(701b) Model-Based Characterisation of Organic and Aqueous Tablet Film Coating Processes: Parameter Estimation and Risk Management

Tablet coating is an important processing step in the
pharmaceutical industry in which tablets are coated with an aqueous or organic
film coating for both aesthetic and functional reasons.

Mathematical models of tablet film coating are important in
pharmaceutical development as they aid in design of experiments, scale-up and
determining optimal process conditions as formulations change. A universal
steady-state film coating model has previously been developed (am Ende,
Berchielli, 2005) with the aim of providing process engineers with a means of
predicting target operating conditions for optimization, scale-up and
robustness studies. In that work, the model was validated with experimental
conditions and the predictions obtained were found to be in good agreement with
data not used for model validation.

In this study, the steady-state model was first validated
against steady state plant data using gSOLIDS (Process Systems Enterprise, UK).
It was found that starting with one experiment, as experiments were added, the
95% confidence interval decreased rapidly reducing to less than 10% with four
or more experiments.

Figure 1: Change in estimated value of heat loss factor as experimental data is added

In order to quantify whether sufficient data was used for
model validation, the 95% T-value was compared to the reference T-value. (If
the 95% T-value is greater than the reference T-value, this indicates that
sufficient data was used to for model validation). The results obtained
indicated that at least three experiments are needed to accurately estimate the
unknown model parameter. This was consistent with the results obtained for the
95% confidence interval which was more than 50% when only two experiments were
used.

Figure 2: Changes in reference and 95% T-values as experimental data is added

As indicated by the 95% confidence intervals, the estimated
value of the model parameter is not a perfect estimate. Therefore in order to
determine a reasonable estimate of the model prediction a Monte Carlo
simulation was carried out. In this simulation several instances of the model
were run with each instance having the unknown model parameter sampled from a
normal distribution centred at the parameter estimate and with a standard
deviation obtained from the 95% confidence interval. The results from these
numerous simulations were then averaged to obtain an estimate of the model
prediction. In addition, the results from these simulations were used to obtain
a 95% confidence interval on the model predictions. The results obtained
indicated that the model predictions were in good agreement with the
experimental data used for parameter estimation. Further, given the confidence
interval of the estimated value of the model parameter, the standard deviation
of the model prediction was much smaller than that of the data indicating that
the predictions of the model vary very little with respect to the uncertainty
in the parameter estimate.

Figure 3: Comparison of model predictions with experimental data

A similar analysis was conducted using dynamic data. In this
case however, although the data used for parameter estimation was deemed
sufficient, the quality of the fit was quantified as being unsatisfactory even
if several experiments were used. This indicates insufficiencies in the model
which is expected as a steady state model was used to study dynamic plant data.

In summary, the results presented above indicate that with
relatively few steady state experiments, an accurate estimate can be obtained
of the unknown model parameter in the steady state film coating model. The
model predictions were found to be in good agreement with the experimental
data. The uncertainty in the model parameter was quantified and it was found
that the model predictions were relatively unaffected given the uncertainty in
the parameter estimate.

The analysis presented above is generic and can be used to
quantity uncertainty in any mathematical model. This information can be
especially useful as it can be used to quantify the risk associated with
decisions made using these mathematical models. Further, the rigour of the
analysis helps determine whether more experimentation is needed or whether
further model development is needed (or possibly a combination of both).

References

M. am Ende, A Berchielli (2005) A thermodynamic model for
organic and aqueous tablet film coating. Pharmaceutical Development and
Technology, 1:47-58