Characterizing Mechanical Properties of Soft Tissues Using Non-contact Displacement Measurements: How Should We Assess the Uncertainty?

Techniques aimed at the non-invasive characterization of soft tissues according to elastic properties are rapidly evolving. Virtual touch-based elastographic methods including acoustic radiation force imaging (ARFI) and optical elastography measure the peak axial displacement (PD) and time-to-peak-displacement (TTP) of tissue in response to a localized force. These measurements have been used clinically to differentiate tissues, albeit with mixed results. However, to date, the reason has not been fully understood. In this study, we apply a novel modeling approach to explore the mechanistic link between simplistic displacement measurements and tissue viscoelasticity in the application of virtual touch-based elastographic methods to staging chronic liver disease (CLD). To our knowledge, such a study has not been reported in the literature. Specifically, a numerical screening study was first conducted to identify factors that most strongly determine PD and TTP. Response surface experimental designs were then applied to these factors to produce meta-models of expected PD and TTP probability density functions (PDFs) as functions of identified factors. Results from the screening study suggest that both PD and TTP measurements are primarily influenced by three factors: the initial Young's modulus of the tissue, the first viscoelastic Prony series time constant, and pre-compression applied during acquisition. To investigate the implications of these results, stochastic inputs for these three factors associated were used to determine a robust response surface. The identified response surface methodology can be used to determine optimal cutoff values for PD and TTP that could be used in order to stage chronic liver disease.