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The validity of the adaptive finite element method for reconstruction of dielectrics in a symmetric structure is verified on time-resolved data in two dimensions. This problem has practical interest in the reconstruction of the structure of photonic crystals or in the imaging of land mines. Dielectric permittivity, locations, and shapes/sizes of dielectric abnormalities are accurately imaged using adaptive finite element algorithm.

During neurosurgery, the brain significantly deforms. Despite the enormous complexity of the brain (see Chap. 2) many aspects of its response can be reasonably described in purely mechanical terms, such as displacements, strains and stresses. They can therefore be analyzed using established methods of continuum mechanics. In this chapter, we discuss approaches to biomechanical modeling of the brain from the perspective of two distinct applications: neurosurgical simulation and neuroimage registration in image-guided surgery. These two challenging applications are described below.1