Kinetics of Wheat–Oat Dough Degradation Under Non-Traditional Farinographic Parameters Linked to Baking Trial Results

Abstract

Recent trends in cereal chemistry emphasize sustainable food systems and functional fortification through upcycling and gluten reduction. This study addresses the challenges of reformulating wheat bakery products with four technologically distinct oat forms at three levels (5, 10, 15% substitution of wheat flour) by focusing on dough’s structural integrity. While conventional farinographic metrics such as Stability (STA) or Degree of Dough Softening (DSD) usually are not able to capture the dynamic fatigue of the gluten–starch matrix of wheat dough, several innovative kinetic descriptors are introduced, e.g., dough development slope angle (DDSA), and the time-resolved of both the dough curve width (DW) and farinograph elasticity loss (FEL) foursomes. Analytical results revealed that fiber-rich oat bran induced a mechanical ‘pseudostabilization’, whereas germinated diastatic malt caused a severe enzymatically driven structural collapse of wheat dough cohesiveness. This degradation was corroborated by a sharp non-linear decline in Falling Number (from 482 s to 196 s) and by a dramatic rise in the DSD/STA ratio (from 6.4 to 149.2). Statistical analysis indicated the proposed descriptors, particularly late-stage DW₁₅–DW₂₀ and FEL₁₅–FEL₂₀, provided more sensitive associations with quality parameters of small round breads baked at a laboratory scale—height, bread slice area, and specific volume—than traditional static indicators of the farinogram. As usual in such cases, a critical threshold of wheat flour substitution was identified at 10–15%. These results demonstrate that time–resolved kinetic modeling of dough elasticity serves as a robust complementary tool for predicting baking performance, enabling the rational optimization of formulations and the prevention of structural defects in industrial production.

1. Introduction

Cereal-based foods represent a cornerstone of human nutrition, with wheat flour serving as the technological and structural foundation of most fermented bakery products [1]. Growing global interest in functional foods and nutritionally enriched cereal products is driven by consumers seeking to prevent lifestyle-related chronic diseases through diet, which has stimulated demand for the partial replacement of refined wheat flour with wholegrain or otherwise nutritionally valuable cereal components [1,2].

Oats (Avena sativa L.) have gained prominence in this context, owing to their distinctive nutritional profile. Compared with wheat, oats provide higher levels of high-quality proteins, lipids rich in unsaturated fatty acids, and, most importantly, soluble dietary fiber in the form of β-D-glucans [3,4]. These compounds are associated with cholesterol reduction, improved glycemic response, and enhanced gut health [5,6], supporting the rising consumer demand for oat-based bakery products [7]. A practical advantage of oats lies in their long-standing incorporation into human diets in the form of flakes and porridge. Consequently, contemporary processes of oat grain transformation into edible raw materials or ready-to-eat foods are well established and safe. In the case of sprouted oat grains, germination protocols may be adapted from brewing technology, enabling processing similar to barley malt.

Despite their nutritional benefits, incorporating oats into wheat dough systems presents significant technological challenges [8]. Oats naturally lack gluten, the key protein network that is essential for gas retention and loaf volume in leavened wheat products. Substituting wheat flour with oat-derived materials therefore disrupts gluten network development and alters dough rheology [9,10,11]. Moreover, various processed forms of oats, wholegrain oat flour, bran, flakes, and germinated grain, differ markedly in particle morphology, hydration properties, and enzymatic activity, resulting in complex and heterogeneous effects on the dough structure [12].

Previous studies consistently report reduced gluten mechanical tolerance, impaired gas-holding capacity, and deterioration of the crumb structure with increasing oat levels, particularly above 10–15% in the recipe [13,14]. These effects arise from a combination of competitive water binding by non-starch polysaccharides [15], mechanical disruption by coarse particles [16], and, in the case of germinated or malted oats, enzymatic degradation of starch and proteins [17,18,19]. Nevertheless, the mechanistic understanding of how individual oat forms influence the time-dependent development and degradation of dough viscoelasticity during mixing and kneading remains insufficient.

For nearly a century, dough rheology has been assessed by traditional farinograph parameters such as water absorption, dough development time, stability, and softening degree [20,21,22,23]. Although suitable for routine quality evaluation, these metrics primarily describe changes in the central line of the farinogram and provide limited insight into the elastic component of dough behavior [24,25]. They lack sensitivity to the gradual loss of gluten elasticity under mechanical stress and do not distinguish between mechanical weakening and enzymatically driven degradation [24,26]. In the Central European practice, this weakening is quantified through the dough softening degree (DSD); within the Hungarian classification system only, the farinograph quality area (FQA) is used additionally (MSZ 6383:2012) [27]. The FQA integrates DSD over time, categorizing wheat flours from ‘Elite’ (A1) to ‘Weak’ (C2) based on their structural stability. Consequently, a critical research gap remains; conventional point-based metrics do not account for the dynamic, time-dependent attenuation of the gluten–starch matrix integrity. This lack of sensitivity to the progressive fatigue of dough elasticity limits the ability to predict the stability of complex composite flour systems during intensive industrial processing.

Recent advances in digitalized farinography now permit the extraction of additional geometric descriptors, particularly the farinograph curve width, which reflects the elastic response of dough to transient deformation [28,29,30]. This approach aligns with dynamic methodologies that evaluate the entire time–consistency curve through an envelope system (upper and lower boundaries like in the case of the mixograph record), rather than relying on a single central line. By analyzing the convergence of these boundaries, it is possible to quantify the real-time fatigue of the dough matrix. Time-resolved monitoring of the curve width offers a unique opportunity to evaluate the gluten network development, fatigue, and collapse as kinetic processes rather than static endpoints [28,30,31,32]. The logic of employing these descriptors lies in their ability to reflect the actual-time fatigue of the gluten–starch matrix, providing a sensitive indicator of structural integrity than the simple central-line torque. However, these non-standard parameters have not yet been applied systematically, and their technological relevance to baking performance remains poorly understood.

Such analyses are particularly relevant for wheat–oat doughs (and, more broadly, wheat-flour-based doughs enriched with non-traditional plant raw materials), where oat components introduce competitive hydration behavior, structural heterogeneity, elevated lipid content, and, depending on processing, enhanced enzymatic activity. These factors generate complex, non-linear viscoelastic responses that are adequately captured by conventional farinograph indicators. A quantitative framework that is capable of distinguishing decelerated gluten development, mechanical fatigue, and enzymatic structural breakdown is therefore required to guide the rational formulation of nutritionally enriched baked products.

This study advances cereal research by systematically evaluating a set of non-traditional farinograph parameters—dough curve width (DW), farinograph elasticity loss (FEL), farinograph quality area (FQA), and dough elasticity area (DEA)—in wheat doughs that are partially substituted with milled oat material in four technologically distinct forms. In addition, two experimentally integrated energy-like areas were compared to the original data rendered by the software of the Brabender company. The oat cultivar ‘Peter’, chosen for its stable nutritional profile, was used to avoid confounding due to genetic variability. By analyzing dough elasticity kinetics under standardized mixing conditions and linking the resulting rheological descriptors to laboratory baking test outcomes, an integrated framework is proposed that connects viscoelastic degradation kinetics with the practical baking quality. This approach provides a deeper mechanistic understanding of the technological limits of wheat fortification with oats.

2. Materials and Methods

2.1. Materials

2.1.1. Control Wheat Flour

Commercial refined wheat flour (WF; Mlyn Pohronský Ruskov, Pohronský Ruskov, Slovakia) was used as the base material. The flour was characterized by an ash content of 0.70%, a crude protein content of 14.7% d.m., a wet gluten content of 34.9%, and a Zeleny sedimentation value of 40 mL. These quality specifications were provided by the producer.

2.1.2. Preparation of Oat Forms and Binary Mixtures

Oat Material Processing

Grains of the Slovak hulled oat variety ‘Peter’ were dehulled at the National Agricultural and Food Centre—Research and Breeding Station at Vígľaš–Pstruša (Slovakia). This material was used to prepare four oat forms:

• Wholegrain flour (WFL): Dehulled grains milled using an ultra-centrifugal mill (ZM 100, Retsch GmbH, Haan, Germany) to granulation ≤500 µm.
• Diastatic malt flour (DMF): Grains soaked in distilled water for 12 h, germinated at 25 °C for 3 days in darkness with daily rinsing, air-dried at 40 °C to 12% moisture, and milled as above.
• Milled flakes (FLA): Commercial fine oat flakes (Mlyn Štúrovo, Štúrovo, Slovakia) disintegrated using the same ultra-centrifugal mill as the dehulled oat grains.
• Oat bran (BRA): Commercial bran purchased from a retail shop (Country Life, Prague, Czech Republic).

When considered in the order WFL, BRA, FLA, DMF, these four forms represent an increasing rate of oat technological processing, which was used in statistical interpretation.

Binary mixtures were formulated by replacing the control WF with each oat form at 5, 10, and 15% (w/w). Homogenization was performed using a horizontal rotational mixer (BS–P06, Mezos, Náchod, Czech Republic) at 100 rpm for 30 min. Samples were coded by oat form and substitution level (e.g., 5WFL, 10WFL, 15WFL); pure WF served as the control. Mixtures were stored in airtight glass containers at 20–23 °C, ~55% RH. The detailed chemical composition of the WF and all 12 binary blends was previously published in Jurkaninová et al. [14].

2.2. Methods

2.2.1. Flour Analytical Characterization

All chemical and physical analyses were performed in duplicate independent runs (N = 2). This approach is in strict accordance with the internal reproducibility requirements of the applied international standards (Standard ISO 5530-1:2013 [33], Standard ISO 5529:2010 [34] and AACC Approved Method 38-12.01 [35]), where the consistency of twin results is a mandatory criterion for data validity. The moisture content was determined gravimetrically using a semi-automatic moisture analyzer (MA 45, Sartorius, Göttingen, Germany) by drying at 110 °C to constant weight following the gravimetric AOAC Official Method 925.10 [36]. The ash content was determined by combustion of 3.0 g samples at 525 °C, AOAC Official Method 923.03 [37]. The total dietary fiber (TDF) was quantified using a Megazyme K–TDFR kit (Megazyme, Wicklow, Ireland), including corrections for residual protein and ash according to the AOAC Official Method 991.43 [38].

The wet gluten content and Gluten Index (GI) were determined using a Glutomatic 2100 system and a CF2015 centrifuge (Perten Instruments, Stockholm, Sweden; nowadays a brand of PerkinElmer, USA). Owing to the examination of high-fiber materials, the process was carried out in two steps with fine and rough sieves, in agreement with the AACC Approved Method 38–12.01 [39]. The protein quality was assessed via the Zeleny sedimentation test (ZET) according to ISO 5529:2010 [34]. The ZET/PROTEIN ratio, serving as a predictor of dough viscoelastic properties (elasticity-to-extensibility ratio), was calculated as described by Hellin et al. [40]; the protein data for this calculation (ranging from 14.43% to 15.09%) were sourced from Jurkaninová et al. [14]. Following the AACC Approved Method 56-81.03 [41], α–amylase activity was estimated as the Falling Number (FN), employing the Falling Number 1000 apparatus (Perten Instruments, Stockholm, Sweden).

2.2.2. Farinograph Analysis and the Dough Curve Modeling

Proposed Descriptive Framework

The modeling of the farinographic curve aims to transform the static point-measurements into time-resolved kinetic descriptors. While conventional parameters focus on torque at specific points and fewer intervals, the set of innovative descriptors introduced here (DDSA, dough curve width DW, farinograph elasticity loss FEL) are designed to quantify the dynamic loss of dough elasticity. By monitoring the DW at several fixed time points, the model captures the progressive fatigue of the gluten–starch matrix. This kinetic approach allows for a clearer distinction between mechanical weakening (typical for bran-rich doughs) and enzymatic structural collapse (typical for diastatic flours).

Standard Farinograph Parameters

The analysis was performed according to international protocols (Standard ISO 5530-1:2013 [33]). The standard parameters, illustrated in Figure 1a (except the first one), include:

• Water absorption (WAB, % of flour weight): Volume of water required to reach consistency 500 Brabender unit, BU.
• Dough development time (DDT, min): From the proof beginning, time to reach maximal consistency.
• Stability (STA, min): Time the curve remains above or at 500 BU.
• Dough softening degree (DSD, BU): Drop in the dough consistency 12 min after the DDT.

Figure 1. Representative farinograph diagram of wheat flour—farinogram; Upper and bottom dotted line of the farinogram—dough curve width, representing its elasticity; The mean line of the farinogram, used for calculations of the traditional (‘static’) farinograph parameters: (a) Standard ‘static’ farinograph features: DDT—dough development time, STA—stability of dough consistency, DSD—degree of the dough softening (read 12 min after max. consistency—ICC 115/1 [42]; BU—Brabender unit), and FQN—farinograph quality number. Innovative supplementary farinograph features (point): DW_t—dough curve width at defined times (at DDT, and at 2, 5, 10, 15, and 20 min of the rheology proof, respectively. (b) Innovative supplementary farinograph features (integrated): DEA—dough elasticity area, and FQE—farinograph quality energy: time–consistency integrals of the selected part of the farinogram [43] and as the total area representing the energy input (a deformation energy), respectively.

Figure 1. Representative farinograph diagram of wheat flour—farinogram; Upper and bottom dotted line of the farinogram—dough curve width, representing its elasticity; The mean line of the farinogram, used for calculations of the traditional (‘static’) farinograph parameters: (a) Standard ‘static’ farinograph features: DDT—dough development time, STA—stability of dough consistency, DSD—degree of the dough softening (read 12 min after max. consistency—ICC 115/1 [42]; BU—Brabender unit), and FQN—farinograph quality number. Innovative supplementary farinograph features (point): DW_t—dough curve width at defined times (at DDT, and at 2, 5, 10, 15, and 20 min of the rheology proof, respectively. (b) Innovative supplementary farinograph features (integrated): DEA—dough elasticity area, and FQE—farinograph quality energy: time–consistency integrals of the selected part of the farinogram [43] and as the total area representing the energy input (a deformation energy), respectively.

Kinetic Modeling of Dough Development

At the onset of the analysis, the dough development slope angle (DDSA or α_slope) was introduced to quantify the kinetics of the initial structuring process. The DDSA is based on a linear regression anchored at the coordinates’ origin [0; 0] and the DDT point (Figure 1a), incorporating a geometric scaling factor:

$$\mathrm{D}\mathrm{D}\mathrm{S}\mathrm{A}={\alpha }_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}}=arctan{\displaystyle \frac{0.2·{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{\mathrm{D}\mathrm{D}\mathrm{T}}}{10·t_{\mathrm{D}\mathrm{D}\mathrm{T}}}} (°)$$

(1)

where CONZ_DDT is maximal mid-line consistency of the farinogram at time of DDT (t_DDT).

The constants k₁ = 0.2 and k₂ = 10 reflect the factual proportion of the x—time and y—consistency axes on the original endless roll of paper—1 min corresponds to 10 mm, while 100 BU corresponds to 17 mm (here rounded up to 20 mm). This adjustment represents a defined standard scale applied uniformly to all samples, ensuring full comparability of the results and the stability of mathematical transformations.

The DDSA can be transformed into the dough development area (DDA; Equation (S2) in the Supplementary Equation Summary), a right-angle triangle representing the ‘hydration void’ and capturing the geometric essence of the energy input Energy_DDT, evaluated by the MetaBridge^® software v. 3.4. The triangle is delimited by the vertical y—axis from the left, α_slope vector and the consistency line 500 BU from above. It can be hypothesized that the DDA, acting as a geometric representation of that ‘hydration void’ and energy input, serves as a predictor for the ‘void fraction’ in the final bread structure (i.e., the total volume of entrapped air).

Time-Resolved Dough Elasticity (DW_t and FEL_t)

The dough elasticity is qualitatively reflected by the vertical bandwidth of the farinograph curve, defined as the dough curve width (DW_t). To characterize the evolution of the viscoelastic properties, the DW values were read at t_DDT, and at 2, 5, 10, 15, and 20 min.

To accurately quantify DW_t at the early stage of the farinograph proof across diverse wheat–oat systems, a trigonometric correction was applied to normalize the width with respect to the hydration kinetics of each sample by using the angle α_slope (Figure 1a).

The corrected width was calculated as follows:

$${\mathrm{D}\mathrm{W}}_{2 \mathrm{c}\mathrm{o}\mathrm{r}\mathrm{r}}=cos·{(\alpha }_{\mathrm{s}\mathrm{l}\mathrm{o}\mathrm{p}\mathrm{e}})·{\mathrm{D}\mathrm{W}}_2 (\mathrm{B}\mathrm{U})$$

(2)

where cos (α_slope) represents the normal projection of DW₂ onto the development vector (perpendicular to the direction of dough development). The rationality of employing this scaling factor lies in its ability to account for the hydration velocity (α_slope). This normalization is necessary to reduce bias caused by rapid polysaccharide swelling in high-fiber systems, which often results in ‘pseudoelasticity’ during the early stages of mixing. By applying the cosine-based correction, we can more effectively differentiate between transient mechanical resistance and true viscoelastic integrity, a principle that is consistent with multivariate modeling of cereal systems [43,44,45].

The subsequent narrowing of the curve reflects the mechanical or enzymatic degradation of the protein network. This ‘elasticity fatigue’ is quantified by the five and four–member series of the farinograph elasticity loss (FEL_t) and eventually by the relative elasticity (RE_t), respectively:

$${\mathrm{F}\mathrm{E}\mathrm{L}}_t={\displaystyle \frac{{\mathrm{D}\mathrm{W}}_{\mathrm{D}\mathrm{D}\mathrm{T}}-{\mathrm{D}\mathrm{W}}_t}{{\mathrm{D}\mathrm{W}}_{\mathrm{D}\mathrm{D}\mathrm{T}}}} (\%)$$

(3)

$${\mathrm{R}\mathrm{E}}_t=100·{\displaystyle \frac{{\mathrm{D}\mathrm{W}}_t}{{\mathrm{D}\mathrm{W}}_{\mathrm{D}\mathrm{D}\mathrm{T}}}} (\%)$$

(4)

where t = DDT, and 2, 5, 10, 15, or 20 min. For this study, the FEL index was employed solely. To account for the rising bandwidth at t ≤ DDT, the order of the terms in the numerator (Equation (3)) was reversed to ‘DW₂ − DW_DDT’, resulting in negative values to indicate the increase in consistency (‘a negative loss’). In the context of cereal rheology, these indices are interpreted as follows:

• Negative FEL index (≤0%): Indicates delayed hydration and slow dough development; optimal curve width is reached only after prolonged kneading.
• Low FEL index (0–15%): Represents superior elasticity and high gluten stability. The matrix resists mechanical stress, making the flour suitable for frozen-dough or long-fermentation processes.
• Medium FEL index (15–30%): Characteristic of standard bread-making wheat; structural weakening remains within acceptable bakery limits.
• High FEL index (>35%): Signifies rapid degradation of the gluten network and a transition to a predominantly plastic state. This results in reduced gas retention, lower loaf volume, and lateral spreading during baking.

For the relative elasticity (RE_t) index, the similar states to the FEL_t are defined as follows:

• RE_t < 100% (pre-DDT): Pre-development stage with ongoing hydration.
• RE_t = 100% (at DDT): Point of peak elasticity and maximum structural integrity.
• RE_t < 100% (post-DDT): Signifies ‘gluten fatigue’ and progressive breakdown of the protein skeleton, often accompanied by the release of previously bound water.

Integrated Areas DEA and FQE

To quantify the cumulative loss of elasticity and total mechanical energy input, numerical integration by a trapezoidal rule was applied to the farinogram boundaries (Figure 1b). The dough elasticity area (DEA) assesses the integrated bandwidth from DDT to t_DDT+12, while the farinograph quality energy (FQE) covers the entire 20 min test:

$$\mathrm{D}\mathrm{E}\mathrm{A}\approx \sum _{t_{DDT}}^{t_{DDT+12}}(t_{i + 1} - t_i)·{\displaystyle \frac{({\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{upper, i}-{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{bottom, i})+({\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{upper, i+1}-{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{bottom, i+1})}{2}} (\mathrm{B}\mathrm{U}·\mathrm{m}\mathrm{i}\mathrm{n})$$

(5)

$$\mathrm{F}\mathrm{Q}\mathrm{E}\approx \sum _{t=0}^{n-\Delta t}(t_{i+1}-t_i)·{\displaystyle \frac{{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{mean, i}+{\mathrm{C}\mathrm{O}\mathrm{N}\mathrm{Z}}_{mean, i+1}}{2}} (\mathrm{B}\mathrm{U}·\mathrm{m}\mathrm{i}\mathrm{n})$$

(6)

where DDT is the dough development time, Δt = 0.03 min, n = 20.00 min, and CONZ denotes the dough consistency of the upper and bottom line on the curve (the farinogram envelope width, BU).

Pseudo-Loss Factor tan δ

In fundamental rheology, the loss factor tan δ describes the viscous-to-elastic ratio of the material tested. In the case of the farinogram, a ‘pseudoloss’ factor could be calculated for two distinct phases:

• tan₁ δ = DW_DDT/STA: Describes network formation and overall quality.
• tan₂ δ = DSD/STA: Reflects the breakdown phase.

2.2.3. Farinograph Quality Area (FQA)

To complete the geometric characterization of the farinogram, the farinograph quality area (FQA) was evaluated according to the Hungarian Standard MSZ 6383:2012 [27].

Geometrically, it is defined as the triangular area bounded by the 500 BU consistency line and the center line of the farinograph curve, spanning from the end of the DDT to the point of the DSD reading (Figure 1a). Values of the FQA obtained from the Brabender MetaBridge^® software were verified by numerical integration according to Equation (5), setting the variable CONZ_upper,i = 500 BU. This crosscheck calculation distinguished between FQA_REAL (cm²) and FQA_INTEGRAL (BU·min).

2.2.4. Bread Preparation and Quality Evaluation

The standardized bread formulation was based on the flour weight (100% basis) and consisted of 5.0% compressed bakery yeast, 1.5% non-iodized kitchen salt, 1.0% sucrose, 1.0% commercial pork lard, and an optimized water dose (55.75–60.95%) required to reach a farinograph consistency of 500 BU.

Dough batches (250 g of flour) were prepared using a professional RM 800 A–B kneader (Gastrolux, Ryomgaard, Denmark). Primary fermentation was carried out at 32 °C for 30 min and 80% RH in a BT 12 thermostat (1–CUBE, Havlíčkův Brod, Czech Republic). After maturation, the dough was manually divided into five equal portions (82.1–84.7 g) and shaped into rounded buns. The final proofing was conducted for 25 min at 32 °C and 70–80% RH.

Baking was performed in a DOMINO steam-injected deck oven (Marton, Bratislava, Slovakia) at 230 °C for 15 min. After cooling for 2 h at room temperature, three standardized buns were selected twice from each five-piece batch for evaluation to minimize the variability caused by manual shaping and outliers. The following parameters were then determined in duplicate, using these representative samples:

• Specific volume: Determined by the rapeseed displacement method (internal repeatability ±15 cm³·100 g⁻¹).
• Shape descriptor (‘vaulting’, ’arching’): Measured using a digital caliper to determine the loaf height and diameter, enabling subsequent calculation of the height-to-diameter ratio (for standard wheat buns, the optimal range is 0.60–0.65).
• Bread slice area: After the bread had cooled and after the above two characteristics had been measured, one bun from each variant was cut vertically with a finely serrated knife and scanned in a printed format on a standard office multifunction device at 200 × 200 dpi. The slice area was then determined using a digital planimeter Plancom KP-92N (Koizumi, Osaka, Japan; [46]).

2.2.5. Statistical Analysis

All analytical, rheological, and baking data were processed using Statistica 13.0 (TIBCO Software Inc., Palo Alto, CA, USA). The effects of two independent factors, Oat form and Oat addition level of the milled oat, were evaluated using Analysis of Variance (ANOVA) followed by Tukey’s HSD test at a significance level of p ≤ 0.05. For the WF control and 12 binary samples tested, the resulting correlation matrix was further processed using an innovative approach based on a direct trigonometric transformation, analogous to the DW₂ → DW_{2 corr} procedure.

This trigonometric transformation was specifically employed to linearize the correlation space and enhance sensitivity among very high values of the Pearson’s correlation coefficient, where standard linear analysis lacks sufficient resolution. To address the non-linear behavior that is inherent to the distribution of the critical correlation coefficient r (derived from Student’s t-distribution for a given significance level α and to enhance the sensitivity to subtle differences (e.g., r = 0.99963 vs. 0.99718 below)), the calculation was performed using the geometric deviation (‘sinus of the angle Θ’) as follows:

$$\mathit{Statistical}\mathit{similarity} = 100 · (1 - \sqrt{sin\left(\Theta \right)}) (\%)$$

(7)

which, for correlation-based data, was transformed into:

$$\mathit{Statistical}\mathit{similarity} = 100 · (1 - \sqrt[4]{(1 - r^2)}) (\%)$$

(8)

where r is the Pearson’s correlation coefficient.

Relationships between qualitative parameters were explored by Principal Component Analysis (PCA). In this explorative statistical method, cosine (Θ) between any two variable/sample vectors originating from the coordinate system center [0; 0] is equivalent to their pairwise correlation coefficient. The PCA was executed, and the resulting plots were compared in two stages:

• Using the standard farinograph parameters (WAB, DDT, STA, DSD, FQA);
• Also incorporating the innovative characteristics (DW, FEL, DEA, FQE, Energy) to evaluate their discriminative power and their functionality in classifying the 13 tested samples.

All Equations (1)–(8) supra are summarized in the additional Excel file ‘Supplementary Equations Summary’ (extended to Equations (S1)–(S12)).

3. Results

The effects of the four technologically distinct oat forms on the analytical properties of the blends, wheat dough rheology, and baking performance were assessed using both standard farinograph parameters and the innovative kinetic descriptors (DW, FEL, FQA, DEA). Considering the pilot nature of our modeling of the farinograph curves course, a complex dataset was compressed into the Supplementary Tables S1–S8 and Figure S1.

3.1. Analytical Characteristics of the Binary Blends Tested

The substitution of WF with all four oat forms led to a significant increase in the flour ash content (p ≤ 0.05), with the steepest increases observed for BRA and DMF (

Table 1. Basic analytical characteristics of the control wheat flour and its binary blends with four forms of milled oat in relation to bakery quality.

Flour Blend	Oat Add. (%)	Flour Ash (%)		Wet Gluten (%)		Total Dietary Fiber (%)		Gluten Index (1)		Zeleny Test (mL)		ZET/PRO 1 (1)		Falling Number (s)
WF	0	0.70	a	34.9	e	3.45	a	97	c	40	f	2.69	f	482	f
WF + WFL	5	0.77	b	33.2	c	3.71	abc	97	c	38	ef	2.58	ef	439	cd
	10	0.83	c	32.1	bh	3.92	abcd	92	c	36	cd	2.41	cd	431	cd
	15	0.90	de	42.3	h	4.31	bcdef	54	a	34	ab	2.35	bc	420	c
WF + BRA	5	0.81	c	36.6	f	4.18	abcde	96	c	37	cd	2.46	cd	467	ef
	10	0.93	f	36.5	f	5.90	jkl	97	c	35	bc	2.35	bc	469	ef
	15	1.02	g	41.1	g	6.56	kl	93	c	33	a	2.23	a	448	de
WF + FLA	5	0.76	b	33.6	cd	3.69	ab	99	c	38	de	2.51	de	469	ef
	10	0.84	c	33.5	c	4.11	abcde	95	c	35	bc	2.41	cd	439	cd
	15	0.91	ef	33.4	c	4.50	cdef	95	c	34	ab	2.28	ab	453	de
WF + DMF	5	0.76	b	33.8	cde	3.63	ab	92	c	40	f	2.68	f	270	b
	10	0.82	c	34.5	de	3.95	abcd	75	b	36	cd	2.47	d	214	a
	15	0.88	d	30.0	a	4.38	bcdef	74	b	34	ab	2.25	ab	196	a

WF—wheat flour (control); Forms of milled oat: wholegrain flour WFL, bran BRA, flakes FLA, diastatic malt flour DMF (WF replacement 5, 10, or 15 wt.%); ¹ ZET/PRO—Zeleny-to-protein-content ratio used according to the reference [40]; in the 13 tested samples, the protein content ranged from 14.43% to 15.09% [14], corresponding to roughly one-third of the wet gluten content. Note: Means within a column followed by the same letter are not statistically different (p ≤ 0.05). For the details of the data scatter (‘average ± SD’), see Table S1.

).

The wet gluten content generally decreased relative to the control, particularly in DMF blends, reaching a minimum of 30.0% at 15% substitution. Conversely, 15% addition of WFL and BRA resulted in an apparent increase in the wet gluten weight (42.3% and 41.1%, respectively). This increase in the wet gluten weight was accompanied by a noticeable change in the physical consistency of the gluten mass, which appeared to be less cohesive than the control based on Gluten Index values. The Gluten Index (GI) remained stable at 5% and 10% levels for WFL, BRA, and FLA, but declined significantly at 15% replacement, with the lowest value recorded for 15WFL (GI = 54).

Total Dietary Fiber (TDF) increased proportionally with the fortification level across all blends, peaking at 6.56% in the 15% BRA sample. Zeleny sedimentation (ZET) and the ZET/PRO ratio decreased with the rising oat content; this trend was most pronounced in BRA and DMF blends. The Falling Number (FN) remained above 420 s for WFL, BRA, and FLA, whereas DMF induced a sharp, dose-dependent decline to 196 s at 15% substitution.

3.2. Farinograph Mixing Profile Under Four Forms of Milled Oat

The farinograms on Figure 2 compare the time-dependent dough consistency course of the WF control and eight selected wheat–oat blends (complete figure of 13 items tested appended as Figure S1). All samples reached the DDT peak between 2.75 and 5.95 min, although individual oat forms significantly influenced the subsequent stability and softening (

Table 2. Standard and two standard-derived farinograph features of the wheat flour and its binary blends with four forms of milled oat flour.

Flour Blend	Oat Add. (%)	WAB 1 (wt.%)		DDSA 2		DDT 3 (min)		STA 4 (min)		DSD 5 (BU)		FQN 6 (mm)		DSD/STA 7 Index (1)
WF	0	56.5	bc	64°	bcd	4.80	bc	7.30	f	47	bc	103	e	6.4	abc
WF + WFL	5	57.6	e	62°	abc	5.40	cde	6.05	de	76	d	97	de	12.6	abcd
	10	58.8	g	59°	a	4.80	bc	5.31	cd	100	e	93	cde	18.7	cd
	15	59.9	h	66°	de	5.10	bcde	4.69	c	111	f	83	c	23.7	d
WF + BRA	5	57.3	de	64°	bcd	5.05	bcd	8.30	g	40	b	130	f	4.8	ab
	10	59.2	g	61°	ab	5.95	e	8.35	g	17	a	163	g	2.0	a
	15	61.0	i	70°	ef	5.75	de	13.05	h	21	a	197	h	1.6	a
WF + FLA	5	57.3	de	63°	abcd	4.65	bc	6.35	e	48	bc	104	e	7.5	abc
	10	58.3	f	65°	cd	4.60	bc	5.25	cd	58	c	94	cde	11.0	abcd
	15	58.8	g	73°	fg	4.45	b	4.62	c	75	d	87	cd	16.3	bcd
WF + DMF	5	56.9	cd	63°	abcd	3.55	a	3.41	b	223	g	55	b	65.2	e
	10	56.2	ab	66°	cd	3.00	a	2.35	a	292	h	42	a	124.7	f
	15	55.8	a	75°	g	2.75	a	2.15	a	321	i	37	a	149.2	g

WF—wheat flour (control); forms of milled oat: wholegrain flour WFL, bran BRA, flakes FLA, diastatic malt flour DMF (WF replacement 5, 10 or 15 wt.%); farinograph features: ¹ water absorption (water dose on basis of flour weight), ² dough development slope angle—angle reflecting the speed of the dough (gluten skeleton) development from the beginning of the test to the point of the DDT and immanent consistency, ³ dough development time, ⁴ stability of dough consistency, ⁵ degree of dough softening (evaluated 12 min after maximal consistency [42]); BU—Brabender unit), ⁶ farinograph quality number, ⁷ ‘Quality Ratio’— an index expressing the rate of dough consistency decline, i.e., the speed at which the gluten skeleton of the dough is degraded by mechanical kneading and enzymatic activity (reflecting its time-stability). It represents an analog of the loss modulus tan δ as determined on rheometers. Note: Means within a column followed by the same letter are not statistically different (p ≤ 0.05). For the details of the data scatter, see Table S2.

).

Substitution with WFL and FLA resulted in profiles closely following the WF control, independently to the actual WF replacement level. WFL blends exhibited a gradual weakening of dough strength only at the 15% level during the final phase of kneading (15–20 min), while FLA blends showed the highest similarity to the control across all three substitution levels, with curves almost completely overlapping the WF baseline.

In contrast, BRA and DMF blends demonstrated divergent mixing behaviors. BRA addition induced a ‘pseudostabilization’ effect, characterized by a significant prolongation of STA (up to 13.05 min) and a marked reduction in dough softening (DSD 21 BU), especially at the 15% level. This phenomenon is likely linked to the high water-binding capacity of oat dietary fiber, which also contributes to the increased gravimetric yield of wet gluten on the Glutomatic device (as presented in Table 1). During the gluten washing out, the entrapment of non-gluten components within the protein matrix occurred obviously. Conversely, DMF blends exhibited a rapid structural collapse after reaching DDT; at 15% substitution, STA was shortened to 2.15 min, while the DSD values rose sharply to the technologically unacceptable value of 321 BU.

The standard and standard-derived farinograph parameters are summarized in Table 2. Water absorption (WAB) increased with the addition of WFL, BRA, and FLA, as expected, whereas DMF induced a slight decrease. The ‘pseudoloss’ DSD/STA index clearly differentiated the mechanical impact of BRA (values ≤ 2) from the severe enzymatic degradation caused by DMF (values ≥ 65).

The most critical finding in this phase is that while traditional metrics (STA, DSD) identify the structural collapse in DMF blends, only the proposed DSD/STA index provides a normalized scale to quantify the intensity of enzymatic vs. mechanical degradation across different oat forms.

3.3. Impact of Oat Forms on Standard Mixing Profiles and Network Stability

The substitution of WF with oat forms significantly influenced the behavior during kneading to optimum and following over-kneading (Table 2). Water absorption (WAB) increased statistically across most blends, with the highest values recorded being for 15BRA (61.0%) and 15WFL (59.9%; about 3.5 percent points higher than for the control). Conversely, DMF addition led to a dose-dependent decrease in WAB, reaching a minimum of 55.8% at the 15% substitution level. This inverse trend results from the high diastatic activity of the malted oat component, where active α-amylases and β-glucanases initiate the breakdown of starch and hydrocolloids immediately upon hydration. This process releases structurally bound water back into the dough matrix, thereby reducing the external water requirement to achieve the target consistency.

The dough development slope angle (α_slope) and DDT reflected the rate of hydration and initial network formation. The steepest slopes and shortest DDT values were observed for WF + 15 DMF blend (75° and 2.75 min, respectively), indicating rapid hydration. In contrast, BRA and WFL blends required longer development periods, with DDT peaking at 5.95 min for 10BRA.

Dough stability (STA) and stability-derived FQN clearly differentiated the impact of oat forms on gluten strength. BRA blends exhibited a pronounced stabilizing effect, with STA reaching 13.05 min at 15% substitution. Conversely, DMF blends showed the shortest stability (2.15 min) and the lowest FQN (37 mm), confirming severe structural destabilization. This divergence confirms that while both additives disrupt the gluten matrix, BRA primarily induces a physical ‘crowding’ effect through high water binding, whereas DMF triggers an active biochemical degradation.

The dough softening degree (DSD) and the DSD/STA ratio quantified the rate of network breakdown. While BRA significantly reduced softening (DSD = 21 BU at 15% level), DMF generated extreme values (up to 321 BU). Consequently, the DSD/STA ratio ranged from 1.6 (15BRA) to 149.2 (15DMF), effectively serving as a high-resolution indicator of the transition from fiber-driven reinforcement to enzymatic degradation.

3.4. Time-Resolved Dough Width and Elasticity Kinetics

The innovative farinograph descriptors provide a detailed insight into the development and breakdown of dough elasticity. While the standard variables describe macroscopic behavior, the time-resolved dough width (DW_t) and the farinograph elasticity loss (FEL) quantify the stability of the gluten–starch matrix under mechanical (mechanic–thermal) and enzymatic stress.

3.4.1. Dynamics of Dough Curve Width (DW)

Dough width is the macroscopic feature of the farinogram, which reflects the dough elasticity, recorded by the sight of a skilled technologist globally at first. After water addition, it multiplies, reaching its own maximum in the time of DDT (t_DDT), and later, it usually gets somewhat narrower owing to transient deformation—kneading in length. However, DW is traditionally fructified in form of the DSD only. As described in the Methods Section (Section 2.2.2), for time points preceding t_DDT, a normal projection (rectangular transversion) of dough elasticity is required. Figure 3 illustrates the rationale for this mathematical correction at 2 min of the farinograph test. Application of cosine correction is the only approach that enables discrimination between flours or flour blends characterized either by a high fiber content or by elevated enzymatic activity. Figure 3 further demonstrates that DW_{2 corr} provides a more reliable descriptor of early dough stability than uncorrected DW₂, particularly in systems affected by enzymatic activity. A comprehensive view of the wheat–oat model system under early-phase kneading conditions, expressed by DW₂, DW_{2 corr}, and DW_DDT, reveals the following trends:

• DW2 verified the potential to predict dough elasticity in optimum (DW_DDT);
• Oat forms WFL, BRA, and FLA indicated a technological limit for wheat flour substitution close to 10 wt.%;
• At 5–10% substitution, wheat flour interacted with milled oat particles and partially buffered their weakening effect. At 15% substitution, oats in the forms of WFL and DMF exhibited the softest but most structurally destructive impact.

Figure 3. Impact of the trigonometrical correction of the dough curve width (DW) in the 2 min of the farinograph proof, and comparison with DW in optimal consistency—dough development time (DDT). (a) Contrast between tested oat types and (b) contrast between oat addition levels (wheat flour substitution). WF—wheat flour (control); forms of the milled oat: WFL—wholegrain flour, BRA—bran, FLA—flakes, and DMF—diastatic malt flour. Note: A detailed dataset of this figure is included in Table S3a.

Figure 3. Impact of the trigonometrical correction of the dough curve width (DW) in the 2 min of the farinograph proof, and comparison with DW in optimal consistency—dough development time (DDT). (a) Contrast between tested oat types and (b) contrast between oat addition levels (wheat flour substitution). WF—wheat flour (control); forms of the milled oat: WFL—wholegrain flour, BRA—bran, FLA—flakes, and DMF—diastatic malt flour. Note: A detailed dataset of this figure is included in Table S3a.

In summary, the results demonstrate that dough properties are considerably more stable over time than is implied by a standard farinograph evaluation.

Early-stage corrected elasticity (DW_{2 corr}) declined with the increasing oat substitution. The control wheat flour reached 30 BU, whereas the lowest values were observed for 15FLA and 15DMF (20 and 18 BU, respectively;

Table 3. Dough curve width (DW_t)—supplementary farinograph feature of the rheological behavior of wheat flour and its binary blends with four forms of milled oat through 20 min farinograph test.

Flour Blend	Oat Add. (%)	DW2 corr (BU)		DWDDT (BU)		DW5 (BU)		DW10 (BU)		DW15 (BU)		DW20 (BU)
WF	0	30	d	63	cd	62	i	48	h	44	i	37	e
WF + WFL	5	29	cd	52	ab	54	def	41	fg	33	fg	27	cd
	10	29	cd	49	a	57	fgh	43	fg	40	h	38	e
	15	25	bcd	56	abc	53	de	37	e	31	ef	29	d
WF + BRA	5	26	cd	51	a	51	de	32	d	29	de	26	cd
	10	25	bcd	50	a	55	efg	43	fg	39	h	35	e
	15	23	abc	61	cd	44	c	25	c	19	c	15	b
WF + FLA	5	24	bcd	49	a	50	d	30	d	28	d	25	c
	10	27	cd	62	cd	58	gh	41	fg	38	h	35	e
	15	20	ab	65	d	36	b	18	b	11	b	8	a
WF + DMF	5	29	d	60	bcd	59	hi	44	gh	39	h	39	e
	10	27	cd	57	abcd	53	def	40	ef	34	g	29	d
	15	18	a	65	d	29	a	13	a	8	a	7	a

WF—wheat flour (control); forms of milled oat: wholegrain flour WFL, bran BRA, flakes FLA, diastatic malt flour DMF (WF replacement 5, 10 or 15 wt.%); DW—dough (vertical) curve width at dough development time and at 2, 5, 10, 15 and 20 min of the rheology test, respectively (BU—Brabender unit); DW_{2 corr}—farinograph curve width at the 2 min, trigonometrically corrected for the dough development slope angle (Equations (1) and (2)). Note: Means within a column followed by the same letter are not statistically different (p ≤ 0.05). For the details of the data scatter (‘average ± SD’), see Table S3a.

). Peak elasticity at optimum development (DW_DDT) varied among blends within a range of 49–65 BU. Notably, 15FLA and 15DMF achieved the highest peak values (65 BU) despite exhibiting rapid structural deterioration thereafter. Notably, 15FLA and 15DMF reached the highest peak values (65 BU) despite showing rapid subsequent deterioration. This transient elasticity maximum, followed by the abrupt narrowing of the farinogram curve, highlights the sensitivity of the DW descriptor in capturing short-lived structural integrity prior to an enzymatically driven collapse. Uncorrected DW₂ values are provided in Table S3a.

A discrepancy between DW₂ and DW_{2 corr} was observed, especially for blends containing diastatic malt flour (DMF). While uncorrected DW₂ values for 15% DMF were comparable to or higher than those of the wheat control, the corrected parameter (DW_{2 corr}) decreased by approximately 20–30%. This divergence suggests that the apparent increase in dough width at 2 min does not reflect improved structural integrity but is associated with rapid hydration and hydrolytic effects. The cosine-based correction reduces this bias and provides a normalized descriptor of early-stage dough behavior.

Across the tested blends, the mid- and late-stage dough elasticity (DW₁₀–DW₂₀) differentiated three stability groups:

• High stability: WF, 10WFL, and 10FLA, all retaining 35–38 BU at 20 min.
• Moderate decline: All BRA blends and 15WFL, with DW₂₀ values ranging from 15 to 29 BU.
• Severe degradation: 15FLA and 15DMF, where DW₂₀ decreased to 8 BU and 7 BU, respectively.

The elasticity decline, expressed as the difference in DW_DDT−DW₁₅, followed a form-specific pattern. For the control and the four substitution groups (WFL, BRA, FLA, DMF), these mean differences were 15, 12, 21, 28, and 29 BU, respectively.

3.4.2. Farinograph Elasticity Loss (FEL)

Based on the DW, the FEL index quantifies the relative narrowing of the farinogram bandwidth. Across all oat forms, FEL increased with the substitution level, although the magnitude and trajectory were strongly form-dependent (Figure 4a).

• WFL blends: Values remained moderate at 5% and 10%. A substantial rise in FEL across all time points was observed only at 15% substitution, indicating accelerated post-peak elastic decline.
• BRA blends: A ‘stabilizing window’ was identified at 10% substitution, where FEL reached a local minimum during the 5–20 min interval. At 15%, FEL increased due to intensified mechanical interference. This structural stability at the 10% level correlates with the previously observed maintenance of the Gluten Index (Table 1), suggesting that fiber-induced water competition only becomes detrimental to the protein network at higher substitution levels (15%).
• FLA blends: FEL increased almost linearly with substitution, showing a pronounced elevation of late-stage indices (FEL₁₀, FEL₂₀) at the 15% level.
• DMF blends: Exhibited the steepest rise in FEL across all substitution levels. The combination of strongly negative FEL_{2 corr} and maximal late-stage FEL values (at 15% DMF) reflects a rapid structural collapse.

At fixed substitution levels (Figure 4b), DMF consistently produced the highest FEL values, while BRA exhibited the lowest (especially at 10%). A critical stability threshold was identified between 10% and 15% substitution, where coarse-particle interference (FLA) and enzymatic activity (DMF) led to a disproportionate loss of elasticity.

The identified critical stability threshold (10–15%) and the late-stage FEL values are further evaluated in Section 4 in direct relation to loaf specific volume and shape descriptors, providing a quantitative link between dough elasticity kinetics and final baking quality.

3.4.3. Integrated Areas and Energy Parameters

The supplementary energy-related parameters (

Table 4. Supplementary farinograph areas and energies—indicators of quality and rheological properties of the wheat flour and its binary blends with four forms of milled oat.

Flour Blend	Oat Add. (%)	Variable Group
		①				②		③				④
		1 FQAREAL (cm2)		2 FQAINTEGRAL (BU·min)		2 DEA (BU·min)		1 EnergyDDT (W·h·kg−1)		2 DDA (BU·min)		1 EnergyTOTAL (W·h·kg−1)		2 FQE (BU·min)
WF	0	4	cd	393	bc	231	a	4.70	c	362	ab	25.20	ef	5565	a
WF + WFL	5	5	de	444	bc	291	ab	4.45	c	370	ab	24.95	ef	5975	b
	10	2	ab	198	ab	518	fg	5.40	de	427	b	25.70	fg	9087	fg
	15	5	de	340	bc	388	cd	5.00	cd	322	ab	25.10	ef	8424	d
WF + BRA	5	6	ef	529	c	339	bc	4.50	c	384	ab	24.15	de	6999	c
	10	1	a	13	a	473	ef	5.90	e	385	ab	26.30	g	9591	h
	15	24	g	1560	d	415	de	3.65	b	317	ab	19.60	c	8711	de
WF + FLA	5	8	f	602	c	458	ef	4.45	c	439	b	23.20	d	9038	efg
	10	4	bcd	341	bc	517	fg	4.75	c	358	ab	25.45	fg	9284	gh
	15	38	h	2165	e	463	ef	2.95	a	273	a	16.85	b	8939	ef
WF + DMF	5	3	abc	232	ab	496	fg	5.60	de	336	ab	26.00	fg	9085	fg
	10	5	de	336	bc	542	gh	5.05	cd	349	ab	25.30	fg	9285	gh
	15	46	i	2499	f	583	h	2.80	a	243	a	15.75	a	8968	efg

WF—wheat flour (control); forms of milled oat: wholegrain flour WFL, bran BRA, flakes FLA, diastatic malt flour DMF (WF replacement 5, 10 or 15 wt.%); ^1,2 in groups ①, ②, ③, and ④, variable evaluated by the Brabender MetaBridge^® software and its alternative integrated in the MS Excel, respectively; DDA—dough development area, based on the dough development slope angle (Table 2), FQA—farinograph quality area (‘time–integral’ of the dough softening degree; 1 cm² ≈ 40 BU·min), DEA—dough elasticity area (‘time–integral’ of the farinogram width in interval ≤t_DDT; t_DDT+12>; and FQE—farinograph quality energy. Area under the central line of the farinogram—estimation of the total energy input [43]. Note: Means within a column followed by the same letter are not statistically different (p ≤ 0.05). For the details of the data scatter (‘average ± SD’), see Table S4.

) are divided into software-derived indices and integrated areas (by using the trapezoidal rule). These metrics provide a cumulative perspective on dough development and mechanical resistance.

Farinograph quality area (FQA_REAL) evaluated by the company’s software and its integral counterpart (FQA_INTEGRAL) quantified the extent of the dough softening. The smallest areas were observed for 10BRA and 10WFL (1–2 cm²), indicating superior resistance to kneading, even surpassing the WF control (4 cm²). Conversely, 15FLA and 15DMF exhibited the highest FQA values (38–46 cm²), confirming extensive structural degradation.

The dough elasticity area (DEA), representing persistent elasticity between DDT and DSD points, showed a distinct increase in all oat-fortified samples compared to the control (231 BU·min). The highest DEA was recorded for 15DMF (583 BU·min). This peak, however, is mathematically driven by the high initial bandwidth (DW_DDT) and should not be misinterpreted as long-term stability. In this specific case, the high DEA value reflects a transient, unstable elasticity that is rapidly lost, as corroborated by the extreme FEL and DSD values.

Energy Demand and Total Input (FQE)

All composite blends required significantly higher mechanical energy (FQE) than the WF control (5565 BU·min). This substantial increase in the mechanical energy requirement (up to 72% for 10% substitution) suggests that industrial processing of these composite flours would necessitate significant adjustments to mixing times and energy inputs to ensure proper dough development. The greatest energy demand was observed for 10% substitution levels across BRA (9591 BU·min), FLA (9284 BU·min), and DMF (9285 BU·min) forms (Table 4). While the Energy_DDT generally peaked at 10% substitution, a subsequent decline was observed at 15% (e.g., reaching 2.80 W·h·kg⁻¹ for 15DMF), indicating the structural limits of the gluten network under coarse-particle interference or enzymatic activity.

As shown in Figure 5, the software-derived indices (Energy_DDT and Energy_TOTAL) closely correspond with the integrated parameters DEA and FQE, thereby validating the proposed geometric modeling of the farinograms. Across all oat forms, Energy_TOTAL values remained consistent, with the exception of the 15% DMF blend, which exhibited a substantial decrease due to severe enzymatic structural collapse.

3.5. Effect of Milled Oat on Laboratory Baking Trial Results

The incorporation of milled oats significantly affected the specific volume, geometry (vaulting), and slice area of the breads (

Table 5. Baking trial results for small, fermented bread from wheat flour and its binary blends with four forms of milled oat.

Flour Blend	Oat Add. (%)	Specific Bread Volume (cm3·100 g−1)		Bread Shape h/d Ratio 1 (1)		Bread Slice Area (cm2)
WF	0	330	ef	0.66	g	38.37	d
WF + WFL	5	317	def	0.47	bcdef	30.10	bc
	10	283	abc	0.45	abcde	30.10	bc
	15	312	cdef	0.44	abcd	24.63	a
WF + BRA	5	289	bcd	0.57	fg	30.87	bc
	10	287	bc	0.55	defg	30.00	bc
	15	333	f	0.57	fg	30.53	bc
WF + FLA	5	255	a	0.57	fg	32.67	bc
	10	293	bcd	0.56	efg	29.83	bc
	15	313	cdef	0.53	cdef	31.30	bc
WF + DMF	5	267	ab	0.43	abc	30.00	bc
	10	285	abc	0.35	ab	27.63	ab
	15	301	cde	0.33	a	23.60	a

WF—wheat flour (control); forms of milled oat: wholegrain flour WFL, bran BRA, flakes FLA, diastatic malt flour DMF (WF replacement 5, 10, or 15 wt.%). ¹ Bun height-to-diameter ratio (for WF-round small breads, the optimum is 0.60–0.65). Note: Means within a column followed by the same letter are not statistically different (p ≤ 0.05). For the details of the data scatter (‘average ± SD’), see Table S5.

). The control WF bread reached the highest specific volume (330 cm³·100 g⁻¹), while most wheat–oat blends showed a significant decrease (p ≤ 0.05).

3.5.1. Specific Volume and Bread Geometry

The response of specific volume was oat form-dependent. WFL blends showed a decline peaking at 10% substitution (283 cm³·100 g⁻¹), whereas BRA breads maintained relatively high volumes (up to 333 cm³·100 g⁻¹ at 15%). Notably, the high specific volume of 15BRA (333 cm³·100 g⁻¹) does not indicate a superior gluten quality but rather a fiber-induced ‘foam-stabilization’ effect, which is, however, offset by a lower h/d ratio (0.57) compared to the control (0.66). FLA blends exhibited high sensitivity at low substitution (minimum 255 cm³·100 g⁻¹ at 5%) but showed improvement at higher levels. DMF blends produced reduced volumes across all levels (267–301 cm³·100 g⁻¹).

The bread shape ratio h/d followed similar trends. The control WF bread exhibited the highest ratio (0.66), covering the optimum experimental range of 0.60–0.65. Substitution with WFL led to a gradual decrease (0.44 at 15%), while BRA and FLA blends demonstrated a higher shape stability of small rounded breads (0.53–0.57). The lowest h/d ratios were recorded for DMF blends, decreasing to 0.33 at 15%, indicating significant gluten net weakening and lateral spreading of molded fermented pieces of dough during baking (insufficiency in dough elasticity, and prevailing extensibility).

3.5.2. Bread Slice Area

The bread slice area (Figure 6) was strongly influenced by both variability factors oat form and oat addition level. In agreement with the specific bread volume, the WF control buns showed the largest area (38.4 cm²). In contrast, the smallest values were recorded for 15% of both FLA (24.6 cm²) and DMF (23.6 cm²). WFL and BRA blends produced intermediate and relatively stable slice areas (≈29–31 cm²) across all substitution levels that evoke the farinograph behavior (Figure 2). The dramatic reduction in slice area for 15% DMF (23.6 cm²) directly corresponds with the highest recorded FEL values in Section 3.4.2, confirming that time-resolved elasticity loss is a superior predictor of crumb structural collapse than standard stability (STA) measurements.

3.6. Statistical Relationships and Correlation Analysis

3.6.1. Effect of Variability Factors: F1—Oat Form and F2—Oat Addition Level

In the paragraphs following, asterisks are used to indicate a correlation provability as usual (e.g., ** means significant at p ≤ 0.05%):

• Correlation analysis (

  Table 6. Correlation analysis—effect of variability factors F1—oat form and F2—oat addition level on quality parameters of flour, dough, and bread from WF control flour and 12 wheat–oat blends.

  (a) Analytical features of flour
  Variable		Ash	Wet Gluten	Gluten Index	Zeleny Test (ZET)	ZET/PRO 1	Falling Number
  F1—Oat Form		0.12 ns	−0.38 ns	−0.10 ns	−0.17 ns	0.13 ns	−0.71 ***
  F2—Oat Addition		0.87 ***	0.24 ns	−0.52 **	−0.93 ***	−0.59 **	−0.24 ns
  (b) Standard farinograph parameters of dough
  Variable	Water Absorption	Dough Development Slope Angle	Dough Development Time (DDT)	Stability (of Dough Consistency; STA)	Quality Ratio DSD/STA	Dough Softening Degree	Farinograph Quality Number
  Oat Form	−0.27 ns	0.39 *	−0.64 ***	−0.46 *	0.62 ***	0.60 **	−0.41 *
  Oat Addition	0.51 **	0.64 ***	−0.08 ns	−0.07 ns	0.27 ns	0.22 ns	0.02 ns
  (c) Supplementary farinograph features of dough
  (ca) Dough Curve Width
  Variable	DW2 corr 2	DWDDT	DW5	DW10		DW15	DW20
  Oat Form	−0.45 *	0.21 ns	−0.45 *	−0.45 *		−0.44 *	−0.36 ns
  Oat Addition	−0.72 ***	0.32 ns	−0.67 ***	−0.62 ***		−0.66 ***	−0.61 ***
  (cb) Farinograph elasticity loss
  Variable	FEL2 corr 2	FEL5	FEL10	FEL15			FEL20
  Oat Form	−0.41 *	−0.45 *	−0.45 *	−0.44 *			−0.36 ns
  Oat Addition	−0.65 ***	−0.67 ***	−0.62 ***	−0.66 ***			−0.61 ***
  (cc) Farinograph areas and energies
  Variable	Dough Development Area	EnergyDDT	Dough Elasticity Area	FQAREAL	FQAINTEGRAL	EnergyTOTAL	Farinograph Quality Energy
  Oat Form	−0.31 ns	−0.21 ns	0.80 ***	0.37 ns	0.34 ns	−0.34 ns	0.71 ***
  Oat Addition	−0.54 **	−0.44 **	0.55 **	0.61 ***	0.58 **	−0.58 **	0.61 ***
  (d) Bread features
  Variable	Bread Height h	Bread Diameter d	Bread Shape h/d	Breads Weight 2	Breads Volume 2	Specific Bread Volume	Bread Slice Area
  Oat Form	−0.45 *	0.32 ns	−0.54 **	−0.16 ns	−0.03 ns	−0.54 **	−0.61 ***
  Oat Addition	−0.52 **	0.50 **	−0.43 *	−0.60 **	−0.53 **	0.23 ns	−0.42 *

  ¹ The index ZET/PRO calculated according to paper [40], where PRO—protein content from the previous study [14] is roughly ¹/₃ of the Wet Gluten content. ² DW_{2 corr}, FEL_{2 corr}—farinograph curve–dough width at the 2 min, trigonometrically corrected for the dough development slope angle, and the related farinograph elasticity loss. Note: Primary and secondary parameters are distinguished by italics; the primary traits were recorded by the equipment used or measured manually, while the secondary ones were calculated (integrated) in the MS Excel. Significance of the pair correlations (N = 26): ^ns, *, **, *** non-significant, p ≤ 0.05, 0.01, or 0.001, respectively. For the details of the calculated probabilities p, see Table S6.

  ) revealed that both the oat form (F1) and oat addition level (F2) significantly influenced the analytical flour quality, dough rheology, and bread characteristics. The comprehensive interrelationships between these parameters are visually summarized in the correlation heatmap (Figure 7), where distinct structural domains reflect the impact of oat fortification.
• Analytical parameters (Table 6a): The oat form (F1) was strongly negatively associated only with the Falling Number (r = −0.71 ***), reflecting the specific enzymatic activity of DMF. In contrast, the substitution level (F2) progressively increased the flour ash (r = 0.87 ***) and significantly reduced the protein quality indicators, such as the Zeleny test (r = −0.93 ***) and Gluten Index (r = −0.52 **).
• Standard farinograph parameters (Table 6b): These were more closely linked to the oat form than to the substitution level. F1 positively influenced DSD (r = 0.60 **) and the DSD/STA ratio (r = 0.62 ***), while showing negative relationships with DDT (r = −0.64 ***) and STA (r = −0.46 *). The substitution level (F2) primarily determined the water absorption (r = 0.51 **) and DDA (r = 0.64 ***).
• Supplementary descriptors (Table 6c): The innovative descriptors provided deeper mechanistic insights. Both F1 and F2 factors were highly negatively correlated with the dough curve width (DW₂–DW₂₀) and positively with farinograph quality energy (FQE; r = 0.71 *** and 0.61 ***, respectively). As indicated by the correlation heatmap (Figure 7), the progressive narrowing of the dough-width envelope (quantified via FEL) provides a high-resolution indicator of the transition from a viscoelastic to a predominantly plastic state. This kinetic descriptor offers a more sensitive diagnostic tool for structural fatigue than conventional stability metrics, particularly in systems where enzymatic activity or fiber interference disrupts the integrity of the gluten–starch matrix.
• Baking trial results (Table 6d): Both factors significantly impaired bread geometry. The Oat form (factor F1) showed the strongest negative impact on the specific bread volume (r = −0.54 **) and bread slice area (r = −0.61 ***). The oat addition level (factor F2) correlated negatively with the bread weight (r = −0.60 **) and bread height (r = −0.52 **).

A detailed correlation matrix is accessible in Table S6.

3.6.2. Statistical Similarity and Descriptor Redundancy

To evaluate the discriminative power of the innovative farinograph descriptors, a statistical similarity matrix was constructed. By applying the trigonometric transformation (Equation (8)) to Pearson’s correlation coefficients (summarized as ranges in

Table 7. Reduced correlation matrix among groups of 12 tested wheat–oat flours and breads vs. wheat control (WF)—influence of the oat form and oat addition (p ≤ 0.000001).

Variable (N = 36)	WF	5WFL, 5BRA, 5FLA, 5DMF	10WFL, 10BRA, 10FLA, 10DMF	15WFL, 15BRA, 15FLA, 15DMF
WF	–	min. 0.99420, max. 0.99963	min. 0.99308, max. 0.99431	min. 0.99244, max. 0.99527
5WFL 5BRA 5FLA 5DMF	min. 0.99420, max. 0.99963	min. 0.99663, max. 0.99957	min. 0.99577, max. 0.99994	min. 0.99529, max. 0.99993
10WFL 10BRA 10FLA 10DMF	min. 0.99308, max. 0.99431	min. 0.99577, max. 0.99994	min. 0.99885, max. 0.99998	min. 0.99851, max. 0.99991
15WFL 15BRA 15FLA 15DMF	min. 0.99244, max. 0.99527	min. 0.99529, max. 0.99993	min. 0.99851, max. 0.99991	min. 0.99847, max. 0.99986

For details, see Table S8a. Note: These extremely high linear correlations justify the necessity of the trigonometric transformation to achieve sufficient statistical resolution (Section 2.2, Equation (8)).

, and fully in Table S8), the sensitivity to subtle differences among high-correlation pairs (r > 0.99) was significantly enhanced. While traditional parameters (e.g., STA and FQN) exhibit high redundancy in standard linear analysis, the innovative kinetic descriptors DW and FEL provide distinct information regarding dough fatigue. Specifically, late-stage elasticity indices (DW₂₀, FEL₂₀) showed lower similarity to peak-consistency parameters, confirming their role in quantifying the structural collapse that remains undetected by standard static indicators.

3.6.3. Correlation Analysis and Statistical Similarity of 13 Tested Samples

As presumed, correlations among the samples confirmed a very high overall similarity of all wheat–oat blends to the wheat control flour (a minimal count of correlations from 0.9924 to 0.9942; Table 7). A gradual decrease in similarity with the increasing oat addition was visible, whereas the differences among the four oat forms remained comparatively small.

Statistical similarity analysis based on the correlation matrix and the Euclidean distance (

Table 8. Statistical similarity of 12 binary flour samples—wheat–oat flours and breads to the wheat control (WF), based on trigonometric transformation of the linear correlations (Equations (7) and (8)).

Variable (N = 36)	15DMF	15FLA	15BRA	15WFL	10DMF	10FLA	10BRA	10WFL	5DMF	5FLA	5BRA	5WFL
WF	65%	68%	69%	67%	66%	67%	66%	67%	67%	68%	73%	84%
5WFL	69%	72%	73%	71%	70%	71%	70%	71%	71%	72%	77%
5BRA	74%	83%	84%	81%	75%	81%	80%	81%	78%	83%
5FLA	78%	90%	88%	88%	79%	91%	88%	90%	82%
5DMF	85%	83%	80%	82%	89%	83%	80%	84%
10WFL	80%	89%	85%	88%	81%	96%	87%
10BRA	77%	86%	86%	87%	78%	89%
10FLA	79%	89%	86%	88%	80%
10DMF	89%	80%	78%	80%
15WFL	79%	88%	86%
15BRA	77%	88%				60–70%		70–80%		80–90%		90–100%
15FLA	79%

WF—Wheat flour (control); forms of milled oat: WFL—wholegrain flour, BRA—commercial bran, FLA—commercial flakes, and DMF—diastatic malt flour. Milled oats were used for the WF replacement in amounts of 5, 10, or 15%. Within the tested set, values 65% represent a minimal to the control WF sample (samples 15DMF, while the maximum of 96% demonstrated blends 10WFL–10FLA. For details, see Table S8b.

) further differentiated the samples, as illustrated, e.g., by the farinograms in Figure 2. As identified by tints of grey, the structure of the similarity half-matrix for 13 × 13 items revealed clustering according to the F2–Oat addition level (WF-substitution level); with 5% blends grouping closest to the control with mean similarity of 73%. As mentioned supra, wheat flour is able to partially buffer the effect of oat dosage. Connected to this, 10% and 15% blends were conjoined into one, 50%-grey cluster—for both doses, coarse oat particles or enzymatically active oat forms acted seriously in the comparable extent (similarity 65–69%). For the total count of 78 original pair correlations, similarity distribution with an increment of 10% follows:

60–70%: 11 items (≈14%), 80–90%: 40 items (≈51%),

70–80%: 23 items (≈29%), 90–100%: 4 items (5%).

Namely, the highest similarity to the WF control was consistently observed for 5WFL (84%) and 5BRA (73%) blends, whereas the lowest one was demonstrated the 15% DMF one (65%). This observation aligns with common bakery praxis—wholegrain flours or brans belong to the raw materials of daily use to enlarge the produced portfolio. Diastatic flour is also a common part of ready-to-use mixtures for special products, but when used alone to support or accelerate the fermentation process; the maximal dose is between 0.1 and 0.2% on the flour/flour mix weight. In accordance with the coupling of WF–5WFL–5BRA together, four further blend pairs 5FLA–10FLA, 5FLA–15FLA, 5FLA–10WFL and finally 10WFL–10FLA have been identified as practically identical—their statistical similarity ranged from 90 to 96%.

The high resolution of this similarity matrix, achieved through a trigonometric transformation, confirms that the proposed kinetic descriptors can effectively distinguish between stable composite systems and those prone to structural failure, even when standard linear correlations appear nearly identical (r > 0.99).

3.6.4. Data Exploration by Principal Components

Principal Component Analysis provides a complex, 2D-graphical overview of the relationships among the variables and cases. Here, the variables are flour analytical traits, farinograph parameters, and bread-quality outcomes, with the potential to monitor the causes and consequences of changes in the composition of flour and baked goods. For completeness, the active and the supplementary (secondary, explaining) variables are drawn in the PCA variable loadings plot, but as defined into the PCA theory, they are and are not included in the calculated PCA model, respectively.

PCA Based on the Standard Farinograph Features

In the first configuration, the active variables included flour analytical parameters, six standard farinograph metrics (WAB, DDT, STA, DSD, FQN, FQA), and bread characteristics (Figure 8a,b). An additional 13 innovative farinograph parameters were used as supplementary variables, together with the ANOVA factors F1 and F2 (written in red). The first two principal components, PC1 and PC2, explained 37% and 28% of the total data variability, respectively. PC1 primarily captured non-fermented dough behavior (the farinograph features listed above) in terms of resistance, cohesiveness, and consistency stability, while PC2 was associated with the flour protein quality (ZET, ZET/PRO, Gluten Index), DDSA (‘DD Angle’—α_slope), FQA, and the baking trial results (the bread physical properties). The factor F1 (oat form) was positioned between PC1 and PC2, whereas factor F2 (oat addition) was more closely aligned with PC2.

In the loadings plot along PC1, there are properties associated with the wet gluten content, the ZET/PRO ratio in part, WAB and particularly with dough resistance and weakening (DDT, STA, DSD, DSD/STA, and FQA; Figure 8a). Only DSD, DSD/STA, and FQA were positioned on the positive PC1 semi-axis. PC2 separated the analytical features of flour (ash, Gluten Index) from the geometric characteristics of bread (diameter, weight, slice area), confirming the significant influence of the flour fraction on the quality of baked goods (e.g., refined wheat flour vs. composite blends). The score plot (Figure 8b) showed that samples containing 5% oat were clustered closely with the wheat control (WF), whereas the 10% blends shifted toward intermediate positions along both PC1 and PC2. Blends and breads fortified by 15% of milled oat forms were located furthest from the control, in agreement with the statistical similarities in Table 8. Among these oat forms, DMF samples displayed the largest displacement toward the ‘weakening-variable’ quadrant, while WFL and FLA tended to remain closer to the negative PC1 region associated with the preserved dough elasticity. Sample BRA occupied intermediate positions across the substitution levels. This gradient reflects a progressive divergence from the control flour with increasing substitution rates, in agreement with the analytical results and correlations.

PCA Based on the Extended Farinograph Profiles

In the extended PCA model (Figure 8c,d), which purposefully incorporated eighteen supplementary farinograph parameters, the explained variability increased to 46% for PC1 and 23% for PC2. It was observed that the dataset extension rotated and flipped the loadings plot while maintaining the grouping and relative importance of individual variables (indicated by their distance from the origin). PC1 represents flour analytical traits, dough elasticity, and bread physical properties, whereas PC2 captures the remaining variance. The impact of both ANOVA factors appears more balanced in this model, likely due to the inclusion of dough elasticity and energy input parameters.

In summary, the importance of standard farinograph parameters was confirmed and further extended by the innovative descriptors. The set of dough elasticity parameters (DW_{2 corr} to DW20 and the FEL indices), together with DDA, Energy_DDT, and Energy_TOTAL, formed a compact cluster on the negative PC1 plane, close to a circle of 100% explanation of the data variance. This cluster showed a strong backward alignment with the protein quality (ZET) and a forward predictive capability for the bread weight, height, and slice area. Moreover, the DDSA (or dough development area) demonstrated the ability to predict dough softening (DSD and FQA) and mechanical energy requirements. Dough softening, as quantified by the FQA (mandatory in the Hungarian national norm), logically reflects the area of dough elasticity loss (DEA).

The score plot under the extended model (Figure 8d) exhibited an even clearer stratification of samples. The control WF and the 5% blends formed a stable, compact cluster, overlapped partially by the 10% blends (especially WFL and FLA, which shifted moderately toward the center). The 15% substitution blends occupied the farthest positions from the WF control. The positions of the WF–DMF samples were primarily determined by the positive PC2 axis, reflecting the dominant influence of enzymatic activity (Falling Number). The PCA thus consistently separated the samples, demonstrating that at the 15% replacement level, both factors F1 and F2 significantly interact to affect rheological and baking outcomes. The inclusion of time-resolved geometric descriptors and energy input data transforms traditional ‘static’ evaluation into a ‘dynamic’ diagnostic tool, providing sensitivity that is comparable to fundamental rheometry.

Furthermore, the kinetics of dough development (e.g., slope angle or integrated area) show potential for predicting the physical properties of the final fermented products.

4. Discussion

4.1. Nutritional Enrichment vs. Structural Integrity

The analytical characterization (Table 1) demonstrates that all four oat forms substantially enhanced the nutritional profile of the composite flours, resulting in significant increases in the total dietary fiber and ash content. However, this compositional enrichment simultaneously imposed a measurable structural load on the wheat dough matrix. A distinct, form- and level-dependent technological threshold emerged between 10% and 15% substitution, beyond which the buffering capacity of the gluten network was exceeded.

In terms of non-fermented dough rheology, this transition manifested as a pronounced rise in FEL values during the 10–20 min interval, an accelerated narrowing of the dough-width envelope (DW₁₅, DW₂₀), and elevated FQA values (Table 2, Table 3 and Table 4; Figure 2, Figure 3, Figure 4 and Figure 5). Collectively, these features indicate a shift from predominantly elastic behavior toward a plastic, mechanically fatigued state during prolonged kneading. Notably, these rheological signatures co-occurred with consistent declines in the values of the protein quality indicators ZET, ZET/PRO, and Gluten Index (GI), ultimately resulting in a reduced bread slice area, impaired shape vaulting of small, rounded breads (h/d ratio), and consecutively decreased specific volume in the baking trial (Table 5). These findings demonstrate a direct mechanistic link between viscoelastic-degradation kinetics and the practical baking performance of binary dough.

The mechanism underlying protein-quality deterioration differed clearly among the oat forms. For BRA, FLA, and WFL, the dominant mode of disruption was mechanical interference. At the 15% substitution level, the sharp declines in ZET and GI reflect an acceleration of the sedimentation as well as an obstruction of glutenin macropolymer crosslinking by coarse particles. This physical hindrance elevated FEL values and depressed dough width in farinogram late stage (DW₁₅, DW₂₀), aligning with the literature describing how bran particles puncture gas cells, disrupt gluten film continuity, and weaken dough elasticity during mixing [47,48,49]. This fragmentation is exacerbated by the competitive water absorption of oat polysaccharides, which deprives the glutenin subunits of the hydration required for optimal network development, thereby increasing the susceptibility of the dough to mechanical fatigue [15,47,50]. These results confirm that in fiber-rich systems, structural weakening arises primarily from particle-mediated mechanical fragmentation, rather than biochemical activity.

In contrast, DMF exhibited a strikingly different degradation pathway driven by enzymatic activity. Already at 10% substitution, early and steep declines in ZET/PRO and GI, combined with FN ≤ 200 s, indicate serious α-amylolytic and proteolytic breakdown of the gluten–starch complex. As seen during the rheological measurements, this biochemical disruption produced a characteristic kinetic signature: short DDT—high α_slope as well as STA, extremely high DSD/STA ratios, elevated FQA, and a dramatic collapse of DW₂₀. These features are diagnostic of enzyme-induced weakening and correspond to prior reports on germinated oats or malted cereals [51,52,53,54]. The enzymatic hydrolysis of starch and proteins not only disrupts the structural scaffold but also likely releases previously bound water into the dough matrix, further reducing the consistency and accelerating the transition to a plastic state [17]. The unique dose-dependent decrease in WAB observed for DMF blends (Section 3.3) further highlights this biochemical impact. While standard oat forms enhance hydration through fiber-mediated water binding, the DMF triggers a reduction in WAB. This phenomenon is driven by three key factors: first, the rapid hydrolytic release of structurally bound water by active α-amylases [17,18,52]; second, the degradation of β-D-glucans by endogenous enzymes, which reduces their inherent water-binding capacity [55,56]; and third, the increased osmotic pressure from low-molecular-weight sugars that reduces early mechanical resistance during mixing [51]. This enzymatic activity excess led to the poorest baking outcomes among all blends, reflected by the lowest h/d ratios and smallest bread slice areas (Table 2, Table 3, Table 4 and Table 5; Figure 4, Figure 5 and Figure 6).

One interesting observation is the apparent increase in the wet gluten content at 15% WFL and BRA testing, which should not be interpreted as an actual rise in the content of gluten-forming proteins. Instead, soluble β-D-glucans and oat lipids interfere with the gluten-washing procedure, entrapping non-gluten solids within the washing-out mass. Similar phenomena affecting wet gluten quantification caused by β-D-glucans or cereal lipids have been widely reported [9,57,58,59,60]. The concurrent decline in GI (e.g., GI = 54 for 15WFL from 97 for WF control) and the increased FEL and bandwidth-narrowing confirm that, despite an apparently higher wet gluten content, the true gluten network was substantially weakened.

While these kinetic descriptors provide a sensitive diagnostic tool for the tested wheat–oat systems, it should be noted that the identified thresholds (10–15%) and degradation patterns may vary with different wheat backgrounds or other non-traditional raw materials, necessitating further validation across broader formulation ranges.

4.2. Kinetics of Viscoelastic Degradation, DW, and FEL as Diagnostic Tools

To move beyond static endpoint metrics, this study exploited time-resolved dough width (DW) and farinograph elasticity loss (FEL) to capture the progressive loss of elasticity (gluten degradation) that precedes macroscopic softening. Traditional farinograph parameters such as DDT and STA quantify only the timing and duration of maximum torque and therefore limit the description of the persistence of the elastic component during over-kneading. The limitation was also noted in earlier farinograph and mixograph studies, focusing on dough development dynamics [43,60]. These conventional endpoints fail to record the gradual geometric narrowing of the farinogram envelope, which is now measurable through the extraction of digital curve data series, as described in the recent literature [29,30].

In contrast, the evolution of the envelope of the farinograph record (DW₂ → DW₂₀) directly tracks the time-dependent bandwidth of the viscoelastic response, while FEL expresses the relative narrowing of this bandwidth with respect to the maximum width at the optimum of DDT. Together, these indices provide higher-resolution markers for gluten network integrity during the late stage of kneading (Table 2, Table 3 and Table 4; Figure 2, Figure 3 and Figure 4), which is consistent with previous work demonstrating that changes in the dough curve width reflect shifts from elastic to plastic flow behavior [22,24].

The use of trigonometric transformation is conceptually consistent with the established rheological approaches, where phase angles tan δ are used to distinguish between elastic and viscous contributions of G’ and G’’ moduli in viscoelastic systems [44]. In this context, the innovative angle α_slope may be interpreted as an empirical analog of a phase descriptor reflecting the balance between hydration kinetics and structural formation. The cosine projection therefore serves as a practical tool to separate true viscoelastic behavior from hydration-driven artifacts in empirical farinographic systems. Although this approach represents a novel adaptation within farinograph analysis, it aligns with previous efforts to convert graphical outputs into quantitative descriptors for predictive modeling [45].

A practical consequence of this kinetic perspective is confirmation that a wide DW at the DDT optimum does not guarantee dough structural cohesivity. Dough systems that initially develop a broad elastic band may still undergo rapid post-peak contraction, which becomes immediately visible in declining DW₂₀ and rising FEL₁₅–FEL₂₀ values (Table 4, Figure 4; Table S3b). Rapid late-stage narrowing of the elastic envelope is a known indicator of gluten fatigue or enzymatically accelerated breakdown, as documented in studies on weakened or modified gluten networks [26,28]. In the present study, this pattern was especially pronounced in severe-degradation blends, where high DW_DDT was observed with fast late-stage narrowing, demonstrating that late-stage elasticity metrics (DW₂₀, FEL₂₀) capture the impending collapse far more sensitively than DSD, STA, or FQN (Table 2, Table 3 and Table 4; Figure 2, Figure 3 and Figure 4). This distinction is critical for industrial applications; while fiber-rich systems (BRA, WFL) primarily suffer from physical ‘crowding’ and hindered hydration, diastatic systems (DMF) undergo active biochemical dissolution of the protein scaffold. The DW and FEL metrics effectively quantify the kinetics of both pathways, offering a more nuanced diagnostic of dough matrix integrity than the simple central-line torque [48,49].

Correlation analysis further reinforced this diagnostic value. The DW and FEL metrics exhibited coherent associations with the bread morphology parameters, height, shape ratio (h/d), specific volume, and slice area, unlike FQN and other conventional endpoints, which showed weaker or inconsistent links. The implementation of the trigonometric transformation for similarity analysis proved essential in this context. While standard Pearson’s correlations often fail to differentiate between very high coefficients (r > 0.99), this innovative approach linearized the correlation space, providing the necessary resolution to distinguish between stable composite systems and those prone to subtle structural failure. Comparable findings have been reported for enriched or fiber-modified doughs, where elasticity-loss kinetics, rather than single-point farinograph parameters, more reliably predict gas-cell retention and oven-spring behavior [10,13].

Finally, the introduction of a trigonometric correction (DW_{2 corr}) revealed delayed-hydration behavior in fiber-rich blends. High DW_{2 corr} values combined with negative or near-to–zero FEL_{2 corr} values suggest that the gluten–polysaccharide matrix has not yet achieved optimal structural organization and requires further kneading to reach a coherent elastic consistency. This behavior aligns with findings in β-D-glucans-rich systems, where soluble fibers delay hydration and modify early dough development, thickening the dough without any effect on its elasticity [9,60]. This refinement thus enhances the interpretive value of the early farinogram segment and helps to discriminate between transient early broadening of the curve and genuine elastic stability.

From a practical standpoint, the introduced kinetic descriptor sets (DW and FEL) offer millers and bakers a precise tool for monitoring dough quality beyond standard stability. For instance, in blends with high enzymatic activity or fiber content, these parameters can signal the exact moment of structural collapse, allowing for the optimization of mixing times and the dosage of strengthening additives. This movement from static to dynamic rheological monitoring enables more predictable production cycles in industrial bakeries using composite flours containing non-traditional raw materials.

4.3. The ‘Pseudostabilization’ Paradox of Oat Bran

Standard farinograph outputs sometimes suggest that bran-containing doughs are unusually stable, as indicated by the extended STA values. In the present dataset, BRA 10–15% indeed exhibited long stability periods (8.35 and 13.05 min, respectively), which, if interpreted in isolation, could be misread as evidence of superior gluten strength (Table 2). However, the kinetic indices indicate a different trend at higher bran loads, FEL increases, and DW₂₀ declines, indicating a progressive loss of elasticity below the torque level (Table 3). Comparable reports show that doughs can display the apparent stability of consistency, even when the viscoelastic network is already weakening [24,49].

This ‘pseudostabilization’ arises because torque-based farinograph stability can be dominated by viscosity-driven phenomena, such as water absorption by β-D-glucans (hexosans) and arabinoxylans (pentosans), rather than by real gluten resilience. Non-starch polysaccharides are well known to bind water aggressively and increase dough viscosity, artificially prolonging stability despite underlying structural decay [15,33]. This competition for the available water essentially results in a partially dehydrated gluten network, which is then more susceptible to mechanical fracture by the coarse bran particles, further accelerating the narrowing of the dough envelope width (DW). In addition, coarse bran particles can create mechanical scaffolding within the dough, pressing against the mixer pins and resisting deformation without contributing to the matter of elastic recovery. The disruptive impact of bran particles on gluten-film continuity and hydrated gluten development has been well documented [16,47,48]. Together, these effects explain why STA may prolong even as DW narrows and FEL rises, revealing hidden viscoelastic deterioration.

The baking results further substantiate this decoupling between torque-based stability and actual structural performance. Despite high STA values, bran-enriched breads did not recover the loaf geometry of the wheat control: the shape ratio (h/d) remained consistently lower, and the bread slice area (BSA) was markedly reduced (≈30 cm² vs. 38.4 cm² for WF; Table 5). Similar reductions in loaf expansion and gas cells fluffing up have been attributed to the disruptive effects of bran on gluten extensibility and bubble-wall continuity [10,28].

Consequently, the combined use of DW₂₀ and FEL₂₀ provides an effective diagnostic framework for interpreting viscosity-driven torque levels. Wherever late-stage narrowing of the dough envelope width coincides with rising elasticity loss, the apparent farinograph stability must be interpreted with caution and verified against gas retention by pores and crumb properties quantification. These complementary metrics thus offer a more comprehensive insight into dough behavior than STA alone, particularly in fiber-rich systems where viscous resistance can mask the underlying loss of gluten cohesiveness.

4.4. Energy Demand and Processing Implications, FQE and DEA

Farinograph quality energy (FQE) or Energy_TOTAL, and dough elasticity area (DEA) extend the diagnostic framework from describing what the dough becomes to quantifying how much mechanical work is required to reach the final state. Across all oat materials tested, FQE increased markedly, relative to the wheat control (WF 5565 BU·min, 25.20 W·h·kg⁻¹), with the steepest rises observed at 10% substitution: for example, up to ≈9591 BU·min (26.30 W·h·kg⁻¹) for BRA and ≈9284–9285 BU·min for FLA and DMF (averages 21.83 and 22.35 W·h·kg⁻¹, respectively; Table 4). These elevated energy requirements reflect delayed hydration and intensified water binding mediated by non-starch components such as β-D-glucans and pentosans, which are known to increase dough viscosity and mixing resistance [15,60]. From a processing perspective, higher FQE values imply increased shaft power demand, higher friction-induced dough temperatures, and, in enzyme-active systems, an intensified effect of α-amylolytic and proteolytic activity if kneading is not carefully controlled, which is consistent with known interactions between the mechanical energy input and biochemical softening mechanisms of the cereal biopolymers [51,53].

The DEA parameter complements this picture by integrating the post-DDT elastic trajectory. Moderate substitution with WFL or FLA produced elevated DEA values that were indicative of sustained elasticity, whereas extreme cases, such as 15% DMF, exhibited exceptionally high DEA (≈583 BU·min) paired with rapid late-stage narrowing of the farinogram elasticity envelope. This combination signals initial over-expansion followed by accelerated collapse, rather than genuine structural robustness (Table 3), aligning with reports on enzyme-compromised doughs, where early mechanical development masks early-onset degradation [52,54]. This early mechanical development, driven by the rapid hydration of malted components, creates a false sense of dough strength. In reality, the analytical protein-quality indicators (Table 1) confirm that the gluten scaffold is already being biochemically cleaved, a process that is accelerated by the mechanical energy input during this phase [53]. Together, FQE and DEA delineate the operational kneading window: as the energy demand rises and elastic bandwidth diminishes, the safe kneading interval narrows, increasing the risk of over-mixing-induced loss of gas-holding capacity (Table 2, Table 3 and Table 4; Figure 5).

Implications for Scale-Up

• First, adjustment of the formulation and kneading protocols for oat-fortified systems.

→

Mixing endpoints may be more effectively monitored using DW- and FEL-based milestones (e.g., DW₁₅, DW₂₀ or FEL₁₅, FEL₂₀ thresholds), as these late-stage elasticity metrics can offer a more sensitive signal of structural fatigue than torque-derived stability alone [28,30].

• Second, the dough temperature should be controlled.

→

Limiting specific mechanical energy once FEL begins to increase steeply, preventing thermal acceleration of enzymatic softening. Since α-amylase activity is highly temperature-dependent (as reflected by the low Falling Number in Table 1), the frictional heat generated by the increased FQE requirement creates a synergistic effect that accelerates the matrix collapse [51].

• Third, controlled operation with enzyme-active blends is necessary.

→

A blend such as DMF may require shorter development times or targeted enzyme control (e.g., a thermal or pH-based one) to limit the exposure of the gluten–starch matrix to peak α-amylolytic and proteolytic activity (Table 1, Table 2, Table 3, Table 4 and Table 5; Figure 3, Figure 4, Figure 5 and Figure 8), which is consistent with observations that germination-derived enzymes amplify dough weakening under prolonged mechanical input [51,53].

4.5. Predictive Value of Non-Traditional Farinograph Indices DW, FEL, FQA, DEA, FQE

Traditional farinograph descriptors such as DDT, STA, DSD, and FQN remain useful for routine quality evaluation, yet their predictive capacity is fundamentally constrained by their focus on the central torque trajectory. As repeatedly highlighted in modern farinograph, mixograph and mixolab analyses, torque-based endpoints provide limited information about the evolution of the elastic component during mechanical fatigue, particularly once the dough enters the weakening phase [20,21]. In contrast, the non-traditional, time-resolved indices introduced in this study capture the kinetics of viscoelastic degradation and thus supply a more powerful diagnostic framework for wheat–non-wheat composite systems.

Among these indices, dough width (DW) offers a direct measure of instantaneous elastic bandwidth, while farinograph elasticity loss (FEL) quantifies the rate at which this bandwidth narrows, relative to the DDT peak. These complementary measures reveal degradation patterns obscured by conventional parameters. For example, blends that exhibit broad DW_DDT but rapid post-peak contraction, reflected by high FEL₁₅ or FEL₂₀, demonstrate that early elasticity does not ensure long-term structural endurance. This discrepancy is especially evident in the severe degradation systems (Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6; Table 3 and Table 4), which is consistent with prior observations that gluten fatigue often proceeds despite adequate early development [22,24].

Correlation analysis reinforces this kinetic perspective. Close-to-endpoint DW values (DW₂₀) correlated positively with key baking-performance indicators, including shape vaulting (h/d ratio), bread slice area, and specific volume; the FEL₂₀, as a function of the DW₂₀, displayed strong negative correlations with the same traits, too (Figure 7). In contrast, widely used static metrics such as FQN and DSD exhibited weaker and inconsistent associations. Similar findings have been reported for dough systems modified by fiber or enzymatic activity, where the rate of elasticity decay, rather than torque-based stability, best predicts the gas-cell retention and oven-spring capacity (volume rise in dough piece during the initial phase of baking [10,13]. These relationships confirm that dynamic elasticity parameters more reliably capture the mechanisms governing the loaf expansion.

The dough development area (DDA), farinograph quality area (FQA), and dough elasticity area (DEA) extend the predictive ability of the dataset by integrating elasticity and softening behavior into single descriptors of structural persistence. High FQA values correspond to rapid softening of the over–kneaded dough and therefore identify doughs that are prone to premature collapse, whereas high DEA values differentiate between genuinely sustained elasticity (e.g., moderate WFL/FLA substitution) and unstable over-expansion followed by accelerated narrowing of the recorded curve (e.g., 15% DMF). These distinctions align with earlier findings on enzyme-active systems, where excessive early expansion masks accelerated late degradation [52,54].

Finally, the marked increases in the farinograph quality energy (FQE) and Energy_TOTTAL across the fortified systems tested, particularly at 10% and 15% substitution, link the energetic cost of mixing directly to structural outcomes. Samples requiring higher mechanical energy input to reach peak consistency were the same systems that displayed reduced long-term elasticity and poorer bread morphology (Table 2, Table 3, Table 4 and Table 5). This interplay between energy consumption and viscoelastic decay underscores the importance of kinetic indices (DDSA, DW, FEL, FQA, DEA, FQE, Energy) for defining safe kneading windows and preventing over-machination, especially in fiber-dense or enzymatically active blends.

Overall, the integrated analysis demonstrates that the non-traditional farinograph indices together provide a mechanistically grounded and more sensitive predictive framework compared with traditional farinograph metrics. By resolving how the gluten–starch complex evolves under sustained deformation, these indices enable precise identification of the substitution thresholds at which structural coherence is compromised. Consequently, they offer a robust framework for rational formulation, process control, and optimization in nutritionally enriched cereal products. While this study focuses on the farinograph system, it is expected that similar technological thresholds and kinetic principles could be derived using other recording mixers, such as the mixograph or mixolab, provided that time-resolved geometric descriptors are systematically applied.

5. Conclusions

This study demonstrates that time-resolved farinograph indices; dough width (DW), reflecting instantaneous elastic bandwidth; and farinograph elasticity loss (FEL), quantifying the rate of elasticity decay, represent a robust extension of traditional static metrics for predicting dough quality. Specifically, FEL₂₀ was identified as a sensitive indicator of the transition from elastic to plastic flow, offering enhanced predictive power for baking performance compared to conventional stability parameters. Additionally, the integrated dough development slope angle (DDSA) and dough development or dough elasticity areas (DDA and DEA) demonstrate the capacity to describe changes in wheat dough structure leading to structural reinforcement or softening.

Consistent with trends in non-gluten fortification, a critical substitution threshold was established at 10–15%, beyond which the gluten matrix fails to compensate for oat-induced structural or enzymatic loads. Notably, oat bran introduces a ‘pseudostabilization’ paradox, in which a high water-binding capacity masks underlying elastic decay. These findings offer a systematic framework for optimizing the formulation of nutritionally enriched cereal products.

From a processing perspective, the significant rise in the total mechanical energy input (quantified as FQE) highlights the increased mechanical work required for fortified blends. Although the sensitivity of the proposed kinetic descriptors was successfully demonstrated using a standardized wheat–oat model, further validation across a wider spectrum of cultivars and protein quality levels is required to confirm the universal applicability of these parameters. While these findings are specific to the tested wheat–oat systems, the proposed integrated model offers a more sensitive and mechanistically grounded approach for the rational formulation and process optimization of fortified bakery goods, which is potentially applicable to a wider range of composite flour systems.