A Simple One-Parameter Percent Dissolved Versus Time Dissolution Equation that Accommodates Sink and Non-sink Conditions via Drug Solubility and Dissolution Volume

Abstract

Abstract In vitro dissolution generally involves sink conditions, so dissolution equations generally do not need to accommodate non-sink conditions. Greater use of biorelevant media, which are typically less able to provide sink conditions than pharmaceutical surfactants, necessitates equations that accommodate non-sink conditions. One objective was to derive an integrated, one-parameter dissolution equation for percent dissolved versus time that accommodates non-sink effects via drug solubility and dissolution volume parameters, including incomplete solubility. A second objective was to characterize the novel equation by fitting it to biorelevant dissolution profiles of tablets of two poorly water-soluble drugs, as well as by conducting simulations of the effect of dose on dissolution profile. The Polli dissolution equation was derived, $$\% \;dissolved=100\%\left[1-\frac{\left({{M}_{0}-c}_{s}V\right)}{{M}_{0}-{{c}_{s}Ve}^{{-k}_{d}\left(\frac{{{M}_{0}-c}_{s}V}{V}\right)t}}\right]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>%</mml:mo> <mml:mspace/> <mml:mi>d</mml:mi> <mml:mi>i</mml:mi> <mml:mi>s</mml:mi> <mml:mi>s</mml:mi> <mml:mi>o</mml:mi> <mml:mi>l</mml:mi> <mml:mi>v</mml:mi> <mml:mi>e</mml:mi> <mml:mi>d</mml:mi> <mml:mo>=</mml:mo> <mml:mn>100</mml:mn> <mml:mo>%</mml:mo> <mml:mfenced> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:mfrac> <mml:mfenced> <mml:msub> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>V</mml:mi> </mml:mfenced> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:msup> <mml:mrow> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>V</mml:mi> <mml:mi>e</mml:mi> </mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mo>-</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msub> <mml:mfenced> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>-</mml:mo> <mml:mi>c</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> </mml:msub> <mml:mi>V</mml:mi> </mml:mrow> <mml:mi>V</mml:mi> </mml:mfrac> </mml:mfenced> <mml:mi>t</mml:mi> </mml:mrow> </mml:msup> </mml:mrow> </mml:mfrac> </mml:mfenced> </mml:mrow> </mml:math> , where M 0 is the drug dose (mg), c s is drug solubility (mg/ml), V is dissolution volume (ml), and k d is dissolution rate coefficient (ml/mg per min). Maximum allowable percent dissolved was determined by drug solubility and not a fitted extent of dissolution parameter. The equation fit tablet profiles in the presence and absence of sink conditions, using a single fitted parameter, k d , and where solubility ranged over a 1000-fold range. k d was generally smaller when c s was larger. FeSSGF provided relatively small k d values, reflecting FeSSGF colloids are large and slowly diffusing. Simulations showed impact of non-sink conditions, as well as plausible k d values for various c s scenarios, in agreement with observed k d values. The equation has advantages over first-order and z -factor dissolution rate equations. An Excel file for regression is provided. Graphical Abstract

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