Modeling in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics
The state of the art in Biopharmaceutics, Pharmacokinetics, and Pharmacodynamics Modeling is presented in this book. It shows how advanced physical and mathematical methods can expand classical models in order to cover heterogeneous drug-biological proces
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Drug Dissolution The rate at which a solid substance dissolves in its own solution is proportional to the difference between the concentration of that solution and the concentration of the saturated solution. Arthur A. Noyes and Willis R. Whitney Massachusetts Institute of Technology, Boston Journal of the American Chemical Society 19:930-934 (1897)
The basic step in drug dissolution is the reaction of the solid drug with the fluid and/or the components of the dissolution medium. This reaction takes place at the solid—liquid interface and therefore dissolution kinetics are dependent on three factors, namely the flow rate of the dissolution medium toward the solid—liquid interface, the reaction rate at the interface, and the molecular diffusion of the dissolved drug molecules from the interface toward the bulk solution, Figure 5.1. As we stated in Section 2.4.2, a process (dissolution in our case) can be either diffusion or reaction limited depending on which is the slower step. The relative importance of interfacial reaction and molecular diffusion (steps 2 and 3 in Figure 5.1, respectively) can vary depending on the hydrodynamic conditions prevailing in the microenvironment of the solid. This is so since both elementary steps 2 and 3 in Figure 5.1 are heavily dependent on the agitation conditions. For example, diffusion phenomena become negligible when externally applied intense agitation in in vitro dissolution systems gives rise to forced convection. Besides, the reactions at the interface (step 2) and drug diffusion (step 3) in Figure 5.1 are dependent on the composition of the dissolution medium. Again, the relative importance can vary according to the drug properties and the specific composition of the medium. It is conceivable that our limited knowledge of the hydrodynamics under in vivo conditions and the complex and position- and time-dependent composition of the gastrointestinal fluids complicates the study of dissolution phenomena in particular when one attempts to develop in vitro—in vivo correlations. Early studies in this field of research formulated two main models for the interpretation of the dissolution mechanism: the diffusion layer model and the 89
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5. DRUG DISSOLUTION
Figure 5.1: The basic steps in the drug dissolution mechanism. (1) The molecules (◦) of solvent and/or the components of the dissolution medium are moving toward the interface; (2) adsorption—reaction takes place at the liquid—solid interface; (3) the dissolved drug molecules (•) move toward the bulk solution.
interfacial barrier model. Both models assume that there is a stagnant liquid layer in contact with the solid, Figure 5.2. According to the diffusion layer model (Figure 5.2 A), the step that limits the rate at which the dissolution process occurs is the rate of diffusion of the dissolved drug molecules through the stagnant liquid layer rather than the reaction at the solid—liquid interface. For the interfacial barrier model (Figure 5.2 B), the rate-limiting step of the dissolution process is the initial transfer of drug from the
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