Table 2.

Relevant mathematical models and corresponding equations

Mathematical model	Diagrams	Equations
Zero-order	Cumulative percentage of drug release versus time	${\text{Q}}_1={\text{Q}}_0+{\text{k}}_0\text{t}$
First-order	The logarithm of cumulative drug residual percentage versus time	$log{\text{Q}}_{\text{t}}=log{\text{Q}}_0-{\text{K}}_{\text{t}}/2.303$
Higuchi	The square root of cumulative percent drug release versus time	${\text{Q}}_{\text{t}}={\text{k}}_{\text{H}}{\text{t}}^{1\left./\phantom{12}\right)2}$
Hixson–Crowell	Cubic root ratio time for a percentage of drugs remaining	${\text{W}}_0^{1\left./\phantom{13}\right)3}-{\text{W}}_{\text{t}}^{1\left./\phantom{13}\right)3}={\text{K}}_{\text{s}}\text{t}$
Korsemeyer–Peppas	The logarithm of cumulative percent drug release versus cumulative time	${\text{Q}}_{\text{t}}\left./\phantom{{\text{Q}}_{\text{t}}{\text{Q}}_{\infty }}\right){\text{Q}}_{\infty }={\text{K}}_{\text{k}}{\text{t}}^{\text{n}}$

Q_t = amount of drug released in time “t”, Q₀ = initial dose by dosage form, ${\text{Q}}_{\text{t}}\left./\phantom{{\text{Q}}_{\text{t}}{\text{Q}}_{\infty }}\right){\text{Q}}_{\infty }$ = fraction of drug released in time “t”; K₀, K_t, K_H, K_s, and K_k = release rate constants, and n = release index (“release mechanism indication”)