U.S. Department of Health and Human Services


Date of this Version


Document Type



Comprehensive Quality by Design for Pharmaceutical Product Development and Manufacture, First Edition. Edited by Gintaras V. Reklaitis, Christine Seymour, and Salvador García-Munoz.


U.S. government work.


A model is a representation of an underlying physical–chemical phenomenon. In the pharmaceutical industry, mathematical‐based models can be applied at all stages of development, starting with formulation design, continuing through process development and scale‐up, and extending into process monitoring and control of the commercial process. Implementation of models offers many benefits. These include, but are not limited to, (i) enhanced process understanding, (ii) reduction of experimentation cost, and (iii) improvement of productivity and product quality.

Models can be broadly categorized as either qualitative or quantitative. The focus of this chapter is quantitative models. These can be classified into three broad areas: mechanistic, empirical, and hybrid. As illustrated in the knowledge pyramid in Figure 2.1, overall understanding and the information needed to derive from these models increases from empirical to mechanistic models.

Mechanistic models are based on first principles, capture the underlying physical/chemical phenomena through sets of equations, and can be time independent (i.e., steady‐state) or dynamic. As indicated by Singh et al. [1], mechanistic models can be an excellent way to represent process knowledge. In such models, the input–output dynamics in a unit operation can be represented by a set of differential equations. Model building necessitates the availability of balance equations (e.g., mass and energy balance equations), constitutive equations, and an understanding of the constraints. Since mechanistic models are a true representation of the underlying phenomenon, predictions from these models can sometimes be extrapolated beyond the range covered by input data, depending on the validity of the underlying assumptions. Typically, the bottleneck in developing mechanistic models is coming up with equations as well as associated parameters that accurately represent the system.