Value for XdT

Value for XdT is used for each particle size fraction. In summary, simulation of the dissolution of a polydisperse powder is accomplished by treating it as a collection of monosized fractions. At time zero, dissolution is the fastest because there is the most surface area and the con- centration gradient is the greatest. Using the Runge–Kutta numerical method and Equations 21 and 22, the amount of drug that has dissolved from each particle size fraction is calculated, and after each step of the simulation, Equations 23 and 24 are used to sum up all the contributions from each particle size fraction. The total amount of dissolved drug from all fractions is then used during the next step of the numerical method so that each particle size fraction is dissolving against the same concentration gradient. Dissolution slows with time because the surface area and concentration gradient are getting smaller. Typically, milled drug powders are distributed lognormally by mass about some geometric mean particle size. This means that one can find a collection of particles of similar size that are smaller than the mean particle size and another collection of particles of similar size that are larger than the mean particle size, both collections of which are roughly equivalent in mass. However, since both collections are approximately equal in mass, the collection of smaller particles is made up of more particles and represents more surface area than the larger col- lection. As a result, the collection of smaller particles will dissolve faster and completely dissolve before the larger collection. Both the number and particle size distribution will change during the dissolution of a polydisperse powder, whereas only the particle size would change within each monosized fraction until complete dissolution was reached. At that point, the number within the frac- tion would become zero. It is uncertain at what particle size one would be able to say that a particle is no longer a solid and that complete dissolution had occurred. However, particles calculated in the size range of molecular dimensions could probably be con- sidered as completely dissolved. In computer simulation, without some statement as to when solid particles are completely dissolved, the calculated particle size will continue to decrease until the lower numerical limit of the computer system is reached. In agreement with the model described earlier for a polydis- perse powder, it has been shown that during dissolution, the number of particles in a smaller particle size fraction decreased more rapidly relative to larger particle size fractions.