Relationship of 2D ultrasonic spectral parameters to the physical properties of soft tissue scatterers

We have conducted a general study that relates calibrated 2-D ultrasonic spectral parameters to the physical properties of sub-resolution tissue scatterers. Our 2-D spectra are computed form digital radio-frequency echo data obtained as the transducer linearly scans along the cross-range (scan direction) with increments smaller than the half beam width. Acquired data are Fourier transformed with respect to range (beam) and cross-range (scan) directions. To quantitatively measure and classify the physical properties of tissues, we have defined two spectral functions and four spectral parameters. The 2-D spectral functions are: radially integrated spectral power (RISP) and angularly integrated spectral power (AISP). The summary parameters are: peak value and 3-dB width of the RISP, slope and intercept of the AISP. These parameter are understood in terms of the beam properties, transducer parameters and the physical properties of the tissue microstructures including size, shape, orientation, concentration and acoustic impedance. Our theoretical model indicates that 1) the 3-dB width of the RISP is predominantly determined by the scatterer size along the beam direction; 2) the slope of the linear fit of the AISP is predominantly determined by the scatterer size along range direction; 3) the concentration and the relative acoustic impedance fluctuation of the scatterers change the overall spectrum magnitude. The predictions of the theoretical model have been verified using beef muscle fibers examined with 40 MHz center frequency.