MatNLI: An open-source MATLAB-based solver for the non-linear inversion in elastography

Abstract

Elastography has emerged as one of the most promising non-invasive clinical tools. In elastography, a stiffness map or elastogram is generated by solving an inverse problem of elasticity utilizing the tissue motion data acquired using magnetic resonance imaging or ultrasound. Among various inverse algorithms devoted to elastography, non-linear inversion coupled with the finite element method has demonstrated excellent applicability in extracting complex physics of the tissue. The development and implementation of such an inverse algorithm are challenging and often unavailable to clinicians. In the present work, we offer an open-source parallel MATLAB implementation of an efficient non-linear inversion algorithm based on the finite element method for different isotropic material models, viz., linear elastic and viscoelastic materials in the regime of compressible and nearly incompressible materials. Additionally, the framework has been extended to account for anisotropy by assuming transversely isotropic material. For the optimization module, the gradient of the objective function to the model parameters has been computed using the Adjoint method. Different case studies involving smooth variations and piece-wise discontinuities in the material property distribution are explored, and the efficacy of the inversion algorithm in reconstructing the stiffness map is discussed. In addition, noise is added to the synthetic data to depict a realistic setup, i.e., to prevent inverse crimes, and enhance the numerical stability and robustness of the current implementation. The present framework with general-purpose computer implementation could be beneficial for academic and clinical uses and may aid researchers in strengthening their existing frameworks and developing new algorithmic ideas.