Table 7.

Kinetic equations used in the drug release analysis.

Kinetic Model	Equation
Zero-order	${\mathrm{m}}_{\mathrm{t}}{=\mathrm{m}}_{\mathrm{b}}{+\mathrm{k}}_0\mathrm{t}$
First-order	$\ln \left({\mathrm{m}}_0{-\mathrm{m}}_{\mathrm{t}}\right)=\ln \left({\mathrm{m}}_0\right){-\mathrm{k}}_1\mathrm{t}$
Second-order	$\frac{1}{\left({\mathrm{m}}_0{-\mathrm{m}}_{\mathrm{t}}\right)}=\frac{1}{{\mathrm{m}}_0}{-\mathrm{k}}_2\mathrm{t}$
Higuchi	${\mathrm{m}}_{\mathrm{t}}{=\mathrm{k}}_{\mathrm{H}}{\mathrm{t}}^{0.5}$
Korsmeyer–Peppas	$\log \left(\frac{{\mathrm{m}}_{\mathrm{t}}}{{\mathrm{m}}_{\infty }}\right){=\mathrm{logk}}_{\mathrm{K}-\mathrm{P}}+\mathrm{nlogt}$
Hixon–Crowell	${\mathrm{m}}_0{}^{1/3}{-\mathrm{m}}_{\mathrm{rtnd}}{}^{1/3}{=\mathrm{k}}_{\mathrm{H}-\mathrm{C}}\mathrm{t}$

where m_t—the amount of the drug released during time t; m_b—the amount of the drug in the solution before the release, usually 0; k₀—the zero-order release rate constant; m₀—the amount of the drug in the formulation before the dissolution; k₁—the first-order release rate constant; k₂—the second-order release rate constant; k_H—the Higuchi rate constant; m_∞—the amount of the drug released after an infinitive time, k_K-P—the Korsmeyer–Peppas rate constant, n—the parameter indicative of the drug release mechanism; m_rtnd—the amount of the drug retained in the formulation after time t; k_H-C—the Hixon-Crowell rate constant.