Effects of Four Essential Oils on Wheat Dough Structural Transformations Assessed by Extended Mixolab Evaluation, Variance Components Analysis, and Adapted Principal Components Method

1. Introduction

Bakery products are among the most important cereal-based foods and represent a major source of energy, carbohydrates, and plant proteins in the human diet [1,2]. Increasing consumer’s demand for clean-label foods and reduced use of synthetic additives has stimulated interest in natural ingredients capable of improving food quality, safety, and shelf life [3]. Consequently, plant-derived bioactive compounds have emerged as promising alternatives to conventional preservatives and technological additives [4].

Among such substances, essential oils (EOs) are particularly attractive due to their antioxidant, antibacterial, and antifungal properties [5,6]. They consist mainly of terpenes, terpenoids, and phenylpropanoids, whose composition depends on botanical origin and extraction conditions [6,7]. The antioxidant activity of phenolic EO constituents contributes to product stability through inhibition of lipid oxidation [8,9].

The four EOs investigated in this study differ substantially in their chemical composition. Cinnamon EO is rich in cinnamaldehyde and eugenol [10,11], oregano and thyme EOs contain predominantly carvacrol and thymol, respectively [12]; lemongrass one is characterized by a high content of citral (mix of stereoisomers geranial and neral) [13,14]. These compositional differences are likely to determine their specific interactions with cereal biopolymers during dough processing [15]. While most studies have focused on the ability of these EOs to inhibit fungal growth and delay spoilage [5,7,16,17,18], they also significantly influence dough rheology, dough fermentation performance, and final bread quality [19,20]. Specifically, EO constituents can affect yeast metabolism and modify gluten-starch network formation [15,21,22,23,24].

The technological behavior of wheat dough is governed by complex interactions among gluten proteins, starch granules, enzymes, and water [25,26]. During mixing, heating, and cooling, wheat dough undergoes protein weakening, starch gelatinization, enzymatic starch degradation, and retrogradation [27,28,29]. The chemical structure of EO constituents strongly influences these transformations: thymol and carvacrol interact with starch [30], cinnamaldehyde reacts with protein amino groups through Schiff-base formation [31], and citral modifies starch structure and thermal properties [32,33]. Consequently, chemically distinct EOs induce different rheological responses during thermal processing [15,24].

Among empirical rheological methods, Mixolab (ICC Standard No. 173; AACC Approved Method 54-60.01) provides a unique opportunity to monitor these dough transformations under simultaneous mechanical and thermal stresses [34]. The test characterizes dough development (C1), protein weakening (C2), starch gelatinization (C3), hot-gel stability (C4), and starch retrogradation (C5) [35,36]. However, conventional interpretation remains restricted to characteristic torque points and a limited set of derived parameters [35,37], to maintain comparable to the most-used Farinograph proof. These standard indicators do not fully describe the kinetics of structural transformations and fail to clearly distinguish between mechanical and thermally induced protein weakening [34,38,39]. Despite increasing interest in EOs, the mechanisms through which chemically distinct EO groups influence individual stages of dough development remain poorly understood, particularly regarding whether these effects can be quantified using advanced kinetic and geometrical descriptors [15,16,24]. Likewise, limited attention has been devoted to transforming conventional Mixolab parameters into physically interpretable characteristics [34,35,40,41]; the pair differences and relative geometric slopes (e.g., C1 – C2 and angle α) of the standard evaluation of the Mixolab records are too robust for changes observation ‘in vivo’.

Therefore, the aim of the present study was to expand the conventional interpretation of Mixolab curves by introducing novel kinetic and geometrical descriptors. Particular attention was paid to newly proposed indexes of mechanical protein weakening (MWP), thermomechanical weakening (TMW), their mutual ratio, and the transformation of Mixolab curve slopes into physically interpretable kinetic and angular characteristics. These descriptors were subsequently used to describe the effects of cinnamon, oregano, thyme, and lemongrass essential oils on wheat dough behavior and to identify mechanistic differences in protein weakening, starch transformations, and structural recovery during thermomechanical processing.

2. Materials and Methods

2.1. Materials

2.1.1. Control Wheat Flour and Essential Oils

A commercial white wheat flour (WF) was obtained from Mlýny J. Voženílek Ltd. (Předměřice nad Labem, Czech Republic). The flour was characterized by a fine granulation, and contents of moisture 11.7%, ash 0.52%, protein 15.0%, and wet gluten 32.0%. The Zeleny sedimentation value reached a volume 55 mL and the Gluten Index of 65, as determined according to ICC Standard Methods No. 110/1 [42], No. 104/1 [43], No. 105/2 [44], No. 137/1 [45], No. 116/1 [46], and No. 155 [47], respectively. According to these quality characteristics, the flour represented a medium-to-strong breadmaking material suitable for non-gluten enrichment and rheological thermomechanical testing. All compositional parameters were expressed on a dry matter basis.

2.1.2. Essential Oils (EOs)

Four EOs, representing structurally diverse classes of volatile plant secondary metabolites, were procured from Sigma-Aldrich (St. Louis, MO, USA). The selected fluids comprised essential oil from plants: cinnamon (Cinnamomum verum; CinO; origin: Sri Lanka), oregano (Origanum vulgare; OreO; origin: Czech Republic), lemongrass (Cymbopogon citratus; LmgO; origin: India), and thyme (Thymus vulgaris; ThyO; origin: Spain). Pycnometric density determination at 20 °C yielded the following values: 1.025 g·mL^–¹ (CinO), 0.888 g·mL⁻¹ (OreO), 0.896 g·mL⁻¹ (LmgO), and 0.917 g·mL⁻¹ (ThyO).

Prior to analysis, the essential oils were stored in sealed amber-glass vials at laboratory temperature under light-protected conditions. To ensure accurate dosing, the required EO additions were calculated on a mass basis (mg·100 g⁻¹ WF) and subsequently converted to volumetric doses (µL) using the actual density of each essential oil.

2.1.3. Preparation of Binary Flour-Essential Oil Blends

A two-factor experimental design was applied, consisting of Essential oil type foursome (factor F1) and Essential oil dosage fivesome (factor F2). Based on preliminary experiments and published literature, EO concentrations of 5, 10, 20, 40, and 80 mg·100 g⁻¹ flour were selected; control sample without EO addition (0 mg·100 g⁻¹ flour). For each treatment, the required EO amount was calculated according to the measured density of the respective oil and added directly to the flour using a calibrated micropipette. The flour-essential oil mixtures were manually homogenized for 5 min and prepared immediately before analysis to ensure uniform distribution of the volatile compounds throughout the flour matrix and to minimize potential losses of volatile constituents. Sample codes consisted of a letter identifying the EO type followed by the applied dose. To avoid overlapping of the point labels in graphs presented, binary blends o WF and CinO, OreO, LmgO, and ThyO were designated as C5–C80, O5–O80, L5–L80, and T5–T80, respectively.

Prior to each Mixolab determination, the moisture content of the prepared flour-essential oil blends was measured using an infrared moisture analyzer (MA 110.R, Radwag, Radom, Poland) and subsequently used for correction of water addition during automated dough preparation.

2.2. Methods

2.2.1. Mixolab Rheological Profiling and Curve Interpretation

Dough thermomechanical behavior was characterized using a Mixolab analyzer (software of Chopin Technologies, Villeneuve-la-Garenne, France) following the standard Chopin+ protocol (ICC Standard No. 173 [48]). The primary rheological parameters extracted from the Mixolab curves were defined as follows:

• WAB_MIX (%): Mixolab water absorption; the percentage of distilled water required to hydrate the flour matrix to a target optimum torque (consistency of 1.10 ± 0.05 N·m).
• C₁ (N·m) and t_C1 (min): Maximum dough consistency (torque) during the initial mixing and the corresponding dough development time required to reach this optimum viscoelastic equilibrium.
• CS (N·m) and t_CS (min): Dough torque and time recorded at the end of the initial isothermal mixing phase (30 °C for 8.00 min), immediately prior to the controlled heating ramp (4 °C·min⁻¹).
• C2 (N·m) and t_C2 (min): Minimum torque representing protein network weakening induced by the synergistic effects of mechanical shear and thermal stress (at 15.00 min).
• C3 (N·m) and t_C3 (min): Peak torque reflecting the maximum rate of starch granules gelatinization.
• C4 (N·m) and t_C4 (min): Minimum torque during the heating plateau, indicating the physical stability of the hot polysaccharide (amylaceous) gel against mechanical shear (at 90 °C).
• C5 (N·m) and t_C5 (min): Final torque at the end of the cooling phase (50 °C, 45.00 min), quantifying the extent of starch amylose retrogradation.
• STA_C1 and STA_CS (min): Mechanical stability of dough consistency at the C₁ and CS points, respectively, defined as the time interval during which the upper curve envelope remains above the threshold of C1, CS − 11%.
• AMP_C1 (N·m): Curve amplitude at the C₁ torque peak, representing the vertical width of the trace as an indicator of dough elasticity.

To comprehensively evaluate the dynamics of the viscoelastic alterations, the company software calculated the standard torque differentials (Ci – Cj, shortened to Cij as usual) and kinetic slope angles as follows:

• C12 (N·m) / α (N·m·min⁻¹): Total consistency loss and its corresponding negative slope angle, representing gluten network thermomechanical degradation (comparable to the Farinograph Dough Softening Degree according to ICC Standard No. 115/1). Here, angle renamed to alpha°.
• C32 (N·m) / β (N·m·min⁻¹): Gelatinization peak amplitude and its positive slope angle, quantifying the velocity and intensity of starch gelatinization. Here, angle renamed to beta°.
• C34 (N·m) / gamma (N·m·min⁻¹): Hot gel breakdown and its negative slope angle, indicating the rate of thermal/amylolytic starch gel degradation and structural stability (analogous to the Breakdown viscosity in a Rapid Visco Analyser test Flour.rvc). Here, angle renamed to gamma°.
• C54 (N·m): Starch gelling intensity, measuring the magnitude of starch recrystallization during the cooling phase.

2.2.2. Innovative Mixolab Parameters

In addition to the conventional Mixolab descriptors, a set of innovative kinetic, geometrical, and transformation indexes was calculated from the original torque-time records according to the approach previously developed for farinograph curve kinetics [41].

The actual water absorption (WAB_MIXactual) was firstly normalized to a flour moisture content of 14% (WAB_MIX14%) and subsequently corrected to the standard Mixolab consistency of 1.10 N·m (WAB_MIXcorr) using Equations (1) and (2):

WABMIX 14% =	100 ·	WABMIX actual + MOI – 14	(% flour weight) (eq. 1)
		100 – MOI
WABMIX corr =	WABMIX 14% + k flour · (C1 – 1.10)		(% flour weight) (eq. 2)

where MOI is flour moisture content (%), C1 is the actual torque reached during hydration, and k_flour is the correction coefficient for wheat flour (≈ 7.0).

To facilitate comparison with farinograph-derived quality parameters, all characteristic torque points (C1, CS, C2, C3, C4, and C5) and the curve amplitude at optimum development (AMP_C1) were transformed into farinograph-like Brabender units (BU) assuming the premise ‘1.10 N·m = 500 BU’:

fCi, fAMPC1 =	454 · Ci, AMPC1	(BU) (eq. 3)
fDSDICC =	fC1 – fC2 = 454 · C12	(BU) (eq. 4)

where fDSD_ICC represents the Gluten Destruction Intensity Index, analogous to the farinograph Dough Softening Degree.

Additional derived indexes included:

• C12/STA_C1 – specific rate of thermo-mechanical dough weakening;
• C5/C1 – Structural Recovery Index (alternatively Finite Rigidity Index), expressing the extent of structural transformation between raw dough and the cooled denatured dough ~ bread crumb-like matrix;
• MWP (Mechanical Weakening of Proteins) and TMW (Thermo-Mechanical Weakening of Proteins), calculated as:

MWP =	100 ·	C1 – CS	(–) (eq. 5)
		C1
TMW =	100 ·	CS – C2	(–) (eq. 6)
		C1

where MWP and TMW represent the proportions of mechanical and thermo-mechanical protein weakening, respectively.

The ratio MWP/TMW was used to estimate the relative contribution of mechanical and thermo-mechanical weakening processes within the dough matrix.

Interestingly, the MWP/TMW ratio reflects the relative contribution of purely mechanical dough shearing to the subsequent thermomechanical protein destabilization. This parameter functions similarly to the Gluten Performance Index (GPI) derived from the Solvent Retention Capacity profile (SRC; AACC Method 56-11); the GPI means an absorption of solvent by gluten proteins solely, i.e., a value of the lactic acid-SRC purified from binding capacities of starch and non-starch polysaccharides. In case of the MWP/TMW ratio, it effectively isolates the intrinsic structural integrity and enzymatic/mechanical resistance of the gluten matrix of mixed dough from confounding thermal and starch-related phenomena. Further, if eq. 5 and eq. 6 are combined together, a man reveals these conjoined novel indexes are a function of the torque difference C12:

MWP + TMW =	100	·	(C1 – CS) + (CS – C2) =	k · (C1 – C2) ≈ C12
	C1

To complement the conventional Mixolab angles alpha°, beta°, and gamma°, two additional geometric descriptors were introduced:

• omega° – angle describing dough development between the beginning of the test [0.0 min; 0.0 N·m] and torque point C1 (slope C01);
• delta° – angle describing starch retrogradation during cooling and corresponding to the standard torque difference C54.

The angles were calculated according to eq. 7 where k_scale corresponds to the ratio between the horizontal (time) and vertical (torque) scales of the Mixolab curve (eq. 8):

omega°, delta° =	arctan	${\displaystyle \frac{180}{\pi }}·\left({\displaystyle \frac{\mathrm{C}\mathrm{i}\mathrm{j}[\mathrm{N}·\mathrm{m}]}{k_{scale}}}\right)$	(1) (eq. 7)
where kscale =	Scale of X-axis [min]	=	45	(1) (eq. 8)
	Scale of Y-axis [N · m]		5

For consistency, the original Mixolab angles alpha°, beta°, and gamma° could be recalculated in degrees in MS Excel:

angle° (N·m·min–1) =

=DEGREES(ARCTG((Cij / kscale)))

($°$) (eq. 9)

Finally, torque differences (C01, C12, C32, C34, and C54) were transformed into micro-scaled kinetic descriptors expressing the rate of torque change:

where ΔmC01, ΔmC12, ΔmC32, ΔmC34, and ΔmC54 represent the kinetic rates of dough development, protein weakening, starch gelatinization, hot-gel breakdown, and starch retrogradation, respectively. The prefix ‘m’ denotes the physical scaling factor milli- (10⁻³).

Figure 1. Representative Mixolab curve of white wheat flour obtained using the standard Chopin+ protocol according to ICC Standard Method No. 173 [49]. Adapted from Dubat and Boinot [50]. The test consisted of five consecutive phases: ① dough mixing at 30 °C; ② heating from 30 to 90 °C at 4 °C·min⁻¹; ③ holding at 90 °C; ④ cooling to 50 °C at 4 °C·min⁻¹; and ⑤ final holding at 50 °C. Standard Mixolab parameters: C1, optimum dough consistency corresponding to water absorption (WAB_MIX); CS, dough consistency at the end of the mixing phase; C2, minimum torque associated with protein weakening; C3, torque related to starch gelatinization; C4, hot-gel stability; C5, starch retrogradation during cooling; tC1-tC5 and TC1-TC5, times and temperatures corresponding to the characteristic torque points; STA, dough stability; alpha°, slope of thermo-mechanical protein weakening; beta°, slope of starch gelatinization; gamma°, slope of hot-gel breakdown. Supplementary parameter: AMP_C1, curve amplitude at C1, corresponding to dough elasticity. Innovative parameters introduced in this study: omega°, dough development and hydration angle (C0-C1); delta°, starch retrogradation angle (C5-C4). Note: At the end of the test (t_C5 ≈ 45 min), the Power Acquisition parameter reached approximately 131 W, as shown in the inset.

Figure 1. Representative Mixolab curve of white wheat flour obtained using the standard Chopin+ protocol according to ICC Standard Method No. 173 [49]. Adapted from Dubat and Boinot [50]. The test consisted of five consecutive phases: ① dough mixing at 30 °C; ② heating from 30 to 90 °C at 4 °C·min⁻¹; ③ holding at 90 °C; ④ cooling to 50 °C at 4 °C·min⁻¹; and ⑤ final holding at 50 °C. Standard Mixolab parameters: C1, optimum dough consistency corresponding to water absorption (WAB_MIX); CS, dough consistency at the end of the mixing phase; C2, minimum torque associated with protein weakening; C3, torque related to starch gelatinization; C4, hot-gel stability; C5, starch retrogradation during cooling; tC1-tC5 and TC1-TC5, times and temperatures corresponding to the characteristic torque points; STA, dough stability; alpha°, slope of thermo-mechanical protein weakening; beta°, slope of starch gelatinization; gamma°, slope of hot-gel breakdown. Supplementary parameter: AMP_C1, curve amplitude at C1, corresponding to dough elasticity. Innovative parameters introduced in this study: omega°, dough development and hydration angle (C0-C1); delta°, starch retrogradation angle (C5-C4). Note: At the end of the test (t_C5 ≈ 45 min), the Power Acquisition parameter reached approximately 131 W, as shown in the inset.

2.2.4. Statistical Analysis

2.2.4.1. Analysis of Variance and Correlation Analysis

The experiment was designed as a two-factor model consisting of four EO types (factor F1) and five EO dosage levels (factor F2), yielding 20 treatment combinations evaluated in duplicate. The experimental error was therefore estimated from:

DFError =

(4 oils · 5 doses) · (2 repetitions – 1) = 20

(eq. 11)

Statistical analyses were performed using Statistica 13.0 (TIBCO Software Inc., Palo Alto, USA). The effects of essential oil type, its dosage level, and their interaction were evaluated by two-way analysis of variance (ANOVA)—namely the Tukey's HSD test at a significance level of p ≤ 0.05. Only the primary Mixolab parameters were included in the ANOVA. Secondary—calculated descriptors (e.g., C12, C32, C34, C54, MWP, TMW, slopes omega°, delta°, and ΔmCij) were as derived variables excluded from the significance testing.

2.2.4.2. Correlation Analysis

Pearson's correlation analysis was performed at the same significance level (p ≤ 0.05). To evaluate the information content of the proposed descriptors, three correlation matrices were constructed separately for:

• Standard Mixolab parameters (matrix 20 × 20),
• Innovative Mixolab parameters (matrix 14 × 14),
• The combined dataset containing both parameter groups (matrix 20 x 14).

To improve visualization of large correlation matrices, statistically significant positive and negative correlations were converted into double-sided frequency histograms. Cumulative sums of significant positive (Σ⁺) and negative (Σ⁻) correlation coefficients were further calculated into two separate columns, to estimate the overall contribution of individual variable to the samples’ differentiation and multivariate data structure.

2.2.4.3. Principal Component Analysis (PCA) and Variance Component Analysis (VCA)

Multivariate relationships among rheological variables were investigated using PCA. Three separate PCA models were constructed:

• Standard Mixolab dataset (PCA_STD), comprising characteristic torque points (C1, CS, C2, …, C5), corresponding times (t_C1–t_C5), dough stability parameters (STA_C1 and STA_CS), curve amplitude (AMP_C1), torque differences (C12, ..., C54), and conventional slopes (angles) alpha°, beta°, and gamma°).
• Innovative Mixolab dataset (PCA_INOV), comprising STA_C1rel, indexes C5/C1, C12/STA_C1, MWP, TMW, MWP/TMW, ΔmC01, ΔmC12, ΔmC32, ΔmC34, ΔmC54, and slopes omega° – delta°.
• Representative dataset (PCA_REPRE), generated after the Variance Component Analysis (VCA) filtering and containing 17 selected standard and innovative variables (of 34 in total).

Data variance assessment by VCA was performed prior to the PCA and served as a variable-selection tool. The relative contributions of factor F1–EO type), factor F2–EO dose), and their interaction (F1 × F2) were quantified for all 34 evaluated Mixolab descriptors. Variables explaining at least 30% of the total variance through factor F1 were classified as PCA-active variables, whereas the remaining parameters were treated as supplementary descriptors. This threshold was adopted according to established variance-partitioning and experimental-design approaches.

Both factors were treated as random effects within the Statistica 13.0 software package (TIBCO Software Inc., Palo Alto, USA) to quantify the between-group variance correctly and avoid exclusion of potentially informative variables. The final representative dataset consisted of 17 PCA-active variables selected for subsequent multivariate analysis.

For PCA interpretation, F1 – Essential oil dose was included as a supplementary (explanatory) variable (EOD). Although not involved in the calculation of principal components, EOD was projected into both loading and score plots to facilitate interpretation of concentration-dependent effects on wheat dough rheology.

2.2.4.3. Innovative Graphical Interpretation of the Triaxial Principal Component Space

The conventional graphical representation of PCA results typically employs scatterplots of the PC1 × PC2 and PC1 × PC3 planes. To improve visualization of three-dimensional relationships among variables and samples, a modified projection system was developed. The traditional PC1 × PC2 projection was transformed into a PC2 × PC1 arrangement, while the PC1 × PC3 projection was replaced by the orthogonal PC2 × PC3 projection.

To facilitate direct comparison of both planes, the PC2 axis was shared between the two plots, forming a unified graphical representation of the first three principal components. In the PC2 × PC3 projection, the PC3 axis was displayed in an inverted orientation, with negative values positioned at the top and positive values at the bottom (Figure 2a). This approach enabled simultaneous visualization of the three-dimensional PCA space while preserving the original variance distribution among the principal components.

Figure 2b illustrates the conceptual geometric principle underlying the proposed visualization approach. The first three principal components (PC1, PC2, and PC3) are represented as a triaxial 3D-space, which is geometrically unfolded along the shared PC2 axis to generate two orthogonal projections (PC2 × PC1 and PC2 × PC3). The same visualization concept was subsequently applied to both loading and score plots throughout the study, creating a paired representation of variables and samples while preserving their common relationship to PC2.

3. Results

3.1. Effect of Essential Oil Incorporation on Standard Mixolab Parameters

The incorporation of EOs exerted no statistically significant influence on dough water absorption. Both actual and corrected WAB_MIX values remained statistically identical to the control flour (Table 1), oscillating within a narrow range (56.7–57.0%). Similarly, the maximum torque C1 was not significantly altered by individual treatments or group factors (Table 1b, c), confirming that the tested EOs did not disrupt initial dough hydration or optimal consistency development. The mathematical correction of WAB_act revealed up a necessity to lower or to increase about <-0.49; 0.61> percent point of water on flour weight in average, if the mixolab tests series could be repeated for the third time. Within the complete samples set, the variance was accidental – any tendency could be addressed to the EO type or EO dose.

In contrast, the protein weakening stage (CS and C2) exhibited significant dependency on both EO type and dose. Group means (Table 1b) showed that cinnamon (CinO) and oregano (OreO) oils significantly reduced the minimum torque C2 to 0.390 and 0.414 N·m, respectively, compared to the control (0.503 N·m), indicating a weakened gluten network under combined mechanical and thermal stress. This destabilization was dose-dependent; pooled dose effects (Table 1c) revealed a progressive decline in C2 with increasing concentrations. Individually, the most pronounced disruption was induced by 80 mg·100 g^–1 of CinO, where C2 significantly dropped to 0.349 N·m (Table 1a). Conversely, LmgO maintained C2 values statistically equivalent to the control across all doses.

The starch gelatinization phase (C3) and amylase activity stage (C4) were robust against EO fortification, showing no statistically significant variations among any individual treatments or group means.

However, significant modifications emerged during the cooling stage (C5), reflecting altered starch retrogradation. Group means (Table 1b) demonstrated that OreO and thyme oil (ThyO) significantly increased the final torque C5 to 2.802 and 2.757 N·m, respectively, versus the control (2.630 N·m). At individual levels (Table 1a), 20 and 80 mg·100 g^–1 of OreO and 80 mg·100 g^–1 of ThyO produced significantly higher C5 values (up to 2.894 N·m), suggesting that these specific EOs promote the formation of a more rigid cooled starch gel matrix.

Conventional Mixolab parameters effectively detected the effects EO impacts, identifying CinO as a protein disruptor and OreO/ThyO as starch retrogradation promoters. Nevertheless, because these standard torque points provide only a static overview, supplementary kinetic and geometrical descriptors are required to fully elucidate the underlying molecular mechanisms.

The effects of EOs were clearly reflected in the timing and stability characteristics of the Mixolab curves (Table 2). All fortified samples exhibited significantly longer dough development times than the control flour. The pooled dose effects (Table 2c) revealed a progressive, dose-dependent prolongation of t_C1 from 1.70 min up to 4.02 min at the highest concentration, regardless of the EO type. Significant differences also emerged in the time to reach protein weakening (t_C2). According to the group means (Table 2b), lemongrass oil (LmgO) delayed the onset of protein weakening (16.08 min) compared to the control (15.93 min), whereas cinnamon (CinO) and oregano (OreO) oils significantly accelerated this process, shortening t_C2 to 15.46 and 15.53 min, respectively.

Dough stability parameters were significantly reduced by most EO treatments. The control flour exhibited a STA_C1 value of 9.25 min. The group means (Table 2b) demonstrated that CinO, OreO, and thyme oil (ThyO) significantly reduced dough stability (to 6.48, 6.76, and 7.21 min, respectively). At the individual sample level (Table 2a), this destabilization was evident for almost all doses of CinO and OreO, dropping to values around 6.00–6.80 min. In stark contrast, LmgO preserved dough stability at levels statistically equivalent to the control, particularly at higher doses of 20 and 80 mg·100 g^–1, where STA_C1 reached 9.30 and 9.19 min, respectively. A matching trend was observed for the relativized stability parameter (STA_{C1 rel}), which remained highest for LmgO and lowest for CinO and OreO.

Taken together, the standard Mixolab parameters revealed highly distinct, oil-specific rheological responses of the wheat dough. CinO and OreO acted as primary disruptors within the protein-related region of the Mixolab profile, concurrently accelerating the onset of protein weakening (shorter t_C2) and reducing matrix resistance against thermal and mechanical stress (lower CS, C2, and stability values). Conversely, LmgO demonstrated a protective effect on the gluten network, maintaining structural dough stability and delaying protein degradation. During the subsequent starch-dominated phases, OreO and ThyO emerged as the most influential agents, substantially increasing the final torque C5 and thus altering starch retrogradation behavior during cooling. Nevertheless, while these conventional Mixolab parameters effectively map macro-rheological changes, they fail to decouple purely mechanical degradation from thermally induced protein and starch modifications. To overcome this limitation and fully elucidate the underlying molecular mechanisms, the experimental dataset was further evaluated using newly proposed kinetic and geometrical curve descriptors.

3.2. Novel Kinetic and Geometrical Descriptors Reveal Distinct Mechanisms of Dough Transformation

The transformation of conventional Mixolab parameters into farinograph-like ones, scaled into the Brabender units (BU) and innovative torque indexes provided a deeper mechanistic insight into dough behavior during kneading—mixing, heating, and cooling (Table 3). Because these newly proposed indexes were excluded from the two-way ANOVA as secondary calculated variables, the observed variations are evaluated as clear mathematical and numerical trends.

Recalculation of the basic torque points C1, CS, C2, …, C5 plus the amplitude AMP_C1 to Farinograph-like equivalents fC1, fCS, fC2, …, fC5 and amplitude fAMP_C1 illustrates well manufacturing of 50 g of flour in the Mixolab test vs. 300 g flour on the Farinograph (roughly 75 g vs. 480 g of water dough, respectively). In a case of the mandatory consistency C1, all values fC1 fell logically into the normalized range 480–520 BU. The oscillation fAMP_C1 represent approximately one-third of the farinograph Dough Width values, ranging for white wheat flour of standard bakery quality from 80 to 120 BU. Reversely, dough (gluten net) weakening fDSD_ICC is magnified by an initial thermal change (244–339 BU)—farinograph Dough Softening Degree should not overcome 100 BU to prevent expansion collapse of yeasted dough and a sureness of baking of the expected loaf volume. In case of additional calculation of the fC1 – fCS difference, group averages in order of CinO, OreO, LmgO and ThyO blends are 77, 85, 39 and 70 BU, respectively (against 35 BU for the WF control); a twice higher softening by OreO contrasted to LmgO could be considered as verifiable (data not shown). Intervals of the fC3 and fC4 were observed as very narrow (<817; 847> BU and <740; 795> BU), but still in common scaling 0–1000 BU of the farinograph endless paper. Nevertheless, scatter of the starch retrogradation 1154–1315 BU (Table 3a) would be unmeasurable on the older farinograph types; actual digitized Farinograph-E or Farinograph-TS are able to measure dough resistance against kneading up to 2250 BU (own research, unpublished data). Aiming on the samples’ subgroup and related averages, differences seem to be too close one to each other with exceptions of the trait fC2 and fC5. For the mentioned traits pair, measured results and averages accurately confirmed the theoretical assumption of inverse correlation between the torsions C2 and C5—dependence of bread staling on protein weakening. The addition of EO has been shown to weaken the protein matrix, and with this decrease, there is a support in starch retrogradation (from CinO to ThyO and from dose 5 to 80 mg·100^–1 g flour).

The newly proposed C12/STA_C1 confirmed the balanced and stable structure of pure wheat dough, which did not undergo dramatic softening (value 1.08). Cinnamon and oregano oils disrupted the protein matrix most severely, leading to the highest index values (~1.80) due to pronounced protein weakening relative to dough stability. Conversely, rheological data of the LMGO blends demonstrated that this oil acted as the 'most gentle' additive. Regarding EO doses, a structural degradation phase was identified at 5, 10, and 20 mg per 100 g of flour. At higher doses (40 and 80 mg/100 g), the index declined to a plateau of ~1.65 (Table 3b, 3c), indicating system saturation. In baking practice, a higher C12/STA_C1 index implies poorer dough tolerance during maturation as well as a reduced capacity to retain fermentation gases.

The mechanical weakening of proteins (MWP index), which quantifies gluten network disruption during the cold kneading phase, rose markedly from 7.2% in the control flour up to group means of 17.0% for oregano oil and 15.6% for cinnamon oil. At the individual treatment level (Table 3a), the highest dose of CinO (80 mg·100 g^–1) elevated MWP to 18.5%. This prominent rise indicates a substantial destabilization of hydrated gluten proteins under purely mechanical stress, likely driven by interactions of cinnamaldehyde or carvacrol with the protein matrix. In stark contrast, lemongrass oil (LmgO) maintained an overall group mean MWP of 7.9%, remaining closely aligned with the control. Thyme oil (ThyO) exhibited an intermediate group value of 13.7%.

In contrast to MWP, the thermomechanical weakening of proteins (TMW) varied within a much narrower interval across all treatments (group means between 45.6% and 48.9%), suggesting that EOs exert less influence on thermally induced protein denaturation. Consequently, the MWP/TMW ratio emerged as a highly sensitive descriptor to differentiate the primary mode of action of individual EOs. The control flour showed an MWP/TMW ratio of 15.3%. For CinO, OreO, and ThyO, this ratio practically doubled to group means of 31.9%, 37.4%, and 30.4%, respectively, demonstrating a disproportionately higher contribution of mechanical shearing relative to thermal weakening. LmgO stood out by preserving the control-like balance, maintaining a group mean of 16.7%.

The structural recovery C5/C1 index, which quantifies the overall dough-to-pastry hardening process, followed a different response pattern. While the control reached 238%, OreO and ThyO increased this parameter to group means of 253% and 251%, respectively, with a peak value of 263% observed for ThyO at 80 mg·100 g^–1. This elevation implies an enhanced rigidity development and starch gel reinforcement during cooling. Interestingly, CinO exerted negligible impact on the C5/C1 index (group mean of 238%), despite its severe disruption of the protein matrix, confirming that gluten destabilization and starch-gel reinforcement under EO influence operate via independent molecular pathways. Critical dose of EO varies around 20 mg·100^–1 flour. In a connection to the C12/STA_C1 index, early-stage collapse of the cold gluten network directly enables the subsequent acceleration of starch recrystallization during cooling of ‘bread crumb-like’ material tested.

The transformation of conventional Mixolab torque-point differences into kinetic rates of torque micro-change (ΔmCij) by dividing them by the proper Δt_Cij and geometrical slope angles provided a highly detailed, continuous description of dough structural transformations (Table 4). Because these innovative mathematical descriptors were excluded from the two-way ANOVA as secondary calculated variables, the observed variations are evaluated as distinct numerical and geometrical trends.

Generalized, the ΔmCij confirmed two-sided effect of EO both on magnifying of the gluten disruption extent and on its velocity at the same time. In the protein-related region of the profile, the torque difference C12, the kinetic rate ΔmC12, and the slope alpha° highlighted substantial differences among the tested EOs. Cinnamon (CinO) and oregano (OreO) oils accelerated and enhanced gluten network weakening, as evidenced by an increase in group mean C12 values to 0.702 and 0.696 N·m, respectively, compared to the control (0.602 N·m). This was accompanied by a marked steepening of the alpha° angle from -21.8° (control) to group averages of -28.7° (CinO) and -28.2° (OreO). At the individual sample level, the sharpest decline was recorded for OreO at 20 mg·100 g^–1 (-30.3°). Thyme oil (ThyO) induced intermediate weakening trends, whereas lemongrass oil (LmgO) maintained C12 (0.585 N·m) and alpha° (-23.4°) values much closer to the control, demonstrating its low impact on mechanical gluten degradation.

The starch gelatinization phase (C32, ΔmC32, beta°) displayed a completely different response pattern. Blends containing LmgO produced the highest group mean of the beta° angle (59.0°) and an individual peak of 61.1° at 5 mg·100 g^–1, indicating an enhanced and rapid torque development during starch swelling. In contrast, OreO and ThyO substantially flattened the gelatinization curve, reducing the group mean of the beta° slopes to 53.8° and 54.0°, respectively, with individual minima reaching approximately 46.0°–47.4° at the highest doses (80 mg·100 g^–1). The corresponding kinetic parameter ΔmC32 mirrored these geometric variations, dropping to 1.86 for OreO and 1.96 N·mm·s^-1 for ThyO at 80 mg·100 g^–1, which supports the hypothesis that phenolic-rich oils physically interfere with starch granule swelling and water binding during heating.

Particularly pronounced modifications emerged in the transition region between starch gelatinization and hot-gel stability (C34, ΔmC34, gamma°). Lemongrass EO markedly accelerated viscosity breakdown during this hot phase, as evidenced by a severe steepening of the gamma° angle to a group mean of -11.4°, driven heavily by the 80 mg·100 g^–1 dose which plummeted to -20.6° (compared to -9.4° in control). This was accompanied by a corresponding drop in the kinetic rate ΔmC34 to -0.69 N·mm·s^-1. This behavior indicates that citral-rich oil uniquely destabilizes the developing hot starch paste under continuous shearing.

During the cooling stage (C54, ΔmC54, delta°), OreO and ThyO generated the most intensive starch gel restructuring. This was manifested by elevated group mean C54 values (1.092 and 1.059 N·m, respectively) and a substantial steepening of the delta° angle for ThyO (group mean 35.9°). At the individual level, the steepest delta° angles were recorded for ThyO at 20 mg·100 g^–1 (38.7°) and OreO at 80 mg·100 g^–1 (37.7°), confirming an accelerated and enhanced formation of a rigid crystalline starch network during retrogradation, which aligns with the structural recovery index trends.

Kinetic and geometric descriptors combined resulted in the identification of three very distinct rheological characteristics. As described, CinO primarily enhances gluten weakening during the initial mixing stage, LmgO predominantly alters the starch gelatinization rate and accelerates hot-gel breakdown, whereas OreO and ThyO uniquely impact both protein degradation and final starch retrogradation. These distinct mechanistic insights validate the high interpretative power of the proposed mathematical approach over traditional torque parameters.

Figure 3 presents a coherent mechanistic interpretation of protein weakening, successfully decoupling the mechanical and thermal contributions to gluten matrix disruption. Across all treatments, the orange bars (TMW) systematically exceed the blue bars (MWP), visually confirming that temperature-driven denaturation remains the dominant driver of protein weakening compared to isolated mechanical shear.

However, the purple line trajectories (MWP/TMW ratio) reveal highly divergent, oil-specific dose-response profiles:

• Cinnamon oil (3a): Induces a progressive, almost linear climb in the MWP/TMW ratio up to the maximum dose, signifying a steady shifting of the weakening mechanism toward mechanical vulnerability. Temperature degradation played a secondary role here.
• Oregano oil (3b): Triggers a sharp, early threshold jump at a dose of 10 mg·100 g^–1, where the ratio peaks above 60% and plateaus, showing an immediate saturation of mechanical gluten disruption. Damaged dough structure could not be destroyed more by heat input.
• Lemongrass oil (3c): Exhibits a unique parabolic response, where the ratio peaks transiently at a low dose (5 mg·100 g^–1) before declining back toward control levels at higher concentrations. The structure of the dough remains protected when cold.
• Thyme oil (3d): Displays a delayed response step, where the ratio remains flat up to 10 mg·100 g^–1, then surges abruptly to a maximum plateau of 60% at intermediate doses. There is an immediate mechanical degradation during cold phase, identical to the OreO.

These distinct visual profiles demonstrate that the proposed indexes do not merely quantify the magnitude of dough softening. By mapping the shift in the MWP/TMW balance, this graph effectively fingerprints the molecular pathways through which chemically diverse essential oils alter dough matrix integrity.

3.3. Diverging Correlation Histograms—Functionality of Innovative Mixolab Parameters

The suitability of the proposed kinetic and geometrical descriptors was evaluated using correlation balanced profiles across the standard, innovative, and combined Mixolab data matrices (Figure 4a–4c). Given that multivariate approaches, such as principal component analysis (PCA), hinge on a sufficiently interconnected data topology, variables displaying numerous significant correlations function as primary drivers of sample variance. Conversely, weakly correlated variables contribute orthogonal, complementary data that mitigate multicollinearity.

Within the baseline matrix of 20 standard Mixolab parameters (Figure 4a), the most pronounced interconnectivity was exhibited by dough stability (STA_C1), the torque point CS, the protein weakening index C12, and the corresponding slope alpha°. These variables exhibited both a high frequency of significant pairwise relationships and elevated cumulative correlation weights (Σ⁺ and Σ⁻), underscoring their centrality in capturing macro-rheological shifts. Notably, STA_C1 (Σ⁻ = -2.20; Σ⁺ = 4.71), CS (Σ⁻ = -1.72; Σ⁺ = 4.69), and alpha° (Σ⁻ = -2.27; Σ⁺ = 4.71) emerged as major integrative descriptors, effectively bridging the distinct phases of initial gluten hydration, mechanical development, and subsequent thermal transformation.

In contrast, the innovative parameters set (Figure 4b) displayed a distinctly decoupled correlation topology. Most of these novel descriptors exhibited low correlation frequencies and suppressed cumulative weights. This systemic divergence confirms that the proposed parameters do not represent mathematical redundancies of conventional Mixolab outputs; rather, they capture discrete, previously unquantified facets of dough behavior. The tightest intra-set relationships were confined to ΔmC32, ΔmC12, and STA_{C1 rel}, which primarily manifested as localized negative correlations. Even so, their cumulative sums remained substantially below those of the standard matrix. Furthermore, the supplementary variable *EOD¹ demonstrated near-total independence (Σ⁻ = -0.95; Σ⁺ = 0), verifying that enzyme dosage effects were structurally decoupled from the intrinsic novel descriptors.

The simultaneous evaluation of standard and innovative variables (Figure 4c) revealed that only a selective subset of conventional parameters served as interactive bridges between the two domains. The highest network centrality was achieved by C34, which exhibited five negative and four positive significant correlations (Σ⁻ = -2.95; Σ⁺ = 1.96). This behavior aligns robustly with the biophysical significance of C34, which delineates the critical transition from protein-dominated rheology to starch-dominated gel formation. During this phase, phenomena such as gluten network breakdown, water redistribution, starch swelling, and early enzymatic hydrolysis occur concurrently. Consequently, C34 acts as a natural thermodynamic link, embedding the newly proposed kinetic variables into the established framework of conventional Mixolab diagnostics.

Finally, the factor F2–EO dose showed almost exclusively negative correlations with the rheological properties of the dough. Negative sum of significant correlations Σ⁻ was -1.14 [panel (a)] and -0,95 [panels (b), (c)]. This mathematically confirms that essential oils dampened stability across the board, reduce torsional moments and loosen the structure.

The correlation balance analysis validates the structural integrity and functionality of the innovative Mixolab descriptors. While standard parameters form a highly dense, partially redundant informational network, the novel kinetic and geometrical variables offer low interdependence. This reduced redundancy enhances their utility for predictive multivariate modeling and mechanistically grounded interpretations, ensuring that each descriptor captures physical phenomena during thermomechanical processing.

3.4. Multivariate Characterization of Essential-Oil Effects

The correlation topology confirmed that several innovative Mixolab descriptors captured unique rheological information not accessible via conventional parameters. To rigorously evaluate their discriminatory power and quantify their contribution to essential-oil-induced dough transformations, the experimental dataset was subjected to Variance Component Analysis (VCA) followed by Principal Component Analysis (PCA).

3.4.1. Variance Component Analysis and Selection of Representative Variables

To mitigate data redundancy and eliminate uninformative noise prior to principal component modeling, VCA was applied to the comprehensive suite of standard and innovative Mixolab descriptors (Table 5). This statistical procedure partitioned the total variance to quantify the relative contributions of the EO type (factor F1), EO dose (factor F2), and their binary interaction (F1 × F2). Adopting a stringent threshold from manufacturing metrology frameworks [51], a minimum of 30% explained variance attributable to the botanical origin (F₁) was established to differentiate PCA-active variables from supplementary ones.

Within the conventional Mixolab architecture, the primary drivers of diversity under factor F₁ were C34 (98%), C₁ (92%), STA_C1 (66%), followed by CS and C4 (49% each), C32 (48%), C2 (44%), C12 (39%), and t_C2 (37%). These profiles indicate that the chemotypic profile and botanical source of the volatile oils exerted a far more dominant influence on macro-rheological variance than the absolute concentration applied. Notably, features tracking gluten network collapse (C2, C12, t_C2), dough stability kinetics (STA_C1, CS), and thermal starch transitions (C32, C34, C4) exhibited acute sensitivity to the unique chemical signatures of individual oils.

Concurrently, a selective subset of innovative descriptors satisfied the selection criterion, validating their structural functionality. The geometric angle ω° demonstrated an exceptionally high discriminatory capacity (93%), emerging as the second most sensitive parameter across the entire dataset. In addition, MWP (36%), ΔmC12 (35%), ΔmC01 (33%), and STA_C1rel (33%) surpassed the 30% F1–threshold, qualifying them as active variables. The retention of these novel features proves that the proposed kinetic and structural slope parameters successfully register distinct, fingerprint-like alterations induced by the unique chemical constituents of the tested essential oils.

Conversely, a substantial block of descriptors fell below the analytical threshold, including MWP/TMW (29%), TMW (28%), ΔmC54 (26%), STA_CS (25%), AMP_C1 (22%), alpha° (15%), ΔmC32 (13%), beta° (4%), C3 (1%), as well as gamma°, WAB_MIX, C12/STA_C1, and ΔmC34 (all showing 0% variance allocation to F1). Consequently, these features were designated as supplementary variables; they were excluded from the construction of the principal component spaces to prevent model distortion, yet they were retained as descriptive trajectories to aid mechanical interpretation.

A notable phenomenon unveiled by the VCA was the massive contribution of the interactive term (F1 × F2) for specific responses, most prominently C5 (67%), ΔmC01 (65%), STA_{C1 rel} (63%), and ΔmC12 (62%). This cross-over behavior demonstrates that the ultimate rheological outcome was not dictated by a simple linear dose response, but rather by non-linear synergies between the oil’s specific chemical components and their matrix concentrations. Such complex interplay strongly reinforces the hypothesis that different essential oils alter dough matrices through entirely distinct chemical and physical mechanisms.

The VCA filtered the original diagnostic matrix down to a highly responsive subset of 17 active variables that balance standard Mixolab benchmarks with innovative mathematical descriptors. This optimized array ensures maximum statistical sensitivity and mechanistic clarity for subsequent multivariate modeling.

3.4.2. PCA Model Performance—Eigenvalues and Communalities

The mathematical validity and dimensionality reduction efficiency of the three multivariate configurations were rigorously benchmarked using eigenvalue distributions and cumulative communality allocations (Figure 5). Discrete Principal Component Analysis (PCA) frameworks were executed for the baseline standard Mixolab parameters (PCA_STD), the innovative degradation descriptors (PCA_INOV), and the parsimonious representative variable set established via Variance Component Analysis (PCA_REPRE).

For all three data topologies, the primary extracted eigenvalue safely exceeded Kaiser’s threshold (eigenvalue > 1.0), validating the presence of highly structured, non-random latent patterns suitable for robust multivariate modeling (Figure 5a). The PCA_STD matrix exhibited a steep eigenvalue decay curve, driven by a heavily dominant first principal component (PC1). Conversely, the PCA_INOV descriptor network distributed its latent variance more uniformly across subsequent components. This balanced eigenvalue profile reflects the lower degree of baseline inter-correlation previously demonstrated for the innovative variables, confirming that these geometrical and kinetic features capture distinct, orthogonal, and complementary facets of dough biophysical behavior rather than redundant mathematical transformations.

The internal robustness of the models was further substantiated by the relative communality distributions (Figure 5b). Within the conventional Mixolab architecture, PC₁ functioned as the primary driver, capturing 42% of the global variability, with PC₂ and PC3 providing meaningful orthogonal contributions of 19% and 12%, respectively. In contrast, the innovative dataset showcased a restructured variance hierarchy: PC1 accounted for 39% of the total variance, while the structural weights of PC3 (15%) and PC4 (12%) were markedly elevated. This systematic redistribution confirms that the newly proposed kinetic slope and micro-torque descriptors succeed in mapping complex thermomechanical events—such as localized phase transitions—that remain undetected by standard macro-rheological benchmarks.

To surpass the standard 70% threshold of total explained variance, both the standard and innovative configurations required a three-component solution, yielding cumulative communalities of 73% and 71%, respectively. Conversely, the VCA-filtered representative dataset (PCA_REPRE) achieved the highest degree of mathematical compactness and informational density. Within this optimized framework, PC1 alone captured an exceptional 53% of the total variance, while a simple two-component pair (PC1–PC2) was sufficient to account for 72% of the overall data scatter, effectively eliminating multi-collinearity and informational redundancy.

Across all three modeling attempts, the cumulative explanatory power of the first five principal components (PC1–PC5) spanned between 86% and 94%, limiting stepwise the residual noise from 14% to a minor 6%. The absolute lowest residual variance was achieved by the VCA-filtered representative model (6% unexplained scatter), demonstrating that a targeted fusion of standard rheological benchmarks with innovative kinetic variables yields the most mathematically parsimonious and mechanism-rich representation of essential-oil-fortified wheat dough systems.

3.4.3. PCA of Standard Mixolab Parameters

To evaluate the macro-rheological transformations driven by volatile oil addition, the standard Mixolab parameters were projected into a 3D-PCA space and visualized via interconnected 2D-orthogonal projections sharing a common PC2 axis (Figure 6). As established by the communality profiles, the primary PC1 axis accounted for 42% of the total variance, while PC2 and PC3 explained 19% and 12%, respectively.

The structural trajectory of the supplementary explaining variables, vector of the supplementary variable—factor F2–Essential oil dose (*EOD), was predominantly aligned with the thermal starch-gel characteristics, specifically torques C4, C5, and the micro-torque difference C54. This spatial orientation demonstrates that incremental essential oil concentrations primarily affect the later, temperature-induced stages of the Mixolab profile. In contrast, variables tracking early kneading kinetics, such as dough stability (STA_C1) and the angle alpha°, were aligned perpendicularly to the *EOD vector and were located within the I and III quadrants of the PC1 × PC2 space. The lowest discriminatory power along these axes was associated with the secondary stability index (STA_CS) and the slope gamma°.

In the PC2 × PC3 projection, the protein- and starch-dominated phases of the Mixolab profile were segregated vertically, with the *EOD vector expanding more than twofold along the PC3 axis. This expansion was accompanied by a prolongation of the kinetic time markers t_C1 and t_C3. In this projection plane, the slopes beta° and gamma° occupied diametrically opposed positions.

These interactions were explicitly reflected in the distribution of sample scores (Figure 6ab, bb). In the PC2 × PC1 plane, the most heavily fortified binary blends, specifically C80, O80, and T80, were clustered along the negative region of the PC1 axis (quadrants II and III).

The score plot distribution across the PC2 × PC3 plane revealed further structural differentiation. Most notably, the PC3 axis successfully isolated the control wheat flour (WF) at the extreme positive pole, completely decoupled from all oil-blended matrices. Furthermore, PC3 segregated the wheat–essential oil blends into discrete groups based on their chemical composition. The oregano samples (O10 and O20) shifted toward the lower-right quadrant, whereas the thyme (T) and lemongrass (L) blends formed a synchronized cluster near the origin and along the precise trajectory of the *EOD vector. At maximum concentrations (e.g., L80), these samples tracked the path of the *EOD vector down the negative region of the PC3 axis.

3.4.4. PCA of Innovative Mixolab Parameters

To evaluate the precise degradation dynamics and structural recovery of the dough matrix, the innovative Mixolab parameters were projected into the 3D-PCA space and visualized via 2D-orthogonal projections sharing a common PC2 axis (Figure 7). The primary PC1 axis accounted for 39% of the total variance, while PC2 and PC3 captured 17% and 15% of the data scatter, respectively.

In the PC2 × PC1 projection plane (Figure 7aa, 7ab), the supplementary explanatory variable vector—essential oil dose (^*EOD)—was positioned in the upper-left quadrant (quadrant II). It was closely aligned with the C₅/C₁ ratio (Structural Recovery Index), the angle delta°, and the torque micro-change ΔmC₅₄. Diametrically opposite to these parameters, within the lower-right quadrant, were the kinetic indexes ΔmC₃₂ and ΔmC₁₂. The relativized dough stability index (STA_{C1 rel}) was located at the extreme bottom of the semi-plane along the negative PC1 axis. Along the positive region of the PC1 axis, the Mechanical Weakening Profile (MWP), the MWP/TMW ratio, and the C12/STA_C1 index were tightly clustered, while the Thermal Weakening Profile (TMW) vector extended horizontally into the lower-right quadrant.

The sample score distribution within the PC2 × PC1 plane (Figure 7ab) separated the highly fortified samples along the horizontal and vertical axes. The maximum dose treatments of cinnamon, oregano, and thyme oils (C80, O80, T80, alongside O40 and T40) clustered closely together in the upper-left quadrant, tracking the exact direction of the ^*EOD vector. In contrast, all cinnamon treatments at lower and intermediate doses (C5, C10, C20, and C40) occupied the upper-right quadrant, mapping near the C5 marker. The control flour (WF) and the lemongrass samples (L10, L20, L40, L80) clustered tightly around the central origin.

In the orthogonal PC2 × PC3 projection plane (Figure 7ba, 7bb), the ^*EOD vector shifted into the lower-left quadrant (Quadrant III), maintaining its strong alignment with the C5/C1 ratio. This rotation vertically segregated the geometric parameters, positioning the angle omega°, ΔmC₀₁, and ΔmC34 at the extreme positive pole of the PC3 axis. This projection safely isolated the control wheat flour (WF) at the absolute northern apex of the diagram (Figure 7bb), completely detached from all essential-oil-fortified sample cohorts.

3.4.5. PCA of Representative Variables

To establish a parsimonious multivariate framework, a final PCA model was constructed using the 17 representative variables (Figure 8), pre-filtered via Variance Component Analysis. This optimized combination of standard and innovative descriptors was projected into a 3D-PCA space and visualized via 2D-orthogonal projections sharing a common PC2 axis. Within this streamlined topology, the primary PC1 axis accounted for an exceptional 53% of the total variance, while PC2 and PC3 captured 19% and 13% of the data scatter, respectively.

In the PC2 × PC1 projection plane (Figure 8aa, 8ab, 8ac), the active variables exhibited maximum spatial segregation along the vertical PC1 axis. The upper semi-plane (positive PC1 region) was strongly dominated by indicators of hot-gel behavior and thermal breakdown, including C32, C4, C34, the innovative torque micro-change ΔmC12, and the structural recovery vector C5/C1. Concurrently, the supplementary explanatory vector—essential oil dose (^*EOD)—was positioned vertically along the positive PC1 axis. In opposition, the lower semi-plane (negative PC1 region) harbored variables related to initial dough mixing and protein strength, specifically the torque parameters C1, C2, CS, dough stability (STA_C1, STA_CS), and the time marker t_C2.

The corresponding sample score distribution in the PC2 × PC1 plane (Figure 8ac) revealed a sharp, dose-dependent vertical stratification. Regardless of the botanical origin, all highly fortified sample blends (C80, O80, T80, alongside O40 and T40) were tightly clustered at the extreme northern pole, tracking the path of the ^*EOD vector. Conversely, the control flour (WF) and the lowest fortification levels (such as L5 and C5) were clustered at the negative pole of the PC1 axis.

In the orthogonal PC2 × PC3 projection plane (Figure 8ba, 8bb, 8bc), the vertical segregation shifted to differentiate the matrices based on their specific chemical profiles rather than absolute dosage. The PC₃ axis successfully isolated the control wheat flour (WF) at the positive apex of the plot. Along the lower semi-plane (negative PC3 axis), a clear separation emerged between the chemotypes: the oregano samples (O10, O20, O40, O80) and thyme samples (T40, T80) shifted toward the lower-left quadrant, whereas the lemongrass oil blends (L10, L20, L40, L80) projected uniquely along the lower-right quadrant, showing a distinct layout relative to the aromatic monoterpene cohorts.

4. Discussion

Thermomechanical profiling of wheat dough enriched with chemically diverse EOs revealed complex, phase-specific interactions that fundamentally alter both the protein network and the dynamics of polysaccharides. While conventional monitoring using the Mixolab instrument successfully identifies macro-rheological changes at the peaks of absolute torque [35,48,52], fundamental molecular factors such as competitive binding, steric hindrance, and covalent modification remain largely hidden in standard static outputs. To fully uncover these phenomena, we have integrated conventional Mixolab rheological data with newly proposed kinetic and geometric curve descriptors through a mechanism-based approach.

4.1. Essential Oils Differently Affect Gluten Weakening and Kneading Kinetics

The mechanical breakdown and thermal destabilization of the gluten network are comprehensively mapped by a highly interconnected network of descriptors, including C2, CS, t_C2, STA_C1, MWP, ΔmC12, alpha°, and the MWP/TMW ratio. The univariate and multivariate profiles collectively reveal a sharp split in gluten integrity based on the chemotypic profile of the added EOs. As mentioned supra, CinO and oregano OreO acted as the primary disruptors of protein structure, ThyO exerted a moderate destabilizing effect, while LmgO uniquely demonstrated a protective, matrix-stabilizing influence.

The intense disruption induced by CinO, evidenced by a suppressed C2 minimum (0.349 N·m) and elevated mechanical weakening (MWP), is driven by the distinct chemical reactivity of cinnamaldehyde. As an aromatic conjugated aldehyde, cinnamaldehyde possesses a highly reactive carbonyl group capable of forming covalent cross-links with the solvent-exposed amino acid residues of gluten proteins, particularly via nucleophilic addition with the ε-amino groups of lysine, Schiff base formation, or free thiol groups of cysteine [53,54,55]. This chemical modification alters the native charge distribution and sterically limits the natural gluten interactions [56,57]. Consequently, the network undergoes higher mechanical degradation during mixing, accelerating the drop in torque (ΔmC12) and yielding a steep thermal degradation slope (alpha°).

A physically distinct but equally severe destabilization mode was observed for OreO and ThyO. Their dominant components, carvacrol and thymol, are structural isomers belonging to the class of phenolic monoterpenes. Due to their highly hydrophobic nature and sterically demanding aromatic rings, these molecules partition aggressively into the hydrophobic cores of folding protein fragments as the temperature rises [40,58]. This insertion weakens the cooperative hydrogen bonding and hydrophobic cohesiveness of the glutenin-gliadin matrix [59,60,61], strong lowering dough stability (STA_C1) and rendering the network highly sensitive to continuous mechanical shear stress (MWP/TMW).

In sharp contrast, LmgO preserved gluten integrity, exhibiting the highest STA_C1 and lowest MWP values. This stabilization is governed by the acyclic open-chain geometry of citral, represented by its stereoisomers geranial and neral. Lacking a rigid, sterically demanding phenolic ring, the flexible hydrocarbon tail of citral aligns smoothly along the aliphatic side chains of the gluten network. By functioning as an interstitial, low-friction molecular cushion rather than an aggressive matrix disruptor, citral buffers the protein network against continuous mechanical shear [62,63,64], effectively protecting the gluten matrix from premature thermal collapse.

The perpendicular orientation of dough stability (STA_C1) relative to the EOD vector in the subsequent standard PCA projection mathematically confirms that early mixing kinetics and mechanical gluten development operate independently of the oil concentration matrix, being governed instead by initial protein hydration. This behavior matches the mathematical and biophysical definitions of the innovative descriptors, when a sample undergoes intense mechanical destruction during the initial cold mixing stage (high MWP), less structural integrity is maintained within the dough matrix, which subsequently minimizes thermal collapse under rising temperatures, resulting in a low TMW, because the torque had already decreased substantially [34,35,65,66]. The clustering of the C12/ STA_C1 (specific rate of dough softening) and MWP/TMW indexes reveals that the volatile oils act as initial structural plasticizers. By inserting themselves between gluten protein chains, they reduce the matrix's resistance to continuous mechanical shear stress, accelerating the early torque drop (ΔmC12) while dampening subsequent thermal collapse [62].

4.2. Differential Effects on Starch Gelatinization and Hot-Gel Stability

As the thermomechanical profile transitions into the starch-dominated domain, the kinetic dynamics are finely captured by C32, beta°, ΔmC32, C34, gamma°, and ΔmC34. The results demonstrate that LmgO significantly accelerated the velocity of starch gelatinization (indicated by an elevated slope beta° and torque micro-rise ΔmC32); whereas OreO and ThyO systematically restricted the gelatinization kinetics. Concurrently, LmgO accelerated the subsequent hot-gel breakdown phase to the highest degree.

The mechanical explanation for these differences may lie in the specific interactions between the oil molecules and the shifting starch polymer layout. The linear, open-chain structure of citral potentially allows it to slip easily between expanding amylose and amylopectin chains during the early stages of granule swelling [67]. By acting as a localized plasticizer within the amorphous regions of the starch granule, citral lowers the structural resistance to water ingress, thereby accelerating the kinetic rate of gelatinization (beta°) [68]. However, this rapid disruption of granule integrity may also reduce the shear tolerance of the hot starch gel under continuous mixing at high temperatures, driving an accelerated breakdown rate (gamma°, ΔmC34) [67,68,69,70]. Conversely, the sterically demanding phenolic monoterpenes carvacrol and thymol (OreO and ThyO) exert an opposite effect. These bulky hydrophobic molecules may alter water availability and starch-water interactions, thereby restricting starch granule hydration and swelling [67,71]. This physical masking dampens the early starch viscosity rise, can resulting in a suppressed beta° slope and a lower ΔmC32 development rate, aligning robustly with established models of thymol- and carvacrol-starch encapsulation kinetics [68,72].

The structural trajectory of the *EOD vector in the standard parameter PCA loading plots provides a direct multivariate visualization of these phenomena, being predominantly aligned with the thermal starch-gel characteristics (C4, C5, and the micro-torque difference C54). In the corresponding PC2 × PC3 projection, the prolonged t_C1 and t_C3 marks, alongside the dampening of slopes beta° and gamma°, indicate that the essential oils may act as physical lubricants and swelling inhibitors, decelerating both amylose’s leaching and hot-gel breakdown [34,73]. Furthermore, the score distribution of the innovative descriptor models confirms that adding even minor doses of essential oils fundamentally alters early dough development kinetics (captured by angle omega° and ΔmC01) and enzymatic α-amylase activity (ΔmC34), separating the control flour completely from all fortified cohorts.

4.3. Promotion of Starch Retrogradation and Structural Recovery During Cooling

The structural recovery and crystalline restructuring of the cooled polysaccharide gel are tracked in high resolution by C5, C54, slope delta°, ΔmC54, and the C5/C1 ratio. This phase represents a major structural shift in the study, revealing an intense, clear promotion of starch retrogradation driven exclusively by the phenolic monoterpene cohorts (OreO and ThyO), which manifested the highest final torque (C5), steepest retrogradation slopes (delta°, ΔmC54), and elevated Structural Recovery Index (C5/C1).

Mechanistically, during the cooling phase from 90 °C down to 50 °C, the linear amylose chains that leached out during gelatinization begin to reassociate via hydrogen bonding into an ordered, crystalline 3D-network [74,75]. When carvacrol and thymol are dispersed through the continuous aqueous phase, their intensely hydrophobic segments may act as non-polar nucleation templates [76,77]. To minimize unfavorable interactions with the aqueous phase, hydrophobic essential-oil constituents may promote the reassociation and ordering of amylose chains into more densely packed crystalline arrangements during cooling, facilitating the formation of amylose-lipid inclusion complexes [78,79]. This action accelerates the rate of retrogradation and promotes the formation of amylose-lipid inclusion complexes that bridge adjacent starch helices [80,81].

The consistency of the C5, C54, angle delta°, and C5/C1 responses strongly suggests that oregano and thyme oils predominantly affect starch structuring during cooling rather than gluten behavior alone. The formation of ordered crystalline domains during cooling contributes to the stabilization of the 3D-starch network and substantially influences the final mechanical properties of the gel [82,83]. This phenomenon may be explained by interactions between hydrophobic essential-oil components and amylose chains during cooling, promoting the formation of more ordered amylose structures and contributing to increased gel consistency, as reflected by the parallel alignment between the *EOD vector and the C5/C1 ratio (Structural Recovery Index) [80,82].

4.4. Chemo-Rheological Synthesis of Multivariate Models and Descriptors Added Value

Beyond mapping the specific effects of the essential oils, the findings highlight the significant methodological advantage of the newly proposed kinetic and geometric Mixolab descriptors over conventional diagnostics. A standard Mixolab evaluation provides only a static overview of absolute torque points, concluding that CinO diminishes protein resistance (↓ C2) and OreO increases final gel firmness (↑ C5). However, these conventional markers fail to capture the complex, underlying transition dynamics.

The innovative descriptors successfully decouple these overlapping thermomechanical events, offering precise insights that are otherwise hidden: they differentiate whether matrix damage is primarily driven by mechanical shear or thermal stress (MWP versus TMW), quantify the real-time velocity of gluten network softening (ΔmC12), track the precise kinetic rates of initial starch gelatinization (ΔmC32) and subsequent enzymatic breakdown (ΔmC34), measure the real-time dynamics of crystalline starch restructuring during the cooling phase (delta°, ΔmC54), and provide a holistic measure of the material's total structural transformation from a raw, kneaded dough to a rigidified cooled gel (C5/C1).

The representative PCA framework validates the utility of using Variance Component Analysis (VCA) as a mathematical filter [84]. By retaining the 17 most active descriptors only, the model successfully condensed 72% of the total experimental variance into a simple two-component space (PC1–PC2), effectively removing uninformative background noise and reducing model redundancy to an absolute minimum of 6%. The vertical alignment of the EOD vector along the positive PC1 axis, running parallel to the Structural Recovery Index (C5/C1) and thermal starch features (C4, C32), demonstrates that essential oil dosage acts as the primary switch governing the transition from protein-mediated dough rheology to starch-dominated gel properties. The strong spatial opposition between early kneading parameters (C1, CS, STA_C1) at the bottom of the biplot and the^*EOD vector at the top underscores a dual molecular mechanism: at low concentrations, initial protein hydration and mechanical gluten development dictate matrix strength, whereas elevated volatile oil content triggers an intense, dose-dependent promotion of amylose-lipid inclusion complexes that dominate the mechanical profile during cooling [80,82].

Finally, the sample score distribution across the PC2 × PC3 plane provides the final chemo-rheological confirmation of the study's structural model, successfully isolating the sample matrices based on their specific chemical geometries. The clear segregation of the pure control flour (WF) at the extreme positive pole of the PC3 axis mathematically proves that even a minimal inclusion of volatile oils (5 mg·100 g^-1) induces immediate structural and conformational modifications within the gluten-starch network that are qualitatively distinct from the native rheological profile of pure dough [15,19,22,85].

The subsequent split between the different essential oils is directly driven by the molecular geometry and chemical functionality of their dominant components. The oregano samples (rich in sterically demanding aromatic monoterpenes like carvacrol and thymol) shifted toward the lower-right quadrant, revealing a discrete interaction mode with the starch matrix during the cooling phase [22,30,33]. Conversely, the tight, centralized alignment of the lemongrass oil (LmgO) scores along the vertical axis, even at maximum fortification (L80), highlights the unique behavior of citral. Conversely, the tight, centralized alignment of the lemongrass oil (LmgO) scores along the vertical axis, even at maximum fortification (L80), highlights the unique behavior of citral. Due to its relatively flexible acyclic molecular structure, citral may experience less steric restriction within the dough matrix than the bulkier aromatic constituents present in oregano and thyme EOs. Its relatively small and flexible molecular structure may favor association with amylose helices and potentially promote the formation of amylose inclusion complexes, similarly to other hydrophobic ligands reported in starch systems [80]. At higher concentrations, this linear configuration drives the sample scores precisely along the *EOD vector down the PC3 axis, suggesting a dose-dependent promotion of amylose inclusion complexes and enhanced starch reassociation during cooling [86,87]. In stark contrast, the dense clustering of maximum-dose cinnamon (C80), oregano (O80), and thyme (T80) samples reflects the strong matrix disruption caused by sterically demanding aromatic rings, which severely weaken the gluten network's shear tolerance while simultaneously triggering an intense, dose-dependent promotion of amylose-lipid inclusion complexes during starch retrogradation [86,88].

Overall, the four essential oils produced distinct rheological fingerprints in wheat dough structure and behavior. Cinnamon oil predominantly intensified gluten weakening during mixing, lemongrass oil mainly altered starch gelatinization and hot-gel stability, whereas oregano and thyme oils affected both protein weakening and starch retrogradation. The newly proposed kinetic and geometrical Mixolab descriptors successfully differentiated these mechanisms and provided substantially deeper insight into dough structural transformations than conventional torque parameters alone.

5. Conclusions

This study demonstrated that essential oils induce distinct and highly specific modifications of wheat dough thermomechanical behavior, which can be effectively characterized by a rheological test on the Mixolab rheometer, combining conventional parameters with newly proposed kinetic and geometrical descriptors of the viscoelastic curves recorded. The extended approach of collected data analysis enabled a detailed differentiation of protein weakening, starch gelatinization, hot-gel stability, and starch retrogradation processes that remain only partially visible through standard Mixolab records evaluation.

Three clearly differentiated rheological fingerprints were identified. Cinnamon essential oil predominantly affected the protein phase, causing the strongest increase in mechanical protein weakening, accelerated dough destabilization, and a marked reduction in gluten stability. In contrast, lemongrass essential oil has maintained gluten integrity at levels comparable to the control dough but significantly modified starch-related transformations by accelerating gelatinization kinetics and enhancing hot-gel breakdown. Oregano and thyme essential oils exhibited a dual effect, simultaneously promoting protein weakening and increasing structural recovery during cooling.

The integrated framework of the Variance Components—Principal Components Analyses demonstrated principally the newly proposed descriptors provide non-redundant information relative to conventional Mixolab parameters. Their low-frequency correlation structure improved discrimination among essential oils and enabled the identification of kinetic phenomena that were not captured by traditional torque characteristics alone. Particularly informative proved to be the indexes MWP, ΔmC12, ΔmC01, STAC1rel, C5/C1, and the newly transformed geometrical angles of the dough development and starch retrogradation rate.

From a practical perspective, the results indicate that essential oils cannot be considered a homogeneous group of functional additives. Instead, their effects depend strongly on their chemical composition and concentration. The proposed analytical-statistical framework therefore offers a useful tool for predicting and directing rheological changes in clean-label cereal formulations, closely ‘in situ’ the processes occurring. Lemongrass essential oil appears suitable for applications requiring preservation of dough stability, whereas oregano and thyme essential oils may represent promising ingredients for targeted modification of starch retrogradation, crumb firmness, and storage behavior of bakery products.