Nonlinear torsional wave propagation in cylindrical coordinates to assess biomechanical parameters

A formulation in cylindrical coordinates of the nonlinear torsional wave propagation on a hyperelastic material characterized by Hamilton's strain energy function is proposed. The objective of this formulation is to study and assess soft tissues, taking into account both geometrical and physical nonlinearity. Specifically, this work analyzes the propagation of torsional shear waves through an isotropic axisymmetric medium, so the only non-zero velocity component is associated with the angular coordinate. To transform the equations from Cartesian to cylindrical coordinates, the covariant and contravariant transformations are employed. A transverse torsional wave propagating through a quasi-incompressible hydrogel from the emitter to the receiver is considered. As the close form solution is not straightforward, a numerical simulation using the Finite Difference Time Domain method is performed. The results are obtained for a realistic range of wave frequencies and nonlinear parameters for medical applications.