Table 3.

Dissolution models along with the governing equations to model dissolution of micronized stock and NanoClusters. Includes description of variables and assumptions.

Model	Main Dissolution Equation	Other Equations	Variables	Assumptions
Classical Higuchi41	$$Mt=k\sqrt{t}$$ Eqn 1	$$k=A\sqrt{2\mathit{CiDCs}}$$ Eqn 2	Ci = initial concentration Cs = drug solubility A = surface area D = diffusion coefficient t = time Mt = released drug	Thin polymer film Constant D Minimal edge effects Higher drug concentration than solubility Homogenous drug dispersion
Higuchi – Peppas Derivation 42	$$Mt=1-\frac{6}{{\pi }^2}\sum _{n=1}^{\infty }\frac{1}{n^2}{\mathit{exp}}^{\frac{-{Dn}^2{\pi }^{2}t}{a^2}}$$ Eqn 3	$$Mt=6\sqrt{\frac{Dt}{\pi a^2}}-3\frac{Dt}{a^2}$$ Eqn 4 (short time approximation)	a = radius of sphere D = diffusion coefficient t = time n = diffusional exponent characteristic of release mechanism Mt = released drug	Constant D 1 dimensional radial release Sink boundary conditions Short term approx. only for first 40% of drug released
Siepmann 43	$$Mt=1-\frac{6}{{\pi }^2}\sum _{n=1}^{\infty }\frac{1}{n^2}{\mathit{exp}}^{\frac{-{Dn}^2{\pi }^{2}t}{a^2}}$$ Monolithic solution $$Mt=-\frac{3D}{R^2}\frac{Cs}{Ci}t$$ Eqn 5 Monolithic Dispersion	$$Mt=1-\frac{6}{{\pi }^2}\mathit{exp}\frac{-Dt{\pi }^2}{R^2}$$ Eqn 6 (late time approximation)	Ci = initial concentration Cs = drug solubility a = radius of sphere D = diffusion coefficient R = radius of sphere t = time Mt = released drug	Sink conditions Constant D Drug transport in system is rate limiting Homogenous drug distribution Late time after 60% of drug released