Finite-element Modeling of Elastic Surface Modes and Scattering from Spherical Objects Omar Falou *,1 , J. Carl Kumaradas 2 , and Michael C. Kolios 1,2 1 Dept. of Electrical and Computer Engineering, Ryerson University, 2 Dept. of Physics, Ryerson University *Corresponding author: 350 Victoria Street, Toronto, Ontario M5B 2K3, Canada, ofalou@ryerson.ca Abstract: A finite-element model of wave propagation using COMSOL Multiphysics (COMSOL Inc., Burlington, MA) was developed to solve the problem of high frequency ultrasound scattering from spheres. This model is used to predict ultrasound backscatter from cells for ultrasound tissue characterization. In this work, the backscatter from an elastic sphere was used to validate the computational model against analytical solutions (Faran theory). Agreements between analytical and finite element solutions were found in the scattered far-field over a range of frequencies of interest (10 - 70 MHz). Oscillations of the elastic sphere at various resonance frequencies (peaks in the power spectrum) were also investigated. The resonance frequencies predicted by the analytical solutions corresponded to surface modes. A systematic relationship between the resonance frequency and its corresponding surface mode was found. The oscillations of the elastic sphere were visualized at these resonances. An ultrasound scattering model by a single cell is also presented. The model treats the cell as an elastic sphere (nucleus) surrounded by a fluid shell (cytoplasm). Comparison of the theoretical backscatter predicted by the model and experimental measurements for Acute Myeloid Leukemia (AML) cell is also shown. Finally, the implications of these results on the prediction of ultrasound backscatter from cells, and on ultrasound tissue characterization techniques are discussed. Keywords: Ultrasound imaging, acoustic scattering, elastic surface modes, cell scattering 1. Introduction It has been shown that high frequency ultrasound (20MHz - 60MHz) can be used to detect structural and physical changes in cell ensembles during cell death (Sherar et al. 1987), including apoptosis (Czarnota et al. 1997; Czarnota et al. 1999; Kolios et al. 2004). Ultrasonic backscatter from cell ensembles treated with the chemotherapeutic cisplatin, which induces apoptosis, increased the ultrasound backscatter by 9-13dB resulting in much brighter images. However, the precise physical mechanism that causes this increase is not known. A theoretical model of acoustic wave scattering is required to better understand scattering from cells, which would then allow us to determine the proportion of cells undergoing apoptosis in a given ensemble. The effect of the morphological changes during apoptosis on ultrasound backscatter cannot be modeled using analytical methods. Most scattering models used for lower frequency ultrasonic tissue characterization assume a random distribution of scatterers (Lizzi et al. 1983; Insana et al. 1990; Oelze et al. 2002). These models have been used to diagnose various tissue pathologic states (Lizzi et al. 1988; Lizzi et al. 1997; Ursea et al. 1998; Feleppa et al. 2000). However, they do not take into account the elastic nature of cells, which may be significant at higher frequencies. There is evidence of an elastic nature to cells with a variation in elasticity within the cell (Caille et al. 2002; Zinin et al. 2005). For example, the cell nucleus has been shown to be stiffer (Tseng et al. 2004) and more viscous (Guilak et al. 2000) than the cytoplasm. Moreover, there is an increasing interest in the modeling of ultrasound contrast agents’ oscillations, collapse, and scattering in ultrasound fields for a better understanding of contrast agent imaging (Stride et al. 2003). Current models used cannot easily take into account features such as non-radial bubble oscillations due to inhomogeneity and the interactions of bubbles with their surroundings. Analytical solutions to the problem of wave scattering from simple, isotropic, and homogeneous three dimensional structures such as spheres have been studied extensively in the Excerpt from the Proceedings of the COMSOL Conference 2007, Boston