Integrating Mixture Design within the Property Clustering Framework
Chemical Product Design and Engineering (CPD&E)
Chemical Product Design & Engineering - II (CPD&E - 2)
Keywords: Design of Experiments, Property Clusters, Mixture Design, Regression Analysis, Paracetamol
Mixture Design is a Design of Experiments (DOE) tool used to determine the optimum combination of chemical constituents that deliver a desired response (or property) using a minimum number of experimental runs. While the approach is sufficient for most experimental designs, it suffers from combinatorial explosion when dealing with the multi-component mixtures found in pharmaceutical excipient design. To circumvent this problem, a recently developed design technique called Property Clustering is applied. In this type of design the properties are transformed to conserved surrogate property clusters described by property operators, which have linear mixing rules even if the operators themselves are nonlinear. Product and process property targets are then used to describe a feasibility target region. To solve the mixture design, components are mixed according to property operator models in a reverse problem format until the mixture falls within the feasibility target region. Once candidate solutions are found, they can be screened with additional criteria per the experimenter’s preference.
The degree of accuracy of this modeling technique depends heavily on the ability of the property operator models to adequately describe the property within the studied design space. These models may be obtained from two venues: pure component data and experimental mixture data. Traditionally property operator models have focused on the former, assuming no interaction affects. However, in excipient design, the properties that give the desired powder and tablet characteristics are not fully understood and pure component models with the necessary degree of accuracy do not yet exist. Therefore, in this work the development of property operator models using experimental data is explored with a particular emphasis on the regression analysis techniques of mixture design. In the first phase, linear regression models are used as the property operator models to demonstrate the proof of concept. In the subsequent phases, higher order regression models are used to account for the interaction effects. In each of these phases we use a case study of a mixture design from the International Journal of Pharmaceutics titled “Optimization of poorly compactable drug tablets manufactured by direct compression using mixture experimental design” by Martinello et al, 2006. Due to the nature of the regression coefficients in this case study, the advent of negative property cluster space is required. Here it is shown that using regression coefficients as property operators can lead to a projection of infeasible pure component properties. It is also shown that these infeasible properties can be augmented within the feasible property cluster design space using algebraic techniques.
Combining property operator equations with regression analysis also provides a deeper insight in to the adequacy of the experimental design points. While the location of the design points is set by optimality criteria to minimize variation in the property response, their locations should be adjusted to ensure the entire property design space is utilized. In this work we explore the technique of adjustment and the balance of optimality with property design space in a mixture design.
See the full pdf manuscript of the abstract.
Presented Wednesday 19, 15:00 to 15:20, in session Chemical Product Design & Engineering - II (CPD&E - 2).
