Kinetics of the crust thickness development of bread during baking

Abstract

The development of crust thickness of bread during baking is an important aspect of bread quality and shelf-life. Computer vision system was used for measuring the crust thickness via colorimetric properties of bread surface during baking process. Crust thickness had a negative and positive relationship with Lightness (L^*) and total color change (E^*) of bread surface, respectively. A linear negative trend was found between crust thickness and moisture ratio of bread samples. A simple mathematical model was proposed to predict the development of crust thickness of bread during baking, where the crust thickness was depended on moisture ratio that was described by the Page moisture losing model. The independent variables of the model were baking conditions, i.e. oven temperature and air velocity, and baking time. Consequently, the proposed model had well prediction ability, as the mean absolute estimation error of the model was 7.93 %.

Introduction

Crust thickness of bread is an important aspect of bread quality and is effective on its shelf-life properties. During baking crust forms as maximum evaporation takes place there (Therdthai et al. 2002). Color of this region of baked bread is different and distinguishable from other section, i.e. crumb due to browning reactions occurred at surface of bread. The browning is mainly the result of a Maillard type browning reaction rather than of caramelization. The formation of crust and browning during baking appear to be primary contributors to the formation of bread flavor (Pedreschi et al. 2006) and according to Mondal and Datta (2008), crust formation is one of the reasons that caused to the understanding of the whole baking process be not very clear.

As soon as the product is placed in the oven, water evaporates from the warmer region, absorbing latent heat of vaporization and the surface layers start drying. Beneath this drying region, water vapor diffuses through the interconnected pores towards the surface, under the influence of the water vapor concentration gradient. A concomitant liquid water gradient is formed and ensures the diffusive transfer of water from the core to the surface. As the diffusive flow of liquid water from the core is less rapid than evaporation flow at the surface, a drying zone is developed, which slowly increases in thickness and forms the crust. Crust formation is one of the limiting factors, which restricts the expansion of the dough (Zhang et al. 2007), so crust thickness development effected on the volume of bread and crumb bubbles size and tissue that are the most important factors in determination of bread quality.

Bread crust is known to be closely related to moisture loss of bread during baking and the crust formation affects the amount of moisture evaporating from wet dough during the baking process as a thicker crust is produced with a higher moisture loss in bread (Mohd Jusoh et al. 2009; Wiggins 1999). Besides that, moisture content or water activity of bread surface has an important effect on beginning of browning reactions. Purlis and Salvadori (2009) expressed that minimum requirements for initiation of color formation are temperature greater than 120 °C and water activity less than 0.6. Also, in relating bread crust properties in terms of its color with moisture loss, Purlis and Salvadori (2007) presented a strong correlation between the moisture loss and the crust color formation in their study on browning kinetics of bread. From these literatures, it seems viable to control moisture loss from bread during baking process and after that. So kinetics models of crust thickness variations, in order to predict the crust thickness developmental behavior of bread during baking at various baking conditions, can be useful in bread making industries.

Whereas bread dehydration during baking affects only the external zones (crust) of bread during baking (Wagner et al. 2007; Zanoni et al. 1993), and this moisture loss caused to crust formation and browning of the bread surface. In fact, the main reason of crust formation in food products during heating processes is the moisture losing from outer zones of food samples. So it seems that the moisture content variations would have strong influence on crust development of foods, especially white bread. However, temperature of bread surface has an important effect on beginning of browning reactions (Shibukawa et al. 1989; Broyart et al. 1998; Wahlby and Skjoldebrand 2002; Mondal and Datta 2008; Purlis and Salvadori 2009), which caused to emerge the colorimetric distinguishable crust.

The crust properties are known to be useful in terms of moisture loss and control hence may contribute a great deal in lowering its staling rate as crust has significant influences on bread quality and its shelf-life. Though considering the actual mechanisms involved in the formation of crust would be the best approach, the chemistry of the surface browning and crust formation phenomenon have not been well elucidated yet, being a controversial issue until now (Martins et al. 2001). In spite of that, it is always useful to search for a mathematical model of crust development for technological applications. Taking into account the importance of crust development in bread making and its effect on storage period, only few articles were published concerning crust thickness kinetics modeling with prediction aims. Recently, Mohd Jusoh et al. (2009) developed a simple digital imaging method for the evaluation of baking process on bread quality through the measurement of bread crust thickness. Their results showed that the crust thickness has a negative relationship with each of the L, a, and b values and a positive correlation with the total color difference (E^*) of bread crust. Hence, in this work, in order to predict the bread crust thickness, a mathematical model was proposed, which depended the crust thickness of bread to moisture ratio of the loaf during baking. It is worth to note that the mathematical model of moisture loss of bread samples during baking has been previously developed in Soleimani Pour-Damanab et al. “Determination of suitable drying curve model for bread moisture loss during baking”. Int Agrophysics (in press), and the crust thickness was measured via a method similar to Mohd Jusoh et al. (2009) method with little differences in implementation.

Materials and methods

Bread sample preparations

Dough samples were prepared from Varamin bread flour (Sanaye Ard Varamin Milling Co) with protein, moisture and ash contents of 11.8 (%db), 13.9 % and 48 (%db), respectively. Water absorption characteristic of this flour type was 62.5 % (Farinograph moisture requirement of the flour), so ingredients of dough formulation were as: flour (100 %), water (62.5 %), sugar (1.5 %), salt (1.5 %), and dry yeast (1 %). The percentages of the ingredients were based on the dry bases of flour (300 g) and the straight dough method was used for mixing the ingredients. All the ingredients were mixed for 10 min in a home multi functions food processor. The dough was let to rest for 5 min after mixing. After first resting dough samples were formed with dividing and weighting dough into 120 g balls and rounded with hand until uniform dough samples (ca. 0.15 m length and 0.025 m diameter) achieved and then let to rest for another 5 min. The prepared dough samples were put in stainless steel trays and for surviving proofing stage stored in an experimental fermentation oven for 60 min at 35 °C and 85 % relative humidity. After proofing process samples volume was twice.

Dough samples were baked in an electrical static oven (Delongi EO1258, Italy) in two conditions of convection mode: natural convection (with 0 m/s air velocity) and forced convection (with 0.4 m/s air velocity). Three baking temperature was selected for bread baking: 180, 200, 220 °C. At each of baking conditions combinations, samples were baked for four given time up to: 15, 20, 25, 30 min. One sample was baked in each test and two cross-section slices (with 10 mm thickness) was prepared by cutting the bread with a serrate knife, which used to determine the crust thickness. Oven temperature was measured using K-type thermocouples (Maxtermo-Gita, Taiwan). For better controlling of oven temperature a digital temperature controller was used as additional mechanism. Therefore the oven temperature was controlled with high accuracy (approximately 1–2 °C). Moreover, before each experiment run, a calibration procedure of the baking conditions was carried out in order to ensure the validity of results. The tray with sample was placed in central zone of the oven.

Totally, four replicate experiments were carried out and two set data were collected. One set with two replicates was used for modeling and another set with two replicates was used for evaluation of the model prediction ability. At each baking run two cross-section slices was prepared, so each replicate was mean of two crust thickness data. In order to statistically analyzing of results, all baking tests data were applied. Therefore, statistical analysis was conducted by 8 (n = 8) set data and performed using Microsoft Excel (XP Edition, Microsoft Corporation, USA). The crust thickness at four time intervals (15, 20, 25 and 30 min) was chosen to investigate the influences of various baking conditions on the crust thickness formation.

Moisture ratio determination

The moisture ratio of bread samples during the baking experiments can be calculated using the following equation:

1

Where M_t is the mean moisture content at t, % d.b.; M₀ is the initial moisture content, % d.b.; M_e is the mean equilibrium moisture content, % d.b.

In general, the moisture loss of agricultural products during heating processes modeled on basis of moisture ratio variation with time, and several models as theoretical, semi-theoretical and empirical was proposed in literatures for this aim (Sagar and Suresh Kumar 2010; Balasubramanian et al. 2010; Kumar et al. 2012). About bread, the variation of moisture ratio of bread sample during baking was previously determined as a Page drying model in Soleimani Pour-Damanab et al. “Determination of suitable drying curve model for bread moisture loss during baking”. Int Agrophysics (in press):

2

Where the model coefficients was determined as function of baking temperature and air velocity:

3

4

These equations were used to predict the moisture ratio that applied for modeling the crust thickness development kinetics of bread in current study.

Crust and slice color of bread measurements

Computer vision system provides one alternative for an automated, non-destructive and cost-effective technique to accomplish various inspection purpose works of food and agricultural products. This method does not imply contact with sample, which is essential in deformable materials. Furthermore, the measured surface size in a single determination with a computer vision system is higher than that evaluated by a conventional colorimeter. This inspection approach based on image analysis and processing has found a variety of different applications in the food industry (Patel et al. 2012). In this work, computer vision technique was used to evaluate color variation of bread surface and slice during baking. This computer vision system includes a high resolution digital camera (12 mega pixel) (OLYMPUS FE5020, Malaysia), an imaging room with correct lighting system and a PC (AMD Sempron 2,200+, 1,024 MB of RAM). The L^*a^*b^* color model was used to describe color development. The L^*a^*b^* color consists of a luminance or lightness component (L^* value, ranging from 0 to 100), along with two chromatic components (ranging from −120 to +120): the a^* component (from green to red) and the b^* component (from blue to yellow). The L^*a^*b^* values are often used in food research studies (Yam and Papadakis 2004). 160 Since images were acquired in the RGB color space, the following steps were carried out to obtain CIE L^*a^*b^* model parameters: image in RGB space converted to XYZ tristimulus space and then XYZ converted to L^*a^*b^* space. From achieved data extracted the mean value of L^*, a^* and b^* for each image. The total color change (E^*) value of each image was determined as:

5

Where the L^*₀, a^*₀ and b^*₀ were the reference value of same sample image taken from unbaked dough (initial time of baking).

The color of bread slice from all baked samples and surface color were measured using the computer vision system with proper lightening by taking image of bread slice to determine its color of crust and crumb regions in terms of L^* and E^* values. The image acquiring of the surface color and bread slice was performed in a certain lightening conditions and consistent manner by placing the bread sample and its slice into the imaging room. The average values of L^* and E^* colors describing the crust and crumb regions were obtained from all baked samples of bread. It is worth mentioning that baking experiments was carried out at four time duration, i.e. 15, 20, 25 and 30 min, and after each color measurement the sample discarded, because with slicing the sample was destroyed.

Crust thickness measurement

Crust thickness in this study is defined as the distance between outer crust and the pixel of inner crust where its color satisfies the colors as crust pre-determined in the Crust and slice color of bread measurement Section. This means the pixel where the inner crust color such that the L^* value is the minimal and the E^* values are the maximal of the crumb regions is taken as the thickness. For determining this crust thickness, a sample slice of bread was placed into imaging room and image took. The scanned bread slice image in .jpg file was transferred to the MATLAB computer program (The MathWorks, Inc., Natick, MA, USA) to determine the crust thickness by counting the number of pixels which meets the requirement of L^* and E^* values known as the crust region. Therefore, the bread crust thickness contain the number of pixels from the point of the slice crumb near to top surface of bread slice where the L^* and E^* values meet the requirement of the crust region, which is L^* <62.3 and E^* >9.2, up to the surface. A conversion factor, computed from a reference object, was used to convert the crust thickness from pixels to SI units during the image processing stage. This method was previously applied by Yam and Papadakis (2004); Collar et al. (2005) and Mohd Jusoh et al. (2009), and in this work is improvised. It is worth to note that all of described operations were performed by an algorithm that developed in MATLAB computer program.

Modeling of crust thickness development

The crust thickness development of bread during baking was mathematically modeled. By considering this hypothesis that bread crust thickness development is dependent on moisture content during baking. A simple linear model was used that was a new model and related the crust thickness to moisture ratio of bread during baking, as:

6

Where CT is the crust thickness, MR is the moisture ratio that described in the Moisture ratio determination Section. The constants in Eq. 6, k₀ and k₁ (mm) are fit parameters that related the crust thickness to moisture ratio. These model parameters were estimated using mean value of duplicate experimental data, and other baking practice was done in order to validate the model. Evaluating of the performance of proposed model made by the absolute relative error, which compared experimental and predicted values, was defined as:

7

Results and discussions

Crust and crumb color regions

After image acquisition and processing were performed, L^*a^*b^* parameters were calculated for each pixel of each sample image. Then the total color change (E^*) value was determined by Eq. 5. In summary, for each sampling time, the mean values of the color parameters were obtained from two different images involving almost (1,260 × 420) pixels (9.12 pixels/mm) every time (this value depends on image resolution settings when acquisition is made). This demonstrates the advantage of using a computer vision system over other colorimetric techniques, since it allows handling a large amount of data for each determination, besides it is a rapid and non-destructive method. Moreover, because of that during data acquisition process in computer vision system, data obtained without operator interfere, so the human error decreases to the lowest amount. In about crust thickness measuring computer vision technique can be a useful measurement tool, which this procedure requires to very precision. Despite the fact that all three parameters of the CIELAB model were evaluated, the subsequent procedure in order to crust thickness distinguishing for analysis of the development of crust thickness was based on L^* and E^* variation of samples during baking. Lightness is a good descriptor of the browning progress since it represents the intensity of images, and is decoupled from color changes denoted by a^* and b^* values (Gonzalez and Woods 2008). The total color change (E^*) was also applied in many food quality researches (Zanoni et al. 1995; Brosnan and Sun 2004; Purlis and Salvadori 2007) and is a useful factor in colorimetric works.

Table 1 shows the average color ranges for outer crust and inner crumb regions from all the baked bread samples. In identifying the color region for determining crust thickness, the inner crust region was identified as the region lying between the extreme colors of external crust and internal crumb. This table demonstrated distinguishable color regions of the outer crust and inner crumb in terms of L^* and E^* values for determination of color ranges for inner crust region as L^* <62.3 and E^* >9.2. The color pigments formed on the crust generally agree to the fact that crust experiences caramelization and Maillard reactions which are highly influenced by the quality and quantity of the precursors, thermal processing parameters, pH and quantitative ratio of amino nitrogen to reducing sugar during baking (Martins et al. 2001). Figure 1a shows clear negative correlations between the L^* value with crust thickness and Fig. 1b shows positive correlations between E^* and crust thickness. The strength of the relationships is strong with good correlation coefficients, R², of 0.9039, and 0.8968 for the lightness and total color difference, respectively. These R² values infer that the color components obtained from the outer crust could be used to determine its crust thickness. In terms of L^* value, a lower L^* value obtained from a darker crust surface infers a thicker crust. As the crust thickness, the more browning implied by the E^* value increased.

Table 1.

Color characteristics variation range for difference regions of bread slice

Bread regions	Total color change (E*)	Lightness (L*)
Outer crust	28.5–51.4	11.4–51.6
Inner crust	9.2–28.5	51.6–62.3
Crumb	0.013–9.2	62.3–71.2

The data are mean of two replicate experiments that collected for modeling

Fig. 1.

Relationship between crust thickness of bread with (a) Lightness of surface (L ^*), (b) Total color change of surface respect to unbaked dough (E ^*) and (c) Moisture ratio of bread during baking (under natural convection: □ 180 °C, ◊ 200 °C, ○ 220 °C, and under forced convection: ■ 180 °C, ♦ 200 °C, ● 220 °C)

Modeling of crust thickness development

Figure 2 shows the variations of crust thickness of bread versus baking time for all six baking conditions. As expected, the crust thickness of samples increased with baking time and with increasing oven temperature. In addition, this figure showed the effect of convection mode on crust thickness. As can be seen at same conditions of temperature and time, value of crust thickness under forced convection mode is greater than natural convection. Therefore, this result demonstrated that oven air velocity is one of practical effective factors on the development of crust thickness, further baking time and temperature. Results showed that the crust thickness at forced convection baking was averagely 17 % more than natural convection baking at given conditions of temperature and time, also a 20 °C increase in baking temperature caused a 31 % increase in crust thickness at given conditions of convection mode and baking time. These results are consistent with existing findings on crust thickness as affected by its baking conditions and time (Zanoni et al. 1993; Jefferson et al. 2006; Mohd Jusoh et al. 2009). Zanoni et al. (1993) found that an extension of 5 min’ baking at a fixed baking temperature of 203 °C caused bread crust thickness to increase 50 % from its original thickness while Jefferson et al. (2006) discovered that a 14 % increase in baking temperature caused a 10 % increase in crust thickness. A higher heat and mass transfer, and evaporation process occur at higher baking temperatures which cause a thicker crust formation. Mohd Jusoh et al. (2009) found that with increasing of oven temperature and baking time, the surface color of baked bread becomes darker and crust thickness increased. They results showed that the temperature has more significant impact on both crust properties, the color and thickness as compared with time. Current research results corroborate these findings as showed that a 20 °C increase in baking temperature caused an averagely 33 % increase in crust thickness. It is worth to note that this increase at upper temperatures was greater, which may be occurred by reason of more rapid increase in the loaf temperature. In case of air velocity, could be said that at higher air velocity, heat transfer occurred faster and led to form thicker crust. Also, at forced convection baking (V_a >0) the heat influx into sample definitely greater than natural convection baking (V_a = 0), due to higher pressure of baking air on the surface of sample. Results showed that at forced convection (V_a = 0.4), the crust thickness averagely was 10 % greater than natural convection. Table 2 shows the absolute values of the crust thickness at 15, 20, 25 and 30 min after baking for all process conditions. The ANOVA results also confirmed the significant effect of baking air velocity on crust formation. However, this results showed that the oven temperature (p < 0.0001) causes more significant effect on crust formation during baking compared to the oven air velocity (p < 0.001).

Fig. 2.

Variation of crust thickness of bread with baking time (under natural convection: □ 180 °C, ◊ 200 °C, ○ 220 °C, and under forced convection: ■ 180 °C, ♦ 200 °C, ● 220 °C)

Table 2.

Crust thickness at 15, 20, 25 and 30 min of baking for breads baked in two convection modes and three baking temperatures

Temperature (°C)	Convection mode	Crust thickness (mm)
		15 min		20 min		25 min		30 min
		Mean	SD	Mean	SD	Mean	SD	Mean	SD
180	NC	1.18a	0.009	2.12a	0.014	2.68a	0.015	3.21a	0.011
	FC	1.22a	0.021	2.21a	0.023	3.09b	0.018	3.51b	0.015
200	NC	1.55a	0.022	2.62a	0.035	3.39a	0.025	4.03a	0.009
	FC	2.46b	0.018	3.43b	0.017	4.08b	0.012	4.50b	0.016
220	NC	2.71a	0.014	3.73a	0.027	4.60a	0.017	5.18a	0.012
	FC	3.19b	0.011	4.38b	0.024	5.16b	0.010	5.62b	0.007

Different superscripts denote statistical difference (P < 0.001) between the modes of convection at each time interval (n = 8)

NC natural convection; FC forced convection

Correlation between crust thickness and moisture ratio was linear. Moreover, this linear behavior was similar at all baking temperatures, independently of convection mode. Although, the rate of crust thickness development and moisture ratio decreasing, at forced convection were higher than natural convection. It is worth to note that in the modeling of crust thickness development, first stage of baking (approximately, the 10 min of baking start) be ignored. Because in this stage, creation of color difference between outer crust and inner crumb is not enough to distinguish these regions from theirs colors. Correlation of the crust thickness with moisture ratio, under both convection modes, was almost perfect. As is shown in Fig. 1c, parameters of Eq. 3 were obtained as: k₀ (−11.34) and k₁ (9.423 mm) (R² = 0.942).

Using the obtained predictive model, the crust thickness of bread samples at any time during the baking process could be easily estimated. Validation of the established model was made by comparing the computed crust thickness data with another set of crust thickness data that measured for validation of the model in any particular baking run under given conditions. The performance of the model at all air temperatures and under both natural and forced convections is shown in Fig. 3. It is obvious from this figure that the predicted data generally banded around the straight line, which indicated the suitability of the model proposed in describing the development of crust thickness behavior of bread samples, as the mean relative errors produced by the models were 7.93 %. The crust properties especially the crust thickness of bread is known to be useful in controlling moisture loss during baking process and storage period.

Fig. 3.

Experimental and predicted crust thickness of bread under both convection modes and all baking temperature

Conclusions

The development of crust thickness of bread was successfully determined via the application of digital imaging method. The system is a useful tool for determination of crust thickness during baking process. The crust thickness development profiles showed that the crust thickness of bread affected with baking time and baking conditions, i.e. oven temperature and air velocity. The strong positive correlation between crust thickness and the bread moisture ratio during baking was found and this allows prediction of crust thickness from the moisture ratio of baked bread for bread quality evaluation at various temperatures and air velocity. Goodness of presented model was acceptable as the mean relative error of model was equal with 7.93 %. A useful bread quality index such as crust thickness can be easily estimated by knowing the baking time and conditions. This proposed model to predict the crust thickness via moisture ratio can be established for various bakery products as crust thickness of bread and other bakery products has significant influences on bread quality during baking process and storage period and is one of main features considering consumer preference.