Derivation of the Extended Kawakita Equation for Estimating the Yield State of Powder in Die.

For powder compaction, the Kawakita equation has been used to estimate the powder behavior inside the die. The compression pressure exerted on powders is not homogeneous because of the friction on the die wall. However, the yield pressure and porosity estimated using the Kawakita equation are defined based on the assumption that homogeneous voids and compression pressure are distributed throughout the powder bed. In this study, an extended Kawakita equation was derived by considering the variation in the compression pressure as it corresponds to the distance from the loading punch surface. The yield time section estimated from the extended Kawakita equation was wider than that which was estimated via the classical equation. This result is consistent with the assumptions used to derive the extended Kawakita equation. Furthermore, a comparison of the porosity changes before and after the yield pressure was applied indicate that the direct cause of the yield is the spatial constraints of the powder particles. Equivalent stresses were defined to clarify the critical factor that constitutes the extended Kawakita equation. As a result, "taking into account the die wall friction" was considered to be the critical factor in the extended Kawakita equation. As these findings were theoretically determined by the extended Kawakita equation, a useful model was derived for a better understanding of powder compaction in die.

Prediction of Critical Quality Attributes Based on the Numerical Simulation of Stress and Strain Distributions in Pharmaceutical Tablets.

Various stresses and strains are generated on the surface and inside of pharmaceutical tablets when an external force is applied. In addition, stresses in various directions can remain on the surface and inside the tablets because they are generally prepared by compaction of pharmaceutical powders using dies and punches. As it is difficult to measure the stress and strain generation in the tablets experimentally, a numerical simulation was applied by employing a finite element method (FEM). An elastic model is often used to represent stress and strain generation after loading an external force to tablets, and the Drucker-Prager cap (DPC) model has been widely recognized for representing the remaining stress distributions during the compaction of powder to tablet form. Firstly, this article describes an FEM simulation of the stress generation on the surface of the scored tablets after loading the bending force from the back side of the tablets. Next, the FEM simulation was introduced to determine the effect of diametrical compression on the stress and strain generation in the tablets by comparing the results measured experimentally. Furthermore, the residual stresses remaining inside the tablets were simulated using FEM, in which powder compaction was represented as the DPC model. A clear difference was observed in the residual stress distributions between the flat and convex tablets. This indicates that FEM simulation is useful for achieving a science-based understanding of critical quality attributes in various types of tablets.

Development of invaethosomes and invaflexosomes for dermal delivery of clotrimazole: optimization, characterization and antifungal activity.

The objective of this study was to develop novel invaethosomes (I-ETS) and invaflexosomes (I-FXS) to enhance the dermal delivery of clotrimazole (CZ). Twenty model CZ-loaded I-ETS and I-FXS formulations were created according to a face-centered central composite experimental design. CZ-loaded vesicle formulations containing a constant concentration of 0.025% w/v CZ and various amounts of ethanol, d-limonene, and polysorbate 20 as penetration enhancers were prepared using the thin film hydration method. The physicochemical characteristics, skin permeability, and antifungal activity were characterized. The skin permeability of the experimental CZ-loaded I-ETS/I-FXS was significantly higher than that of conventional ethosomes, flexosomes, and the commercial product (1% w/w CZ cream). The mechanism of action was confirmed to be skin penetration of low ethanol base vesicles through the disruption of the skin microstructure. The optimal I-ETS in vitro antifungal activity against C. albicans differed significantly from that of ETS and the commercial cream (control). The response surface methodology predicted by Design Expert® was helpful in understanding the complicated relationship between the causal factors and the response variables of the 0.025% w/v CZ-loaded I-ETS/I-FXS formulation. Based on the available information, double vesicles seem to be promising versatile carriers for dermal drug delivery of CZ.

Latent Structure Analysis of Wet-Granulation Tableting Process Based on Structural Equation Modeling.

Quality by design (QbD) is an essential concept for modern manufacturing processes of pharmaceutical products. Understanding the science behind manufacturing processes is crucial; however, the complexity of the manufacturing processes makes implementing QbD challenging. In this study, structural equation modeling (SEM) was applied to understand the causal relationships between variables such as process parameters, material attributes, and quality attributes. Based on SEM analysis, we identified a model composed of the above-mentioned variables and their latent factors without including observational data. Difficulties in fitting the observed data to the proposed model are often encountered in SEM analysis. To address this issue, we adopted Bayesian estimation with Markov chain Monte Carlo simulation. The tableting process involving the wet-granulation process for acetaminophen was employed as a model case for the manufacturing process. The results indicate that SEM analysis could be useful for implementing QbD for the manufacturing processes of pharmaceutical products.

Design and Optimization of Scored Tablets with Concave Surface and Application of Bayesian Estimation for Solving Scaleup Problem.

From the viewpoint of self-medication, it is valuable to develop patient-friendly scored tablets that possess dividing uniformity. In this context, we attempted to optimize the preparation conditions for a tablet with a unique shape, such as a concavely curved scored tablet (CCST). Employing a design of experiment and a response surface method incorporating a thin-plate spline interpolation, and a bootstrap resampling technique, the optimal preparation conditions for CCST were successfully developed. To make it possible to scaleup the optimal solution estimated on a trial-scale, a Bayesian estimation was applied. Credible ranges of critical responses in large-scale manufacturing were estimated as a posterior probability from the trial-scale experiment as a prior probability. In terms of the large-scale manufacturing, the possibility of solving the scaleup problem was suggested using Bayesian estimation. Furthermore, a simulation study using a finite element method revealed that strong tensile stresses generated along the tip of the score line in CCST when an outer force was applied to the back surface of CCST. An advantage in dividing uniformity is indicated by the unique shape of CCST.

The Usefulness of Definitive Screening Design for a Quality by Design Approach as Demonstrated by a Pharmaceutical Study of Orally Disintegrating Tablet.

Definitive screening design (DSD) is a new class of small three-level experimental design that is attracting much attention as a technical tool of a quality by design (QbD) approach. The purpose of this study is to examine the usefulness of DSD for QbD through a pharmaceutical study on the preparation of ethenzamide-containing orally disintegrating tablet. Model tablets were prepared by directly compressing the mixture of the active pharmaceutical ingredient (API) and excipients. The five evaluated factors assigned to DSD were: the contents of API (X1) and lubricant (X2), and the compression force (X3) of the tableting process, the mixing time (X4), and the filling ratio of powder in the V-type mixer (X5). After tablet preparation, hardness and disintegration time were measured. The same experiments were performed by using the conventional design of experiments [i.e., L8 and L16 orthogonal array designs and central composite design (CCD)]. Results showed that DSD successfully clarified how various factors contribute to tablet properties. Moreover, the analysis result from DSD agreed well with those from the L8 and L16 experiments. In additional experiments, response surfaces for tablet properties were created by DSD. Compared with the response surfaces created by CCD, DSD could produce reliable response surfaces for its smaller number of experiments. We conclude that DSD is a powerful tool for implementing pharmaceutical studies including the QbD approach.

Nondestructive Monitoring of the Dispersion State of Titanium Dioxide Nanoparticles in Concentrated Suspensions Using Magnetic Resonance Imaging.

The purpose of the present study is to demonstrate the applicability of magnetic resonance imaging, especially T2 relaxation time mapping, for nondestructive monitoring of the dispersion state of nanoparticles (NPs) in concentrated suspensions. TiO2 15-nm-diameter NPs, for use in sunscreen lotion products, were examined as a test NP. First, this study investigated whether T2 is sensitive to the NP concentration. In experiments with pulsed nuclear magnetic resonance on TiO2 NP suspensions with different organic solvents (ethanol, acetone, and decamethylcyclopentasiloxane), the T2 of each solvent varied in the suspensions according to the NP concentration. This study also confirmed that T2 mapping was effective for visualizing differences in NP concentration. Subsequently, gravitational sedimentation of the test suspensions was investigated. T2 mapping exhibited better detection sensitivity to sedimentation occurring in concentrated suspensions than visual observation, as it enabled the detection of changes in NP distributions that could not be visible to the naked eye. In addition, measurements of backscattered light enabled the full understanding of the dispersion stability of the TiO2 NPs in each solvent. Finally, the present study evaluated the centrifuge sedimentation of a commercial TiO2 NP suspension. T2 mapping clearly showed the complicated sedimentation behavior induced by the centrifugation treatment. The simulated fluid flow was consistent with the particle distribution in the centrifuged sample; thus, the sedimentation was believed to have developed in accordance with the vorticity generated by the centrifugation.

Combination Strategy with Complexation Hydrogels and Cell-Penetrating Peptides for Oral Delivery of Insulin.

In previous studies we showed that the complexation hydrogels based in poly(methacrylic acid-g-ethylene glycol) [P(MAA-g-EG)] rapidly release insulin in the intestine owing to their pH-dependent complexation properties; they also exhibit a high insulin-loading efficiency, enzyme-inhibiting properties, and mucoadhesive characteristics. Cell-penetrating peptides (CPPs), such as oligoarginines [hexa-arginine (R6), comprising six arginine residues], have been employed as useful tools for the oral delivery of therapeutic macromolecules. The aim of our study was to investigate the combination strategy of using P(MAA-g-EG) hydrogels with R6-based CPPs to improve the intestinal absorption of insulin. A high efficiency of loading into crosslinked P(MAA-g-EG) hydrogels was observed for insulin (96.1±1.4%) and R6 (46.6±3.8%). In addition, immediate release of the loaded insulin and R6 from these hydrogels was observed at pH 7.4 (80% was released in approximately 30 min). Consequently, a strong hypoglycemic response was observed (approximately 18% reduction in blood glucose levels) accompanied by an improvement in insulin absorption after the co-administration of insulin-loaded particles (ILP) and R6-loaded particles (ALP) into closed rat ileal segments compared with that after ILP administration alone. These results indicate that the combination of P(MAA-g-EG) hydrogels with CPPs may be a promising strategy for the oral delivery of various insulin preparations as an alternative to conventional parenteral routes.

Strength Simulation of Scored Tablets Based on the Finite Element Method Using an Extreme Vertices Design.

The mechanical strain distribution of scored tablets was simulated using the finite element method (FEM). The score was fabricated as a triangular runnel with the pole on the top surface of flat tablets. The effect of diametral compression on the tablet surface strain was evaluated by changing the angle between the scored line and the diametral compression axis. Ten types of granules were prepared according to an extreme vertices design. Young's modulus and the Poisson ratio for the model powder bed were measured as elastic parameters. The FEM simulation was then applied to the scored tablets represented as a continuous elastic model. Strain distributions in the inner structure of the tablets were simulated after the application of external force. The maximum principal strain (ε1) value was obtained with tablets containing a large amount of corn starch, in all scored line positions. In contrast, the ε1 value of the tablets containing a large amount of microcrystalline cellulose was minimal. The adequacy of the simulation was evaluated by experiments with scored tablets. The results indicated a fairly good agreement between the FEM simulation and experiments. Moreover, it was found that the ε1 value correlated negatively with the value of tablet hardness. These results suggest that the FEM simulation was advantageous for designing scored tablets.

Optimization of Premix Powders for Tableting Use.

Direct compression is a popular choice as it provides the simplest way to prepare the tablet. It can be easily adopted when the active pharmaceutical ingredient (API) is unstable in water or to thermal drying. An optimal formulation of preliminary mixed powders (premix powders) is beneficial if prepared in advance for tableting use. The aim of this study was to find the optimal formulation of the premix powders composed of lactose (LAC), cornstarch (CS), and microcrystalline cellulose (MCC) by using statistical techniques. Based on the "Quality by Design" concept, a (3,3)-simplex lattice design consisting of three components, LAC, CS, and MCC was employed to prepare the model premix powders. Response surface method incorporating a thin-plate spline interpolation (RSM-S) was applied for estimation of the optimum premix powders for tableting use. The effect of tablet shape identified by the surface curvature on the optimization was investigated. The optimum premix powder was effective when the premix was applied to a small quantity of API, although the function of premix was limited in the case of the formulation of large amount of API. Statistical techniques are valuable to exploit new functions of well-known materials such as LAC, CS, and MCC.

Determining the Influence of Granule Size on Simulation Parameters and Residual Shear Stress Distribution in Tablets by Combining the Finite Element Method into the Design of Experiments.

The influence of granule size on simulation parameters and residual shear stress in tablets was determined by combining the finite element method (FEM) into the design of experiments (DoE). Lactose granules were prepared using a wet granulation method with a high-shear mixer and sorted into small and large granules using sieves. To simulate the tableting process using the FEM, parameters simulating each granule were optimized using a DoE and a response surface method (RSM). The compaction behavior of each granule simulated by FEM was in reasonable agreement with the experimental findings. Higher coefficients of friction between powder and die/punch (µ) and lower by internal friction angle (αy) were generated in the case of small granules, respectively. RSM revealed that die wall force was affected by αy. On the other hand, the pressure transmissibility rate of punches value was affected not only by the αy value, but also by µ. The FEM revealed that the residual shear stress was greater for small granules than for large granules. These results suggest that the inner structure of a tablet comprising small granules was less homogeneous than that comprising large granules. To evaluate the contribution of the simulation parameters to residual stress, these parameters were assigned to the fractional factorial design and an ANOVA was applied. The result indicated that µ was the critical factor influencing residual shear stress. This study demonstrates the importance of combining simulation and statistical analysis to gain a deeper understanding of the tableting process.

Prediction of Skin Permeation of Flurbiprofen from Neat Ester Oils and Their O/W Emulsions.

Although many in silico models were reported to predict the skin permeation of drugs from aqueous solutions, few studies were founded on the in silico estimation models for the skin permeation of drugs from neat oil formulations and o/w emulsions. In the present study, the cumulative amount of a model lipophilic drug, flurbiprofen (FP), that permeated through skin was determined from 12 different kinds of ester oils (Qoil) and an in silico model was developed for predicting the skin permeation of FP from these ester oils. Thus, the obtained Qoil values were well predicted with the FP solubility in the oils (Soil), the amount of FP uptake into the stratum corneum (SCoil) and molecular descriptors of dipolarity/polarizability (π2H) and molecular density. This model suggests that the thermodynamic activities of FP both in the formulations and skin are the key factors for predicting the skin permeation of FP from the ester oils. In addition, a high linear relationship was observed in the double-logarithm plots between the Qoil and the cumulative amount of FP permeated through skin from 20% ester oil in water emulsion (Qemul20%). Furthermore, the skin permeations of FP from 5 and 10% ester oil in water emulsions, Qemul5% and Qemul10%, respectively, were also predicted by the horizontal translation of the y-axis intercept of the liner equation for the relation between the Qoil and Qemul20%. These prediction methods must be helpful for designing topical oily and/or o/w emulsion formulations having suitable and high skin permeation rate of lipophilic drugs.

Modeling of quantitative relationships between physicochemical properties of active pharmaceutical ingredients and tensile strength of tablets using a boosted tree.

OBJECTIVES: The aim of this study was to explore the potential of boosted tree (BT) to develop a correlation model between active pharmaceutical ingredient (API) characteristics and a tensile strength (TS) of tablets as critical quality attributes. METHODS: First, we evaluated 81 kinds of API characteristics, such as particle size distribution, bulk density, tapped density, Hausner ratio, moisture content, elastic recovery, molecular weight, and partition coefficient. Next, we prepared tablets containing 50% API, 49% microcrystalline cellulose, and 1% magnesium stearate using direct compression at 6, 8, and 10 kN, and measured TS. Then, we applied BT to our dataset to develop a correlation model. Finally, the constructed BT model was validated using k-fold cross-validation. RESULTS: Results showed that the BT model achieved high-performance statistics, whereas multiple regression analysis resulted in poor estimations. Sensitivity analysis of the BT model revealed that diameter of powder particles at the 10th percentile of the cumulative percentage size distribution was the most crucial factor for TS. In addition, the influences of moisture content, partition coefficients, and modal diameter were appreciably meaningful factors. CONCLUSIONS: This study demonstrates that BT model could provide comprehensive understanding of the latent structure underlying APIs and TS of tablets.

Enhancement of Galantamine HBr Skin Permeation Using Sonophoresis and Limonene-Containing PEGylated Liposomes.

This study aimed to investigate the effect of low-frequency sonophoresis (SN) and limonene-containing PEGylated liposomes (PL) on the transdermal delivery of galantamine HBr (GLT). To evaluate the skin penetration mechanism, confocal laser scanning microscopy (CLSM), Fourier transform infrared spectroscopy (FTIR), and differential scanning calorimetry (DSC) were employed. The application of SN led to more GLT penetration into and through the skin than GLT solution alone. The liposomes also improved GLT permeation, and 2% limonene-containing PL (PL-LI2%) exhibited the highest GLT permeation, followed by PL-LI1%, PL-LI0.1%, and PL. The CLSM images of PL-LI2% resulted in the highest fluorescence intensity of fluorescent hydrophilic molecules in the deep skin layer, and the rhodamine PE-labeled liposome membrane was distributed in the intercellular region of the stratum corneum (SC). PL-LI2% induced significant changes in intercellular lipids in the SC, whereas SN had no effect on intercellular lipids of the SC. DSC thermograms showed that the greatest decrease in the lipid transition temperature occurred in PL-LI2%-treated SC. SN might improve drug permeation through an intracellular pathway, while limonene-containing liposomes play an important role in delivering GLT through an intercellular pathway by increasing the fluidity of intercellular lipids in the SC. Moreover, a small vesicle size and high membrane fluidity might enhance the transportation of intact vesicles through the skin.

Prediction of Dissolution Data Integrated in Tablet Database Using Four-Layered Artificial Neural Networks.

A large number of dissolution data were measured and integrated into a previously constructed tablet database composed of 14 kinds of compounds as model active pharmaceutical ingredients (APIs) with contents ranging from 10 to 80%. The database has contained physicochemical and powder properties of APIs, together with basic physical attributes of tablets such as the tensile strength and the disintegration time. In order to enhance the value of this database, drug dissolution data are essential to improving key information for designing tablet formulations. A four-layered artificial neural network (4LNN), newly implemented in commercially available software, was employed to predict dissolution data from physicochemical and powder properties of APIs. Our results showed that an excellent model for the prediction of dissolution data was achieved with 4LNN method. The function of 4LNN was appreciably better than that of conventional three-layered model, despite both models adopting the same number of nodes and algorithms for activation functions. Furthermore, linear regression models resulted in poor prediction of dissolution data.

Molecular Interaction between Intercellular Lipids in the Stratum Corneum and l-Menthol, as Analyzed by Synchrotron X-Ray Diffraction.

l-Menthol increases drug partitioning on the surface of skin, diffusion of drugs in the skin, and lipid fluidity in the stratum corneum and alters the rigidly arranged lipid structure of intercellular lipids. However, l-menthol is a solid at room temperature, and it is difficult to determine the effects of l-menthol alone. In this study, we vaporized l-menthol in order to avoid the effects of solvents. The vaporized l-menthol was applied to the stratum corneum or lipid models comprising composed of ceramides (CER) [EOS], the longest lipid acyl chain of the ceramides in the stratum corneum lipids that is associated with the barrier function of the skin; CER [NS], the shorter lipid acyl chain of the ceramides, and the most components in the stratum corneum of the intercellular lipids that is associated with water retention in the intercellular lipid structure of the stratum corneum; cholesterol; and palmitic acid. Synchrotron X-ray diffraction, differential scanning calorimetry, and attenuated total reflection Fourier transform infrared spectroscopy analyses revealed that the lipid models were composed of hexagonal packing and orthorhombic packing structures of different lamellar periods. Taken together, our results revealed that l-menthol strongly affected the lipid model composed of CER [EOS]. Therefore, l-menthol facilitated the permeation of drugs through the skin by liquid crystallization of the longer lamellar structure. Importantly, these simple lipid models are useful for investigating microstructure of the intercellular lipids in the stratum corneum.

Stability of Mixed Preparations Consisting of Commercial Moisturizing Creams with an Ointment Base Investigated by Magnetic Resonance Imaging.

A moisturizing cream mixed with a steroid ointment is frequently prescribed to patients suffering from atopic dermatitis. However, there is a concern that the mixing operation causes destabilization. The present study was performed to investigate the stability of such preparations closely using magnetic resonance imaging (MRI). As sample preparations, five commercial moisturizing creams that are popular in Japan were mixed with an ointment base, a white petrolatum, at a volume ratio of 1 : 1. The mixed preparations were stored at 60°C to accelerate the destabilization processes. Subsequently, the phase separations induced by the storage test were monitored using MRI. Using advanced MR technologies including spin-spin relaxation time (T2) mapping and MR spectroscopy, we successfully characterized the phase-separation behavior of the test samples. For most samples, phase separations developed by the bleeding of liquid oil components. From a sample consisting of an oil-in-water-type cream, Urepearl Cream 10%, a distinct phase-separation mode was observed, which was initiated by the aqueous component separating from the bottom part of the sample. The resultant phase separation was the most distinct among the test samples. To investigate the phase separation quantitatively and objectively, we conducted a histogram analysis on the acquired T2 maps. The water-in-oil type creams were found to be much more stable after mixing with ointment base than those of oil-in-water type creams. This finding strongly supported the validity of the mixing operation traditionally conducted in pharmacies.

Membrane Microdomain Structures of Liposomes and Their Contribution to the Cellular Uptake Efficiency into HeLa Cells.

The purpose of this study is to obtain a comprehensive relationship between membrane microdomain structures of liposomes and their cellular uptake efficiency. Model liposomes consisting of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC)/1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC)/cholesterol (Ch) were prepared with various lipid compositions. To detect distinct membrane microdomains in the liposomes, fluorescence-quenching assays were performed at temperatures ranging from 25 to 60 °C using 1,6-diphenyl-1,3,5-hexatriene-labeled liposomes and (2,2,6,6-tetramethylpiperidin-1-yl)oxyl. From the data analysis using the response surface method, we gained a better understanding of the conditions for forming distinct domains (Lo, Ld, and gel phase membranes) as a function of lipid composition. We further performed self-organizing maps (SOM) clustering to simplify the complicated behavior of the domain formation to obtain its essence. As a result, DPPC/DOPC/Ch liposomes in any lipid composition were integrated into five distinct clusters in terms of similarity of the domain structure. In addition, the findings from synchrotron small-angle X-ray scattering analysis offered further insight into the domain structures. As a last phase of this study, an in vitro cellular uptake study using HeLa cells was conducted using SOM clusters' liposomes with/without PEGylation. As a consequence of this study, higher cellular uptake was observed from liposomes having Ch-rich ordered domains.

Effect of Nerolidol and/or Levulinic Acid on the Thermotropic Behavior of Lipid Lamellar Structures in the Stratum Corneum.

Permeation enhancers are required to deliver drugs through the skin efficiently and maintain effective blood concentrations. Studies of the barrier function of the stratum corneum using l-menthol, a monocyclic monoterpene widely used in medicines and foods, have revealed an interaction between characteristic intercellular lipid structures in the stratum corneum and permeation enhancers. The variety of permeation enhancers that can be used to contribute to transdermal delivery systems beyond l-menthol is increasing. In this study, we focused on nerolidol and levulinic acid and investigated their influence on stratum corneum lipid structures. Nerolidol, a sesquiterpene, has been reported to enhance the permeation of various drugs. Levulinic acid is reported to enhance the permeability of buprenorphine and is used as a component of the buprenorphine® patch. Synchrotron X-ray diffraction and attenuated total reflectance Fourier transform IR spectroscopy measurements revealed that nerolidol disturbs the rigidly arranged lipid structure and increases lipid fluidity. Levulinic acid had a smaller effect on stratum corneum lipid structures, but did increase lipid fluidity when co-administered with nerolidol or heat. We found that nerolidol has an effect on stratum corneum lipids similar to that of l-menthol, and levulinic acid had an effect similar to that of oleic acid.

Application of Response Surface Methodology to Estimate the Design Space of Pharmaceutical Diluents for Dispensing Powdered Formulations.

Scientific approaches for dispensation are important for the quality and efficacy of drug treatments. Therefore, for the dispensation of powdered medicines, we have developed a powder blending method using a planetary centrifugal mixer (PCM) to replace the empirical manual method involving a mortar and pestle. The aim of this study was to optimize the formulation of pharmaceutical diluents for dispensing powdered medicines, using PCM. The diluents, composed of powdered lactose, crystalline lactose, and corn starch were assigned to a {3,2}-Simplex Lattice design. Then, the designed diluents were blended with model powders, such as carbazochrome sodium sulfonate powder, rifampicin capsule contents, and crushed sulfasarazine tablets, at ratios of 1 : 4, 1 : 1, and 4 : 1 using PCM at 800 rpm for 60 s at a 20% filling rate. The mixtures were examined for content uniformity relative standard deviation (RSD) and flowability angle of repose (AOR). Response surface methodology was applied to optimize the formulation with the smallest RSD and AOR, and then the design space of desired diluents was estimated. On the basis of the design space, crystalline lactose, the mixture of lactose powder and crystalline lactose at a ratio of 1 : 4, and the mixture of corn starch and crystalline lactose at a ratio of 1 : 4, were suitable diluents for the powdered formulation, the content of the capsules, and the crushed tablets, respectively. The selected diluents were successfully applied to other model medicines showing a sufficient RSD and AOR. This technique could contribute to the development of scientific approaches for dispensation.