In the heart, cardiac muscle fibers curve creating zones of membrane forces resulting in regions of mechanotransduction. This study uses the finite difference method to solve the mechanical bidomain equations numerically for a complex fiber geometry. The magnitude of the active tension T is constant but its direction makes an angle with the x-axis that varies with position. Differences between the intracellular and extracellular displacements result from the bidomain behavior of the tissue that gives rise to forces on the integrin proteins in the membrane. The long-term goal is to use the mechanical bidomain model to suggest experiments and make predictions about growth and remodeling in the heart.
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http://dx.doi.org/10.1088/1478-3975/aadacd | DOI Listing |
J Theor Biol
January 2024
Zu Chongzhi Center for Mathematics and Computational Sciences (CMCS), Duke Kunshan University, Kunshan, 215316, China. Electronic address:
Communication via action potentials among neurons has been extensively studied. However, effective communication without action potentials is ubiquitous in biological systems, yet it has received much less attention in comparison. Multi-cellular communication among smooth muscles is crucial for regulating blood flow, for example.
View Article and Find Full Text PDFInt J Numer Method Biomed Eng
February 2023
Chair of Continuum Mechanics, Ruhr University Bochum, Bochum, Germany.
We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude-found in a previous one-dimensional analytical study by Spiteri and Ziaratgahi-to construct the new time step controller for three-dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step.
View Article and Find Full Text PDFBiophys Rev (Melville)
December 2021
Department of Physics, Oakland University, Rochester, Michigan 48309, USA.
Throughout the history of cardiac research, there has been a clear need to establish mathematical models to complement experimental studies. In an effort to create a more complete picture of cardiac phenomena, the bidomain model was established in the late 1970s to better understand pacing and defibrillation in the heart. This mathematical model has seen ongoing use in cardiac research, offering mechanistic insight that could not be obtained from experimental pursuits.
View Article and Find Full Text PDFIEEE Trans Ultrason Ferroelectr Freq Control
June 2020
With the recent thriving of low-power electronic microdevices and sensors, the development of components capable of scavenging environmental energy has become imperative. In this article, we studied bidomain congruent LiNbO (LN) single crystals combined with magnetic materials for dual, mechanical, and magnetic energy harvesting applications. A simple magneto-mechano-electric composite cantilever, with a trilayered long-bar bidomain LN/spring-steel/metglas structure and a large tip proof permanent magnet, was fabricated.
View Article and Find Full Text PDFPhys Rev E
December 2019
Department of Physics, Oakland University, Rochester, Michigan 48309, USA.
The properties of cardiac muscle are anisotropic, and the degree of anisotropy may be different in the intracellular and extracellular spaces. In the electrical bidomain model, such "unequal anisotropy ratios" of the conductivity lead to unanticipated behavior. In the mechanical bidomain model, unequal anisotropy ratios of the mechanical moduli might also result in unanticipated behavior.
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