Optimization of controlled release nanoparticle formulation of verapamil hydrochloride using artificial neural networks with genetic algorithm and response surface methodology

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19 May 2015 European Journal of Pharmaceutics and Biopharmaceutics xxx (2015) xxx–xxx 1

Contents lists available at ScienceDirect

European Journal of Pharmaceutics and Biopharmaceutics journal homepage: www.elsevier.com/locate/ejpb

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Research Paper

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Optimization of controlled release nanoparticle formulation of verapamil hydrochloride using artificial neural networks with genetic algorithm and response surface methodology

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Yongqiang Li a, Mohammadreza R. Abbaspour a, Paul V. Grootendorst a,b, Andrew M. Rauth c, Xiao Yu Wu a,⇑ a

Advanced Pharmaceutics and Drug Delivery Laboratory, Leslie Dan Faculty of Pharmacy, University of Toronto, Toronto, ON M5S 3M2, Canada Department of Economics, McMaster University, Hamilton, ON L8S 4M4, Canada c Faculty of Medicine, University of Toronto, ON M5G 2M9, Canada b

a r t i c l e

i n f o

Article history: Received 2 March 2015 Revised 17 April 2015 Accepted in revised form 27 April 2015 Available online xxxx Keywords: Optimization Artificial neural networks Continuous genetic algorithm Response surface methodology Polymer–lipid hybrid nanoparticles Verapamil hydrochloride

a b s t r a c t This study was performed to optimize the formulation of polymer–lipid hybrid nanoparticles (PLN) for the delivery of an ionic water-soluble drug, verapamil hydrochloride (VRP) and to investigate the roles of formulation factors. Modeling and optimization were conducted based on a spherical central composite design. Three formulation factors, i.e., weight ratio of drug to lipid (X1), and concentrations of Tween 80 (X2) and Pluronic F68 (X3), were chosen as independent variables. Drug loading efficiency (Y1) and mean particle size (Y2) of PLN were selected as dependent variables. The predictive performance of artificial neural networks (ANN) and the response surface methodology (RSM) were compared. As ANN was found to exhibit better recognition and generalization capability over RSM, multi-objective optimization of PLN was then conducted based upon the validated ANN models and continuous genetic algorithms (GA). The optimal PLN possess a high drug loading efficiency (92.4%, w/w) and a small mean particle size (100 nm). The predicted response variables matched well with the observed results. The three formulation factors exhibited different effects on the properties of PLN. ANN in coordination with continuous GA represent an effective and efficient approach to optimize the PLN formulation of VRP with desired properties. Ó 2015 Elsevier B.V. All rights reserved.

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1. Introduction

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Verapamil hydrochloride (VRP) is a calcium channel blocker commonly used to treat hypertension, cardiac arrhythmias and angina [5,16]. It has also been used as a P-glycoprotein (P-gp)-inhibitor to enhance chemotherapy of multidrug resistant cancer [7,27,29]. Although VRP is well absorbed through the gastrointestinal tract (P90%), its systemic bioavailability (20–35%) is

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Abbreviations: PLN, polymer–lipid hybrid nanoparticles; VRP, verapamil hydrochloride; DS, dextran sulfate sodium; DA, dodecanoic acid; VRP-PLN, verapamil hydrochloride loaded polymer–lipid hybrid nanoparticles; ITC, isothermal titration calorimetry; TEM, transmission electron microscopy; CCD, central composite design; ANN, artificial neural networks; RSM, response surface methodology; GA, genetic algorithms; AIC, Akaike’s information criterion; DLE, drug loading efficiency; DLC, drug loading capacity; HLB, hydrophile–lipophile balance; DDI water, distilled and deionized water. ⇑ Corresponding author. Tel.: +1 (416) 978 5272; fax: +1 (416) 978 8511. E-mail address: [email protected] (X.Y. Wu).

poor and variable due to the extensive first-pass metabolism by cytochrome CYP450 3A4 [31]. Its short elimination half-life (2.8– 7.4 h) demands dosing of 3–4 times per day [17]. Hence a sustained release nanoparticle delivery system able to bypass liver metabolism would increase bioavailability and reduce dosing frequency. As lipids are absorbed mainly through the lymphatic system in the intestines, lipid-based particulate systems offer a promising approach to bypassing first-pass metabolism via lymphatic transport thus enhancing drug bioavailability [9,21,35,36,39]. In particular, solid lipid nanoparticles (SLN) [37] have been reported to improve oral bioavailability and optimize plasma profiles of loaded drugs [6,8,30,32,34,52]. Owing to the hydrophobic nature, SLN is not an ideal carrier for sustained release of a highly water-soluble drug like VRP with an aqueous solubility of 83 mg/mL. In order to deliver ionic water-soluble drugs while maintaining the advantages of SLN, our group exploited the characteristic physicochemical properties of polymer counterions and developed a novel polymer–lipid

http://dx.doi.org/10.1016/j.ejpb.2015.04.028 0939-6411/Ó 2015 Elsevier B.V. All rights reserved.

Please cite this article in press as: Y. Li et al., Optimization of controlled release nanoparticle formulation of verapamil hydrochloride using artificial neural networks with genetic algorithm and response surface methodology, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/j.ejpb.2015.04.028

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Y. Li et al. / European Journal of Pharmaceutics and Biopharmaceutics xxx (2015) xxx–xxx

hybrid nanoparticle (PLN) system [51]. This system exhibited sufficient drug loading, lowered initial burst release and subsequently sustained drug release. To further improve the performance of PLN, drug–polymer–lipid interactions, internal structure, drug loading and release mechanisms were investigated [25]. These efforts resulted in a rationally designed formulation with high drug loading capacity and sustained release kinetics [26]. Nevertheless, the variables of PLN formulation (e.g. drug to lipid ratio and surfactant concentrations) need to be further optimized in order to obtain relatively uniform particle size in the range of 100 nm for effective intestinal lymphatic uptake [12,46] while maintaining maximal drug loading levels. Our preliminary tests suggested that for PLN, the drug loading capacity and particle size depended on the processing conditions and formulation factors including the weight ratio of drug to lipid, and the amounts and ratio of surfactants (e.g. Pluronic F68 and Tween 80). Owing to multiple variables and their unclear cause-and-effect relationship, we applied factorial experiment design [3,41,42,53] and numerical modeling techniques to optimize the PLN formulation. The central composite design (CCD), a second-order polynomial model [38] was employed, as CCD is very efficient and able to provide much information on the effects of experiment variables and overall experimental error with a minimum number of required runs. Combining the factorial design with statistical modeling techniques provides a particularly useful way of understanding the underlying structure between the independent and dependent variables. Models, established by the response surface methodology (RSM) or artificial neural networks (ANN) [18], can then be used to predict the responses to the combinations of the independent factors that are not explicitly studied experimentally. Due to the simplicity and ease of deployment, RSM utilizing a quadratic equation to fit the experimental data has been widely used in pharmaceutical research [33,50]. Compared to RSM, ANN are less restrictive and hence suitable for recognizing more complex, multi-dimensional and non-linear patterns [4,19,20,40,45,48]. Since different modeling strategies are adopted in RSM and ANN, and each method has its own inherent advantages and limitations, we elected to compare their modeling performance in the optimization of PLN in this work. Once the model is established, contour plots are normally constructed to visualize the relationship between independent and dependent variables so as to search the optimal formulation manually. However, three independent variables and two dependent variables are involved in the optimization of PLN in this study. Identifying an optimal formulation of this system using the superimposing contour method is cumbersome. To overcome this difficulty, the equations for each of the dependent variables were incorporated into a single equation, i.e., a generalized distance function [22], which is called a ‘cost function’ or an objective function in the optimization process. Then a numerical optimizer can be used to locate the values of the independent variables that minimize the cost function. We employed the continuous genetic algorithms (GAs) [11,44,15] to minimize the cost function with respect to the three independent variables. GA is a robust, stochastic, adaptive heuristic searching algorithm. It can avoid the problem of being stuck in local minima which is common to the gradient-based algorithms. Moreover, continuous GA is better than binary GA as it utilizes original experimental data as input and thus can avoid the loss of information which takes place in the transformation of data. In summary, we used a three-factor spherical second-order CCD to map the underlying pattern between each of the dependent variables (particle size and drug loading of PLN) and independent variables (drug to lipid ratio and concentrations of Pluronic F68 and Tween 80). RSM and ANN were used to model and predict

the responses. Continuous GA was utilized to perform the search for a global optimum.

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2. Materials and methods

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2.1. Materials

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Verapamil HCl (pKa = 8.6, solubility: 83 mg/mL), dodecanoic acid (DA, MP: 44–46 °C), dextran sulfate sodium (DS, MW: 5000 Da) and Tween 80 were purchased from Sigma–Aldrich Canada (Oakville, ON, Canada). Calcium chloride, potassium dihydrogen phosphate and di-sodium hydrogen orthophosphate anhydrous (dibasic) were purchased from Fisher Chemicals (Pittsburgh, PA, USA). Pluronic F68 was a gift from BASF (Mississauga, ON, Canada). AmiconÒ centrifugal filters (MWCO: 30,000 Da) were acquired from Millipore Inc. (Toronto, ON, Canada). Distilled and deionized (DDI) water was prepared with a Milli-Q water purifier (Milli-Pore, Etobicoke, ON, Canada).

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2.2. Preparation of VRP-PLN

158

PLN were prepared by a modified micro-emulsion method followed by ultrasonication [51]. The process of PLN formation is schematically illustrated in Fig. 3. Briefly, the lipid, DA, was melted using a thermostated water bath at 50 °C. A particular amount of VRP (dependent on the desired drug loading capacity of PLN) was added to the molten lipid. Under constant magnetic stirring with a Corning stirring plate, an aqueous phase was prepared by dissolving specific amounts of Pluronic F68 and Tween 80 in DDI water and heating to the same temperature as the lipid phase. The hot aqueous phase was added to the lipid phase subsequently. A known amount of DS was added slowly to the mixture to obtain an ionic molar ratio of DS to VRP at 1.0. The coarse o/w micro-emulsion was left in the water bath for 20 min under vigorous stirring at 700 rpm and then sonicated for another 5 min at the same temperature. The PLN nanoparticles were obtained by injecting the final emulsion into a fixed volume of cold water (2–4 °C) under magnetic stirring.

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2.3. Measurements of particle size and surface charge

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The hydrodynamic diameters and surface charge of PLN were measured by a particle sizer equipped with the function for zeta potential measurements (Nicomp, Model 380 ZLS, Particle Sizing Systems Inc., Santa Barbara, CA, USA). All values were measured in DDI water at a fixed angle of 90° at 25 °C in 10 mm diameter cells with a He/Ne laser light source at 632.8 nm. Each experiment was performed in triplicate.

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2.4. Determination of drug loading efficiency

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The drug loading efficiency of the system was determined by measuring the concentration of free drug remained in the dispersion medium, compared to the initial drug added. Briefly, 3 mL of undiluted sample of PLN was placed in the sample chamber of a Millipore filter consisted of a membrane with MWCO of 30,000 Da. The unit was centrifuged at 4000 rpm (relative centrifugal force: 3150g for 45 min). The PLN containing encapsulated drug–polymer complex remained in the sample chamber and the aqueous phase passed into the recovery chamber through the filter membrane. The aqueous filtrate (i.e., first filtrate from centrifugation) was collected, the recovery chamber was washed three times using DDI water to remove uncapsulated drug, 1 mL of the 3 diluted filtrate was incubated with the same volume of 0.3 M CaCl2 solution for 24 h at room temperature. The concentrated

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CaCl2 solution was used to displace all ionically-bound VRP in the VRP-DS complex; divalent Ca2+ is more effective than monovalent Na+ as it can exchange two VRP+ ions out of the VRP-DS complex [43,1,24,26,28,51]. The VRP content in the aqueous filtrate was analyzed with a UV–vis spectrophotometer (Hewlett–Packard 8452A, Palo Alto, CA) at 278 nm. Drug loading efficiency (DLE) and drug loading capacity (DLC) were calculated using the following equations:

DLE ð%Þ ¼

W initial drug added  W free drug  100 W initial drug added

ð1Þ

DLC ð%Þ ¼

W drug in PLN  100 W lipid

ð2Þ

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where Winitial drug added refers to the amount of the drug initially added, Wfree drug is the amount of drug that has not been incorporated into PLN, Wdrug in PLN is the amount of drug incorporated into the PLN, and Wlipid is the weight of lipid phase.

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2.5. Transmission electron microscopy

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The morphology of PLN particulates was examined by transmission electron microscopy (TEM) (Hitachi 7000, Tokyo, Japan). The samples were stained with 2% (w/v) negatively charged phosphotungstic acid (PTA) for 2 min before TEM imaging. 12.4% drug loading level of PLN (w/w, with respect to the lipid) was used in this study.

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2.6. Experimental design

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Three formulation factors, i.e., weight ratio of drug to lipid (X1), concentrations of Tween 80 (X2) and Pluronic F68 (X3), were chosen as independent variables. Drug loading efficiency (Y1) and mean particle size (Y2) of PLN were selected as dependent variables. A spherical central composite design was constructed to perform 15 experiments as shown in Fig. 1 and Table 1. This design is also called the three-factor spherical second-order composite experimental design [23,48]. Of the 15 runs, the first eight

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Table 1 Spherical center composite design (CCD) for three factors with three levels. Formulation no.

Code of drug to lipid ratio (w/w)

Code of conc. of Tween 80

Code of conc. of Pluronic F68

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 1 1 1 1 1 1 1 1.73 1.73 0 0 0 0 0

1 1 1 1 1 1 1 1 0 0 1.73 1.73 0 0 0

1 1 1 1 1 1 1 1 0 0 0 0 1.73 1.73 0

experiments (formulations # 1–8) constituted a factorial design of three factors (X1, X2, and X3), each evaluated at two levels (1, 1), i.e., 23 experiments. In the other three levels, 0 represents a middle level between the factorial points, 1 and 1, and the axial points, a = ±31/2 = ±1.73 represent the extreme levels. With the addition of the center point and the axial points, the experiments include five levels for each factor (see Table 2). Note that the formulation #15 is a repetition of the center experiment (n = 6) and is expressed as the mean ± S.D. (standard deviation). The unique feature of this three-factor spherical second-order composite design is that each experimental point has the same distance to the center experiment, so that all point estimates are estimated with the same degree of precision (see Fig. 2).

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2.7. ANN modeling and structure

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Our ANN model expresses Y1 and Y2 as the following function of X1, X2 and X3:

247

Anionic polymer

Drug-polymer complex

hq ¼

+

+

ehij þe 1 þ ehij

j ¼ 1; 2

ð3Þ

where a is the threshold (or bias) value of each logit (neuron) to fire, k is the number of logits being averaged, /ij is the weight attached to the ith logit, hij is a linear function of exploratory variables X1, X2, X3 (as defined in Eq. (4)), and e is the ‘error term’, i.e. the effect on Yj of all other factors, besides those that are explicitly modeled. Therefore, Yj is modeled as a weighted sum of several sigmoids (logit curves), each of which is a function of the independent variables, X1, X2, X3. Specifically, the sum of input (hq) to the nodes in the hidden layer (i.e., the layer between the input and output layers) is expressed as

Cationic drug

Pluronic F68 Tween 80

Melted lipid

X

236 237 238 239 240 241 242 243 244 245

248

251 252 253 254 255 256 257 258 259 260 261

262

wpq xq

ð4Þ

264

where wpq is the weight connection between the node q in the present layer (hidden layer or unknown parameters) and the node p in the previous layer (input layer or independent variables) and xq is

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Table 2 Levels of causal factors in physical form. Factor

Nanoparticles Fig. 1. Schematic illustration of preparation of polymer–lipid hybrid nanoparticles (PLN) and the processes for drug loading.

235

249 k X Yj ¼ a þ /ij i¼1

+

234

Ratio of VRP to DA (%, w/w) Conc. of Tween 80 (%, w/v) Conc. of Pluronic F68 (%, w/v)

Factor level in coded form 1.73

1

0

1

1.73

5.00 1.50 1.50

12.38 1.92 1.92

22.50 2.50 2.50

32.62 3.08 3.08

40.00 3.50 3.50

Please cite this article in press as: Y. Li et al., Optimization of controlled release nanoparticle formulation of verapamil hydrochloride using artificial neural networks with genetic algorithm and response surface methodology, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/j.ejpb.2015.04.028

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#4

#8

#2

#6

#12 #9

#10 #11

X3

#15 #3

X2

#7

X1

#1

#5

#13

Simulations using different Nhidden values demonstrated that for drug loading efficiency (Y1), an ANN model with 2 or 3 hidden nodes had close AIC values, i.e., 47.54 and 40.31, respectively. In comparison, the ANN models for mean particle size (Y2) with 2 or 3 hidden nodes exhibited distinct AIC values of 2.74 and 25.06, respectively. Therefore, as an optimal ANN structure, the ANN model with 2 nodes in the hidden layer was selected for the modeling of drug loading efficiency (Y1) and a model with 3 nodes in the hidden layer for mean particle size (Y2) in the subsequent analysis (see Fig. 3).

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2.8. Response surface methodology

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Classic response surface methodology (RSM) employs a second-order polynomial regression equation to predict the response variables [14]. A general quadratic model with three variables is defined as follows:

325

Fig. 2. Diagram of three-factor second-order composite experimental design.

FðXÞ ¼ a0 þ 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286

the output value from the previous layer (input layer or independent variables). In this study, three formulation factors corresponding to the weight ratio of drug to lipid (X1), the concentration of Tween 80 (X2) and the concentration of Pluronic F68 (X3) constituted the units of the input layer. The output layer was composed of the response variables of drug loading efficiency (Y1) and mean particle size (Y2) of each formulation. ANN models for the optimization of PLN were developed with a simulator that combines an ANN module for modeling and prediction and a continuous GA module for multi-objective optimization. A partitioned ANN structure proposed to model dependent variables individually was applied in this study to address the problem of the limited availability of experimental training pairs, while still achieving reasonably good generalization capability of ANN models [49]. The number of hidden nodes in the hidden layer, determined by the number of training pairs, was estimated according to the equation introduced by Carpenter and Hoffman [10] as follows:

287 289

Nhidden ¼

N sample =b  Noutput Ninput þ Noutput þ 1

ð5Þ

305

where Nhidden is the number of hidden nodes (i.e., different logits); Nsample is the number of training data pairs; Ninput is the number of input nodes and Noutput is the number of output nodes (i.e., output variables being modeled). b refers to the degree of determination of the network and its value is determined by the number of the inputs, the outputs and the size of data available for training. b has three values: b < 1, under-determined; b = 1, exactly determined and b > 1, over-determined. To prevent the occurrence of overfitting, b P 1 is preferred in modeling practice. In this study, Nsample = 15, Ninput = 3 and Noutput = 1 for ANN models approximating each response variables separately. Thus Nhidden was calculated from Eq. (5) to be 3 for b = 0.94 and 2 for b = 1.36, respectively. The optimality of ANN models with different Nhidden values was evaluated using Akaike’s information criterion (AIC) [2,13] as follows:

306 308

AIC ¼ nS  lnðSSÞ þ 2  nW

290 291 292 293 294 295 296 297 298 299 300 301 302 303 304

309 310 311 312 313

3 X

3 X

i¼1

i¼1

bi X i þ

cii X 2i þ

þ eijk X i X j X k þ e;

XX

316 317 318 319 320 321 322 323

326 327 328

329

dij X i X j

i
ði 6 3; j 6 3; k 6 3 and i < j < kÞ

ð7Þ

331

where F(X) is the individually predicted response variable; a0 is a constant; bi, cii, dij and eijk are the unknown coefficients of each individual monomial item; and Xi, Xj and Xk are the levels of causal factors; e is the error term. In this work, X1, X2 and X3 respectively represent the vector of three causal factors, namely, weight ratio of drug to lipid, concentration of Tween 80 and concentration of Pluronic F68. Note that because Eq. (7) is a linear regression model, the unknown coefficients can be estimated using ordinary least squares (OLS). We used the OLS routine implemented in SAS (version 8.0) (SAS Institute Inc., Cary, NC, USA).

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2.9. Simultaneous optimization

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A procedure for the multi-objective optimization of PLN is described below and illustrated in Fig. 4: Independent variables: X1, X2, X3 Dependent variables: Y1, Y2

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Step 1: Building mathematical models relating responses to independent variables, i.e., Y1 = F(X1, X2, X3) Y2 = G(X1, X2, X3) Step 2: Training/fitting, and validating the models of Y1 and Y2; Step 3: Incorporating the dependent variables of Y1 and Y2 into the generalized distance function S(X) [22,47]:

347

X1

X2

X3 X1

X2

X3

ð6Þ

where nS is the number of data pairs, nW is the number of weights in the ANN models, and SS is the sum of square differences between the observed and predicted response variables. The AIC embodies a particular trade-off between the complexity of a model (nW) and the goodness of fit of the model (SS).

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Y1

Y2

Fig. 3. Optimized ANN models of the drug loading efficiency (Y1) and the mean particle size (Y2) of PLN as a function of the weight ratio of drug to lipid (X1), the concentration of Tween 80 (X2) and the concentration of Pluronic F68 (X3).

Please cite this article in press as: Y. Li et al., Optimization of controlled release nanoparticle formulation of verapamil hydrochloride using artificial neural networks with genetic algorithm and response surface methodology, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/j.ejpb.2015.04.028

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Initialization

New formulations

Mutation

Crossover Predicted properties

Fitness evaluation

No

Good

Optimal formulation

Selection

Continuous genetic algorithms

Fig. 4. Schematic representation of the simultaneous multi-objective optimization processes including ANN for modeling and continuous GA for optimization.

SðXÞ ¼ 356 357 358 359 360 361 362

(

2  2 )12 FDðY 1 Þ  FOðY 1 Þ FDðY 2 Þ  FOðY 2 Þ þ SDðY 1 Þ SDðY 2 Þ

ð8Þ

where S(X) is the generalized distance function; SD(Y1) and SD(Y2) are the standard deviation of the observed values for Y1 and Y2, respectively; FD(Y1) and FD(Y2) are the desired values of each response variable (100% and 100 nm respectively), and FO(Y1) and FO(Y2) are the predicted optimal values of Y1 and Y2, respectively.

Fig. 5. Transmission electron microscopy (TEM) image (40,000) of PLN (formulation: 12.4% VRP, 2.25% Tween 80, 2.25% Pluronic F68; coded form: 1, 0.4325, 0.4325).

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Step 4: Searching for a set of casual factors (X1, X2, X3) which minimize the value of S(X) in the given search domain by employing Eq. (8) as the cost function and continuous GA.

Table 3 Results of experimental design (n = 3) and predictions by ANN models. Formulation

Drug loading efficiency (Y1, %) Observed

Predicted

Observed

Predicted

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

99.16 ± 0.29 98.66 ± 0.29 99.63 ± 0.09 99.40 ± 0.42 98.25 ± 2.08 91.95 ± 0.88 90.53 ± 1.53 – 90.35 ± 0.79 92.3 ± 1.44 92.29 ± 0.23 90.96 ± 0.82 92.66 ± 0.25 94.98 ± 0.86 93.81 ± 1.79

92.36 93.02 93.01 98.38 92.35 92.36 91.77 0 92.99 88.31 92.37 88.65 92.37 92.76 92.96

334.73 ± 46.06 332.73 ± 45.70 338.73 ± 17.83 403.53 ± 55.36 891.77 ± 0.32 893.17 ± 0.29 889.40 ± 1.73 – 345.17 ± 40.13 250.70 ± 12.15 110.73 ± 38.30 419.17 ± 47.00 125.17 ± 7.62 390.03 ± 33.30 260.57 ± 63.72

280.66 309.47 308.85 317.47 836.82 855.94 851.85 938.64 322.01 205.60 69.19 371.99 83.68 340.51 238.06

368 369

2.10. Statistical analysis

370 372

Statistical comparison of two independent means (or two independent groups) was performed by using a two-tailed Student’s t-test. A value of p < 0.025 was considered statistically significant.

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3. Results and discussion

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3.1. Morphology and surface charge of VRP-PLN

375

383

VRP-PLN were prepared according to the process presented schematically by Fig. 3. Drug–polymer complexation and the partition of drug–polymer complex between the aqueous and oily phases play a critical role in the formation of PLN. The TEM image of VRP incorporated PLN (12.4%, w/w, with respect to lipid) in Fig. 5 demonstrates that PLN nanoparticles have a nearly spherical shape. VRP-PLN nanoparticles possess a negative zeta potential (f) 20.14 ± 0.52 mV (n = 3). The drug loading capacity (DLC) of nanoparticles ranged from 4.5% to 36.9%.

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3.2. Experimental design of VRP-PLN

385

The dependent variables, namely, drug loading efficiency (Y1) and mean particle size (Y2) of corresponding PLN formulations for training and validation, were well characterized and the results are summarized in Tables 3 and 4, respectively. For formulation #8, the PLN flocculated after preparation. As a penalty measure, the drug loading efficiency of formulation 8 was set to be 0 and the mean particle size to be 1000 nm. In this formulation the

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376 377 378 379 380 381 382

386 387 388 389 390 391

Particle size (Y2, nm)

Note: the mean particle size (Y2) was measured by dynamic laser scattering (DLS).

concentrations of Tween 80 and Pluronic F68 were relatively high (3.08%); however, it is not high enough to stabilize the PLN with high VRP content (32.6% VRP/DA ratio). The dextran-VRP complex is essentially insoluble in water as it precipitated from water forming a gel-like mass if left unstirred and unsolubilized. Although the surfactant concentration is sufficient to facilitate formation of small PLN particles in the beginning, the small particles collide with one another and merge to form larger precipitates due to ‘‘sticky’’ dextran-VRP components exposed on the PLN surface.

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3.3. RSM model fitting

401

Based on the training pairs listed in Table 3, response variables, drug loading efficiency (Y1) and mean particle size (Y2), were fitted

402

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Table 4 Validation experiments. No.

Drug to lipid ratio (%, w/w)

Tween 80 (%, w/v)

Pluronic F68 (%, w/v)

Drug loading efficiency (Y1, %)

Particle size (Y2, nm)

1 2 3

8.00 15.00 25.00

2.00 2.50 2.69

2.00 1.92 1.50

94.16 ± 0.47 92.33 ± 1.76 90.58 ± 0.39

289.83 ± 19.50 287.60 ± 31.10 279.97 ± 20.65

Note: the mean particle size (Y2) was measured by dynamic laser scattering (DLS).

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Y2

separately according to Eq. (7). OLS estimation produced the following equation that describes the drug loading efficiency of PLN (Y1) as a function of the formulation factors (R2 = 0.66):

predicted

þ 3:71X 1 X 2 þ 6:15X 1 X 3 þ 22:00X 2 X 3 þ 82:55X 21 þ 71:53X 22 þ 69:08X 23

ð10Þ

418

Eq. (10) demonstrates that the interaction terms play a less pronounced role than the formulation factors alone in the determination of mean particle size (Y2). Increasing the values of formulation factors shows a positive effect on the mean particle size of PLN (Y2) as manifested by the positive sign of these terms in Eq. (10). The R2 is 0.35.

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3.4. Evaluation of model fitness

425

The goodness of fit of ANN and RSM models was evaluated through AIC values and their predictive performance. As noted

426

407

Y1

predicted

¼ 93:87  8:06X 1  7:02X 2  6:69X 3  12:61X 1 X 2  12:01X 1 X 3 10:50X 2 X 3 

(a)

40.00

(d)

500.00

0.00

Residuals

0.00

-500.00

-40.00

(b)

40.00

(e)

0.00

Residuals

415

30.00 val. #3 val. #2 ANN

0.00 val. #3 val. #1

val. #2

RSM

val. #1 -40.00

-30.00

(f) (c)

180.00

500.00

0.00

val. #3

Residuals

414

Residuals

413

Residuals

412



1:46X 23

It is evident from Eq. (9) that the formulation factors (X1, X2, and X3) and their interaction items impose direct effects on the value of drug loading efficiency (Y1). An increase in the formulation factors will lead to the decrease of the drug loading efficiency (Y1). Regression of the data also resulted in the following equation for the mean particle size of PLN (Y2):

Residuals

411



2:19X 22

ð9Þ

409 410

2:29X 21

¼ 257:64 þ 150:24X 1 þ 50:97X 2 þ 45:26X 3

val. #1 val. #2

ANN

0.00 val. #3

val. #1

RSM

val. #2

-500.00

-180.00

Fig. 6. Comparison of predictive performance of ANN and RSM – residuals of training and validation data pairs of ANN and RSM. For training data pairs, drug loading efficiency: (a) RSM and (b) ANN; mean particle size: (c) RSM and (d) ANN. For validation data pairs: drug loading efficiency (e) and mean particle size (f). The legends indicate the validation data set numbers shown in Table 4.

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above, the ANN model for the drug loading efficiency (Y1) with 2 hidden nodes had a minimum AIC value of 47.54 and the ANN model for the mean particle size (Y2) with 3 hidden nodes had a minimum AIC value of 25.06. In comparison, using second-order polynomial equations, the AIC value was found to be 2.06 for Eq. (9) and 20.95 for Eq. (10). We next assessed the predictive performance of the candidate models, which was measured by the goodness of their predictions using both ‘‘exposed’’ (i.e., used for the model development) and ‘‘unseen’’ (i.e., unused for the model development) data pairs (a total of 18 data pairs were involved). As for the modeling of the drug loading efficiency (Y1) of PLN, Fig. 6a and b compares and visualizes the residual distribution of the training data pairs for RSM and ANN models, respectively. Much smaller and randomly distributed residuals were observed for the ANN model. Fig. 6e compares the residual distribution of the validation data pairs for ANN and RSM models. Similar results were also observed for the prediction of mean particle size (Y2) of PLN, as illustrated in Fig. 6c–f. These results suggest that in this typical formulation study, ANN models outperformed RSM models, with a stronger recognition and generalization capability. Therefore, subsequent investigation of the roles of formulation factors and the optimization of PLN were conducted based on the ANN models. In general, either RSM or ANN model can provide sufficient prediction if the unknown relationship (pattern) between the independent factors and dependent variables is straightforward. However, if the unknown pattern is complex, multi-dimensional and non-linear, ANN model would provide better prediction and fitting of the data than RSM model due to its non-linear in nature, flexibility in tailoring the value of number of hidden nodes to improve fitness, and its capability of accommodating multiple independent factors. In this study, there are three independent factors and two dependent variables as described above. The relationship between these variables and independent factors could be rather complex and non-linear, which may not be described well by the RSM model.

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3.5. Simultaneous optimization of PLN

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With desired initial values of each response variable, simultaneous optimization was conducted by the ANN simulator automatically as illustrated in Fig. 4. The optimal formulation was then identified to include 22.34% of drug (w/w, with respect to the lipid), 2.10% (w/v) Tween 80 and 2.04% (w/v) Pluronic F68 (coded form: 0.0161, 0.6857, 0.7957). The predicted and experimental results for the optimal formulation were compared and are presented in Table 5. The observed values of drug loading efficiency (Y1) and mean particle size (Y2) of PLN agree well with the predictions (p > 0.025). The optimized PLN possessed a zeta potential of 20.57 ± 0.32 mV (n = 3), close to that of the solid lipid nanoparticles without the negatively charged polymer DS, suggesting the relative stability of this formulation and the complete neutralization of sulfate groups on DS.

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3.6. Effect of weight ratio of drug to lipid

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Fig. 7a and b illustrates the effect of drug to lipid weight ratio (X1) on the drug loading efficiency of PLN (Y1) when the

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concentration of Tween 80 (X2) or Pluronic F68 (X3) was fixed at 1.92% (w/v, coded form: 1). The predicted results indicate that, within the studied range of surfactant concentrations, i.e., from 1.50% to 3.50% (w/v), the drug loading efficiency of PLN essentially remains high and steady as the drug to lipid ratio increases from 5.00% (code form: -1.73) to 32.6% (code form: 1), except at a high drug to lipid ratio (40.0%, code form: 1.73) and high surfactant concentrations. The drug loading efficiency of PLN decreases sharply to 75.8% in a formulation consisting of 40% VRP, 1.92% (w/v) Tween 80 and 3.5% (w/v) Pluronic F68 (coded forms: 1.73, 1, 1.73) (Fig. 7a), and to 55.9% with 3.5% (w/v) Tween 80 and 1.92% (w/v) Pluronic F68 (coded forms: 1.73, 1.73, 1) (Fig. 7b). The relatively high drug loading efficiency of PLN at a wide range of weight ratio of drug to lipid (X1) is consistent with the compatibility between VRP-DS complex and DA found in previous work [25,26]. The dramatic drop in the loading efficiency at a drug to lipid ratio higher than 32.6% and high surfactant levels may be due to the exhaustion of encapsulation capacity of the lipid phase and increased solubilization power of the surfactants. Unlike the loading efficiency, the mean particle size of PLN (Y2) is sensitive to the weight ratio of drug to lipid (X1) and shows a complex pattern (Fig. 8). The mean particle size of PLN (Y2) decreases with increasing drug to lipid ratio initially up to 22.5% (coded forms: 0), and then increases till a peak value at 32.6% (code form: 1) before decreasing again.

Table 5 Predicted and experimental response variables for the optimal formulation.

a

Response

Predicted

Experimentala

Drug loading efficiency (%) Mean particle size (nm)

92.39 100.58

92.51 ± 0.32 105.42 ± 18.30

The mean ± S.D. for three measurements.

Fig. 7. Predicted response surface of drug loading efficiency (Y1) of PLN as a function of drug to lipid weight ratio (X1) and (a) the concentration of Pluronic F68 (X3) with the concentration of Tween 80 (X2) being fixed at 1.92% (w/v) (code form: 1); or (b) Tween 80 (X2) with the concentration of Pluronic F68 (X3) being fixed at 1.92% (w/v) (code form: 1).

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Fig. 8. Predicted response surface of mean particle size (Y2) of PLN (a) as a function of weight ratio of drug to lipid (X1) and the concentrations of Pluronic F68 (X3) with a fixed concentration of Tween 80 (X2) at 1.92% (w/v); and (b) as a function of weight ratio of drug to lipid and the concentration of Tween 80 (X2) with a fixed concentration of Pluronic F68 (X3) at 1.92% (w/v).

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3.7. Effect of Pluronic F68 and Tween 80 concentration

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The effect of Pluronic F68 and Tween 80 on the drug loading efficiency of PLN (Y1) is illustrated by the three-dimensional surface plots of the drug loading efficiency of PLN (Y1) against the concentration of Pluronic F68 (X3) and weight ratio of drug to lipid (X1) (Fig. 7a) or Tween 80 (X2) and weight ratio of drug to lipid (X1) (Fig. 7b). It is seen that when the concentration of Pluronic F68 increases at a fixed Tween 80 concentration of 1.92% (w/w), the drug loading efficiency remains high and relatively steady until it reaches a high level at high drug to lipid ratios. A similar trend is also observed in case of Tween 80 (Fig. 7b). However, the drug loading efficiency decreases more dramatically with increasing concentration of Tween 80; it dropped to 55.9% (w/w) as compared to 75.8% (w/w) for Pluronic F68 at the same concentration of 3.08%. Fig. 9a shows that the concentration of surfactant plays an important role in the drug loading efficiency of PLN. At a fixed drug to lipid weight ratio (X1) of 17.44% (w/w, coded form: 0.5), when the concentration of Tween 80 or Pluronic F68 exceeds a certain threshold, the drug loading efficiency (Y1) of PLN drops drastically to zero and the formulation becomes flocculated. This phenomenon is also seen in Fig. 9b at high drug to lipid ratios when the concentration of Pluronic F68 remains constant at 2.21% (w/v, coded form: 0.5). The concentration of surfactants also affects the mean particle size of the final product (Y2), as shown in Fig. 10a and b. The degree of the influence depends on the weight ratio of drug to lipid (X1) and the concentration of the second surfactant. When the drug to lipid weight ratio (X1) is given, increasing the concentration of Tween 80 (X2) leads to larger mean particle size (Y2) of PLN. However, the mean particle size and the change pattern at a drug to lipid ratio of 17.4% (coded form: 0.5) differ from those at 32.6% (coded form: 1). The particle size is much larger for PLN at a drug to

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Fig. 9. Predicted response surface of drug loading efficiency (Y1) of PLN (a) as a function of the concentrations of Tween 80 (X2) and Pluronic F68 (X3) with the weight ratio of drug to lipid (X1) being fixed at 17.4% (w/w); and (b) as a function of the concentration of Tween 80 (X2) and the weight ratio of drug to lipid (X1) with the concentration of Pluronic F68 (X3) being fixed at 2.21% (w/v).

lipid ratio of 32.6% than at 17.4%; nonetheless, the sharp increase in the particle size occurs in the high surfactant concentration region for both (Fig. 10a and b). The interaction between the concentration of the two surfactants or the surfactant concentration and the drug to lipid ratio is evident in Fig. 8a and b and Eq. (10). Although the interaction terms are less significant than the individual terms, their values propagate rapidly as the values of X1, X2, and X3 all become big.

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3.8. Functions of Pluronic 68 and Tween 80

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Tween 80, a non-ionic surfactant with a hydrophilic–lipophilic balance value (HLB) of 15, was used as a solubilizer in this study. It mainly lowers the surface tension at the oil–water interface to form the oil in water (o/w) emulsion. Pluronic F68 (HLB = 17) is a non-ionic, di-functional block copolymer surfactant composed of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO). It was used as a co-emulsifier and a suspension stabilizer in the present study. It is mainly adsorbed onto the surface of PLN particles through the hydrophobic interaction, preventing them from aggregation via steric repulsion due to its high percentage of hydrophilic groups of ethylene oxide (EO). The number of EO units for a single Tween 80 molecule is 20, while that for Pluronic F68 is 75. As compared to Pluronic F68, Tween 80 is a smaller molecule with a molecular weight (Mn) of 1310 Da and a shorter hydrophobic chain. Pluronic F68 is a tri-block co-polymer with a molecular weight of 8500 Da. In addition to the longer PEO chains, Pluronic F68 has a long hydrophobic chain containing 30 propylene oxide (PO) units. This difference in

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Fig. 10. Predicted response surface of mean particle size (Y2) of PLN as a function of the concentration of Tween 80 (X2) and the concentration of Pluronic F68 (X3). (a) The weight ratio of drug to lipid (X1) was fixed at 17.4% (w/w), and (b) the weight ratio of drug to lipid (X1) was fixed at 32.6% (w/w).

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593 595

the molecular structure between Pluronic F68 and Tween 80 imparts them different roles in the preparation and formulation stability of the PLN. The major function of Tween 80 in the preparation of PLN is as a solubilizer, while Pluronic F68 as a stabilizer. Although both Tween 80 and Pluronic F68, with HLB > 10, are suitable for stabilizing oil-in-water (O/W) emulsions, Tween 80 (HLB 15) can make more stable emulsions than Pluronic F68 (HLB17) [38]. This may explain why drug loading efficiency dropped dramatically at high Tween 80 concentrations when the Pluronic F68 concentration was fixed (Figs. 7 and 9). Tween 80, at high concentrations, could solubilize both melted lipid (oil) and drug–polymer complex, separate them from merging, and thus reduce drug loading efficiency. When the concentrations of Tween 80 (X2) or Pluronic F68 (X3) are fixed, the drug loading efficiency (Y1) decreased sharply (Figs. 7 and 9) while particle size increased at high weight ratio of drug to lipid (X1) (Fig. 10) might be attributed to the limitation of the solubilization capacity of the surfactants at this composition and the change in the HLB value of the oil phase with changing drug to lipid ratio. As the ionic molar ratio of drug to polymer was fixed at 1:1, an increase in the drug to lipid ratio led to a higher concentration of the drug and the hydrophilic polymer. As a consequence, the HLB of the oil phase increases and thus a different HLB value of surfactants is required to form stable emulsions [38]. When two surfactants are applied in the preparation, the combined HLB value can be estimated from the weighted average as follows:

p  HLB1 þ ð1  pÞ  HLB2 ¼ HLBcombined

ð11Þ

9

where p is the proportion of surfactant 1; HLB1 and HLB2 are respectively the HLB value of surfactant 1 and surfactant 2. As the HLB value of Pluronic F68 (HLB = 17) is quite different from that of Tween 80 (HLB = 15), the HLB value of their mixture is sensitive to their ratio. The correlation between the surfactant concentrations and the drug loading efficiency and particle size has been established from ANN models. With these correlations and understanding of the functions of the surfactants, one may develop more formulations for desirable PLN properties.

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4. Conclusion

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We successfully optimized the formulation of PLN of VRP using the spherical central composite design and the ANN methodology. The resultant PLN exhibited high drug loading efficiency (92%) and small mean particle size (100 nm) which is desirable for lymphatic transport via oral administration. We found that ANN fit the experimental data better than RSM in this typical study attributable to ANN’ capacity to accommodate more complex and non-linear functional relationships. The combined application of factorial design, ANN and continuous GA in modeling and multi-objective optimization can facilitate the development of PLN with desired properties.

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Acknowledgments

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This work was partially supported by the Canadian Institutes of Health Research. The authors would like to thank Dr. T.V. Chalikian for kind permission on use of ITC and valuable discussion, and Mr. B. Calvieri for TEM imaging. In addition, financial support from the Natural Sciences and Engineering Research Council (NSERC) postgraduate scholarship (doctoral level) and University of Toronto Top-up award to Y. Li is also gratefully acknowledged.

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