Computational feasibility of deformable mirror microwave hyperthermia technique for localized breast tumors

Figures & data

Figure 1. (a) Schematic illustration of the dual mirror microwave technique for thermal therapy of localized breast cancer (not drawn to scale). (b) Arrangement of the mirror and breast coronal section in the computational model; a1 = a2 = 1.25λ_c, b1 = b2 = 3.75λ_c, c1 = c2 = D, d1 = d2 = 2λ_c, D = max{X_len, Y_len}; s₁, s₂: sources (figure drawn approximately to scale; see Table II for λ_c).

Figure 2. (a) Focusing strategy (ε_r2: tissue dielectric permittivity; ε_r1: couplant dielectric permittivity; μ₀: magnetic permeability), and (b) surface tangents inside S for adaptive field focusing.

Figure 3. Mirror shape estimation (a) Mirror deformations estimated for given source and tumor locations. (b) Path lengths from to computed for mirror 1 in (3a).

Figure 4. Two-dimensional representation of the (a) dual mirror microwave technique for hyperthermia, (b) computational model.

Figure 5. Normalized field magnitude maintained inside the tank. (a) 500 MHz and (b) 700 MHz for single mirror; (c) 500 MHz and (d) 700 MHz for dual mirror (x denotes target location).

Figure 6. Tissue permittivity map for the MR breast image. Boundary extraction for (a) skin and (b) tumor; (c) relative permittivity and (d) electrical conductivity (S/m) obtained using Equation 10 and [10], [24].

Table I.  Patient information for MR derived breast models.

Model	Age	Pathology	Lesion size	Tissue heterogeneity
I	33	Lobular carcinoma	23 × 12 mm in right breast	Heterogeneously dense
II	42	Lobular carcinoma	7 × 7 mm in left breast	Scattered fibro-glandular tissue
III	42	Lobular carcinoma	19 × 17 mm in left breast	Moderately scattered fibro-glandular tissue
IV	58	Ductal carcinoma in situ	14 × 13.5 mm in right breast	High fibro-glandular tissue

Figure 7. Coronal MR breast images used in the hyperthermia simulations (a) patient data I, (b) patient data II, (c) patient data III, (d) patient data IV (black contours indicate tumor sites).

Figure 8. Tissue SAR (W/kg/m) inside MR derived breast models for which and (a) Model I, (b) Model II, (c) Model III, (d) Model IV.

Table II.  Electrical and thermal properties of breast tissues [10], [24–26] (ε = ε′–jε″, couplant permittivity, ε_c = 43.76-j22.82, c_b = 4000 (J/kg/°C), T_b = 37°C, f = 500 MHz, λ_c = 0.0907m).

Tissue type	εr	σ (S)	κ (W/m/C)	wb (kg/m^3/s)	ρ (kg/m^3)
Normal	18.00 [10]	0.13 [10]	0.22 [25]	1.1 [25]	888 [25]
Malignant	57.60 [10]	0.90 [10]	0.56 [25]	1.8 [25]	1050 [25]
Skin	48.63 [24]	0.705 [24]	0.42 [26]	2.275 [26]	1040 [26]

Figure 9. Steady state temperature for the tissue SAR in Figure 8 (T₀ = 30°C), (a) Model I, (b) Model II, (c) Model III, (d) Model IV.

Table III.  Tumor and normal tissue damage for the hyperthermia simulations.

Model	% Tumor damage (TD)	% Normal tissue damage (CTD)	T90 (°C)
I	80.34	3.17	40.46
II	97.56	0.16	41.35
III	87.95	1.62	40.81
IV	97.14	5.53	41.97

Figure 10. Hyperthermia simulation for model III with 60% decrease in ε_tumor. (a) Dielectric constant; (b) electrical conductivity at 500 MHz using Equation 10 and [10], [24]; (c) steady state thermal contours.

Figure 11. EM energy deposited inside the benign breast tissue for field focus at (−0.093, − 0.0475). (a) Tissue dielectric constant, (b) electrical conductivity, (c) coronal MR breast image, (d) Tissue SAR within the breast model (W/kg/m).

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