of the human left ventricle. Our study shows that, under normal physiological conditions, ventricular aspiration plays a key role in the ventricular filling process.     

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.     

A multiscale, spatially distributed model of asthmatic airway hyper-responsiveness

We present a multiscale, spatially distributed model of lung and airway behaviour with the goal of furthering the understanding of airway hyper-responsiveness and asthma. The model provides an initial computational framework for linking events at the cellular and molecular levels, such as Ca²⁺ and crossbridge dynamics, to events at the level of the entire organ. At the organ level, parenchymal tissue is modelled using a continuum approach as a compressible, hyperelastic material in three dimensions, with expansion and recoil of lung tissue due to tidal breathing. The governing equations of finite elasticity deformation are solved using a finite element method. The airway tree is embedded in this tissue, where each airway is modelled with its own airway wall, smooth muscle and surrounding parenchyma. The tissue model is then linked to models of the crossbridge mechanics and their control by Ca²⁺ dynamics, thus providing a link to molecular and cellular mechanisms in airway smooth muscle cells. By incorporating and coupling the models at these scales, we obtain a detailed, computational multiscale model incorporating important physiological phenomena associated with asthma.     

Identification process based on shear wave propagation within a phantom using finite element modelling and magnetic resonance elastography

Magnetic resonance elastography (MRE), based on shear wave propagation generated by a specific driver, is a non-invasive exam performed in clinical practice to improve the liver diagnosis. The purpose was to develop a finite element (FE) identification method for the mechanical characterisation of phantom mimicking soft tissues investigated with MRE technique. Thus, a 3D FE phantom model, composed of the realistic MRE liver boundary conditions, was developed to simulate the shear wave propagation with the software ABAQUS. The assumptions of homogeneity and elasticity were applied to the FE phantom model. Different ranges of mesh size, density and Poisson's ratio were tested in order to develop the most representative FE phantom model. The simulated wave displacement was visualised with a dynamic implicit analysis. Subsequently, an identification process was performed with a cost function and an optimisation loop provided the optimal elastic properties of the phantom. The present identification process was validated on a phantom model, and the perspective will be to apply this method on abdominal tissues for the set-up of new clinical MRE protocols that could be applied for the follow-up of the effects of treatments.     

A framework for biomechanics simulations using four-chamber cardiac models

Computational cardiac models have been extensively used to study different cardiac biomechanics; specifically, finite-element analysis has been one of the tools used to study the internal stresses and strains in the cardiac wall during the cardiac cycle. Cubic-Hermite finite element meshes have been used for simulating cardiac biomechanics due to their convergence characteristics and their ability to capture smooth geometries compactly–fewer elements are needed to build the cardiac geometry–compared to linear tetrahedral meshes. Such meshes have previously been used only with simple ventricular geometries with non-physiological boundary conditions due to challenges associated with creating cubic-Hermite meshes of the complex heart geometry. However, it is critical to accurately capture the different geometric characteristics of the heart and apply physiologically equivalent boundary conditions to replicate the in vivo heart motion. In this work, we created a four-chamber cardiac model utilizing cubic-Hermite elements and simulated a full cardiac cycle by coupling the 3D finite element model with a lumped circulation model. The myocardial fiber-orientations were interpolated within the mesh using the Log-Euclidean method to overcome the singularity associated with interpolation of orthogonal matrices. Physiologically equivalent rigid body constraints were applied to the nodes along the valve plane and the accuracy of the resulting simulations were validated using open source clinical data. We then simulated a complete cardiac cycle of a healthy heart and a heart with acute myocardial infarction. We compared the pumping functionality of the heart for both cases by calculating the ventricular work. We observed a 20% reduction in acute work done by the heart immediately after myocardial infarction. The myocardial wall displacements obtained from the four-chamber model are comparable to actual patient data, without requiring complicated non-physiological boundary conditions usually required in truncated ventricular heart models.     

Simplified Aeroelastic Model for Fluid Structure Interaction between Microcantilever Sensors and Fluid Surroundings

Fluid-structural coupling occurs when microcantilever sensors vibrate in a fluid. Due to the complexity of the mechanical characteristics of microcantilevers and lack of high-precision microscopic mechanical testing instruments, effective methods for studying the fluid-structural coupling of microcantilevers are lacking, especially for non-rectangular microcantilevers. Here, we report fluid-structure interactions (FSI) of the cable-membrane structure via a macroscopic study. The simplified aeroelastic model was introduced into the microscopic field to establish a fluid-structure coupling vibration model for microcantilever sensors. We used the finite element method to solve the coupled FSI system. Based on the simplified aeroelastic model, simulation analysis of the effects of the air environment on the vibration of the commonly used rectangular microcantilever was also performed. The obtained results are consistent with the literature. The proposed model can also be applied to the auxiliary design of rectangular and non-rectangular sensors used in fluid environments.     

Abnormal cardiac inflow patterns during postnatal development in a mouse model of Holt-Oram syndrome

Tbx5(del/+) mice provide a model of human Holt-Oram syndrome. In this study, the cardiac functional phenotypes of this mouse model were investigated with 30-MHz ultrasound by comparing 12 Tbx5(del/+) mice with 12 wild-type littermates at 1, 2, 4, and 8 wk of age. Cardiac dimensions were measured with two-dimensional and M-mode imaging. The flow patterns in the left and right ventricular inflow channels were evaluated with Doppler flow sampling. Compared with wild-type littermates, Tbx5(del/+) mice showed significant changes in the mitral flow pattern, including decreased peak velocity of the left ventricular (LV) early filling wave (E wave), increased peak velocity of the late filling wave (A wave), and decreased or even reversed peak E-to-A ratio. The prolongation of LV isovolumic relaxation time was detected in Tbx5(del/+) neonates as early as 1 wk of age. In Tbx5(del/+) mice, LV wall thickness appeared normal but LV chamber dimension was significantly reduced. LV systolic function did not differ from that in wild-type littermates. In contrast, the Doppler flow spectrum in the enlarged tricuspid orifice of Tbx5(del/+) mice demonstrated increased peak velocities of both E and A waves and increased total time-velocity integral but unchanged peak E/A. In another 13 mice (7 Tbx5(del/+), 6 wild-type) at 2 wk of age, significant correlation was found between Tbx5 gene expression level in ventricular myocardium and LV filling parameters. In conclusion, the LV diastolic function of Tbx5(del/+) mice is significantly deteriorated, whereas the systolic function remains normal.