Modified error in constitutive equations (MECE) approach for ultrasound elastography

A partial differential equation-constrained optimization approach is presented for reconstructing mechanical properties (e.g., elastic moduli). The proposed method is based on the minimization of an error in constitutive equations functional augmented with a least squares data misfit term referred to as MECE for "modified error in constitutive equations." The main theme of this paper is to demonstrate several key strengths of the proposed method on experimental data. In addition, some illustrative examples are provided where the proposed method is compared with a common shear wave elastography (SWE) approach. To this end, both synthetic data, generated with transient finite element simulations, as well as ultrasonically tracked displacement data from an acoustic radiation force (ARF) experiment are used in a standard elasticity phantom. The results indicate that the MECE approach can produce accurate shear modulus reconstructions with significantly less bias than SWE.