The Particle Size Equation
Particle size distribution for a pharmaceutical suspension is a delicate balance
Many pharmaceutical products are presented as easy-to-administer particle-liquid suspensions. Two parameters of considerable importance in these formulations are particle size and particle size distribution, both of which have a direct influence on in vivo dissolution and the rate of uptake of active pharmaceutical ingredient (API). The particle size of the API and of the excipients may also affect physical characteristics such as viscosity, which itself has an impact on, for example, mouth feel and long-term stability.
To investigate how particle size, particle size distribution, and rheology are linked with the performance characteristics of a suspension, we compared two different indigestion treatments. One product is promoted as fast acting and the other as long lasting. Both are suspension-based products with the same composition.
Particle Size and Product Performance
Particle size is a significant parameter for a wide range of pharmaceutical preparations. It influences dissolution, solubility or bioavailability, processability, stability, dose-content uniformity, and appearance. If particle size is critical to any of these properties, the FDA recommends particle size analysis.1 Furthermore, where these properties influence a product's activity, as discussed below, specifications of particle size are essential.
Let's examine the factors in turn. Dissolution rate of an API is of major importance because it determines the time of release into the bloodstream. The relationship between particle surface area and dissolution rate is described by the Noyes-Whitney equation:
In the equation, dW/dT is the dissolution rate, A is the surface area of the solid, C is the concentration of the solid in the bulk dissolution medium, CS is the concentration of the solid in the diffusion layer surrounding the solid, D is the diffusion coefficient, and L is the diffusion layer thickness.
What this indicates is that dissolution rate is directly proportional to the surface area of the solid, itself a function of particle size. A suspension containing a specific mass of active ingredient will release it more rapidly into the bloodstream if the particle size is relatively small. This means that reducing particle size enhances bioavailability.
Both particle size and particle size distribution affect product stability. For example, polydisperse suspensions are often more susceptible to sedimentation or creaming (separation into two phases). A wide particle size distribution can also compromise dose uniformity, particularly in a population of large particles containing a significant mass of API.
Large particles (greater than 20-30 microns) are also detrimental to perception of the product. Large particles can be detected on the tongue, making the liquid feel gritty and unpleasant to drink. Suspension rheology is also affected if the size distribution is broad or if there is a high fine particle fraction; these can alter perception of the product, as well as its appearance and the ease with which it can be swallowed.
Clearly, optimizing the particle size of suspension-based products-such as the indigestion liquids characterized in this study-is essential for balancing the sometimes conflicting requirements of bioavailability, stability, dose uniformity, storage, and mouth feel.
We analyzed samples of two different indigestion treatments to assess differences between them. Both products are predominantly made up of calcium and sodium carbonate suspended in a sodium alginate solution (see Table 1, below); one is described as being fast acting, the other long lasting. The particle size of the suspensions was determined using the technique of laser diffraction (Mastersizer 2000; Malvern Instruments, Inc.; Westborough, Mass.). Viscosity was studied as a function of shear rate using a rotational rheometer.
Laser diffraction is a well-established, rapid technique for particle sizing. It is covered by an international standard, and its use for pharmaceutical applications is described in both the U.S. and European pharmacopoeias.2-4 Some of the advantages of laser diffraction include its wide dynamic range (0.02 to 2,000 �m) and the flexibility it offers for measuring dry powders, suspensions, and emulsions. Because laser diffraction measurements capture a large number of particles, statistically significant data are generated in each measurement, even for very polydisperse distributions.
Laser diffraction instruments exploit the physics of light scattering: Large particles scatter light at small angles, while smaller particles scatter light less intensely at wider angles. Particle size and distribution can therefore be determined from a detected diffraction pattern using an appropriate scattering model. Table 2 (see p. 42) shows particle size parameters Dv10, Dv50, and Dv90 for the two indigestion liquids (Dv10 being the particle size below which 10% of the volume of material exists, and so on). Although a comparison of Dv50 and Dv90 values indicates little difference between the two samples, Dv10 values are different. The Dv10 value of the fast-acting liquid is three microns smaller than the Dv10 for the long-lasting remedy.
Particle size and distribution are important parameters for pharmaceutical suspensions, influencing both dissolution rate and bioavailability. Equally important is the fact that particle size has a direct impact on other performance characteristics.
The particle size distribution curves for the two products are more illuminating (see Figure 1, above). The red curve relates to the fast-acting product, while the green curve shows the data for the long-lasting formulation. The fast-acting product shows a shoulder of fine particles that will be rapidly solubilized following administration. These particles may therefore be responsible for the claims made regarding the fast onset of relief associated with this product. Conversely, the higher concentration of larger particles in the long-acting product may explain why this product will deliver indigestion relief for a longer period of time.
Modern rotational rheometers allow viscosity measurement over a wide range of shear rates, making it possible to assess how a suspension will behave under low shear (when stored, for example) or when subjected to greater stress (vigorous agitation). By inhibiting sedimentation, high viscosity gives suspension products stability during storage. On the other hand, suspension viscosity is directly related to product perception, with viscous liquids perceived as unpleasant to drink. Figure 2 (see p. 42) shows flow curves for the two samples measured using the Gemini HR nano rheometer (Malvern Instruments) over a shear rate range of 0.001s-1 to 100s-1. Data for the long-lasting formulation are once again shown in green.
The results suggest that at low shear rates, the long-lasting product has higher viscosity. Differences in viscosity at lowshear rates are generally caused by weak interactions between any particulate or polymeric species present within the formulation. These interactions are overcome as shear rate is increased and the high shear viscosity for the long-lasting product is less than that reported for the fast-acting formulation. The correlation between the rheological properties of suspensions at low shear rate and particle size distribution is described by the Krieger-Dougherty equation:
In this equation, ? is the viscosity of the suspension as a whole, ?medium is the viscosity of the base liquid, f is the volume fraction of solids in the suspension, fm is the maximum packing fraction of solids in the suspension, and [?] is the intrinsic viscosity (2.5 for rigid spheres).
The Krieger-Dougherty equation predicts that, for a fixed-volume fraction, suspension viscosity will decrease with increasing maximum packaging fraction. The presence of the shoulder of fine particles within the fast-acting product gives it a higher maximum packing fraction than that of the long-acting product. This is because the fine particles are able to pack into the gaps around the larger particles within the suspension. The smaller particles act like a lubricant, allowing the larger particles to move past each other more freely and reducing suspension viscosity. The lower viscosity of the fast-acting product is therefore directly attributable to particle size distribution.
At high shear rates, the fast-acting product has a higher viscosity, breaking with the correlation above. The differences in viscosity at higher shear rates are attributable to a different type of interaction, as the weak interactions present at low shear rates are broken down by the application of shear. The relatively high viscosity of the fast-acting product at high shear rates is due to strong, attractive van der Waals forces between the particles in suspension. Van der Waals forces increase as specific surface area increases and, therefore, become more dominant as particle size decreases. This explains why these interactive forces are stronger in the fast-acting product with its higher concentration of smaller particles.
According to the rheological properties described above, the long-acting product has more desirable properties for both the manufacturer and the user. When the product is stored it has lower shear rates and higher viscosity, making it physically stable. At high shear rates, during shaking of the product and administration, this viscosity is reduced, making the liquid thinner and more pleasant to drink.
Particle size and distribution are important parameters for pharmaceutical suspensions, influencing both dissolution rate and bioavailability. Equally important is the fact that particle size has a direct impact on other performance characteristics. Large particles, for example, feel gritty and unpleasant in the mouth. Additionally, by affecting suspension rheology, particle size has an indirect impact. The rheological properties of the product affect parameters such as mouth feel and stability.
Particle size data and rheological flow curves obtained for two indigestion treatments, one promoted as fast-acting and the other as long-lasting, demonstrate the practical importance and relevance of the data. The fast-acting product includes a population of smaller particles that can be absorbed quickly to give rapid relief. The inclusion of these particles does, however, compromise rheological properties. Data for the long-lasting treatment indicate its superiority in terms of mouth feel and stability.
The study shows how optimizing the particle size distribution for a pharmaceutical suspension involves achieving a delicate balance among the required dissolution rate (bioavailability), stability, and product characteristics. Without a doubt, it is important to effectively characterize and control particle size distribution. �
Kippax is product manager, diffraction products; Virden is a product technical specialist, diffraction; and Fletcher is an applications specialist, rheology, at Malvern Instruments. For more information, e-mail firstname.lastname@example.org, call (508) 768-6400, or visit www.malvern.com.
1. United States Food and Drug Administration, Center for Drug Evaluation and Research. Guidance for Industry: Analytical Procedures and Methods Validation. Rockville, Md.: United States Food and Drug Administration; August 2000: Section XI, Part F.
2. International Organization for Standardization. Particle size analysis-laser diffraction methods-Part 1: General Principles. Geneva, Switzerland: ISO Standards Authority; 1999. ISO 13320-1.
3. United States Pharmacopeial Convention. General chapter 429: Light diffraction measurement of particle size. In: Supplement to USP 27. Vol. 29, No. 4. In-Process Revision. Rockville, Md.: United States Pharmacopeial Convention; 2003.