Table 3 Change in Various Drug Particle Parameters During Dissolution
| Time (min) | Fraction 1 | Fraction 2 | Fraction 3 | |
| Particle size | of each fraction (fim) | |||
| 0 | 6.25 | 25.0 | 100 | |
| 5 | 0.00 | 23.4 | 99.4 | |
| 30 | 0.00 | 17.5 | 97.3 | |
| 60 | 0.00 | 12.5 | 96.0 | |
| 120 | 0.00 | 3.66 | 94.8 | |
| 1440 | 0.00 | 0.00 | 78.6 | |
| Drug mass in | each fraction (mg) | |||
| 0 | 10.7 | 78.7 | 10.7 | |
| 5 | 0.00 | 64.6 | 10.4 | |
| 30 | 0.00 | 26.8 | 9.81 | |
| 60 | 0.00 | 9.92 | 9.43 | |
| 120 | 0.00 | 0.247 | 9.06 | |
| 1440 | 0.00 | 0.000 | 5.17 | |
| Number of particles | in each fraction/10,000 | |||
| 0 | 6410 | 740 | 1.56 | |
| 5 | 0 | 740 | 1.56 | |
| 30 | 0 | 740 | 1.56 | |
| 60 | 0 | 740 | 1.56 | |
| 120 | 0 | 740 | 1.56 | |
| 1440 | 0 | 0 | 1.56 | |
| Drug surface | area in | each fraction (mm ) | ||
| 0 | 7.87 | 14.5 | 0.492 | |
| 5 | 0.00 | 12.7 | 0.485 | |
| 30 | 0.00 | 7.08 | 0.465 | |
| 60 | 0.00 | 3.65 | 0.453 | |
| 120 | 0.00 | 0.311 | 0.441 | |
| 1440 | 0.00 | 0.00 | 0.304 | |
Note: Simulation represents 100 mg of drug with a solubility of 0.1 mg/mL dissolving in 1000 mL of water.
Was 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 the experimental data and the log-normal distribution function. For the other simulation, the powder was treated as a monodisperse powder with a size equivalent to the measured mean of 36 microns. The polydisperse simulation fitted the data much better than the monodisperse simulation as determined by the sum of residuals squared. Compared to the monodisperse simulation, the actual powder dissolved more quickly initially due to the presence of smaller particles with greater surface area, and slower later on, due to the presence of larger particles with less surface area. These phenomena, faster initial dissolution rate and slower final, are simulated better by modelling the drug as a polydisperse powder. Excellent agreement has also been reported between observed and simulated dissolution data for cilostazol at each of three median particle diameters of 13, 2.4, and 0.22 m when modelled as polydisperse particles versus monodisperse (19).
Under certain special conditions, the described treatment of polydisperse powder dissolution would indicate that the mean particle size could increase; not because any particles were increasing in size, but because the smaller particles dissolve first, skewing the particle size distribution toward larger particles. As can be seen 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, leaving only particles in fraction 3. At that time, the particles in fraction 3 have gone from an initial value of 100 to 78.6 microns, leaving a mean particle size of 78.6 microns that is greater than the initial geometric mean of 25 microns.
One of the applications of trying to predict dissolution based on the Noyes-Whitney theory, solubility, and drug particle size is to identify potential formulation problems, such as wetting and slow disintegration. This is accomplished by comparing the predicted dissolution profile with the actual profile of the formulation. If the actual dissolution profile of the dosage form is similar to that predicted by theory, one could reasonably conclude that the formulation was disintegrating rapidly and that the surface area of the released drug particles were well wetted. However, dissolution slower than predicted should be investigated to determine the cause. To this end, drug powder dissolution in the absence of excipients but with the judicial use of surfactants and agitation to promote wetting but not to increase solubility or reduce particle size can help establish problems with agglomeration and poor wetting. Dissolution profiles faster than expected might indicate a change in drug form, resulting in a higher solubility or an increase in drug surface area, either of which might occur due to formulation processing.
The approach of using the dissolution theory described earlier to evaluate the dispersion process for furosemide has been reported (20). Good agreement between theoretical and experimental dissolution profiles were found when furosemide powders were dispersed by ultrasonication in a surfactant solution for all but the smallest of three batches of powder. The mean particle sizes for the batches were 3, 10, and 19 am when particle size was measured after sonication. Without sonication, the particle sizes were measured to be 108, 38, and 27 am corresponding to the post-sonicated measurements of 3, 10, and 19 am, respectively. The relative order of the dissolution rates were also reversed before and after dispersion, indicating that comparing theoretical profiles with actual profiles would reveal the problem with agglomeration. For the smallest particle size batch of furosemide that did not agree well with the theoretically calculated dissolution rate, the drug particles were observed to agglomerate during dissolution, which would explain why the actual dissolution rate was slower than predicted by theory (M.M. De Villiers, personal communication, 2005).
Part of the value in using mathematical models to simulate dissolution, absorption, and pharmacokinetics comes from the training and insight that can be gained quickly and inexpensively relative to developing actual dosage forms and testing them in the clinic. Just as a pilot would use a flight simulator to learn how to fly, the formulation scientist can develop a feeling for how changes in various parameters affect the drug product without the large expense of laboratory and clinical studies. Writing differential equations also tests and strengthens understanding. Applying numerical methods to solve the equations eliminates the need to solve them analytically and frees the scientist to use equations that have no analytical solutions.
As with any good scientific approach, theory is validated through experimentation and modified to agree with confirmed experimental findings. An example of this would be the treatment of the hydrodynamics for simulating the dissolution of a polydisperse powder. Any dissolution model would need to explain why the rate of dissolution increases when the energy of stirring is increased. Including a diffusion layer thickness into the denominator of the Noyes-Whitney equation that becomes smaller when stirring is increased is used to explain this. As an initial attempt to simulate actual powder dissolution data (16,17), the assumption that the diffusion layer thickness is approximately equal to the radius of the dissolving particles was used (22). However, this assumption did not result in a good fit of the experimental data. Further search of the literature indicated that the diffusion layer thickness might plateau with increasing particle size (23). Applying this approach resulted in a much better fit of the data, and subsequent studies have confirmed the existence of a plateau diffusion layer thickness under typical drug dissolution testing conditions and particle sizes (24,25). However, the author anticipates that future work will lead to better understanding of the hydrodynamics of dissolving powders. More understanding is particularly needed in the in vivo environment.
The model described by Equations 26 to 33 has been applied to nifedipine to demonstrate how its physicochemical and pharmacokinetic properties could have been utilized to develop the controlled-release dosage form (26). The effect of particle size on dissolution and absorption of drug released from an osmotic pump controlled-release dosage form was simulated.
