Skin Impedance Analysis for Drug Delivery: Integration of Poisson–Boltzmann–Nernst–Planck Model and Ebola Optimisation Algorithm

L Maceal Tony; R.S Shaji

doi:10.2478/msr-2025-0038

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Skin Impedance Analysis for Drug Delivery: Integration of Poisson–Boltzmann–Nernst–Planck Model and Ebola Optimisation Algorithm

Measurement Science Review

Volume 25 (2025): Issue 6 (December 2025)

By: L Maceal Tony and R.S Shaji

Open Access

|Dec 2025

Figures & Tables

Sequence of steps adopted in this research for drug delivery.

Flowchart of the proposed model for predicting drug penetration across various skin layers.

Flowchart of the Ebola Optimisation Algorithm for SLRC circuit parameter normalisation.

Visual representation of (a) Anatomical sites on the human body considered for iontophoretic drug delivery simulation. (b) Simulated drug concentration profiles across skin depths using the proposed model.

Table 1.

Impedance [Ω cm²] across different skin layers for all models.

Layer	Montague	CPE	Tregear-1	Tregear-2	SLRC (proposed)
SC	8452.34	8339.12	8210.89	6543.78	6520.43
Epidermis	6295.12	6203.98	6289.67	5082.34	4752.89
Dermis	783.12	710.45	735.56	850.92	903.78
Hypodermis	365.45	285.67	299.45	522.34	610.12
Depth	8.21	0.12	0.00	276.45	371.54

Table 2.

Electrotransport flux [μg/mm²s] across different skin layers for all models.

Layer	Montague	CPE	Tregear-1	Tregear-2	SLRC (proposed)
SC	167.12	162.34	165.45	139.87	126.78
Epidermis	125.87	122.76	123.56	103.45	95.34
Dermis	17.12	15.78	16.45	18.12	17.89
Hypodermis	7.12	6.45	6.89	11.34	13.56
Depth	0.34	0.00	0.12	5.87	7.34

Table 3.

Total drug concentration [mole/m³] across different skin layers for all models.

Layer	Montague	CPE	Tregear-1	Tregear-2	SLRC (proposed)
SC	390.67	387.12	392.34	418.12	378.56
Epidermis	328.45	324.67	326.12	275.67	260.78
Dermis	7.12	6.89	7.34	6.12	7.45
Hypodermis	3.89	2.87	3.23	4.45	5.34
Depth	0.65	0.00	0.12	1.78	2.56

(a) Skin impedance; (b) Electrotransport flux; and (c) Drug concentration derived from the electrotransport component with variation in skin depth.

Table 4.

Total drug concentration [mole/m³] with variations in current density (I, mA/cm²).

I [mA/cm²]	I = 0.1	I = 0.2	I = 0.4	I = 0.5	I = 1.0
SC	140.12	205.36	329.85	392.47	710.29
Epidermis	89.34	132.19	218.76	261.42	480.14
Dermis	2.32	3.76	6.45	7.84	15.08
Hypodermis	1.63	2.42	3.89	4.51	8.12
Depth	1.24	1.62	2.36	2.72	4.51

Total drug concentration [μg/mm³] at different skin layers in current density [mA/cm²].

Analysis of the proposed model based on *MAPE* and R² values across various body regions.

Performance analysis of the proposed model based on *MAPE* vs Frequency for TDD.

Table 5.

Mean and SD [Ω] of impedance for various body parts.

Body parts	2 × 10³ Hz		4 × 10³ Hz		8 × 10³ Hz
Body parts	Mean	SD	Mean	SD	Mean	SD
Face	5.60 × 10³	1840.12	4.20 × 10³	1450.25	6.80 × 10³	2115.37
Neck	1.02 × 10⁴	2155.20	7.85 × 10³	1780.55	1.12 × 10⁴	2401.28
Shoulder	1.10 × 10⁴	2250.30	8.20 × 10³	1720.45	1.18 × 10⁴	2435.12
Chest	1.25 × 10⁴	2445.41	9.05 × 10³	1865.33	1.34 × 10⁴	2560.11
Belly	1.30 × 10⁴	2235.75	9.50 × 10³	1900.25	1.38 × 10⁴	2710.32
Hip	1.18 × 10⁴	2145.88	8.70 × 10³	1805.40	1.26 × 10⁴	2605.45
Back	1.12 × 10⁴	2140.82	8.50 × 10³	1775.55	1.22 × 10⁴	2525.87
Ventral	1.25 × 10⁴	2195.65	9.20 × 10³	1825.75	1.32 × 10⁴	2650.20
Dorsal	1.50 × 10⁴	2280.34	1.05 × 10⁴	1950.45	1.60 × 10⁴	2755.30
Palm	1.75 × 10⁴	2370.12	1.20 × 10⁴	2050.50	1.85 × 10⁴	2855.20
Knee	1.45 × 10⁴	2200.55	1.00 × 10⁴	1850.15	1.55 × 10⁴	2705.75
Ankle	1.60 × 10⁴	2335.22	1.12 × 10⁴	1955.40	1.70 × 10⁴	2800.35

*MAPE* value comparison of different models for different body parts (a) Upper body regions and (b) Lower body regions.

Table 6.

Comparison analysis of the proposed SLRC circuit with existing models across various body parts.

	MAPE values					R_sc	C_T	S_F	R²
Body parts	Montague	CPE	Tregear-1	Tregear-2	Proposed	Proposed	Proposed	Proposed	Proposed
Face	0.613	0.531	0.665	0.582	0.483	72.476	0.495	1.000	0.945
Neck	0.561	0.342	0.585	0.506	0.309	17.465	0.496	0.924	0.961
Shoulder	0.518	0.320	0.578	0.501	0.284	13.584	0.451	0.870	0.964
Chest	0.501	0.320	0.564	0.507	0.225	10.027	0.447	0.884	0.972
Belly	0.505	0.256	0.515	0.519	0.250	45.268	0.312	0.998	0.968
Hip	0.520	0.280	0.528	0.498	0.261	38.923	0.315	0.962	0.965
Back	0.505	0.284	0.546	0.415	0.250	15.385	0.286	0.984	0.966
Ventral	0.494	0.343	0.556	0.506	0.268	23.948	0.471	0.908	0.962
Dorsal	0.475	0.272	0.495	0.512	0.283	80.638	0.352	1.000	0.958
Palm	0.494	0.211	0.472	0.418	0.134	18.225	0.441	0.844	0.981
Knee	0.463	0.297	0.424	0.495	0.257	55.687	0.346	0.975	0.969
Ankle	0.505	0.266	0.532	0.483	0.220	40.315	0.417	0.903	0.974

Table 7.

Comparison of different optimisation algorithms.

Algorithm	MAPE	R²	Convergence time [s]
BO	0.307	0.961	18.6
PSO	0.276	0.948	14.1
GA	0.265	0.954	12.5
EOA (ours)	0.234	0.982	9.3

Table 8.

Comparison evaluation: State-of-the-art models vs the Proposed model.

Reference	R²	MAPE	Complexity	Training time [s]	Inference time [ms]
[28]	0.81	0.492	O(n²)	180	50
[29]	0.84	0.478	O(n²)	240	60
[6]	0.76	0.529	O(n²)	300	70
[8]	0.79	0.507	O(n² log n)	220	65
Proposed	0.96	0.134	O(n log n)	95	20

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DOI: https://doi.org/10.2478/msr-2025-0038 | Journal eISSN: 1335-8871

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Language: English

Page range: 347 - 357

Submitted on: Mar 12, 2025

Accepted on: Jul 25, 2025

Published on: Dec 23, 2025

Published by: Slovak Academy of Sciences, Institute of Measurement Science

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

transdermal drug delivery,

iontophoresis,

spine–leaf resistor–capacitor,

Ebola Optimisation Algorithm,

Poisson–Boltzmann–Nernst–Planck

Related subjects:

Engineering,

Electrical engineering,

Control engineering, metrology and testing

© 2025 L Maceal Tony, R.S Shaji, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 25 (2025): Issue 6 (December 2025)

Skin Impedance Analysis for Drug Delivery: Integration of Poisson–Boltzmann–Nernst–Planck Model and Ebola Optimisation Algorithm

Figures & Tables

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Fig. 5.

Table 1.

Table 2.

Table 3.

Fig. 6

Table 4.

Fig. 7.

Fig. 8.

Fig. 9.

Table 5.

Fig. 10.

Table 6.

Table 7.

Table 8.

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