Water Absorption Index and Water Solubility Index Prediction for Extruded Food Products

Abstract

The wide variation of water absorption and water solubility index values of extruded food products makes their utilization difficult in food process applications. The published values of water absorption and water solubility indices of various extruded starchy and proteinaceous food products were classified and analyzed statistically in order to reveal the influence of die temperature, feed moisture content, and screw speed. A power law model relating the water absorption or water solubility index to independent extrusion variables was fitted to all literature data for each food product. The predicted values were carefully screened and successfully correlated to experimental values. In the case of the water absorption index, seven products and seven blends were evaluated and the correlation for most food products and blends was very good. However, in the case of the water solubility index, six products and two blends were evaluated and the correlation for most food products and blends was satisfactory.

Keywords:

• Cereals
• Extrusion variables
• Legumes
• Model foods
• Vegetables

INTRODUCTION

Extrusion is a technological process, commonly used in the field of the human and animal feed industry, applied successively on a broad spectrum of commercially manufactured products. Hot extrusion is a thermomechanical processing operation that makes use of high temperatures applied on the processed material for a short time. As a result of this process, a variety of chemical reactions and functional changes occur on the extruded material, which leads to changes of its sensory characteristics, nutritional value, and components and the reduction of the microbiological contamination.[1–6,17,18] Conclusions upon the quality of the derived products can be drawn by measuring several functional properties of the final product. Usually most of the gathered data allow us to make further useful assumptions. In particular, water solubility index (WSI) and water absortion index (WAI) are two indices linked to the estimation of the behavior of the material if further processed for use as a binder, a stabilizer, or a source of protein in beverages, health and nutrition bars, dairy, baked, and emulsified/ground meat food systems.[7–12]

Anderson et al.[13] recorded a method to estimate the amount of material that can be extracted by water from an extruded product. The method involves milling the extruded product and then adding a known weight of powder to distilled water. The sample is then stirred and the suspension is poured into a tare centrifuge tube. After centrifugation, the supernatant is dried and the weight of solids in the supernatant is used to calculate the WSI as a percentage of dry weight of the extrudate. The weight of the sediment in the centrifuge tube is used to calculate the WAI as a percentage of the water bound per 100 g of dry extrudate. All the collected values are measured according to the above method. WSI and WAI values extend in a wide range of prices depending on the specific parameters applied during each extrusion process. Factors affecting the values of indices can be classified into two main groups: the first one consists of the parameters that are linked to the raw material subjected to extrusion, and the second one includes parameters related to the extruder equipment. In particular, the first group refers to the initial composition of the raw material, the raw material formulation, the pre-processing treatments, the initial particle size of milled materials, and the milling procedure.[10–12] The second group is related to the extruder conditions, such as extruder type, last section barrel temperature, or die temperature, feed moisture content, feed rate, screw speed, screw configuration, screw compression ratio, die dimension, and die configuration.[14,15] Many previous studies related the final state of raw materials transformation during extrusion to such processing parameters as barrel temperature, water content, feed rate, or screw speed without examining the influence of the other factors on the final product.

Various models have been proposed based on statistical analysis, in order to correlate the WAI or WSI with the barrel temperature, water content, and screw speed for the extruded food products. These models are generally second- or third-order polynomials and describe the effects of independent variables in the first, second, and third order, as well as the product between them on WAI or WSI. Unfortunately, comprehending the physical values of these second- and third-order polynomials or the products between the independent variables is very difficult. The present study proposes a mathematical model that overcomes the above difficulties in understanding, as it is a simple power law model. The proposed mathematical model investigates the effect of die temperature, feed moisture content, and screw speed on the WAI and WSI properties for some food products. The model is fitted to relevant data available from the literature and the model parameters were estimated for every category of food products.

DATA-MATHEMATICAL MODEL

According to Oikonomou and Krokida[15] a database was developed, which includes experimental values for WAI and WSI from a wide range of extruded food products. Part of this database (63 articles which include 877 and 577 values for WAI and WSI, respectively) was used for statistical analysis and modeling mainly for starchy and proteinaceous extruded food products (Table 1). The WAI and WSI can be predicted using a model, which considers power law dependency of all independent variables:

Table 1 Number of papers and literature data which were used for analysis

	WAI		WSI
Material	Number of papers	Number of data	Number of papers	Number of data
Cereal Products
Barley cv.	2	54	^FV	^FV
Corn	8	208	7	153
Oat	3	21	3	21
Rice cv.	11	94	9	67
Wheat	5	29	4	21
Legumes
Beans Ph. vulgaris L. cv. and Chickpeas C. Arietinum L. cv.	10	67	7	24
Model Foods
Banana, cassava, corn and wheat starch	15	76	10	80
Blends
Cereal Products
Corn:DDG ^a	2	45	^FV	^FV
Corn:Lentil	1	146	1	146
Rice:DDG ^a	1	18	^NR	^NR
Wheat:DDG ^a	3	33	^FV	^FV
Model Foods
Corn starch ^b :WPC ^c	3	40	3	40
Rice starch SPI ^d	1	28	^NR	^NR
Vegetables
Potato:DDG ^a	1	18	^NR	^NR
^aDried distillers grains from corn and wheat; ^bVarious levels of amylose; ^cWhey protein concentrate; ^dSoy protein isolate; ^FVFew values for statistical analysis; ^NRNot reported.

(1)

and

(2)

where WAI is the water absorption index; WSI is the water solubility index %; T is the die temperature of the extruder (°C); T_o = 150°C is a reference die temperature; X is the feed moisture content % (wb); X_o = 15% is a reference feed moisture content; S is the screw speed (rpm); S_o = 200 rpm is a reference screw speed; M is the % mixture; M_o = 20% is a reference mixture; and a, b, c, d, and e are the parameters of the models, different in each case. The term (M/M_o)^e in Eqs. (1) and (2) is used only in the case of blends.

STATISTICAL ANALYSIS

Curve fitting was performed using the solver function in Microsoft® Office Excel 2003 (XP Edition, Microsoft Corporation, WA, USA) adopting the nonlinear optimization equation to determine the parameters, a, b, c, d, and e in the power law model (Eqs. 1 and 2). Therefore, the parameters are estimated simultaneously by minimization of the residual sum of squares (SST):[16,17]

(3)

where is the experimental value of the response variable (WAI or WSI) of the uth replicate of the jth experiment, is the calculated value of the model for the jth experiment, is the number of replicates in the jth experiment, and m is the number of different values of independent variables. The residual sum of squares consists of the pure error sum of squares and the lack of fit sum of squares:

(4)

where the first term on the right-hand side of equation is the pure error sum of squares and the second is the lack of fit sum of squares, and is the average experimental value of the response variable of the jth experiment. The standard experimental error and the standard deviation between experimental and calculated values can be calculated from the following equations:

(5)

(6)

where p is the number of parameters. Altogether, there are experimentals.

A model is considered acceptable if the standard deviation between experimental and calculated values is close to the standard experimental error . The parameters described above do not have the same affect on the SST. In order to check if the model contains the required number of parameters for predicting the values of WAI and WSI, the following process was adopted. Initially excluding one parameter at a time, the values of were calculated for all the remaining parameters. The parameter selected for elimination was the one that, when excluded, produced the minimum . Continuing the former procedure, the minimum values of were evaluated for (4), 3, 2, and 1 parameters, respectively. Another statistical test that determines the accuracy of the parameter estimates is the calculation of the confidence intervals (95%) for each parameter and for all the products (Tables 4 and 5).

RESULTS

The results of the nonlinear regression analysis of fitting Eq. (1) to the experimental points are shown in Table 2. In this table, the standard experimental error (Eq. 5) and the standard deviation between experimental and calculated values (Eq. 6) are also presented. In most cases the values of the standard experimental error are a little smaller (or a little bigger in the cases of corn starch: whey protein concentrate (WPC) and rice starch: sou protein isolate (SPI)) than the values of the standard deviation between the experimental and calculated values indicating that the model (Eq. 1) is satisfactory in predicting the WAI of products. In the cases of wheat, wheat: distiller's dried grains (DDG), and potato:DDG, the difference in the values was a little bigger than that in the above cases showing that there is an adequate fit to Eq. (1). Similarly, in Table 3 the results of the nonlinear regression analysis of fitting Eq. (2) for WSI are presented. In most cases, the values of the standard experimental error are relatively close to the values of standard deviation between experimental and calculated values . Therefore, the model provides a good fit for the various food products.

Table 2 Standard experimental error (), standard deviation between experimental and calculated values (), parameters of the model and the experimental limits of die temperature (T), feed moisture content (X), screw speed (S), and the mixture (M) for the WAI prediction

Material	Se	Sr	a	b	c	d	e	T max (°C)	T min (°C)	X max %	X min %	S max (rpm)	S mix (rpm)	M max %	M min %
Barley cv.	0.60	1.29	4.62	−0.69	0.44	0.86	—	210	110	26	10	230	50	—	—
Corn	0.42	0.69	5.23	0.07	0.16	0.35	—	230	60	28	11	840	30	—	—
Oat	0.24	0.55	2.26	−0.68	−0.14	−0.06	—	240	77	26	11	230	90	—	—
Rice cv.	1.12	1.21	5.97	0.09	0.60	0.01	—	250	95	30	12	500	100	—	—
Wheat	0.26	1.88	4.63	−1.07	−0.46	0.46	—	250	120	24	14	500	60	—	—
Beans and chickpeas cv.	0.42	1.51	4.07	0.11	0.49	0.05	—	205	90	30	15	300	25	—	—
Starch	1.08	3.06	7.54	1.23	0.91	−0.06	—	200	75	70	14.2	750	40	—	—
Blends
Corn:DDG ^a	0.40	0.74	0.04	0.11	−0.06	−7.46	−0.17	250	100	22	11	120	100	40	10
Corn:Lentil	0.28	0.53	4.39	0.28	0.15	1.00	−0.00	230	170	19	13	200	200	50	10
Rice:DDG ^a	0.41	1.21	7.54	0.17	0.32	1.00	−0.08	250	160	22	15	100	100	40	10
Wheat:DDG ^a	0.40	1.78	4.07	−0.60	−0.13	0.34	−0.12	250	120	22	12	350	100	40	10
Corn starch:WPC ^b	1.55	1.21	5.37	0.30	0.54	0.14	−0.08	180	70	30	2	200	45	50	5
Rice starch:SPI ^c	1.02	0.51	19.40	0.15	−0.33	1.00	−0.29	180	140	30	20	42	42	75	25
Potato:DDG^a	0.53	2.07	9.40	0.03	0.19	1.00	−0.12	250	160	22	15	100	100	40	10
^aDried distillers grains from corn and wheat; ^bWhey protein concentrate; ^cSoy protein isolate.

Table 3 Standard experimental error (), standard deviation between experimental and calculated values (), parameters of the model and the experimental limits of die temperature (T), feed moisture content (X), screw speed (S), and the mixture (M) for the WSI prediction

Material	Se	Sr	a	b	c	d	e	T max (°C)	T min (°C)	X max %	X min %	S max (rpm)	S mix (rpm)	M max %	M min %
Corn	5.96	11.99	19.76	−0.16	−0.34	−0.20	—	230	90	28	12.1	400	130	—	—
Oat	0.18	1.20	6.24	−0.08	−0.51	−0.07	—	240	77.5	26	11	230	90	—	—
Rice cv.	2.53	18.70	23.17	1.36	0.10	−0.04	—	200	100	30	12	300	150	—	—
Wheat	3.34	9.96	10.42	2.57	0.02	1.45	—	185	120	24	14	350	60	—	—
Beans and chickpeas cv.	2.96	16.58	33.98	−1.48	1.12	0.26	—	190	130	30	20	300	85	—	—
Starch	7.91	27.30	27.80	0.70	−0.41	−1.09	—	200	90	40	14.2	750	50	—	—
Blends
Corn:Lentil	6.23	7.57	12.76	0.52	−0.72	1.00	−0.11	230	170	19	13	200	200	50	10
Corn starch:WPC ^a	10.00	15.48	27.18	−0.20	0.02	0.60	−0.11	180	70	30	2	200	43	50	5
^aWhey protein concentrate.

The experimental limits of independent variables are shown in Tables 2 and 3. The same limits are used for the prediction of WAI and WSI. The variation of experimental WAI values ranges from 0.3 to 12.8, while predicted values of WAI varied from 1.3 to 9.5. Experimental WSI values varied from 2.7 to 73.2%, while predicted WAI varied from 4.5 to 61.6% for all extruded food products. The smaller range of predicted values compared to experimental values may be explained by the low ability of the model to predict accurate values at low and high values of independent variables.

The plots, which relate the WAI and WSI, with die temperature of extruded products at X = 15% and S = 150 rpm are presented in Figs. 1a and 2a, respectively. An increase in die temperature does not have a consistent effect on experimental and predicted WAI and WSI for all raw materials examined. Figure 3a presents the plot of WAI versus die temperature at X = 15%, S = 150 rpm, and M = 25% for blends. In general, an increase in die temperature leads to a slight increase of WAI, except for starch and the blend of starch:DDG. Similar results were obtained for the other ranges of independent variables (data not shown). Figure 1b illustrates that the WAI increases sharply with feed moisture content for all of the extruded food products, except for wheat and oat products. An increase in feed moisture content leads to a slight decrease in the WSI for all food products, except beans (Fig. 2b). In the extruded blends, the effect of feed moisture content on WSI has no definite correlation for the food products (Fig. 3b). In Figs. 1c and 2c the curves do not have a distinct slope as screw speed increases for all the extruded products. As can be seen, the increase in mixture on proteinaceous materials has as a result a slight decrease in WAI (Fig. 3c). Overall, when the extrusion variables are increased, the WAI and WSI are increased only in the cases of corn, rice, beans, starch, corn:lentil, rice, and wheat products, respectively.

Figure 1 Effect of (a) die temperature °C; (b) feed moisture content %; (c) screw speed rpm on WAI for barley (▴), corn (•), oat (■), rice (x), wheat (◊), beans (○), and starch (□). Lines are calculated model values using parameters given in Table 2.

Figure 2 Effect of (a) die temperature °C; (b) feed moisture content %; (c) screw speed rpm on WSI for corn (•), oat (■), rice (x), wheat (◊), beans (○), and starch (□). Lines are calculated model values using parameters given in Table 3.

Figure 3 Effect of (a) die temperature °C; (b) feed moisture content %; (c) mix lever % on WAI for: (1) (▲) corn:DDG, (2) (•) corn:lentil, (3) (■) rice:DDG, (4) (x) wheat:DDG, 5 (◊) corn starch:WPC, (6) (○) rice starch:SPI, and (7) (□) potato:DDG. Lines are calculated model values using parameters given in Table 2.

Figures 4a and b present typical charts of and as a function of the number of parameters for WAI the rice and for WSI the blend corn:lentil. The results presented on the charts indicate that the number of parameters is necessary for the accurate prediction of the model. In Tables 4 and 5, the confidence intervals (95%) for all parameters for all food products are shown for WAI and WSI. These tables include parameters with confidence intervals that range from negative to positive values, showing that these specific parameters are not required in Eqs. (1) and (2). The products with two or more parameters having zero within the range of their confidence intervals are also those products where the differences in the values of and was great, such as wheat, beans, and wheat:DDG.

Figure 4 The lack of fit () and standard experimental error () as a function of the number of parameters: (a) predicted model for WAI of rice; (b) predicted model for WSI of blend corn:lentil.

Table 4 Confidence intervals (95%) for the parameters of the model for the WAI prediction

	Confidence interval
	a		b		c		d		e
Material	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper
Barley cv.	3.96	5.29	−1.45	−0.02	−0.14	1.02	0.59	1.15	—	—
Corn	5.15	5.31	0.09	0.23	0.09	0.23	0.31	0.39	—	—
Oat	2.01	2.53	−1.00	−0.37	−0.52	0.23	−0.47	0.34	—	—
Rice cv.	5.71	6.25	0.43	0.77	0.43	0.77	−0.11	0.14	—	—
Wheat	3.10	4.64	−1.66	−0.49	−1.07	0.15	0.28	0.66	—	—
Beans and chickpeas cv.	4.18	5.16	−0.26	0.48	0.08	0.91	−0.06	0.17	—	—
Starch	6.19	8.94	0.78	1.69	0.07	1.75	−0.24	0.11	—	—
Blends
Corn:DDG ^a	0.03	0.06	−0.01	0.23	−0.18	−0.05	−8.00	−6.91	−0.22	−0.14
Corn:Lentil	4.27	4.54	0.20	0.37	0.08	0.22	1.00	1.00	−0.02	−0.01
Rice:DDG ^a	7.04	8.21	−0.03	0.37	0.13	0.51	1.00	1.00	−0.15	−0.02
Wheat:DDG ^a	3.32	4.83	−1.12	−0.09	−0.72	0.46	0.09	0.59	−0.27	0.03
Corn starch:WPC ^b	3.58	7.14	−0.07	0.69	0.21	0.86	−0.16	0.45	−0.28	0.1
Rice starch:SPI ^d	14.60	24.78	−1.40	1.70	−1.29	0.62	1.00	1.00	−0.50	−0.08
Potato:DDG ^a	9.00	10.01	−0.10	0.18	0.06	0.33	1.00	1.00	−0.17	−0.08
^aDried distillers grains from corn and wheat; ^bWhey protein concentrate; ^cSoy protein isolate.

Table 5 Confidence intervals (95%) for the parameters of the model for the WSI prediction

	Confidence interval
	a		b		c		d		e
Material	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper	Lower	Upper
Corn	16.00	30.47	0.45	0.12	−0.73	0.04	−0.51	0.12	—	—
Oat	5.52	7.77	−0.32	0.16	−0.75	−0.26	−0.34	0.19	—	—
Rice cv.	4.27	43.81	0.45	2.27	−0.64	0.85	−0.92	0.83	—	—
Wheat	0.09	6.31	−0.33	4.80	−1.78	1.82	0.65	2.26	—	—
Beans and chickpeas cv.	11.83	42.99	−3.32	0.35	0.03	2.22	−0.36	0.89	—	—
Starch	51.44	82.76	−0.20	1.61	−1.05	0.22	−0.49	−0.70	—	—
Blends
Corn:Lentil	10.91	14.65	0.14	0.92	−1.02	−0.42	1.00	1.00	−0.18	−0.05
Corn starch:WPC ^a	13.66	40.71	−1.30	0.89	−0.30	0.34	−0.05	1.26	−0.48	0.25
^aWhey protein concentrate.

CONCLUSION

The present study proposes a mathematical model that investigates the effects of the main extrusion variables on the WAI and WSI properties for some food products. The model is fitted to literature data and the model parameters were estimated for every category of food products. The method used for curve fitting was a nonlinear regression that was based on the minimization of residual sum of squares. The check of the accuracy of the model and the need for the number of parameters was undertaken with the aid of the standard experimental error , standard deviation between experimental and calculated values , and the confidence intervals of the parameters, respectively. In most cases, the modeling of the WAI of food products showed that the power law equation is fitted satisfactory to the available experimental values. In contrast, when modeling WSI the fit of the power law equation to experimental data is adequate. Unfortunately, enough data exists only for limited products to carry out a successful regression analysis.

NOMENCLATURE

WAI	=	Water absorption index
WSI	=	Water solubility index
T	=	Die or last section temperature of extruder (°C)
X	=	Feed moisture content of food product in wet base %
S	=	Screw speed of extruder (rpm)
M	=	% mixture of blend
	=	Standard experimental error
	=	Standard deviation between experimental and calculated values
a, b, c, d, e	=	Dimensionless parameters
	=	Experimental value of WAI or WSI
	=	Calculated value of WAI or WSI
	=	Arithmetic mean of experimental value of WAI or WSI
Subscripts	=
	=	Reference value of independent variables