Abstract
We aim to extend existing models of single-cell mechanics to the EMI framework, to define spatially resolved mechanical models of cardiac myocytes embedded in a passive extracellular space. The models introduced here will be pure mechanics models employing fairly simple constitutive laws for active and passive mechanics. Future extensions of the models may include a coupling to the electrophysiology and electro-diffusion models described in the other chapters, to study the impact of spatially heterogeneous ion concentrations on the cell and tissue mechanics.
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Ambrosi D, Pezzuto S (2012) Active stress vs. active strain in mechanobiology: constitutive issues. Journal of Elasticity 107(2):199–212
2. Campbell KS (2009) Interactions between connected half-sarcomeres produce emergent mechanical behavior in a mathematical model of muscle. PLoS computational biology 5(11):e1000560
3. Campbell SG, Lionetti FV, Campbell KS, McCulloch AD (2010) Coupling of adjacent tropomyosins enhances cross-bridge-mediated cooperative activation in a markov model of the cardiac thin filament. Biophysical journal 98(10):2254–2264
4. Chase PB, Macpherson JM, Daniel TL (2004) A spatially explicit nanomechanical model of the half-sarcomere: myofilament compliance affects ca 2+-activation. Annals of biomedical engineering 32(11):1559–1568
5. Guccione J, McCulloch A,Waldman L (1991) Passive material properties of intact ventricular myocardium determined from a cylindrical model. Journal of Biomechanical Engineering 113(1):42–55, https://doi.org/10.1115/1.2894084
Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering.Wiley
7. Jæger KH, Tveito A (2020) Derivation of a cell-based mathematical model of excitable cells. In: Tveito A, Mardal KA, Rognes ME (eds) Modeling excitable tissue - The EMI framework, Simula Springer Notes in Computing, SpringerNature
8. Laadhari A, Ruiz-Baier R, Quarteroni A (2013) Fully eulerian finite element approximation of a fluid-structure interaction problem in cardiac cells. Int J Numer Meth Engng 96:712–738
9. LeGrice IJ, Smaill B, Chai L, Edgar S, Gavin J, Hunter PJ (1995) Laminar structure of the heart: ventricularmyocyte arrangement and connective tissue architecture in the dog. American Journal of Physiology-Heart and Circulatory Physiology 269(2):H571–H582
Mijailovich SM, Nedic D, Svicevic M, Stojanovic B,Walklate J, Ujfalusi Z, GeevesMA(2017) Modeling the actin. myosin atpase cross-bridge cycle for skeletal and cardiac muscle myosin isoforms. Biophysical journal 112(5):984–996
11. Nakagome K, Sato K, Shintani SA, Ishiwata S (2016) Model simulation of the spoc wave in a bundle of striated myofibrils. Biophysics and physicobiology 13:217–226
12. Nash MP, Panfilov AV (2004) Electromechanical model of excitable tissue to study re-entrant cardiac arrhythmias. Progress in Biophysics and Molecular Biology 85(2-3):501–522
13. Rice JJ,Wang F, Bers DM, de Tombe PP (2008) Approximate Model of Cooperative Activation and Crossbridge Cycling in Cardiac Muscle Using Ordinary Differential Equations. Biophysical Journal 95(5):2368–2390
14. Ruiz-Baier R, Gizzi A, Rossi S, Cherubinie C, Laadhari A, Filippi S, Quarterone A (2014) Mathematical modelling of active contraction in isolated cardiomyocytes. Mathematical medicine and biology 31:259–283
Sundnes J, Lines GT, Cai X, Nielsen BF, Mardal KA, Tveito A (2007) Computing the electrical activity in the heart, vol 1. Springer Science & Business Media
Telle Å (2020) Software for EMI – Modeling cardiac mechanics on a sub-cellular scale. https://doi.org/10.5281/zenodo.3702168, URL https://doi.org/10.5281/zenodo.3702168
17. Tveito A, Jæger KH, Lines GT, Paszkowski Ł, Sundnes J, Edwards AG, M¯aki-Marttunen T, Halnes G, Einevoll GT (2017) An evaluation of the accuracy of classical models for computing the membrane potential and extracellular potential for neurons. Frontiers in computational neuroscience 11:27
Tveito A, Jager KH, Kuchta M, Mardal KA, Rognes ME (2017) A cell-based framework for numerical modeling of electrical conduction in cardiac tissue. Frontiers in Physics 5:48, https://doi.org/10.3389/fphy.2017.00048, URL https://www.frontiersin.org/article/10.3389/fphy.2017.00048
19. Usyk TP, LeGrice IJ, McCulloch AD (2002) Computational model of three-dimensional cardiac electromechanics. Computing and Visualization in Science 4(4):249–257
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Telle, Å., Wall, S.T., Sundnes, J. (2021). Modeling Cardiac Mechanics on a Sub-Cellular Scale. In: Tveito, A., Mardal, KA., Rognes, M.E. (eds) Modeling Excitable Tissue. Simula SpringerBriefs on Computing(), vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-61157-6_3
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