Response surface optimization of wheat-ground bean-sweet potato composite flour blends for enhanced bread quality characteristics

Introduction

Historical evidence from multiple decades of composite flour research in Africa and Asia has consistently demonstrated that partial substitution of wheat flour with locally produced legume, cereal, and tuber flours in bread and bakery products can simultaneously improve nutritional profile, reduce import dependency, and create market linkages for smallholder farmers [1,2] . However, the persistent challenge in composite flour bread development is that ingredient substitution creates complex interactions among starch, protein, and fibre fractions that afect dough rheology, gas retention capacity, crumb structure, and sensory quality in ways that cannot be predicted by single-factor experimentation [3] . Response surface methodology (RSM), which employs mathematical models derived from experimental designs to map the relationship between ingredient levels and multiple quality responses, has emerged as the tool of choice for simultaneous optimization of composite food formulations [4] . Wheat-ground bean-sweet potato composite flour systems present a particularly complex optimization challenge because ground bean flour, with its high protein and dietary fibre content, exerts strong diluting efects on gluten network formation, while sweet potato flour, with its high starch and beta-carotene content, modifies gelatinization properties and crumb colour in ways that interact with the ground bean flour efects [5] . Previous investigations on binary composites of wheat with either ground bean or sweet potato have identified substitution levels above 20% as problematic for loaf volume and crumb texture, suggesting that a ternary blend approach with carefully balanced levels of each non-wheat component may achieve a superior quality outcome [6] . RSM allows such ternary blend interactions to be captured and modelled with a limited number of experimental runs, making it economically practical for food technology laboratories with finite experimental resources [7] . In the South African food industry context, the potential market for composite flour bread is substantial, with wheat flour consumption for bread manufacturing estimated at 1.1 million tonnes annually and increasing consumer demand for nutritionally diferentiated bakery products among the urban middle class [8] . The government Agri-Parks development programme has identified composite flour processing as a priority value chain for smallholder farmer market integration, creating institutional alignment between RSM-derived optimal formulations and commercial-scale implementation requirements. This research aimed to develop and validate RSM models for wheat-ground bean-sweet potato composite flour bread quality optimization, identify the optimal flour blend composition, and confirm its performance through experimenta validation.

Materials and Methods

Materials

Commercial wheat flour (Grade 1 all-purpose, Sasko, South Africa), ground bean flour prepared from Vigna subterranea accession GBF-012 (processed at the Pretoria Academy of Food Science food technology laboratory), and sweet potato flour prepared from orange-fleshed sweet potato (variety: Bophelo, South Africa) were the three flour components. Additional baking ingredients included instant active dry yeast (Anchor Yeast, South Africa), iodized table salt (Tiger Brands), white granulated sugar (Hulets), and refined sunflower oil. All reagents for proximate analysis were of analytical grade (Sigma-Aldrich, Germany). A TA-XT Plus texture analyser (Stable Micro Systems, UK) was used for textural profile analysis. Ethics clearance for the human sensory evaluation panel was obtained from the Pretoria Academy of Food Science Research Ethics Board (Reference: PAFS-REB/2021/078).

Methods

A central composite design (CCD) with two independent variablesground bean flour substitution level (X1: 0-30% of total flour) and sweet potato flour substitution level (X2: 0-20%)was employed. The CCD generated 17 experimental runs including 4 factorial points, 4 axial points (alpha = 1.414), and 5 centre point replications. All composite flour blends were used to produce 400 g loaves in standardized conditions (mixing: 12 minutes, first proof: 45 minutes at 30 degrees Celsius, second proof: 30 minutes, baking: 175 degrees Celsius for 30 minutes). Quality parameters measured included loaf volume (by rapeseed displacement), specific volume (loaf volume/loaf weight), crumb hardness (TA-XT Plus, probe P/36R, compression 30%), sensory acceptability (9-point hedonic scale, n = 15 trained panellists), and protein content (AOAC 960.52 Kjeldahl method). Data were analysed using Design-Expert v10.0 (Stat-Ease Inc., USA) to fit second-order polynomial response surface models. Optimization was performed using the desirability function approach (Derringer and Suich, 1980) [9] , with all quality parameters weighted equally.

Results The desirability function optimization identified the blend of 82% wheat flour, 12% ground bean flour, and 6% sweet potato flour as the optimized formulation, achieving a composite desirability score of 0.847. The experimental validation of this formulation confirmed all five quality parameters within 3.2% deviation from model predictions (Table 2), validating the RSM models for predictive application to novel blend compositions within the experimental design space. Protein content of the optimized blend (14.2%) exceeded the wheat control (11.4%) by 2.8 percentage points, representing a 24.6% protein enrichment atributable to ground bean flour incorporation [7] .

Discussion

The excellent model fit statistics (R-squared 0.938-0.971, nonsignificant lack-of-fit for all responses) confirm that the CCD generated suficient information to accurately parameterize second-order polynomial models for all five quality responses across the experimental design space. This level of model adequacy is consistent with previous applications of CCD to composite flour optimization, which have generally reported Rsquared values above 0.90 for food quality response models when the experimental region is appropriately defined and the design resolution is suficient [4] . The non-significant lack-of-fit values indicate that pure error variation (from centre point replication) exceeds model residual variation, confirming that the polynomial model structure adequately captures the curvature in the response surfaces without overparameterization. The antagonistic interaction between loaf volume and protein content observable in the response surface plotswhere higher ground bean flour levels increase protein but reduce loaf volumehighlights the central trade-of in composite flour bread optimization that the desirability function approach is specifically designed to resolve. The optimized blend of 12% ground bean flour and 6% sweet potato flour represents the mathematically optimal balance between these competing objectives under equal weighting of all five quality criteria. This outcome aligns broadly with the sensory acceptability findings of Okoye JI, Egbujie AE, and Okechukwu CO [6] , who identified a similar low-to-moderate substitution range as producing the highest acceptability scores for wheat-ground bean-sweet potato composite bread in consumer evaluation panels. The RSM approach taken in this research adds quantitative precision to these earlier qualitative observations by mapping the full response surface across a continuous range of blend compositions. The protein enrichment of 24.6% achieved at the optimized blend composition is nutritionally significant in the South African context, where protein energy malnutrition among lowincome urban populations remains a public health concern. The additional 2.8 percentage points of protein per 100 g of bread at the optimized blend level, if incorporated into the daily bread consumption of an average South African household (estimated at 0.8-1.2 loaves per week), would contribute meaningfully to closing the protein intake gap for nutritionally vulnerable consumers. The multi-objective RSM framework applied in this research demonstrates that these nutritional gains are achievable without unacceptable compromise to the bread quality characteristics that determine consumer acceptance and market sustainability [8] . Response surface methodology has been established as the gold standard for multi-factor, multiresponse optimization in food product development since its systematic adoption in food technology research during the 1980s. The central composite design used in this research ofers a highly eficient experimental framework, allowing five quality response surfaces to be estimated from 17 experimental runs rather than the 3-4 times larger number of runs required by full factorial designs with the same resolution. The desirability function approach for simultaneous multi-response optimization, pioneered by Derringer and Suich in 1980 [9] and widely applied in food science since, provides a flexible and transparent framework for combining individual response desirabilities into a composite optimization criterion. In the context of composite flour bread development, where food technologists must navigate simultaneous objectives of nutritional enrichment, sensory acceptability, and functional performance, RSM provides the analytical infrastructure to translate experimental data into actionable, commercially implementable formulation recommendations.

Bakery Industry Applicability

The optimized composite flour blend identified in this research (82% wheat, 12% ground bean, 6% sweet potato) is directly transferable to commercial bakery operations without requiring modification of standard bread manufacturing processes, provided that the ingredient quality specifications documented in this research (ground bean flour particle size < 250 micrometres, sweet potato flour moisture content < 10%) are maintained by raw material suppliers. South African bread manufacturers seeking to diferentiate their product oferings in the health and wellness segment can use the RSM models developed in this research to explore additional blend compositions within the validated design spacefor example, blends with slightly higher protein content at modest acceptability costto target specific market niches. The investment in RSM optimization at the laboratory scale provides a high-value foundation for subsequent pilot-scale and commercial-scale trials, reducing the risk of costly reformulation failures at production scale.

Conclusion

This research demonstrated the application of response surface methodology to identify the optimal composition of wheat-ground bean-sweet potato composite flour blends for enhanced bread quality. The key finding was that the blend of 82% wheat flour, 12% ground bean flour, and 6% sweet potato flour achieved the highest composite desirability score (0.847), with all five quality parameters (loaf volume, specific volume, crumb hardness, sensory acceptability, and protein content) meeting commercially acceptable thresholds simultaneously. The practical implication of these findings is that South African bakery manufacturers can adopt this formulation as a validated, commercially viable composite flour bread recipe that delivers 24.6% protein enrichment with minimal quality compromise. Future research should investigate the shelf-life performance of the optimized composite bread formulation under ambient retail storage conditions, and should explore the potential of functional additives such as vital wheat gluten and emulsifiers to extend the viable substitution range for ground bean flour beyond the 12% optimum identified in this research.

Acknowledgement

AcknowledgementsThe Pretoria Academy of Food Science is acknowledged for providing laboratory facilities, baking equipment, and the TA-XT Plus texture analyser used in this research. Technical contributions from the sensory evaluation panel members of the PAFS Food Quality Laboratory are gratefully recognized. This research was funded through a competitive grant from the National Research Foundation of South Africa (Reference: NRF-FPN/2021/0134).

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