Quantifying uniaxial prestress and waveguide effects on dynamic elastography estimates for a cylindrical rod.

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of materials by noninvasively measuring mechanical wave motion in them. The target motion is typically transversely-polarized relative to the wave propagation direction, such as bulk shear wave motion. In addition to neglecting waveguide effects caused by small lengths in one dimension or more, many reconstruction strategies also ignore nonzero, non-isotropic static preloads. Significant anisotropic prestress is inherent to the functional role of some biological materials of interest, which also are small in size relative to shear wavelengths in one or more dimensions. A cylindrically shaped polymer structure with isotropic material properties is statically elongated along its axis while its response to circumferentially-, axially-, and radially-polarized vibratory excitation is measured using optical or magnetic resonance elastography. Computational finite element simulations augment and aid in the interpretation of experimental measurements. We examine the interplay between uniaxial prestress and waveguide effects. A coordinate transformation approach previously used to simplify the reconstruction of un-prestressed transversely isotropic material properties based on elastography measurements is adapted with partial success to estimate material viscoelastic properties and prestress conditions without requiring advanced knowledge of either.

Decoupling Uniaxial Tensile Prestress and Waveguide Effects From Estimates of the Complex Shear Modulus in a Cylindrical Structure Using Transverse-Polarized Dynamic Elastography.

Dynamic elastography, whether based on magnetic resonance, ultrasound, or optical modalities, attempts to reconstruct quantitative maps of the viscoelastic properties of biological tissue, properties altered by disease and injury, by noninvasively measuring mechanical wave motion in the tissue. Most reconstruction strategies that have been developed neglect boundary conditions, including quasi-static tensile or compressive loading resulting in a nonzero prestress. Significant prestress is inherent to the functional role of some biological tissues currently being studied using elastography, such as skeletal and cardiac muscle, arterial walls, and the cornea. In the present article a configuration, inspired by muscle elastography but generalizable to other applications, is analytically and experimentally studied. A hyperelastic polymer phantom cylinder is statically elongated in the axial direction while its response to transverse-polarized vibratory excitation is measured. We examine the interplay between uniaxial prestress and waveguide effects in this muscle-like tissue phantom using computational finite element simulations and magnetic resonance elastography measurements. Finite deformations caused by prestress coupled with waveguide effects lead to results that are predicted by a coordinate transformation approach that has been previously used to simplify reconstruction of anisotropic properties using elastography. Here, the approach estimates material viscoelastic properties that are independent of the nonhomogeneous prestress conditions without requiring advanced knowledge of those stress conditions.