A new three-dimensional elastography using phase based shifted Fourier transform

Abstract

Elastography is an imaging technique with the ability to determine low quantities of some of the mechanical properties of tissues. The aim of our research is to design a new 3D algorithm using the Shifted Fourier Transform (SFT) to perform a quasi-static elastography. Our innovative idea is implementation of a 3D convolution instead of using three 2D convulsions. At first, we collected the raw data from Abaqus engineering software in the form of breast tissue with a coefficient of elasticity of healthy tissue and tumor tissue with a coefficient of elasticity of tumor tissue. The primary raw data consists of a number of points with x, y and z specified for tumor and healthy breast tissue. At this step, we simulated the displacements in directions of x, y and z at each point of the prescribed tissues for 15 ​mm displacement of probe in –Y direction then we collected 1831 points for tumor and 4186 points for breast before and after pressure. After applying a novel reconstruction algorithm, we convolved all images with the 3D Gabor filters to obtain phases, represented displacements of the breast and tumor images for before and after pressure. To reach this goal, we designed a Gabor filter bank based on the dimensions of the input images in different scales, directions, and deviations. Using the 3D SFT, we calculated the displacements of the breast and tumor tissues followed by 3D elastogram representation of the images. Finally, we implemented a 2D analysis of SFT in order to investigate validation of the 3D SFT. In 2D algorithm, we used three two-dimensional convulsions in XY, YZ and XZ planes. The results obtained from the small displacements marked by circles, confirmed the accuracy of the 3D SFT algorithm. These areas of interest are the tumor areas in the 2D analysis.

Keywords

• 3D elastography
• 3D shifted Fourier Transform
• 3D and 2D Gabor filters
• Breast and tumor tissues
• Reconstruction algorithm