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

• Published in: Advances in engineering software (1992) Vol. 181; p. 103476
• Main Authors: Awasthi, Abhilash, Dinachandra, Moirangthem, Mahajan, Puneet, Suri, Ashish, Roy, Sitikantha
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2023
• Subjects: Adjoint methods; Elasticity imaging; Elastography; Inverse elasticity; Non-invasive clinical diagnosis; Elasticity imaging; Non-invasive clinical diagnosis; Adjoint methods; Elastography; Inverse elasticity
• ISSN: 0965-9978
• DOI: 10.1016/j.advengsoft.2023.103476

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. •An open-source framework for the Non-linear Inversion used in elastography is presented.•The framework has been successfully implemented with numerous examples considering isotropic and anisotropic material models.•A computationally efficient adjoint method of gradient calculation has been employed to reduce the computational cost.•The algorithm utilizes only Dirichlet boundary conditions, making it suitable for other elastography-based applications.•An efficient MATLAB-based parallel implementation is provided for the further development of the framework.