Reconstruction of the shape of conductivity spectra using differential multi-frequency magnetic induction tomography

Abstract

Magnetic induction tomography (MIT) of biological tissue is used for the reconstruction of the complex conductivity distribution κ inside the object under investigation. It is based on the perturbation of an alternating magnetic field caused by the object and can be used in all applications of electrical impedance tomography (EIT) such as functional lung monitoring and assessment of tissue fluids. In contrast to EIT, MIT does not require electrodes and magnetic fields can also penetrate non-conducting barriers such as the skull. As in EIT, the reconstruction of absolute conductivity values is very difficult because of the method's sensitivity to numerical errors and noise. To overcome this problem, image reconstruction in EIT is often done differentially. Analogously, this concept has been adopted for MIT. Two different methods for differential imaging are applicable. The first one is state-differential, for example when the conductivity change between inspiration and expiration in the lung regions is being detected. The second one is frequency-differential, which is of high interest in motionless organs like the brain, where a state-differential method cannot be applied. An equation for frequency-differential MIT was derived taking into consideration the frequency dependence of the sensitivity matrix. This formula is valid if we can assume that only small conductivity changes occur. In this way, the non-linear inverse problem of MIT can be approximated by a linear one (depending only on the frequency), similar to in EIT. Keeping this limitation in mind, the conductivity changes between one or more reference frequencies and several measurement frequencies were reconstructed, yielding normalized conductivity spectra. Due to the differential character of the method, these spectra do not provide absolute conductivities but preserve the shape of the spectrum. The validity of the method was tested with artificial data generated with a spherical perturbation within a conducting cylinder as well as for real measurement data. The measurement data were obtained from a potato immersed in saline. The resulting spectra were compared with reference measurements and the preservation of the shape of the spectra was analyzed.

Reduction of low-frequency noise in magnetic induction tomography systems

“…6) should be nearly symmetric but due to different vibration dynamics of different coils the symmetry is not perfect. The achieved system performance is sufficient for low contrast conductivity imaging such as in [8].…”

“…We have developed a fast parallel multi-frequency imaging system which operates from 50 kHz to 1 MHz [7]. It comprises 16 RXC and 16 TXC and allows frequency differential imaging [8], whereas 8+8 coils can be operated in single shot mode. However, due to the the low sensitivity vibrations and thermal drifts cause significant errors [7].…”

Magnetic induction tomography methods and applications: a review

“…Of additional interest is frequency difference imaging, which could be useful if the test subjects show different responses to frequency variation. The reconstruction of pathophysiological information using multi-frequency data and frequency dependence sensitivity matrix was studied in [46], which showed that low resolution similar to those obtained from electrical impedance tomography is possible.…”

On a continuation approach in Tikhonov regularization and its application in piecewise-constant parameter identification

“…Magnetic induction tomography is a non-contact technique, in contrast to widely studied electrical impedance tomography [33]. Another advantage of MIT is its explicit frequency dependence, which allows for more accurate reconstruction of the body properties [34].…”

“…where the function A is the solution of the problem (34) for any e ∈ L 2 (Γ) and ω > 0 fixed, is a well-defined and strongly continuous map from the set…”