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Objective To prepare silymarin phospholipids complex（SM-PC） and investigate its physicochemical properties. Methods On the basis of single-factor tests, the drug-lipid ratio, drug concentration and reaction temperature were selected as the factors of the central composite design and response surface methodology in the preparation of SM-PC by solvent volatilization, and the best process was optimized with the compound rate as the index. And its in vitro dissolution was measured. Results The optimum preparation technology of SM-PC was as follows: acetone was used as compound solvent, the concentration of SM was 8.0 mg/ml, the mass ratio of SM to phospholipid was 1∶1.8, the reaction temperature was 56 ℃ and the recombination rate was（95.15±1.55）% with deviation of less than 3%. The in vitro dissolution test showed that the dissolution of SM-PC was close to 90% in 60 min. The dissolution behavior of main component of silybin was similar to that of silymarin capsules（Legalon ®）, which was higher than SM-API. Conclusion SM-PC was successfully prepared by central composite design response surface method, which significantly improved the dissolution and laid a foundation for the study of subsequent preparations.
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Objective Optimizing the extraction process of prescription medicinal materials of hospital preparation of compound Yangshe granules. Methods A high performance liquid chromatograph (HPLC) quantitative method was established for deacetyl asperulosidicacid methyl ester (DME) and ferulic acid (FC) of the active ingredient. Based on the content of DME, FC and the yield of extract, the extraction process of compound Yangshe granule extract was optimized using central composite design-response surface methodology. Results The established HPLC method of quantification of active components in compound Yangshe granules met the requirements of method validation. The optimal extraction process optimized by central composite design-response surface methodology were as follows: the weight of extraction solvent was 12 times of the medicinal slices, the alcohol concentration was 73% and the extraction time was 60 min. Conclusion In this study, the quantitative method of active components in compound Yangshe granule by HPLC has been successfully established, and the optimized extraction process is simple and easy to operate with good repeatability.
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Objective:To optimize the extraction process of Shangke Huoxue Granule.Methods:Taking the factors of extraction solvent multiple, extraction time and extraction times as investigation factors, and extraction amount of ferulic acid, paeoniflorin and the ratio of extraction as comprehensive evaluation indices, one-factor experimental design and central composite design-response surface methodology were adopted to optimize the extraction process of Shangke Huoxue Granule.Results:The binomial fitting equation was Y=96.16+2.42 A+0.63 B-3.76 AB-1.57 A2-1.87 B2 ( P<0.01). The optimal extraction process parameters were confirmed to be adding 16 times of water, 64 minutes each time, twice. The deviation rates between the measured values of three verification experiments and the predicted value were 2.00%, 3.23% and 0.66%. Conclusion:The established model of central composite design-response surface methodology has high predictability and the optimized extraction process is stable and feasible.
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The effective components of flavonoids in the "Pueraria lobata-Hovenia dulcis" drug pair have low bioavailability in vivo due to their unstable characteristics. This study used microemulsions with amphoteric carrier properties to solve this problem. The study drew pseudo-ternary phase diagrams through titration compatibility experiments of the oil phase with emulsifiers and co-emulsifiers and screened the prescription composition of blank microemulsions. The study used average particle size and PDI as evaluation indicators, and the central composite design-response surface method(CCD-RSM) was used to optimize the prescription; high-dosage drug-loaded microemulsions were obtained, and their physicochemical properties, appearance, and stability were evaluated. The results showed that when ethyl butyrate was used as the oil phase, polysorbate 80(tween 80) as the surfactant, and anhydrous ethanol as the cosurfactant, the maximum microemulsion area was obtained. When the difference in results was small, K_(m )of 1∶4 was chosen to ensure the safety of the prescription. The prescription composition optimized by the CCD-RSM was ethyl butyrate(16.28%), tween 80(9.59%), and anhydrous ethanol(38.34%). When the dosage reached 3% of the system mass, the total flavonoid microemulsion prepared had a clear and transparent appearance, with average particle size, PDI, and potential of(74.25±1.58)nm, 0.277±0.043, and(-0.08±0.07) mV, respectively. The microemulsion was spherical and evenly distributed under transmission electron microscopy. The centrifugal stability and temperature stability were good, and there was no layering or demulsification phenomenon, which significantly improved the in vitro dissolution of total flavonoids.
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Polysorbates/composition chimique , Flavonoïdes , Pueraria , Tensioactifs/composition chimique , Éthanol , Émulsions , Taille de particule , SolubilitéRésumé
Proteases are ubiquitously present and are among the largest groups of commercially important enzymes. Here, we investigated a wood-rot basidiomycete Trametes versicolor (L.) Lloyd [Syn. Coriolus versicolor (L.) Quél.; Polyporus versicolor (L.) Fr.] as a source of the enzyme serine protease, its production, and optimized to obtain a higher yield of the enzyme.. The significant variables with optimized values for maximum production of the enzyme were temperature (30?C), incubation time (120 h) and wheat bran (10 g). The yield increased by 30.76% by statistically optimizing the media. The optimized temperature and pH for the maximum protease activity was 50?C and pH 7.0, respectively. The enzyme was purified through ion exchange (using DEAE cellulose 52 resin) and gel filtration chromatography (using Superdex 200 column). The purified enzyme had a retention time of 7 min in RP-HPLC. The enzyme was stable at a broad range of temperature (30-60?C) and pH (5.0-8.0) with a half-life of 58.72 min, Vmax of 37.17 ?M min/mL and Km of 0.657 mg/mL. Its activity was enhanced by Na+, Ca2+, Mg2+ ions and SDS surfactant. These properties make this enzyme a valuable candidate for industrial applications
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Cookies are versatile foods that can supply specific needs and can be used as food vehicles to increase the intake of various nutrients. The objective was to create a gluten-free butter cookie based on rice flour (Oryza sativa). A central composite design 22 was used for analyzing the substitution of rice flour for bean flour (Phaseolus vulgaris, L.) (0-60%) and the substitution of butter for avocado puree (Persea americana) (0-100%). Response Surface Methodology were used to analyze the data with a significance of 10% (p<0.1) and a minimum R2 of 0.6. Variables analyzed were protein content (%), fat content (%), spread ratio, weight loss (%), water activity, moisture content (%), and ash content (%). Increases in the percentage of substitution of bean flour and avocado puree increased the amount of protein, ash, and moisture significantly. Fat content increased significantly following the decrease in avocado substitution. The minimum weight loss was obtained on intermediate values of bean flour. Water activity and spread ratio were not affected by changes in the variables measured. Three different formulas were obtained for the optimization: 46% bean flour and 86% of avocado puree, a formulation with an appropriate moisture range by reducing the lipid oxidation (59% bean flour and 82% avocado puree), and a formulation with 100% avocado (40% bean flour and 100% avocado puree). Sensory evaluation results of optimized treatments indicated that the formula with 46% bean flour and 86% avocado puree presented the highest global acceptance. Results from this study showcase the possibility of producing gluten-free cookies with good protein content.
Las galletas son alimentos versátiles que pueden suplir necesidades específicas y ser utilizados como vehículos para aumentar la ingesta de distintos nutrientes. El objetivo fue elaborar galletas de mantequilla libres de gluten a base de harina de arroz. Se realizó un diseño central compuesto 22 donde se estudió la sustitución parcial de harina de arroz por harina de frijol (Phaseolus vulgaris, L.) (0-60%) y la sustitución de la mantequilla por puré de aguacate (Persea americana) (0-100%). Los resultados fueron analizados por la Metodología de Superficie de Respuesta con un nivel de significancia del 10% (p<0.1) y con un mínimo R2 de 0.6. Las variables de respuesta fueron: proteína (%), grasa (%), diámetro/altura, pérdida de peso (%), humedad (%) y cenizas (%). A valores altos de las dos variables estudiadas la cantidad de proteína, de cenizas y de humedad aumentó significativamente. La cantidad de grasa se incrementó al utilizar bajos niveles de puré de aguacate. Los menores valores de pérdida de peso se obtuvieron en niveles intermedios de harina de frijol. La relación diámetro/altura no fue afectada por las variables estudiadas. Al optimizar se obtuvieron 3 formulaciones diferentes: 46% de harina de frijol y 86% puré de aguacate; 59% de frijol y 82% de puré de aguacate y otra (no estadística) 40% de frijol y 100% de puré de aguacate. Los resultados del análisis sensorial de las muestras optimizadas indicaron que la formulación con mayor aceptación global fue la elaborada con 46% de harina de frijol y 86% de puré de aguacate, concluyendo que es posible elaborar una galleta libre de gluten y con una adecuada cantidad de proteína.
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O BJECTIVE To optimize stir-frying with saltwater technology of Citrus reticulata . METHODS Taking the contents of limonin ，nomilin and obacunone ，color difference value and free radical scavenging rate of 1，1-diphenyl-2-trinitrophenyl hydrazine （DPPH） as the indexes ，the entropy weight method was used for comprehensive evaluation. The stir-frying with saltwater technology of C. reticulata was optimized by central composite design-response surface method by using water-salt ratio ，stewing time，frying temperature and frying time as factors. RESULTS The optimal stir-frying with saltwater technology of C. reticulata included water-salt ratio of 8 ∶ 1（mL/g），stewing time of 22 min，frying time of 9 min and frying temperature of 158 ℃. After three times of validation tests ，the average comprehensive score of the optimized technology was 92.35（RSD＝2.19％），and its relative error with the predicted value （93.25）was 1.10％. CONCLUSIONS The optimal stir-frying with saltwater technology is stable and feasible.
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Objective To prepare berberine hydrochloride nanoemulsion, optimize its formulation composition and preparation process, and investigate its in vitro characteristics. Methods BBR-NE was prepared by water drop addition and pseudo-ternary phase diagram was drawn. The formulation of NE was optimized by central composite design-response surface methodology to choose the optimal formulation composition. The particle size, potential and appearance of the prepared BBR-NE were characterized. Results The optimal prescription of BBR-NE was determined as the oil phase Capryol 90 accounted for 32.84% of the system, the surfactant Tween-80 accounted for 33.90%, the co-surfactant 1,2-propylene glycol accounted for 16.95%, and water relative system accounted for 15.25%. The prepared NE was clear and transparent in appearance, regular in shape and uniform in size, with an average particle diameter of (68.85±8) nm, polydiseperse index of (0.245±0.03) and drug loading of 0.83 mg/g. The in vitro drug release results of NE showed that the in vitro drug release behavior was passive diffusion, which had a certain slow releasing effect and met the first-order release equation. Conclusion The BBR-NE can provide a new dosage form for the clinical use of berberine.
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Objective:To optimize the ethanol reflux extraction process of total saponins in total saponins of Trillium tschonoskii Rhizome. Methods:On the basis of single factor tests, making the total extraction rate of three main compounds [paris saponin Ⅵ, paris saponin Ⅶ and pennogenin-3- O-α-L-rhamnopyranosyl-(1→4)-[O-α-L-rhamnopyranosyl (1→2)]- O-β-D-glucopyranoside (PRRG)] as the indicator, the optimal extraction parameter was selected with the main influencing factors: the ethanol concentration, solid-liquid ratio, and extraction time by the central composite design-response surface method.Results:The optimal extraction parameter for the ethanol extract of total saponins of Trillium tschonoskii Rhizome was as follows: ethanol concentration 69%, extraction time 1.9 h, and solid liquid ratio 1∶9.7. The binomial fitting complex correlation coefficient r = 0.966 1, and the deviation between the extracted predicted value and the actual value is 4.68%. Conclusion:The central composite design-response surface method is simple and reliable for the optimization of extraction process of total saponins of Trillium tschonoskii Rhizome.
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Central composite design (CCD) is one of the most commonly used design methods in response surface optimization and has been widely applied in the field of pharmaceutics to optimize preparations. On the 20th anniversary of the introduction of CCD into China, the paper reviews its application in domestic pharmaceutical researches. Based on the brief introduction of basic principle and operation steps of CCD, the mistakes emerging in the application of CCD are summarized, including conceptual confusion with Box-Behnken design and face-centered CCD as well as wrong designs. Besides, the issues concerning the selection of factors and responses are discussed. The article is helpful for researchers to comprehensively understand the CCD and facilitates the rational application of this method.
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OBJECTIVE：To establish t he metho d for the content determination of pulegone in Schizonepetae tenuifolia decoction pieces and its compound preparation. METHODS ：Hollow fiber liquid-phase microextraction coupled with HPLC （HF-LPME-HPLC） was adopted. Based on single factor tests ，HF-LPME condition of S. tenuifolia decoction pieces and its compound preparation （taking Compound S. tenuifolia granule as an expample ） was optimized by central composite design-response surface methodology using pulegone enrichment multiple as index ，with the concentration of sample phase solution （NaCl），extraction time and stirring speed as factors. Validation test was conducted. HPLC method was adopted to determine the content of pulegone. The determination was performed on Hypersil C 18 column with mobile phase consisted of methanol- 0.3％ phosphoric acid （gradient elution ）at the flow rate of 1.0 mL/min. The detection wavelength was set at 252 nm，the column temperature was 25 ℃. The sample size was 20 μL. The feasibility of HF-LPME-HPLC method established in this study was validated by using HPLC method stated in the item of S. tenuifolia decoction pieces in 2020 edition of Chinese Pharmacopoeia （part Ⅰ）as reference. RESULTS ：The optimum HF-LPME conditions included n-nonanol as the extraction solvent ，sample phase solution with 11％ NaCl and pH value of 7，stirring speed of 800 r/min，extraction time of 36 min. Results of HPLC methodology investigation showed that linear range of pulegone were 0.05-5 μg/mL（r＝0.999 0）. The limits of detection and quantitation were 0.4 and 1.3 ng/mL，respectively. RSDs of intra-day and inter-day precision were 1.8％-4.0％ and 1.5％-4.1％（n＝3），respectively. RSDs of reproducibility and stability tests （24 h）were all lower than 8％（n＝6）. Average recoveries of S. tenuifolia decoction pieces and Compound S. tenuifolia granule were 102.6％-105.1％ and 97.2％-102.3％，respectively；RSDs were not higher than 4.1％ and 6.2％（n＝3）. The average contents of pulegone in S. tenuifolia decoction pieces determined by pharmacopoeia method and established method were 0.84 mg/g（RSD＝4.3％ ，n＝3）and 0.87 mg/g（RSD＝5.5％ ，n＝3），respectively，with no significant difference （P＞0.05）. CONCLUSIONS ：The established HF-LPME-HPLC method can enrich and concentrate pulegone ， shows strong purification ability and high sensitivity ，and can be used to determine the contents of pulegone in S. tenuifolia decoction pieces and its compound preparation.
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Objective:To optimize the preparation technic of Chuanxiong Rhizoma with vacuum steam method, and to investigate the anti-inflammatory and analgesic activity of Chuanxiong Rhizoma decoction pieces with Central Composite Design-Response Surface Method. Methods:Taking the content of ferulic acid as the evaluation index and the moistening temperature, moistening time and vacuum time as the observation indexes, the moistening technic of Chuanxiong Rhizoma was optimized by Response Surface Method, and selected the optimized plan. The anti-inflammatory and analgesic activities of Chuanxiong Rhizoma were investigated by auricle swelling induced by xylene and writhing induced by glacial acetic acid. Results:The optimum vacuum moistening technic was that the softening temperature was 80 ℃, the softening time was 50 min and the vacuum time was 45 min. The content of ferulic acid in Chuanxiong Rhizoma produced by this technic is highand could decreased the times of wrinkle reaction induced by acetic acid in mice, prolonged the latent period, and obviously or partially inhibitied the ear swelling degree induced byxylene in rats. Conclusions:The Response Surface Method technic of Chuanxiong Rhizoma is easy to operate with high accuracy. The vacuum steam treatment was more obvious than traditional technology group. It provides reference for the subsequent production of Chuanxiong Rhizoma decoction pieces and have the certain value for its promotion and application.
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Objective:To optimize the matrix formulation of Erhuang analgesic gels. Methods:Central composite design-response surface methodology was adopted to optimize the best formulation of Erhuang analgesic gels by using carbomer 940, triethanolamine and glycerine as independent variables, the appearance, stability, viscosity and in vitro release of berberine hydrochloride as comprehensive evaluation indices. Results:The fitting regressing equation was Y= 82.25 + 4.95 A+ 5.19 B + 1.41 C+ 1.51 AB + 0.904 0 AC- 0.531 9 BC- 2.92 A2-1.80 B2-0.182 1 C2. P value of the model was less than 0.000 1, and the correlation coefficient r value was 0.977. The optimal formulation of Erhuang analgesic gels consisted of 1.84% carbomer 940, 1.30 times triethanolamine of carbomer 940 and 13.99 grams of glycerine. The average comprehensive scores of three verification experiments was 88.56, and the deviations from the predicted values were 2.93%, 2.85% and 1.55%. Conclusion:The formulation process by central composite design-response surface methodology was stable and the formulation of Erhuang analgesic gels has been optimized.
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The drug formulation design of self-emulsifying drug delivery systems (SEDDS) often requires numerous experiments, which are time- and money-consuming. This research aimed to rationally design the SEDDS formulation by the integrated computational and experimental approaches. 4495 SEDDS formulation datasets were collected to predict the pseudo-ternary phase diagram by the machine learning methods. Random forest (RF) showed the best prediction performance with 91.3% for accuracy, 92.0% for sensitivity and 90.7% for specificity in 5-fold cross-validation. The pseudo-ternary phase diagrams of meloxicam SEDDS were experimentally developed to validate the RF prediction model and achieved an excellent prediction accuracy (89.51%). The central composite design (CCD) was used to screen the best ratio of oil-surfactant-cosurfactant. Finally, molecular dynamic (MD) simulation was used to investigate the molecular interaction between excipients and drugs, which revealed the diffusion behavior in water and the role of cosurfactants. In conclusion, this research combined machine learning, central composite design, molecular modeling and experimental approaches for rational SEDDS formulation design. The integrated computer methodology can decrease traditional drug formulation design works and bring new ideas for future drug formulation design.
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Citalopram is an antidepressant used for treating major depressive disorder. In the current work Citalopram HBr is formulated as mouth dissolving film with enhanced drug dissolution. The Central Composite Design (CCD), employed to examine the effects of amount of HPMC E50 (A), amount of maltodextrin (B) and amount of glycerol (C) on response variables tensile strength, disintegration time and cumulative % drug release. 27 formulations prepared according to CCD and evaluated for physicochemical parameters and in vitro dissolution studies. Citalopram HBr mouth dissolving films formulated by employing solvent-casting method using HPMC E50, maltodextrin and glycerol, optimized for the effective dosage of superdisintegrants. The formulation CF21 with maximum tensile strength of 67.21±1.31 gm, least disintegration time of 9±1.60 sec and highest drug release of 98.41±1.81% is chosen optimal formulation with maximum content uniformity and folding endurance. It is evident from the above results that the developed formulation can be an innovative dosage form to improve the drug delivery, quick onset of action as well as improve patient compliance in the effective management of depression.
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The premise of the study was to develop and optimize multiple unit gastroretentive microspheres of itraconazoleto prolong its localization in the stomach and analyzed using response surface methodology. The emulsion solventdiffusion evaporation method was used to prepare hollow microsphere of ethyl cellulose and Eudragit RS100 as lowdensity shell-forming polymers. The experimental design matrix was prepared using a central composite design tostudy the effect of various process parameters over response variables. The optimized microspheres showed a particlesize of 285.1µm, drug entrapment efficiency of 86.8%, buoyancy of 51.1%, and cumulative drug release of 77.80%.The experimental responses were in good harmony with the predicted values. The compatibility between drug andexcipients was determined by Fourier-transform infrared and differential scanning calorimetry analysis. The resultssignify that gastroretentive hollow microspheres are a promising vehicle to extend the retention time of itraconazolein the upper GI tract, and it can be floated in an acidic medium for a prolonged period.
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Rutin is a flavonoid glycoside, mainly consists of phenolic compounds, responsible for many biological activities. The objective of the present study was to develop and validate a precise, simple, robust, rapid and reliable reverse phase high -performance liquid chromatography (RP-HPLC) technique by using Qbd approach for evaluating the rutin in nanoparticles. Central composite design (CCD) was employed for optimizing the experimental conditions of RP-HPLC method. Buffer pH, methanol content in the mobile phase composition, flow rate, and wavelength were selected as independent variables whereas retention time, peak area, and asymmetry factor was selected as dependent variables. The retention time, peak area and asymmetric factor of rutin by using optimized independent variables were found to be 3.75 min, 1014.79 mV, and 1.26 respectively. The limit of detection and limit of quantitation values were found to be 0.005 µg/mL and 0.15 µg/mL respectively. For confirming linearity, accuracy, precision, and robustness, the optimized assay condition was validated as per ICH guidelines. The proposed method, which was optimized by QbD approach was found to be a suitable method for analyzing the rutin in chitosan-sodium alginate nanoparticles.
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Rutoside/analyse , Flavonoïdes/analyse , Chromatographie en phase liquide à haute performance/méthodes , Nanoparticules/analyse , Composés Phénoliques/effets indésirables , Concentration en ions d'hydrogèneRésumé
OBJECTIVE: To optimize the formulation of citalopram hydrobromide (CTH ) thermosensitive nasal gel and further evaluate its in vitro properties. METHODS: With gelling temperature and gelling time as evaluating indexes, central composite design-response surface and single factor experimental design method were used to optimize the formulation of CTH thermosensitive nasal gel by using poloxamer 407(F127) and carbomer 940 (CP940) as gel materials. Meanwhile, nasal mucosa permeation enhancer for CTH was then sieved by using Franz diffusion cell and ex vivo sheep nasal mucosa as experimental model. Finally, CTH thermosensitive nasal gel was prepared with cold method and then its in vitro properties was evaluated. In vitro cumulative erosion and cumulative release rate of the drug thermosensitive nasal gel were investigated by membrane-free dissolution method and dialysis membrane method, respectively. Moreover, the effect of temperature and pH on the viscosity of the drug nasal gel formulation was also evaluated. RESULTS: The optimal formulation of the thermosensitive nasal gel consisted of CTH 8.0%, F127 20.27%, CP940 0.17%, DM-β-CD 3.0%, ethylparaben 0.05% and distilled water. The gelling temperature, gelling time and pH of the drug thermosensitive nasal gel were found to be about 32.5 ℃,42 s and 5.0, respectively. The in vitro cumulative erosion and cumulative release percentage were both greater than 90% in 55 min and furthermore there was good linear correlation between these two parameters (r=0.998 6). Additionally, in vitro cumulative release of the drug from the gel formulation was determined to be 92% within 8 h, which conformed to Higuchi kinetic equation. Furthermore, the viscosity of the drug nasal gel was influenced by temperature as well as pH in different extent. CONCLUSION: The optimized formulation of the CTH thermosensitive nasal gel with central composite design-response surface method and single factor design method shows suitable gelling temperature, gelling time, pH value for nasal preparation and obvious in vitro drug sustained release characteristics.
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OBJECTIVE: To design and evaluate the formula of Weisu microemulsion-ion sensitive gel. METHODS The prescription of microemulsion-ion sensitive gel was conducted on the basis of single factor method and pseudotemary phase diagram method combining with central composite design-response surface methodology. The final formulation was evaluated by particle size, viscosity, potential, contents of naringin, hesperidin and neohesperidin. RESULTS: The optimum prescription ratio of Weisu microemulsion-ion sensitive gel was as following:volatile oil 3 g, RH-40 9 g, PEG-400 3 g, 0.3% deacetylated gellan gum made into 333 mL microemulsion gel. The results of physicochemical properties showed that microemulsion gel appearance was clear. The particle diameter was 20.14 nm. The Zeta potential was -4.04 mV. pH value was 5.43. The contents of naringin, hesperidin and neohesperidin are respectively 6.122 4, 2.094 1, 4.277 mg•mL-1. CONCLUSION: The preparation process of Weisu microemulsion gel is reasonable and feasible. The prepared microemulsion gel is system are stable.
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OBJECTIVE: To prepare simvastatin tablets and optimize its formulation by 3D printing technology. METHODS: A cylindrical tablet with a radius of 4 mm and a thickness of 4.8 mm were prepared by a 3D printer. The dosage of the adjuvant povidone 30(PVP K30), lactose/microcrystalline cellulose (MCC) and absolute ethanol were taken as an investigation factor, the cumulative dissolution rate of 5, 15 and 30 min were used as an evaluation index,and the central composite design-response surface method was used to optimize the formulation and verify, the effect of dissolution were researched by compared with the traditional preparation. RESULTS: The optimal formulation value: the ratio of PVP K30 was 30%, the mass ratio of lactose/MCC was 2.5, the ratio of absolute ethanol was 74%, and the cumulative dissolution in vitro of the printed tablets at 5, 15, 30 min was (45.7±0.5)%, (70.9±0.7)%, (89.7±2.3)% respectively, the deviation between the verification result and the predicted value were less than 5%. The preparation of dissolutioncurve is similar with commercially available formulations. CONCLUSION: The successful preparation of 3D printed simvastatin tablets is simple and the mathematical model is predictive.