Extraction of electrical characteristics from pixels of multifrequency electrical impedance tomographs

Full text: Multi-frequency electrical impedance tomography (MFEIT) is a modality that provides images of the change in the electrical response of tissue at a number of discrete frequencies relative to the response at a selected reference frequency (H Griffiths and A Ahmed, Clin. Phys. Physiol. Meas. 8A:103-107, 1987). This method overcomes the need, when forming in vivo static images, to measure or calculate the voltage profiles of a resistive, homogeneous reference medium and therefore avoids the errors introduced due to boundary shape and electrode location inaccuracies. Information on the spectral response of the tissue is contained within the pixel values, hence characteristics of the tissues and the state of health can be obtained by extracting this information from in vivo MFEIT images. Griffith and Jossinet (Physiol Meas. 15A: 59-63, 1994) used computer modelling to demonstrate that the Cole-Cole plot (variations of resistance and reactance with frequency) can be extracted from pixel values of MFEIT images provided the reference set was obtained from a purely resistive and homogeneous medium. To date it has not been possible to extract true Cole-Cole plots from in vivo MFEIT images because tissue contains a reactive component of impedance which introduces an unknown phase angle into the reference data set. Instead, an impedance spectrum, equivalent to a Cole-Cole plot rotated about the origin by the unknown phase angle, may be extracted. A correction for this rotation of the Cole-Cole plot is necessary since parameters derived from the impedance spectrum do not accurately reflect the electrical response of the imaged tissue. We have developed two distinct methods to determine this unknown phase angle and hence enable the extraction of parameters that more accurately reflect the true electrical response of tissue from in vivo MFEIT images. The first method is an empirical method based on observation of the distribution of frequency data around the Cole-Cole plot. The second technique is based on the analytical expressions that describe the Cole-Cole plot. This paper presents both methods and compares the parameters obtained from MFEIT data using the two techniques