Polydisperse Structure Factor Model for understanding the ultrasonic scattering from apoptotic cells
Abstract
Quantitative UltraSound (QUS) techniques for determining the tissue microstructure are promising tools to detect and quantify cell death, and thus monitor the tumor response to therapy. QUS techniques rely on theoretical scattering models to fit the BackScatter Coefficient (BSC) from biological tissues to an estimated BSC using an appropriate model. The model adapted to densely packed cells in tumors is the structure factor model. The aim of this work was to use the polydisperse structure factor model to go further in the understanding of the measured BSCs from cells undergoing apoptosis.
Ultrasonic backscatter measurements were performed at frequencies ranging from 10 to 42 MHz on centrifugated colon adenocarcinoma (HT29) cell pellets. The cell pellets were employed as simplified in vitro versions of real tumors. The HT29 cells were exposed for 24 hours to different concentrations of the apoptosis inducer staurosporine (0, 0.50, 0.75 and 1 mu M). A parameter estimation procedure was developed in order to estimate the cell size distribution that could explain the measured BSC from all the studied staurosporine concentrations using the polydisperse structure factor model. This procedure assumes that the volume fractions and the relative impedance contrast between the cells and the surrounding medium are the same for all the drug concentrations. The cell size distributions estimated using our parameter estimation procedure were compared to the true size distribution obtained by flow cytometry and histological image analysis.
The estimation procedure results revealed that the polydisperse structure factor model could explain the frequency dependence and amplitude of the measured BSCs. The width factor estimated with the polydisperse structure factor model are equal to 67, 32, 17 and 13 for the staurosporine concentrations of 0, 0.50, 0.75 and 1 mu M, respectively. So the width of the distribution becomes larger (with the decrease of the width factor) when the cell death index increases, as observed from the true cell size distribution obtained from flow cytometry and histology. The relative impedance contrast estimates (=0.26) and the volume fraction of the centrifugated cells (=0.70) seem also to be in a reasonable range of value. This study demonstrates that the polydisperse structure factor model could prove to be an invaluable tool for monitoring cell death process.