A DUAL MESH SCHEME FOR FINITE-ELEMENT BASED RECONSTRUCTION ALGORITHMS

The finite element (FE) method has found several applications in emerg ing imaging modalities, especially microwave imaging which has been sh own to be potentially useful in a number of areas including thermal es timation. In monitoring temperature distributions, the biological phen omena of temperature variations of tissue dielectric properties is exp loited, By imaging these properties and their changes during such ther apies as hyperthermia, temperature distributions can be deduced using difference imaging techniques, This paper focuses on a microwave imagi ng problem where the hybrid element (HE) method is used in conjunction with a dual mesh scheme in an effort to image complex wavenumbers, k( 2). The dual mesh scheme is introduced to improve the reconstructed im ages of tissue properties and is ideally suited for systems using FE m ethods as their computational base. Since the electric fields typicall y vary rapidly over a given body when irradiated by high-frequency ele ctromagnetic sources, a dense mesh is needed for these fields to be ac curately represented, Conversely, k(2) may be fairly constant over sub regions of the body which would allow for a less dense sampling of thi s parameter in those regions, In the dual mesh system employed, the fi rst mesh, which is uniformly dense, is used for calculating the electr ic fields over the body whereas the second mesh, which is nonuniform a nd less dense, is used for representing the k(2) distribution within t he region of interest. This paper examines the 2-D TM polarization cas e for a pair of dielectric distributions on both a large and small pro blem to demonstrate the flexibility of the dual mesh method along with some of the difficulties associated with larger imaging problems, Res ults demonstrate the capabilities of the dual mesh concept in comparis on to a single mesh approach for a variety of test cases, suggesting t hat the dual mesh method is critical for FE based image reconstruction where rapidly varying physical quantities are used to recover smoothe r property profiles, as can occur in microwave imaging of biological b odies.