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.

翻译：根据ICH Q8指南，生物制药生产商在监管审批申请中需提交设计空间（DS）定义，在此空间内的工艺参数（PP）偏差不视为变更，无需触发监管后批准程序。设计空间可通过非线性PP范围描述，即某个PP的取值范围取决于另一PP的特定取值。然而，独立PP范围（线性组合）因其操作简便性而更受生物制药生产领域的青睐。尽管部分统计软件支持计算由线性组合构成的设计空间，但这些方法通常基于参数空间离散化——该策略在PP数量增加时扩展性不佳。本文提出一种新方法，通过数值优化器寻找线性PP组合，基于回归模型预测的关键质量属性（CQA）边界满足可接受标准，在参数空间内计算最大设计空间。采用预先计算的容差区间近似值构建不等式约束，通过单次矩阵乘法实现边界快速评估。该方法在不同已知设计空间的基准验证中证实其正确性。与基于网格的先进方法相比，基于优化器的程序更精确，通常能获得更大的设计空间，并支持高维计算。此外，所提出的加权方案可优先考虑特定PP，从而实现更具动态性的设计空间定义与探索。更大的设计空间带来的扩展PP范围，为生物制药生产商提供了更高的操作灵活性。