Strain imaging was the first attempt to infer the mechanical property composition of tissues [2] based on the assumption that the stress distribution is uniform in the problem domain. This concept evolved to solving actual mathematical problems for the mechanical property distribution using measured displacement fields and is referred to as inverse problems in solid mechanics. Displacements are often measured using ultrasound based techniques that utilize sequentially recorded images during tissue deformation. This technique relies on random speckles in the tissue’s domain of interest to track displacements on grid points via “window” similarities. The discrete displacement points are then interpolated throughout the entire problem domain to continuously determine the displacement field.

The solution of the mechanical property distribution discussed above utilizes full field displacement fields, i.e., displacement fields measured in the entire domain. An alternative approach we propose here is to utilize displacements measured solely on the domain’s boundary. This idea has been successfully developed in other disciplines, namely in computed tomography, ultrasound tomography [3], and geological sciences. Consequently, we term this methodology as “

We note that past works by other research groups aiming to recover the mechanical property distribution from measured surface displacements made major simplifications. In those works, it was assumed that the shear modulus values in the problem domain (e.g., background value and inclusion value) were known, but they were unknown within each finite element. Other works assumed the locally homogenous regions (e.g., location and geometry of inclusions) to be known. In our studies, we do not make such assumptions and assume that the shear moduli are unknowns on the finite element mesh nodes. In the problem presented in this talk, we will solve for more than 50,000 unknowns in the problem domain. With that, the proposed method is not confined to simple inclusion geometries, but allows distributions of any type. KW - Mechanical Property Characterization; inverse problems; computational mechanics; mechanics based tomography; elasticity imaging; elastography DO - 10.32604/mcb.2019.07348