Development of a multi-route physiologically based pharmacokinetic (PBPK) model for nanomaterials: a comparison between a traditional versus a new route-specific approach using gold nanoparticles in rats

Table 2 Final multivariate linear regression models describing relationships between the physicochemical properties of AuNPs and biodistribution parameters following intravenous injection in rats

Tissue/Organ	β ₀	β₁	β₂	β₃	β₅	β₆	β₇	BIC	Adj-R²	p-value
Intravenous injection (IV)
Maximum endocytosis/phagocytosis uptake rate
Lung	3.77	0.01					− 0.11	5.54	0.93	0.03
GI tract	48.2	− 0.08					− 1.47	15.8	0.99	0.02
Liver	317		4.69				− 10.7	41.8	0.91	0.04
Spleen	− 1.23E4			178		5.28E3		50.9	0.80	0.09
Kidney	2.02		− 0.49		3.59			11.0	0.93	0.03
Rest of body	0.067		0.12		− 0.38			5.21	0.83	0.08
Endocytosis/phagocytosis uptake capacity
Lung	− 448		3.01		44.7			35.8	0.97	0.01
GI tract	29.4		− 3.04		46.6			34.7	0.98	0.01
Liver	8.21E3				1.08E3		− 251	69.7	0.95	0.03
Spleen	− 76.1		131				− 151	74.7	0.91	0.05
Kidney	228		− 64		467			57.2	0.96	0.02
Rest of body	− 126				12.2		6.01	36.7	0.98	0.01
Release rate constant of phagocytic cells
Lung	− 4.17			0.058		1.78		− 24.3	0.48	0.26
GI tract	− 1.17		0.015	− 0.052				− 23.5	0.99	0.001
Liver	0.07	− 3E−4			− 0.029			− 15.4	0.07	0.49
Spleen	− 0.22		0.004	− 0.009				− 56.5	0.99	3.64E-5
Kidney	4.56	− 0.03			1.56			26.8	0.14	0.43
Rest of body	− 0.11	3E−3	0.031					− 11.8	0.96	0.018
Urinary and fecal excretion constant rate
Urine	3.5E−4		− 1E−4		7.4E−4			− 76.4	0.96	0.019
Feces	− 1.36	0.002					0.054	− 18.1	0.97	0.015
Biliary	0.03	1.4E−4		0.001				− 58.6	0.98	0.001

β₀ and β_i represent intercept and slope of variables included in the multivariate linear regression model, respectively [1: hydrodynamic diameter (HD); 2: surface area (SA); 3: Zeta potential (Z); 4: log(HD); 5: log(SA); 6: log(Z); 7: log-transformed number of NPs, log(NPs)]. The values in bold represent statistical significance of p < 0.05
BIC Bayesian information criterion, Adj-R² adjusted R²

ISSN: 1743-8977