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Table 1 List of independent factors considered at different levels and the dependent variables with desired constraints

-1 0 1

A= Total amount of Drug (mg) 200 300 400

B= homogenization speed(rpm) 10000 12000 14000

C= concentration of surfactant (%) 1 1.5 2

- Dependent variables Constraints
- Y1=Entrapment efficiency (%) Maximum
- Y2= Particle size(nm) Minimum
- Y3= Zeta Potential(mV) Maximum

The NLCs of hydrophilic drug, ceftriaxone sodium, were prepared by hot homogenization technique with slight modifications. The oil and aqueous phases were prepared separately. The oil phase was prepared by mixing solid lipid and liquid lipid in a ratio of 85:15, respectively and both were heated to melt at 800C to give a clear oil phase.

A given amount of drug(90mg) was added to the clear oily phase. The aqueous phase which was comprised of double distilled water and surfactant was also heated to 800C. The aqueous phase was mixed with the oil phase and agitated at 1200 rpm for 15 mins.

This was further followed by agitation in bath sonicator for 15 mins. The pre-emulsion obtained was subjected to high speed homogenization for 2.5 hrs at different rotational speeds ranging from 10,000 to 14,000 rpm using speeds Ultra Turrax (T25) homogenizer. During the homogenisation process, the temperature was maintained at 800C and the hot dispersion was subsequently cooled to room temperature to facilitate the formation of lipid nanoparticles. Excess of lipids were removed by filtering the nano dispersion through a filter paper (0.45?m).22,23

Table 2 Box Behnken experimental design depicting the independent variable and dependent variable

Runs Independent variables Dependent variables

A= Total amount of lipid (mg) B = homogenization speed(rpm) C= concentration of surfactant (%) Y1= Entrapment efficiency (%) Y2= Particle size (nm) Y3= Zeta Potential (mV)

- 200 10,000 1.5 189.8 32.3 -24.4
- 400 10,000 1.5 178.0 38.3 -27.9
- 200 14,000 1.5 139.8 28.5 -26.5
- 400 14,000 1.5 168.7 40.5 -28.6
- 200 12,000 1 180.0 30.6 -25.3
- 400 12,000 1 177.5 39.6 -26.8
- 200 12000 2 93.9 29.5 -24.8
- 400 12,000 2 124.9 37.4 -29.0
- 300 10,000 1 198.7 36.5 -26.2
- 300 14,000 1 186.0 34.2 -25.7
- 300 10,000 2 137.8 35.2 -26.4
- 300 14,000 2 124.0 34.8 -28.1
- 300 12,000 1.5 145.0 36.4 -28.5
- 300 12,000 1.5 147.0 36.2 -28.7
- 300 12,000 1.5 142.0 35.9 -28.4

Determination of particle size, polydispersity index and zeta potential of prepared NLCs

Dynamic light scattering technique was used to measure the particle size and polydispersity index (PDI) of the nano structured lipid carrier formulations using Malvern Panalytical, Zetasiser Ver. 7.13, measuring particle sizes ranging from 0.3 nm – 10 um Zeta potential was also measured simultaneously using of electrophoretic light scattering technique measuring electrophoretic mobility of particles in formulation. Preceding to measurements, all the illustrations were diluted with distilled water and all the measurements were carried out in triplicate.27-29

Determination of % entrapment efficiency (EE) and drug loading (DL)

The amount of drug entrapped in the lipid matrix was determined by centrifuging the prepared NLCs at 15,000 rpm for 30 mins at 250C, followed by the estimation of the amount of drug remaining in the supernatant by UV spectrophotometer at 266 nm (UV 1700, Shimadzu, Japan).

EE and DL were calculated using the following formula:

%EE=(w_(1-W_2 ) )/w_1 X100 (1)

%DL= (w_(1-W_2 ) )/(?(w?_(1-W_2 ))+w_lipid )x 100 (2)

Where, w1, W2 and wlipid represented weight of drug in formulation, weight of drug in supernatant and weight of lipid in formulation, respectively30,31

The optimized formulation was lyophilized to increase the stability of the preparation. Further evaluations were done using freeze dried preparations. Tween 80 was used as surfactant in the preparation of NLCs since it had an added advantage of cryoprotective property, the presence of which helps in the redispersion of lyophilized powder ensuring the formation of nano dispersion.

The thermal behaviour of drug, solid lipid, physical mixture of solid lipid, liquid lipids and drug and lyophilized formulation of the prepared NLCs optimized was measured using differential scanning calorimeter (DSC), 131 PVO. 2 mg of each sample was weighed and the instrument ran from 00C to 1800 C temperature. Rate of heating of the pans were regulated at 100C/min33.

An X-ray diffractometer (Ultima IV, Rigaku, Japan) with Scintillation counter and K-beta filter, was used to investigated the crystalline structure of the samples like drug (ceftriaxone sodium), solid lipid (glyceryl monostearate), physical mixture of drug, solid lipid, and liquid lipid and freeze dried NLCs of optimised formulation.

All samples were characterised in their solid form with a scanning rate of 8.00 deg./min. over a 2 theta with scan range of 10 – 80 deg33,34.

The best solid and liquid lipids selected were glyceryl monostearate and capryol 90, respectively, as drug showed maximum solubility in these lipids. Tween 80 was considered as suitable surfactant according to the transmission of dispersion of lipids in surfactant.

Formulations designed as per Box Behnken design using Minitab 19 software have been prepared and evaluated to find the effect of the independent variables, viz., total amount of lipid, homogenisation speed and concentration of surfactant, on the dependent variables, viz., particle size, zeta potential and % entrapment efficiency. Significance of the model has been, determined by using ANOVA and for each response, Pareto graph has been plotted; these graphs are based on the principal of 80/20 rule, which indicated that 80% of effect has been caused due to 20% of cause. These are special type of bar graph indicating the effect of factors on responses and help the formulator to focus on those factors which can give the desired response. A reference line was drawn on the chart and values extending beyond theses line were considered as statistically significant. For further analysis residual plots are referred to find the goodness-of-fit in regression and ANOVA. The S value is known as standard error of regression, denotes the average distance between observed value and regression line. Lesser the value of S the better it explains the models.

In this experiment 3 residual plots are used to explain adequacy to model and ascertain the assumption of regression. The assumption that the residuals are normally distributed are verified from normal probability plot of residuals. It is depicted by a straight line. Residual versus fits are used to verify that the residuals have constant variance. The point should fall randomly on both sides of zero, without forming a pattern. Residual versus order of data are used to find that the residuals are not correlated with each other. The residuals points should not show any trend. The three residual plot were found to show a goodness-of -fit, normal distribution and residual versus fit and residual versus order showed randomized fall of point on both side of zero without forming any pattern or trend line respectively and indicating the residual have constant variance and no correlation between them for all the above mentioned three responses, for all the points. The contours and the 3D response curve were used to analyse the relationship between the independent factors and the interference of factors on the response. After analysis the three independent factors were optimised to get the desired response.

The mean particle size range found was between 198.7 nm and 93.9 nm (Table no.). It was found that the particle size reduction was influenced by total amount of lipid and concentration of surfactant. As the total amount of lipids decreased to 300 mg the size of the particle decreased, up to a certain limit only and further decrease in amount of the lipid to 200 mg, had shown no significant effect on particle size. Further increase in surfactant concentration reduced the particle size as shown in table. After fitting the response data and ANOVA study, it was found that the model best fitted with p< .001, with F value 34.80; A, C, A?, C?, AC were significant model terms. The R2, adjusted R2 and predicted R2 was found to be 0.98, 0.96 and 0.76, respectively. The difference between adjusted R2 and predicted R2 was found to be 0.20 showing good arrangement between the adjusted R2 and predicted R2 values. The Particle size was not influenced by homogenisation speed. Particle size played a significant role in determining absorption and stability study of NLCs. The negative value of coefficient of the variables denoted that those variables were inversely proportional with particle size and positive value of coefficient indicated that these factors had a direct effect on particle size. The polydispersity index was found to range from 0.21 to 0.43. The model summary and ANOVA details and equation cited are given in table 3 and Pareto chart, Residual plots, contour plots and response surface curve is given in figure 1.

PS=1294 – 1.010 A – 0.1461 B – 64.1 C + 0.000343 A*A + 0.000005 B*B – 16.1 C*C+ 0.000051 A*B + 0.1675 A*C – 0.00027 B*C (3)

Table 3 ANOVA of the particle size of the experimental design

6.23854 0.98 0.95 0.76

Source Degree of freedom Sum of Square Mean Square F-Value P-Value

- Model 9 12190.8 1354.53 34.80 0.001
- Linear 3 9734.4 3244.81 83.37 0.000
- A 1 259.9 259.92 6.68 0.049
- B 1 920.2 920.20 23.64 0.005
- C 1 8554.3 8554.32 219.80 0.000
- Square 3 1761.4 587.12 15.09 0.006
- A*A 1 43.4 43.42 1.12 0.339
- B*B 1 1625.1 1625.08 41.76 0.001
- C*C 1 59.7 59.69 1.53 0.271
- 2-Way Interaction 3 695.0 231.66 5.95 0.042
- A*B 1 414.1 414.12 10.64 0.022
- A*C 1 280.6 280.56 7.21 0.044
- B*C 1 0.3 0.30 0.01 0.933
- Error 5 194.6 38.92
- Lack-of-Fit 3 181.9 60.64 9.58 0.096
- Pure Error 2 12.7 6.33
- Total 14 12385.4

A= Total amount of lipid, B= homogenisation speed, C= Conc. of surfactant.

?

Figure 1 Represents the Pareto Chart,Normal Plot, Normal probability plot, Versus Fit, Versus order, contour plot and Surface plot of Particle size (PS)

The physical stability of the prepared NLCs was determined in terms of zeta potential, which was found to range from -24.4 to -29.0 mV. The effect of independent factors on zeta potential was best explained by the 2F1 model. The F value was 38.69, indicating that the model was significant at p < 0.0001. The R2, adjusted R2 and predicted R2 values were found to 0.99, 0.96 and 0.79 respectively. The difference between adjusted R2 and predicted R2 values was found to be less than 0.20 which indicated a practical agreement between the adjusted R2 and predicted R2 values. The zeta potential depended on A, C, C2 values.

The equation no. 4 was used to explain the individual parameters effecting the zeta potential of the prepared NLCs.

ZP= 17.22 – 0.0691 A – 0.00463 B – 4.27 C + 0.000090 A*A + 0.000000 B*B + 4.617 C*C+ 0.000002 A*B – 0.01350 A*C – 0.000550 B*C (4)

The positive coefficients, had positive effect on the responses and the negative values of coefficient had negative effect on zeta potential. The response curves and contour plots obtained from the study represented the effect of different independent variables on zeta potential It was found that the values of zeta potential shifted from -24.4 to -29.00mV with increase in concentrations of surfactant and amount of lipids. The zeta potentials were not affected by homogenisation speed. The model summary and ANOVA details are given in table 4 and Pareto chart, Residual plots, contour plots and response surface curve is given in figure 2, the regression equation given in equation

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