Engineered cardiac tissue analyzed using the mechanical bidomain model

2023

Academia Biology

This article reviews the mechanical bidomain model, a mathematical description of how the extracellular matrix and intracellular cytoskeleton of cardiac tissue are coupled by integrin membrane proteins. The fundamental hypothesis is that the difference between the intracellular and extracellular displacements drives mechanotransduction. A one-dimensional example illustrates the model, which is then extended to two or three dimensions. In a few cases, the bidomain equations can be solved analytically, demonstrating how tissue motion can be divided into two parts: monodomain displacements that are the same in both spaces and therefore do not contribute to mechanotransduction, and bidomain displacements that cause mechanotransduction. The model contains a length constant that depends on the intracellular and extracellular shear moduli and the integrin spring constant. Bidomain effects often occur within a few length constants of the tissue edge. Unequal anisotropy ratios in the intra-and extracellular spaces can modulate mechanotransduction. Insight into model predictions is supplied by simple analytical examples, such as the shearing of a slab of cardiac tissue or the contraction of a tissue sheet. Computational methods for solving the model equations are described, and precursors to the model are reviewed. Potential applications are discussed, such as predicting growth and remodeling in the diseased heart, analyzing stretch-induced arrhythmias, modeling shear forces in a vessel caused by blood flow, examining the role of mechanical forces in engineered sheets of tissue, studying differentiation in colonies of stem cells, and characterizing the response to localized forces applied to nanoparticles.

Section: Extending the Mechanical Bidomain Model To Two Dimensionsmentioning

confidence: 99%

Section: Incompressibilitymentioning

confidence: 99%

See 1 more Smart Citation

A mathematical model of mechanotransduction

2023

Academia Biology

Bidomain modeling of electrical and mechanical properties of cardiac tissue

2021

Biophysics Reviews

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. Introduced from a historical perspective, the origins of the bidomain model are reviewed to provide a foundation for researchers new to the field and those conducting interdisciplinary research. The interplay of theory and experiment with the bidomain model is explored, and the contributions of this model to cardiac biophysics are critically evaluated. Also discussed is the mechanical bidomain model, which is employed to describe mechanotransduction. Current challenges and outstanding questions in the use of the bidomain model are addressed to give a forward-facing perspective of the model in future studies.

Indentation of Anisotropic Tissue Using a Three-Dimensional Mechanical Bidomain Model

Wijesinghe¹,

2022

Fibers

Computation-based mathematical models of tissue indentation are capable of predicting the distribution of forces and mechanical properties of soft tissues. This paper presents a three-dimensional mathematical model of anisotropic tissue indentation developed using the mechanical bidomain model. The mechanical bidomain model hypothesizes that the relative displacement between intra- and extracellular spaces triggers a force on the mechanosensitive proteins in the membrane: integrins. Some soft tissues, such as cardiac muscle, are anisotropic, a property which arises from the fibrous structure of the tissue. The degree of anisotropy in intra- and extracellular spaces can be different. Tissue indentation for different anisotropy ratios that indicate isotropy, equal anisotropy and unequal anisotropy, were tested using the model. Results of the tissue indentation analysis compared the spatial distribution of the magnitude of bidomain displacement for different anisotropy conditions between monodomain and bidomain models. The proposed mathematical model predicted unexpected spatial patterns of cardiac mechanotransduction for unequal anisotropy ratios of mechanical modulus.