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.     

In Situ Forming Formulation: Development, Evaluation, and Optimization Using 33 Factorial Design

The present investigation concerns with the development and optimization of an in situ forming formulation using 3³ full factorial design experimentation. Metformin, an antidiabetic drug with upper part of gastrointestinal tract as absorption window was used as a model drug. The formulations were designed with an objective to retain in stomach for an extended time period. The effect of three independent factors—concentrations of sodium alginate (X ₁), gellan gum (X ₂), and metformin (X ₃) on in vitro drug release were used to characterize and optimize the formulation. Five dependent variables—release exponent (Y ₁), dissolution efficiency (Y ₂), drug release at 30 min (Y ₃), 210 min (Y ₄), and 480 min (Y ₅) were considered as optimization factors. The data were statistically analyzed using ANOVA, and a p < 0.05 was considered statistically significant. Three dimensional surface response plots were drawn to evaluate the interaction of independent variables on the chosen dependent variables. Of the prepared 27 formulations, the responses exhibited by batch F17 containing medium level sodium alginate (X ₁), low level gellan (X ₂), and medium level metformin (X ₃) were similar to the predicted responses.     

Kneading Technique for Preparation of Binary Solid Dispersion of Meloxicam with Poloxamer 188

The aim of the present study was to enhance the dissolution rate of meloxicam (MLX), a practically water-insoluble drug by preparation of solid dispersion using a hydrophilic polymer, poloxamer 188 (PXM). The kneading technique was used to prepare solid dispersions. A 3² full factorial design approach was used for optimization wherein the drug, polymer ratio (X ₁), and the kneading time (X ₂) were selected as independent variables and the dissolution efficiency at 60 min (%DE₆₀) and yield percent were selected as the dependent variable. Multiple linear regression analysis revealed that for obtaining higher dissolution of MLX from PXM solid dispersions, a high level of X ₁ and a high level of X ₂ were suitable. The use of a factorial design approach helped in optimization of the preparation and formulation of solid dispersion. The optimized formula was characterized by solubility studies, angle of repose, and contact angle; Fourier transform infrared spectroscopy, differential scanning calorimetry, x-ray diffraction studies, and scanning electron microscopy demonstrated that enhanced dissolution of MLX from solid dispersion might be due to a decrease in the crystallinity of MLX and PXM. Analysis of dissolution data of optimized formula indicated the best fitting with Korsemeyer–Peppas model and the drug release kinetics as Fickian diffusion. In conclusion, dissolution enhancement of MLX was obtained by preparing its solid dispersion with PXM using kneading technique.     

Process optimization and characterization of poloxamer solid dispersions of a poorly water-soluble drug

The objective of the present investigation was to improve the dissolution rate of Rofecoxib (RXB), a poorly water-soluble drug by solid dispersion technique using a water-soluble carrier, Poloxamer 188 (PXM). The melting method was used to prepare solid dispersions. A 3² full factorial design approach was used for optimization wherein the temperature to which the melt-drug mixture cooled (X ₁) and the drug-to-polymer ratio (X ₂) were selected as independent variables and the time required for 90% drug dissolution (t₉₀) was selected as the dependent variable. Multiple linear regression analysis revealed that for obtaining higher dissolution of RXB from PXM solid dispersions, a low level ofX ₁ and a high level ofX ₂ were suitable. The differential scanning calorimetry and x-ray diffraction studies demonstrated that enhanced dissolution of RXB from solid dispersion might be due to a decrease in the crystallinity of RXB and PXM and dissolution of RXB in molten PXM during solid dispersion preparation. In conclusion, dissolution enhancement of RXB was obtained by preparing its solid dispersions in PXM using melting technique. The use of a factorial design approach helped in identifying the critical factors in the preparation and formulation of solid dispersion. Published: April 13, 2007     

Development and in vitro evaluation of an oral floating matrix tablet formulation of diltiazem hydrochloride

The purpose of this research was to prepare a floating drug delivery system of diltiazem hydrochloride (DTZ). Floating matrix tablets of DTZ were developed to prolong gastric residence time and increase its bioavailability. Rapid gastrointestinal transit could result in incomplete drug release from the drug delivery system above the absorption zone leading to diminished efficacy of the administered dose. The tablets were prepared by direct compression technique, using polymers such as hydroxypropylmethylcellulose (HPMC, Methocel K100M CR), Compritol 888 ATO, alone or in combination and other standard excipients. Sodium bicarbonate was incorporated as a gas-generating agent. The effects of sodium bicarbonate and succinic acid on drug release profile and floating properties were investigated. A 3² factorial design was applied to systematically optimize the drug release profile. The amounts of Methocel K100M CR (X₁) and Compritol 888 ATO (X₂) were selected as independent variables. The time required for 50% (t₅₀) and 85% (t₈₅) drug dissolution were selected as dependent variables. The results of factorial design indicated that a high level of both Methocel K100M CR (X₁) and Compritol 888 ATO (X₂) favors the preparation of floating controlled release of DTZ tablets. Comparable release profiles between the commercial product and the designed system were obtained. The linear regression analysis and model fitting showed that all these formulations followed Korsmeyer and Peppas model, which had a higher value of correlation coefficient (r). While tablet hardness had little or no effect on the release kinetics and was found to be a determining factor with regards to the buoyancy of the tablets. Published: September 7, 2007     

Floating granules of ranitidine hydrochloride-gelucire 43/01: Formulation optimization using factorial design

The purpose of this research was to develop and optimize a controlled-release multiunit floating system of a highly water soluble drug, ranitidine HCl, using Compritol, Gelucire 50/13, and Gelucire 43/01 as lipid carriers. Ranitidine HCl-lipid granules were prepared by the melt granulation technique and evaluated for in vitro floating and drug release. ethyl cellulose, methylcellulose, and hydroxypropyl methylcellulose were evaluated as release rate modifiers. A 3² full factorial design was used for optimization by taking the amounts of Gelucire 43/01 (X ₁) and ethyl cellulose (X ₂) as independent variables, and the percentage drug released in 1(Q₁), 5(Q₅), and 10 (Q₁₀) hours as dependent variables. The results revealed that the moderate amount of Gelucire 43/01 and ethyl cellulose provides desired release of ranitidine hydrochloride from a floating system. Batch F4 was considered optimum since it contained less Gelucire and was more similar to the theoretically predicted dissolution profile (f₂=62.43). The temperature sensitivity studies for the prepared formulations at 40°C/75% relative humidity for 3 months showed no significant change in in vitro drug release pattern. These studies indicate that the hydrophobic lipid Gelucire 43/01 can be considered an effective carrier for design of a multiunit floating drug delivery system for highly water soluble drugs such as ranitidine HCl. Published: April 13, 2007     

Statistical optimization of gastric floating system for oral controlled delivery of calcium

The development of an optimized gastric floating drug delivery system is described. Statistical experimental design and data analysis using response surface methodology is also illustrated. A central, composite Box-Wilson design for the controlled release of calcium was used with 3 formulation variables: X₁ (hydroxypropyl methylcellulose [HPMC] loading), X₂ (citric acid loading), and X₃ (magnesium stearate loading). Twenty formulations were prepared, and dissolution studies and floating kinetics were performed on these formulations. The dissolution data obtained were then fitted to the Power Law, and floating profiles were analyzed. Diffusion exponents obtained by Power Law were used as targeted response variables, and the constraints were placed on other response variables. All 3 formulation variables were found to be significant for the release properties (P<,05), while only HPMC loading was found to be significant for floating properties. Optimization of the formulations was achieved by applying the constrained optimization. The optimized formulation delivered calcium at the release rate of 40 mg/hr, with predicted n and T_50% values at 0.93 and 3.29 hours, respectively. Experimentally, calcium was observed to release from the optimized formulation with n and T_50% values of 0.89 (±0.10) and 3.20 (±0.21) hours, which showed an excellent agreement. The quadratic mathematical model developed could be used to further predict formulations with desirable release and floating properties.     

Optimization of bilayer floating tablet containing metoprolol tartrate as a model drug for gastric retention

The purpose of the present study was to develop an optimized gastric floating drug delivery system (GFDDS) containing metoprolol tartrate (MT) as a model drug by the optimization technique. A 2³ factorial design was employed in formulating the GFDDS with total polymer content-to-drug ratio (X₁), polymer-to-polymer ratio (X₂), and different viscosity grades of hydroxypropyl methyl cellulose (HPMC) (X₃) as independent variables. Four dependent variables were considered: percentage of MT release at 8 hours, T_50%, diffusion coefficient, and floating time. The main effect and interaction terms were quantitatively evaluated using a mathematical model. The results indicate that X₁ and X₂ significantly affected the floating time and release properties, but the effect of different viscosity grades of HPMC (K4M and K10M) was nonsignificant. Regression analysis and numerical optimization were performed to identify the best formulation. Fickian release transport was confirmed as the release mechanism from the optimized formulation. The predicted values agreed well with the experimental values, and the results demonstrate the feasibility of the model in the development of GFDDS.     

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.     

Optimization of Hydrogels for Transdermal Delivery of Lisinopril by Box–Behnken Statistical Design

The aim of this study was to investigate the combined influence of three independent variables on the permeation kinetics of lisinopril from hydrogels for transdermal delivery. A three-factor, three-level Box–Behnken design was used to optimize the independent variables, Carbopol 971 P (X ₁), menthol (X ₂), and propylene glycol (X ₃). Fifteen batches were prepared and evaluated for responses as dependent variables. The dependent variables selected were cumulative amount permeated across rat abdominal skin in 24 h (Q ₂₄; Y ₁), flux (Y ₂), and lag time (Y ₃). Aloe juice has been first time investigated as vehicle for hydrogel preparation. The ex vivo permeation study was conducted using Franz diffusion cells. Mathematical equations and response surface plots were used to relate the dependent and independent variables. The regression equation generated for the cumulative permeation of LSP in 24 h (Q ₂₄) was Y ₁ = 1,443.3–602.59X ₁ + 93.24X ₂ + 91.75X ₃ − 18.95X ₁ X ₂ – 140.93X ₁ X ₃ – 4.43X ₂ X ₃ – 152.63X ₁ ² – 150.03X₂ ² − 213.9X ₃ ². The statistical validity of the polynomials was established, and optimized formulation factors were selected by feasibility and grid search. Validation of the optimization study with 15 confirmatory runs indicated high degree of prognostic ability of response surface methodology. The use of Box–Behnken design approach helped in identifying the critical formulation parameters in the transdermal delivery of lisinopril from hydrogels.     

Response surface methodology for the optimization of ubiquinone self-nanoemulsified drug delivery system

The aim of the present study was to prepare and evaluate an optimized, self-nanoemulsified drug delivery system of ubiquinone. A 3-factor, 3-level Box-Behnken design was used for the optimization procedure with the amounts of Polyoxyl 35 castor oil (X₁), medium-chain mono- and diglyceride (X₂), and lemon oil (X₃) as the independent variables. The response variable was the cumulative percentage of ubiquinone emulsified in 10 minutes. Different ubiquinone release rates were obtained. The amount released ranged from 11% to 102.3%. Turbidity profile revealed 3 regions that were used to describe the progress of emulsion formation: lag phase, pseudolinear phase, and plateau turbidity. An increase in the amount of surfactant decreased turbidity values and caused a delay in lag time. Addition of cosurfactant enhanced the release rates. Increasing the amount of the eutectic agent was necessary to overcome drug precipitation especially at higher loading of surfactants and cosurfactants. Mathematical equations and response surface plots were used to relate the dependent and independent variables. The regression equation generated for the cumulative percentage emulsified in 10 minutes was Y1=90.9–22.1X₁+5.03X₂+13.95X₃+12.13X₁X₂+15.13X₁X₃-14.40X₁ ²-6.25X₃ ². The optimization model predicted a 93.4% release with X₁, X₂, and X₃ levels of 35, 35, and 30 respectively. The observed responses were in close agreement with the predicted values of the optimized formulation. This demonstrated the reliability of the optimization procedure in predicting the dissolution behavior of a self-emulsified drug delivery system. Published: February 8, 2002.     

Preparation and In Vitro Evaluation of Solid Dispersions of Total Flavones of Hippophae rhamnoides L.

The purpose of this study was to enhance the dissolution of total flavones of Hippophae rhamnoides L. (TFH) by solid dispersions consisting of the drug and a polymeric carrier, poloxamer 188 (PXM). The solvent evaporation method was used to prepare solid dispersions. A 3² full-factorial design approach was used for optimization wherein the amount of solvent (X ₁) and the drug-to-polymer ratio (X ₂) were selected as independent variables and the percentage of TFH dissolved in 10 min (Q ₁₀) was selected as the dependent variable. Multiple linear regression analysis revealed that a suitable level of X ₁ and X ₂ was required for obtaining higher dissolution of TFH from PXM solid dispersions. Solid dispersions were characterized by differential scanning calorimetry, X-ray diffraction, Fourier transform infrared spectroscopy, scanning electron microscopy, and dissolution tests. Characterization studies revealed that solid dispersion of TFH–PXM showed enhancement of TFH dissolution due to the conversion of TFH into a less crystalline and/or amorphous form. In conclusion, dissolution enhancement of TFH was obtained by preparing its solid dispersions in PXM using solvent method.     

Modulation and Optimization of Drug Release from Uncoated Low Density Porous Carrier Based Delivery System

The purpose of this research work was to explore an application of uncoated porous drug carrier prepared by single-step drug adsorption for a delivery system based on integration of floating and pulsatile principles intended for chronotherapy. This objective was achieved by utilizing 3² factorial design, solvent volume (X ₁) and drug amount (X ₂) as selected variables, for drug adsorption using solvents, methanol, and dichloromethane (DCM), of varying polarity. Nitrogen adsorption (N₂), scanning electron microscopy of cross-sections, and atomic force microscopy were done to study adsorption patterns and their effect on release pattern. Drug release study was customized by performing for 6 h in acidic environment to mimic gastroretention followed by basic environment akin to transit phase. Correlation between porous data from mercury and N₂ adsorption was probably studied for the first time. Observed regression analysis values for pore volume, surface area, and drug release indicated the influence of selected variables. Total release range in acidic medium was 12.77–24.57% for methanol, 8.79–15.26% for DCM, and final release of 69.45–92.23% for methanol, and 60.16–99.99% for DCM influenced by varying internal geometries was observed. Present form of drug delivery system devoid of any additives/excipients influencing drug release shows distinct behavior from other approaches/technologies in chronotherapy by (a) observing desired low drug release (8%) in acidic medium, (b) overcoming the limitations of process variables caused by multiple formulation steps and different characteristic polymers, (c) reducing time consumption due to single step process, and (d) extending as controlled/extended release.     

Gastroretentive drug delivery system of carbamazepine: Formulation optimization using simplex lattice design: A technical note

Summary and Conclusion  An attempt was made to develop a gastroretentive drug delivery system of carbamazepine using HPMC, sodium bicarbonate, and EC as matrixing agent, gas-generating agent, and floating enhancer, respectively. A simplex lattice design was applied to investigate the combined effect of 3 formulation variables (ie, amount of HPMC (X ₁), EC (X ₂), and sodium bicarbonate (X ₃). Results of multiple regression analysis indicated that low levels ofX ₁ andX ₂ and a high level ofX ₃ should be used to manufacture the tablet formulation with desired in vitro floating time and dissolution. Formulation S3 was selected as a promising formulation and was found stable at 40°C temperature and 75% RH for 3 months. Published: February 9, 2007     

Formulation and evaluation of mucoadhesive glipizide microspheres

The purpose of this research was to formulate and system-atically evaluate in vitro and in vivo performances of mucoadhesive microspheres of glipizide. Glipizide microspheres containing chitosan were prepared by simple emulsification phase separation technique using glutaraldehyde as a cross-linking agent. Results of preliminary trials indicate that volume of cross-linking agent, time for cross-linking, polymer-to-drug ratio, and speed of rotation affected characteristics of microspheres. Microspheres were discrete, spherical, and free flowing. The microspheres exhibited good mucoadhesive property in the in vitro wash-off test and also showed a high percentage drug entrapment efficiency. A 3² full factorial design was employed to study the effect of independent variables, polymer-to-drug ratio (X ₁), and stirring speed (X ₂) on dependent variables percentage mucoadhesion, t₈₀, drug entrapment efficiency, and swelling index. The best batch exhibited a high drug entrapment efficiency of 75% and a swelling index of 1.42; percentage mucoadhesion after 1 hour was 78%. The drug release was also sustained for more than 12 hours. The polymer-to-drug ratio had a more significant effect on the dependent variables. In vivo testing of the mucoadhesive microspheres to albino Wistar rats demonstrated significant hypoglycemic effect of glipizide.     

Predictive modelling of Fe(III) precipitation in iron removal process for bioleaching circuits

In this study, the applicability of three modelling approaches was determined in an effort to describe complex relationships between process parameters and to predict the performance of an integrated process, which consisted of a fluidized bed bioreactor for Fe³⁺ regeneration and a gravity settler for precipitative iron removal. Self-organizing maps were used to visually evaluate the associations between variables prior to the comparison of two different modelling methods, the multiple regression modelling and artificial neural network (ANN) modelling, for predicting Fe(III) precipitation. With the ANN model, an excellent match between the predicted and measured data was obtained (R ² = 0.97). The best-fitting regression model also gave a good fit (R ² = 0.87). This study demonstrates that ANNs and regression models are robust tools for predicting iron precipitation in the integrated process and can thus be used in the management of such systems.     

Response surface methodology for optimization and characterization of limonene-based coenzyme Q10 self-nanoemulsified capsule dosage form

The aim of this study was to systematically obtain a model of factors that would yield an optimized self-nanoemulsified capsule dosage form (SNCDF) of a highly lipophilic model compound, Coenzyme Q10 (CoQ). Independent variables such as amount of R-(+)-limonene (X ₁), surfactant (X ₂), and cosurfactant (X ₃), were optimized using a 3-factor, 3-level Box-Behnken statistical design. The dependent variables selected were cumulative percentage of drug released after 5 minutes (Y ₁) with constraints on drug release in 15 minutes (Y ₂), turbidity (Y ₃), particle size (Y ₄), and zeta potential (Y ₅). A mathematical relationship obtained,Y ₁=78.503+6.058X ₁ +13.738X ₂+5.986X ₃−25.831X ₁ ² +9.12X ₁X₂−26.03X ₁X₃−38.67X ₂ ² +11.02X ₂X₃−15.55X ₃ ³ (r ²=0.97), explained the main and quadratic effects, and the interaction of factors that affected the drug release. Response surface methodology (RSM) predicted the levels of factorsX ₁,X ₂, andX ₃ (0.0344, 0.216, and 0.240, respectively), for a maximized response ofY ₁ with constraints of >90% release onY ₂. The observed and predicted values ofY ₁ were in close agreement. In conclusion, the Box-Behnken experimental design allowed us to obtain SNCDF with rapid (>90%) drug release within 5 minutes with desirable properties of low turbidity and particle size.     

The use of ladder particle swarm optimisation for quantitative structure–activity relationship analysis of human immunodeficiency virus-1 integrase inhibitors

This contribution focuses on the use of ladder particle swarm optimisation (LPSO) on modelling of oxadiazole- and triazole-substituted naphthyridines as human immunodeficiency virus-1 integrase inhibitors. Artificial neural network (ANN) and Monte Carlo cross-validation techniques were combined with LPSO to develop a quantitative structure–activity relationship model. The techniques of LPSO, ANN and sample set partitioning based on joint x–y distances were applied as feature selection, mapping and model evaluation, respectively. The variables selected by LPSO were used as inputs of Bayesian regularisation ANN. The statistical parameters of correlation of deterministic, R ², and root-mean-square error for the test set were 0.876 and 0.23, respectively. Robustness of the model was confirmed by Y-randomisation method. Comparison of the LPSO–ANN results with those of stepwise multiple linear regression (MLR), LPSO–MLR and LPSO–MLR–ANN showed the superiority of LPSO–ANN. Inspection of the selected variables indicated that atomic mass, molecular size and electronic structure of the molecules play a significant role in inhibitory behaviour of oxadiazole- and triazole-substituted naphthyridines.     

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     

Statistical optimization of culture media for production of phycobiliprotein by Synechocystis sp. PCC 6701

Synechocystis sp. PCC 6701 has a brilliantly colored pigment, phycobiliprotein containing phycoerythrin. Culture medium was optimized by sequential designs in order to maximize phycobiliprotein production. The observed fresh weights after 6 days were 0.58 g/L in BG-11, 0.83 g/L in medium for Scenedesmus sp. and 0.03∼0.52 g/L in the other tested media. Medium for Scenedesmus sp. was selected to be optimized by fractional factorial design and central composite design since the medium maintained a more stable pH within a desirable range due to higher contents of phosphate. The fractional factorial design had seven factors with two levels: KNO₃, NaNO₃, NaH₂PO₄, Na₂HPO₄, Ca(NO₃)₂, FeEDTA, and MgSO₄. From the result of fractional factorial design, nitrate and phosphate were identified as significant factors. A central composite design was then applied with four variables at five levels each: nitrate, phosphate, pH, and light intensity. Parameters such as fresh weight and phycobiliprotein contents were used to determine the optimum value of the four variables. The proposed optimum media contains 0.88 g/L of nitrate, 0.32 g/L of phosphate under 25 μE·m⁻²·s⁻¹ of light intensity. The maximum phycobiliprotein contents have been increased over 400%, from 4.9 to 25.9 mg/L after optimization.