The frequency-dependent ultrasonic backscatter coefficient (BSC) from tissues, a fundamental parameter estimated by quantitative ultrasound (QUS) techniques, contains microstructure information useful for tissue characterization. To extract the microstructure information from the BSC, the tissue under investigation is often modeled as a collection of discrete scatterers embedded in a homogeneous background. From a discrete scatterer point of view, the BSC is dependent on not only the properties of individual scatterers relative to the background, but also the scatterer spatial arrangement (described by the structure function). Recently, the two-dimensional structure function was computed from histological tissue sections, and was shown to be related to the volumetric structure function extracted from QUS measurements. In the current study, a stereological method is proposed to extract the volumetric (three-dimensional) structure function from two-dimensional histological tissue sections. Simulations and experimental cell pellet biophantom studies were conducted to evaluate the proposed method. Simulation results verified the proposed method. Experimental results showed that the volumetric structure function extracted using the proposed method had a significantly better agreement with the QUS-extracted structure function than did the two-dimensional structure function extracted in the previous study. The proposed stereological approach provides a useful tool for predicting the structure function from histology.
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