Reduction of signal decorrelation from mechanical compression of tissues by temporal stretching: applications to...

Elastography is based on the estimation of strain due to tissue compression. Strain is computed from the estimates of time delays between gated precompression and postcompression echo signals. Time delay estimates are obtained from the location of the peak of the crosscorrelation function between gated precompression and postcompression signals. It is of paramount importance to accurately estimate the time delays for good quality elastograms. A main source of time delay estimation (TDE) error in elasticity imaging is the decorrelation of the echo signal as a result of tissue compression (decorrelation noise). The effect of decorrelation on the mean of the crosscorrelation function and the correlation coefficient has been investigated. The expected value of the cross-correlation function between the precompression and postcompression signals was shown to be a filtered version of the autocorrelation function of the precompression signal. In this article, the effect of temporal stretching of the postcompression echo signal on the cross-correlation function will be investigated along the same line. The applied compression is assumed to be uniform; the decorrelations introduced by the lateral and elevational tissue movements are ignored. The theory predicts that if the postcompression echo signals are stretched before the TDE step, then for small strains, the cross-correlation function very closely resembles the autocorrelation function. For larger strains, correlation is improved if temporal stretching is applied. The theory is corroborated by results from simulation and homogeneous phantom experiments. Thus, the decorrelation noise in elastograms can be reduced by temporal stretching of the postcompression signal.