Multivariate Analysis and Response Surface Methodology

One example of response surface analysis applied to capsules examines the critical formulation variables for a piroxicam capsule formulation.41 This example is particularly interesting because it links in vitro outcomes with in vivo outcomes in human subjects. Piroxicam is a BCS Class II drug (low solubility and high permeability) drug. Thirty-two batches of 20-mg piroxicam capsules were manufactured according to a resolution V central composite (face-centered) experimental design. Five formulation (independent) variables were studied at each of three levels (see Table 1.1 and additional comments in Chapter 15). Colloidal silica (glidant) and sodium starch glycolate (disintegrant) were fixed at 0.1% and 5%, respectively, in all batches. Because it is a BCS II drug, the effect of piroxicam particle size on drug dissolution was of particular importance. This aspect was evaluated by comparing the piroxicam powder as received (termed unmilled in the study) with the same lot of piroxicam that was remilled (termed milled in the study). The remilling of piroxicam substantially reduced its particle size, as reflected in a nearly threefold increase in its specific surface area from 1.79 to 4.91 m2/g. The capsules were filled with a consistent plug compression force using an instrumented Zanasi LZ-64 automatic capsule filling machine. USP monograph dissolution profiles (% piroxicam dissolved vs. time) were obtained for the batches. Statistical analysis revealed a number of interesting insights. For example, the percent lactose, and an interaction between piroxicam particle size and sodium lauryl sulfate level were the most important variables affecting the percentage of piroxicam dissolved at 10 min. However, the most important variable affecting the percent dissolved in 45 min was the wetting agent, sodium lauryl sulfate, followed closely by piroxicam particle size. When the piroxicam is milled, the sodium lauryl sulfate level has comparatively little effect on dissolution (see Figure 1.2), presumably because the milled drug is more rapidly dissolving because of its larger specific surface area. The apparent reduced significance of the level of lactose at 45 min may be attributed to its complete dissolution by that time. Overall, the magnesium stearate level and its blending time were either not significant or among the least significant factors affecting piroxicam dissolution in these formulations. This observation may be largely explained by the ability of sodium lauryl sulfate to overcome the hydrophobicity of magnesium stearate. The water solubility of lactose and the presence of the disintegrant, sodium starch glycolate, may also help overcome hydrophobic lubricant effects.

Figure 1.2Effect of piroxicam-specific surface area, sodium lauryl sulfate (SLS), and lactose on dissolution. (Plotted from University of Maryland–FDA data [Food and Drug Administration, RFP 223-91-3401].) Q10 = percent dissolved in 10 min; Q45 = percent dissolved in 45 min; % SLS = percent sodium lauryl sulfate; % lactose = percentage of lactose in a binary filler consisting of a blend of lactose and microcrystalline cellulose.

Three formulations from this study having Fast, Moderate, and Slow dissolution were chosen for comparison to a lot of the innovator’s product in a human bioavailability study.41 The resulting pharmacokinetic data provided still another opportunity to examine the effects of formulation variables. Using the following previously developed deconvolution-based model (Equation 1.1),47 Polli developed an in vitro–in vivo relationship (IVIVR) that pointed up the role of formulation in overcoming piroxicam’s low solubility/high permeability properties.48

Fa=1fa(1−αα−1(1−Fd)+1α−1(1−Fd)α)1.1

1.1

Fd is the fraction of the dose dissolved in time t, Fa is the fraction of the dose of the drug absorbed in time t, fa is the fraction of the total amount of drug absorbed at t = ∞, and α is the ratio of the apparent first-order permeation rate constant, kp1, to the first-order dissolution rate constant, kd. The model makes the following simplifying assumptions: apparent first-order permeability, first-order dissolution under sink conditions, drug is stable in the gastrointestinal lumen or at the gastrointestinal wall, in vitro and in vivo dissolution profiles are identical, and the absence of a lag time for permeation or dissolution. The term α is of particular interest to this discussion. If an analysis reveals α ≫ 1, the permeation rate constant is much greater than the dissolution rate constant and drug absorption is expected to be dissolution rate-limited. If α ≪ 1, then the permeation rate constant is much less than the dissolution rate constant, signifying that the rate-limiting step to absorption is intestinal permeation.

The values of α determined for the Slow, Moderate, and Fast formulations and a lot of the Innovator product are given in Table 1.2. An examination of the data indicates that piroxicam exhibits generally dissolution rate-limited (i.e., α > 1) absorption, which is consistent with piroxicam’s BCS classification. For the Slow formulation, α = 6.50, which indicates that dissolution was dominating over permeability about sevenfold in controlling overall piroxicam absorption. What is particularly interesting about the analysis in Table 1.2 are the formulation implications. For example, the use of milled piroxicam, 1% sodium lauryl sulfate, and lactose filler so promoted dissolution in the Fast formulation that kd≅kp1 and α is slightly less than 1, indicating that because of formulation design, the Fast product is slightly more permeability rate-limited than dissolution rate-limited, thereby overcoming piroxicam’s biopharmaceutic properties. It is also interesting that the in vitro dissolution test (USP) proved more sensitive to the piroxicam formulation variables than the biodata. Despite their differences in dissolution rate, the Fast, Moderate, and Slow products were found bioequivalent to each other and to the lot of Innovator product studied. It is possible that either the formulation variables studied did not affect in vivo dissolution or the differences were not discernible because of the long biological half-life of piroxicam.49

Statistical methods have also been applied to the formulation development of dry powder inhalation (DPI) capsules. Nearly half of marketed DPIs are single-dose delivery systems consisting of a powder formulation in a hard shell gelatin capsule. In practice, the capsule is punctured in a specially designed inhalation device and the powder is inhaled by the patient. In one example, Faulhammer et al.50 undertook a study aimed at development of a predictive model for the filling of the typically low fill-weight capsule inhalation products with a dosator nozzle. Based on an assessment of the effects of the critical process parameters (CPPs) and critical material attributes (CMAs) on fill weight and weight variability, they developed and validated a predictive model for fill weight variation for two groups of powders: those that flow well and those that are cohesive. The model provided a “good approximation” of fill weight variability for each powder group and permitted the establishment of a DS for different types of inhalation grade lactose in low-fill weight capsule filling.

In another study of low-fill weight capsule filling, Faulhammer et al.51 examined the effect of CMAs on the critical quality attributes (CQAs) of capsules filled on a dosator machine using six different grades of microcrystalline cellulose representing a wide range in physical properties. An experimental design was developed using four filling machine process parameters as controllable variables: dosator size, dosing chamber length (sometimes referred to as the piston height setting), powder layer height (often also called powder bed height), and filling speed. The data were analyzed by multivariate analysis with partial least squares regression (PLA). The Faulhammer group also used experimental design to evaluate the effect of these dosator machine process parameters on the capsules with various forms of lactose.52 A partial least square (PLS) method was used to examine the correlations between the material properties and process parameters and capsule fill weight and weight variability.