In-line monitoring of the freeze-drying process by means of heat flux sensors

The final qualities of a pharmaceutical product can be adversely affected by a suboptimized freeze-drying process. Multiple variables and operating conditions come into play, thus making the overall process difficult to control. In this study, we show how heat flux sensors can guide the in-line monitoring of freezing and primary drying of placebo formulations, leading to significant insights that contribute to our understanding of the phenomena involved. It was found that heat flux sensors can be used as a practical and robust tool to monitor a lyophilization cycle by defining the processing time and investigating different process scenarios. Concerning the freezing step, the heat flux sensors proved to be an effective way to detect both nucleation and end of crystal growth. Additionally, the sensors' signal highlighted the end of cooling and freezing steps and thus helped to eliminate uncertainty about the time required to reach thermal equilibrium across the batch. An ultimate potential of the devices was addressed to build the design space for freezing and primary drying, laying the foundations for new research on this topic

Effect of freeze-dryer design on heat transfer variability investigated using a 3D mathematical model

International audienceIn the freeze-drying process, vials located at the border of the shelf usually present higher heat flow rates which in turn result in higher product temperatures than central vials. This phenomenon, named edge vial effect, can result in product quality variability within the same batch of vials and between batches at different scales. Our objective was to investigate the effect of various freeze-dryer design features on the heat transfer variability. A 3D mathematical model previously developed in COMSOL Multiphysics and experimentally validated was used to simulate heat transfer of a set of vials located at the edge and in the centre of the shelf. The design features considered were the loading configurations of the vials, the thermal characteristics of the rail, the walls and the shelves and some relevant dimensions of the drying chamber geometry. The presence of the rail in the loading configuration and the value of the shelf emissivity strongly impacted on the heat flow rates received by the vials. Conversely, the heat transfer was not significantly influenced by modifications of the thermal conductivity of the rail, the emissivity of the walls and by the geometry of the drying chamber. The developed model revealed to be a powerful tool to predict the heat transfer variability between edge and central vials for the cycle development and scale-up and to compare various freeze-dryer design features

Dynamic shortest paths minimizing travel times and costs

Dynamic Shortest Paths Minimizing Travel Times and Costs In this paper, we study dynamic shortest path problems that determine a shortest path from a specified source node to every other node in the network where arc travel times change dynamically. We consider two problems: the minimum time walk problem and the minimum cost walk problem. The minimum time walk problem is to find a walk with the minimum travel time. The minimum cost walk problem is to find a walk with the minimum weighted sum of the travel time and the excess travel time (over the minimum possible travel time). The minimum time walk problem is known to be polynomially solvable for a class of networks called FIFO networks. In this paper: (i) we show that the minimum cost walk problem is an NP-hard problem; (ii) we develop a pseudopolynomial-time algorithm to solve the minimum cost walk problem (for integer travel times); and (iii) we develop a polynomial-time algorithm for the minimum time walk problem arising in road networks with traffic lights

A multi-exchange heuristic for the single source capacitated facility location problem

This paper presents a very large scale neighborhood (VLSN) search algorithm for the capacitated facility location problem with single-source constraints. The neighborhood structures are induced by customer multi-exchanges and by facility moves. We consider both single-customer multi-exchanges, detected on a suitably defined customer improvement graph, and multi-customer multi-exchanges, detected on a facility improvement graph dynamically built through the use of a greedy scheme. Computational results for some benchmark instances are reported, which demonstrate the effectiveness of the approach for solving large-scale problems

Scale-up of freeze-drying cycles, the use of process analytical technology (PAT), and statistical analysis

Chapter 10Traditionally, the quality of pharmaceutical drugs is tested on the final freeze-dried product following a regulatory framework known as Quality-by-Testing (QbT) (Yu, Pharm Res 25: 781–91, 2008). In this system, product quality and performance are ensured by performing extensive tests on the final product, and by using a fixed formulation and manufacturing process. In contrast, the US Food and Drug Administration (FDA) proposed the Quality by Design (QbD) initiative with the idea that quality cannot be “tested into” the product, but it should be built into it (FDA, Guidance for industry, Q8(R2) pharmaceutical development. Dept. of Health and Human Services, Center for Drug Evaluation and Research. Rockville, MD, 2009). Quality by Design consists of a systematic approach to pharmaceutical product development that begins with predefined objectives and emphasizes product and process understanding and process control, based on sound science and quality risk management (FDA, Guidance for industry, Q8(R2) pharmaceutical development. Dept. of Health and Human Services, Center for Drug Evaluation and Research. Rockville, MD, 2009; Mockus et al, Pharm Dev Technol 16: 549–76, 2011; Yu, Pharm Res 25: 781–91, 2008). In this chapter, a statistical model for the sublimation step in freeze-drying was used to construct the design space for the cycle development and to select adequate parameters for scaling up from pilot to commercial scale. Three critical operating variables of the process were tested: freezing rate, shelf temperature, and chamber pressure in primary drying. The model was used to predict the sublimation rate and the product temperature, since their selection is of paramount importance to obtain a product of high quality. The obtained results were then used to define the design space of the product at pilot scale

A Multi-Exchange Heuristic for the Single Source Capacitated Facility Location Problem

We present a very large-scale neighborhood (VLSN) search algorithm for the capacitated facility location problem with single-source constraints. The neighborhood structures are induced by customer multiexchanges and by facility moves. We consider both traditional single-customer multi-exchanges, detected on a suitably defined customer improvement graph, and more innovative multicustomer multi-exchanges, detected on a facility improvement graph dynamically built through the use of a greedy scheme. Computational results for some benchmark instances are reported that demonstrate the effectiveness of the approach for solving large-scale problems. A further test on real data involving an Italian factory is also presented

Finding Tractable Formulas in NNF

Many applications in Computer Science require to represent knowledge and to reason with non normal form formulas. However, most of the advances in tractable reasoning are applied only to CNF formulas. In this paper, we extend tractability to several classes of non normal formulas which are of high practical interest. Thus, we first define three non normal Horn-like classes of formulas F1 F2 : : : Fn where each F i is constituted by a disjunction of two optional terms F i = NNF \Gamma i C + i : the first one is in Negation Normal Form (NNF) composed exclusively with negative literals and the second one is a conjunction of positive propositions. These formulas codify the same problems that the Horn formulas but with significantly, even exponentially, less propositional symbols. Second, we define sound and refutational complete inference rule sets for each class. Our third contribution consists in the design of a sound, complete and strictly linear running time algorit..