Definition of Design Spaces Using Mechanistic Models and Geometric Projections of Probability Maps

Following a model-centric strategy in the development of a manufacturing process for a new medicine empowers the simultaneous study of a large number of process parameters, which is large enough to exceed the capability of a graphic representation of the interactions across them. This work presents a discussion regarding the identification, description, and communication of multidimensional design spaces of high order. It introduces the reader to mathematical tools developed by the process systems engineering community that become relevant in the challenge to replace graphics as a means to describe and communicate a design space. Concepts like process flexibility are discussed and illustrated. The paper also introduces geometric projection as a way to capture and describe the shape of the design space in an easier form (than that of the complete mechanistic model) that can be communicated to the regulator. An assessment is presented regarding the key elements communicated by a graphical representation of a design space, and alternate ways of conveying the same information using mathematics are suggested. These ideas are illustrated by applying them to the identification and definition of a design space for a chemical reaction step and the digital risk assessment for a packed bed adsorption step.