Transcript ppt - School of Computing

Investigations into tablet dissolution in a paddle type apparatus
Dr. Martin Crane,
School of Computing,
Dublin City University
Introduction - What are we doing?
Why this type of tablet?
We are modelling a tablet dissolving in a well-defined
in-vitro environment (specifically, we are estimating the
mass transfer rate).
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.
Tablet
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].
Fig. 1: Multi-layered tablet
Environment
Nominally a USP 24 type 2 paddle dissolution apparatus,
with the tablet positioned 3mm above the bottom.
3. It was used in associated studies. This
allows us to compare their results with
ours.
Approach - How are we doing this?
To simulate mass transfer, the time dependent
diffusion-advection equation is used with
simplifying assumptions.
Prof. Heather Ruskin,
School of Computing,
Dublin City University
Prof. Lawrence Crane,
School of Mathematics,
Trinity College Dublin
Results - Where are we now?
Conclusions
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).
The good agreement between this finite difference
scheme and the other methods for the trivial case
indicates that the scheme is behaving as expected.
This is encouraging and we are currently extending
the model to describe dissolution from a multi-layered
tablet.
Single layered tablet results
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?
This close match is demonstrated by the concentration
profiles shown in figure 4.
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Dimensionless Concentration
Mr. Niall McMahon,
School of Computing,
Dublin City University
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Lévêque
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We look forward to these challenges.
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Finite
Difference
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Fig. 2: Paddle dissolution apparatus
Why are we doing this?
We want to explore the mathematics of drug dissolution
and build effective simulations!
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.
*excipients are inert substances that together with the
drug form a tablet
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Normal Distance from Tablet Surface / cm
Fig. 3: Simplified diffusion-advection equation
For example, the diffusion is considered to be twodimensional, steady state and from a flat plate
rather than a cylinder.
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 important results are the drug mass fluxes and
transfer rates.
In the short term we hope to build a simple multilayered 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.
Fig. 4: A comparison of drug concentration profiles at
the trailing edge of the tablet
Our estimate has a relative error of 0.9 % with
respect to a semi-analytical (Pohlhausen type)
solution proposed by Crane et al. [1]
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.
www . google . com + “Niall McMahon” + Search
email: [email protected]
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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.
References
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.
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.