A biphasic model for full cycle simulation of the human heart aimed at rheumatic heart disease (original) (raw)
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MATEC Web of Conferences
This research is part of an on-going project aimed at describing the mechanotransduction of rheumatic heart disease (RHD), in order to study long-term effects of new therapeutic concepts to treat inflammatory heart diseases and ultimately, estimate their effectiveness to prevent heart failure. RHD is a condition which is mostly common amongst low-income countries and accounts for approximately 250 000 deaths per annum. The Theory of Porous Media (TPM) can represent the proliferative growth and remodelling processes related to RHD within a thermodynamically consistent framework and is additionally advantageous with application to biological tissue due to the ability to couple multiple constituents. The research presented will extend an existing biphasic TPM model for the solid cardiac tissue (solid phase) saturated in a blood and interstitial fluid (liquid phase) [1], to a triphasic model with the inclusion of a third nutrient phase towards growth. This inclusion is motivated by the ...
Journal of …, 2011
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.
A two-dimensional prototype multi-physics model of the right ventricle of the heart
International Journal for Numerical Methods in Fluids, 2008
The heart operates as a delicate function of the interactions among its electro-chemical, structural and fluid components. The objective of this paper is to describe the computational modelling of the interaction between simplified forms of the electro-chemical, structural and fluid behaviour. It is because the objective here is to evaluate the interactions among the phenomena that the specific models of the electro-chemical, fluid and structural behaviour are kept as simple as possible. The electro-chemical model is drawn from that of Clayton and Holden, while the blood is assumed to be a conventional slightly compressible Navier-Stokes fluid and the heart wall is a simple elastic structure modelled via the static equations. The model is implemented within a multi-physics finite volume solver environment using an unstructured mesh approach, which enables the implementation of models for each of the specific phenomenon and their interactions. The model is two dimensional, but shows how the electric field drives a cross section of the wall so that it pumps the blood in and out of the right ventricle geometry. behaviour of the heart. This understanding has been embedded within a wide range of mathematical models, normally based on what are called bi-domain equations, of which those by the teams of Trayanova et al. , Plank and Vigmond [5], Sundnes [6] are typical, although probably the most comprehensive is due to the work of Noble and co-workers . This work has provided the basis for genuine significantly functional virtual heart models that may be used in clinical research and treatment assessment. These models would be enhanced if they could be embedded within suitable models of the fluid-structure interaction between the blood and heart wall.
An electromechanics-driven fluid dynamics model for the simulation of the whole human heart
arXiv (Cornell University), 2023
We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the biophysically detailed RDQ20 activation model (Regazzoni et al., 2020) that is able to reproduce the physiological range of hemodynamic biomarkers. Then, we demonstrate that the ability of the force generation model to reproduce certain microscale mechanisms, such as the dependence of force on fiber shortening velocity, is crucial to capture the overall physiological mechanical and fluid dynamics macroscale behavior. This motivates the need for using multiscale models with high biophysical fidelity, even when the outputs of interest are relative to the macroscale. We show that the use of a high-fidelity electromechanical model, combined with a detailed calibration process, allows us to achieve a remarkable biophysical fidelity in terms of both mechanical and hemodynamic quantities. Indeed, our electromechanical-driven CFD simulationscarried out on an anatomically accurate geometry of the whole heart-provide results that match the cardiac physiology both qualitatively (in terms of flow patterns) and quantitatively (when comparing in silico results with biomarkers acquired in vivo). Moreover, we consider the pathological case of left bundle branch block, and we investigate the consequences that an electrical abnormality has on cardiac hemodynamics thanks to our multiphysics integrated model. The computational model that we propose can faithfully predict a delay and an increasing wall shear stress in the left ventricle in the pathological condition. The interaction of different physical processes in an integrated framework allows us to faithfully describe and model this pathology, by capturing and reproducing the intrinsic multiphysics nature of the human heart.
Computational modeling of passive myocardium
International Journal For Numerical Methods in Biomedical Engineering, 2011
This work deals with the computational modeling of passive myocardial tissue within the framework of mixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model, which has originally been designed for exactly incompressible deformations, is extended towards entirely three-dimensional inhomogeneous deformations by additively decoupling the strain energy function into volumetric and isochoric parts along with the multiplicative split of the deformation gradient. This decoupled constitutive structure is then embedded in a mixed finite element formulation through a threefield Hu-Washizu functional whose simultaneous variation with respect to the independent pressure, dilatation, and placement fields results in the associated Euler-Lagrange equations, thereby minimizing the potential energy. This weak form is then consistently linearized for uniform-pressure elements within the framework of an implicit finite element method. To demonstrate the performance of the proposed approach, we present a three-dimensional finite element analysis of a generic biventricular heart model, subjected to physiological ventricular pressure. The parameters employed in the numerical analysis are identified by solving an optimization problem based on six simple shear experiments on explanted cardiac tissue.
Siam Journal on Applied Mathematics, 2022
\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft. The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model. \bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs. cardiac perfusion, nonlinear poromechanics, constitutive modeling \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs. 92C10, 68U20, 74F10 \bfD \bfO
Structural modelling of the cardiovascular system
Biomechanics and Modeling in Mechanobiology, 2018
Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.
A framework for multi-scale modelling of the myocardium
The last decades have shown tremendous improvement in modelling the electromechanical behaviour of the myocardium. Early attempts at modelling the gross structure of the heart assumed an ellipsoidal shape of the left ventricle and transversely isotropic material behaviour. Recent studies have generalized these models to fully orthotropic finite element models, capturing the anatomy of both ventricles and the transmural changes of fiber, sheet and normal directions. However, material properties are described in terms of theories which are based on continuum electromechanics, therefore being restricted to a certain scale; usually the macro scale. Microstructural data of the myocyte arrangement and its enclosing collagen is now available and can be utilized for a model that encapsulates both the micro-and the macro-structural scales. In particular, this data informs an algorithm that is capable of generating an anatomically realistic finite element model of the myocyte topology that also provides a scaffold for the various collagen types (mechanical behaviour) as well as gap junctions (electrical features). The macro parameters can then be explained by means of the micro parameters. This paper presents a framework for the parameter identification in the context of system identification theory based on the setup of the microstructural topology.