TY - JOUR

T1 - Reconstruction of the shape of conductivity spectra using differential multi-frequency magnetic induction tomography

AU - Brunner, Patricia

AU - Merwa, Robert

AU - Missner, Andreas

AU - Rosell, Javier

AU - Hollaus, Karl

AU - Scharfetter, Hermann

PY - 2006/5/1

Y1 - 2006/5/1

N2 - 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.

AB - 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.

KW - Conductivity spectrum

KW - Frequency-differential

KW - Magnetic induction tomography (MIT)

KW - Reproducibility of Results

KW - Electric Impedance

KW - Magnetics

KW - Plethysmography, Impedance/methods

KW - Algorithms

KW - Models, Biological

KW - Computer Simulation

KW - Sensitivity and Specificity

KW - Image Interpretation, Computer-Assisted/methods

KW - Tomography/methods

UR - http://www.scopus.com/inward/record.url?scp=33745165595&partnerID=8YFLogxK

U2 - 10.1088/0967-3334/27/5/S20

DO - 10.1088/0967-3334/27/5/S20

M3 - Article

C2 - 16636414

SN - 0967-3334

VL - 27

SP - 237

EP - 248

JO - Physiological Measurement

JF - Physiological Measurement

IS - 5

M1 - S20

ER -