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Excipients & Actives for <strong>Pharma</strong><br />

No. 26, 2011<br />

Based on <strong>the</strong>se calculations, <strong>the</strong> apparent diffusion<br />

coefficient of <strong>the</strong> drug in <strong>the</strong> polymeric<br />

matrix could be determined: D = 1.7, 2.4 and<br />

4.0 x 10 -7 cm²/s for 10, 20 and 40% initial drug<br />

content. Knowing <strong>the</strong>se values, <strong>the</strong> resulting<br />

drug release kinetics can be predicted for arbi trary<br />

tablet dimensions. One example is shown in<br />

figure 5 (dotted curves). These <strong>the</strong>oretical predictions<br />

could successfully be confirmed by<br />

independent experiments (symbols in figure 5).<br />

Equation 1<br />

M t<br />

M∞<br />

= 1-<br />

32<br />

π²<br />

·∑∞<br />

n=1<br />

Fick’s second law of diffusion<br />

1<br />

·exp<br />

q² ( -<br />

n<br />

R c<br />

q² n<br />

² ·D·t ) ·∑∞<br />

p=0<br />

1<br />

(2·p+1) 2 ·exp ( - (2·p+1)2· π²<br />

H ²<br />

·D·t<br />

)<br />

Conclusion Diprophylline release from Kollidon ®<br />

SR tablets is primarily controlled by diffusion. The<br />

ma<strong>the</strong>matical model presented allows for a facilitated<br />

optimization of this type of drug delivery<br />

system. Based on this ma<strong>the</strong>matical approach, a<br />

drug release profile can be easily adapted to <strong>the</strong><br />

specific <strong>the</strong>rapeutic application by reducing <strong>the</strong><br />

necessary experiments and hereby facilitating<br />

faster formulation development.<br />

REFERENCES<br />

[1] Siepmann, F; Eckart, K; Maschke, A; Kolter,<br />

K; Siepmann, J. Modeling drug release from<br />

PVAc/PVP matrix tablets. Journal of Controlled<br />

Release 141, 216-222, 2010.<br />

[2] J. Crank. The Ma<strong>the</strong>matics of Diffusion. Clarendon<br />

Press, Oxford, 1975.<br />

Drug released [%]<br />

100<br />

75<br />

50<br />

25<br />

0<br />

FIGURE 4<br />

40% diprophylline<br />

20%<br />

10%<br />

<strong>the</strong>ory<br />

0 6 12 18 24<br />

Time [h]<br />

Experiment (symbols) and <strong>the</strong>ory (curves):<br />

Diprophylline release from Kollidon SR tablets<br />

with different initial drug loadings in phosphate<br />

buffer pH 7.4. (diameter = 11.3 mm). Reprinted<br />

from reference [1], with permission<br />

Drug released [%]<br />

100<br />

75<br />

50<br />

25<br />

0<br />

FIGURE 5<br />

<strong>the</strong>oretical prediction<br />

1.3mm, experiment<br />

3.9mm, experiment<br />

0 6 12 18 24<br />

Time [h]<br />

Theoretical prediction (dotted curves) and independent<br />

experimental verification (symbols):<br />

Effects of <strong>the</strong> tablet height on diprophylline<br />

release from Kollidon SR tablets in phosphate<br />

buffer pH 7.4 (drug loading: 20%, diameter = 11.3 mm).<br />

Reprinted from reference [1], with permission<br />

Page 10

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