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Martonová D, Holz D, Duong MT, Leyendecker S. Smoothed finite element methods in simulation of active contraction of myocardial tissue samples. J Biomech 2023; 157:111691. [PMID: 37441914 DOI: 10.1016/j.jbiomech.2023.111691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2023] [Revised: 05/12/2023] [Accepted: 06/14/2023] [Indexed: 07/15/2023]
Abstract
In modelling and simulation of cardiac mechanics, tetrahedral meshes are often used due to the easy availability of efficient meshing algorithms. This is beneficial in particular when complex geometries such as cardiac structures are considered. The gold standard in simulating the cardiac cycle is to solve the mechanical balance equations with the finite element method (FEM). However, using linear shape functions in the FEM in combination with nearly-incompressible material models is known to produce overly stiff approximations, whereas higher order elements are computationally more expensive. To overcome these problems, smoothed finite element methods (S-FEMs) have been proposed by Liu and co-workers. So far, S-FEMs in 3D have been utilised only in simulations of passive mechanics. In the present work, different S-FEMs are for the first time used for simulation of an active cardiac contraction on three-dimensional myocardial tissue samples. Further, node-based S-FEM (NS-FEM), face-based S-FEM (FS-FEM) and selective FS/NS-FEM are for the first time implemented as user subroutine in the commercial software Abaqus. Our results confirm that all S-FEMs perform softer than linear FEM and volumetric locking is reduced. The FS/NS-FEM produces solutions with the relative error in maximum displacement and rotation being less than 5% with respect to the reference solution obtained by the quadratic FEM for all considered mesh sizes, although linear shape functions are used. We therefore conclude that in particular FS/NS-FEM is an efficient and accurate numerical method in the simulation of an active cardiac muscle contraction.
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Affiliation(s)
- Denisa Martonová
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, 91058 Erlangen, Germany.
| | - David Holz
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, 91058 Erlangen, Germany
| | - Minh Tuan Duong
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, 91058 Erlangen, Germany; School of Mechanical Engineering, Hanoi University of Science and Technology, 1 DaiCoViet Road, Hanoi, Vietnam
| | - Sigrid Leyendecker
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, 91058 Erlangen, Germany
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Holz D, Martonová D, Schaller E, Duong MT, Alkassar M, Weyand M, Leyendecker S. Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations. J Biomech 2023; 156:111643. [PMID: 37321157 DOI: 10.1016/j.jbiomech.2023.111643] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2022] [Revised: 02/10/2023] [Accepted: 05/15/2023] [Indexed: 06/17/2023]
Abstract
It is well known that the orthotropic tissue structure decisively influences the mechanical and electrical properties of the heart. Numerous approaches to compute the orthotropic tissue structure in computational heart models have been developed in the past decades. In this study, we investigate to what extent different Laplace-Dirichlet-Rule-Based-Methods (LDRBMs) influence the local orthotropic tissue structure and thus the electromechanical behaviour of the subsequent cardiac simulation. In detail, we are utilising three Laplace-Dirichlet-Rule-Based-Methods and compare: (i) the local myofibre orientation; (ii) important global characteristics (ejection fraction, peak pressure, apex shortening, myocardial volume reduction, fractional wall thickening); (iii) local characteristics (active fibre stress, fibre strain). We observe that the orthotropic tissue structures for the three LDRBMs show significant differences in the local myofibre orientation. The global characteristics myocardial volume reduction and peak pressure are rather insensitive to a change in local myofibre orientation, while the ejection fraction is moderately influenced by the different LDRBMs. Moreover, the apical shortening and fractional wall thickening exhibit a sensitive behaviour to a change in the local myofibre orientation. The highest sensitivity can be observed for the local characteristics.
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Affiliation(s)
- David Holz
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, Erlangen, 91058, Germany.
| | - Denisa Martonová
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, Erlangen, 91058, Germany
| | - Emely Schaller
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, Erlangen, 91058, Germany
| | - Minh Tuan Duong
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, Erlangen, 91058, Germany; School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi, 1 DaiCoViet Road, Viet Nam
| | - Muhannad Alkassar
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Department of Cardiac Surgery, Krankenhausstraße 12, Erlangen, 91054, Germany
| | - Michael Weyand
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Department of Cardiac Surgery, Krankenhausstraße 12, Erlangen, 91054, Germany
| | - Sigrid Leyendecker
- Friedrich-Alexander-Universität Erlangen-Nürnberg, Institute of Applied Dynamics, Immerwahrstraße 1, Erlangen, 91058, Germany
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Martonová D, Holz D, Brackenhammer D, Weyand M, Leyendecker S, Alkassar M. Support Pressure Acting on the Epicardial Surface of a Rat Left Ventricle—A Computational Study. Front Cardiovasc Med 2022; 9:850274. [PMID: 35872914 PMCID: PMC9299250 DOI: 10.3389/fcvm.2022.850274] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2022] [Accepted: 05/31/2022] [Indexed: 11/13/2022] Open
Abstract
The present computational study investigates the effects of an epicardial support pressure mimicking a heart support system without direct blood contact. We chose restrictive cardiomyopathy as a model for a diseased heart. By changing one parameter representing the amount of fibrosis, this model allows us to investigate the impairment in a diseased left ventricle, both during diastole and systole. The aim of the study is to determine the temporal course and value of the support pressure that leads to a normalization of the cardiac parameters in diseased hearts. These are quantified via the end-diastolic pressure, end-diastolic volume, end-systolic volume, and ejection fraction. First, the amount of fibrosis is increased to model diseased hearts at different stages. Second, we determine the difference in the left ventricular pressure between a healthy and diseased heart during a cardiac cycle and apply for the epicardial support as the respective pressure difference. Third, an epicardial support pressure is applied in form of a piecewise constant step function. The support is provided only during diastole, only during systole, or during both phases. Finally, the support pressure is adjusted to reach the corresponding parameters in a healthy rat. Parameter normalization is not possible to achieve with solely diastolic or solely systolic support; for the modeled case with 50% fibrosis, the ejection fraction can be increased by 5% with purely diastolic support and 14% with purely systolic support. However, the ejection fraction reaches the value of the modeled healthy left ventricle (65.6%) using a combination of diastolic and systolic support. The end-diastolic pressure of 13.5 mmHg cannot be decreased with purely systolic support. However, the end-diastolic pressure reaches the value of the modeled healthy left ventricle (7.5 mmHg) with diastolic support as well as with the combination of the diastolic and systolic support. The resulting negative diastolic support pressure is −4.5 mmHg, and the positive systolic support pressure is 90 mmHg. We, thereby, conclude that ventricular support during both diastole and systole is beneficial for normalizing the left ventricular ejection fraction and the end-diastolic pressure, and thus it is a potentially interesting therapy for cardiac insufficiency.
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Affiliation(s)
- Denisa Martonová
- Institute of Applied Dynamics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
- *Correspondence: Denisa Martonová
| | - David Holz
- Institute of Applied Dynamics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Dorothea Brackenhammer
- Institute of Applied Dynamics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Michael Weyand
- Department of Cardiac Surgery, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Sigrid Leyendecker
- Institute of Applied Dynamics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
| | - Muhannad Alkassar
- Department of Cardiac Surgery, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
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