Application of Box–Behnken design to prepare gentamicin-loaded calcium carbonate nanoparticles

Figures & data

Table I. Factor-setting for the experimental design.

Factors\Codes	− 1	0	1
Molar ratio of CaCl2: Na2CO3 (X1)	1:1	3:1.5	5:2
Drug concentration (X2)	1 g/dl	3 g/dl	5 g/dl
Speed of homogenization (X3)	2000 rpm	7000 rpm	12,000 rpm

Table II. Particle size (PS) and percent entrapment efficiency (EE %) values for fifteen formulations.

Formulation code	Molar ratio of CaCl2:Na2CO3 (X1)	Drug Concentration (X2)	Speed of Homogenization (X3)	PS ± SD (nm)	EE% ± SD
1	−1	0	1	280.00 ± 0.5	37.0 ± 1.0
2	−1	0	−1	269.30 ± 1.7	34.2 ± 4.7
3	0	−1	1	259.00 ± 2.3	33.2 ± 5.6
4	−1	1	0	300.12 ± 1.6	42.1 ± 1.8
5	0	1	−1	280.00 ± 0.9	35.0 ± 10.7
6	1	1	−1	80.00 ± 13.2	24.0 ± 15.7
7	0	1	1	280.20 ± 0.6	33.0 ± 1.0
8	0	−1	−1	210.00 ± 1.6	26.1 ± 9.0
9	0	0	0	120.30 ± 1.8	24.2 ± 1.7
10	0	0	0	109.00 ± 1.1	23.5 ± 0.7
11	−1	−1	0	200.00 ± 7.1	25.3 ± 0.2
12	1	0	1	109.63 ± 1.9	24.5 ± 4.7
13	1	1	0	89.00 ± 1.0	27.5 ± 0.7
14	1	−1	0	87.40 ± 0.1	20.0 ± 0.2
15	0	0	0	100.00 ± 1.1	23.0 ± 0.9

Figure 1. Counter plot and response surface plot for the effects of the homogenization speed and drug concentration on particle size.

Figure 2. Counter plot and response surface plot for the effects of the homogenization speed and the molar ratio of CaCl₂:Na₂CO₃ on particle size.

Figure 3. Counter plot and response surface plot for the effects of the drug concentration and the molar ratio of CaCl₂:Na₂CO₃ on particle size.

Figure 4. Counter plot and response surface plot for the effects of the drug concentration and the homogenization speed on entrapment efficiency.

Figure 5. Counter plot and response surface plot for the effects of the drug concentration and the molar ratio of CaCl₂:Na₂CO₃ on entrapment efficiency.

Figure 6. Counter plot and response surface plot for the effects of the homogenization speed and the molar ratio of CaCl₂:Na₂CO₃ on entrapment efficiency.

Figure 7. Optimization plot for the preparation of gentamicin sulfate–CaCO3 nanoparticles. The optimum points (PS = 90.12 nm, EE% = 26.49%) were defined as − 0.52, 0.89, and 1, which gives the values of 2:1.25, 4.89 g/dl, and 12,000 rpm for the molar ratio of CaCl₂:Na₂CO₃, concentration of drug, and the homogenization speed respectively.

Table III. Percent error (PE) and mean percent error (MPE) between calculated and observed values for each response.

Set number	Calculated *PS (nm)	Observed PS (nm)	PE for PS	Calculated *EE%	Observed EE%	PE for EE%
1	300.00	320.10	6.25	40.35	37.0	9.05
2	210.02	244.22	14.00	32.21	28.09	14.66
3	80.23	96.50	16.86	39.32	33.64	16.89
			MPE = 12.37			MPE = 13.53

*No statistical analysis has been performed for calculation of PS in the validation step and the reported values have been estimated according to the equation in “validation of the model” section.

Figure 8. Particle size distribution for the optimized formulation actually prepared.