Mathematical and Experimental Investigation of the Quasi-static Conditions for Multi-frequency Electrical Impedance Tomography

F Kleinermann1, N J Avis1 and F A Alhargan1,2

1 The Centre for Virtual Environments, University of Salford, Salford, M5 4WT, UK

2 Computer and Electronics Research Institute, KACST, P.O. Box 6086, Riyadh 1142, Saudi Arabia E-mail : F.Kleinermann@pgr.salford.ac.uk N.J.Avis@salford.ac.uk Alhargan@kacst.edu.sa

ABSTRACT

Image reconstruction algorithms in Multi-frequency Electrical Impedance Tomography (MEIT) are based on those used in Electrical Impedance Tomography (EIT) where the quasi-static assumptions are assumed to be valid. For early EIT systems which operated at a single frequency between 10 kHz and 100 kHz, these quasi-static assumptions appear reasonable when investigating biological tissues. However, recently constructed MEIT system can record impedance measurements at frequencies above 1 MHz and this raises the question of the validity of the quasi-static conditions at these frequencies. This paper presents a new analytical solution to the Forward Problem where the quasi- static conditions are not assumed to be valid. The new analytical solution is compared for human blood (packed red cells) with experimental measurements and with a previous analytical solution that assumed the validity of the quasi-static conditions.

Keywords Multi-frequency EIT, Quasi-static conditions, Helmholtz’s equation, Human Blood