Sticky Hard Sphere Model for Characterizing Tumor Microstructure via Quantitative Ultrasound

The use of the structure function (SF) to model inter-scatterer contribution to ultrasonic scattering is a major step to improve the capability and accuracy of quantitative ultrasound (QUS) and tissue characterization. However, existing QUS-based SF models rely on the hard-sphere (HS) model, which is limited in its applicability for complex scatterer distributions in real tissue. This paper introduces the sticky hard-sphere (SHS) model for QUS and tissue characterization, which considers a very short-range attractive potential that accounts for the adhesive nature of biological cells and yields a new parameter called stickiness. Herein, the analytical SF expression is presented for monodisperse scatterer size and validated using simulations of scatterer distributions with varying degrees of grouping and volume fractions (0.16, 0.32, and 0.40) over the frequency range from 15 to 110 MHz. The SHS model is applied to three mammary tumor types with differing spatial distributions of tumor cells. The histology-derived SF is computed by considering the nuclei as the main sources of scattering. The results show that the SHS model provides more accurate scatterer radius and volume fraction estimates than the HS model when fitted to histology-derived SF versus frequency curves. Furthermore, the new stickiness parameter provided by SHS is sensitive to the grouping structure in tumor cell distribution. This stickiness parameter, combined with the radius and volume fraction estimated from the SHS model, enables better differentiation between different tumor types than using the radius and volume fraction obtained from the HS model. This study demonstrates the potential of the SHS model to improve QUS tissue characterization.