We propose the in silico use of the Design of Experiments (DoE) methodology in the analysis of parametric sensitivity of a detailed process model, so that we overcome the substantial limitation of current state-of-the-art Global Sensitivity Analysis (GSA) methods, which require a large and often prohibitive number of model evaluations. This is achieved by the calculation of an accurate and much simpler response surface meta-model (RSM) that is able to provide all the required nonlinear global sensitivity information. To benchmark the efficiency of the proposed methodology, we utilize an unstructured dynamical model that describes hybridoma cell growth and proliferation in batch cultures. [From the work of D. J. Jang and J. P. Barford, Biochem. Eng. J. 2000 4 (2), 153-168.] We show that using the DoE methodology to generate a response surface meta-model approximation of the full model can lead to the same quality of sensitivity information as the established variance-based GSA methods at a significantly lower computational cost. Finally, we evaluate, through the application of GSA on the estimated RSM meta-model, its ability to capture the nonlinear interaction effects present in the detailed model.