Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles
This work concerns the mathematical and numerical modeling of the heart. The aim is to enhance the understanding of the cardiac function in both physiological and pathological conditions. Along this road, a challenge arises from the multi-scale and multi-physics nature of the mathematical problem at...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2020-10-01
|
| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/10.3934/mine.2020028/fulltext.html |
| _version_ | 1818245454478966784 |
|---|---|
| author | Luca Azzolin Luca Dedè Antonello Gerbi Alfio Quarteroni |
| author_facet | Luca Azzolin Luca Dedè Antonello Gerbi Alfio Quarteroni |
| author_sort | Luca Azzolin |
| collection | DOAJ |
| description | This work concerns the mathematical and numerical modeling of the heart. The aim is to enhance the understanding of the cardiac function in both physiological and pathological conditions. Along this road, a challenge arises from the multi-scale and multi-physics nature of the mathematical problem at hand. In this paper, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. In this paper, we study the influence of different fibre directions and incompressibility constraint and penalization on the compressibility of the material (bulk modulus) on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific biventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show how various fibre configurations and bulk modulus modify relevant clinical quantities such as stroke volume, ejection fraction and ventricle contractility. |
| first_indexed | 2024-12-12T14:33:10Z |
| format | Article |
| id | doaj.art-aebb365c2bb641ed8b6829d499db37e3 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-12T14:33:10Z |
| publishDate | 2020-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-aebb365c2bb641ed8b6829d499db37e32022-12-22T00:21:27ZengAIMS PressMathematics in Engineering2640-35012020-10-012461463810.3934/mine.2020028Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventriclesLuca Azzolin0Luca Dedè1Antonello Gerbi2Alfio Quarteroni31 Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 1, D-76131, Karlsruhe, Germany2 Modeling and Scientific Computing (MOX), Mathematics Department, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy3 Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Avenue Piccard, CH-1015, Lausanne, Switzerland2 Modeling and Scientific Computing (MOX), Mathematics Department, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milan, Italy 3 Institute of Mathematics, École Polytechnique Fédérale de Lausanne, Avenue Piccard, CH-1015, Lausanne, SwitzerlandThis work concerns the mathematical and numerical modeling of the heart. The aim is to enhance the understanding of the cardiac function in both physiological and pathological conditions. Along this road, a challenge arises from the multi-scale and multi-physics nature of the mathematical problem at hand. In this paper, we propose an electromechanical model that, in bi-ventricle geometries, combines the monodomain equation, the Bueno-Orovio minimal ionic model, and the Holzapfel-Ogden strain energy function for the passive myocardial tissue modelling together with the active strain approach combined with a model for the transmurally heterogeneous thickening of the myocardium. Since the distribution of the electric signal is dependent on the fibres orientation of the ventricles, we use a Laplace-Dirichlet Rule-Based algorithm to determine the myocardial fibres and sheets configuration in the whole bi-ventricle. In this paper, we study the influence of different fibre directions and incompressibility constraint and penalization on the compressibility of the material (bulk modulus) on the pressure-volume relation simulating a full heart beat. The coupled electromechanical problem is addressed by means of a fully segregated scheme. The numerical discretization is based on the Finite Element Method for the spatial discretization and on Backward Differentiation Formulas for the time discretization. The arising non-linear algebraic system coming from application of the implicit scheme is solved through the Newton method. Numerical simulations are carried out in a patient-specific biventricle geometry to highlight the most relevant results of both electrophysiology and mechanics and to compare them with physiological data and measurements. We show how various fibre configurations and bulk modulus modify relevant clinical quantities such as stroke volume, ejection fraction and ventricle contractility.https://www.aimspress.com/article/10.3934/mine.2020028/fulltext.htmlheart modellingcoupled problemelectromechanicsfinite element methodventriclesfibre orientation |
| spellingShingle | Luca Azzolin Luca Dedè Antonello Gerbi Alfio Quarteroni Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles Mathematics in Engineering heart modelling coupled problem electromechanics finite element method ventricles fibre orientation |
| title | Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles |
| title_full | Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles |
| title_fullStr | Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles |
| title_full_unstemmed | Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles |
| title_short | Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles |
| title_sort | effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles |
| topic | heart modelling coupled problem electromechanics finite element method ventricles fibre orientation |
| url | https://www.aimspress.com/article/10.3934/mine.2020028/fulltext.html |
| work_keys_str_mv | AT lucaazzolin effectoffibreorientationandbulkmodulusontheelectromechanicalmodellingofhumanventricles AT lucadede effectoffibreorientationandbulkmodulusontheelectromechanicalmodellingofhumanventricles AT antonellogerbi effectoffibreorientationandbulkmodulusontheelectromechanicalmodellingofhumanventricles AT alfioquarteroni effectoffibreorientationandbulkmodulusontheelectromechanicalmodellingofhumanventricles |