Artificial neural network as an alternative to multiple regression analysis in optimizing formulation parameters of cytarabine liposomes

The objective of the study was to optimize the formulation parameters of cytarabine liposomes by using artificial neural networks (ANN) and multiple regression analysis using 3(3) factorial design (FD). As model formulations, 27 formulations were prepared. The formulation variables, drug (cytarabine)/lipid (phosphatidyl choline [PC] and cholesterol [Chol]) molar ratio (X1), PC/Chol in percentage ratio of total lipids (X2), and the volume of hydration medium (X3) were selected as the independent variables; and the percentage drug entrapment (PDE) was selected as the dependent variable. A set of causal factors was used as tutorial data for ANN and fed into a computer. The optimization was performed by minimizing the generalized distance between the predicted values of each response and the optimized one that was obtained individually. In case of 3(3) factorial design, a second-order full-model polynomial equation and a reduced model were established by subjecting the transformed values of independent variables to multiple regression analysis, and contour plots were drawn using the equation. The optimization methods developed by both ANN and FD were validated by preparing another 5 liposomal formulations. The predetermined PDE and the experimental data were compared with predicted data by paired t test, no statistically significant difference was observed. ANN showed less error compared with multiple regression analysis. These findings demonstrate that ANN provides more accurate prediction and is quite useful in the optimization of pharmaceutical formulations when compared with the multiple regression analysis method.     

Artificial neural network as an alternative to multiple regression analysis in optimizing formulation parmaeters of cytarabine liposomes

The objective of the study was to optimize the formulation parameters of cytarabine liposomes by using artificial neural networks (ANN) and multiple regression analysis using 3³ factorial design (FD). As model formulations, 27 formulations were prepared. The formulation variables, drug (cytarabine)/lipid (phosphatidyl choline [PC] and cholesterol [Chol]) molar ratio (X ₁, PC/Chol in percentage ratio of total lipids (X ₂), and the volume of hydration medium, (X ₃) were selected as the independent variables; and the percentage drug entrapment (PDE) was selected as the dependent variable. A set of causal factors was used as tutorial data for ANN and fed into a computer. The optimization was performed by minimizing the generalized distance between the predicted values of each response and the optimized one that was obtained individually. In case of 3³ factorial design, a second-order full-model polynomial equation and a reduced model were established by subjecting the transformed values of independent variables to multiple regression analysis, and contour plots were drawn using the equation. The optimization methods developed by both ANN and FD were validated by preparing another 5 liposomal formulations. The predetermined PDE and the experimental data were compared with predicted data by pairedt test, no statistically significant difference was observed. ANN showed less error compared with multiple regression analysis. These findings demonstrate that ANN provides more accurate prediction and is quite useful in the optimization of pharmaceutical formulations when compared with the multiple regression analysis method.     

Formulation of liposomes gels of paeonol for transdermal drug delivery by Box-Behnken statistical design

The aim of this study was to design and optimize a transdermal liposomes gel formulation for paeonol (PAE). A three-factor, three-level Box-Behnken design was used to derive a second-order polynomial equation to construct three-dimensional (3-D) contour plots for prediction of responses. Independent variables studied were the DC-Chol concentration (X₁), molar ratio of lipid/drug (X₂), and the polymer concentration (X₃), and the levels of each factor were low, medium, and high. The dependent variables studied were the encapsulation efficiency (%EE) of PAE (Y₁), flux of PAE (Y₂), and viscosity of the gels (Y₃). Response surface plots were drawn and statistical validity of the polynomials was established to find the compositions of optimized formulation, which was evaluated using the Franz diffusion cell. The %EE of PAE increased proportionally with the molar ratio of lipid/drug, but decreased with polymer concentration, whereas the flux of PAE increased proportionally with polymer concentration and the DC-Chol concentration. The viscosity of gels increased with the polymer concentration. Gels showed a non-Fickian diffusion release mechanism for PAE, and the in vitro release profiles were fit for Higuchi’s order model. The design demonstrated the role of the derived polynomial equation and 3-D contour plots in predicting the values of dependent variables for the preparation and optimization of gel formulation for transdermal drug release.     

Formulation of Dacarbazine-loaded Cubosomes—Part II: Influence of Process Parameters

The purpose of this study was to investigate the combined influence of three-level, three-factor variables on the formulation of dacarbazine (a water-soluble drug) loaded cubosomes. Box–Behnken design was used to obtain a second-order polynomial equation with interaction terms to predict response values. In this study, the selected and coded variables X ₁, X ₂, and X ₃ representing the amount of monoolein, polymer, and drug as the independent variables, respectively. Fifteen runs of experiments were conducted, and the particle size (Y ₁) and encapsulation efficiency (Y ₂) were evaluated as dependent variables. We performed multiple regression to establish a full-model second-order polynomial equation relating independent and dependent variables. A second-order polynomial regression model was constructed for Y ₁ and confirmed by performing checkpoint analysis. The optimization process and Pareto charts were obtained automatically, and they predicted the levels of independent coded variables X ₁, X ₂, and X ₃ (−1, 0.53485, and −1, respectively) and minimized Y ₁ while maximizing Y ₂. These corresponded to a cubosome formulation made from 100 mg of monoolein, 107 mg of polymer, and 2 mg with average diameter of 104.7 nm and an encapsulation efficiency of 6.9%. The Box–Behnken design proved to be a useful tool to optimize the particle size of these drug-loaded cubosomes. For encapsulation efficiency (Y ₂), further studies are needed to identify appropriate regression model.     

Formulation of Dacarbazine-Loaded Cubosomes—Part I: Influence of Formulation Variables

The purpose of this study was to investigate the combined influence of three-level, three-factor variables on the formulation of dacarbazine (a water-soluble drug) loaded cubosomes. Box–Behnken design was used to obtain a second-order polynomial equation with interaction terms to predict response values. In this study, the selected and coded variables X₁, X₂, and X₃ representing the amount of monoolein, polymer, and drug as the independent variables, respectively. Fifteen runs of experiments were conducted, and the particle size (Y₁) and encapsulation efficiency (Y₂) were evaluated as dependent variables. We performed multiple regression to establish a full-model second-order polynomial equation relating independent and dependent variables. A second-order polynomial regression model was constructed for Y₁ and confirmed by performing checkpoint analysis. The optimization process and Pareto charts were obtained automatically, and they predicted the levels of independent coded variables X₁, X₂, and X₃ (−1, 0.53485, and −1, respectively) and minimized Y₁ while maximizing Y₂. These corresponded to a cubosome formulation made from 100 mg of monoolein, 107 mg of polymer, and 2 mg with average diameter of 104.7 nm and an encapsulation efficiency of 6.9%. The Box–Behnken design proved to be a useful tool to optimize the particle size of these drug-loaded cubosomes. For encapsulation efficiency (Y₂), further studies are needed to identify appropriate regression model.Key words: Box–Behnken design, cubosomes, dacarbazine, formulation variables     

Comparative Study on the Effects of Some Polyoxyethylene Alkyl Ether and Sorbitan Fatty Acid Ester Surfactants on the Performance of Transdermal Carvedilol Proniosomal Gel Using Experimental Design

The aim of this work was to investigate the effects of formulation variables on development of carvedilol (CAR) proniosomal gel formulations as potential transdermal delivery systems. Different non-ionic surfactants; polyoxyethylene alkyl ethers, namely Brij 78, Brij 92, and Brij 72; and sorbitan fatty acid esters (Span 60) were evaluated for their applicability in preparation of CAR proniosomal gels. A 2³ full factorial design was employed to evaluate individual and combined effects of formulation variables, namely cholesterol content, weight of proniosomes, and amount of CAR added on performance of proniosomes. Prepared proniosomes were evaluated regarding entrapment efficiency (EE%), vesicle size, and microscopic examination. Also, CAR release through cellulose membrane and permeation through hairless mice skin were investigated. Proniosomes prepared with Brij 72 and Span 60 showed better niosome forming ability and higher EE% than those prepared with Brij 78 and Brij 92. Higher EE% was obtained by increasing both weight of proniosomes and amount of CAR added, and decreasing cholesterol content. Release rate through cellulose membrane was inversely affected by weight of proniosomes. In Span 60 proniosomes, on increasing percent of cholesterol, a decrease in release rate was observed. While in Brij 72 proniosomes, an enhancement in release rate was observed on increasing amount of CAR added. Permeation experiments showed that skin permeation was mainly affected by weight of proniosomes and that Span 60 proniosomal gels showed higher permeation enhancing effect than Brij 72. Proniosomal gel could constitute a promising approach for transdermal delivery of CAR.     

Effect of pulsed electric fields on the activity of neutral trehalase from beer yeast and RSM analysis

The trehalase activity plays an important role in extraction of trehalose from beer yeast. In this study, the effect of pulsed electric field processing on neutral trehalase activity in beer yeast was investigated. In order to develop and optimize a pulsed electric field (PEF) mathematical model for activating the neutral trehalase, we have investigated three variables, including electric field intensity (10-50 kV/cm), pulse duration (2-10 μs) and liquid-solid ratio (20-50 ml/g) and subsequently optimized them by response surface methodology (RSM). The experimental data were fitted to a second-order polynomial equation and profiled into the corresponding contour plots. Optimal condition obtained by RSM is as follows: electric field intensity 42.13 kV/cm, liquid-solid ratio 30.12 ml/g and pulse duration 5.46 μs. Under these conditions, with the trehalose decreased 8.879 mg/L, the PEF treatment had great effect on activating neutral trehalase in beer yeast cells.     

响应曲面法优化菌丝体中红曲色素的提取条件

以红曲菌丝体为原料,通过单因素实验及Box-Behnken设计响应曲面分析优化了红曲色素的提取工艺条件。通过实验,得到了提取率的回归方程Y=0.923-0.011X1-0.011X2-0.017X12-0.027X22-0.026X32-0.028X1X2-0.019X1X3,通过对模型解逆矩阵得优化方案:乙醇浓度X1=66%、超声功率X2=200 w、提取温度X3=52℃,模型预测结果为92.5%。在该工艺条件下进行验证实验,提取率达到92.1±0.6%(n=3)。     

Optimization of polysaccharides (ABP) extraction from the fruiting bodies of Agaricus blazei Murill using response surface methodology (RSM)

Response surface methodoloty (RSM) was used to optimize the extraction conditions of polysaccharides (ABP) from the fruiting body of Agaricus blazei. A central composite design (CCD) was used for experimental design and analysis of the results to obtain the optimal processing parameters. Four independent variables such as extraction temperature (°C), ratio of water to raw material, number of extraction, and extraction time (h) were investigated. The experimental data obtained were fitted to a second-order polynomial equation using multiple regression analysis and also analyzed by appropriate statistical methods. The 3-D response surface plot and the contour plot derived from the mathematical models were applied to determine the optimal conditions. The optimum extraction conditions were as follows: extraction temperature 91 °C, ratio of water to raw material 14, number of extraction 6, and extraction time 2.1 h. Under these conditions, the experimental value was 65.8 ± 1.42, which is well in close agreement with value predicted by the model.     

Light- and nucleotide-dependent binding of phosphodiesterase to rod disk membranes: correlation with light-scattering changes and vesicle aggregation

Under conditions in which large guanosine cyclic 3',5'-phosphate (cGMP)- and phosphodiesterase (PDE)-dependent changes in near-infrared transmission and vesicle aggregation and disaggregation occur, we have observed a striking change in the binding of PDE to rod disk membranes. The change in PDE binding is nucleotide and light dependent as are the light-scattering changes. The cGMP- and PDE-dependent light-scattering signal can be produced by a 500-nm light flash which bleaches 1/(1 X 10(7] rhodopsin molecules. Mg ions are an essential cofactor for the nucleotide-dependent PDE binding and light-scattering changes. 3-Isobutyl-1-methylxanthine and other competitive inhibitors of PDE hydrolytic activity support increased PDE binding to the disk membrane, vesicle aggregation, and the light-scattering signal. However, treatments which block GTP-dependent activation of PDE hydrolytic activity (colchicine, GDP, or ethylenediaminetetraacetic acid) also block these phenomena. Thus, GTP-dependent activation of PDE rather than its hydrolytic activity appears to be correlated with the light-scattering signal.     

Dynamic Modeling of a Non-Uniform Flexible Tail for a Robotic Fish

In this paper, a non-uniform flexible tail of a fish robot was presented and the dynamic model was developed. In this model, the non-uniform flexible tail was modeled by a rotary slender beam. The hydrodynamics forces, including the reactive force and resistive force, were analyzed in order to derive the governing equation. This equation is a fourth-order in space and second-order in time Partial Differential Equation (PDE) of the lateral movement function. The coefficients of this PDE were not constants because of the non-uniform beams, so they were approximated by exponential functions in order to obtain an analytical solution. This solution describes the lateral movement of the flexible tail as a function of material, geometrical and actuator properties. Experiments were then carried out and compared to simulations. It was proved that the proposed model is suitable for predicting the real behavior of fish robots.     

Dimensional analysis yields the general second-order differential equation underlying many natural phenomena: the mathematical properties of a phenomenon’s data plot then specify a unique differential equation for it

Background

This study uses dimensional analysis to derive the general second-order differential equation that underlies numerous physical and natural phenomena described by common mathematical functions. It eschews assumptions about empirical constants and mechanisms. It relies only on the data plot’s mathematical properties to provide the conditions and constraints needed to specify a second-order differential equation that is free of empirical constants for each phenomenon.

Results

A practical example of each function is analyzed using the general form of the underlying differential equation and the observable unique mathematical properties of each data plot, including boundary conditions. This yields a differential equation that describes the relationship among the physical variables governing the phenomenon’s behavior. Complex phenomena such as the Standard Normal Distribution, the Logistic Growth Function, and Hill Ligand binding, which are characterized by data plots of distinctly different sigmoidal character, are readily analyzed by this approach.

Conclusions

It provides an alternative, simple, unifying basis for analyzing each of these varied phenomena from a common perspective that ties them together and offers new insights into the appropriate empirical constants for describing each phenomenon.

     

Use of response surface method for the determination of demineralization efficiency in fermented shrimp shells

A Box-Behnken design with three variables (sucrose concentration, initial pH value and soaking time) and three levels were used for studying the demineralization efficiency in fermented shrimp shells by Pediococcus sp. L1/2. First, the bacterial cells were inoculated into the media with various concentrations of sucrose and initial pH values, and fermentation took place under static conditions at 37 degrees C for 24h. Significant differences in the levels of total titratable acid were observed. This was followed by adding shrimp shells and soaking them in the fermentation media for 12, 24 and 36 h. The results showed that when the sucrose concentration was 50 g/L, and the initial pH value was 6.00, soaking for 36 h gave a demineralization efficiency of 68.38%. By solving the equation and also analyzing the response surface contour plots, optimum conditions occurred when the sucrose concentration was 50 g/L, the initial pH value was 7.00 and the soaking time was 36 h with a predicted value of demineralization of 83.03% whereas our experiment gave 83.47%.     

Optimization of isolation of cellulose from orange peel using sodium hydroxide and chelating agents

Response surface methodology was used to optimize cellulose recovery from orange peel using sodium hydroxide (NaOH) as isolation reagent, and to minimize its ash content using ethylenediaminetetraacetic acid (EDTA) as chelating agent. The independent variables were NaOH charge, EDTA charge and cooking time. Other two constant parameters were cooking temperature (98 °C) and liquid-to-solid ratio (7.5). The dependent variables were cellulose yield and ash content. A second-order polynomial model was used for plotting response surfaces and for determining optimum cooking conditions. The analysis of coefficient values for independent variables in the regression equation showed that NaOH and EDTA charges were major factors influencing the cellulose yield and ash content, respectively. Optimum conditions were defined by: NaOH charge 38.2%, EDTA charge 9.56%, and cooking time 317 min. The predicted cellulose yield was 24.06% and ash content 0.69%. A good agreement between the experimental values and the predicted was observed.     

A 48 kDa protein arrests cGMP phosphodiesterase activation in retinal rod disk membranes

Photolyzed rhodopsin (R) catalyzes GTP-binding to alpha-transducins (T alpha); T alpha X GTPs then activate cGMP phosphodiesterase (PDE). PDE activation is arrested by ATP in two ways: (i) initial velocity is suppressed, and (ii) PDE velocity rapidly returns to preactivation levels (turnoff). Arrestin (a 48 kDa protein) markedly enhances turnoff while not affecting initial velocity. Arrestin in the presence of ATP achieves rapid turnoff by directly inhibiting activated PDE, as indicated by its ability to inhibit the direct activation of PDE by T alpha X GMP--PNP (guanylyl-imidodiphosphate). Double reciprocal plots reveal a competition between arrestins and activated transducins for sites on PDE. Blocking R phosphorylation blocks initial velocity suppression but does not disturb rapid turnoff. Our data suggest a 2-fold mechanism for PDE deactivation: (i) formation of T alpha X GTPs is suppressed by R phosphorylation, while (ii) activation of PDE by T alpha X GTPs is competitively inhibited by arrestins when ATP is present.     

A planar biaxial constitutive relation for the luminal layer of intra-luminal thrombus in abdominal aortic aneurysms

The rupture risk of abdominal aortic aneurysms (AAAs) is thought to be associated with increased levels of wall stress. Finite element analysis (FEA) allows the prediction of wall stresses in a patient-specific, non-invasive manner. We have recently shown that it is important to include the intra-luminal thrombus (ILT), present in approximately 70% of AAA, into FEA simulations of AAA. All FEA simulations to date assume an isotropic, homogeneous material behavior for this material. The purpose of this work was to investigate the multi-axial biomechanical behavior of ILT and to derive an appropriate constitutive relation. We performed planar biaxial testing on the luminal layer of nine ILT specimens obtained fresh in the operating room (9 patients, mean age 71+/-4.5 years, mean diameter 5.9+/-0.4 cm), and a constitutive relation was derived from this data. Peak stretch and maximum tangential modulus (MTM) values were recorded for the equibiaxial protocol in both the circumferential (theta) and longitudinal (L) directions. Stress contour plots were used to investigate the presence of mechanical anisotropy, after which an appropriate strain energy function was fit to each of the specimen datasets. The peak stretch values for the luminal layer of the ILT were (mean+/-SEM) 1.18+/-0.02 and 1.13+/-0.02 in the theta and L directions, respectively (p=0.14). The MTM values were 20+/-2 and 23+/-3N/cm(2) in the theta and L directions, respectively (p=0.37). From these results and our observation of the symmetry of the stress contour plots for each specimen, we concluded that the use of an isotropic strain energy function for ILT is appropriate. Each specimen data set was then fit to a second-order polynomial strain energy function of the first invariant of the left Cauchy-Green strain tensor, resulting in an accurate fit (average R(2)=0.92+/-0.02; range 0.80-0.99). Comparison of our previously reported, uniaxially derived constitutive relation with the biaxially derived relation derived here shows large differences in the predicted mechanical response, underscoring the importance of the appropriate experimental methods used to derive constitutive relations. Further work is merited in an effort to produce more accurate predictions of wall stresses in patient-specific AAA, and viscoelastic behaviors of the ILT.     

Understanding the structure-activity and structure-selectivity correlation of cyclic guanine derivatives as phosphodiesterase-5 inhibitors by molecular docking, CoMFA and CoMSIA analyses

Molecular docking and 3D-QSAR analyses were performed to understand how PDE5 and PDE6 interact with a series of (49) cyclic guanine derivatives. Using the conformations of the compounds revealed by molecular docking, CoMFA and CoMSIA analyses resulted in the first quantitative structure-activity relationship (QSAR) and first quantitative structure-selectivity relationship (QSSR) models (with high cross-validated correlation coefficient q(2) and conventional correlation coefficient r(2) values) for predicting the inhibitory activity against PDE5 and the selectivity against PDE6. The high q(2) and r(2) values, along with further testing, indicate that the obtained 3D-QSAR and 3D-QSSR models will be valuable in predicting both the inhibitory activity and selectivity of cyclic guanine derivatives for these protein targets. A set of 3D contour plots drawn based on the 3D-QSAR and 3D-QSSR models reveal some useful clues to improve both the activity and selectivity by modifying structures of the compounds. It has been demonstrated that both the steric and electrostatic factors should appropriately be taken into account in future rational design and development of more active and more selective PDE5 inhibitors for the therapeutic treatment of erectile dysfunction (ED).     

Optimization on preparation condition of polyunsaturated fatty acids nanoliposome prepared by Mozafari method

This study presents the application of the response surface methodology (design) to develop an optimal preparation condition (independent variables) namely shear rate (600–1000?rpm), mixing time (30–60?min), and sonication time (10–20?min) for polyunsaturated fatty acids (docosahexaenoic acid and eicosapentaenoic acid) nanoliposomes. Fifteen lipid mixtures were generated by the Box–Behnken design and nanoliposomes were prepared by the Mozafari (direct hydration and without using organic solvents) method. Nanoliposomes were characterized with respect to entrapment efficiency (EE) and vesicle size as Y₁ and Y₂ dependent variables, respectively. The results were then applied to estimate the coefficients of response surface model and to find the optimal preparation conditions with maximum EE and minimum vesicle size. The response surface analysis exhibited that the significant (p?p?>?0.05) lack of fit for the reduced models. The response optimization of experiments was the shear rate: 795?rpm; mixing time: 60?min; and sonication time: 10?min. The optimal nanoliposome had an average diameter of 81.4?nm and EE of 100%. The experimental results of optimal nanoliposomes characterization confirmed an accurate fitness of the predicted values by reduced response surface models.     

Improvement of antioxidant activity of peptides with molecular weights ranging from 1 to 10 kDa by PEF technology

Egg white protein powder was hydrolyzed with Alcalase to produce antioxidant peptides. Then, the peptides were fractionated with ultrafiltration membranes. The peptides (1-10 kDa) were further treated by pulsed electric field (PEF) to investigate its effect on the antioxidant activity of the peptides. Antioxidant activity was evaluated using a 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical inhibition assay. The results indicated that optimal electric field intensity and standing times of PEF can enhance the antioxidant activity of the peptides. Therefore, a Box-Behnken design (BBD) with three independent variables including concentration, electric field intensity and pulse frequency was used to establish the regression equation of second-order response surface. The optimal conditions were as follows: concentration 8 mg/ml, electric field intensity 10 kV/cm and pulse frequency 2400 Hz. Under these conditions, the peptides antioxidant activity was 62.64% ± 0.98%. The present study demonstrated that the antioxidant activity of peptides (1-10 kDa) could be improved using PEF.     

Characterization of statistically produced xylanase for enrichment of fruit juice clarification process

Critical factors for xylanase production of Bacillus stearothermophilus under batch fermentation and for clarification of citrus fruit juice using this xylanase were optimized through central composite design of response surface methodology. Statistical approach resulted in an increase of 1.19-fold in xylanase yield over conventional method. Model equation for juice clarification included independent variables viz. temperature, incubation time and enzyme dose to study the dependent variables such as yield, acidic neutrality and filterability etc. Coefficient of determination, R(2) for enzyme production model and for different juice properties were in accordance with the linearity of the model. On the basis of the contour plots the optimum enzyme dose was 12.5 IU/g of xylanase. Enzymatic treatment has resulted in the improvement of twofold in the release of reducing sugars and 52.97% in juice yield, whereas 35.34% reduction in turbidity was observed.