2D boundary-condition-free nonlinear inversion technique applied to optical shear vibration induced microelastography

Abstract

Optical microelastography (OME) has emerged as a new technique for quantifying cellular mechanical properties. However, accurately reconstructing viscoelastic properties at the microscale level from noisy 2D displacement fields remains a challenge. This study introduces a 2D boundary-condition-free nonlinear inversion (2D-NoBC-NLI) approach, addressing challenges of interpreting noisy data and deducing full-field 3D displacements from 2D measurements. OME requires vibrating the cell and mapping the shear modulus based on wave-induced displacements within the cell. The shear modulus distribution is recovered via a coupled adjoint field NLI reconstruction to allow 2D-NoBC-NLI. Validation was conducted through numerical simulations at 36 kHz on a homogeneous sphere of 75 μm diameter and an assigned viscoelastic modulus, G*, of 800 + i150 Pa. The same reconstruction approach was also applied to experimental data obtained from polyacrylamide (PAAm) microbeads of the same diameter. Results demonstrated relative differences from true simulated values of 0.7% and 45% for storage and loss moduli, respectively, with a coefficient of variation under 1% for homogeneous regions. When applying this method to PAAm microbeads, viscoelastic reconstructions showed the potential of OME under experimental conditions. These findings highlight the accuracy of 2D-No BC-NLI reconstruction in OME for precise microscale characterization and mapping of the viscoelastic cell structure.