Evaluation of algorithms for calculating bioimpedance phase angle values from measured whole-body impedance modulus

This paper addresses the problem of calculating the bioimpedance phase angle from measurements of impedance modulus. A complete impedance measurement was performed on altogether 20 healthy persons using a Solatron 1260/1294 system. The obtained impedance modulus (absolute impedance value) values were used to calculate the Cole parameters and from them the phase angles. In addition, the phase angles were also calculated using a Kramers-Kronig approach. A correlation analysis for all subjects at each frequency (5, 50, 100 and 200 kHz) for both methods gave R-2 values ranging from 0.7 to 0.96 for the Cole approach and from 0.83 to 0.96 for the Kramers-Kronig approach; thus, both methods gave good results compared with the complete measurement results. From further statistical significance testing of the absolute value of the difference between measured and calculated phase angles, it was found that the Cole equation method gave significantly better agreement for the 50 and 100 kHz frequencies. In addition, the Cole equation method gives the four Cole parameters (R-0, R-infinity, tau(z) and alpha) using measurements at frequencies up to 200 kHz while the Kramers-Kronig method used frequencies up to 500 kHz to reduce the effect of truncation on the calculated results. Both methods gave results that can be used for further bioimpedance calculations, thus improving the application potential of bioimpedance measurement results obtained using relatively inexpensive and portable measurement equipment.