. Author manuscript; available in PMC: 2016 Aug 14.

Published in final edited form as: Nanomedicine (Lond). 2013 Aug;8(8):1323–1333. doi: 10.2217/nnm.13.117

Table 2.

Description of terms and variables in model by Huang et al.

Equation no.	Equation	Description	Variables	Description of variables
7	$\frac{\partial T}{\partial t} = α \nabla^{2} T + \frac{Q}{ρ C_{D}} (1 - 10^{- O D})$	Heat transport
7A	α ^∇ ² T	Heat conduction	T	Temperature (degrees)
			α	Tissue or fluid thermal diffusivity (area · time⁻¹)
7B	$\frac{Q}{ρ C_{p}} (1 - 10^{- O D})$	Heat from laser-irradiated gold nanorods	Q	Laser energy (power · volume⁻¹)
			ρ	Tissue or fluid density (mass · volume⁻¹)
			C_p	Tissue or fluid heat capacity (energy · mass⁻¹ · degrees⁻¹)
			OD	Optical density (unitless)
8	$k \frac{\partial T}{\partial n} = U (T - T_{0})$	Boundary condition for temperature of surroundings	U	Heat transfer coefficient for region neighboring boundary (power · area⁻¹ · degrees⁻¹)
			T₀	Bulk temperature of surroundings (degrees)
			k	Scaling constant (power · length⁻¹ · degrees⁻¹)
9	$k = A e^{- \frac{E_{α}}{R T}}$	Heat-induced cell injury	A	Scaling factor (time⁻¹)
			E_α	Activation energy (energy · mol⁻¹)
			R	Gas constant (energy · degree⁻¹ · mol⁻¹)
10	$F_{D} = 1 - e^{- \int_{0}^{t} k d t}$	Tissue injury as an aggregate of cell injury	k	Cell injury rate (time⁻¹)
11	$\frac{\partial C_{b}}{\partial t} = k_{α} C_{b s} C - k_{d} C_{b}$	Cell–nanorod interactions
11A	k_αC_bsC	Binding of free nanorods to open binding sites	k_α	Binding association rate (time⁻¹)
			C_bs	Open binding sites (concentration)
			C	Free nanorods (concentration)
11B	k_dC_b	Dissociation of nanorods from binding sites	k_d	Binding dissociation rate (time⁻¹)
			C_b	Nanoparticles bound to binding sites (concentration)

Equations are taken from the model by Huang et al. [37].