Optical microelastography via a 2D boundary condition-free nonlinear inversion approach

The mechanical phenotype of a cell, including its viscoelastic properties, is recognized as a label-free biomarker for diagnosing cellular states. Optical microelastography (OME) assesses intracellular mechanical heterogeneity by mapping the shear modulus distribution within cells using time-harmonic elastic waves observed within an optical image plane. However, reconstructing viscoelastic properties at the microscale is challenging not only because of inherent scale limitations, but also because, in OME, the complex 3D wave motion is only tracked within a single 2D plane. To address this challenge, a 2D boundary-condition-free nonlinear inversion (2D-NoBC-NLI) method is introduced to reconstruct viscoelastic properties from noisy 2D displacement fields. Numerical simulations of a homogeneous sphere, a heterogeneous sphere, and an asymmetric nucleated cell were designed to assess the robustness of 2D-NoBC-NLI reconstructions. Experiments were conducted on homogeneous, 75 µm-diameter polyacrylamide (PAAm) microbeads, which were expected to yield uniform viscoelasticity maps. With optimum parameter conditions, the proposed 2D-NoBC-NLI approach achieved mean reconstruction errors ranging from 1 to 13% across all simulated models. Within homogeneous PAAm microbeads, the method demonstrated frequency dependency of viscoelastic parameters consistent with previous measurements. The proposed nonlinear inversion algorithm enables storage and loss moduli imaging without out-of-plane motion data, and without using simplifying 2D approximations. This technique supports 2D elastography imaging and may enable OME-based cell mechanobiology studies through spatially resolved viscoelastic property mapping.