An In Silico Platform for 3D Ultrasound and Collateral Ligament Mechanics to Validate 3D Speckle Tracking

Quantifying ligament strain with three-dimensional ultrasound can improve assessment of the medial and lateral collateral ligaments and support soft-tissue balancing during knee arthroplasty. However, accurate motion and strain tracking remain challenging because these ligaments are small, anisotropic, and subject to out-of-plane motion. Limited availability of volumetric ultrasound systems and the absence of paired ground-truth strain fields further hinder systematic algorithm development. An in silico framework combining realistic biomechanics with controlled ultrasound image formation can accelerate the optimization and validation of strain-tracking techniques.

We developed an in silico platform coupling finite element simulations of ligament deformation with volumetric ultrasound synthesized using the Field II simulation program. To demonstrate its utility, we designed a ligament-specific three-dimensional speckle-tracking pipeline. Displacements were estimated using normalized cross-correlation, and infinitesimal strain tensors were computed by distance-weighted least-squares fitting of local displacement gradients. Two cadaveric knee specimens were simulated under varus and valgus loading. Agreement with the finite element ground truth was assessed using the Pearson correlation coefficient, root mean square error, and Bland-Altman analysis.

Across the two specimens, the medial collateral ligament achieved a Pearson correlation coefficient of 0.992±0.008 with a root mean square error of 0.276±0.323 for maximal principal strain, and 0.990±0.011 with 0.295±0.363 for minimal principal strain. The lateral collateral ligament achieved 0.988±0.006 with 0.421±0.344 for maximal and 0.942±0.040 with 0.376±0.060 for minimal principal strain. Bland-Altman analysis indicated small biases, with wider limits of agreement for the lateral collateral ligament in compression.

The proposed framework accurately quantifies ligament strains derived from three-dimensional ultrasound and provides a controlled environment for developing and benchmarking speckle-tracking methods. By linking realistic biomechanics to ultrasound image formation, it enables standardized evaluation before cadaveric and clinical studies and supports translation of three-dimensional ultrasound strain mapping to intra-operative and longitudinal assessments of soft-tissue balance.