Abstract
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
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)
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In the pharmaceutical literature the exponential in the Weibull function is written as \(\exp \left (-\lambda t^{\mu }\right )\) and therefore \(\lambda\) has dimension time−μ. In the version used herein (equation 5.11), the dimension of \(\lambda\) is time−1.
Bibliography
Kopelman, R.: Fractal reaction kinetics. Science 241, 1620–1626 (1988)
Rinaki, E., Dokoumetzidis, A., Macheras, P.: The mean dissolution time depends on the dose/solubility ratio. Pharm. Res. 20(3), 406–408 (2003)
Levich, V.: Physicochemical Hydrodynamics. Prentice Hall, Englewood Cliffs (1962)
Noyes, A., Whitney, W.: The rate of solution of solid substances in their own solutions. J. Am. Chem. Soc. 19, 930–934 (1897)
Nernst, W., Brunner, E.: Theorie der Reaktionsgeschwindigkeit in heterogen Systemen. Z. Phys. Chem. 47, 52–110 (1904)
Hixson, A., Crowell, J.: Dependence of reaction velocity upon surface and agitation. I. Theoretical considerations. Ind. Eng. Chem. Res. 51, 923–931 (1931)
Avnir, D., Farin, D., Pfeifer, P.: Surface geometric irregularity of particulate materials. J. Colloid Interface Sci., 103, 112–123 (1985)
Li, T., Park, K.: Fractal analysis of pharmaceutical particles by atomic force microscopy. Pharm. Res. 15(8), 1222–1232 (1998)
Schroder, M., Kleinebudde, P.: Structure of disintegrating pellets with regard to fractal geometry. Pharm. Res. 12(11), 1694–1700 (1995)
Fini, A., Holgado, M., Rodriguez, L., Cavallari, C.: Ultrasound-compacted indomethacin/polyvinylpyrrolidone systems: effect of compaction process on particle morphology and dissolution behavior. J. Pharm. Sci. 91(8), 1880–1890 (2002)
Pettit, F., Bowie, J.: Protein surface roughness and small molecular binding sites. J. Mol. Biol. 285(4), 1377–1382 (1999)
Farin, D., Avnir, D.: Use of fractal geometry to determine effects of surface morphology on drug dissolution. J. Pharm. Sci. 81(1), 54–57 (1992)
Farin, D., Avnir, D.: The reaction dimension in catalysis on dispersed metals. J. Am. Chem. Soc. 110, 2039–2045 (1988)
Valsami, G., Macheras, P.: Determination of fractal reaction dimension in dissolution studies. Eur. J. Pharm. Sci. 3(3), 163–169 (1995)
Weibull, W.: A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293–297 (1951)
Langenbucher, F.: Linearization of dissolution rate curves by the Weibull distribution. J. Pharm. Pharmacol. 24(12), 979–981 (1972)
Djordjevic, A., Mendas, I.: Method for modelling in vitro dissolution profiles of drugs using gamma distribution. Eur. J. Pharm. Biopharm. 44(2), 215–217 (1997)
Smoluchowski, M.: Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Loesungen. Z. Phys. Chem. 92, 129–168 (1917)
Elkoshi, Z.: On the variability of dissolution data. Pharm. Res. 14(10), 1355–1362 (1997)
Dokoumetzidis, A., Macheras, P.: On the heterogeneity of drug dissolution and release. Pharm. Res. 17(2), 108–112 (2000)
Lansky, P., Weiss, M.: Does the dose-solubility ratio affect the mean dissolution time of drugs? Pharm. Res. 16(9), 1470–1476 (1999)
Dokoumetzidis, A., Macheras, P.: A population growth model of dissolution. Pharm. Res. 14(9), 1122–1126 (1997)
Dokoumetzidis, A., Papadopoulou, V., Valsami, G., Macheras, P.: Development of a reaction-limited model of dissolution: application to official dissolution tests experiments. Int. J. Pharm. 355(1–2), 114–125 (2008)
May, R.: Simple mathematical models with very complicated dynamics. Nature 261(5560), 459–467 (1976)
Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 3rd edn. Springer, New York (1990)
Shah, V., Noory, A., Noory, C., McCullough, B., Clarke, S., Everett, R., Naviasky, H., Srinivasan, B., Fortman, D., Skelly, J.: In vitro dissolution of sparingly water-soluble drug dosage forms. Int. J. Pharm. 125, 99–106 (1995)
Yamamoto, K., Nakano, M., Arita, T., Takayama, Y., Nakai, Y.: Dissolution behavior and bioavailability of phenytoin from a ground mixture with microcrystalline cellulose. J. Pharm. Sci. 65(10), 1484–1488 (1976)
Suzuki, H., Sunada, H.: Influence of water-soluble polymers on the dissolution of nifedipine solid dispersions with combined carriers. Chem. Pharm. Bull. 46(3), 482–487 (1998)
Valsami, G., Dokoumetzidis, A., Macheras, P.: Modeling of supersaturated dissolution data. Int. J. Pharm. 181(2), 153–157 (1999)
Charkoftaki, G., Dokoumetzidis, A., Valsami, G., Macheras, P.: Supersaturated dissolution data and their interpretation: the TPGS-carbamazepine model case. J. Pharm. Pharmacol. 63(3), 352–361 (2011)
Lansky, P., Weiss, M.: Modeling heterogeneity of particles and random effects in drug dissolution. Pharm. Res. 18(7), 1061–1067 (2001)
Lansky, P., Weiss, M.: Classification of dissolution profiles in terms of fractional dissolution rate and a novel measure of heterogeneity. J. Pharm. Sci. 92(8), 1632–1647 (2003)
Lansky, P., Lanska, V., Weiss, M.: A stochastic differential equation model for drug dissolution and its parameters. J. Control. Release 100(2), 267–274 (2004)
Lansky, P., Weiss, M.: Role of heterogeneity in deterministic models of drug dissolution and their statistical characteristics. Biosystems 71(1–2), 123–131 (2003)
Tsong, Y., Hammerstrom, T., Sathe, P., Shah, V.: Statistical assessment of mean differences between two dissolution data sets. Drug Inf. J. 30, 1105–1112 (1996)
Costa, P., Lobo, J.: Modeling and comparison of dissolution profiles. Eur. J. Pharm. Sci. 13, 123–133 (2001)
CDER: Guidance for Industry. Dissolution testing of immediate release solid oral dosage forms. Technical Report, Center for Drug Evaluation and Research, Food and Drug Administration (1997)
CDER: Guidance for Industry. Waiver of in vivo bioavailability and bioequivalence studies for immediate release solid oral dosage forms based on a biopharmaceutics classification system. Technical Report, Center for Drug Evaluation and Research, Food and Drug Administration (2000)
CPMP: Note for guidance on the investigation of bioavailability and bioequivalence. Technical Report, Committee for Proprietary Medicinal Products, European Medicines Agency (2001)
Liu, J., Ma, M., Chow, S.: Statistical evaluation of similarity factor f2 as a criterion for assessment of similarity between dissolution profiles. Drug Inf. J. 31, 1255–1271 (1997)
Shah, V., Tsong, Y., Sathe, P., Liu, J.: In vitro dissolution profile comparison-statistics and analysis of the similarity factor, f2. Pharm. Res. 15(6), 889–896 (1998)
Vertzoni, M., Symillides, M., Iliadis, A., Nicolaides, E., Reppas, C.: Comparison of simulated cumulative drug versus time data sets with indices. Eur. J. Pharm. Biopharm. 56(3), 421–428 (2003)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Macheras, P., Iliadis, A. (2016). Drug Dissolution. In: Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics. Interdisciplinary Applied Mathematics, vol 30 . Springer, Cham. https://doi.org/10.1007/978-3-319-27598-7_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-27598-7_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27596-3
Online ISBN: 978-3-319-27598-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)