The effect of magnetic nanoparticle dispersion on temperature distribution in a spherical tissue in magnetic fluid hyperthermia using the lattice Boltzmann method

Figures & data

Figure 1. Schematic plot of the D3Q15 lattice.

Figure 2. Curved boundary and lattice nodes (open large circle is computational boundary node, open small circle is media node, filled circle is the physical boundary node in the link of media node and computational boundary).

Figure 3. Schematic plot of tissue and tumour. Left, section; right, perspective.

Table 1.  Properties of the tissue, the blood, the FCC FePt MNPs and the magnetic field.

Blood and tissue						FCC FePt MNPs and magnetic field
Property	Unit	Quantity	Property	Unit	Quantity	Property	Unit	Quantity
Qm1	W/m^3	540	ρ1	kg/m^3	1060	ρMNP	kg/m^3	15200
Qm2	W/m^3	540	ρ2	kg/m^3	1060	cpMNP	J/(kg K)	327
Wb1	s^−1	0.0064	cp1	J/(kg K)	3600	Md	kA/m	446
Wb2	s^−1	0.0064	cp2	J/(kg K)	3600	K	kJ/m^3	9
ρb	kg/m^3	1000	Tb	°C	37	δ	nm	1
cpb	J/(kg K)	4180	T0	°C	37	D	nm	9
k1	W/(m K)	0.502	R1	cm	0.5	H0	mT	50
k2	W/(m K)	0.502	R2	cm	1.5	f	kHz	300

Figure 4. Effect of particle diameter on power dissipation of FCC FePt MNPs.

Figure 5. Effect of volume fraction on power dissipation of 9-nm FCC FePt MNPs.

Figure 6. Steady state temperature distribution in the infinite spherical tissue for where B = 800 k W/m³ and r₀ = 5 mm.

Figure 7. Temperature elevation in the injection site in agarose gel for a gel concentration of 0.2% and an infusion flow rate 4 µl/min for SAR(r) = Be^−r2/r20 where B = 887.8 k W/m³ and r₀ = 5.62 mm.

Figure 8. History of temperature at the centre of the tumour deposited with 9-nm FCC FePt MNPs.

Figure 9. Temperature distributions in the tissue deposited with 9-nm FCC FePt MNPs at t = 600 s.

Figure 10. Temperature distributions in the tissue deposited with 9-nm FCC FePt MNPs at t = 50 s and t = 100 s.

Figure 11. Temperature distributions in the tissue deposited with 9-nm FCC FePt MNPs at t = 600 s in case II as a function of r₀.