Comments on “Bioelectrical parameters of the whole human body obtained through bioelectrical impedance analysis”

Abstract

The question of the existence of inductive phenomena in the human body that could affect bioimpedance measurements has been raised several times through the history of this technique. In a recent paper from Lafargue et al. [2002], an inductor is introduced in the so-called Cole-Fricke-Cole (CFC) model in order to fit experimental data. The inclusion of inductors in the low frequency range (f < 10 MHz) should not be required to explain any measured impedance data from the whole human body. In addition, the paper displays other issues that need to be addressed:Experimental data from 23 normal healthy subjects is presented in Lafargues's Figures 3, 4, and 5 for the real part, reactive part, and phase angle of the measured impedance. ''Error'' bars are included in the figures (standard deviation?). The displayed deviations are smaller than AE2% of the lowest resistance, which is in agreement with the deviations for the parameters of the model displayed in Table 1 of that paper. However, deviations found by other researchers are far larger than those. Ward et al. [2000], using data from about 5000 subjects, display deviations for the normalized impedance (resistance/height) ranging from AE10 to AE20% within ethnic groups and much larger if the total sample had been used. It is possible to calculate the probability of having such a group of 23 people displaying a deviation of AE2% out of a population that displays a deviation of AE10% by using a w 2 law; it is far below 10 À10 . Consequently, such a group of people cannot exist in practice. Rather, the data displayed look like having been obtained from a single subject measured several times (Lukaski [1990] reports a deviation of AE2% for a single subject measured during several consecutive days.) (b) MODEL FITTINGThe paper relies on the impossibility of fitting the experimental data to a CFC model. That model, which in fact is derived from the Maxwell-Wagner mixture equations, can be mathematically described as:where R 0 is the resistance measured at low frequencies, R 1 is the resistance measured at high frequencies, and t 0 is relaxation time constant (the absolute value for the imaginary part is maximum at o ¼ o 0 ¼ 1/t 0 ). It is clear from the data that neither R 1 nor o 0 can be obtained, since the imaginary part grows monotonically and the real part is decreasing monotonically. Only R 0 can be estimated. In this situation, there are multiple solutions to the fitting problem, so it is not credible that the best obtainable is the one displayed in Lafargue's Figures 3, 4, and 5. In fact, using R 0 ¼ 695 O, R 1 ¼ 372 O, and o 0 ¼ 400p krad/s, a mean square error (mse) of about 7% is obtained, while the fitting proposed by the authors has a mse of about 80%, excluding the measurement at 1 kHz in both cases. (c) THE ECFC MODELThe addition of an inductor is used mainly to explain the measurement point at 1 kHz. The real part of the impedance decreases, while the imaginary part increases suddenly. It is not clear if that imaginary part increases or changes its sign fro...

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