Mathematical modeling for the prediction of some quality parameters of white rice based on the strength properties of samples using response surface methodology (RSM)

Abstract One of the major problems in predicting the quality properties of rice is that conducting experiments in the food industry can be highly expensive. The objective of this study was to predict some quality properties in varieties (Domsiah, Hashemi, Dorfak, and Kadus) via compression test at moisture levels 9 and 14% w.b. Based on historical data design, RSM was used to model and estimate of dependent variables (amylose (AC) and protein content (PC), gelatinization temperature, gel consistency GC), minimum (Min.V), final (FV), breakdown (BDV) and setback viscosity (SBV), peak time (PT) and pasting temperature (Pa.T)) through independent variables (the rate of force, deformation, rupture energy, tangent, and secant modulus). An ANOVA test showed that models were significant (p < 0.05). The most appropriate model for response variables prediction of AC and GC (Kadus 14%), PC (Domsiah 9%), Min.V, FV, and SBV (Dorfak 9%), BDV (Dorfak 14%), PT (Hashemi 14%), and Pa.T (Kadus 9%) was Rpred2 as 0.86, 0.85, 0.93, 0.955, 0.953, 0.94, 0.94, 0.86, and 0.91, respectively, with the most appropriate optimal values as 23.52%, 48, 10%, 164.95 RVU, 304.12 RVU, 162.66 RVU, 64.52 RVU, 6.09 min, and 92.45°C and desirability as 0.91, 0.95, 0.95, 0.80, 0.89, 0.83, 0.84, 0.89, and 0.96, respectively. The optimal values of the independent variables have a decreasing trend, and the optimal values of the response variables are proportional to the optimal conditions. The results indicated that the RSM could be quite useful in the optimization of the models developed for predicting the rice quality properties.

in the final quality of rice (Ferreira, Oliveira, Pathania, Almeida, & Brites, 2017). To determine some strength properties of rice grain used a single kernel to estimate rice quality (Yu et al., 2019). With all its simplicity, the measurement of strength properties is very important in determining the quality of rice, which has been studied by various researchers in different grains, especially in cereals. Although the quality properties are determined using quality analysis tools in food industry laboratories, experiments with these tools are highly protracted and expensive. Thus, the development of more inexpensive and convenient methods can help precipitate the marketing process of the product. Up until now, several studies have been conducted on the quality and strength properties of rice. However, very few of them have addressed the relationship between these properties.
The mechanical attributes of individual kernels are more relevant to the quality properties of the various cereals. The relationship between kernel hardness, a quality parameter used for grading cereals, e.g., wheat, and some mechanical attributes, e.g., the maximum compressive force (Osborne & Anderssen, 2003). They are also used in the determination of the relationship between hardness and quality parameters to grade cereals. In their study, Cao, Nishiyama, and Koide (2004) explored the effect of moisture content (MC) on some mechanical properties of brown rice. They showed that MC drastically affects the mechanical properties; that is, compressive strength and tensile strength decreased with increasing MC. Some researchers have attempted to extract the strength attributes of the rice grain. For example, Kamst, Vasseur, Bonazzi, and Bimbenet (1999) reported that Young's moduli from the diametral compression tests are not significantly different from those from uniaxial compression tests. The repeatability of the diametral compression tests is of the same order as the repeatability of uniaxial compression tests.

RSM consists of a collection of statistical and mathematical tech-
niques that are used to improve, expand, and optimize processes that can demonstrate the relationship between response and independent variables through mathematical models (Montgomery, 2008).
Numerous studies have exploited RSM. For instance, Taghinezhad and Brenner (2016) investigated the mathematical modeling of starch gelatinization and some quality attributes of parboiled rice through RSM. They asserted that this model is the most appropriate model for predicting the degree of starch gelatinization, hardness, lightness, color value, and head rice yield of samples (R 2 ≥ 0.86).
Moreover, Yousaf et al. (2017) studied the optimization and mathematical modeling of the quality attributes of parboiled rice using RSM. They posited that it is the most appropriate model that can predict the effect of temperature, soaking time, and steaming time on head rice yield, hardness, cooking time, lightness, and color of samples (R 2 ≥ 0.88). They also introduced an optimal model for their

research.
A review of the literature revealed that some studies have been conducted on optimizing the quality of different types of grainy cereals, especially rice. Besides, they have mainly focused on a very limited number of factors involved. The effect of mechanical properties on the quality properties of rice has either not been addressed or been regarded attentively. Therefore, it is necessary to study the effects of mechanical properties on the quality attributes of rice through analyzing single kernels of rice. In this study, some strength components of rice grains were extracted from a series of compression tests performed on four typical Iranian rice varieties and assessed by RSM due to the importance of strength parameters of rice and the feasibility of SKCS in quality evaluation. The factors focused in this study were strength components including the rate of force, deformation, rupture energy, tangent and secant modulus, and the quality indices of processed rice including amylose content (AC), protein content (PC), gelatinization temperature (GT), gel consistency (GC), minimum viscosity (Min.V), peak viscosity (PV), final viscosity (FV), breakdown viscosity (BD.V), setback viscosity (SB.V), peak time PT), and pasting temperature (Pa.T). With fewer expenses, and less acceptable accuracy via focusing on the mechanical properties of single kernels, the results of this research are expected to lead to the development of instruments for determining the quality of rice. Finally, the independent variables were optimized for the prediction of the quality characteristics (dependent variables) of rice samples.

| Row specimen provision
The four common varieties of rice bulk samples were acquired in sufficient amounts directly from the field of Rice Research Institute located in Rasht, Iran. The initial moisture content (MC) was determined by placing three samples each weighing 15 g into an oven with a temperature of 130°C for 24 hr (Li, Li, Ding, Chen, & Ding, 2014). The MC of the samples ranged from 15% to 16% (w.b). Then, to reduce MC to 9% and 14%, the paddies were spread on a flour in thin layers and dehydrated by a laboratory drier at the temperature of 35°C. After crushing their skin, they were milled using a UDY cyclone miller (USA) under the same condition and then stored at the temperature of about 4°C for the subsequent experiments.

Practical Applications
All existing methods for measuring the rice quality indexes are labor-expensive or time-consuming. The development of more inexpensive methods can help precipitate the marketing process of the rice. The results are expected to lead to the development of mechanical tests to prediction the quality. The results can be used for designing and developing devices to test the quality indices of kernels, similar to those are being used to test the wheat quality according to single kernel characterization (SKCS).

| Compression test
The strength of rice grain was measured using a uniaxial compression test, which was performed on whole and sound grains laying on the floor on their side by loading tow flat plate. The tests were conducted by SANTAM uniaxial compression testing machine (STM-20, Iran) according to the standard (ASAE, 2009) at the deformation rate of 1.24 mm/min (Arana, 2012). From the force-deformation plotting, values of several parameters were measured such as force value at the deformation of 0.05 mm (F 0.05 ), rupture force (F max ), maximum deformation (D max ), rupture energy (EF), tangent modulus at the deformation of 0.05 mm (Et 0.05 ), maximum tangent modulus (Et max ), secant modulus at the deformation of 0.05 mm (Es 0.05 ), and maximum secant modulus (Es max ). According to the data obtained from the tests, the first point that underwent force loss as the deformation increased was the rupture point. The amount of force at this point was measured as the F max . F max was obtained by measuring the area under the curve of force-deformation to the rupture point (Li et al., 2014). Tangent modulus; the slope of the curve at any point and secant modulus; and the slope of the line from the origin to any point on the force-deformation curve (Henry, Zhang, & Onks, 2000) were measured at different points on the curve. forming an iodine-starch complex (Kong, Zhu, Sui, & Bao, 2015). In order to determine the GT, Little's method was used (champagne et al., 1999). Then, six whole grains of the white rice were added to Petri dishes and 10 ml of potassium hydroxide (KOH) 1.7% was added to them. Then, the samples were located inside the oven with a temperature of 30°C for 23 hr. The changes in starch were recorded by a number ranging from 1 to 7. Then, the GC of the white rice was determined by transferring the rice into a pot of 0.2 normal potash, which indicated the movement of the gel of the cooked rice in millimeters (Vandeputte & Delcour, 2004). The PC of the rice flour was determined by the Kjeldahl procedure with a nitrogen conversion factor of 5.95 (Xu, Xiong, Li, & Zhao, 2008).

| Determination of the quality attributes of rice
To measure the physicochemical properties of the grain starch, samples were milled using a UDY cyclone miller (USA, Colorado) at 100 mesh. Then, three grams of each sample was separated. After that, 25 ml of distilled water was added to the separated samples.
The resultant mixtures were then placed inside the metal cylinder of a rapid visco-analyzer (RVA-3D, Australia) (Kesarvani, Chiang, & Chen, 2016). Finally, the result of the test is a curve which shows the changes in the viscosity of the samples at various temperatures of cooking.

| Experimental design and statistical analysis
The experiments were conducted in a historical design with a quadratic model, using RSM in Design-Expert Software (Version 11), and the data were analyzed by ANOVA. The significance of the relationships between variables was determined via the analysis of variance, and the models were verified by various techniques including explanatory factors of R 2 , adjusted R 2 , and predicted R 2 .
The responses could then be related to the factors by linear or quadratic models, enabling optimization. A quadratic model is shown in the following (Yousaf et al., 2017): where β 0 , β i , and β ij are regression coefficients for intercept, linear, quadratic, and interaction coefficients, respectively, and x i and x j are coded independent variables. This is a signal-to-noise ratio. It compares the range of the predicted values at the design points to the average prediction error. Ratios greater than 4 indicate adequate model discrimination.

| Experimental design and model development
The analysis of variance (ANOVA) demonstrated that all of the independent variables affect the response variables (p < 0.01) and (p < 0.05) significantly. The regression equations for the response variables and P value, Std. Dev, coefficient of variation, adequate precision, and R 2 pred values are presented in Table 1. In this study, only 17 response variables were predicted by the independent variables predicted

| The effect of independent variables on response variables
Statistical interaction effects of the independent variables on the possibility of predicting the response variables are shown in 14%), P.C increased from 6.4% to 6.82% with the increase of F max from 36.9 to 49.3 N and Et max from 320.9 to 390.9 N/mm. Similarly, in Figure 1c Yan and Zhu (2001).
As the MC increases from 12% to 18%, the strength properties of the rice grain decrease (Wouters & Baerdemaeker, 1988), which was confirmed by data observed in other researches (Cnossen, Jienez, & Siebenmorgen, 2003;Saiedirad et al., 2008). As a result, as Figure 1d shows, the slopes of variation in the variables related to Kadus variety at the MC of 14% are lower than those at the MC of 9%.
In Figure 2a  By cooling down the samples by reducing the temperature, the soluble AC increases. As a result, the Min.V decreases to its lowest level and the BD.V increases (Allahgholipour et al., 2006). These findings are all consistent with the results reported by Kong et al. (2015).
Consequently, the grains become soft and suitable leading to the decrease in their strength (Allahgholipour et al., 2006), which was confirmed by data observed in other researches (Asante et al., 2013).
In this study, the mean BD.V in Dorfak variety was higher than other varieties except for Kadus. Since the mean PC in Dorfak was obtained 6.6, which is relatively lower, this finding is in line with the one reported by Champagne et al. (2009). Similarly, the mean Pa.T (93.56) in Kadus variety was lower than that of other varieties except for Dorfak. Moreover, its GT was higher than that of other varieties. On the other hand, Pa.T is negatively correlated with GT (Allahgholipour et al., 2006;Mestres et al., 2011). Similar results can be drawn from the research of Kong et al. (2015). Also, higher AC results in higher Pa.T (Sodhi & Singh, 2003) and more hardness (Allahgholipour et al., 2006;Kang, Kim, Kim, & Murata, 1994). As a result, the rupture force and the grains hardness decrease as the Pa.T decreases.
In Figure 2c,d, the GT in Kadus variety was estimated to be 3.52, which is considered relatively high. As a result, the grain strength is lower at the time of cooking (Mestres et al., 2011). Also, GC is negatively correlated with GT (Vandeputte & Delcour, 2004;Wang et al., 2010). Therefore, the grain strength at low GT and high GC is higher. Considering the AC, our results are similar to those reported by Kaur et al. (2014).
In Figure 2e, PT is suggestive of the time required for cooking the sample and reaching the PV. Pa.T has a reverse association with the GT, the higher the Pa.T, the lower the GT and the shorter the time required for cooking the sample (Fitzgerald, McCouch, & Hall, 2009;Mestres et al., 2011). These findings are consistent with the results reported by Kong et al. (2015). The obtained GT of the Hashemi variety was 4.5 which is considered to be in the intermediate to low   with the decrease of F max from 110.7 to 79.5 N and Et max from 647.7 to 529.6 N/mm.
In Figure 3, rice with high AC can be either soft or firm after cooking, depending on its GC (Champagne et al., 1999), which was confirmed by data observed in other researches (Wang & Wang, 2001). The AC is negatively correlated with Min. V (Kesarvani et al., 2016), and high AC causes grain volume expansion (Ogawa, 2008). The increase of moisture in the cells close to the endosperm surface causes the cells to expand and compress together (Ogawa, 2008). Similar results can be drawn from the research of Cnossen and Siebenmorgen (2000). As a result, internal stress occurs, which causes internal failure in the grain; reduces the grain resistance (Cnossen & Siebenmorgen, 2000), which was confirmed by data observed in other researches (Cnossen et al., 2003); and consequently decreases F max and Et max values. The AC in Dorfak and Kadus varieties were obtained 23.74 and 24.25, respectively, which were higher than that of the other cultivars. Therefore, it is concluded that Min.V decreases by the increase of F max . It was also observed that as the MC increases from 9% to 14%, the slope of Fmax also increases.
These findings are consistent with Mesters et al. (2011) finding that hardness decreases with the increase of viscosity.
In Figure 4a (Dorfak, MC 9%), the F.V value increased from 304.1 to 306.7 RVU with the increase of Es max from 424.7 to 509.6 N/mm and Et 0.05 from 420.6 to 469.9 N/mm. In Figure 4a, also, the mean values of AC and F.V were obtained to be 23.74% and 305.5 RVU, respectively. FV is positively   correlated with AC (Allahgholipour et al., 2006). Cooked grains from the rice types with high amylose are usually firm and dry (Mestres et al., 2011;Wang et al., 2010). In this research, the AC of Dorfak was higher than that of all other cultivars. Therefore, the FV of this variety was higher and the grains were steady after cooking, and as a result, the grain strength was higher. Considering the PC, the results obtained in our study are similar to those reported by Champagne et al. (2009).
In Figure 4b-d, different varieties have different levels of strength against stresses applied (Cnossen et al., 2003), which was confirmed by data observed in other researches (Cnossen & Siebenmorgen, 2000). In general, the SB.V in the modified varieties (Dorfak and Kadus) is higher than that of the local varieties (Hashemi and Domsiah). Moreover, the modified varieties have lower cooking quality and their grains become hard and stiff after cooking (Allahgholipour et al., 2006). In this study, the mean SB.V of Dorfak and Kadus varieties was higher than that of all other varieties. In Figure 4c, the E.F is positively correlated with F max and the grain strength (Li et al., 2014). Therefore, E.F changes with the changes in F max . On the other hand, it has been observed that cultivars showing low-soluble AC generally have higher SB.V, lower BD.V, harder GC (Allahgholipour et al., 2006;Kaur et al., 2014), and harder texture after cooking (Allahgholipour et al., 2006), which was confirmed by data observed in other researches (Sodhi & Singh, 2003).

| Optimization
Input means (IM) and results of optimal values (OV) of response and independent variables in the compressive tests are shown in Table 3.
Ten solutions were developed to determine the optimal conditions for the data extracted from the compression test. The software determined the optimal conditions of the independent variables based on the maximum goal and minimization of the response variables.
Using the desirability function method, the optimum extrusion conditions were obtained. The desirability value was obtained more than 0.80. The optimal values of the independent variables of F 0.05 , F max , D max , Et 0.05 , Et max , Es 0.05 , Es max , and EF to predicting of the response variable of PC (Domsiah with MC 9%) was as 16.49, 105.0, 0.23, 498.5, 654.8, 328.86, 579.9, and 11.52, respectively. As shown in Table 3, the optimal values of the independent variables have a decreasing trend, and the optimal values of the response variables are proportional to the optimal conditions. Also, the advantage of optimization conditions is in Table 3 the optimal use of independent variables in predicting response variables.

| CON CLUS ION
The present study investigated the prediction of some quality prop-  RVU, 64.52 RVU, 6.09 min, and 92.45°C) with desirability more than 0.80. Also, the results showed that the optimal values of the independent and response variables are proportional to the optimal conditions. This finding will pave the way for designing and developing devices to test the properties of single kernels of rice, similar to those that are now being employed to examine the kernels of other products such as wheat.

CO N FLI C T O F I NTE R E S T
None declared.