Dissolution as Discussed

Table 3 shows how dissolution occurs as discussed earlier. For simplicity, the example of a polydisperse powder in Table 3 is made up of only three monodisperse fractions. In practice, more fractions would be needed to describe a more typical milled polydisperse drug powder. The simulation was done for 100 mg of drug with a solubility of 0.1 mg/mL dissolving in 1000 mL of water. With these par- ameters, the concentration of drug would be at the solubility when complete dissol- ution is reached. As can be seen in Table 3, the 100 mg of powder has an initial geometric mean of 25 mm containing most of the mass with smaller but equal amounts of mass at 6.25 and 100 mm. However, the 6.25 mm particle size fraction has the greatest number of particles and the most surface area per unit weight. In less than five minutes, the 6.25 mm particle size fraction has completely dissolved. The 25 mmparticle size fraction took slightly more than two hours to dissolve, with the size, mass, and surface area decreasing proportionately as determined by geo- metry and density. Only the number of particles remained constant until dissolution was complete. The largest particle size fraction starting at 100 mm dissolved the slowest because it had the smallest surface area and also because the two smallerparticle size fractions have dissolved more quickly, thereby reducing the concen-tration gradient environment for the remaining large particles. Even after 24hours, the largest particle size fraction did not completely dissolve.Evidence that dissolution occurs as described earlier can also be seen in theshape of actual dissolution data from a polydisperse powder. Figure 2 shows thepowder dissolution of hydrocortisone (17). Experimental measurement of theoriginal powder showed it had a geometric mean particle size of approximately36 microns with a geometric standard deviation of 2.4. Two simulations basedon the Noyes–Whitney theory are also shown. For one simulation, the powderwas treated as a polydisperse powder using 16 monosized fractions to describe it.The mass and size of drug particles in each fraction were calculated based on theexperimental data and the log-normal distribution function. For the other simu-lation, the powder was treated as a monodisperse powder with a size equivalentto the measured mean of 36 microns. The polydisperse simulation fitted the datamuch better than the monodisperse simulation as determined by the sumof residualssquared. Compared to the monodisperse simulation, the actual powder dissolvedmore quickly initially due to the presence of smaller particles with greater surfacearea, and slower later on, due to the presence of larger particles with lesssurface area. These phenomena, faster initial dissolution rate and slower final, aresimulated better by modeling the drug as a polydisperse powder. Excellent agree-ment has also been reported between observed and simulated dissolution data forcilostazol at each of three median particle diameters of 13, 2.4, and 0.22 mmwhen modeled as polydisperse particles versus monodisperse (19).Under certain special conditions, the described treatment of polydispersepowder dissolution would indicate that the mean particle size could increase; notbecause any particles were increasing in size, but because the smaller particles dis-solve first, skewing the particle size distribution toward larger particles. As can beseen in Table 3, the initial geometric mean particle size was 25 microns. However,at 24 hours, all particles in fractions 1 and 2 have completely dissolved, leavingonly particles in fraction 3. At that time, the particles in fraction 3 have gonefrom an initial value of 100 to 78.6 microns, leaving a mean particle size of 78.6microns that is greater than the initial geometric mean of 25 microns.