Assessment of Uncertainty Propagation in Dynamic Process Flowsheets for Pharmaceutical Manufacturing

Recent work in the development of integrated solids-based flowsheet models for continuous pharmaceutical manufacturing [1], which are associated with various types of model and experimental data uncertainty, has given rise to the need for the development of techniques for assessing the analysis of the effects of input variability to the final prediction uncertainty. In light of the rising demands of the pharmaceutical industry to produce high quality tablets and deliver maximum profit, researchers have started developing tools essential to integrate, simulate, and design continuous manufacturing systems for pharmaceutical products.  The advantage of continuous processing and process modeling tools, such as flowsheet simulation, which allow the design of  equipment for the production of a wide range of quantities, minimize the need for scale-up studies and the time-to-market, have been newly recognized by both pharmaceutical industries as well as regulatory authorities [1-2]. However, especially in the case of pharmaceutical solids-based modeling, there are various types of uncertainties which affect the end result of a simulation, such as raw material property variability- since powders are far more complex than bulk liquid materials- as well as model parameter uncertainty- since powder handling process models are still in their early developments, rarely validated and have a large number of parameters. Therefore a method for identification of the most important sources of variability, the interaction of uncertainty sources within and across units, as well as the propagation of uncertainty from the initial process stages to the final product properties is required.  This work describes the results yielded from a performance of global sensitivity analysis from a flowsheet simulation of a direct compaction process for the production of pharmaceutical tablets, developed in the gPROMS flowsheet simulation environment [3].

The principle of this work can be broken down into four specific steps: (a) development of an integrated dynamic flowsheet for solids-based pharmaceutical manufacturing process, (b) identification of the  major sources of variability in each unit operation within the flowsheet, (c) analysis of the effect of different sources of uncertainty on final product qualities, and lastly (d) study of the effects of uncertainty propagation and uncertainty interaction effects throughout the integrated flowsheet. This process starts off with identifying all possible sources of variability from either the different unit operators or from different sources like parameter uncertainty and/or operating condition variability. Subsequently, these identified inputs are assigned probability distributions based on prior knowledge, or given product/process specifications. Next, a stochastic computer multi-scenario design is developed based on Latin Hypercube sampling and results are collected for the identified significant outputs under different conditions. Results are analyzed in order to estimate the sampling-based and variance-based sensitivity measures in accordance with the global Sensitivity Analysis theory [4].

The analysis can be performed as steady state or time-dependent, subjective to the level of criticality in demand. Dynamic sensitivity indexes predict at which precise time periods, will the output variables and units be more sensitive to the perturbations produced through various interactions. In a flowsheet simulation, every unit operation interacts with other process operations and the slightest variation of a parameter in one unit may highly affect the outcome of the entire process. For example, in this work, it was discovered that input variables in the initial feeders (i.e. API and Excipient rpm and mean particle size parameters) seemed to impact many of the outputs from the remaining units of operation. This is the reason why there is a need to perform global Sensitivity Analysis techniques as opposed to a local Sensitivity Analysis. The success of a dynamic sensitivity analysis framework will precisely identify significant uncertain model parameters and material properties during different phases of dynamic operation of the integrated process. In this simulation, it was inferred that although propagation of uncertainty throughout the process was attributed to some of the initial input parameters that were varied (in the feeder); a lot of uncertainty in the output arose from the variability introduced in the same unit. (e.g. the feed frame rotation rate affected the total flow rate of the feed frame and the compression force of the tablet press affected the volume fed in the tablet press)

In conclusion, this analysis underlined a crucial aspect of flowsheet modeling as changing the input variables by even the smallest degree may result in a high uncertainty in the output. In regards to the four principles, which were introduced earlier, the development of a detailed simulation will enable not only the optimization of the integrated process and quantify uncertainty propagation from early stages of the manufacturing line down to the final product properties, but it will also facilitate the identification of possible process integration bottlenecks, conflicting design and control objectives of the simulation [1].

References:

1. Boukouvala, F, Niotis, V, Ramachandran, R, Muzzio, F.J, & Ierapetritou, M.G (11 July 2012): An integrated approach for dynamic flowsheet modeling and sensitivity analysis of a continuous tablet manufacturing .Computers & Chemical Engineering, 42, p.30-47.

2. Leuenberger, H.,  New trends in the production of pharmaceutical granules: batch versus continuous processing. European Journal of Pharmaceutics and Biopharmaceutics, 2001. 52(3): p. 289-296.

3. ProcessSystemsEnterprise, gPROMS Advanced User Guide. 2003: London, UK.

4. Saltelli, A., K. Chan, and E.M. Scott, Sensitivity analysis. Wiley series in probability and statistics. 2000, Chichester ; New York: Wiley. xv, 475 p.