Quantitative Imaging of Young's Modulus of Soft Tissues from Ultrasound Water Jet Indentation: A Finite Element Study

Indentation testing is a widely used approach to evaluate mechanical characteristics of soft tissues quantitatively. Young's modulus of soft tissue can be calculated from the force-deformation data with known tissue thickness and Poisson's ratio using Hayes' equation. Our group previously developed a noncontact indentation system using a water jet as a soft indenter as well as the coupling medium for the propagation of high-frequency ultrasound. The novel system has shown its ability to detect the early degeneration of articular cartilage. However, there is still lack of a quantitative method to extract the intrinsic mechanical properties of soft tissue from water jet indentation. The purpose of this study is to investigate the relationship between the loading-unloading curves and the mechanical properties of soft tissues to provide an imaging technique of tissue mechanical properties. A 3D finite element model of water jet indentation was developed with consideration of finite deformation effect. An improved Hayes' equation has been derived by introducing a new scaling factor which is dependent on Poisson's ratios v, aspect ratio a/h (the radius of the indenter/the thickness of the test tissue), and deformation ratio d/h. With this model, the Young's modulus of soft tissue can be quantitatively evaluated and imaged with the error no more than 2%.