Analysis of Optimal Treatment Starting Time for Photothermal Therapy Through Analysis of Diffusion Behavior of Gold Nanoparticles

Figures & data

Figure 1 Schematic of numerical model.

Table 1 Thermal and Optical Properties of Skin Layers and SCC^31–35

	ρ (kg/m^3)	cp (J/kgK)	km (W/mK)	t (mm)	ωb (1/s)	μabs (1/mm)	μ’sca (1/mm)
Epidermis	1200	3589	0.235	0.1	0	0.4	9
Papillary dermis	1200	3300	0.445	0.5	0.0031	0.38	6
Reticular dermis	1200	3300	0.445	0.6	0.0031	0.48	2.5
Subcutaneous fat	1000	2674	0.19	3	0.0031	0.43	1
SCC	1070	3421	0.495	2	0.0063	0.047	0.221

Table 2 Parameters of Numerical Analysis

Parameter	Case	Number	Remarks
Laser power (Pl)	0 to 1 W	51	Intv: 0.02 W
Injection dose of GNRs	100 to 400 μg/mL	4	Intv: 100 μg/mL
Elapsed time after injection (τh)	1 min to 24 h	14	1,2,3,5,10,20,30 min 1,2,4,8,12,18,24 h

Figure 2 Diffusion validation result.²¹

Figure 3 Temperature validation result.²¹

Figure 4 Radial Concentration Distribution (center position, depth = 1 mm). (a) τ_h = 2 h; (b) Injection dose = 200 μg/mL; (c) Injection dose = 200 μg/mL (1 m < τ_h < 30 m).

Figure 5 Temperature variation with laser irradiation time (center position, depth = 1 mm, P_l = 0.2 W). (a) τ_h = 2 h; (b) Injection dose = 200 μg/mL.

Figure 6 Continued.

Figure 6 Apoptosis retention ratio(θ*_A) for various P_l and τ_h. (a) Injection dose = 100 μg/mL; (b) Injection dose = 200 μg/mL; (c) Injection dose = 300 μg/mL; (d) Injection dose = 400 μg/mL.

Figure 7 Continued.

Figure 7 Thermal hazard retention value (θ*_H) for various P_l and τ_h. (a) Injection dose = 100 μg/mL; (b) Injection dose = 200 μg/mL; (c) Injection dose = 300 μg/mL; (d) Injection dose = 400 μg/mL.

Figure 8 Continued.

Figure 8 Effective apoptosis retention ratio (θ*_eff) for various P_l and τ_h. (a) Injection dose = 100 μg/mL; (b) Injection dose = 200 μg/mL; (c) Injection dose = 300 μg/mL; (d) Injection dose = 400 μg/mL.

Figure 9 Optimal value of θ*_eff and P_l for various injection dose. (a) Maximum effective apoptosis retention ratio; (b) Optimal power.

Table 3 Optimal Conditions for Various Injection Dose

Injection dose (μg/mL)	τh (h)	Pl (W)	θ*eff
100	12	0.22	0.62909
200	12	0.14	0.63003
300	12	0.12	0.63803
400	18	0.12	0.64116

Gheflati B, Naghavi N. Computational study of nanoparticle assisted hyperthermia in tumors embedded with large blood vessels. Int J Heat Mass Transf. 2020;151:119415 doi:10.1016/j.ijheatmasstransfer.2020.119415.

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