Non-invasive bioimpedance of intact skin: mathematical modeling and experiments

Abstract

The functional integrity and pathology of the skin is reflected in its electrical impedance spectra. Non-invasive electrical impedance measurements of intact skin are dominated by the high impedic stratum corneum in low frequencies and with increasing frequency gradually comes to be dominated by viable skin. Models of this multi-layered organ can increase our understanding of the actual physical properties/dimensions and facilitate better diagnostics in certain applications. Therefore, a mathematical model considering conservation of charge in the various layers of the skin and adjacent electrodes is derived and validated with experimental findings; the latter was carried out on 60 young female subjects. The impact of the stratum corneum thickness, inundation, solvent and cohort size on the electrical properties is studied. Both model parameters and experimental conditions were adjusted for calibration and subsequent validation of the model with measurements. It is found that both the model's thickness of the stratum corneum as well as experimental soaking conditions (both time and saline concentration) affect the fit between the model and measurements. It is concluded that it is essential that the electrical properties of the skin are presented in the context of the ion concentration (if a moisturizer is employed) as well as the soaking time. Further refinements should be made to determine even more accurate dielectrical properties of the stratum corneum and viable skin layers by accounting for the true skin thickness and the heterogeneity of the skin layers-this would be useful in applications where subtle alterations in the skin are of interest.

Analysis of a Mechanistic Model for Non-invasive Bioimpedance of Intact Skin

“…We start with the mathematical model for EIS measurements derived by Birgersson et al [12], which treats the skin as a three-layer entity: stratum corneum (SC) as the outermost layer characterized by corneocytes; viable skin (VS) consisting of both living epidermis and dermis; and adipose tissue (AT) to account for the subcutis layer containing a high percentage of fat, as illustrated in Fig. 1ab.…”

“…1ab. While the non-invasive EIS probe in the studies by Birgersson et al [12] comprised four electrodes -one current detector (sense), one guard and two injects -we will here consider a simpler probe with similar dimensions but only one current detector (at ) and one voltage injector (at ). The dimensions and material properties of the electrodes and skin layers can be found in Table 1 [20] Tab.…”

“…All permutations of these parameters are considered for a total of 7200 parameter combinations. For the two skin layer thicknesses, we have taken the mean values ± two standard deviations [12]; i.e. 14±6 µm for stratum corneum and 1.2 0.4  mm for viable skin.…”

“…Out of these models, equivalent-circuit constructs are the most common [1][2][3][4][5][6][7][8][9][10], where the electrical properties of the skin are estimated through a tissue-equivalent circuit comprising real and hypothetical electrical components. Mechanistic models based on the Maxwell equations and various degrees of resolution of the various skin layers have also been derived [11][12][13][14][15][16]. The key advantage of the mechanistic models is that they are based on actual physical phenomena in the form of conservation equations, as opposed to theoretical equivalent-circuit models.…”

“…In light of the inherent disadvantages of a mechanistic model for EIS of human skin, our aims are threefold: (i) to elucidate the leading-order terms of our earlier mechanistic model [12], which has been shown to agree well with experimental measurements from clinical studies; (ii) to derive a reduced counterpart that brings with it significant computational savings whilst capturing the leading-order physics; and (iii) to secure approximate solutions of the skin impedance that are valid in the 1 kHz to 1 MHz frequency range we consider here and are as easy to employ as equivalent circuits.…”