Fundamental Limitations on the Contrast-transfer Efficiency in Elastography: an Analytic Study

Elastography is a new ultrasonic imaging technique introduced to produce images of the Young's modulus distribution of compliant tissue. This Young's modulus distribution is derived from the ultrasonically estimated longitudinal internal strains induced by an external compression of the tissue. The displayed two-dimensional images are called elastograms. Recently, contrast-transfer efficiency, defined as the ratio of elasticity contrast as measured from elastogram to the true contrast, was used to illustrate by simulation the fundamental limitation of elastography in displaying the elastic modulus contrast of soft inclusion in a hard background and vice versa. In this paper, using a classical analytic solution of the elasticity equations derived for an infinite medium subjected to a uniaxial compression, we confirm such earlier simulations results. For this purpose we derive an analytic expression predicting the observed contrast in elastograms.