A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation
In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient co...
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doaj-655ed24c998d41eb924dbb0a1577eb972021-08-13T10:30:21ZengFrontiers Media S.A.Frontiers in Physiology1664-042X2021-08-011210.3389/fphys.2021.712816712816A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart SimulationKazunori Yoneda0Jun-ichi Okada1Jun-ichi Okada2Masahiro Watanabe3Seiryo Sugiura4Toshiaki Hisada5Takumi Washio6Takumi Washio7Section Solutions Division, Healthcare Solutions Development Unit, Fujitsu Japan Ltd., Tokyo, JapanUT-Heart Inc., Kashiwa, JapanFuture Center Initiative, University of Tokyo, Kashiwa, JapanSection Solutions Division, Healthcare Solutions Development Unit, Fujitsu Japan Ltd., Tokyo, JapanUT-Heart Inc., Kashiwa, JapanUT-Heart Inc., Kashiwa, JapanUT-Heart Inc., Kashiwa, JapanFuture Center Initiative, University of Tokyo, Kashiwa, JapanIn a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.https://www.frontiersin.org/articles/10.3389/fphys.2021.712816/fullheart simulationMonte Carlo methodfinite element methodexcitation contraction couplingmultiple time step methodactive stiffness |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Kazunori Yoneda Jun-ichi Okada Jun-ichi Okada Masahiro Watanabe Seiryo Sugiura Toshiaki Hisada Takumi Washio Takumi Washio |
spellingShingle |
Kazunori Yoneda Jun-ichi Okada Jun-ichi Okada Masahiro Watanabe Seiryo Sugiura Toshiaki Hisada Takumi Washio Takumi Washio A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation Frontiers in Physiology heart simulation Monte Carlo method finite element method excitation contraction coupling multiple time step method active stiffness |
author_facet |
Kazunori Yoneda Jun-ichi Okada Jun-ichi Okada Masahiro Watanabe Seiryo Sugiura Toshiaki Hisada Takumi Washio Takumi Washio |
author_sort |
Kazunori Yoneda |
title |
A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation |
title_short |
A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation |
title_full |
A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation |
title_fullStr |
A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation |
title_full_unstemmed |
A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation |
title_sort |
multiple step active stiffness integration scheme to couple a stochastic cross-bridge model and continuum mechanics for uses in both basic research and clinical applications of heart simulation |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Physiology |
issn |
1664-042X |
publishDate |
2021-08-01 |
description |
In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction. |
topic |
heart simulation Monte Carlo method finite element method excitation contraction coupling multiple time step method active stiffness |
url |
https://www.frontiersin.org/articles/10.3389/fphys.2021.712816/full |
work_keys_str_mv |
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