A key element of the Quality-by-Design initiative set forth by the pharmaceutical regulatory agencies (such as the U.S. Food and Drug Administration) is the determination of the design space (DS) for a new pharmaceutical product. When the determination of the DS cannot be assisted by the use of a first-principles model, one must heavily rely on experiments. In many cases, the DS is found using experiments carried out within a domain of input combinations (e.g., raw materials properties and process operating conditions) that result from similar products already developed. This input domain is the so-called knowledge space, and the related experimentation can be very demanding, especially if the number of inputs is large. To limit the extension of the domain over which the experiments are carried out (hence, to reduce the experimental effort), a methodology is proposed that aims at segmenting the knowledge space in such a way as to identify a subspace of it (which we call the experiment space) that most likely brackets the DS. The methodology relies on the exploitation of historical databases on products that have already been developed and are similar to the new one, and is based on the inversion of a latent-variable model. The relationship between the regulatory concept of DS and the mathematical concept of null space is discussed for products characterized by one equality constraint specification, and the effect of model prediction uncertainty is accounted for. Three simulated examples are used to test the effectiveness of the proposed segmentation methodology. The segmentation results are shown to be effective, in that the designated experiment space is able to effectively bracket the DS and is much narrower than the historical knowledge space.

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A methodology is proposed to diagnose the root cause of the process/model mismatch (PMM) that may arise when a first-principles (FP) process model is challenged against a set of historical experimental data. The objective is to identify which model equations or model parameters most contribute to the observed mismatch, without carrying out any additional experiment. The methodology exploits the available historical data set and a simulated data set, generated by the FP model using the same inputs as those of the historical data set. A data-based model (namely, a multivariate statistical model) is used to analyze the correlation structure of the historical and simulated data sets, and information about from where the PMM originates is obtained using diagnostic indices and engineering judgment. The methodology is tested on two simulated systems of increasing complexity: a jacket-cooled continuous stirred reactor and a solids milling unit. It is shown that the proposed methodology is able to discriminate between parametric and structural mismatch, pinpointing the model equations or model parameters that originate the mismatch.

An experimental nanoparticle preparation process by solvent displacement in passive mixers is considered. The problem under investigation is to estimate the operating conditions in a target device (Mixer B) in order to obtain a product of assigned properties that has already been manufactured in a source device of different geometry (Mixer A). A large historical database is available for Mixer A, whereas a limited historical database is available for Mixer B. The difference in device geometries causes a different mixing performance within the devices, which is very difficult to capture using mechanistic models. The problem is further complicated by the fact that Mixer B can only be run under an experimental setup that is different from the one under which the available historical dataset was obtained. A joint-Y projection to latent structures (JY-PLS) model inversion approach is used to transfer the nanoparticle product from Mixer A to Mixer B. The Mixer B operating conditions estimated by the model are tested experimentally and confirm the model predictions within the experimental uncertainty. Since the inversion of the JY-PLS model generates an infinite number of solutions that all lie in the so-called null space, experiments are carried out to provide (to the authors’ knowledge) the first experimental validation of the theoretical concept of null space. Finally, by interpreting the JY-PLS model parameters from first principles, the understanding of the system physics is improved

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