P1252108903JxLon - PowerPoint PPT Presentation

Title: P1252108903JxLon


1
Investigations into tablet dissolution in a
paddle type apparatus
Dr. Martin Crane, School of Computing, Dublin
City University
Prof. Heather Ruskin, School of Computing, Dublin
City University
Mr. Niall McMahon, School of Computing, Dublin
City University
Prof. Lawrence Crane, School of
Mathematics, Trinity College Dublin
Introduction - What are we doing?
Why this type of tablet?
Results - Where are we now?
Conclusions

1. Although relatively simple compared with "real"
   drug delivery systems, a successful model of this
   tablet would demonstrate the possibility of
   accurately simulating drug dissolution. It would
   give us reason to believe that we can potentially
   model more complex systems.

We are modelling a tablet dissolving in a
well-defined in-vitro environment (specifically,
we are estimating the mass transfer rate).  
The good agreement between this finite difference
scheme and the other methods for the trivial case
indicates that the scheme is behaving as
expected.
We are currently considering the multi-layered
configuration as well as our recent results for
the trivial case of a single layered tablet (that
is a tablet consisting purely of drug).
Tablet
This is encouraging and we are currently
extending the model to describe dissolution from
a multi-layered tablet.
Single layered tablet results
Simple compressed system consisting of
alternating layers of drug (salicylic acid) and
excipient (benzoic acid). 
2. Previous studies indicate that accurately
predicting the surface area change (with time)
for this type of system may ultimately lead to
better models for multi-component systems 1.
For a given set of input parameters, the finite
difference mass flux value, calculated as
outlined above, and the exact Lévêque estimate
agree to within 0.1 .
Future Work - Where to next?
In the short term we hope to build a simple
multi-layered model and compare the results with
previous work. In the medium to long term we will
consider more realistic systems. Real dissolution
systems (those in therapeutic use) have moving
boundaries (as the drugs and excipients dissolve)
and often the drug is dispersed through a matrix
of excipient. Some real systems also use new
polymer technologies to protect and deliver the
drug. Simulating these systems will almost
certainly require the use of alternative
mathematical techniques.
This close match is demonstrated by the
concentration profiles shown in figure 4.
Fig. 1 Multi-layered tablet
3. It was used in associated studies. This allows
us to compare their results with ours.
Environment
Nominally a USP 24 type 2 paddle dissolution
apparatus, with the tablet positioned 3mm above
the bottom.
Approach - How are we doing this?
To simulate mass transfer, the time dependent
diffusion-advection equation is used with
simplifying assumptions.
We look forward to these challenges.
Acknowledgements
The authors would like to thank the Irish
National Institute for Cellular Biotechnology
(NICB) for supporting this work and Anne-Marie
Healy in the School of Pharmacy at Trinity
College Dublin who produced the experimental data
mentioned in this poster.
Fig. 3 Simplified diffusion-advection equation
Fig. 2 Paddle dissolution apparatus
Fig. 4 A comparison of drug concentration
profiles at the trailing edge of the tablet
For example, the diffusion is considered to be
two-dimensional, steady state and from a flat
plate rather than a cylinder.
Why are we doing this?
References
Our estimate has a relative error of 0.9 with
respect to a semi-analytical (Pohlhausen type)
solution proposed by Crane et al. 1
1. Crane, M. Crane, L. Healy, A. M. Corrigan,
O.I. Gallagher, K.M. McCarthy L.G. 2003. A
Pohlhausen Solution for the Mass Flux From a
Multi-layered Compact in the USP Drug Dissolution
Apparatus. Submitted to Simulation Modelling
Practice and Theory, Elsevier, 2003.
We want to explore the mathematics of drug
dissolution and build effective simulations!
The equation is discretised using an explicit
Forward Time Central Space (FTCS) finite
difference scheme with initial values provided by
the exact Lévêque solution (cited by Schlichting
2).
The potential benefits of mathematical simulation
are as unlimited as imagination allows. An ideal
simulation could reduce the need for experiment
in the design of drug delivery systems, cutting
associated costs.
Mass fluxes computed by Crane et al. agree well
with experimental data for both single layered
(that is a tablet consisting purely of drug) and
multilayered tablets.
The important results are the drug mass fluxes
and transfer rates.
2. Schlichting, H. 1979. Boundary-Layer Theory
7th Edition. New York London etc.
McGraw-Hill. Chap. XII p285 eqn. (12.51c). and
p291 eqn. (12.60). Note it seems there is a
square root missing in the denominator of
equation (12.60) in this edition.
excipients are inert substances that together
with the drug form a tablet
www . google . com Niall McMahon Search
email nmcmahon_at_computing.dcu.ie