Fractional Factorial Designs Research Articles

Enhancing early-stage cell culture process development efficiency using an integrated approach of high-throughput miniaturized bioreactors and definitive screening design

Rapidly expanding pipelines in biopharmaceutical industry and increasingly stringent requirements from regulatory agencies call for a more efficient and rational study design at early-stage cell culture process development. Recent developments in high-throughput bioreactor system and design of experiments (DoE) enable cell culture process development sector to meet such demand by integrating both technological advances. In this study, we compared varied forms of fractional factorial designs (FFDs) and definitive screening design (DSD) covering key process parameters such as temperature shift target, temperature shift timing, feed strategy, pH, dissolved oxygen, harvest time and additives in Ambr® 15 bioreactors to better understand the initial cell culture process and thus optimize it. Results showed that DSD was more effective and efficient in detecting both main and quadratic effects comparing to FFDs. Comparison of varied available model development strategies revealed that two-stage forward regression combined with corrected Akaike's information criterion (AICc) and least absolute shrinkage and selection operator (LASSO) regression combined with self-validated ensembled models (SVEM) offered superior predictive capability. Moreover, key DoE regularities was evaluated for their validity. In conclusion, DSD is a suitable experimental design for the early-stage cell culture process development if quadratic effects might exist. Statistical models derived based on DSD-based dataset could be applied for predictive optimization of antibody producing bioprocess while regularities such as effect heredity and effect hierarchy might be relaxed considering higher-order interaction effects are more likely to existed for a cell-based biological system.

Construction of mixed-level fractional factorial split-plot designs with combined minimum aberration

Running agricultural experiments in split-plot configurations is an efficient way to estimate main-effect contrasts with higher precision. In a fractional factorial split-plot design, the hard-to-vary factors are called whole-plot (WP) treatment factors and the easy-to-vary factors are called subplot treatment factors. Yan and Zhao (2022) proposed the combined minimum aberration criterion of WP (WP-MAc) for mixed-level split-plot designs. This article studies the construction methods of the WP-MAc 2 ( n 1 + n 2 ) − ( k 1 + k 2 ) 4 1 designs with four-level factor in subplot. Some examples are given to illustrate the theories. Finally, the results of 8, 16, 32, 64 runs WP-MAc 2 ( n 1 + n 2 ) − ( k 1 + k 2 ) 4 s 1 designs are tabulated for possible employ by practitioners.

Alta producción de ácido cítrico en fermentación en estado sólido por Aspergillus brasiliensis sobre espuma de poliuretano

A statistical approach based on fractional and complete factorial designs to increase the citric acid yield was used. Polyurethane foam (PUF) was used as inert support for solid-state fermentation (SSF) due to its high-water retention capacity (up to 60-fold of its weight), resulting in the recovery of concentrated citric acid by squeezing it. The maximum yields for citric acid (0.62 Cmol/Cmol glucose) and polyols (0.11 Cmol/Cmol glucose) are obtained by growing Aspergillus brasiliensis in a well-defined culture medium (at 30°C for 120 h). Citric acid, polyols, and glucose consumption are negatively affected by a high glucose concentration (250 g/L). In contrast, enrichment of the culture medium with yeast extract only enhances citric acid production yield (0.54 Cmol/Cmol glucose). This study demonstrates that the citric acid production yield is negatively affected by phosphate (> 4.54 g/L) and magnesium (> 0.26 g/L). The PUF for SSF is an inexpensive and useful support for the commercial production of citric acid. The utilization of low-cost inert supports through SSF can contribute to achieving industrially viable and sustainable citric acid production. As far as we know, this work reports the highest citric acid production yield using SSF on an inert support such as PUF soaked with a defined medium.

Implementation of the QbD Approach to the Development and Validation of an Analytical Method for Alpha-beta Arteether

Background: The development of effective, cost-effective, robust, sensitive, and specific analytical techniques for the analysis of drug(s), degradation product(s), and contaminants in dosage forms and biological samples is constantly required as part of the pharmaceutical product life-cycle. The adoption of systematic analytical development methodologies such as quality by design (QbD) is particularly advantageous for enhancing method performance since analytical method development encompasses a number of variables that are significant in explaining variability in method performance. Analytical Quality by Design (AQbD) is a standardised method to process validation that covers all aspects of an analytical procedure. It comprises determining the analytical target profile (ATP), identifying critical method parameters or variables, and selecting critical method attributes (CMAs) or qualities. Objective: Spectroscopic and chromatographic methods were developed, conferring the Quality by Design (QbD) tactic as per ICH Q8(R2) guidelines for analytical method development of α-β-arteether. Methods: Understanding dependent variables, various factors, and their interaction effects through a desired series of experiments on the answers to be examined is referred to as QbD. Various variable factors were detected using the Ishikawa diagram. As a result, many essential factors for chromatography methods were investigated. A desired set of experiments on the answers to be evaluated was used to comprehend dependent variables, various factors, and their interaction effects using Design-Expert software version 13. Statistical research such fractional factorial designs and Plackett-Burman were employed for this. The QbD methodology was used to establish a durable, precise, and accurate HPLC analytical method for arteether. Result: Using Design Expert 13's statistical software, the findings of the Plackette Burman research were studied, and the influence of each parameter on the answers was analysed using an overlay plot. Mobile phase (Acetonitrile: water), column C18250nmX4.6mm, column temperature 300 οC, wavelength: 254 nm, injection volume 20l/min, run time 10 mins, detector waters 2489 UV/Visible detector, retention time 4.149 are among the critical parameters estimated for the development of an analytical method for α,β- arteether. Conclusion: The analytical method developed by the QbD approach was validated according to ICH Q2(R1) guidelines, and it was found that the developed analytical method is robust and specific.

Novel experimental design paradigm for development of eco-friendly gradient chromatographic method for simultaneous determination of metronidazole and spiramycin.

This work describes the innovative experimental design-assisted development of a green gradient chromatographic method for concomitant analysis of metronidazole (MTR) and spiramycin (SPR). Two different designs including fractional factorial and Box-Behnken designs were implemented for screening and optimization steps, respectively. The optimum chromatographic conditions involved a mobile phase consisting of ethanol and 20mM sodium dihydrogen phosphate solution (pH adjusted to 2.5) in the ratio 2:98 (v/v) for 2 min then the ratio changed to 30:70 (v/v). The flow rate was 1.3mL/minute. Separation and analysis were performed on X-bridge C18 (150mm × 4.6mm × 3.5μm) column with diode array detector set at 230nm. Column oven temperature was 40°C. A linear response was acquired over the range of 5-125μg/mL for both drugs. Detection and quantitation limits were 0.86 and 2.62μg/mL for MTR and 0.92 and 2.83μg/mL for SPR, respectively. The method was implemented for determination of both drugs in three tablet formulations. The method was proved to be green as evaluated by three assessment tools. The application of experimental designs assists in development of a robust green chromatographic method in gradient elution mode for determination of both drugs within reasonable time.

Bayesian-inspired minimum contamination designs under a double-pair conditional effect model

In two-level fractional factorial designs, conditional main effects can provide insights by which to analyze factorial effects and facilitate the de-aliasing of fully aliased two-factor interactions. Conditional main effects are of particular interest in situations where some factors are nested within others. Most of the relevant literature has focused on the development of data analysis tools that use conditional main effects, while the issue of optimal factorial design for a given linear model involving conditional main effects has been largely overlooked. Mukerjee, Wu and Chang [Statist. Sinica 27 (2017) 997–1016] established a framework by which to optimize designs under a conditional effect model. Although theoretically sound, their results were limited to a single pair of conditional and conditioning factors. In this paper, we extend the applicability of their framework to double pairs of conditional and conditioning factors by providing the corresponding parameterization and effect hierarchy. We propose a minimum contamination-based criterion by which to evaluate designs and develop a complementary set theory to facilitate the search of minimum contamination designs. The catalogues of 16- and 32-run minimum contamination designs are provided. For five to twelve factors, we show that all 16-run minimum contamination designs under the conditional effect model are also minimum aberration according to Fries and Hunter [Technometrics 22 (1980) 601–608].

Fast construction of efficient two-level parallel flats designs

Two-level parallel flats designs (PFDs) are nonregular designs that retain some of the simplicity of regular fractional factorial designs. PFDs have many desirable properties, such as flexible run sizes and block diagonal information matrices. In this article, we develop a fast algorithm for constructing efficient two-level PFDs, optimizing the parallel flats structure via a novel application of coordinate exchange. The resulting designs fill gaps among existing nonregular designs and outperform many comparably-sized designs in terms of G- and G2-aberration. An efficient implementation of the proposed algorithm in Matlab and GNU Octave can be found in the online Supplementary Material. Several new designs with desirable properties are generated and tabulated.

Examining the impact of nanoplastics and PFAS exposure on immune functions through inhibition of secretory immunoglobin A in human breast milk

Emerging contaminants such as nanoplastics (NPs) and per- and polyfluoroalkyl substances (PFAS), have been detected in the environment and breast milk, thus exposing infants to potentially harmful chemicals during breastfeeding. Breast milk contains secretory immunoglobulin A (SIgA), an antibody that plays a vital role in disease protection and the development of the infant's immune system. This study employed molecular simulation and fractional factorial designs to assess the toxicity of NPs and PFAS on breast milk and their influence on infant immunity by inhibiting SIgA. The research found that NPs and PFAS have higher binding affinities to SIgA compared to the control compound. Polycarbonate (−10.7 kcal/mol) had the highest binding affinity among plastics, while Perfluorodecanoic acid (PFDA, - 8.0 kcal/mol) had the highest binding affinity among PFAS. The relative toxic index was higher for PFAS (2.4) than for plastics (1.9), suggesting that PFAS may pose a higher overall toxicity burden on the protein. The presence of specific combinations of NPs and PFAS in breast milk may potentially harm breastfeeding infants, although additional experimental studies are required to validate these findings. These results underscore the potential risks associated with these emerging contaminants in breast milk and their impact on infant immunity.

Three-level saturated orthogonal arrays with less β-wordlength pattern

Saturated orthogonal array is an important type of fractional factorial designs in experimental design. On the basis of guaranteeing orthogonality, it maximizes the number of factors and saves the cost of experiments. Therefore, it is increasingly used in practical experiment. For quantitative factors, the minimum β-aberration criterion is suitable for selecting good designs under a polynomial model. However, construction methods of designs with less β-aberration have not been fully investigated. In this article, we apply the Rao-Hamming method to construct a class of three-level saturated orthogonal arrays, and perform a special level permutation on the designs of the Rao-Hamming construction, which makes the resultant designs mirror-symmetric ones. Furthermore, we analyze the distribution of elements in each row and among all possible pairs of rows of the mirror-symmetric designs, and discuss some properties of the β-wordlength pattern for three-level mirror-symmetric designs constructed by the Rao-Hamming method. In addition, we provide the explicit expressions of β 3 and β 4 for three-level mirror-symmetric designs, which can reduce the computational complexity of the β-wordlength pattern, and provide an effective idea for finding designs under the minimum β-aberration criterion. Finally, numerical examples are used to illustrate and verify the results.

Optimal two-level regular fractional factorial split-plot designs when the effects of subplot factors are more important

Optimal two-level regular fractional factorial split-plot designs when the effects of subplot factors are more important

Enumeration of regular fractional factorial designs with four-level and two-level factors

Abstract Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalogue of designs with two-level factors as well as four-level factors. To create the catalogue, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of nonisomorphic designs. Finally, we use the most efficient method to generate a catalogue of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalogue by revisiting the motivating examples.

Individual Word Length Patterns for Fractional Factorial (Split-Plot) Designs

Individual Word Length Patterns for Fractional Factorial (Split-Plot) Designs

Is designed data collection still relevant in the big data era? – A discussion

Is designed data collection still relevant in the big data era? – A discussion

A class of space‐filling designs with low‐dimensional stratification and column orthogonality

AbstractStrong orthogonal arrays are suitable designs for computer experiments because of stratification in low‐dimensional projections. However, strong orthogonal arrays may be very expensive for a moderate number of factors. In this article, we develop a method for constructing space‐filling designs with more economical run sizes. These designs are not only column‐orthogonal but also enjoy a large proportion of low‐dimensional stratification properties that strong orthogonal arrays ought to have. Moreover, a class of proposed designs can be 3‐orthogonal. In addition, some theoretical results on regular fractional factorial designs are obtained as a by‐product.

A Note on Early Termination in the 2^(k-p) Designs

A complete factorial experiment can resolve problems that occur in experiments that to determine suitable tolerances for the factors in a manufacturing process. Two-level fractional factorial designs have been widely used to investigate the effect of factors in which several factors are involved. In many circumstances, the experiment may be stopped before all the points have been run. This article argues that one should not arrange the points of the experiment in random order. Instead, one should consider adjusting the run order to protect against the risk of early termination, that is, a systematic run order should be carefully applied to the case. In this article, we will use semi-folding design as examples to illustrate the idea of how to take advantage of the sequential run order.

Construction of Split-Plot Designs with General Minimum Lower Order Confounding

Fractional factorial split-plot design has been widely used in many fields due to its advantage of saving experimental cost. The general minimum lower order confounding criterion is usually used as one of the attractive design criterion for selecting fractional factorial split-plot design. In this paper, we are interested in the theoretical construction methods of the optimal fractional factorial split-plot designs under the general minimum lower order confounding criterion. We present the theoretical construction methods of optimal fractional factorial split-plot designs under general minimum lower order confounding criterion under several conditions.

Optimisation of data acquisition towards continuous cardiac Magnetic Resonance Fingerprinting applications

PurposeAssess and optimise acquisition parameters for continuous cardiac Magnetic Resonance Fingerprinting (MRF). MethodsDifferent acquisition schemes (flip angle amplitude, lobe size, T2-preparation pulses) for cardiac MRF were assessed in simulations and phantom and demonstrated in one healthy volunteer. Three different experimental designs were evaluated using central composite and fractional factorial designs. Relative errors for T1 and T2 were calculated for a wide range of realistic T1 and T2 value combinations. The effect of different designs on the accuracy of T1 and T2 was assessed using response surface modelling and Cohen’s f calculations. ResultsLarger flip angle amplitudes lead to an improvement of T2 accuracy and precision for simulations and phantom experiments. Similar effects could also be shown qualitatively in in-vivo scans. Accuracy and precision of T1 were robust to different design parameters with improved values for faster flip angle variation. Cohen’s f showed that T2-preparation pulses influence the accuracy of T2. The number of pulses used is the most important parameter. Without T2-preparation pulses, RMSE were 3.0 ± 8.09 % for T1 and 16.24 ± 14.47 % for T2. Using those pulses reduced the RMSE to 2.3 ± 8.4 % for T1 and 14.11 ± 13.46 % for T2. Nonetheless, even if the improvement is significant, RMSE are still too high for reliable quantification. ConclusionIn contrast to previous study using triggered MRF sequences using < 30° flip angles, large flip angle amplitudes led to better results for continuous cardiac MRF sequences. T2-preparation pulse can improve the accuracy of T2 estimation but lead to longer scan times.

Efficient Blocked Fractional Factorial Designs for Stated Choice Experiments of Size Two and Four

Stated choice experiments are increasingly becoming popular due to their ability to optimize information gain with limited resources. Many designs have been developed for the selection of various attributes and their levels to form choice sets. One such design is blocked fractional factorial design (BFFD). Stated choice experiments for symmetric attributes of 4 choice sets of sizes 2 and 4 and 8 choice sets of sizes 2 and 4 were developed using BFFDs. Generators for the stated choice set of sizes 2 and 4 with resolution three, four, and five were developed. The alias structures and confounding effects for the designs were derived, as well as their clear effects if any for estimation. The A‐efficiency was used to compute the efficiencies of the proposed designs since it has better statistical properties. The computed efficiencies for the proposed designs reveal that 4 choice sets of size 4 designs are more efficient. Finally, a practical application of the proposed method was carried out for four choice sets of size 4 using design with attributes and levels of service quality in public transport.

Level permutations and factor projections of multiple quadruple designs

One of the motivating forces for the current surge of interest in non-regular fractional factorial designs (non-RFrFDs) is that they have partially aliased effects that can be estimated together. Thus, from some estimation perspectives, non-RFrFDs outperform their regular counterparts that have either fully aliased or orthogonal effects. Elsawah (Communications in Mathematics and Statistics 10:623-652, 2022) presented a novel class of four-level non-RFrFDs, called multiple quadruple designs (MQDs), that are attractive from the practical perspective due to their structural and analytical simplicities. Level permutations and factor projections are widely used techniques for improving the eligibility and estimation efficiency of non-RFrFDs that are desirable for factor screening. This paper investigates the potential benefits of level permutations and factor projections for improving the performance of the MQDs in the full-dimension and any low-dimension and constructing new non-isomorphic four-level non-RFrFDs. The results provide theoretical benchmarks and conditions for improving the efficiency of the MQDs and constructing non-isomorphic MQDs. The efficiency is investigated in view of the widely used optimality criteria and modeling performance. The main numerical results show that the generated designs provide good representative points for the experimental domains that help investigators to effectively design and model high-dimensional experiments without prior assumptions about the forms of their underlying models.

Minimum Cost Trend-Free 2n−(n−k) Fractional Factorial Designs of Resolution IV Derivable from the Normalized Sylvester-Hadamard Matrices

Minimum Cost Trend-Free 2n−(n−k) Fractional Factorial Designs of Resolution IV Derivable from the Normalized Sylvester-Hadamard Matrices