Numerical Estimation of SAR and Temperature Distributions inside Differently Shaped Female Breast Tumors during Radio-Frequency Ablation
Abstract
:1. Introduction
2. Materials and Methods
2.1. Female Breast Phantom Model
2.2. Material Properties
2.3. RF Applicator Model
2.4. Equivalent Tumor Models
2.5. Electro-Conductive Field and Generalized Laplace Equation
2.6. Modified Pennes Bioheat Transfer Equation
2.7. SAR and Power Dissipation Values
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Tissue | σ (S/m) | ρ (kg/m3) | C (J/kg/K) | k (W/m/K) | HTR * (mL/min/kg) | HTR * (W/m3) | HGR ** (W/kg) |
---|---|---|---|---|---|---|---|
Blood | 0.7030 | 1050 | 3617 | 0.517 | 10,000 | 6.646 × 105 | 0 |
Breast fat | 0.0250 | 911 | 2348 | 0.209 | 47 | 2710 | 0.728 |
Breast gland | 0.5370 | 1041 | 2960 | 0.334 | 150 | 9884 | 2.323 |
Fat | 0.0434 | 911 | 2348 | 0.211 | 33 | 1903 | 0.507 |
Muscle | 0.3618 | 1090 | 3421 | 0.495 | 37 | 2553 | 0.906 |
Skin | 0.0005 | 1109 | 3391 | 0.372 | 106 | 7441 | 1.648 |
Tumor | 0.3618 | 1090 | 3437 | 0.563 | Equation (9) | Equation (9) | 12 |
Breast Tumor Tissues | x-axis Length a (mm) | y-axis Length b (mm) | z-axis Length c (mm) | Total Surface Area Acalc (cm2) | Total Surface Area Ameas (cm2) | Total Volume Vcalc (cm3) | Total Volume Vmeas (cm3) | Total Mass mcalc (g) | Total Mass mmeas (g) |
---|---|---|---|---|---|---|---|---|---|
Ellipsoid E1 | 16.412 | 29.354 | 10.866 | 13.153 | 12.716 * | 2.740 | 2.749 * | 2.989 | 2.998 * |
Sphere S1 | 17.474 | 17.474 | 17.474 | 9.593 | 9.538 * | 2.794 | 2.771 * | 3.046 | 3.021 * |
Ellipsoid E2 | 26.574 | 42.588 | 27.675 | 31.498 | 32.153 * | 16.395 | 16.310 * | 17.882 | 17.790 * |
Sphere S2 | 36.000 | 36.000 | 36.000 | 40.715 | 40.484 * | 24.429 | 24.270 * | 26.637 | 26.460 * |
Tumor T | 38.630 | 24.269 | 24.269 | 12.320 ** | 12.722 * | 2.844 ** | 2.791 * | 3.101 ** | 3.043 * |
Breast Tissues | Total Mass m (g) | Total Volume V (cm3) | Maximum Local SAR SARmax (W/kg) | Mass-Average Local SAR SARmass (W/kg) | Total Loss Power Density p = SARvol (W/m3) | Spatial-Average Local SAR ** psSAR1g (W/kg) | Total Loss Power P (W) |
---|---|---|---|---|---|---|---|
Breast fat * | 4766.2 | 5232.1 | 9560 | 4.95 × 10−3 | 13.525 | 650.82 | 0.0254 |
Breast gland * | 814.8 | 783.0 | 2,7440 | 7.099 | 7388.65 | 699.33 | 1.1485 |
Fat * | 441.3 | 484.4 | 11,430 | 4.41 × 10−2 | 40.153 | 1050.0 | 0.0195 |
Muscle * | 731.3 | 670.6 | 1.61 × 10−6 | 8.24 × 10−7 | 8.99 × 10−4 | 1.58 × 10−6 | 6.0 × 10−7 |
Skin * | 495.6 | 446.9 | 4.10 × 10−4 | 8.31 × 10−7 | 9.22 × 10−4 | 0.142 | 19.524 |
Ellipsoid E1 | 2.998 | 2.749 | 152,700 | 326.435 | 355 984 | 823.41 | 0.9786 |
Sphere S1 | 3.021 | 2.771 | 151,900 | 327.576 | 357,163 | 825.05 | 0.9897 |
Ellipsoid E2 | 17.79 | 16.31 | 155,600 | 58.844 | 64,175 | 833.98 | 1.0467 |
Sphere S2 | 26.46 | 24.27 | 155,800 | 39.733 | 43,325 | 835.40 | 1.0515 |
Tumor T | 3.043 | 2.791 | 167,200 | 327.894 | 357,506 | 824.83 | 0.9978 |
Breast Tissues | Ablation Volume VISO-50 (mm3) | Relative Error δ (%) |
---|---|---|
Ellipsoid E1 | 242.536 | 8.656 |
Sphere S1 | 226.064 | 1.276 |
Ellipsoid E2 | 201.253 | 9.839 |
Sphere S2 | 204.365 | 8.445 |
Tumor T | 223.215 | – |
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Miaskowski, A.; Gas, P. Numerical Estimation of SAR and Temperature Distributions inside Differently Shaped Female Breast Tumors during Radio-Frequency Ablation. Materials 2023, 16, 223. https://doi.org/10.3390/ma16010223
Miaskowski A, Gas P. Numerical Estimation of SAR and Temperature Distributions inside Differently Shaped Female Breast Tumors during Radio-Frequency Ablation. Materials. 2023; 16(1):223. https://doi.org/10.3390/ma16010223
Chicago/Turabian StyleMiaskowski, Arkadiusz, and Piotr Gas. 2023. "Numerical Estimation of SAR and Temperature Distributions inside Differently Shaped Female Breast Tumors during Radio-Frequency Ablation" Materials 16, no. 1: 223. https://doi.org/10.3390/ma16010223