title: Analysis of dissolution data using modified versions of Noyes-Whitney equation and the Weibull function.
abstract: OBJECTIVE
  The aim of the study is to develop modified, branched versions of the Noyes-Whitney and the Weibull equations, including explicitly the solubility/dose parameter, for the analysis of dissolution data, which reach the plateau either at infinite or finite time.
  
  
  METHODS
  The modified Weibull function is applied to the analysis of experimental and literature dissolution data. To demonstrate the usefulness of the mathematical models, two model drugs are used: one highly soluble, metoprolol, and one relatively insoluble, ibuprofen.
  
  
  RESULTS
  The models were fitted successfully to the data performing better compared with their classic versions. The advantages of the use of the models presented are several. They fit better to a large range of datasets, especially for fast dissolution curves that reach complete dissolution at a finite time. Also, the modified Weibull presented can be derived from differential equations, and it has a physical meaning as opposed to the purely empirical character of the original Weibull equation. The exponent of the Weibull equation can be attributed to the heterogeneity of the process and can be explained by fractal kinetics concepts. Also, the solubility/dose ratio is present explicitly as a parameter and allows to obtain estimates of the solubility even when the dissolution data do not reach the solubility level.
  
  
  CONCLUSIONS
  The use of the developed branched equations gives better fittings and specific physical meaning to the dissolution parameters. Also, the findings underline the fact that even in the simplest, first-order case, the speed of the dissolution process depends on the dose, a fact of great importance in biopharmaceutic classification for regulatory purposes.
authors.affiliation: School of Pharmacy and Pharmaceutical Sciences, University of Manchester, M13 9PL, UK.
authors.forename: Aristides
authors.initials: A
authors.lastname: Dokoumetzidis
authors.forename: Vasiliki
authors.initials: V
authors.lastname: Papadopoulou
authors.forename: Panos
authors.initials: P
authors.lastname: Macheras
mesh_terms: D000319:Adrenergic beta-Antagonists / Q000008:administration & dosage / Q000737:chemistry; D000465:Algorithms; D000894:Anti-Inflammatory Agents, Non-Steroidal / Q000008:administration & dosage / Q000737:chemistry; D002626:Chemistry, Pharmaceutical / Q000706:statistics & numerical data*; D007052:Ibuprofen / Q000008:administration & dosage / Q000737:chemistry; D008790:Metoprolol / Q000008:administration & dosage / Q000737:chemistry; D015233:Models, Statistical; D004364:Pharmaceutical Preparations / Q000008:administration & dosage; D012995:Solubility
chemical_list: D000319:Adrenergic beta-Antagonists; D000894:Anti-Inflammatory Agents, Non-Steroidal; D004364:Pharmaceutical Preparations; D008790:Metoprolol; D007052:Ibuprofen