Zhang, Tingting; Bera, Tushar Kanti; Woo, Eung Je; Seo, Jin Keun Spectroscopic admittivity imaging of biological tissues: challenges and future directions. (English) Zbl 1322.92023 J. Korean Soc. Ind. Appl. Math. 18, No. 2, 77-105 (2014). Summary: Medical imaging techniques have evolved to expand our ability to visualize new contrast information of electrical, optical, and mechanical properties of tissues in the human body using noninvasive measurement methods. In particular, electrical tissue property imaging techniques have received considerable attention for the last few decades since electrical properties of biological tissues and organs change with their physiological functions and pathological states. We can express the electrical tissue properties as the frequency-dependent admittivity, which can be measured in a macroscopic scale by assessing the relation between the timeharmonic electric field and current density. The main issue is to reconstruct spectroscopic admittivity images from 10 Hz to 1 MHz, for example, with reasonably high spatial and temporal resolutions. It requires a solution of a nonlinear inverse problem involving Maxwell’s equations. To solve the inverse problem with practical significance, we need deep knowledge on its mathematical formulation of underlying physical phenomena, implementation of image reconstruction algorithms, and practical limitations associated with the measurement sensitivity, specificity, noise, and data acquisition time. This paper discusses a number of issues in electrical tissue property imaging modalities and their future directions. Cited in 1 Document MSC: 92C55 Biomedical imaging and signal processing 35R30 Inverse problems for PDEs 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:inverse problem; electrical tissue property imaging; Maxwell’s equations; homogenization; electrical impedance tomography; bioimpedance PDFBibTeX XMLCite \textit{T. Zhang} et al., J. Korean Soc. Ind. Appl. Math. 18, No. 2, 77--105 (2014; Zbl 1322.92023) Full Text: DOI