Table 1
Thermophysical and electromagnetic properties of prostate and tumour tissue for frequency f = 100 kHz used in Pennes bioheat equation and in magneto-quasi-static solver [18]
| Tissue name | Mass density | Specific heat capacity | Thermal conductivity | HGR (W/kg) | HTR (W/m3/K) | Conductivity |
|---|---|---|---|---|---|---|
| ρ [kg/m3] | c [J/kg/K] | k [W/m/K] | σ (S/m) | |||
| Prostate | 1045.0 | 3760.0 | 0.5115 | 6.10369 | 27820.2 | 4.39·10−1 |
| Tumour | 1090.4 | 3421.2 | 0.4500 | 0.9061 | 2705.95 | 3.63·10−1 |
HGR – Heat Generation Rate per unit mass.
HTR – Heat Transfer Rate coefficient per unit volume and temperature difference.
Source: data from Baumgartner et al.
Figure 1
The designed air coil and the human model.
Figure 2
Comparison of geometric primitives to the naturalistic irregular tumour model: (a) cube, (b) sphere, and (c) cylinder.
Table 2
Volume and surface area of the analysed tumour models
| Tumour model | Dimensions (mm) | Volume (mm3) | Area (mm2) |
|---|---|---|---|
| Irregular | — | 392.624 | 317.599 |
| Cylinder | r = 4, h = 10.5 | 525.112 | 363.58 |
| Sphere | R = 5.48 | 689.008 | 377.971 |
| Cube | a = 9 | 728.489 | 479.669 |
Table 3
Properties of magnetic nanoparticles [6]
| Magnetic material | M d (kA/m) | K (kJ/m3) |
|---|---|---|
| Maghemite | 414 | 4 |
| Magnetite | 446 | 41 |
| Cobalt ferrite | 425 | 190 |
| Barium ferrite | 380 | 315 |
Source: data from Rosensweig.
Figure 3
Magnetic field distribution (H) in the XY cross-section for f = 100 kHz with regard to the prostate (white).
Figure 4
Magnetic field distribution (H) in the XZ cross-section for f = 100 kHz with regard to prostate (white).
Table 4
Comparison of magnetic nanoparticle parameters required to achieve therapeutic temperatures in different tumour models for H = 2.67 kA/m and f = 100 kHz
| Tumour model | φ (%) | Maximum power density | ||
|---|---|---|---|---|
| Maghemite | Cobalt ferrite | Barium ferrite | P (W/m3) | |
| Naturalistic | 0.489 | 5.49 | 6.87 | 712890 |
| Cylinder | 0.293 | 3.30 | 4.12 | 427734 |
| Sphere | 0.269 | 3.02 | 3.78 | 392089 |
| Cube | 0.244 | 2.75 | 3.43 | 356445 |
Figure 5
Volumetric power density P required to achieve therapeutic temperature in the analysed tumour models (XY cross-section (left) and XZ cross-section (right)).
Figure 6
The temperature rise over time in analysed models regarding (a) naturalistic tumour (P = 712890 W/m3), (b) cylinder (P = 427734 W/m3), (d) sphere (P = 392089 W/m3), and (e) cube (P = 356445 W/m3).