Intracellular, extracellular, and membrane forces in remodeling and mechanotransduction: The mechanical bidomain model

Sharma, Kharananda; Al-Asuoad, Nofe; Shillor, Meir; Roth, Bradley J.

doi:10.1166/jcsmd.2015.1079

Cited by 8 publications

(12 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Each expression for the displacement contains a monodomain term (first term in the brace) that is the same in the intra-and extracellular spaces, and two bidomain terms that are different in the two spaces (one is -ν/µ times the other). The first bidomain term is proportional to σ 2 , where σ = νµ K(ν+µ) is a length constant characteristic of the mechanical bidomain model [15]. The exponential in the second bidomain term decays with length constant σ.…”

Section: Resultsmentioning

confidence: 99%

“…The displacements (Eqs. [13][14][15][16] have interesting properties as r goes to zero. If you expand the exponential as a Taylor series, you will find that the terms in the expression for the intracellular displacement that are singular at the origin cancel and it remains finite there.…”

Section: Resultsmentioning

confidence: 99%

“…The fundamental hypothesis of the mechanical bidomain model is that mechanotransduction depends on the difference uw [15]. The monodomain terms are the same in the two spaces and do not contribute to uw; only the bidomain terms generate the displacement difference that drives mechanotransduction,…”

Section: Resultsmentioning

confidence: 99%

“…The figure illustrates a two-dimensional version of the model, but this article analyzes a three-dimensional version. [11], [15]. It predicts displacements of the intraand extracellular spaces individually.…”

Section: Introductionmentioning

confidence: 99%

“…Similar stress-strain relationships exist for the extracellular pressure q and extracellular shear modulus µ. The equations of mechanical equilibrium are [10], [15] −…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Mechanotransduction caused by a point force in the extracellular space

Roth

2018

BIOMATH

View full text Add to dashboard Cite

The mechanical bidomain model is a mathematical description of biological tissue that focuses on mechanotransduction. The model’s fundamental hypothesis is that differences in the intracellular and extracellular displacements activate integrins, causing a cascade of biological effects. This paper presents analytical solutions of the bidomain equations for an extracellular point force. The intra- and extracellular spaces are incompressible, isotropic, and coupled. The expressions for the intra- and extracellular displacements each contain three terms: a monodomain term that is identical in the two spaces, and two bidomain terms, one of which decays exponentially. Near the origin the intracellular displacement remains finite and the extracellular displacement diverges. Far from the origin the monodomain displacement decays in inverse proportion to the distance, the strain decays as the distance squared, and the difference between the intra- and extracellular displacements decays as the distance cubed. These predictions could be tested by applying a force to a magnetic nanoparticle embedded in the extracellular matrix and recording the mechanotransduction response.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Similar stress-strain relationships exist for the extracellular pressure q and extracellular shear modulus µ. The equations of mechanical equilibrium are [10], [15] −…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Mechanotransduction caused by a point force in the extracellular space

Roth

2018

BIOMATH

View full text Add to dashboard Cite

show abstract

Prediction of Stem Cell Differentiation for Cardiac Tissue Engineering Using the Finite Element Method (FEM)

Souza,

Carbonari,

Simbara

2023

IFMBE Proceedings

View full text Add to dashboard Cite

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Roth

2021

Biophysics Reviews

View full text Add to dashboard Cite

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.

show abstract

Intracellular, extracellular, and membrane forces in remodeling and mechanotransduction: The mechanical bidomain model

Cited by 8 publications

References 0 publications

Mechanotransduction caused by a point force in the extracellular space

Mechanotransduction caused by a point force in the extracellular space

Prediction of Stem Cell Differentiation for Cardiac Tissue Engineering Using the Finite Element Method (FEM)

Bidomain modeling of electrical and mechanical properties of cardiac tissue

Contact Info

Product

Resources

About