A Cross-Performance Relationship Between Carr's Index and Dissolution Rate Constant: The Study of Acetaminophen Batches

Abstract

The aim of this paper is to promote a simple and scalable approach to accelerate the formulation development of wet granules using acetaminophen batches as a model system. Only two thorough experiments with five processing steps of: crystallization → dry blending → wet granulation → drying → dissolution, were required to establish a specific linear relationship between the overall effect of the particle size distribution and the dissolution performance for a given formulation of any batch of acetaminophen. With this specific linear relationship at hand, dissolution rates of the granules prepared from batches of acetaminophen with various particle size distribution could be predicted without the need of doing any wet granulation, drying and dissolution for the same formulation. It was found that the Carr's Index, C, an overall manifestation of particle size distribution, of only a few grams of the dry blended acetaminophen was good enough to be linearly related to the dissolution rate constant, k, of the formulated granules by ln k = α ln C + ln A (or exponentially by a power law of k = AC^α) where A was the exponential factor and α was the power index. A and α were dependent on the mass transfer of acetaminophen powders and the rheological properties of the formulated dry blended powders, respectively. The three linear relationships for 75, 62, and 30 wt % formulations were ln k = 2.9 ln C –12.3, ln k = 2.8 ln C –12.5, and ln k = 4.2 ln C –18.0, respectively. The power laws for 75, 62, and 30 wt % formulations were k = 4.7 × 10⁻⁶ C^2.9, k = 3.9 × 10⁻⁶ C^2.8, and k = 1.5 × 10⁻⁸ C^4.2, respectively. The formulation used in our study contained acetaminophen, microcrystalline cellulose, and polyvinylpyrrolidone. The validation of the linearity between k and C was verified (1) by acetaminophen batches from different processes and sources, (2) by the various formulation compositions of acetaminophen of 75, 62, and 30 wt%, and (3) by the growth mechanisms of wet granulation and the resultant granular structures determined by dry sieve analysis, optical microscopy (OM), mercury intrusion porosimetry (MIP), the Brunauer-Emmett-Teller (BET) method, scanning electron microscopy (SEM), and Fourier transformed infrared (FT-IR) microscopic mapping. In general, granules grown from the small-size ranged acetaminophen powders of a given formulation had a higher C. Since the growth mechanism was dominated by agglomeration, the granules were more porous, higher in surface area, more homogenous, and higher in dissolution rate constant, k, as opposed to granules grown from the large-size ranged acetaminophen powders of a given formulation having a lower, C, whose growth was dominated via consolidation and layer-by-layer mechanism and resulted in a lower dissolution rate constant, k.

Keywords:

• cross-performance relationship
• power law
• Carr's index
• dissolution rate constant
• FT-IR microscopic mapping
• acetaminophen