Heats of combustion representative of the carbohydrate mass contained in fruits, vegetables, or cereals

Abstract The obtainment of suitable values for metabolizable energy requires the previous knowledge of accurate and precise values of the heat of combustion of the different macronutrients. Thus, in this work, the heats of combustion of six carbohydrates (glucose, fructose, sucrose, maltose, starch, and cellulose) were experimentally measured, and such values were statistically compared with equivalent bibliographic values collected in a parallel work (Heats of combustion of the main carbohydrates in vegetable foods: a bibliographic approach, 2019), proposing, for each carbohydrate, an “overall interval” and an actualized representative value, which were estimated considering jointly the bibliographic and experimental information. Besides, a numerical methodology that used such parameters and the relative content of the different carbohydrates in selected foods was proposed, to estimate the global heat of combustion producible by the carbohydrate mass contained in such foods. The results estimated for 68 foods were globalized to propose the following generalized heats of combustion: (a) for fruits: 3.88 kcal/g, (b) for vegetables: 3.98 kcal/g and, and (c) for cereals: 4.13 kcal/g. These results demonstrated that the use of the Atwater's value (4.2 kcal/g of carbohydrate of vegetable source) involves a clear overestimation of the heat of combustion of the carbohydrate mass contained in vegetable source foods.

first paper of this series (Sánchez-Peña et al., 2017), an exhaustive critical review of the experiments carried out by Atwater to obtain such values was presented, demonstrating that there is a series of weakness in the experimental design that could compromise the validity of such values.
Regarding carbohydrates, Atwater (1900) proposed that the metabolizable energy of carbohydrates (ME c ) can be estimated as follows: ME c = (HC c )A c , being HC c , the heat of combustion produced by each gram of carbohydrate and, A c , the availability coefficient of such macronutrient. Focusing on the A c values characterizing the vegetal source foods, Atwater and Bryant (1900) proposed the following values for such coefficient: for cereals: 0.98, for legumes: 0.97, for vegetables: 0.95, and for fruits: 0.90; although the deficiencies and information absences related to the obtainment procedure of such factors have been recently summarized (Sánchez-Peña et al., 2017), implicitly, such factors are still used. Therefore, even recognizing certain inaccuracy level on the A c factors reported by Atwater and Bryant (1900), it could be expectable that such factors are very close to 1.0; thus, the accuracy and precision level of the ME c value characterizing a given sample must be strongly dependent on the accuracy and precision level of its correspondent HC c value. Therefore, as a first step in the estimation of a suitable ME c value, the establishment of a suitable HC c value is required.
With respect to the HC c value, Atwater and Bryant (1900) proposed that, for vegetal source carbohydrates, HC c = 4.2 kcal/g.
Nevertheless, since such value was proposed considering an arbitrary "averaging procedure" that probably used inaccurate data (Sánchez-Peña et al., 2017), it could be considered necessary to reevaluate such parameter.
With such background, in a parallel work , an exhaustive bibliographic analysis related to the heats of combustion of glucose, fructose, sucrose, maltose, starch, and cellulose was performed. In this analysis, the experimental errors possibly involved in the original sources were taken into account, and following rigorous statistical arguments, the outlier data were eliminated.
In that work , the following information was reported for each carbohydrate: (a) a representative value for the heat of combustion of the respective carbohydrate (which could be considered as the best approximation to the real heat of combus- Therefore, the estimation of the agreement level between such parameters and a set of experimental values currently measured could be considered as necessary. Thus, to reinforce the validity of the previously mentioned bibliographic parameters (first intermediate aim of this work), an experimental procedure to measure the heat of combustion of the carbohydrates of interest was here implemented, where the experimental inaccuracy of the previous works were carefully minimized (see details below); for each carbohydrate, an "overall interval" and an actualized representative value were statistically estimated, considering jointly the bibliographic information collected by Sánchez-Peña (2019) and the experimental data obtained in this work.
Then, a mathematical procedure was here proposed, which allow to estimate a global representative value by mass unit (global value) and a global interval for the heat of combustion by mass unit (global interval) that could be properly used to characterize to the carbohydrate mass contained in a given food; second intermediate goal of this work. In such procedure, the statistically estimated parameters mentioned in the previous paragraph, as well as the contents of the different carbohydrates contained in the considered vegetal products (obtained from the USDA Food Composition Database (National Nutrient Database for Standard Reference, 2016)) were used.
Finally, the global objective of this work was to propose a final representative value and a global interval that could be used to adequately characterize the heat of combustion per unit mass, corresponding to the carbohydrate mass contained in each food group.
For this, the global intervals calculated for each one of the considered foods were grouped, following a procedure proposed here.

| Pretreatment and bromatological characterization
Samples were carefully dried in a vacuum oven (Fisher Scientific; Model 281A) heated at around 65°C. However, since the glucose, fructose, and sucrose samples exhibited a perceptible degradation process during such heating (e.g., browning and/or characteristic odor production), they were dried at vacuum conditions and room temperature. The dried samples were characterized, following the AOAC procedures (to avoid the humidification of samples, a careful handling was performed); the crude protein content was obtained by Kjeldahl method (Tests: 979.09; Official Methods of Analysis. AOAC International. Protein in grains, 2018a), considering a conversion factor of 5.83 g of protein/g of nitrogen (FAO Food and Nutrition, 2002), whereas the lipid content was measured by Soxhlet extraction (Test 920.39; Official Methods of Analysis. AOAC International. Fat (crude) or ether extract in animal feed, 2018b).

| Calorimetric characterization
The heat of combustion measurements were performed using an isoperibolic calorimeter, which included a combustion static bomb (Parr Model 1108; inner volume: 342 cm 3 ); the used calorimeter has been described in more detail elsewhere . The total calorific capacity of the calorimeter was determined by calibrating, using a certified standard of benzoic acid (certified heat of combustion: 6.318 ± 0.001 kcal/g) as the reference material and averaging 10 experimental measurements; benzoic acid samples used in these experiments were carefully handled to avoid any kind of contamination. Calorimetric measurements were performed in triplicate (using the same pattern sample), reporting as the representative value the mean value of the three experiments (HC exp ; expressed in kcal/g). The HC exp value was corrected considering the relative amounts of lipids and proteins contained in the characterized samples, which were determined by means of the above mentioned test. The correction equation used is as follows: In Equation 1, HC is the corrected value of the heat of combustion (expressed in kcal/g), and M T, M l and M p are, respectively, the mass of the tested sample and the masses of the lipids and proteins contained in such sample (expressed in g). Equation 1 considers the heats of combustion reported by Atwater and Bryant (1900), that is, 9.3 kcal/g for the vegetable source lipids and 5.8 kcal/g for proteins contained in cereals.
To validate the respective "bibliographic intervals" with the corrected experimental data (i.e., the respective HC values), as in our previous work , the boxplot (Iglewicz, 2011) and/or the Grubbs' test (Grubbs, 1969;NIST/SEMATECH, 2012) were used to assign, or not, the considered data as "statistically outlier data." Thus, the possible assignation of the experimental data (HC values) as "non-outlier data" (Sánchez-Peña et al., 2019) could be interpreted as a self-validation of the two information sources, the bibliographic, and the experimental one. In that case, the "overall intervals" can be estimated following the same procedure used to determine the correspondent "bibliographic intervals" (Sánchez-Peña et al., 2019), but considering as an additional datum of the each set of data the correspondent HC value. Since our experimental data were very carefully measured, following our parallel work (Sánchez-Peña et al., 2019), they were considered type L-III data. Henceforth, the respective "overall intervals" will be defined by means of their respective extreme values, that is, the HC h i (the highest value of the "overall interval" for the carbohydrate i ) and HC l i (the lowest value of the "overall interval" for the carbohydrate i ) values; from now on, for glucose, i = 1; fructose, i = 2; sucrose, i = 3 ; maltose, i = 4; starch, i = 5; cellulose, i = 6. Besides, the respective actualized representative values were estimated, like the correspondent representative values in our parallel paper (Sánchez-Peña et al., 2019), but considering the correspondent experimental value (HC value) as an additional type L-III datum.
To estimate the HC value of an anhydrous substance (HC anh ), the following equation can be used (Sánchez-Peña et al., 2019): where HC anh and HC hyd are, respectively, the heats of combustion for the anhydrous and hydrated forms of the tested substance, whereas MH and MA are, respectively, the relative masses of the hydrated and anhydrous substance, finally, HH substance is the hydration heat of the tested substance. Due to crystallographic reasons, there are X + 18 g of hydrated substance by each X g of anhydrous substance and 18 g of water, being X the molar mass (expressed in g/mol) of the tested substance. Since the HC exp value for the anhydrous maltose could not be experimentally determined, the equation 2 will be used to estimate the actualized representative value and the "overall interval" for such substance.

| Estimation of the "global interval"
for the heat of combustion and the global heat of combustion of the carbohydrate mass contained in a given food

Composition intervals
In the case of the carbohydrates contained in vegetal source foods, the information required to estimate the experimental interval for the respective compositions (C i and se i values; a pair for each carbohydrate contained in the considered food) was obtained from the USDA Food Composition Database (National Nutrient Database for Standard Reference, 2016), being such intervals estimable as follows (Montgomery, 2001): where h i is the statistical factor assignable to each carbohydrate (1 ≤ i ≤ 6; see definitions above), which depend on the number of data measured (n value), the desired level of distribution coverage (here, a coverage of 90% was selected) and the defined confidence level (in this work, a 90% was chosen, assuming a distribution with two tail) (Montgomery, 2001), C i are the respective mean values for the compositions of each carbohydrate contained in the different foods (expressed in mass percentage; 1 ≤ i ≤ 6; see definitions above), and se i are the respective standard errors of the experimental data used to calculate the corresponding C i values (1 ≤ i ≤ 6; see definitions above). Alternatively, such intervals can be defined by means of their respective extreme values, that is, the values; note that, when se i = 0, or this datum is not

The "overall interval" for the heats of combustion
Equivalently to the indicated intervals in section "Composition intervals", for each carbohydrate, there is an "overall interval" for the respective heats of combustion, which is defined by their respective extreme values, that is, the above defined HC h i and HC l i values (section 2.1.3.).

Estimating the "global interval" for the heat of combustion of the carbohydrates contained in a given food
When the six composition intervals (one for each carbohydrate type; section "Composition intervals") and the six "overall intervals" for the heats of combustion (one for each carbohydrate type; section The "overall interval" for the heats of combustion) are available, it is possible to define an interval (the "global interval") that very probably includes the heat of combustion produced by the carbohydrate mass contained in a given food.
To estimate such "global interval," the following calculation procedure is proposed: a Consider the extreme values of the six composition intervals (one interval for each carbohydrate type; i = 1, 2,…up to 6), that is, the six pairs of values C h i and C l i ; see section "Composition intervals". b Define 64 (=2 6 ) different sets, each one containing six values (one for each carbohydrate type, that is, one for each value of i ), utilizing all the combinations that result from selecting for each value of i , one of the two following values: C h i or C l i . Please consider the following example: C h 1 ,C h 2 ,C l 3 ,C h 4 ,C l 5 ,C h 6 ; in this set, the first term could be: C h 1 or C l 1 , having been selected in this case C h 1 , the second one could be, C h 2 or C l 2 , having been selected for this set C h 2 , and so on up to the last term, C h 6 , which was chosen between C h 6 and C l 6 .
c Consider now the extreme values of the six "overall intervals" for the heats of combustion (one interval for each carbohydrate type, that is, for i = 1, 2,…up to 6), that is, the six pairs of values HC  where C i is the mean percentage composition reported for the respective carbohydrate i in a given food (e.g., those values reported for the USDA Food Composition Database (National Nutrient Database for Standard Reference, 2016)), and HC i is the actualized representative value for the heat of combustion of the corresponding carbohydrate (estimated according to section 2.1.3.).

| Global heat of combustion
However, when the information required to estimate the "global interval" for the heat of combustion of the carbohydrates contained in a given food is available (section "Estimating the "global interval" for the heat of combustion of the carbohydrates contained in a given food"), an alternative option to estimate the global heat of combustion representative of the carbohydrate mass contained in such food (HC f c ), is to average the 4,096 HC f c | x values (section "Estimating the "global interval" for the heat of combustion of the carbohydrates contained in a given food"). Note that, although the HC f c value could a priori be considered equivalent to the HC cinf value, the statistical superiority of the first one is evident; numerical comparisons on this topic will be presented below.
For this study, a computational program was specifically designed to perform the calculation procedures described in sections "Estimating the "global interval" for the heat of combustion of the carbohydrates contained in a given food" and 2.2.2.   Figure 1, the data referring to vegetables were presented in Figure 2 and, finally, the values regarding cereals were showed in Figure 3.

| D ISCUSS I ON
Since the respective HC values could not be statistically classified as "outlier data" (Grubbs,1969;Iglewicz, 2011;NIST/SEMATECH, 2012),  Regarding the global intervals, the first aspect that should be mentioned is related with the corresponding "interval lengths" (e.g., the maximum value minus the minimum one of the respective global interval). About this topic, although the USDA Food Composition Database (National Nutrient Database for Standard Reference, 2016) lists the contents of the different carbohydrates present in numerous foods, for some of them, the reported se values were comparatively high, which produced "interval lengths" that were herein considered too long. In this work, the "interval lengths"> 0.32 kcal/g were considered too long, therefore, the foods that fulfill this condition were not considered in this report. Taking into account only the 68 foods considered in Tables 1-3, only in five of them, the "interval lengths" were in the proposed limit value (0.32 kcal/g or, equivalently, ±4%).
Thus, looking for a estimation of the inaccuracy level expectable to use the HC cinf parameter as a representative value for a given food (its calculation facility makes it a "very attractive" parameter) instead of the correspondent global interval, in Tables 1-3 it can be noticed that, in the vast majority of considered foods (87%), the correspondent global intervals are within the generic interval HC cinf ± 4%; only in nine foods, one of the extremes of the individual interval exceeded to the generic interval, falling out of it around 0.01 kcal/g. Based on the previous results, it could be affirmed that the expectable error to consider as representative of the calorimetric behavior of a given food to its HC cinf value is ≤4%; by its evident calculation facility, at least in some cases, this could be an attractive option to approximate the calorimetric behavior in a given food.
To facilitate the analysis of the global intervals of the samples corresponding to the same type of food (fruits, vegetables, or cereals), Figures 1-3 are presented. Thus, Figure 1 includes the available information for fruits, being there possible to appreciate that the 31 global intervals can be suitably represented by the following globalizing mathematical expression: 3.88 kcal/g ± 4%; such expression is graphically represented by the horizontal lines in Figure 1.  Table 1. The proposed interval to represent the set of global intervals is limited by dotted lines and its central line is represented by the continuous horizontal line (see additional information in text) The previous expression was ex-profeso calculated to "exclude," in both extremes (superior and inferior), less than 2.5% of the "global interval length" (calculated as the arithmetic sum of the 31 "interval lengths").
Per the above, and considering the available data for fruits ( Figure 1), it can here be generalized that: HC fruits c = 3.88kcal/g ± 4% . When comparing this value with the equivalent one proposed by Atwater for vegetable source foods (HC c = 4.2kcal/g), it is evident that an overestimation that ranges between 4% and 11% is involved when Atwater's value is used.
In Figure 2, the available information relative to the considered vegetables is presented. Then, after an equivalent analysis to the previously described, it was found that the mathematical expression suitable for vegetables is as follows: HC vegetables c = 3.98kcal/g ± 5%; in this type of foods, the use of Atwater's value (4.2 kcal/g) involves an overestimation on the heat of combustion value that can become as high as 10%.
Finally, when the available results for cereals are analyzed in Figure 3, it can be proposed that the representative expression for this type of foods is as follows: HC cereals c = 4.13kcal/g ± 3%. As in previous food groups (fruits and vegetables), the use of Atwater's value involves an overestimation of the correspondent heat of combustion value, which, in this specific food group can become as high as 5%.

| CON CLUS IONS
The mutual consistency between the experimental results determined herein and the bibliographic data collected in our parallel work (Sánchez-Peña et al., 2019) allow us to consider them as experimentally validated, allowing its suitable use in later calculations.
In addition, the obtained generalized intervals demonstrate that, in the case of vegetable source foods, the use of Atwater's value  Table 3. The proposed interval to represent the set of global intervals is limited by dotted lines and its central line is represented by the continuous horizontal line (see additional information in text) the heat of combustion of the carbohydrates contained in vegetable source foods, but, besides (and maybe mainly), represents a set of values much more supported/argued from the experimental and statistical point of views.

ACK N OWLED G M ENTS
Authors thank the University of Guadalajara for the financial support, and the students Martínez-Navarro A.G. and Muñiz-Mendoza P. are grateful for their respective Conacyt scholarships.

CO N FLI C T O F I NTE R E S T
Authors declare that they do not have any conflict of interest.

E TH I C A L R E V I E W
This study does not involve any human or animal testing.

I N FO R M E D CO N S E NT
Does not apply.