Regional Shear Wave Speeds Track Regional Axial Stress in Nonuniformly Loaded Fibrous Soft Tissues

Abstract

Ligaments and tendons undergo nonuniform deformation during movement. While deformations can be imaged, it remains challenging to use such information to infer regional tissue loading. Shear wave tensiometry is a promising noninvasive technique to gauge axial stress and is premised on a tensioned beam model. However, it is unknown whether tensiometry can predict regional stress in a nonuniformly loaded structure. The objectives of this study were to (1) determine the relationship between regional shear wave speed and regional axial stress, and (2) determine the sensitivity of regional axial stress and regional shear wave speed measurements to nonuniform load distribution and fiber alignment in the presence of variable tissue geometry and constitutive properties. We created a representative set of 12,000 dynamic finite element models of a fibrous soft tissue with probabilistic variations in fiber alignment, stiffness, and aspect ratio. In each model, we applied a randomly selected, nonuniform load distribution, and then excited a shear wave and tracked its regional propagation. We found that regional shear wave speed was an excellent predictor of the regional axial stress (RMSE=0.55 MPa) and that the nature of the wave speed-stress relationship was consistent with a tensioned beam model (R² = 0.99). Variations in tissue geometry, nonuniform loading, fiber material properties, and fiber alignment did not substantially alter the wave speed-stress relationship, particularly at higher loads.  Thus, these finding suggests that shear wave tensiometry could provide for a quantitative estimate of regional tissue stress in ligaments and tendons.