Case Background
Globally, child malnutrition remains a serious problem. According to statistics, approximately 51 million children worldwide are affected by wasting, of which nearly 17 million children suffer from severe wasting ( FAO, IFAD, UNICEF, WFP, & WHO, 2017 ). 5.9 million children under the age of five die each year, half of whom die from malnutrition ( UNICEF, 2016 ). To address this challenge, Ready-to-Use Therapeutic Food (RUTF), a high-energy, micronutrient-rich paste-like food, is widely used in the Community-based Management of Acute Malnutrition (CMAM) of children under five years of age in low-income countries. RUTF can be provided directly to children without clinical complications at home, avoiding hospitalization.
However, the current mainstream formulation of RUTF is affected by some ingredient issues, such as the high cost of skimmed milk powder, the nutritional properties of palm oil, and the allergenicity of peanuts.
Therefore, the case we are going to discuss this time is an interpretation of a food research paper from Food and Bioproducts Processing. It will introduce how to combine D-optimal mixture design (DOE) with functional data analysis (FDA) to develop alternative ready-to-use therapeutic foods (RUTF) for treating childhood malnutrition, optimize the particle size distribution (PSD) curve and apparent viscosity curve of food suspensions, and determine the design space of the formula based on the QbD concept. The case aims to develop an alternative RUTF formulation using low-cost local ingredients that are easily available in low-income countries to improve quality and acceptability and meet the nutritional needs of children.
The main ingredients of the widely used commercial RUTF Plumpy'Nut® include: peanut butter, flour, sucrose, palm oil, sunflower oil, skimmed milk powder, minerals and vitamins (A, C, D, E, B1, B2, B6, B12, biotin, folic acid, pantothenic acid and niacin), with an average macronutrient content of 36% lipids, 14% protein and about 43% carbohydrates (500 kcal per 92 g package).
The main ingredients that replaced the RUTF suspension formulation in this study included: lipid phase (sunflower oil and soy lecithin), flour mixture (hulled and toasted soy flour and sorghum flour), powdered sugar, and Spirulina microalgae dry powder. Shelled and roasted soybeans and sorghum are used as protein sources, powdered sugar is used as a glucose source, sweetener and filler, sunflower oil is selected for its availability, technological properties and nutritional properties, and spirulina microalgae powder ensures adequate micronutrients.
Case Study
Analytical methods
Use D-optimal mixture design to generate a formula to replace RUTF suspension, apply functional data analysis to fit the particle size distribution (PSD) curve and apparent viscosity curve, extract the functional principal components (FPC) of the curve as responses, and establish a regression model of the functional principal components and the proportion of formula components. Combine the regression model with the functional data prediction formula, and establish the connection between the curve-type response data and the formula mixing factor. Finally, determine the design space of the formula based on the constraints of the target curve, as shown in the figure below.
Experimental design: Using D-optimal mixture design to explore the effects of three ingredients on food properties
- Factor variables: ratio of flour (x1), lipid phase (x2) and powdered sugar (x3). Spirulina powder was used as a constant ingredient (3%).
- Response variables: Particle size distribution (PSD) and apparent viscosity curve.
The effect of ingredient ratio on formulation properties was investigated using a D-optimal mixture design. The experimental design included three mixing factors: the ratio of flour (x1), lipid phase (x2) and icing sugar (x3), where x1+x2+x3=1 . As for Spirulina powder, it was not included in the mixing design because it was kept constant at 3% (w/w) throughout the design.
The lipid phase, mixed flour and powdered sugar accounted for 97% of the final suspension and was varied in 20 recipes. The low and high levels of blending factors, 0.30–0.40 g/g, 0.25–0.35 g/g, and 0.25–0.35 g/g, corresponding to x1, x2, and x3, respectively, were initially selected based on suspension workability and specific nutritional requirements of the RTU. A special cubic model was selected as the regression model and five replicates were set, thus generating a total of 20 alternative RUTF suspension formulations.
(Table 1) reports the formulation design solution generated by JMP.
(Table 1) D-optimal mixture design used in this study
x1, x2 and x3 represent the mass fractions of mixed flour, lipid phase and powdered sugar, respectively.
FPC1-oversize represents the FPC score of the oversize vs. log-transformed class sizes function data
FPC1-viscosity represents the FPC score of the log-transformed viscosity vs. log-transformed shear rate function data
The order of experiments was completely randomized to avoid systematic bias. For each formulation, the rheological curve and particle size distribution were the averages of three and two replicate measurements, respectively. Particle size distribution (PSD) and apparent viscosity curves are functional response data, and the test results are shown in (Figure 1).
Figure 1 Particle size distribution (a) and apparent viscosity curve (b) of suspensions with different components
Function data analysis
In a previous study2, to characterize the particle size distribution (PSD) curves and apparent viscosity curves of food suspensions, the curve data were statistically analyzed using scalars, and then the scalar statistics were regressed on the mixture components as responses. However, simplifying the curve characteristics into a scalar description will lose the information of the curve data and affect the modeling effect.
Functional Data Analysis [ii] (FDA) is particularly suitable for processing functions, signals, spectra or time series data . It creates a functional model by fitting the data with B-spline, P-spline, Fourier or wavelet basis function models to achieve curve fitting, and achieves dimensionality reduction of curve data by extracting functional principal components (FPC)1. In this study, the response data of the particle size distribution curve and the apparent viscosity curve were transformed, fitted by B-spline (as shown in Figure 2), and functional principal component analysis (FPCA) was performed. The first principal component FPC1 of FPCA (as shown in Table 1) explains approximately 99% and 88.5% of the variation in the oversize and viscosity curve data, respectively, and can fully describe the information contained in the curve data. The principle of function data analysis is shown in the Appendix Formula (1) and Formula (2).
Figure 2 Functional data analysis of experimental design curve response (coordinate axes were natural logarithmic transformed)
Regression Modeling
The function principal component scores FPC1-oversize and FPC1-viscosity were respectively used with the mixture components to construct the regression model of the mixture response surface, which was then used to predict the particle size distribution (PSD) and apparent viscosity curve. The mixture response surface model is shown in Appendix Formula (3).
As shown in Table 2, the regression model has a high goodness of fit for the prediction of PSD and apparent viscosity curves (R² values are 0.87 and 0.75, respectively). As shown in Figure 3, the predicted values are consistent with the actual values.
Table 2 Summary of functional principal component (FPC) and mixture component regression modeling statistics
Coefficient estimates and standard errors (SE) for mixture response surface models, t0 values and corresponding p-values (Prob>|t0|), R2, root mean square error (RMSE), p-value for lack-of-fit test (p-valueLoF), and number of observations for the FPC scores calculated for the first principal component of the oversize and viscosity function data
Figure 3. “Predicted value - actual value” diagram of functional principal component (FPC1) and mixture component regression modeling
By analyzing Table 1 and Figure 1 , it can be understood that the FPC1 score is negatively correlated with its corresponding functional response. Therefore, as FPC1 increases, oversize and viscosity decrease. As shown in the mixture profiler in Figure 4, moving from the upper corner to the lower corner at the right edge of the white triangle, the FPC1 scores of oversize and viscosity increase, resulting in a decrease in oversize and viscosity, which is consistent with the target optimization direction of the formulation design space.
Figure 4 Functional principal component (FPC1) and mixture component regression modeling mixture profiler
Model Evaluation
The mixture response surface model can predict the FPC1 score based on the mixture ingredient formula (Formula 3), and the functional data analysis model can predict the curve data Y value based on the FPC1 score (Formula 2). Combining the two, the corresponding relationship between the formula and the curve response can be established, and the oversize and viscosity curve responses of different formulas can be predicted through the model. The results in Figure 5 show that the predicted curve is highly consistent with the experimental data, proving the effectiveness of the model.
Figure 5 Comparison of the curves predicted by the FPC1 regression model in formula (2), formula (3) and Table 2 with the actual test data
Determine the design space
Design Space is a core component of the Quality by Design (QbD) concept and refers to the range of parameters that meet specific constraints. Through the design space, the optimal formula can be determined, and the operating conditions can be flexibly adjusted within the allowable range to ensure that the product meets the quality requirements.
The constraints of this study are:
Particle size distribution (PSD): At class size 45 or 50 μm, oversize is less than 10% to ensure a delicate taste of the product.
Apparent viscosity curve: At a shear rate of 2 s−1, the apparent viscosity should be lower than 60 Pa·s to ensure the extrudability and easy swallowing of the product.
The model constructed by combining the above experimental design with functional data analysis can predict the particle size distribution (PSD) and apparent viscosity curve corresponding to different suspension formula component ratios. Based on the above constraints, the design space of alternative RUTF formulations can be determined, as shown in the white area in Figure 6 .
Figure 6 Design space of oversize and apparent viscosity as mixture composition changes
The class size was kept at 45 μm (a) or 50 μm (b) and the shear rate was kept at 2 s−1
The white area corresponds to feasible experimental conditions that keep the oversize below 10% and the apparent viscosity below 60 Pa·s.
Case Conclusion
Design of experiments (DOE) combined with functional data analysis (FDA) provides an efficient method for analyzing curvilinear responses to study the particle size distribution (PSD) and apparent viscosity curves of alternative RUFT suspensions as a function of formulation, and ultimately determine the design space that meets product requirements. By developing alternatives to RUFT and using low-cost and easily available local ingredients to reduce production costs, the popularity of RUTF can be increased and children's nutrition and health can be protected.
Case extension
In food development, more and more complex instruments and curve data are used for product characterization in food formulation and process development, such as particle size distribution, rheological curves, kinetic data, dynamic sensory curves, and spectral curves (spectra, chromatography, mass spectrometry, and nuclear magnetic resonance spectra). Classical analysis methods only consider scalar responses, which loses information in the curve data. Functional data analysis can maximize the retention of information in the curve, while achieving dimensionality reduction through functional principal component analysis. On this basis, experimental design can be combined to directly study the relationship between curve response and formula ingredients or process parameters, establish a predictive model and determine the design space. This method has broad application prospects in curve data analysis in the food industry [iii] [iv] .
The analysis process of the above paper case was based on JMP Pro 15 to implement functional data analysis and modeling. Based on the latest version of JMP Pro 18, the functional design of experiments (FDOE) can be directly used to implement the above analysis more efficiently, build a prediction model between experimental design factors and curve response data, and efficiently optimize the recipe and process parameters according to the target curve. If you want to know more about sensory analysis and formulation optimization in the food and beverage industry, please sign up for the live seminar on March 26 (this seminar will be taught in Chinese) : https://jmp.zoom.us/webinar/register/WN_eEUCWCNfRcKKWG_afonZgg#/registration
*論文來源：Marcello Fidaleo, Nicoletta A. Miele, Vincenzo Armini, Silvana Cavella, Design space of the formulation process of a food suspension by D-optimal mixture experiment and functional data analysis, Food and Bioproducts Processing, Volume 127, 2021, Pages 128-138, ISSN 0960-3085, https://doi.org/10.1016/j.fbp.2021.02.007.[in]
[i] Formula optimization approach for an alternative Ready-to-Use Therapeutic Food - ScienceDirect
[ii] Function Data Analyzer
[iii] Functional Data Analysis and Design of Experiments Applied to Food Milling Proce... - JMP User Community
[iv] Developer Tutorial: Modeling Spectral Data Using JMP Pro 17
[in] Design space of the formulation process of a food suspension by D-optimal mixture experiment and functional data analysis - ScienceDirect
