Field and Impedance of an Oscillating Sphere in a Viscoelastic Medium with an Application to Biophysics

Abstract

With an application to human tissue in view, a theoretical analysis of the behavior of mechanical vibrations in a medium with elastic, viscous, and relaxational properties is made. For this purpose, the equations of wave motion in a viscoelastic medium are discussed in general and solved for two problems, which are significant for the propagation and the transfer of vibrational energy: (1) energy propagation and absorption in plane waves, (2) field and impedance of an oscillating sphere. The results show that the energy is propagated in two kinds of waves, the relative intensities of which change strongly with frequency: transverse waves, owing to the shear elasticity and viscosity, and compression (acoustical) waves, owing to the volume compressibility of the medium. A more detailed treatment is then accomplished for human muscle tissue by inserting the approximate values of its elastic constants into the general formulas, thus explaining the behavior in a frequency range from 0 up to several hundred kc.