  According to ICH Q8 guidelines, the biopharmaceutical manufacturer submits a
design space (DS) definition as part of the regulatory approval application, in
which case process parameter (PP) deviations within this space are not
considered a change and do not trigger a regulatory post approval procedure. A
DS can be described by non-linear PP ranges, i.e., the range of one PP
conditioned on specific values of another. However, independent PP ranges
(linear combinations) are often preferred in biopharmaceutical manufacturing
due to their operation simplicity. While some statistical software supports the
calculation of a DS comprised of linear combinations, such methods are
generally based on discretizing the parameter space - an approach that scales
poorly as the number of PPs increases. Here, we introduce a novel method for
finding linear PP combinations using a numeric optimizer to calculate the
largest design space within the parameter space that results in critical
quality attribute (CQA) boundaries within acceptance criteria, predicted by a
regression model. A precomputed approximation of tolerance intervals is used in
inequality constraints to facilitate fast evaluations of this boundary using a
single matrix multiplication. Correctness of the method was validated against
different ground truths with known design spaces. Compared to stateof-the-art,
grid-based approaches, the optimizer-based procedure is more accurate,
generally yields a larger DS and enables the calculation in higher dimensions.
Furthermore, a proposed weighting scheme can be used to favor certain PPs over
others and therefore enabling a more dynamic approach to DS definition and
exploration. The increased PP ranges of the larger DS provide greater
operational flexibility for biopharmaceutical manufacturers.
