Fitting of diffusion coefficients in a three-compartment sustained release drug formulation using a genetic algorithm

Abstract This article presents a method of fitting diffusion coefficients in a three-compartment drug formulation to data of concentration measurements. The volume of the central compartment is not constant, but increases with time up to a certain amount. The speed of growth is proportional to the actual distance from the final thickness. A model function based on Fick's second law of diffusion is used to describe the concentration with respect to location and time. In order to find the values of the diffusion coefficients they are encoded to data structures on which the mechanisms of evolution can be applied: mutation and selection. It is shown how the convergence speed is influenced by the optimization parameters: the more individuals are involved in the evolution process, the fewer the generations it takes the algorithm to fit the parameters. There are optimal values for the rate of mutation ( m = 0.008 bit −1 ) and the selection factor, which controls the influence of selection in the mating process. Its optimal value is less than unity, which means that the algorithm converges faster when sometimes the genetic information of the weaker of two individuals is passed on to the next generation.