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Journal of Mathematics in Industry

Table 1 Mathematical models for comparison of dissolution profiles

From: Optimizing similarity factor of in vitro drug release profile for development of early stage formulation of drug using linear regression model

Model

Equation

Zero order [5]

\(Q_{t} = Q_{0} + K_{0} t\)

First order [5]

\(\ln Q_{t} = \ln Q_{0} + K_{1} t\)

Higuchi [16]

\(Q_{t} = K_{H} t^{1/2}\)

Hixson–Crowell [17]

\(Q_{0}^{{1} / {3}} - Q_{t}^{{1} / {3}} = K_{s} t\)

Korsmeyer–Peppas [21]

\({Q_{t}} / {Q_{\infty }} = K_{k} t^{n}\)

Weibull Model [22]

\(m=1-\exp [ \frac{-(t- T_{i} )^{b}}{a} ]\)

  1. \(Q_{{t}}\): Amount of drug released in time t,
  2. \(Q_{0}\): Initial amount of drug in tablet,
  3. \(Q_{{t}}/Q_{\infty }\): Fraction of drug released at time t,
  4. m: The accumulated fraction of the drug in solution at time t
  5. a: Scale parameter,
  6. \(T_{i}\): The location parameter,
  7. b: The shape parameter,
  8. \(K_{0}\), \(K_{1}\), \(K_{{H}}\), \(K_{{s}}\), \(K_{{k}}\): Rate order constants.
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