Design of Experiments (DoE) Studies

Design of Experiments (DoE) is a statistical approach to reaction and process optimization that permits the variation of different factors simultaneously with the goal to screen the reaction space for optimum values.

In chemical development, DoE studies are used to speed up reaction optimization, since they allow the assessment of a large number of reaction parameters in a small number of experiments. Over the last several years, DoE has been used for the implementation of Quality by Design (QbD) in R&D and manufacturing. In Pharmaceutical QbD, product and process understanding is critical for ensuring quality in the manufactured product. 

The advantage of deploying Design of Experiments (DoE) in chemical development is that multiple input parameters, or "factors", such as temperature, raw material and concentration, can be assessed simultaneously to elucidate the conditions at which the product attributes, or "responses", such as yield, selectivity and impurity level, reach an optimum value. 

Since DoE studies usually require fewer experimental repetitions, DoE can result in:

• Better process understanding in less time
• Shorter development cycles in manufacturing

In a Design of Experiments (DoE) study, the factors of interest are varied systematically from their lowest to highest value and all possible factor combinations are executed in the same set of experiments.

In a three-factor DoE with two levels (see graph to the right), the values may be represented in a cube where the corners display the eight test conditions. In a full factorial design, the resulting test conditions are calculated according to 2^3 = 8  test conditions that elicit eight distinct results.

The example to the right shows a schematic example of a full factorial design DoE leading to eight distinct test results with one optimum value (i.e. data highlighted in red).

The data resulting from a DoE study is used to build mathematical functions that best describe the relationship between the factors and the measured responses. These equations can be first, second or higher order, depending on how the responses react to changes in the factors.

Mathematical model with y=response (e.g. yield), and xn=input factors, and βn=function coefficients.

The response (y) can be plotted against one or two input variables (x) to build the so-called Response Surface in two or three dimensions. 

The goal of optimizing a synthetic reaction is to find the maximum value of a function (the optimum), which yields the best desired outcomes. The Response Surface Methodology (RSM) leverages data generated by DoE and visually depicts the dependence of the response (yield) against the three factors (temperature, starting material and catalyst dosing; see example graph). RSM is beneficial to more precisely model the curvature around the reaction optimum. Process chemists are able to get a deeper understanding of a process and identify the region in which the process conditions meet one or more goals, such as yield increase or cost optimization.

With RSM, a large amount of information can be created from a small number of experiments, and reaction and process optimization can be done in less time.

A key requirement in experimental design for DoE is to establish system reliability and reproducibility. This is accomplished by minimizing the risk of measurement errors and precisely controlling all parameters to ensure reproducible conditions. In chemical synthesis, the experimental set-up needs to ensure parameter measurements and control such as temperature, stirring, sampling and substance dosing are accurate and experiment to experiment reproducibility is high.

In addition, the chosen Design of Experiments (DoE) factors should represent the parameters that have the strongest influence on the experimental outcomes. The parameter range from lowest to highest value should be realistic and needs to cover the widest possible range since extrapolation outside the design space is not permitted in DoE.

In this figure, the EasyMax chemical synthesis reactor follows the set temperature precisely, while the difficult to control round bottom flask shows a control variation of around 27 °K between its minimum and maximum.

Automated chemical synthesis reactors provide better results, leading to more precise Design of Experiments studies.

In the set-up of quality DoE studies, manual synthesis equipment, including round bottom flasks, may have potential limitations:

• The precise control of key parameters such as temperature, stirring and dosing within tight constraints is difficult during the reaction
• Experiment repeatabilty is compromised
• The recording of all reaction parameter variations and analytical results during the experiment is cumbersome and error-prone
• Manual reaction sampling to gain reaction data is not reproducible and needs much operator time

Image reproduced with permission from Caron, Stéphane, and Nicholas M. Thomson. "Pharmaceutical process chemistry: Evolution of a contemporary data-rich laboratory environment." The Journal of Organic Chemistry 80.6 (2015): 2943-2958. Copyright 2015 American Chemical Society."

Peptides are complex molecules synthesized in many steps with numerous possible side reactions. In order to operate such processes economically, every step must be optimized and result in a yield of at least 98%.

The goal of the DoE study was to optimize product yield by the systematic variation of four process parameters: temperature, solvent addition, water and peptide concentration. 

The study shows the importance of the reproducible change and control of the DoE factors such as heating, cooling and reactant addition, as well as the control of experimental conditions (e.g. through consistent mixing of the reaction mass). 

Design of Experiments is used for a variety of applications, including:

• Chemical Synthesis
• Crystallization Processes
• Synthesis Reactions
• Polymorphism Identification
• Polymerization Reactions
• Hydrogenation Reactions
• Biocatalysis and Enzymatic Catalysis
• Flow Chemistry
• Downstream Processing
• Viral Inactivation in Bioprocessing

To measure and control multiple sets of reaction parameters in DoE with a high level of reliability and repeatability, chemical synthesis reactors have decisive advantages.

Manual DoE studies with more than two factors require a high experimental effort as all parameters need to be monitored simultaneously over a long reaction time. Chemical synthesis reactors help control all parameters precisely, at the same time, resulting in quality DoE results that are recorded and can be easily retrieved for further data processing. Also, iControl software ensures timely adjustments of individual factors according to the DoE protocol, with protocols' easy reuse in subsequent experiments.

Using EasyMax chemical synthesis reactors, every scientist can enjoy unattended experiments with a wider application range suited for DoE studies for quick discovery of new synthetic pathways. 

Chemical reactors help scientists quickly explore multiple process parameters simultaneously making it a perfect tool for DoE studies. A unique functionality and application set is provided:

• Temperature measurements from -80 °C to 180 °C
• Liquid dosing with dosing rates between 1 and 50 mL/min at high accuracy
• Automated reaction sampling from suspensions and multiphase reactions with EasySampler
• Efficient stirring of all types of reactions to perform mixing studies
• Reaction vessel shape covers a volume range from 0.5 mL to 1000 mL
• Integration of PAT probes, including ReactIR, ReactRaman, ParticleTrack and EasyViewer to perform data-rich DoE studies

Design of Experiment (DoE) is a statistically useful means for minimizing the number of experiments needed to explore the effect of variables on reaction performance in the lab, but scaling-up DoE results to production is fraught with problems. For example, DoE  studies do not typically take into account the effect of mixing and heat transfer, critical parameters in scale-up. Dynochem modeling allows important physical and thermal properties to be accounted for in scale-up. When kinetic information is used with Dynochem modeling, suitable sampling endpoints can be determined for DoE, saving time and resources. Thus, Dynochem modeling enhances the development of critical process parameters and effective process design space.  

Innovation is challenging when equipment limits experimental possibilities. The complexity of synthetic chemistry increases every day. This white paper discusses how chemists are responding with innovative techniques that include:

• Automated reaction planning and execution
• Complete data capture for every experiment
• Synthesis tools that solve common experimental problems

To learn how smart synthesis tools combined with lab digitalization capabilities can transform chemical development, download the white paper "The Modern Synthesis Lab: A New Workplace for Chemists". 

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• Georgakis, C. (2013). "Design of Dynamic Experiments: A Data-Driven Methodology for the Optimization of Time-Varying Processes." Industrial & Engineering Chemistry Research 52: 12369-12382.
  
• P. M. Murray et al., "The application of design of experiments (DoE) reaction optimization and solvent selection in the development of new synthetic chemistry", Org. Biomol. Chem., 2016, 14 Pages, 2373-2384.
  
• Design of Experiments (DoE) and Process Optimization. A Review of Recent Publications. Org. Process Res. Dev., 2015, 19 (11), pp 1605–1633.