Viscoelasticity Imaging Using Ultrasound: Parameters and Error Analysis

Techniques are being developed to image viscoelastic features of soft tissues from time-varying strain. A compress-hold-release stress stimulus commonly used in creep-recovery measurements is applied to samples to form images of elastic strain and strain retardance times. While the intended application is diagnostic breast imaging, results in gelatin hydrogels are presented to demonstrate the techniques. The spatiotemporal behaviour of gelatin is described by linear viscoelastic theory formulated for polymeric solids. Measured creep responses of polymers are frequently modelled as sums of exponentials whose time constants describe the delay or retardation of the full strain response. We found the spectrum of retardation times tau to be continuous and bimodal, where the amplitude at each tau represents the relative number of molecular bonds with a given strength and conformation. Such spectra indicate that the molecular weight of the polymer fibres between bonding points is large. Imaging parameters are found by summarizing these complex spectral distributions at each location in the medium with a second-order Voigt rheological model. This simplification reduces the dimensionality of the data for selecting imaging parameters while preserving essential information on how the creeping deformation describes fluid flow and collagen matrix restructuring in the medium. The focus of this paper is on imaging parameter estimation from ultrasonic echo data, and how jitter from hand-held force applicators used for clinical applications propagate through the imaging chain to generate image noise.