Mechanotransduction caused by a point force in the extracellular space

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.