A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements

Area of Science:

• Biomedical Engineering
• Medical Imaging
• Computational Mechanics

Background:

• Noninvasive quantification of soft tissue elasticity is vital for differentiating malignancy.
• Previous 2D mechanical inverse problem approaches faced ill-conditioning issues due to real-world data noise and configuration limitations.
• A stable and unique determination of shear moduli distribution was challenging.

Purpose of the Study:

• To address the ill-posed nature of 2D mechanical inverse problems in elasticity quantification.
• To develop a computationally efficient and robust numerical method for solving the differential inverse problem.
• To enable accurate, noninvasive diagnosis of soft tissue malignancy through elasticity imaging.

Main Methods:

• Developed a numerical-based implicit-integration approach.
• Incorporated a computationally efficient regularization method.
• Utilized low-pass filtered spectra from strain measurements for solving the inverse problem.
• Evaluated the method using intentionally ill-conditioned models.

Main Results:

• Demonstrated that analytic solutions to the 2D mechanical inverse problem are inherently ill-conditioned in practice.
• The newly developed numerical method provides robust reconstructions of global shear moduli distribution.
• The method effectively overcomes noise and configuration issues present in conventional ultrasound (US) or nuclear magnetic resonance (NMR) imaging data.

Conclusions:

• The developed implicit-integration approach offers a stable and unique solution for quantifying tissue elasticity.
• This method shows high potential as a versatile diagnostic tool for various soft tissues.
• It enables more accurate differentiation of malignancy in soft tissues.