Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles

Azzolin, Luca; Dedè, Luca; Gerbi, Antonello; Quarteroni, Alfio

doi:10.3934/mine.2020028

Cited by 9 publications

(7 citation statements)

References 30 publications

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“…We consider a phenomenological law that keeps into account the local shortening of the fibers γ f at the macroscopic level [9,23,54,55]. Myocardial displacement d and concentration of intracellular calcium ions [Ca 2+ ] i play an important role in the time evolution of γ f .…”

Section: Mechanical Activationmentioning

confidence: 99%

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

Salvador¹,

Fedele²,

Africa³

et al. 2021

Computers in Biology and Medicine

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Section: Mechanical Activationmentioning

confidence: 99%

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

Salvador¹,

Fedele²,

Africa³

et al. 2021

Computers in Biology and Medicine

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“…For this reason, we first setup such calibration procedure for the parameters associated with XB cycling (i.e. (11) or (21)) and, successively, we calibrate the parameters associated with RU activation (i.e. (5) or (15)), so that we can directly see the effect of changes of such parameters on the resulting force (the remaining parameters are automatically adjusted).…”

Section: Parameters Calibrationmentioning

confidence: 99%

“…This is mainly due to the multiphysics (due to the interplay of biochemistry, electricity, solid mechanics, fluid dynamics) and multiscale nature of the heart: characteristic spatial scales range from nanometers to centimeters and the temporal ones from microseconds to seconds. This makes it difficult to devise computationally efficient and accurate algorithms for a plurality of mathematical models featuring a broad degree of details [5,[7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Biophysically detailed mathematical models of multiscale cardiac active mechanics

2020

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We propose four novel mathematical models, describing the microscopic mechanisms of force generation in the cardiac muscle tissue, which are suitable for multiscale numerical simulations of cardiac electromechanics. Such models are based on a biophysically accurate representation of the regulatory and contractile proteins in the sarcomeres. Our models, unlike most of the sarcomere dynamics models that are available in the literature and that feature a comparable richness of detail, do not require the time-consuming Monte Carlo method for their numerical approximation. Conversely, the models that we propose only require the solution of a system of PDEs and/or ODEs (the most reduced of the four only involving 20 ODEs), thus entailing a significant computational efficiency. By focusing on the two models that feature the best trade-off between detail of description and identifiability of parameters, we propose a pipeline to calibrate such parameters starting from experimental measurements available in literature. Thanks to this pipeline, we calibrate these models for room-temperature rat and for body-temperature human cells. We show, by means of numerical simulations, that the proposed models correctly predict the main features of force generation, including the steady-state force-calcium and force-length relationships, the lengthdependent prolongation of twitches and increase of peak force, the force-velocity relationship. Moreover, they correctly reproduce the Frank-Starling effect, when employed in multiscale 3D numerical simulation of cardiac electromechanics.

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“…Although previous efforts to construct numerical models using a type of mean field approximation have successfully reproduced specific tissue-level phenomena (Hunter et al, 1998;Niederer et al, 2006;Negroni and Lascano, 2008;Rice et al, 2008;Guérin et al, 2011;Chapelle et al, 2012;Washio et al, 2012;Syomin and Tsaturyan, 2017;Regazzoni et al, 2018;Caruel et al, 2019), these models have not yet been fully exploited in real-life heart simulations. The uses of ordinary differential equation (ODE) models that adopt the phenomenological approximations of the force-pCa relationship and the force-velocity relationship have become mainstream instead (Smith et al, 2004;Kerckhoffs et al, 2007;Gurev et al, 2011;Shavik et al, 2017;Dabiri et al, 2019;Azzolin et al, 2020;Regazzoni et al, 2020). However, these approaches appear to have difficulties, particularly in reproducing the realistic relaxation phase that is important to ease the influx of blood from the atria to the ventricles.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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Effect of fibre orientation and bulk modulus on the electromechanical modelling of human ventricles

Cited by 9 publications

References 30 publications

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

Electromechanical modeling of human ventricles with ischemic cardiomyopathy: numerical simulations in sinus rhythm and under arrhythmia

Biophysically detailed mathematical models of multiscale cardiac active mechanics

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

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