A Novel in Vitro and Numerical Analysis of Shear-Induced Drug Release from Extended-Release Tablets in the Fed Stomach

Purpose

To design an in vitro apparatus that could simulate the in vivo range of surface shear stresses relevant for the human stomach under fed conditions.

Methods

Computer simulations were combined with in vitro experiments to quantify tablet erosion rate vs. surface shear stress. From two separate computer models, of tablets in the fed stomach and of tablets in vitro, we first estimated the intragastric range of surface stress and Reynolds number (Re), and then designed a dissolution apparatus and parameter space to replicate the in vivo conditions. The in vitro tablet erosion was determined by a new rotating beaker apparatus that provided predictable surface shear on tablets. Tablet mass erosion rates were measured for two different extended-release tablets at a range of in vivo relevant surface shear stresses obtained by varying viscosity of test media and rotation rate of the beaker.

Results

Mass erosion rate and surface shear were found to be highly correlated. Erosion rate increased with surface shear more rapidly at “low” stresses (<35 dyne/cm²) independent of tablet material. At higher surface stress, erosion was strongly material dependent.

Conclusions

Shear force effects on drug release from matrix tablets relevant for fed state are for the first time possible to predict by in vitro dissolution testing.

Appendix

Development of the “Tablet Erosion Model”

To develop the tablet erosion model we applied a systematic procedure that exists in the engineering literature for developing empirical mathematical relationships between an “independent variable,” here the mass erosion rate $\ifmmode\expandafter\dot\else\expandafter\.\fi{m}$and the “dependent variables” that affect mass erosion rate (shear stress, relative velocity, fluid viscosity, etc.). This procedure is a combination of “similarity theory” and “dimensional analysis.” We can only briefly summarize the method here. The reader should refer to standard textbooks in fluid dynamics (21) for further details.

Two different flows around two different tablets are “similar” if the flow patterns around the tablets are the same. This requires, among other things, that the geometry and orientation of the two tablets in the flow be the same. The tablet size, which we define with D, need not be the same. Neither does the velocity U of the flow relative to the tablet, the fluid viscosity μ, nor the fluid density ρ have to be the same to produce the same flow pattern (“similarity”). Using a process called “dimensional analysis” (21), however, it can be shown that the flow patterns will be the same only if a specific combination of μ, ρ, U, and D, given by the “Reynolds number” Re = (ρUD/μ), is the same between the two flows.

We applied “similarity theory” with “dimensional analysis” to generalize the development of empirical mathematical relationships from data. We first argued that, for fixed orientation and tablet shape, average surface shear stress τ _avg depends only on relative flow velocity U, tablet size D, and fluid properties viscosity μ and density ρ. Dimensional analysis leads to the result that an appropriately nondimensionalized τ _avg depends only on Reynolds number. In other words, given sufficient data, we develop a mathematical equation to fit the symbolic form,

$$\frac{{\tau _{{avg}} }}{{{\mu U} \mathord{\left/ {\vphantom {{\mu U} D}} \right. \kern-\nulldelimiterspace} D}} = f{\left( {\frac{{\rho UD}}{\mu }} \right)} = f{\left( {Re} \right)}.$$

(A1)

Dimensional analysis leads to μU/D being the appropriate nondimensionalization for τ _avg , and the symbol “f” implies a mathematical relationship between τ _avg /(μU/D) and Re = ρUD/μ that is to be determined from experimental data. Inthis work we generated this data from computer simulations that replicate the in vitro flow. The important point from Eq. (A1) is that to determine an empirical mathematical relationship between τ _avg , and the variables U, μ, D, and ρ, we need not vary each of the four dependent variables (U, μ, D, ρ) separately. In this study we vary only μ and U (for fixed D and ρ) to collect data from which we empirically estimate the mathematical relationship (f) between the two nondimensional variables τ _avg /(μU/D) and Re = ρUD/μ. Once done, multiplication of right-hand side of the empirical mathematical expression for f by μU/D produces a mathematical relationship between dimensional τ _avg and U, μ, D, and ρ.

We applied the same procedure to develop the form of the mathematical relationship between an appropriately nondimensionalized mass erosion rate by arguing that, for fixed tablet shape and orientation, $\ifmmode\expandafter\dot\else\expandafter\.\fi{m}$depends only on average surface shear stress τ _avg , tablet size D, relative tablet velocity U, a material surface parameter τ _u (see Materials and Methods), and fluid properties μ and ρ. The dimensional analysis procedure leads to the following symbolic relationship:

$$\frac{{\ifmmode\expandafter\dot\else\expandafter\.\fi{m}}}{{{\tau _{{avg}} D^{2} } \mathord{\left/ {\vphantom {{\tau _{{avg}} D^{2} } U}} \right. \kern-\nulldelimiterspace} U}} = h{\left( {\frac{{\tau _{{avg}} }}{{{\mu U} \mathord{\left/ {\vphantom {{\mu U} D}} \right. \kern-\nulldelimiterspace} D}},Re,\frac{{\tau _{u} }}{{\tau _{{avg}} }}} \right)}.$$

(A2)

Here dimensional analysis lead to the result that mass erosion rate, nondimensionalized by τ _avg D²/U, can be written as a mathematical expression “h” that contains $\frac{{\tau _{{avg}} }} {{{\mu U} \mathord{\left/ {\vphantom {{\mu U} D}} \right. \kern-\nulldelimiterspace} D}}$ Re and τ _u /τ _avg . In this work we determined this mathematical relationship by combining experimental and computer simulation data.

However, we can reduce Eq. (A2) to a simpler form. Assuming that (A1) is uniquely invertible, we replace Re in (A2) with a function that depends only on $\frac{{\tau _{{avg}} }} {{{\mu U} \mathord{\left/ {\vphantom {{\mu U} D}} \right. \kern-\nulldelimiterspace} D}}$, producing the following reduced form:

$$\frac{{\ifmmode\expandafter\dot\else\expandafter\.\fi{m}}} {{{\tau _{{avg}} D^{2} } \mathord{\left/ {\vphantom {{\tau _{{avg}} D^{2} } U}} \right. \kern-\nulldelimiterspace} U}} = g{\left( {\frac{{\tau _{{avg}} }} {{{\mu U} \mathord{\left/ {\vphantom {{\mu U} D}} \right. \kern-\nulldelimiterspace} D}},\frac{{\tau _{u} }} {{\tau _{{avg}} }}} \right)}.$$

(A3)

Here “g” implies a mathematical relationship between ${\ifmmode\expandafter\dot\else\expandafter\.\fi{m}} \mathord{\left/ {\vphantom {{\ifmmode\expandafter\dot\else\expandafter\.\fi{m}} {{\left( {{\tau _{{avg}} D^{2} } \mathord{\left/ {\vphantom {{\tau _{{avg}} D^{2} } U}} \right. \kern-\nulldelimiterspace} U} \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {{\tau _{{avg}} D^{2} } \mathord{\left/ {\vphantom {{\tau _{{avg}} D^{2} } U}} \right. \kern-\nulldelimiterspace} U} \right)}}$, τ _avg /(μU/D), and τ _u /τ _avg that we determine through data obtained by combining in vitro experimental measurements of $\ifmmode\expandafter\dot\else\expandafter\.\fi{m}$with computer simulation “measurement” of τ _avg , for tablets in flows with different μ and U, but with fixed orientation, size D and material property τ _u . From the mathematical form of g, the tablet erosion model is obtained by multiplying g by τ _avg D²/U.