Matthew P. Mullarney

Pharmaceutical powders can be very different in their particle chemistry, morphology, and size, which can significantly affect their bulk-flow properties. Free-flowing powders are desirable to enable robust powder processing operations such as bin filling, hopper discharge, and capsule and die filling. It is well established that particle size (mean and distribution) is one of the most significant factors that affects the flow behavior of powders (1, 2). Small particles (<20 μm) have a relatively high surface area to volume ratio, causing interparticulate attractive forces to dominate and resist bulk flow when a shear stress is applied. Larger particles (>100 μm) tend to roll or slide over one another when a shear stress is present and, thus, exhibit superior bulk flow properties compared with small particles. This is because gravity forces significantly exceed interparticle forces such as those caused by electrostatic or van der Waals interactions for particles in this size range. In addition, a broad particle-size distribution (PSD) with both large and small particles enables more efficient particle packing, which leads to an interlocking effect as the small particles fill in the gaps between the contact surfaces of larger particles. The absolute size and distribution of particles in a powder sample, therefore, collectively contribute to the sample's bulk powder-flow behavior. 

The quantification of powder-flow properties with a small quantity of material (<20 g) is essential for material sparing and cost-saving predictive assessments. Amidon and Houghton remark that useful powder-flow evaluation tools should be reproducible, sensitive, yield meaningful results, and require small amounts of material (3). Because only small (expensive) quantities of powder are available during early dosage-form design and because the synthetic process may not be finalized, having a simple material-sparing screening tool that can rapidly evaluate the powder flow of these samples is attractive (3). Even with small-scale tools such as shear cells for the evaluation of powder-flow performance, however, it is desirable to predict powder-flow performance using less than 1 g material during prototype active pharmaceutical ingredient (API) or drug-product design.  

Particle-size analysis tools such as laser diffraction can measure the PSD of less than 1 g of material. It is beneficial to prototype API and solid-dosage formulation design if the flow performance of powders can be predicted using particle-size data. This method offers a significant advantage to a material-sparing approach because bulk property measurements such as flow cannot be scaled down much below a few grams due to the fact that they are dominated by interparticle interactions. 

The authors hypothesize that the relative powder-flow performance of a bulk powder sample is influenced by and can be predicted from its PSD. The objective of this investigation is to develop a quantitative empirical model for predicting an established single flow-performance parameter, the flow-function coefficient (FFC), from input PSD statistics. This model may then be used to predict the flow behavior of new powdered pharmaceutical materials. 

A proprietary database containing PSD and powder-flow data was queried for all powders containing PSD and FFC data. The query produced a representative sample of 185 pharmaceutical powders tested during a three-year period (see Table I). The volume mean diameter (VMD, D[4,3]) and FFC values ranged from 2 to 457 μm and 1.2 to 28.5, respectively. These are typical ranges for powdered bulk materials (4).  

Table I: Linear-regression data for measured versus predicted flow-function coefficient (FFC) values using the partial-least squares (PLS) model. 

The PSD of each sample was evaluated using a Sympatec Helos/Rodos laser diffraction particle-size analyzer (Sympatec Inc., Lawrenceville, NJ) with dry dispersion capability. Small bulk samples (0.5–5.0 g) were introduced to the dry dispersion feeder system using a vibratory feed tray. The dispersion pressure was optimized (0.5–4.0 bar) to reasonably break up any loose agglomerates in the sample. The laser diffraction system, equipped with the appropriate lens for the sample's particle-size range was used to measure the PSD of the sample in 31 channels. The cumulative PSD and common PSD statistics (D10, D50, D90, D[4,3]) were calculated using the Sympatec Windox 4.0 software. 

 The powder-flow behavior of each sample was determined using a Schulze ring shear tester model RST-XS [Dietmar Schulze, Wolfenbuttel, Germany]. In general, the RST-XS medium-sized annular cell (31.37 cm

) was used to conduct each yield locus test because it is suitable for most pharmaceutical testing where bulk quantities are often limited. Where appropriate, the large-sized cell was used for powders with particles larger than 500 μm. Each sample was equilibrated in a closed environment at 20 ± 2 °C and 50 ± 2% relative humidity for 16–24 h before testing to minimize the effects of moisture uptake. Although the influence of humidity on powder-flow properties or PSD were not explicitly explored in this work, the adhesion force between contacting particles is known to often increase with absorbed water, thus inhibiting flow performance (5). 

The equilibrated powder was spooned into the test cell and carefully leveled with the top of the annulus to form an unconsolidated powder bed with minimal voids. The cell was placed on the driving axle of the tester and fitted with the lid to which the shear force tie rods and normal loading rod were connected. The steady-state shear stress of each powder was measured as the powder was subjected to a series of applied normal loads ranging from 1 to 2.6 kPa. Before each load, the powder was sheared to a steady state at 4 kPa, which helped create a consistent initial powder bed condition (i.e., bulk density). From the yield locus plot, the ratio of the principle consolidation stress (σ

) to the unconfined yield strength (FC) was used to calculate the FFC value. 

 The laser-diffraction analysis provided 31 channels of PSD for each powder, which allowed detailed PSD to be constructed. The 10th, 50th, and 90th percentiles of the distribution were calculated for each material. In addition, the VMD (D[4,3]) calculated by the Sympatec Windox software was used as an input for the models. These four parameters were selected because they are commonly used PSD statistics. The response variable, FFC, was subdivided into four categories related to the powder's relative flow performance based on the laboratory's experience with powders (see Table II).  

Table II: Rating categories for flow-function coefficient (FFC) values. 

Two statistical methods were applied for correlating the PSD and FFC values: partial least squares (PLS) and tree-based regression. The PLS method generates a linear model describing the FFC in terms of the PSD values. The output is a linear model containing weighted linear combinations of PSD percentiles, which is used to calculate the FFC value. Preliminary statistical analysis of the data suggested a logarithmic relationship between the FFC and PSD values. This is not surprising because many properties of bulk powder and compacts are related 

 logarithmic relationships (e.g., compact tensile strength and solid fraction) (1). This is consistent with other research demonstrating empirical relationships between powder-flow parameters such as flow function or angle of internal friction and a single particle-size parameter. Kohler and Schubert report a model for describing a relationship between the inverse flow function (1/FF) and the median particle-size diameter (D50) for fine alumina powders (5). Podczeck and Miah found that the angle of internal friction of unlubricated powders is dependent on particle size and shape (6). 

A tree-based model (7) was also used to generate splitting criteria for the powder-flow performance category based on one or more of the PSD statistics (e.g., if distribution statistic 

 μm, then powder flow is classified as poor). Tree-based modeling is often used in data mining investigations such as this where the most important inputs for describing a response must be identified.  

In each method, four common measurements provided in particle-size analysis (D10, D50, D90, D[4,3]) were used to build the models. Initial results showed that there was no significant advantage to using additional PSD statistics to parameterize the model. The four-parameter model, therefore, was pursued; these distribution statistics are typically readily available as outputs from particle-size analysis. 

 PLS regression analysis method was used to develop a model to predict the FFC value from the PSD statistics for each material type. A single model to describe all material types could not predict the FFC value as well as a model built for a single material type. Therefore, separate models were built for active blends, active granulations, excipients, and APIs. This is not surprising considering the shape of the PSD curves and their response to shear stresses can be quite different across material types; for example, single component systems are typically uni-modal, but granulations are typically polymodal. 

The authors developed a four-parameter model using the most commonly reported PSD statistics for each material type to predict the FFC value from the PSD statistics, as shown below.  

A plot of the measured versus predicted FFC value for each material type is shown in Figure 1. Visual inspection of these plots suggests that the predictions for the API and excipient FFC values are superior to the active blends and active granulations. The 

 values in Table I describe the quality of the fit of linear regressions through the data in Figure 1 and, therefore, confirm this observation. The 

 values for the API and excipient models were 0.93 and 0.79, respectively, suggesting good model fits. The 

  values for the active blends and active granulations were all <0.32, suggesting that the models were not able to describe the flow performance of these materials using particle-size data with the same level of confidence. These results suggests that PSD statistics alone in the PLS models are more appropriate for predicting the flow performance of single component APIs or excipients. The models, however, may be useful for investigating potential differences in flow performance for like-composition formulations that have been subjected to different manufacturing process conditions.  

Figure 1 (FIGURES ARE COURTESY OF THE AUTHORS.) 

 A tree-based classification approach was used to categorize flow performance of the powders based on the relevant PSD statistics. The literature has reported similar rules of thumb for estimating flow behavior from particle size. For example, Staniforth reports that particles larger than 250 μm are usually free flowing; particles smaller than 100 μm become cohesive; and particles less than 10 μm are extremely cohesive (2). This statistical method selects the particle size parameters that are most significant in describing or categorizing the flow performance. The tree-based model was generated from the data using four parameters of the PSD: D10, D50, D90, and D[4,3]. 

The classification tree results in Figure 2 show that, for both models, only two distribution statistics were significant when predicting the flow category: the D10 and 50. These results further support the hypothesis formed in the PLS discussion that models that use PSD statistics to predict powder flow do not require (or cannot be any better predicted by) a multitude of parameters. These models are probably the most useful for forming "rules of thumb" when using PSD data to predict powder-flow performance. When higher resolution flow characterization is required, the PLS model described above or measuring the flow performance of the powder is preferred.  

 To investigate the predictive power of the PLS model, the authors evaluated the PSD and powder-flow performance of additional powder samples to test the predictions. Data from these materials were not used for the development of these models. In most cases, the models predicted the FFC value within the same flow category (excellent, good, marginal, poor) as the measured value (see Figure 3). Case 2 was an exception. In this case, the active blend contained an unusually high proportion of fines (D10=4 μm) because of a 25% loading of an API with a median diameter of 10 μm. Even with this discrepancy, however, a simplified set of PSD statistics (i.e., D10, D50, D90, D[4,3]) was found to suitably predict an estimated FFC on average to plus or minus one FFC unit for these newly characterized materials.  

Models have been developed for predicting relative powder-flow performance using PSD data. The PLS model, which used D10, D50, D90, and D[4,3] as input parameters, is suitable for predicting the FFC value for APIs and excipients and may also be appropriate for predicting PSD influences on other materials (e.g., active blends and active granulations). This empirical tool leverages a material and resource-sparing approach to the powder-flow performance characterization. In addition, the tool can be particularly useful during prototype drug-product design, especially with regard to risk assessments when little is known about the flow performance of a new API or excipient. 

The authors would like to thank Bruno Hancock for reviewing this work and providing technical guidance. 

are senior scientists at Pfizer, Inc., Eastern Point Rd., Groton, CT 06340, tel. 860.715.4139, 

*To whom all correspondence should be addressed. 

Submitted: June 16, 2008. Accepted: July 8, 2008. 

What would you do differently? Submit your comments about this paper in the space below.

 1. E.N. Hiestand, "Mechanics and Physical Principles for Powders and Compacts" (SSCI Inc., West Lafayette, IN, 2002), p 110. 

Pharmaceutics: The Science of Dosage Form Design

, M.E. Aulton, Ed. (Churchill Livingstone, Edinburgh, UK, 2002) pp. 197–210. 

 3. G.E. Amidon and M.E. Houghton, "Powder Flow Testing in Preformulation and Formulation Development," 

 4. A.W. Jenike, "Storage and Flow of Solids," in 

Utah Engineering Experiment Station Bulletin 123, 16th ed., 

(University of Utah, Salt Lake City, UT, 1964). 

 5. T. Kohler and H. Schubert, "Influence of Particle Size Distribution on the Flow Behavior of Fine Powders," 

 6. F. Podczeck and Y. Miah, "The Influence of Particle Size and Shape on the Angle of Internal Friction and the Flow Factor of Unlubricated and Lubricated Powders," 

 7. L. Breiman et al., "Classification and Regression Trees" (Chapman & Hall/CRC, Boca Raton, FL, 1984). 

Articles

The authors present a simple and material-sparing approach for estimating the powder-flow performance of previously uncharacterized single-component bulk powders when only particle-size distribution data are available.

Modeling Pharmaceutical Powder-Flow Performance Using Particle-Size Distribution Data

Pharmaceutical scientists have long sought the ability to see inside the solid dosage forms they produce to determine their products' structural features and to better understand their mode of action. Previous studies have used various techniques for visualizing the internal structure of solid dosage forms, including 

H NMR imaging (1), confocal microscopy (2), and conventional microscopy (optical and electron) combined with mechanical slicing of samples (

 microtoming) (3). One drawback of several current techniques is their invasive nature that can destroy the sample and prevent any further testing. Another is the techniques' limited penetration and resolution. Thus, it is probably fair to say that the ideal experimental approach for the three-dimensional structural imaging of pharmaceutical dosage forms has not yet been realized.   

X-ray microtomography is a relatively new approach to imaging the internal structure of solid dosage forms. This technique has been widely used for the 

 imaging of plants, insects, animals, and humans. X-ray microtomography is a nondestructive technique that has a high penetration ability and provides a reasonable level of resolution (~5–20 μm).  

 Figure 1: Schematic of X-ray microtomography instrument (I0 = incident beam, ItMay In the Field section5 = transmitted beam).			

The X-ray microtomography approach used in this work is an extension of the computer aided tomography (CAT) medical imaging technique commonly used in hospitals. X-rays are directed from a high-power source toward a sample, and a detector on the opposite side of the sample measures the intensity of the transmitted X-rays (see Figure 1). A two-dimensional "shadow" image is produced by accurately rastering the X-ray beam across the sample. The sample then is carefully moved (usually rotated) relative to the X-ray beam, and the process is repeated to produce additional two-dimensional images from various view points. Using a sophisticated Fourier transform algorithm, the two-dimensional images then are combined to generate a complete three-dimensional map of the sample.  

 Figure 2: Conventional bilayer tablet structure.						

The intensity of the X-rays reaching the detector is controlled by the sample path length and the X-ray attenuation coefficient of the material that it encounters on that path (4). The longer the path length and the greater the attenuation coefficient of the material (see http://

physics.nist.gov/PhysRefData/XrayMassCoef/tab3.html

 ), the greater the number of diffraction and scattering events, thereby weakening the X-ray beam that reaches the detector. The varying levels of signal intensity provide a gray-scale in the images from which information about the density, thickness, and attenuation properties of the sample can be obtained. Very dense or thick regions and areas that contain heavy elements (

 sodium, chlorine, or iron) will generally create the most contrast in the final images. In very simple terms, X-ray microtomography can be thought of as creating a three-dimensional map of the relative atomic density of the sample under evaluation. 

Figure 3: Cross section of a fast-dissolving tablet manufactured by lyophilization.			

The instrument used in this work was a Skyscan 1072 device (Skyscan, Aartselaar, Belgium) with a 100-kV, 98-mA X-ray source. It was operated in cone-beam mode with 0.90°-step random rotation of the sample between scans and a 180° total sample rotation. Corrections were made for imperfections in the detector output and for obvious beam-hardening effects. The vertical two-dimensional raw data image files (1024 × 1024 pixels) were "reconstructed" using the Skycan proprietary software to create a series of several hundred horizontal cross-sectional views of the samples. These images could be processed further to create complete three-dimensional structural maps of the samples. Gray-scale images also could be manipulated using standard image analysis techniques to produce binary or multiple-colored images and to obtain dimensional information about the sample. The maximum sample size that the instrument can accommodate is ~19 × 19 × 19 mm because of the size of the sample chamber and the effective focal length of the X-ray system. This size is adequate for most solid dosage forms. Because the detector creates raw data files of 1024 × 1024 pixels, the image resolution can be no better than about one-thousandth of the image field of view. For example, in a 15 × 15 mm field of view, each pixel will be ~15 × 15-μm. As the field of view is reduced below ~5 × 5 mm, the resolution of the instrument becomes limited by the effective width of the incident X-ray beam. The instrument manufacturer quotes a maximum resolution of ~5 μm. In this study, typical data acquisition times for solid dosage forms were 30–90 min., and data analysis usually took 1–3 h per sample, depending upon the level of detail required. 

Figure 4: Gel-coated analgesic tablet structure.			

Two- and three-dimensional images of a wide range of solid dosage forms were acquired in this study and used to learn more about their function and structure. The following provides several examples of how such information can be used to aid in the design and testing of pharmaceutical tablets and in solving related technical problems. 

Figure 5: Osmotic tablet structure in the region near the hole in the coating.						

 X-ray microtomography can provide simple information such as the shape and size of the regions of a dosage form that are not readily accessible. For example, the technique is ideally suited for determining the thickness of layers in multilayer tablets and for determining the shape and size of the interface between these layers (see Figure 2). It also can be used to elucidate the microstructure of fast-dissolving tablets such as those manufactured using lyophilization in which the structural features reflect the size and shape of the ice crystals that were present in the tablet before drying (see Figure 3). Reports in the literature also point to the utility of this technique for assessing the morphology and pore-size distribution of pharmaceutical granules (5, 6). Farber 

 concluded that it was especially useful for studying the connectivity and shape of voids within granules made using wet granulation (5). 

Figure 6: Cross section of a liquid-filled soft-gelatin capsule.			

 X-ray microtomography can be used to measure the thickness of a functional coating (see Figure 4) and to assess variations in the film-coating thickness at the corners of the tablet to ensure the integrity of the coating is maintained over the entire surface of the dosage form. For an osmotic controlled-release dosage form it is quite simple to determine the key dimensions (

 location, diameter, and depth) of the hole in the coating from which the active ingredient will be expelled (see Figure 5) (3). Likewise, in a liquid-filled soft-gelatin capsule the thickness and integrity of the capsule's solid shell and its welded seam can be readily determined (see Figure 6). 

Figure 7: Embossing on the surface of an immediate-release uncoated tablet.			

 Embossed markings on a tablet's surface are quite easily resolved and measured using X-ray microtomography (see Figure 7). This capability could be used to help troubleshoot tablet manufacturing problems such as sticking or picking. Defects in or damage to the internal structure of a compacted tablet also can be detected. Researchers have used X-ray microtomography to study small defects and hidden damage in a range of nonpharmaceutical materials, including metals and composites (7, 8). Figure 8 shows a region of an immediate-release tablet with an internal crack that might significantly influence its structural integrity. Although it is not currently possible to enable 100% inspection of all dosage forms from a large-scale batch, this may be feasible in the future as the instrumentation's speed increases and accuracy improves. 

 If the material of interest generates sufficient X-ray contrast, then it is feasible to determine the distribution of an active ingredient or functional excipient in a tablet or capsule using X-ray microtomography. This may provide vital information about the performance of a novel manufacturing process, or, in the future, may enable at-line process monitoring to occur. The distribution of particles (citric acid) in a fast-dissolve tablet is shown in Figure 9, and the distribution of an inorganic excipient incorporated into an osmotic controlled-release tablet is shown in Figure 10. This approach can provide complementary information to spectroscopic chemical images (9). With the rigorous use of three-dimensional image analysis tools, quantitative information about the uniformity of pharmaceutical samples can be obtained. 

Figure 9: Distribution of particles in a fast-dissolving anti-allergy tablet.			

The intensity of the gray scale that appears in the X-ray images is partly a function of the sample's density. The density of standard uni-axially compressed tablets is not uniform (1, 10), and X-ray microtomography may provide a means to study and quantify this density inhomogeneity in tablets. Density differences have been detected in immediate-release tablets (see Figure 11). By using standards of known density, researchers interested in the density of bone samples quantitatively computed this information directly from X-ray microtomography data (11). A similar approach with other materials also has been successful (12, 13). Quantitative studies of this type have been reported for pharmaceutical compacts. One study showed that the tablet shape and the presence of embossing resulted in nonuniformity in the density of compacts made from microcrystalline cellulose (14). In addition, researchers showed that die lubrication and the mode of compression each influenced the degree of this nonuniformity. In another study, X-ray microtomography of several compacted excipients showed how density variations in various regions of a compact control the mechanical response of the sample during tensile failure and indentation hardness tests (15). Researchers also demonstrated in this work that the degree of structural and mechanical anisotropy in a compact is significantly less for highly deformable (plastic) materials.  

Figure 10: Distribution of particles in a controlled- release osmotic tablet.						

A unique application of X-ray microtomography is the detection and location of foreign matter such as a metal particle within a solid dosage form. Such atypical substances show up very clearly as being different from the materials commonly used to manufacture pharmaceutical tablets. A metal particle within a tablet creates a hot spot in the tomographic image that shows it is unmistakably foreign (see Figure 12). This information enables the location of the particle to be exactly pin-pointed even though it is entirely contained within the dosage form and its size is quite small (~50 μm width in this example). 

Figure 11: Density variations in an immediate- release antacid tablet.						

Counterfeit tablets can be difficult to distinguish from authentic dosage forms on the basis of external appearances. By using X-ray microtomography, however, it is possible to compare the internal structures and dimensions of two tablets without destroying the samples, which may be important if the tablet is to be used as evidence in patent litigation or other legal proceedings. Figure 13 shows the images of two tablets, an innovator's patented dosage form and an unofficial copy, in which clear differences in the internal structures (

 layered core structure) can be seen easily. 

Figure 12: A metal particle in a placebo tablet.										

Several researchers have used X-ray microtomography to study changes in the structure of porous composites and foams under applied external stresses (16–18). It is implicit from these studies that the technique also has potential use in research into powder compaction and the formation of compressed tablet dosage forms (12, 17). It is likely that the time-dependent structural information obtained from such studies would provide considerable insight into the pharmaceutical manufacturing processes of tablet manufacture and dry granulation. Current measurement systems cannot collect data rapidly enough to enable powder compaction to be studied under current pharmaceutical manufacturing conditions, nor do they enable the behavior of the smallest individual particles to be resolved. The response time of research instruments is improving rapidly, however, and the need for studying short-lived events and even smaller samples has been recognized by commercial instrument designers and manufacturers. Using synchotron X-ray sources can provide some help in this regard (see http://

www.esrf.fr/Industry/Applications/Tomography/

  ), and enhanced X-ray sources, detector elements, control systems, and analysis software will likely lead to significant improvements in both response time and resolution for commercial instruments within the next 5–10 years.  

Figure 13: Comparison of the structure of a counterfeit (top) and innovators (bottom) osmotic tablet.						

 Recent developments in instrumentation suggest that in the future, X-ray microtomography studies may provide information about the chemical nature of samples (9, 19). This is an exciting advance that could address one of the current limitations of the technique for fully characterizing pharmaceutical products (

 a lack of information about the chemical nature of the sample). Commercial instruments capable of this type of multifaceted analysis are still a long way away, but systems in which X-ray microtomography is combined with more conventional spectroscopic mapping techniques in a single integrated instrument are already under development. Currently these systems require the destruction of the sample to facilitate the spectroscopic mapping of the samples, but they do have the potential for providing a detailed three-dimensional map of the physical and chemical nature of a product based on the analysis of just one or two dosage forms. This is clearly a significant improvement over the capabilities of current nonintegrated systems that each require a comparable number of dosage units to complete a full analysis. 

X-ray microtomography can obtain useful qualitative and quantitative information about the structure of pharmaceutical dosage forms. In the future, it is likely that X-ray microtomography also will be able to provide chemical mapping capabilities and improved spatial resolution of small structural features within these types of samples (9, 19, 20). 			

The authors acknowledge their coworkers at Pfizer Inc. for contributions made to this article. In particular, the work and input of Maureen Whitley and Mark Henson are gratefully acknowledged. 			

 "New Characterization Method for Pore and Packing Structure in Powder Compacts Using Confocal Laser Scanning Microscope," 

 "Osmotic Drug Delivery Using Swellable-Core Technology," 

 "Modeling of Transmitted X-ray Intensity Variation with Sample Thickness and Solid Fraction in Glycine Compacts," 

5. L. Farber, G. Tardos, and J.N. Michaels "Use of X-ray Tomography to Study the Porosity and Morphology of Granules," 

 "Characterization of Porous Microstructure by X-ray Microtomography," 

 "Damage Assessment in an Al/SiC Composite during Monotonic Tensile Tests Using Synchrotron X-ray Microtomography," 

 "Using Synchrotron X-ray Microtomography to Detect Defects," 

Mapping the Chemical States of an Element inside a Sample Using Tomographic X-ray Absorption Spectroscopy," 

X-ray microtomography has great potential for improving the understanding of the structural features of solid dosage forms and the changes in those features during manufacturing, handling, and storage. This article describes the basic principles of the technique and provides examples of its potential applications.