(155b) How to Design a Pharmaceutical Drug Mixture with Prescribed Cohesive Properties Using Particle Scale Parameters

Once an API has been selected, tested, and found useful to treat some ailment the drug formulation enters into later phase work where the main concern is to assure the drug substance can be produced robustly, safely and with very tight tolerances on the quality of the final formulation. Here is where the formulator and process engineer form a critical product design team. The object of this late phase work is to quickly determine the optimal formulation, select the process equipment and process flow that will produce a robust drug substance to meet stringent quality criteria, tight weight or dose control, and economic process systems that limit exposure to safe levels. During this phase of work the drug development team must make decisions concerning wet granulation versus direct compaction or roller compact granulation combined with direct compaction. The team must select the method of drug delivery such as tablets, capsules, oral or inhalation. Then formulators must select reasonable excipients to add to the drug substance to create the most robust product at the lowest production cost. Much of this work is a guess-and-check approach where the formulator creates a formulation based on past experience and then produces a small batch using small scale unit operations. Key parameters are then measured on the final product. With this information, the engineers and formulators sit down and discuss the process constraints based on the product characteristics just created and the formulators discuss what the product constraints are relative to the end use. Often these desires are at odds with each other, resulting in multiple areas of concern. One concern is that the product produced is very prone to segregation and there are worries about quality issues. Another concern is that the final drug mixture is too cohesive and causes flow problems in the proposed process. Additional concerns include breakage of the final product (i.e. tablets) or dissolution of the tablets/pills in an environment similar to the digestive system. The cohesive nature of bulk material influences all of these concerns. If the product is too cohesive then it has flow problems in the handling and tableting system. If the product is not cohesive enough then the drug mixture easily segregates creating quality issues. If the product does not have the right cohesive properties, then the tablets made from the powder product tend to break or cause dissolution or time-release problems in the tablet form. At this final stage the API form is usually set and is generally a fine cohesive powder with very low solubility. The goal is to create a mixture free from these problems by adding the right set of excipients to overcome these issues without causing additional problems. Excipients come in all sizes and shapes, so the question is: what is the best combination to use to create the optimal drug product?

Here is where a product development model can help. It turns out that the bulk cohesive flow property of powders depends on what causes the adhesion between two particles. It also turns out that the bulk unconfined yield strength (fc) for different types of adhesion forces between particles is a function of the reciprocal of the particle size raised to some power 1/Dpⁿ where Dp is the particle size and (n) depends on what causes the adhesion between adjacent particles. Some of these adhesive forces are: capillary bond formation, Van der Waals attractive forces, crystal growth between particles, and/or elastic plastic sintering between particles. Any consistent material can be divided into variously sized class bins with a very narrow size distribution. The narrow size distribution is important because the models that exist relating unconfined yield strength to particle size assume a mono-dispersed particle size distribution (equation 1). The bulk unconfined yield strength of these narrow particles size bins can be measured and the strength plotted as a function of particle size.

fc=K1*1/Dp + K2*1/Dp² + K3*1/Dp^(1/2) + K4*1/Dpⁿ (1)

Bulk strength is mechanistic in nature and is the combined effect of all the various adhesion effects that might act between particles in a mixture. This is expressed in equation 1. The measured strength for the various particle size data can then be curve-fit to equation 1 to find the K-values which include the effects of the multiple possible causes of adhesion between particles.

It is possible to identify the cause(s) of the bulk strength based on their different adhesive forces. This can be done with the API and all of the excipients in the drug product. The result is a model describing bulk unconfined yield strength as a function of particle size for each of the pure components that make up the mixture.

The bulk powder can be thought of as collection of unit cells where the corners of the unit cells consist of particles selected randomly from the coarse size particles in the bulk (greater than D₅₀). The finer size particles (less than Dp₅₀) can then fit in the space between the coarse size particles. The void size between the coarse particles has a certain volume and a certain number of fine particles can fit in this volume depending on the particle size.

As this unit cell shears the particles in the unit cell are pulled apart. The act of pulling adjacent particles apart results in a set of adhesion forces between particles that are in the shear plane. From a continuum point of view, bulk unconfined yield strength is defined as the major principal stress that causes the bulk material to yield in shear. But, from a particle point of view, unconfined yield strength is a function of the collection of all the adhesive and frictional forces formed in the all the possible unit cells where the particles move, on average, the distance of one unit cell. The bulk unconfined yield strength of the unit cell can be thought of as the combined effect of the strength of the pair-wise interaction of adjacent particles for both the fines and coarse particles in the unit cell.

This particle scale model, then, turns into a probabilistic problem where a set of coarse particles is preselected and placed at the corners of the unit cell. The fine particles are also randomly selected based on the fines particle size distribution to fit in the void space between the coarse particles. The strength functions, as a function of particle size for each component, are then used to compute the strength of the material in the unit cell. This random selection process is repeated many times using the probabilities of selecting the fine and coarse particles based on the size distributions that make up the bulk material. The bulk strength is the average strength of all these randomly selected unit cells. The beauty of this method is that, once the mechanistic model is created for the excipients and API relating strength to particle size, the model can be used with the probabilistic model described above to estimate the bulk unconfined yield strength of any vendor-supplied PSD as well as the bulk unconfined yield strength of any combination of excipients and API for any prescribed particle size distribution and prescribed drug loading or excipient concentrations.

This work shows how the model can be generated and then used to predict bulk unconfined yield strength using particle scale properties. It provides formulators and process engineers the means of optimizing product design to create a prescribed behavior without the guess-and-check approach.