Elastic properties of the composite outer hair cell wall

We propose a mathematical model for analyses of the elastic properties of the wall of the outer hair cell (OHC) in the inner ear. The model reflects the properties of the major components of the OHC wall: the subsurface cisternae, the cortical lattice, the plasma membrane, and the radial pillars. The wall is treated as a composite consisting of three elastic cylindrical shells. Two inner shells, isotropic and orthotropic/ are adjacent to each other, and the outermost isotropic shell is connected to the combined inner shell by elastic springs. We derive Flugge-type equations for the composite wall and apply the model to the interpretation of the experiments with axial loading and with inflation of the OHC. We derive expressions for the axial stiffness and the wall strains measured in these experiments in terms of the elastic properties of the wall components. We also consider a conceivable experiment with torsion of the OHC and obtain relations between the torque (the axial reaction) and the angle of torsion. These solutions provide necessary information for the future determination of the OHC elastic properties.