Dissolution rate, modelling

A Shah, K Nelson. Evaluation of a convective diffusion drug dissolution rate model. J Pharm Sci 64 1518, 1975. 

Brun-Cottan, J. C. Stokes Settling and Dissolution Rate Model for Marine... 

Interestingly, exceptions are possible. Stewart et al. [81] reported that the effect of magnesium stearate concentration on the dissolution of a model low-dose drug, riboflavin, from capsules was dependent in some manner on the type of filler. Soluble fillers exhibited the anticipated prolonged times with increasing lubricant levels. However, the trends with insoluble fillers were less predictable. In some cases insoluble fillers were only slightly affected by the concentration of magnesium stearate. For others, such as microcrystalline cellulose, there appeared to be an ideal intermediate concentration of lubricant at which the dissolution rate was maximized. 

The derivation and experimental verification of the MMHS model represented a significant accomplishment and a natural plateau for film models. To be sure, there are general criticisms of film models and more specific criticisms of the MMHS model [6], However, overall the MMHS model should be recognized as a robust but simply applicable model which serves to demonstrate how factors such as intrinsic solubility of the acid drug, ionization and pA of the drug, and concentration of the reactive base all contribute to increasing the dissolution rate and mass transfer. 

Other researchers used flow between two parallel plates as the experimental and theoretical system to incorporate diffusion plus convection into their dissolution modeling and avoid film model approximations [10]. Though they did not consider adding reactions to their model, these workers did show that convection was an important phenomenon to consider in the mass transfer process associated with solid dissolution. In fact, the dissolution rate was found to correlate with flow as... 

GR Carmichael, SA Shah, EL Parrott. General model for dissolution rates of n-component, nondisintegrating spheres. J Pharm Sci 70 1331-1338, 1981. 

C Nystrom, J Mazur, MI Barnett, M Glazer. Dissolution rate measurements of sparingly soluble compounds with the Coulter counter model TAIL J Pharm Pharmacol 37 217-221, 1985. 

JB Dressman, D Fleisher. Mixing-tank model for predicting dissolution rate control of oral absorption. J Pharm Sci 75 109-116, 1986. 

ATK Lu, ME Frisella, KC Johnson. Dissolution modeling Factors affecting the dissolution rates of polydisperse powders. Pharm Res 10 1308-1314, 1993. 

Mechanisms of dissolution kinetics of crystals have been intensively studied in the pharmaceutical domain, because the rate of dissolution affects the bioavailability of drug crystals. Many efforts have been made to describe the crystal dissolution behavior. A variety of empirical or semi-empirical models have been used to describe drug dissolution or release from formulations [1-6]. Noyes and Whitney published the first quantitative study of the dissolution process in 1897 [7]. They found that the dissolution process is diffusion controlled and involves no chemical reaction. The Noyes-Whitney equation simply states that the dissolution rate is directly proportional to the difference between the solubility and the solution concentration ... 

The absorption of class III drugs is limited by their permeability over the intestinal wall. Thus, as this process is not at all modeled by the classical in vitro dissolution test, no IVIVC should be expected. When drug dissolution becomes slower than gastric emptying, a reduction in the extent of bioavailability will be found in slower dissolution rates as the time when the drug is available for permeation over the gut wall in the small intestine will then be reduced. Thus, the same type of relationship can be expected between bioavailability and in vitro dissolution, as shown in Fig. 21.12 for a class I drug. 

One approach to the study of solubility is to evaluate the time dependence of the solubilization process, such as is conducted in the dissolution testing of dosage forms [70], In this work, the amount of drug substance that becomes dissolved per unit time under standard conditions is followed. Within the accepted model for pharmaceutical dissolution, the rate-limiting step is the transport of solute away from the interfacial layer at the dissolving solid into the bulk solution. To measure the intrinsic dissolution rate of a drug, the compound is normally compressed into a special die to a condition of zero porosity. The system is immersed into the solvent reservoir, and the concentration monitored as a function of time. Use of this procedure yields a dissolution rate parameter that is intrinsic to the compound under study and that is considered an important parameter in the preformulation process. A critical evaluation of the intrinsic dissolution methodology and interpretation is available [71]. 

The interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

The diffusion layer theory, illustrated in Fig. 15B, is the most useful and best-known model for transport-controlled dissolution. The dissolution rate here is controlled by the rate of diffusion of solute molecules across a diffusion layer of thickness h, so that kT kR in Eq. (40), which simplifies to kx = kT. With increasing distance, x, from the surface of the solid, the concentration, c, decreases from cs at x = 0 to cb at x = h. In general, c is a nonlinear function of x, and the concentration gradient dddx becomes less steep as x increases. The hyrodynamics of the dissolution process has been fully discussed by Levich [104]. In a stirred solution, the flow velocity of the liquid dissolution medium increases from zero at x = 0 to the bulk value at x = h. 

The diffusion layer model satisfactorily accounts for the dissolution rates of most pharmaceutical solids. Equation (43) has even been used to predict the dissolution rates of drugs in powder form by assuming approximate values of D (e.g., 10 5 cm2/sec), and h (e.g., 50 pm) and by deriving a mean value of A from the mean particle size of the powder [107,108]. However, as the particles dissolve, the wetted surface area, A, decreases in proportion to the 2/3 power of the volume of the powder. With this assumption, integration of Eq. (38) leads to the following relation, known as the Hixon-Crowell [109] cube root law ... 

Investigations such as those by Ferry and Carritt (1946) and Hong-Xi et al. (1998) on the dissolution rate of CU2O particles and the hydrolysis of TBT-MMA polymers can be used as inputs to mathematical AF paint models (Kiil et al., 2001). In the past few years, the study performed by Kiil et al. (2001) has encouraged new experimental studies focused on characterising the main processes responsible for the AF sea water behaviour. The core processes to be quantified are (Yebra et al., 2005c) ... 

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