Optimization of wheat dextrin yogurt formulation using response surface methodology

Abstract

In the current study, response surface methodology was executed to optimize the ingredient formulation and process conditions production such as wheat dextrin, starter culture and incubation time on the responses such as pH, viscosity, syneresis, overall acceptability, L* value and hardness of the wheat dextrin yogurt. The analyses showed that the wheat dextrin yogurts have a pH from 4.09 to 4.98, viscosity from 10,649.5 to 21,410.1 cP, syneresis from 2 to 26.67%, overall acceptability from 5.3 to 7.9, L* value from 81.2 to 84.3 and hardness from 506 to 5943.3 g during the optimization process. From the variance analysis, the R² of five response variables except hardness is more than 0.73, which indicates the model explained a high proportion of variability. To conclude, based on the response surface 3D plot of the pH, viscosity, syneresis, overall acceptability, L* value, and hardness evaluation, the optimum value for the independent variables are wheat dextrin of 15 g, a starter culture of 25 g, and an incubation time of 8 h for the wheat dextrin yogurt.

Introduction

The term yogurt was developed from the Turkish word “jugurt.” Traditional dairy products are a vital part of Indian heritage. About 9% of the total milk produced in India is converted into fermented milk products (Singh 2007). Yogurt is a fermented dairy product having many health benefits, and therefore it is highly focused by dairy researchers. The combined effect of Lactobacillus delbreuckeii bulgaricus and Streptococcus thermophilus organisms is well-defined in yogurt by its flavor and texture. Besides, these two organisms are probiotic and thereby exert maximum health benefits to consumers.

Yogurt is consumed as one of the most healthy and nutritious foods (Shi et al. 2017; Zhi et al. 2018). Protein digestibility is better in the yogurt than milk, which gives a positive effect on the human body with probiotic bacteria. The whole picture of yogurt is further authorized by the incorporation of various fruit preparations that provides fiber and antioxidants in the yogurt (O’Rell and Chandan 2006). Yogurt is also a worthy source of calcium, protein, vitamin B12, and iodine, and its intake has been related to a lesser risk of obesity and cardiometabolic risk in children and adults (Cormier et al. 2016).

Healthy metabolic profiles of children and adults were related to yogurt’s frequent consumption (Zhu et al. 2015; Wang et al. 2013). Lower levels of triglyceride levels, blood glucose level and lower systolic blood pressure was observed with increased yogurt consumption (Wang et al. 2013), and several recent meta-analyses have demonstrated that increased yogurt consumption is inversely connected with the threat of increasing type 2 diabetes (T2D) (Aune et al. 2013; Chen et al. 2014; Gijsbers et al. 2016).

Dietary fiber (DF) is a residue of the edible portion of the plant. They are carbohydrates that resist digestion and absorption in the human intestine and undergo either complete or partial fermentation in the human large intestine. DF includes lignin, oligosaccharides, tannins, resistant starch, and associated plant substances (Tomic et al. 2017).

Many nutrition-associated illnesses were associated with the lack of fibers in the regular diet. European Food Safety Authority (EFSA) has recommended average intake of 25 g fibers daily (EFSA 2010).

Manufacturing of prebiotic ingredients incorporated functional foods is an area that has a leading featuring in the food industry in recent years, and an upcoming market, with both economic and scientific benefits. Consumers are more conscious about the relationship between proper nutrition and increasingly search for food that, to nurture, should also provide health benefits to the consumers (Burgain et al. 2011). Based on this new market, some prebiotics has been included in a wide range of foods and beverages that are part of a healthy diet like bread, dairy products, dietary supplements, cereals, etc. Through this augmentation, consumers can enjoy tasty meals while promoting their health (Coman et al. 2012).

Several studies have reported that prebiotic fortification in yogurt by incorporating dietary fibers in it. Taking excess fiber-containing yogurt may prevent or reduce diabetes, obesity, hypercholesterolemia, cancer, gastrointestinal disorders, constipation, colonic diverticulosis, ulcerative colitis, hypertension, hyperlipidemia, coronary artery disease, and it also supports gastrointestinal immunity and intestinal microflora (Dello Staffolo et al. 2017; Hoppert et al. 2013; Sah et al. 2016; Tomic et al. 2017).

Researchers have reported that different types of fiber sources have different effects on yogurt’s rheological properties (Dello Staffolo et al. 2004; Luana et al. 2014; Raju and Pal 2014). Stabilization of high fat, improved water-holding, gel-forming, and viscosity are the properties of food fibers that permit the improvement of texture and reduced syneresis in the fiber-enriched yogurt (Dello Staffolo et al. 2017; Balthazar et al. 2016).

Wheat dextrin (WD) is a soluble, fermentable fiber made up of a glucose polymer developed by polymerization and hydrolysis of wheat starch. This wheat dextrin, due to its glucoside linkages, resists digestion in the small intestine (Vermorel et al. 2004). This wheat dextrin is widely used in the various food industry due to it is low viscosity and so develops the right consistency when added to plain water, beverages, or soft food (Institute of Medicine 2005).

Experimental studies have revealed that 45 g/day of wheat dextrin is well tolerated in the gastrointestinal tract (Pasman et al. 2006). Wheat dextrin has also revealed to diminish hunger and enhance satiety in a randomized, double-blind, placebo-controlled study (Guerin-Deremaux et al. 2011).

Manufacture of yogurt from different fibers has been attempted by several researchers previously, but no one has used wheat dextrin using Response Surface Methodology (RSM) for optimization purposes.RSM helps to study various factors that influence the responses by varying them simultaneously (Adinarayana and Ellaiah 2002), and it can also be used to learn the associations between one or more responses (dependant variables) and factors (independent variables). Gan et al. (2007) judged that in order to attain optimization, RSM would lessen the number of trials and offer multiple regression approach. The application of RSM has not yet been adopted in studies related to yogurt developed from wheat dextrin. Therefore, this research work aims to optimize the formulation ingredient and process conditions of wheat dextrin yogurt using RSM.

Materials and methods

Raw materials

Milk, starter culture and dextrin

Fresh cow’s milk was procured from nearby Aavin parlor (A unit of Tamil Nadu Co-operative Milk Producers Federation Limited) India, inside our university premises for the preparation of yogurt. Freeze-dried starter cultures containing Lactobacillus bulgaricus and Streptococcus thermophilus were used, and dietary fiber used in this research was wheat dextrin powder (Fibofit^®). Both starter culture and wheat dextrin powder were purchased from a local market shop in Salem city Tamil Nadu, India.

Preparation of starter culture

Two hundred milliliter of cow’s milk was heated up to 82 °C (180 °F) for 3 min. It was then cooled to 23–25 °C (73–77 °F). Five grams of starter culture powder was added, mixed well, and transferred into a glass jar. The cultured glass jar was incubated at 43 °C for 11 h in a Dash Yogurt maker, and the end product was stored at 4 °C, and it was used as a starter culture for further preparations.

Formulation of wheat dextrin yogurt

Dextrin yogurt was prepared as per the method narrated in the preparation of starter culture. However, the quantity of wheat dextrin, starter culture, and incubation time (independent variables) was followed as per the level recommended by response surface methodology (RSM). The prepared samples were refrigerated at 4 °C temperature until the evaluation was carried out.

Experimental design

The analysis

Response surface methodology (RSM) is a commonly employed tool in analyzing experimental data resulting in the optimization of processor or products (1). Central Composite Design (CCD) was used to analyze the interaction of process variables by using RSM (2). The statistical analysis for wheat dextrin yogurt preparation was done by using Design-Expert software (Version 11, Stat-ease, Inc., USA). There are three independent variables, which are Wheat Dextrin (X1), Starter Culture (X2), and Incubation Time (X3). Three coded levels, such as low, medium, and high, and the center points from − α to + α was also used in this study. The quantity of wheat dextrin varied from 5 to 15 g, 10 to 25 ml for the starter culture, and the incubation time is between 8 and 11 h. The design matrix used and the analytical results for the designed responses of wheat dextrin yogurt are depicted in Table 1. Various responses considered for this design experiment were pH (Y1), viscosity (Y2), syneresis (Y3), and overall acceptability (Y4). Using response surface methodology, for wheat dextrin yogurt, the complete quadratic equation of the response variables were derived as given below Eq. 1 as

$$\begin{array}{cc}\hfill \text{Y}& =\mathrm{\beta }0+\mathrm{\beta }1\text{X}1+\mathrm{\beta }2\text{X}2+\mathrm{\beta }3\text{X}3\hfill \\ \hfill & +\mathrm{\beta }11\text{X}12+\mathrm{\beta }22\text{X}22+\mathrm{\beta }33\text{X}32\hfill \\ \hfill & +\mathrm{\beta }12\text{X}1\text{X}2+\mathrm{\beta }13\text{X}1\text{X}3+\mathrm{\beta }23\text{X}2\text{X}3\hfill \\ \hfill \end{array}$$ 1

where Y is responses in the given model, β0 is constant for the above model and β1, β2, β3 is the linear regression model, β11, β22, β33 are interactive regression model and X1, X2, 3 are variables.

Table 1.

Actual levels of independent variables A. Wheat dextrin (g), B. Starter culture (ml) and C. Incubation time (h) used in central composite design with the measured responses

Run	Independent variables (actual level)			Responses
	Wheat dextrin (A)	Starter culture (B)	Incubation time (C)	Y1	Y2	Y3	Y4	Y5	Y6
1	10	17.5	9.5	4.67	12,283.6	17.33	5.7	82.23	1794.67
2	15	10	11	4.12	19,592.2	3.0	6.6	81.2	2289.0
3	5	10	8	4.89	10,649.5	30.0	6.9	82.6	2167.0
4	18.409	17.5	9.5	4.64	14,104.1	17.33	7.7	81.8	1196.3
5	10	30.1134	9.5	4.62	19,609.3	15.0	7.4	82.4	594.0
6	10	17.5	9.5	4.66	14,070.9	17.33	7.9	82.3	4497.3
7	10	17.5	9.5	4.79	13,810.5	18.0	6.3	81.53	3782.0
8	10	17.5	9.5	4.49	15,312.7	17.33	5.3	81.53	3552.0
9	10	4.8865	9.5	4.54	18,790.2	11.67	7.6	82.66	266.33
10	5	25	8	4.92	14,354.3	11.0	6.7	83.96	3883.0
11	15	10	8	4.98	11,003.3	10.67	7.0	82.63	5943.3
12	15	25	8	4.60	18,613.2	2.0	6.7	82.4	1420.3
13	1.59104	17.5	9.5	4.46	10,640.1	9.67	5.5	84.3	506.0
14	10	17.5	9.5	4.87	12,834.8	17.67	7.7	81.83	3603.33
15	5	10	11	4.09	21,410.1	4.67	7.3	81.43	3080.0
16	10	17.5	12.0227	4.67	16,757.4	9.33	7.2	81.7	2351.7
17	5	25	11	4.28	16,240.5	14.33	7.3	83.36	1699.7
18	10	17.5	6.97731	4.63	14,391.9	26.67	7.1	81.8	7951.0
19	10	17.5	9.5	4.52	13,331.3	17.0	7.4	81.9	4009.33
20	15	25	11	4.32	11,759.9	18.33	7.2	82.86	523.67

(Y₁) pH, (Y₂) viscosity (Cp), (Y₃) syneresis (%), (Y₄) overall acceptability, (Y₅) L* value, (Y₆) hardness (g)

The RSM was used to derive the optimum formulation conditions using three-parameter five-level central composite rotatable designs (CCRD), which dictated 20 experimental runs. Table 1 shows the level of codes three independent variables (wheat dextrin, starter culture and incubation time) used in the central composite design. The quantity of wheat dextrin varied from 5 to 15 g, starter culture varied from 10 to 25 ml, and the range of incubation time is between 8 and 11 h. The response of the design experiment was pH (Y1), viscosity (Y2), syneresis (Y3), overall acceptability (Y4), L* value (5), and hardness (6).

Physiochemical and overall acceptability analysis of wheat dextrin yogurt

The pH values of each wheat dextrin yogurt sample were analyzed using a digital pH meter (Testo 206 pH2 I, India).

One series of rotational viscometer (Fungilab S.A, Spain) was used to measure the apparent viscosity of the yogurt sample. The wheat dextrin yogurt sample was taken out from the refrigerator (4 °C), and it was retired at room temperature for 5 min (3). Then the sample was placed in a 100 ml beaker, and the level 4 spindle was dipped into the sample before the viscometer was switched on; the spindle was allowed to spin at 0.3 rpm rotation speed. The viscosity results were recorded in centipoises (cP) after 1 min of shearing.

Syneresis was determined using the centrifugal method, according to Pluta et al. (1999). In a centrifugal method, 10 ml of yogurt after mixing was placed in a calibrated test tube and centrifuged in Redmi R-4C for 12 min at 1500 RPM, and then the volume of liberated whey was measured (5). Syneresis was calculated using the following equations:

$$\text{Syneresis}\left(\%\right)=\frac{\left(\text{Ws}\right)\left(100\right)}{\text{Wy}}$$

where Ws = the supernatant after centrifugation; Wy = the yogurt or fermented milk in the tube.

The sensory evaluation of the formulated wheat dextrin yogurt was done among 10-trained panelists, including the faculty and research scholars of the Nutrition and Dietetics Department of Periyar University, Salem, Tamil Nadu. The panel was selected by their willingness to participate. The panel assessed the overall acceptability of the yogurts. The yogurt sample to be evaluated was served in glass vessels with a volume of 25 ml at room temperature, and also a glass of water was served to neutralize the taste before the next yogurt sample analysis.

Color analysis of wheat dextrin yogurt

The color of the wheat dextrin yogurt was evaluated using a Lovibond tintometer (Model LC 100, UK).CIELAB scale was used to measure reflectance for measuring the parameter called lightness (L*). Before the color evaluation begins, the instrument was calibrated by closing its lid, then the triplicate reading of the sample was taken, and the average value was recorded.

Textural evaluation of dextrin yogurt

A texture analyzer (Perten Instruments TVT 6700, Sweden) was used to measure the TPA (Texture Profile Analysis). The instrument was equipped with a 25 mm diameter stainless steel cylindrical probe to measure the TPA of prepared wheat dextrin yogurt samples. The yogurt was penetrated with the probe at a depth of 10 mm, and the test speed of the probe was 1 mm/s. The hardness (g) of the yogurt samples were taken in triplicates, and the average values were recorded.

Analysis of data

Response surface methodology (RSM) was endorsed in this experimental design and analysis (Khuri and Cornell 1987). Multiple regression analysis was carried out to fit the model. Design-Expert software version 11 was used to carry out the optimization of polynomials. The constraints are assigned to find the coded value of variables between the lower and upper limits. The desirability function was adjusted by assigning a particular weight to each goal. The response surfaces were plotted as a function of two variables while keeping the third one at an optimum level.

Results and discussion

Actual values of independent variables such as Wheat dextrin, starter culture, and Incubation time, along with the measured responses for all the 20 treatments, are given in Table 1. The pH of wheat dextrin yogurt ranged between 4.12 and 4.98 0.26 and viscosity between 10,640.1 and 21,410.1 (Cp)/100 ml. Syneresis ranged between 2.0 and 26.7/100 ml. The overall acceptability was found to be 5.3–7.9. The L* value and hardness of wheat dextrin yogurt ranged between 81.2–84.3 and 506–5943.3 (g).

Diagnostic checking of the fitted models

All the effects, such as linear, quadratic, and interactive, were calculated for each of the models. The model adequacy was tested using F ratio, coefficient of correlation, and also with lack of fit test. All main linear, quadratic, and interactive effects were calculated for each model. The adequacy of the model was tested using the F ratio, coefficient of correlation, and lack of fit test (Table 2). All the responses such as pH, viscosity, syneresis, overall acceptability, L* value, and hardness were fitted with quadratic models. The values of correlation coefficients were high, ranging from 73.94 to 89.37%, except for hardness, which was 51.47%. The lack of fit tests was insignificant for the responses like viscosity, L* value, and hardness and significant for the rest of the responses.

Table 2.

Design summary and estimated regression coefficients and their significance for dependent variables

Factor	pH	Viscosity (Cp)	Syneresis (%)	Overall acceptability	L* value	Hardness (g)
Model	Quadratic significant	Quadratic significant	Quadratic significant	Quadratic significant	Quadratic not significant	Quadratic not significant
Intercept	4.60255	13620.1	17.5416	7.25382	81.8509	3487.24
A	0.1495	0.4548	0.4227	0.8649	0.0140*	0.9280
B	0.1410	0.9500	0.8561	0.3141	0.0772	0.3474
C	0.0373*	0.0066**	0.0220*	0.0665	0.2107	0.3696
AB	0.4662	0.7622	0.2123	0.2717	0.2898	0.1452
AC	0.3714	0.0245*	0.0287*	0.1408	0.6411	0.4521
BC	0.0203*	0.0001**	0.0014**	0.0014**	0.1701	0.9372
A2	0.7138	0.2041	0.0986	0.6477	0.0178**	0.1510
B2	0.1971	0.0006**	0.0906	0.2231	0.1306	0.0816
C2	0.0236*	0.1409	0.6988	0.0747	0.8973	0.7134
R2 (%)	0.7418	0.8937	0.8070	0.7704	0.7394	0.5147
Lack of fit	Significant	Not significant	Significant	Significant	Not significant	Not significant

**p < 0.01; *p < 0.05

Response surface methodology model for pH

The F value for the quadratic model of pH was significant (p ≤ 0.01). The following equation can express the quadratic model for pH.

$$\begin{array}{cc}\hfill \text{pH}& =+4.60-0.1676\text{A}-0.1716\text{B}\hfill \\ \hfill & +0.2577\text{C}+0.1063\text{AB}+0.1313\text{AC}\hfill \\ \hfill & +0.3863\text{BC}+0.0394{\text{A}}^2-0.1444{\text{B}}^2-0.2788{\text{C}}^2\hfill \\ \hfill \end{array}$$ 2

A is the coded factor of wheat dextrin, B is coded factor of starter culture, and C is coded factor of incubation time.

The mean value of the pH ranged from 4.09 to 4.98. It is evident from Table 2 that incubation time at both linear and quadratic levels, as well as starter culture and incubation time at interactive level, were affecting the pH level of the yogurt significantly (p < 0.1).The coefficient of regression (R²) for pH was 0.7418, which indicates that the model could account for 74.18% data. Figure 1a describes that at the interactive level, as the amount of wheat dextrin and starter culture increases, the pH level decreased from 4.8 to 4.4. Figure 1b describes that at linear level, as the amount of wheat dextrin increases, pH decreases on the other hand, as the incubation time increases pH increased first and then decreased. pH is a measure of the acidity or alkalinity of a given solution. In primary stage, starter culture was prepared by rising pure strains in the sterilized milk which indicates its high acidic nature. Figure 1c scientifically proves this fact that at the linear level, as the starter culture increases, the pH decreases sharply at the same time increase in the incubation time has a mild change in the yogurt’s pH level. Similar to the reports of (Kristo et al. 2003; Bitaraf et al. 2012; Lee and Lucey 2004), which specifies high inoculum concentration leads to high acid production, the effect of starter culture on pH was also higher as compared to wheat dextrin and incubation time, which decreased pH sharply and mildly respectively in the present study.

Fig. 1.

Response surface plot for pH (a–c) and viscosity (d–f) as a functions of a wheat dextrin (g), b starter culture (ml) and c incubation time (h)

Response surface methodology model for viscosity

The quadratic model fitted to viscosity was significant (p ≤ 0.01), and also lack of fit was insignificant relative to the pure error. The following equation can indicate the quadratic model for viscosity.

$$\begin{array}{cc}\hfill \text{Viscosity}& =+13620.05+305.78\text{A}-25.31\text{B}\hfill \\ \hfill & +1341.79\text{C}+159.80\text{AB}-1359.40\text{AC}\hfill \\ \hfill & -3044.08\text{BC}-520.07{\text{A}}^2+1893.87{\text{B}}^2+612.21\text{C2}\hfill \\ \hfill \end{array}$$ 3

The mean value of the viscosity ranged from 10,649.5 to 21,410.1 cP. It is evident from Table 2 that incubation time at linear level, wheat dextrin with incubation time as well as the amount of starter culture with incubation time at the interactive level and finally incubation time at quadratic level, were affecting the viscosity of the yogurt significantly (p < 0.1). The coefficient of regression (R²) for viscosity was 0.8937, which indicates that the model could account for 89.37% data. Figure 1d describes that at the interactive level, as the amount of wheat dextrin and starter culture increases, viscosity level decreased slightly from 15,000 to 13,000 cP, and in the end, it resumed its initial viscosity level of 15,000 cP. Figure 1e describes that at linear level, as the amount of wheat dextrin increases slight increase in viscosity was observed compared to incubation time, which showed a sharp increase in viscosity as the incubation time increased in yogurt formulation. Figure 1f depicts at the interactive level, as the amount of starter culture and incubation time increases, average viscosity level increased from 12,000 to 14,000 cP, where the highest increase was observed in increasing the incubation time (18,000 cP) which makes the live cultures to incubate, and leads to thickening of the yogurt compared to starter culture. Few research reports propose that high viscosity (Bitaraf et al. 2012) and better rheology due to improved gel strength (Haque et al. 2001; Skriver et al. 1993) can be obtained at elevated temperature. Similar to this studies both increases in incubation time and wheat dextrin content have increased the viscosity because when the incubation time increases, the starch present in wheat dextrin will form more gel due to the gelatinization process resulting with high viscosity in the yogurt.

Response surface methodology model for syneresis

A quadratic model was significantly (p ≤ 0.01) fitted to syneresis with the F value of 4.65.

$$\begin{array}{cc}\hfill \text{Syneresis}& =+17.54-0.9605\text{A}+0.2138\text{B}\hfill \\ \hfill & -3.11\text{C}+2.00\text{AB}+3.83\text{AC}+6.58\text{BC}\hfill \\ \hfill & -2.04{\text{A}}^2-2.09{\text{B}}^2-0.4454{\text{C}}^2\hfill \\ \hfill \end{array}$$ 4

The mean value of the syneresis ranged from 2 to 26.67%. It is evident from Table 2 that incubation time at linear level, wheat dextrin with incubation time as well as the amount of starter culture with incubation time at interactive level, were affecting the syneresis of the yogurt significantly (p < 0.1).The coefficient of regression (R²) for syneresis was 0.8070, which indicates that the model could account for 80.70% data. Figure 2a describes that at the interactive level, as the amount of wheat dextrin and starter culture increases, Syneresis level increase from 6 to 16%. Figure 2b states that, at linear level, as the amount of wheat dextrin increases, a slight decrease in syneresis, i.e., 8%, was observed compared to incubation time, which showed a sharp decrease in syneresis as the incubation time increased in yogurt formulation. Figure 2c depicted at a linear level as the amount of starter culture increases slightly decrease in syneresis, i.e., 5% was observed, and at the same time as incubation time increases, a sharp decrease in syneresis level up to 10% was observed due to the application of heat which increased the voluminosity and water binding capacity of the whey proteins compared to starter culture in the yogurt formulation. Gonzalez-Martinez et al. (2002) reported that whey protein supplemented yogurts will have syneresis ranging from 23 to 36%. In the current work, yogurt supplemented with wheat dextrin will have the syneresis of 2–26.67%. A similar result was observed by Bakirci and Kavaz (2008) in which they recorded lower syneresis values of about 16–21.4% in a sweet banana yogurt due to the incorporation of banana fiber. In the current study, an increase in the incubation time has sharply increased the syneresis as similar to the study done by Lee and Lucey (2004) in which they reported that an increase in syneresis was more on incubation time when compared to incubation temperature.

Fig. 2.

Response surface plots for syneresis (a–c) and overall acceptability (d–f) as a functions of a wheat dextrin (g), b starter culture (ml) and c incubation time (h)

Response surface methodology for overall acceptability

A significantly (p ≤ 0.01) quadratic model fit overall acceptability with the F value of 3.73.

$$\begin{array}{cc}\hfill \text{Overall acceptability}& =+7.25-0.0230\text{A}-0.1395\text{B}\hfill \\ \hfill & +0.2709\text{C}-0.2000\text{AB}-0.2750\text{AC}\hfill \\ \hfill & -0.7500\text{BC}-0.0603{\text{A}}^2-0.1664{\text{B}}^2-0.2548{\text{C}}^2\hfill \\ \hfill \end{array}$$ 5

The mean value of the overall acceptability ranged from 5.3 to 7.9. It is evident from Table 2 that starter culture with incubation time at the interactive level was affecting the overall acceptability of the yogurt significantly (p < 0.1). The coefficient of regression (R²) for viscosity was 0.7704, which indicates that the model could account for 77.04% data. Figure 2d states that, at the interactive level, as the amount of wheat dextrin and starter culture increases, overall acceptability scores decreased slightly from 7.2 to 6.8. Figure 2e describes that at linear level, as the amount of wheat dextrin increases slight increase in overall acceptability scores was observed compared to incubation time, which showed a sharp increase in overall acceptability scores from 6.6 to 7.4 as the incubation time increased in yogurt formulation. Figure 2f depicted the interactive level, as the amount of starter culture and incubation time increases, and an only slight increase in overall acceptability scores 0.5 was observed, but at linear level, as the amount of starter culture increases slight increase in overall acceptability scores was observed and at the same time as incubation time increases, a sharp increase in overall acceptability scores up to 1.5 was observed compared to starter culture in the yogurt formulation. Our research results showed that yogurt supplemented with wheat dextrin fibers received lesser scores in the sensorial analysis compared with the other yogurt enriched with the food fibers, endorsed by the outcomes presented in the research work of Raju and Pal (2014). Tomic et al. (2017) found that the incorporation of the fibers from various sources such as soy, corn, rice, oat, and sugar beet at the level of 1.32% led to lower overall flavor and texture scores. In the current study also the incorporation of wheat dextrin as a fiber source has reduced the overall acceptability, but it was acceptable by the panel members as both food fiber and yogurt will represent functional food with commercial applications.

Response surface methodology for L* value

The quadratic model fitted to L* value was significant (p ≤ 0.01), and also lack of fit was insignificant relative to the pure error. The following equation can indicate the quadratic model for L* value.

$$\begin{array}{cc}\hfill \text{L}\ast \text{value}& =+81.85-0.4734\text{A}+0.3136\text{B}-0.2129\text{C}\hfill \\ \hfill & -0.2325\text{AB}+0.1000\text{AC}+0.3075\text{BC}\hfill \\ \hfill & +0.4391{\text{A}}^2+0.2552{\text{B}}^2-0.0205{\text{C}}^2\hfill \\ \hfill \end{array}$$ 6

It is evident from Table 2 that wheat dextrin at both linear and quadratic level was affecting the L* value of the yogurt significantly (p < 0.1, p < 0.05). The coefficient of regression (R²) for L* value was 0.7394, which indicates that the model could account for 73.94% data. Figure 3a describes that L* value was increased with the highest contraction of starter culture and the lowest concentration of wheat dextrin. Figure 3b describes L* value decreased gradually when both wheat dextrin and incubation time increased. L* value was minimum at an average incubation time, and it decreased with increasing incubation time then increased with increasing starter culture level in the yogurt(Fig. 3c). These results are in agreement with those attained by Dello Staffolo et al. (2004) who saw no considerable differences between the control yogurt and yogurts comprising wheat, bamboo and inulin fibers but in disagreement with those obtained by Raju and Pal (2014): fibers incorporation leading to notable changes in the color of the yogurt.

Fig. 3.

Response surface plot for L* value (a–c) and hardness (d–f) as a functions of a wheat dextrin (g), b starter culture (ml) and c incubation time (h)

Response surface methodology for hardness

The quadratic model was best suited to hardness, but the model was insignificant, and lack of fit was also insignificant relative to the pure error. The following equation can express the quadratic model for hardness.

$$\begin{array}{cc}\hfill \text{Hardness}& =+3487.24+37.16\text{A}-395.52\text{B}-376.90\text{C}\hfill \\ \hfill & -828.00\text{AB}-410.08\text{AC}-42.33\text{BC}\hfill \\ \hfill & -607.27{\text{A}}^2-756.11{\text{B}}^2-147.58{\text{C}}^2\hfill \\ \hfill \end{array}$$ 7

It is observed from Table 2 that the coefficient of regression (R²) for hardness was 0.5147, which indicates that the model could account for 51.47% data. Figure 3d describes that hardness increased with increasing both wheat dextrin and starter culture, and no significant change was observed in the hardness with increased wheat dextrin and incubation time (Fig. 3e), and standard hardness was recorded with increased starter culture and incubation time (Fig. 3f) in the yogurt. Other researchers reported that medium inoculum concentrations resulted in higher firmness of yogurt (Wu et al. 2009).

Optimization of the level of independent variables

In order to obtain the optimum level of independent variables, the responses, i.e., pH, viscosity, syneresis, overall acceptability, L* value, and hardness, were assigned an equal weight their result on quality and palatability of yogurt. The standard used along with predicted and actual responses is given in Table 3. With the current model, the optimized value for wheat dextrin 15 g, starter culture 25 g, and incubation time 8 h. Wheat dextrin yogurt was formulated as per the optimized process conditions and evaluated. The calculated responses were very close to the predicted values of the optimized independent variables (Table 3). The pH of wheat dextrin yogurt was found to be 3.312; viscosity was 20,229.05 cP, syneresis 7.673%, and overall acceptability of about 7.954. L* value and hardness wheat dextrin yogurt ranged between 83.459 and 1698.743 g, respectively.

Table 3.

Criteria for optimization for process conditions along with responses

Constraints	Goal	Lower limit	Upper limit	Importance	Solution	Actual response value
A. Wheat dextrin	Maximize	5	15	3	15	–
B. Starter culture	Maximize	10	25	3	25	–
C. Incubation time	Minimize	8	11	3	8	–
pH	Minimize	3.05	5.46	3	3.211	3.321
Viscosity	Maximize	10,640.1	21,410.1	3	19,108.017	20,229.05
Synerises	Minimize	2	30	3	6.915	7.673
Overall acceptability	Maximize	5.3	7.9	3	7.164	7.953
L* value	Is in range	81.2	84.3	3	81.938	83.459
Hardness	Minimize	266.33	5943.3	3	1619.236	1698.743

Conclusion

In the present research study, parameter and fermentation conditions for developing wheat dextrin yogurt were optimized by effectively utilizing RSM for analyzing the sole and interactive effects of wheat dextrin, starter culture, and incubation time on wheat dextrin yogurt. Wheat dextrin of 15 g, a starter culture of 25 g, and incubation time at 8 h were found to be optimum for wheat dextrin yogurt preparation. The derived model could be used to find optimum parameters for any factor combination, and the process can be exploited for large scale production of wheat dextrin yogurt of consistent quality. The result showed that wheat dextrin in the form of fiber incorporated in yogurt significantly has an effect on its textural, color properties, and sensory characteristics also but at the acceptable range. Therefore, this research study opens the mode for analyzing other types of fibers obtained as a by-product of industrial food processing to attain enriched yogurts and could be considered a substitute to include fibers in the human diet. Due to its nutritional benefits, yogurt is one of the most consumed healthy and nutritious foodstuffs worldwide. By including fibers in yogurt, researchers have achieved a way to increase fiber consumption in all sectors of the population with an extensive range of valuable effects.