Finite-element Modeling of Elastic Surface Modes and Scattering from Spherical Objects
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.