Nonlinear Oscillation of Biological Membrane: A Lumped Parameter Modelling Approach

The current study proposes the dynamics of a biological membrane in response to electromechanical stimuli considering the mass of the membrane. A membrane’s dynamical aspect is particularly challenging to analyse due to its complex structure and changing material properties. Furthermore, the presence of an electric field affects critical aspects of biological membranes such as thickness, density, tension and curvature. The effect of the electric field on the membrane’s thickness is considered for the current analysis. The membrane is modelled as a dielectric sandwiched between electrodes to demonstrate the electromechanical coupling. Fung’s exponential material model is employed to depict the membrane’s nonlinear elastic behaviour. The governing equation for the system is then derived using lumped parameter model. The analysis is presented in terms of two dimensionless force parameters. The variation of these parameters shows changes in the corresponding dynamic behaviour. The proposed work will aid in demonstrating the dynamics of the biological membrane under the influence of an electrical field for bio-mimicking applications.