Toward noninvasive estimation of nonlinear tumor stiffness from B-mode ultrasound under compression: an in silico...

Tumor stiffness has shown promise as a biomechanical marker of malignancy. However, many elastography studies model tumors as linear elastic materials, which may not fully capture the nonlinear behavior of soft tissue. This study developed and evaluated an inverse finite-element framework for estimating nonlinear tumor stiffness from standard B-mode ultrasound images acquired during controlled compression. Approach: Synthetic B-mode images were generated from finite-element simulations of elliptical tumors embedded in healthy tissue. Three tumor aspect ratios were considered: α = 0.35, 0.50, and 0.75. Both the tumor and surrounding tissue were modeled as nearly incompressible neo-Hookean materials. Tumor stiffness was assigned as 2×, 4×, or 6× the background tissue stiffness, and three levels of compression were applied. Speckle tracking was used to estimate tissue displacements between the undeformed and compressed images. These displacement fields were then used in an inverse finite-element optimization. Two formulations were tested: one in which the background tissue stiffness was known and another in which both tumor and background stiffness were estimated. Main results: The inverse model closely reproduced the speckle-tracking displacement fields, with mean absolute errors below 0.01 mm for all cases. When the background tissue stiffness was known, tumor stiffness was estimated with R² > 0.98. The average prediction errors were 2.57%, 2.90%, and 4.04% for α = 0.35, 0.50, and 0.75, respectively, with a maximum error of 6.87%. Estimating both stiffness parameters reduced accuracy because different tumor and tissue stiffness combinations could produce similar displacement patterns. Significance: These results demonstrate the feasibility of estimating nonlinear tumor stiffness from B-mode ultrasound-derived displacement fields using speckle tracking and inverse modeling in a controlled in-silico setting. The study provides a computational framework for tumor-stiffness estimation, with further methodological development needed to address segmentation, loading, and boundary-condition uncertainties before extending the approach beyond the controlled in-silico setting.