Analysis of the validity of the mathematical assumptions of electrical impedance tomography for human head tissues.
Williams T., Bouazza-Marouf K., Zecca M., Green A.
Objective:To determine the validity of the key mathematical assumptions used in electrical impedance tomography for human head tissues over the frequency range of 10 Hz to 100 GHz.Approach:Conductivity and permittivity data collected from available literature for each tissue within the human head have been evaluated and critiqued. The most relevant dielectric tissue data for each tissue was then used to assess the validity of the mathematical assumptions of electrical impedance tomography in terms of their suitability for human head imaging in order to estimate related errors.Main Results:For induced currents with frequencies greater than 200 Hz the internal current source density is negligible. The assumption that magnetic effects are negligible is valid to an error of 1.7% for human head tissues for frequencies below 1 MHz. The capacitive effects are negligible for CSF, dura mater, blood, bone (cortical), and deep tissue skin for frequencies less than 3.2 MHz, 320 kHz, 25 kHz, 3.2 kHz, and 130 Hz respectively. However, the capacitive effects are not negligible for brain tissues, as the minimum error for brain tissues across the frequency range of 10 Hz to 100 GHz is 6.2% at 800 Hz, and the maximum error is 410% at 20 GHz.Significance:It is often assumed that the mathematical reduction of the base equations is valid for human head tissues over a broad frequency range; this study shows that these assumptions are not true for all tissues at all frequencies. False assumptions will result in greater errors and local distortions within tomographic images of the human head using electrical impedance tomography. This study provides the relationships between injected current frequency and the validity of the mathematical assumptions for each individual tissue, providing greater awareness of the magnitude of possible distortions.