APRIL: Adaptive Regression-Based Two-Dimensional Quantitative Anisotropy Imaging Using Acoustic Radiation Force Impulse

Objective: This study aims to develop and validate a quantitative, depth-resolved anisotropy imaging framework that extends ARFI-based focal degree-of-anisotropy (DoA) estimation into two-dimensional mapping by modeling the depth-dependent relationship between shear modulus ratio (SMR) and peak displacement ratio (PDR). Methods: We propose APRIL (Adaptive Polynomial Regression for anisotropy Imaging via ARFI-induced DispLacements), a framework for quantitative, depth-resolved DoA imaging that adaptively selects polynomial regression or shape-preserving spline interpolation based on excitation PSF asymmetry. Training data were generated using an LS-DYNA3D + Field II simulation pipeline in homogeneous transversely isotropic media (SMR 0.9-4.9). Testing included shifted SMRs under varied acoustic conditions and three heterogeneous inclusion configurations (anisotropic inclusion in isotropic background and vice versa). Experimental validation was performed in an in-vivo murine tumor model over the time, ex-vivo chicken breast, and tissue-mimicking gelatin phantoms, using a Verasonics system with an L11-5v transducer. Results: APRIL achieved depth-resolved SMR prediction errors below 9% over 10-30 mm, with highest accuracy in the focal region (MAE 2.3%, RMSE < 0.1) and stable performance across PSF transition zones. In heterogeneous phantoms, it reconstructed anisotropy maps with SSIM up to 86% and MPE below 7%, accurately delineating inclusion boundaries. Under acoustic parameter variations, mean absolute errors remained below 10%, demonstrating robustness to system and tissue heterogeneity. Conclusion: APRIL enables robust, two-dimensional anisotropy imaging beyond focal estimates. Significance: The method provides a physically grounded and generalizable framework for clinically viable anisotropy biomarkers in muscle, tendon, kidney, tumor and breast tissues.