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Quasi-static ultrasonic elasticity imaging (QUSE) lacks necessary data to solve inverse 3-D elasticity problems mathematically. The autoprogressive method (AutoP) is a recently developed, data-driven approach to QUSE that leverages finite element physics and machine learning techniques primed for sensing complex relationships with limited data. The process involves propagating measured force and displacement data from ultrasound into stress-strain training data through finite element analysis (FEA) to train artificial neural networks (ANNs) to learn both constitutive behavior and spatial heterogeneity. Internal displacement data provides material information about the entire 3-D contiguous volume that is integrated into the learning process through FEA physics. To use FEA for tissues as a solid, we must assume they are somewhat compressible to avoid numeric instability, however this assumption introduces a bias into the training data that impacts the quality of the learned material properties. The trade-off between bias and numeric instability must be resolved to provide the highest quality training data to the networks. To understand this trade-off, force and displacement data were acquired from quasi-static compression of an incompressible, linear-elastic gelatin phantom with a stiff cylindrical inclusion. AutoP tests were performed using simulated and measured displacement data sets. For each data set, ANNs were initialized with stress-strain data from simulated compression of a uniform material with a Poisson’s ratio of 0.30, 0.40, and 0.45. We found improvement in the resulting Young’s modulus distribution using a Poisson’s ratio of 0.4 over 0.3, however using 0.45 resulted in non-physical behavior. We have developed an approach that balances numeric instability with training data bias and considers additional complications of sampling and meshing decisions to generate high-quality material property images. Discerning these trade-offs for linear-elastic materials is essential for the extension into multi-phasic, non-linear and time-dependent material property imaging with AutoP.
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