Skin layer classification by feedforward neural network in bioelectrical impedance spectroscopy

Fig. 1 shows the schematic flow of FNN. FNN is a fully connected layer of the neural network and connections from the network inputs to each subsequent layer from the previous layer, known as multi-layer perceptron (MLP). A structure of FNN consists of one hidden layer with 100 neurons, the four impedance inputs α_ξ in the input layer, and the five source indicators o^k in the output layer. This fully connected FNN structure has (ξ×u)+(u×o) total number of weight connections, where ξ = {1, …, Ξ} is data input in the input layer, u = {1, …, U} is neuron in the hidden layer, and o = {1, …, O} is the number of data output in the output layer. The weight connections are used in order to perform the computation. The computation steps of the network of one hidden layer for nth sample in training data set is as follows: 1)

The first step is summing the weights in the hidden layer: 1 Sun=∑1Uwuξαξ+βξ [$$S_{u}^{n}=\underset{1}{\overset{U}{\mathop \sum }}\,{{w}_{u\xi }}{{\alpha }_{\xi }}+\beta \xi $$] where α_ξ is the input data (which are impedance inputs), w_uξ is the weight vector connecting the input neurons ξth and the hidden layer neuron uth, and β_ξ is the input variable’s bias term,

Fig. 1:

The training process based on the supervised learning employs a tuning process to control the weight (w_uξ and w˜uo $${\tilde w_{uo}}$$) and bias (β_ξ and β_u) parameters based on the minimizing of error rate including both skin layer classification and approximation errors.

In order to minimize the unnecessary training data of FNN, this study introduces impedance inputs α_ξ as a data feature extraction which are the magnitude input (MX) α_|z|, phase angle input (PX) α_θ, resistance input (RX) α_R, and reactance input (IX) α_x. Considering that the skin layer classification of conductivity change is in the time domain. Thus, the impedance inputs α_ξ in the time domain are as the following equations: 4 α| Z |=Z´t−Z´toZ´to [$${{\alpha }_{|Z|}}=\frac{{{{{Z}'}}_{t}}-{{{{Z}'}}_{{{t}_{o}}}}}{{{{{Z}'}}_{t}}_{_{o}}}$$] 5 αθ=θ´t−θ´toθ´to [$${{\alpha }_{\theta }}=\frac{{{{{\theta }'}}_{t}}-{{{{\theta }'}}_{{{t}_{o}}}}}{{{{{\theta }'}}_{t}}_{_{o}}}$$] 6 αR=R′t−R′toR′to [$${\alpha _R} = {{{{R'}_t} - {{R'}_{{t_{\rm{o}}}}}} \over {{{R'}_t}_{_{\rm{o}}}}}$$] 7 αX=X´t−X´toX´to [$${{\alpha }_{X}}=\frac{{{\overset{,}{\mathop{X}}\,}_{t}}-{{\overset{,}{\mathop{X}}\,}_{{{t}_{o}}}}}{{{\overset{,}{\mathop{X}}\,}_{t}}_{_{o}}}$$] where 8 Z´=abs(Zl)abs(Zh) [$$\overset{,}{\mathop{Z}}\,=\frac{{\rm{abs}}({{Z}_{l}})}{{\rm{abs}}({{Z}_{h}})}$$] 9 θ´=arg(Zl)−arg(Zh) [$$\overset{,}{\mathop{\theta }}\,=\arg ({{Z}_{l}})-\arg ({{Z}_{h}})$$] 10 R´=re(Zl)abs(Zh) [$$\overset{,}{\mathop{R}}\,=\frac{{\rm{re}}({{Z}_{l}})}{{\rm{abs}}({{Z}_{h}})}$$] 11 X´=im(Zl)abs(Zh) [$$\overset{,}{\mathop{X}}\,=\frac{{\rm{im}}({{Z}_{l}})}{{\rm{abs}}({{Z}_{h}})}$$] where t is an arbitrary amount of time after a reference time t₀, abs(Z) is the magnitude (modulus) of the complex electrical impedance, arg(Z) is the argument (phase angle) in degrees, re(Z) is the resistance of the complex electrical impedance (re(Z) = abs(Z) * cos [arg(Z)]), and im(Z) is the reactance of the complex electrical impedance (im(Z) = abs(Z) * sin [arg(Z)]). Z_l and Z_h represent the impedance at low and high frequencies, respectively, where the frequencies are based on the frequency pair frlh$$f_{r}^{lh}$$ selection.

In fact, any change in conductivity σ and permittivity ε_r of the skin layer affects all α_ξ. The Ŕ reflects conductivity changes; the X´$${X}'$$ reflects mainly reactance changes, which are of capacitive nature; the Ź reflects changes along the length of the vector describing the impedance in complex space, which is emphasized if the real and reactance change are in the same direction and proportion; the θ´$${\theta }'$$ is emphasized if the real and reactance change are in different directions and different proportions. All α_ξ reside solely on physically fundamental aspects of the behavior of electrical impedance in the selected frequency range [7]. Thus, the accuracy of equations (4) to (7) depends on the frequency pair frlh$$f_{r}^{lh}$$ selection. The DRT is used to select the frequency pair based on the time-constant domain, which is related with the skin layer as explained in the next subsection.

The predicted impedance of DRT Z_drt [Ω] is represented by the following equation: 12 Zdrt(f)=R∞+∫0∞γ(lnτ)1+j2πfτd(lnτ) [$${{Z}_{drt}}(f)={{R}_{\infty }}+\underset{0}{\overset{\infty }{\mathop \int }}\,\frac{\gamma (\ln \,\tau )}{1+j2\pi f\tau }{\rm{d}}(\ln \,\tau )$$] where R_∞[Ω] is resistance at the high frequency, γ(ln τ)[Ω] is the distribution function of the total polarization resistance along the relaxation time τ[s], and ∫−∞∞γ(lnτ)d(lnτ)=Rp$$\underset{-\infty }{\overset{\infty }{\mathop \int }}\,\gamma (\ln \,\tau ){\rm{d}}(\ln \,\tau )={{R}_{p}}$$ is a normalized function over the entire relaxation time τ where R_p is the polarization resistance.

In order to retrieve the distribution of γ(ln τ), an approximation by the sum of M radial basis function (RBFs) is used. Hence, equation (12) can be expressed as follows [17]: 13 Zdrt(f;Θ)=R∞+∑m=1MΘm∫0∞gm(lnτ)1+j2πfτd(lnτ) [$${{Z}_{\rm{drt}}}(f;\Theta )={{R}_{\infty }}+\underset{m=1}{\overset{M}{\mathop \sum }}\,{{\Theta }_{m}}\underset{0}{\overset{\infty }{\mathop \int }}\,\frac{{{g}_{m}}(\ln \,\tau )}{1+j2\pi f\tau }{\rm{d}}(\ln \,\tau )$$] where, g_m(ln τ) ≜ ^{e−(μ(|lnτ−lnτ_m|)2} [Ω] is the RBFs with each function is center at the relaxation time τ_m and a full width at half maximum (FWHM) as μ. While Θ = [Θ₁, ⋯, Θ_m]^T is a vector parameter related to the amplitude of RBFs.

Calculating the γ(ln τ) in equation (13) is an ill-posed problem case. Currently, there are several available methods to overcome the DRT ill-posed problem: an evolutionary programming method proposed by Oz et al. [19], a monte-carlo method proposed by Tuncer and McDonald [20], a discrete Fourier transformation proposed by Schichlein et al. [21] and a fitting approach proposed by Sonn et al. [22]. Using a discrete Fourier transformation is not trivial because of requiring an indispensable data exploration and filtering of high-quality impedance data [23]. Alternatively, a fitting approach for DRT is proposed based on fitting the resistance of the spectra to a number of RC elements with fixed time constants [22]. A further improvement by the Ciucci research group for the fitting approach is employing a Tikhonov regularization [16]. In this study, a mathematical toolbox called the DRTtools toolbox proposed by Wan et al. is used. The main goal is to fit the data between the impedance Z_exp [Ω] from experiment against with the model Z_drt by optimization of γ(ln τ) [16]. The optimization of γ(ln τ) is retrieved as the optimal parameters vector Θ*=argminΘ:Θ≥0V(Θ)$$\Theta *=\underset{\Theta :\Theta \ge 0}{\mathop{\rm{argmin}}}\,\,V(\Theta )$$ by minimizing the error least square between the measured impedance and the predicted impedance as follows: 14 V(Θ)=‖((R∞1)+AreΘ)−Zexpre‖22+‖(AimΘ)−Zexpim‖22+λ‖Θ‖22 where L is the number of frequency points, λ > 0 is the hyperparameters to tune the error computation, and Are∈ℝL×M$${{\mathbf{A}}^{\rm{re}}}\in {{\mathbb{R}}^{L\times M}}$$ and Aim∈ℝL×M$${{\mathbf{A}}^{\rm{im}}}\in {{\mathbb{R}}^{L\times M}}$$ are the matrix notion of parameters obtained from the real Zdrtre$$Z_{drt}^{re}$$ and reactance Zdrtim$$Z_{drt}^{im}$$ of the predicted impedance Z_drt, which are expressed as follows: 15 Zdrtre=R∞+∑m=1MΘm[ ∫0∞gm(lnτ)1+(2πfτ)2d(lnτ)︸Are ] 16 Zdrtim=−∑m=1MΘm[ ∫0∞2πfτgm(lnτ)1+(2πfτ)2d(lnτ)︸Aim ]

Once the γ(ln τ) is retrieved, it provides a plot of γ(ln τ) against τ. Hence, different relaxation mechanisms can be easily identified as a representation of frequency information where the conductivity change influences significantly or insignificantly on the impedance Z. Some of the frequency pairs are selected heuristically in order to calculate the impedance inputs α_ξ as shown in equations (4) to (7).

Numerical simulation studies are employed using finite element method (FEM) software to generate input for training data sets. The simulation of electric potential ϕ(r) inside a subdomain Ω is produced by placing a current across the surface skin in the boundary ∂Ω on each electrode transmitter with the injected current i [24]. 17 ∇⋅(σ*(r))∇ϕ(r)=0,r∈Ω [$$\nabla \cdot (\sigma *(r))\nabla \phi (r)=0,\,r\in \Omega $$] 18 ϕ(r)+Zcσ*(r)∂ϕ(r)∂n=Ul,r∈el,l={ 1,…,L } [$$\phi (r)+{{Z}_{c}}\sigma *(r)\frac{\partial \phi (r)}{\partial n}={{U}_{l}},\,r\in {{e}_{l}},\,l=\{1,\,\ldots ,\,L\}$$] 19 ∫∂Ωelσ*(r)∂ϕ(r)∂ndS=I,r∈∂Ωel [$$\underset{\partial {{\Omega }^{{{e}_{l}}}}}{\mathop \int }\,\sigma *(\mathbf{r})\frac{\partial \phi (\mathbf{r})}{\partial \mathbf{n}}\text{d}S=I,\,\mathbf{r}\in \partial {{\Omega }^{{{e}_{l}}}}$$] 20 σ*(r)∂ϕ(r)∂n=0,r∈∂Ω\∪l=1Lel where σ*:=σ+2πfε∈ℂ[ Sm−1 ]$$\sigma *:=\sigma +2\pi f\varepsilon \in \mathbb{C}[{\rm{S}}\,{{\rm{m}}^{-1}}$$] is the nonhomogenous admittivity property of skin layer, σ and ε are the conductivity and absolute permittivity [F m⁻¹] respectively in Ω at the frequency f, ϕ(r)∈ℂ[V]$$\phi (\mathbf{r})\in \mathbb{C}[V]$$] is the electric potential distribution, and r := (x, y, z) is the coordinate system in subdomain Ω. Table 1 shows the geometry of the skin layer model with BIS electrodes e_l. The contact impedance on each electrode is Z_c = 50 [Ω]. Meanwhile, the electrical properties of stratum corneum [25], epidermis, dermis [26], and fat [27] are adopted from several literatures. Fig. 2 shows the comparison of conductivity σ(r) and relative permittivity ε_r(r) of each skin layer.

Table 1:

Parameters for training data set

Configuration parameter		Measurement parameter
Injection pattern φs	Electrode-length-to-skin-thickness ratio δb	Conductivity-changed layer ψp	Conductivity change Δσq [%]	Frequency pair frlh$$f_{r}^{lh}$$ [kHz]
I. Bipolar II. Tetrapolar	D/H < 1, D/H = 1, D/H > 1 Fixed electrode gap: dg = 1 [mm] Variable electrode diameter: de = {1, 2, 3}[mm] Electrode length: D = dg + de Fixed each layer thickness: hS = 50 [μm], hE = 0.45 [mm], hD = 2.5 [mm], hF = 5 [mm] Fixed skin thickness: H = hS + hE + hD + hF	ψ1 = Stratum Corneum only (S) ψ2 = Epidermis (E) only ψ3 = Dermis (D) only ψ4 = Fat (F) only ψ5 = S + E ψ6 = E + D ψ7 = D + F ψ8 = S + E + D ψ9 = E + D + F ψ10 = S + E + D + F	Δσ1 = −20 Δσ2 = −17.5 Δσ3 = −15 Δσ4 = −12.5 Δσ5 = −10 Δσ6 = −7.5 Δσ7 = −5 Δσ8 = −2.5 Δσ9 = 0 Δσ10 = 2.5 Δσ11 = 5 Δσ12 = 7.5 Δσ13 = 10 Δσ14 = 12.5 Δσ15 = 15 Δσ16 = 17.5 Δσ17 = 20	f1lh=2&10f2lh=2&35f3lh=2&100f4lh=2&225f5lh=10&35f6lh=10&100f7lh=10&225f8lh=35&100f9lh=35&225f10lh=100&225 $$\begin{array}{*{35}{l}} f_{1}^{lh}=2\And 10 \\ f_{2}^{lh}=2\And 35 \\ f_{3}^{lh}=2\And 100 \\ f_{4}^{lh}=2\And 225 \\ f_{5}^{lh}=10\And 35 \\ f_{6}^{lh}=10\And 100 \\ f_{7}^{lh}=10\And 225 \\ f_{8}^{lh}=35\And 100 \\ f_{9}^{lh}=35\And 225 \\ f_{10}^{lh}=100\And 225 \\ \end{array}$$

Δσ₉ = 0 [%] is considered as standard.

For each conductivity-changed layer, the other layer(s) are fixed with standard conductivity change value.

Case number follow this rule: φs_δb_ψp_Δσq_frlh$${{\varphi }_{s\_}}{{\delta }_{b\_}}{{\psi }_{p\_}}\Delta {{\sigma }_{q\_}}f_{r}^{lh}$$

(for example: I_D/H < 1_S_-20_2&10 which refers to injection pattern: φ_I = Bipolar_δ₁ = D/H < 1, ψ₁ = S, Δσ₁ = −20, and f3lh=2&100$$f_{3}^{lh}=2\And 100$$)

Total case: 2(φs)×3(δb)×10(ψp)×17(Δσq)×10(frlh)=10200 $$2({{\varphi }_{s}})\times 3({{\delta }_{b}})\times 10({{\psi }_{p}})\times 17(\Delta {{\sigma }_{q}})\times 10(f_{r}^{lh})=10200$$

Fig. 2:

The FNN in this paper was used as a supervised skin layer classification learner. Feedforward neural network (FNN) in this paper were implemented using a Matlab Machine Learning and Deep Learning Toolbox (Mathworks, Natick, MA, United States) on a laptop with CPU AMD Ryzen 7 PRO 4750U @1.7 GHz. K-fold = 5 is used to validate the accuracy. The accuracy Acc [%] is expressed as follows: 21 Acc=TpredictTsamples×100 [$$Acc=\frac{{{T}_{\rm{predict}}}}{{{T}_{\rm{samples}}}}\times 100$$] where, T_predict is the number of true predictions and T_samples is the number total samples used in the training data.

Fig. 3 shows the comparison of the Nyquist plot from the impedance measurement of two φ_s in the case of all ψ_p with Δσ_q = {−20,0(standard),+20}[%] where D/H < 1 in all frequencies. The impedance spectrums in the Nyquist plot change slightly among the different conductivity change variations. The tendency of the impedance spectrum from the bipolar set-up is similar to the behavior with a Warburg impedance. Meanwhile, in the case of the tetrapolar set-up, the impedance spectrum has some electrical behaviors, which are a charge transfer, dielectric interphase, conductive part, and diffusion part. Nevertheless, the conductivity change is difficult to classify from these data representations.

Fig. 3:

The slight changes due to different conductivity shown in the Nyquist plot from simulation is well translated by DRT as shown in Fig. 4, which displays multiple local maxima towards higher gamma values as the conductivity increases toward different skin layer acquired from two φ_s in the case of all ψ_p with Δσ_q = {−20,0(standard),+20}[%] where D/H < 1 in all frequencies. By inspection, the DRT serves as an indicator given the retrieved relaxation times of each skin layer. The local maxima observed begin and end by local minimum. Hence, this local minimum between the local maxima is important as indication of the frequency range applied to a skin layer. This observation forms the basis for determining the frequency pairs of each skin layer where changes in conductivity have significant or insignificant effects.

Fig. 4:

As part of pre-processing data for FNN, feature extraction is performed to select only the features that would contribute most to the quality of data features that will be highly correlated with the output. The introduction of four impedance inputs with a wide range of frequencies leads to feature extraction with several options called one matrix, two matrices, three matrices, and four matrices profile, as shown in Table 2.

Feature extraction will evaluate the matrices by comparison of average validation accuracy results. Fig. 5 shows the comparison of FNN average accuracy Acc regarding to the matrix of impedance inputs. The figure illustrates that as the number of inputs increases, the accuracy increases for both bipolar and tetrapolar injection patterns. This finding suggests a positive correlation between the number of inputs and accuracy. The four matrices profile shows the highest accuracy in all selected frequency pairs, meaning the selected features on the four matrices profile are relevant to achieve better accuracy on the validation sets, as shown in Fig. 6.

Fig. 5:

Fig. 6:

Fig. 7 shows the experimental setup composed of a co-planar sensor with multiple electrodes, an impedance analyzer (IM3570, Hioki EE Corporation, Tokyo, Japan) as a data acquisition system, a switching, and a PC for command and post-processing. The electrodes are manufactured on a printed circuit board and made of stainless steel with a diameter of 1 mm, a height of 1 mm, and distance between both electrodes is 1 mm.

Fig. 7:

In bipolar mode, one electrode serves as the current injector and high potential electrode in a two-wire measuring system, while the other electrode serves as the ground and low potential electrode. In tetrapolar mode, e₁ acts as the current injector, e₂ serves as the high potential electrode, the low potential electrode is e₃, and the ground electrode is performed by e₄. The ground electrode receives current from the current injector electrode as it passes through the measuring object. The high potential and low potential electrodes simultaneously measure the voltage produced by the current flow.

Porcine skin was used as the measurement object because of its comparable mechanical and electrical characteristics to human skin. Several studies have shown that porcine skin is similar to human skin in general structures [28], thickness [29], lipid composition [30], and dielectric properties [31]. While human skin varies from person to person, porcine skin remains a valuable model for human skin studies.

The porcine skin still bound together the muscle and fat. The sample must first be adjusted to the proper temperature (about 35 °C), after which extra layers of fat and muscle must be removed, leaving only the stratum corneum, epidermis, and dermis, along with one layer of fat and one layer of muscle, to maintain accurate measurements throughout the experiment.

In order to validate the proposed method, an experiment with porcine skin is used by creating variation in conductivity by injecting saline water into the dermis layer. Our study divided a large-sized pig skin into five samples based on the NaCl concentration levels. For both the bipolar and tetrapolar injection patterns, each sample underwent three injections at different locations within the dermis layer. Subsequently, we performed three repeated measurements at each location. Therefore, in summary, each sample was subjected to nine measurements. The average of these measurements was then used as the input for the validation dataset in the FNN model, specifically for the dermis (D) layer, as specified in Table 3. Saline water, with a concentration of C_NaCl = 25 [mM], is considered the standard value. This experiment’s conditions are to mimic the conductivity change at the dermis layer artificially [32]. The impedance measurement method is bipolar and tetrapolar with i = 1 [mA] and frequency pair frlh$$f_{r}^{lh}$$ as used in the simulation. The electrode-length-to-skin-thickness ratios are D/H < 1, D/H = 1, and D/H > 1.

Table 3:

Experimental conditions

Configuration parameter		Measurement parameter
Injection pattern φs	Electrode length ratio to skin thicknessδb	Conductivity-changed layeryp	ConcentrationCNacl [mM]	Frequency pair frlh$$f_{r}^{lh}$$ [kHz]
I. Bipolar II. Tetrapolar	D/H < 1, D/H = 1, D/H > 1	Dermis (D) only	c1 = 15 c2 = 20; c3 = 25; c4 = 30; c5 = 35;	f1lh=2&10;f2lh=2&35;f3lh=2&100;f4lh=2&225;f5lh=10&35;f6lh=10&100;f7lh=10&225;f8lh=35&100;f9lh=35&225;f10lh=100&225$$\begin{array}{*{35}{l}} f_{1}^{lh}=2\And 10; \\ f_{2}^{lh}=2\And 35; \\ f_{3}^{lh}=2\And 100; \\ f_{4}^{lh}=2\And 225; \\ f_{5}^{lh}=10\And 35; \\ f_{6}^{lh}=10\And 100; \\ f_{7}^{lh}=10\And 225; \\ f_{8}^{lh}=35\And 100; \\ f_{9}^{lh}=35\And 225; \\ f_{10}^{lh}=100\And 225 \\ \end{array}$$

The research related to animals use has been complied with all the relevant national regulations and institutional policies for the care and use of animals.

Based on the results from DRT, Fig. 8 and Fig. 9 show the distribution function γ in all frequencies under various concentrations and all electrode-length-to-skin-thickness ratios for bipolar and tetrapolar mode, respectively, for the experimental studies. Different distribution function values of several local maximums also represent different conductivity change values from different concentrations, which means the system is indistinguishable and requires further investigation. Several local maximums are observed in both figures representing optimum frequencies at which the system exhibits maximum sensitivity or the most informative response. Hence, it gives a range of frequencies of interest that could be the location to extract the informative response of the system, which can be used for further investigation, in this particular case, for classification.

Fig. 8:

Fig. 9:

At high-frequency ranges, information about the stratum corneum known to have high resistance requires additional investigation [25]. The distribution function in the medium frequency regions is relatively low, requiring further experiments and analysis regarding the epidermis layer. Finally, the local maxima are due to dermis layer effect at low-frequency ranges since the increased injected saline water concentration is related to the decreased local maxima [17]. The distribution of relaxation time in simulation and experiment shows a similar trend. Thus, the heuristic selection of frequency pair shown in Table 3 is acceptable.

The confusion matrix is a useful tool for evaluating the performance of a classification model. In our studies, the FNN for bipolar mode at f6lh$$f_{6}^{lh}$$ achieved a high classification accuracy of 90.6% for the dermis layer (DE), which is promising. However, there were still some misclassifications, with 2.9% classified as epidermis (EP), 3.5% as fat (FAT), and 2.9% as stratum corneum and epidermis layers (SCEP). For tetrapolar mode at f8lh$$f_{8}^{lh}$$, the result showed that 90.6% of DE was classified correctly, while EP and FAT were classified at 0.0%, stratum corneum (SC) at 5.9%, and the SCEP at 3.5%, as shown in Fig. 10. The 0.0% classification in the confusion matrix does not indicate an error or confusion of DE for SC in bipolar or EP and FAT in tetrapolar injection patterns. Instead, it signifies that there were no instances of misclassification between these specific classes. Furthermore, the amount of data used in the analysis is sufficient for the purpose of this study. Also, it is important to note that the experimental conditions involved only the DE class for the model. While the overall accuracy is accountable, the misclassifications suggest room for improvement in the model.

Fig. 10:

One potential reason for the misclassifications could be the similarity between the dermis and epidermis layers in terms of their electrical properties [26]. Future studies could consider incorporating additional features [33] or imaging techniques [34], highlighting the importance of continuing to refine the model and improving the accuracy of the classification for these layers. Overall, the confusion matrix results demonstrate the potential of the FNN in accurately classifying skin layers but also highlight the need for further optimization and refinement of the model.

Table 4 compares the FNN accuracy Acc between bipolar and tetrapolar injection patterns in each frequency pair variation. It shows that bipolar mode at f6lh$$f_{6}^{lh}$$ achieved the highest accuracy, Acc 90.6% and tetrapolar mode at f8lh$$f_{8}^{lh}$$ achieved the same accuracy. The study focused primarily on evaluating the classification performance and the influence of different injection patterns. It did not explicitly assess the effect of systematic error during the measurement. However, it is important to note that inherent systematic errors exist in the experimental results. Frequency pair is one of the ways to minimize this effect because systematic error due to stray capacitance or contact impedance is also frequency dependent. The discrepancy in performance between bipolar and tetrapolar injection patterns can be attributed to the difference in current pathway lengths. The variation in current pathway length directly affects the sensitivity of the measurement, as shown in Fig. 11. Therefore, the performances observed in Table 4 result from these differences in current pathway length.

Fig. 11:

The study found that the FNN demonstrated promising results as a tool for skin layer classification, along with other bioelectrical impedance spectroscopy post-processing approaches.

Two injection patterns were employed to train the FNN, and while they performed differently, both had high accuracy. In order to validate these discrepancies, the sensitivity matrix map was used, which showed the effective area that passed by the electrical current distribution during the impedance measurement, as shown in Fig. 11. Although the sensitivity matrix map could differ from actual skin layer circumstances, it gave insight into the penetration depth of the electrical current under ideal conditions [35].

Real scenarios often involve an unknown skin thickness, making it difficult to evaluate the penetration depth of the electrical current by adjusting the electrode length. The study tested three different electrode-to-skin thickness ratios (D/H): D/H < 1, D/H = 1, and D/H > 1, corresponding to -10% to +50% of the skin thickness range. Under these conditions, results showed that the FNN had high accuracy rates in classifying skin layers in simulations and experiments. However, it could be challenging to obtain accurate results with electrode lengths similar to those of common biopotential electrodes like ECG (5 mm) or electromyography (10 mm). Further studies are necessary to investigate this issue.

The impedance inputs α_ξ, proposed in this study, shows the reliability of features extraction to classify the conductivity change in the BIS measurement for skin layer classification. Using the impedance inputs α_ξ in the FNN training reduces the number of training data significantly.

The conductivity change of skin layer affects all the impedance measurement parameters, which are impedance, phase angle, resistance, and reactance. By evaluating the results of Fig. 4, the impedance inputs α_ξ in equations (4) to (7) are representations of a ratio metric form that amplifies the presence of conductivity change. As a result, the impedance inputs α_ξ reduce the ill-posed problem of impedance measurement for skin layer classification of conductivity change.

In the experiment, measurement noise and systematic error inherently appear and are difficult to consider in the simulation. Nonetheless, the proposed method was confirmed by the experiment with skin because the data featuring based on impedance inputs α_ξ at the selected frequency pair successfully eliminates the conductivity change that are not from the skin layer.