Studies of equations derived for application to dissolution from heterodisperse micronized suspensions

Abstract

List of Symbols t, ti K s(t) n(t)~xTotal surface area of particles of all sizes at time t Total number of undissolved particles with radii > 0 at time t Total number of undissolved particles with radii > 1/*m at time t Total number of particles at t=0 Undissolved particle radius at time t Undissolved particle radius at time 0 Initial radius of the smallest undissolved particle(s) Initial radius of the largest undissolved particle (s) Probability density function for particle size distribution Probability density of the particle size distribution at l = 0 Fraction of the total number of particles with radii > R Weibul! distribution parameters The development of theories rationalizing the dissolution rates of powdered drugs has stimulated the interest of a number of pharmaceutical scientists for many years. It has been shown that equations derived from a simple Noyes--Whitney model are of only limited utility in defining dissolution phenomena; in particular, they seem to be of little value when the dissolution media is more than about 50% saturated by drug (1).Many dissolution models previously used have implicitly assumed that the powdered material dissolving is homodisperse, i.e., all of the same particle size. In practice this condition is most unlikely to be fulfilled. Since factors such as the surface free energy of a particle varies with particle size, it is more than possible that both the mean and particle size distribution may affect the rate of dissolution of powdered drugs. Little attention appears to have been given to investigating how the particle size spectra of powdered drugs change during the dissolution process, even though the variation in the total surface area of the powdered material can obviously have profound biopharmaceutical implications, especially for controlled release formulation.In this treatment it is not assumed that the particles are identical; it is assumed that the radii of the undissolved particles have a probability density function f(R) where R= R(t) is the radius of an undissolved particle at time t. The total surface area of all undissolved particles at time t is denoted S(t), and the mass of undissolved solute at time t is denoted W(t). Wo denotes the initial mass of undissolved solute and Zs is the mass of W 943