Effects of cell spatial organization and size distribution on ultrasound backscattering

In ultrasound tissue characterization dealing with cellular aggregates (such as tumors), it can be hypothesized that cell microstructure and spatial distribution dominate the backscatter signal. Effects of spatial organization and size distribution of nuclei in cell aggregates on ultrasound backscatter are examined in this work using 2-D computer simulations. The nuclei embedded in cytoplasm were assumed to be weak scatterers of incident ultrasound waves, and therefore multiple scattering could be neglected. The fluid sphere model was employed to obtain the scattering amplitude for each nucleus and the backscatter echo was generated by summing scattered signals originating from many nuclei. A Monte Carlo algorithm was implemented to generate realizations of cell aggregates. It was found that the integrated backscattering coefficient (IBSC) computed between 10 and 30 MHz increased by about 27 dB for a spatially random distribution of mono-disperse nuclei (radius = 4.5 μm) compared with that of a sample of periodically positioned mono-disperse nuclei. The IBSC also increased by nearly 7 dB (between 10 and 30 MHz) for a spatially random distribution of poly-disperse nuclei (mean radius ± SD = 4.5 ± 1.54 μm) compared with that of a spatially random distribution of mono-disperse nuclei. Two different Gaussian pulses with center frequencies 5 and 25 MHz were employed to study the backscatter envelope statistics. An 80% bandwidth was chosen for each case with approximately 0.32 mm as the full-width at half-maximum (FWHM) for the first pulse and 0.06 mm for the second. The incident beam was approximated as a Gaussian beam (FWHM = 2.11 and 1.05 mm for those pulses, respectively). The backscatter signal envelope histograms generally followed the Rayleigh distribution for mono-disperse and poly-disperse samples. However, for samples with partially ordered nuclei, if the irradiating pulse contained a frequency for which ultrasound wavelength and scatter periodicity became comparable (d ~ λ/2), then the histograms were better fitted by the Nakagami distribution. This study suggests that the shape of an envelope histogram depends upon the periodicity in the spatial organization of scatterers and bandwidth of the ultrasound pulse.