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Fig. 5.
Fig. 6
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Fig. 9.
Fig. 10.
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 |
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 |
Comparison analysis of the proposed SLRC circuit with existing models across various body parts_
| MAPE values | Rsc | CT | SF | 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 |
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 |
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 |
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 |
Mean and SD [Ω] of impedance for various body parts_
| Body parts | 2 × 103 Hz | 4 × 103 Hz | 8 × 103 Hz | |||
|---|---|---|---|---|---|---|
| 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 |
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 |