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The influence of the reference method on the results of the secondary method via calibration
Food Chemistry 122 (2010) 429–435
Contents lists available at ScienceDirect
Food Chemistry journal homepage: www.elsevier.com/locate/foodchem
The influence of the reference method on the results of the secondary method via calibration Heinz-Dieter Isengard a,*, Georg Merkh a, Kerstin Schreib a, Inga Labitzke a, Clément Dubois b a b
University of Hohenheim, Institute of Food Science and Biotechnology, D-70593 Stuttgart, Germany École Supérieure d’Agriculture d’Angers, F-49007 Angers Cedex 01, France
a r t i c l e
i n f o
Article history: Received 6 March 2009 Received in revised form 8 February 2010 Accepted 19 February 2010
Keywords: Calibration Reference methods Near infrared spectroscopy Water content Karl Fischer titration Drying techniques
a b s t r a c t Indirect methods have often the advantage to be non-invasive and very rapid. They can sometimes even be applied in-line or at-line. The disadvantage is that they do not measure the target property of the product directly but either another property that depends on the target property or the response of the product to a physical influence. In all these cases it is necessary to know the relationship of the target property and the measured property or the response, respectively. This relationship is often very complex and needs to be established empirically for samples with known properties which have been measured with a reference method. In other words, a calibration must be established. The future predictions depend completely on the calibration. This means that the calibration must be as correct as ever possible. Inadequate calibration leads to erroneous results, although the user of the method may not be aware of this fact. This is shown at the example of near infrared spectroscopy (NIRS) for water content determination. The Karl Fischer titration as a selective method and drying techniques as non-selective methods were used as reference methods. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Direct and indirect analytical methods Direct methods measure the property of the sample or the analyte as such. Direct methods are therefore also called primary methods and often serve as reference methods. Indirect methods measure a property of the sample that depends on the concentration or amount of the analyte. Indirect methods need therefore a connection or relation to a direct method (to which they are ‘‘referred”) in a way that the value measured allows a conclusion to the property of the sample or the concentration or the amount of the analyte (Isengard, 1995). Samples with a known property (analysed with a ‘‘reference” method) are measured with an indirect method and the value found is related to the ‘‘true” value. This is done for several concentrations or amounts. Thus, value pairs are obtained. These pairs (values obtained with the indirect method [ordinate] versus values obtained with the reference method [abscissa]) are plotted and a regression curve (mostly a straight line) is laid through these data points. This is the calibration line in the univariate case.
* Corresponding author. Tel.: +49 711 397 4670; fax: +49 711 397 4674. E-mail address: [email protected] (H.-D. Isengard). 0308-8146/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodchem.2010.02.051
Samples with unknown concentration can then be analysed with the indirect method, the unknown concentration is read from the calibration curve. When chemometric methods are applied, the analytical data points are calculated from many responses each (multivariate case). These values are often called ‘‘predicted values” and are plotted against the ‘‘true values” obtained by the reference method. The ideal line through this plot ‘‘predicted values” (ordinate) versus ‘‘true values” (abscissa) is a straight line with the gradient 1 (45°) running through the origin of the coordinate system. The scattering of the data points around this line (expressed by the regression coefficient) is a measure of the accuracy of the method expressed as standard error of calibration (SEC) for the calibration and standard error of prediction (SEP) for a validation set. The standard errors SEC and SEP are calculated by means of Eq. (1):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 sec xref i¼1 ðxi i Þ SEC or SEP ¼ n1
ð1Þ
where xsec are values for sample i measured by the secondary methi the valod, for instance by near infrared (NIR) spectrometry and xref i ues measured by the reference method derived from the calibration set (for SEC) or derived from the validation set for prediction (for SEP). If cross validation is applied the abbreviation RMSECV is used which stands for root mean square error of cross validation. In this case, n is used instead of n 1 in Eq. (1).
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The whole approach depends, however, on the ‘‘correctness” of the reference method, because it is always possible to draw a regression line through data points. For every analytical measurement, a corresponding concentration of the analyte will be found and even a high precision is no proof of accuracy. A possible error will not be detected because the results are based on the same wrong conditions and assumptions. It is therefore essential that the reference method be ‘‘correct”. The importance of this prerequisite is shown at the example of water content determination. 1.2. Water content determination The Karl Fischer titration (KFT) detects water selectively (Scholz, 1984), whereas oven methods determine mass loss under the applied conditions (other volatiles are also included and strongly bound water is not detected completely). NIR spectra depend on water content. NIR calibrations should therefore be based on a reference method that really determines water and nothing but water (like the Karl Fischer titration). Calibrations can, however, also be carried out on the basis of a drying technique. Multivariate calibration algorithms will always find a calibration model. Water content is referred to wet basis (mass of the sample analysed) throughout this article. 2. Materials and methods 2.1. Samples Wheat semolina was from Alb-Gold Teigwaren, Trochtelfingen, Germany. The particle size distribution of semolina with fine granulation was the following: >500 lm: <1%, 400–500 lm: 3–9%, 250–400 lm: 55–63%, 160–250 lm: 21–29%, <160 lm: 7–12%. The coarse-granulation semolina had the following size distribution: >630 lm: <2%, 500–630 lm: 14–20%, 400–500 lm: 32–40%, 200–400 lm: 41–49%, <200 lm: <2%. Drying results were obtained by drying three replicates of 3–5 g for 2 h at 130 °C, according to the corresponding ICC method (ICC, 1976). Karl Fischer titration was carried out for three replicates at the boiling point of methanol (Isengard & Schmitt, 1995; Isengard & Striffler, 1992) using the one-component technique with
Hydranal-Composite 5 as titrating agent and methanol as working medium. The titrating vessel was a multi-necked round-bottomed flask. Whey powder was received from Nestlé, Switzerland. Whey powder contains high amounts of lactose. Lactose exists in different forms. The a-anomer (monohydrate) is the more stable form at temperatures below 93 °C. It crystallises with one mole of water per mole lactose. At higher temperatures the anhydrous b-monomer is more stable. Lactose occurs also in amorphous form which may include small amounts of water. Depending on the production conditions dried dairy powders contain mixtures of these polymorphs. In addition to included water and water of crystallisation, the product usually contains small quantities of surface water. The usual drying temperature for moisture determination of dairy products in drying ovens is 102 °C (First Commission directive, 1979). At this temperature the water of crystallisation of alactose is not evaporated completely during the usual drying times (Isengard, Felgner, Kling, & Reh, 2006). The separation of this water fraction from the matrix needs a high energy input (Rüegg & Moor, 1987; Rückold, Isengard, Hanss, & Grobecker, 2003). After 2 h, the standard drying time, only a part of this water is detected. The consequence is that drying techniques yield results that differ more or less from the true water content. For this reason, the drying temperature was raised to 145 °C. As lactose occurs in practically all dairy products and is also used in the pharmaceutical industry, this problem affects a wide range of products, particularly those with high lactose content like whey powders or lactose itself. Usually the drying results are lower than water content. In special cases, however, they can be higher. This is possible if the lack in water detection is over-compensated by other volatile substances which are contained in special products or which are formed by decomposition of components during the drying process (Isengard, 2008). Drying results were obtained from duplicates. Titrations were carried out in five replicates using the two-component technique with Hydranal-Titrant 2 as titrating agent and a mixture of Hydranal-Solvent and formamide in a volume ratio of 2:1 at a temperature of 40 °C in a double-walled titration vessel. The baby food Lasana Dauermilch 1 produced by Humana Milchindustrie, Everswinkel, Germany, was bought in a local shop in Germany. It contains 10.1 g/100 g proteins, 56.5 g/100 g carbohydrates (of which are 0.1 g/100 g glucose, 41.2 g/100 g lactose,
Gravimetric loss of mass / water content in g / 100g
16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0 0
50
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Time in minutes Water content in g / 100 g of the original sample determined by Karl Fischer titration Gravimetric loss of mass in g / 100 g of the sample in a drying closet at 145 °C Residual water content in g / 100 g, by Karl Fischer titration, of the sample in a drying closet at 145 °C Fig. 1. Drying curve of whey powder (Lactoserum Euvoserum from Nestlé) at 145 °C and residual water content of the dried fractions.
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Gravimetric loss of mass in g / 100 g predicted by NIR spectrometry
9.00
y = 1.0081x - 0.0425 R² = 99.96 RMSECV = 0.0454
8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00 0.00 -1.00
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Gravimetric loss of mass in g / 100 g measured by oven drying ("true value")
Water content in g / 100 g predicted by NIR spectrometry
4.50
y = 0.9724x + 0.0232 R² = 99.88 RMSECV = 0.0482
4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00
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Water content in g / 100 g measured by KFT ("true value")
Water content minus gravimetric loss of mass in g / 100 g predicted by NIR spectrometry
5.00 y = 0.9933x + 5E-06 R² = 99.96 RMSECV = 0.0454
4.00 3.00 2.00 1.00
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0.00 0.00 -1.00
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Water content minus gravimetric loss of mass in g / 100 g ("true value") Fig. 2. Scatter plots of NIR predictions versus true values based on mass loss by oven drying (above), water content (centre) and water content minus loss of mass (below) of Lasana dried at 140 °C for different times.
0.3 g/100 g maltose, 6.8 g/100 g dextrins and 8.1 g/100 g starch), 25.6 g/100 g lipids and minerals, trace elements and vitamins.
The original water content of Lasana Dauermilch 1 was 4.07 g/ 100 g, determined by Karl Fischer titration.
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Lasana Dauermilch 1, which contains much lactose, was dried in duplicates at 140 °C for 5, 10, 20, 40, 60, 120 and 180 min and the dried fractions analysed for residual water by Karl Fischer titration (same technique as for whey powder). Calibrations were established on the basis of the mass loss and on the basis of residual water determination. If the mass loss is caused only by evaporation of water originally contained in the sample, a calibration on the basis water content minus mass loss must be possible. The same procedure was carried out in a vacuum drying oven at a temperature of 48 °C and a pressure of 300 mbar (instead of 140 °C at normal pressure in a drying oven) and drying times of 15 min, 40 min, 1,5 h, 3 h, 4.67 h, 24 h and 48 h. The corresponding NIR calibrations were established for these techniques.
Fourier transform NIR spectrometer Vector 22/N from Bruker Optik, Ettlingen, Germany. For wheat semolina, three spectra were registered with 20 scans each by the reflectance technique using a rotating dish. Whey powder was measured taking three spectra with three scans each using reflectance. For wheat semolina and whey powder validation was based on the test set/validation set method. Baby food was measured registering one spectrum with 64 scans using reflectance through a transparent window at the bottom of the sample container. For baby food cross validation was applied.
3. Results and discussion 3.1. Wheat semolina
2.2. Karl Fischer titrations Karl Fischer titrations were carried out with volumetric titrators from Metrohm, Herisau, Switzerland: KF Titrino 701 for wheat semolina, KF Titrando 841 for whey powder and for baby food. Chemicals for Karl Fischer titration (Hydranal-Composite 5, Hydranal-Titrant 2, Hydranal-Solvent, methanol, formamide) were from Sigma–Aldrich, Seelze, Germany. 2.3. Drying techniques Products were dried in a drying oven FD 115 from Binder, Tuttlingen, Germany and in a vacuum drying oven VRTK from ElektroWärme, Aachen, Germany. Wheat semolina samples of lower water content were obtained by drying portions of the original sample in a drying oven at 90, 103, 110 and 130 °C for a couple of minutes. After thorough mixing and cooling to room temperature, the samples were stored in sealed flasks. Samples with higher water content than the original sample were received by storing them in a desiccator over water for several days, mixing them and storing them in sealed flasks. 2.4. NIR spectrometry NIR spectra for wheat semolina and whey powder were registered with a Fourier transform NIR spectrometer NIRVIS from Bühler, Uzwil, Switzerland (now represented by Büchi, Essen, Germany). Other NIR measurements were carried out using the
Coarse samples had water contents (KFT, sample size about 100 mg) from 8.05 g/100 g ± 0.03 g to 15.50 ± 0.08 g/100 g with relative standard deviations between 0.19% and 1.98%. Fine samples yielded values from 8.08 g/100 g ± 0.10 g/100 g to 15.48 g/ 100 g ± 0.13 g/100 g with relative standard deviations from 0.14% to 1.42%. The mass loss on drying for the coarse samples ranged from 7.87 g/100 g ± 0.16 g/100 g to 15.90 g/100 g ± 0.03 g/100 g with relative standard deviations from 0.09% to 3.19%. For fine samples the values were from 7.86 g/100 g ± 0.04 g/100 g to 15.05 g/100 g and the relative standard deviations from 0.03% to 0.64%. Calibrations were established for both granulations separately, based on both KFT as well as on oven drying. The calibrations for the two granulations were also combined. For the combined calibration the wave numbers from 4440 to 9000 cm1 were used. Partial least square regression (PLS) was applied. The data pretreatment for the KFT based calibration was First derivative Savitzky-Golay 9 points and normalisation to unit length 4440–9000. The number of primary factors was 5. The data pre-treatment for the oven based calibration was Multiplicative scatter correction (MSC) full 4440–9000, mean vector (5 0 0) and First derivative Savitzky–Golay 9 points. The number of primary factors was 3. The calibration set for oven drying contained 165 samples, the validation set 81 samples. The standard errors were SEC = 0.1212 and SEP = 0.1208. The regression coefficient was rcal = 0.9985 for the calibration set and rval = 0.9982 for the validation set. The slope of the calibration line was mcal = 0.9970 and mval = 0.9989 for the validation line. The so-called Q value which combines all
Fig. 3. NIR spectra of Lasana samples dried for various times at 140 °C.
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Gravimetric loss of mass in g / 100 g predicted by NIR spectrometry
4.00
y = 0.9787x + 0.0344 R² = 99.87 RMSECV = 0.0427
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Gravimetric loss of mass in g / 100 g measured by oven drying ("true value")
Water content in g / 100 g predicted by NIR spectrometry
4.50
y = 0.9824x + 0.0407 R² = 99.93 RMSECV = 0.0316
4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00
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Water content minus gravimetric loss of mass in g / 100 g predicted by NIR spectrometry
Water content in g / 100 g measured by KFT ("true value") 4.50
y = 0.9819x + 0.038 R² = 99.9 RMSECV = 0,0373
4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 0.00
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Water content minus gravimetric loss of mass in g / 100 g ("true value") Fig. 4. Scatter plots of NIR predictions versus true values based on vacuum oven drying (above), residual water content (centre) and water content minus loss of mass (below) of Lasana dried at 48 °C and 300 mbar for different times.
the statistical quality criteria of the method and is in the ideal case 1 was 0.9935.
The calibration set for Karl Fischer titration contained 168 samples and the validation set 72 samples. The standard errors were
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SEC = 0.1176 and SEP = 0.1181. The regression coefficient was rcal = 0.9983 for the calibration set and rval = 0.9985 for the validation set. The slope of the calibration line was mcal = 0.9967 and mval = 0.9918 for the validation line. The Q value was 0.9941. These values indicate that both the oven drying as well as the Karl Fischer titration can be used for calibration in an equivalent way. Obviously, the only material volatile material under the drying conditions is water.
be based on Karl Fischer titration. The temperature ranges for the liberation of water from lactose monohydrate and the degradation of the product overlap. Experiments showed that upon drying of the product at 102 °C the mass loss even after 4 h was only 2.30 g/100 g for a sample that contained 4.52 g/100 g according to KFT. It is not possible to choose a temperature at which water is evaporated completely without degradation of the product. Drying techniques cannot be applied to determine water content correctly in this type of product.
3.2. Whey powder 3.3. Baby food Lasana Dauermilch 1
Gravimetric loss of mass / residual water content in g / 100g
The calibration set for oven drying contained 14 samples, the validation set 7 samples. For the calibration the wave numbers from 4596 to 9996 cm1 were used. Partial least square regression (PLS) was applied. The data pre-treatment was Multiplicative scatter correction (MSC) full 4596–9996, mean vector (5 0 0). The number of primary factors was 11. The values for the calibration based on oven drying at 145 °C were the following: SEC = 0.2492, SEP = 0.2447, regression coefficient for calibration rcal = 0.9977, regression coefficient for validation rval = 0.9977, slope of calibration line mcal = 0.9955, slope for validation line mval = 0.9966, Q value 0.9244. These values let conclude that a calibration is possible. This is, however, only true if the mass loss on drying is really the property to be analysed. This calibration cannot at all be used if the water content is the target property. Whereas mass loss values of more than 12 g/100 g occurred, the maximum water content measured by Karl Fischer titration was approximately 4.5 g/100 g. The reason for this phenomenon is that the product continues to lose mass at the temperature applied for drying. This is depicted in Fig. 1. The dried product was analysed for water content by Karl Fischer titration after various drying times. After some time the residual water remains constant, although the mass loss still increases. The product obviously undergoes degradation, which can also be derived from a more and more darkening colour. Further analyses showed that the relatively constant water content found in the dried fractions is to a great extent due to water which was taken up by the hygroscopic material during handling (cooling in a desiccator and weighing and transfer into the titration vessel). It is not possible to determine the water content of this product by NIR spectrometry if the calibration is based on oven drying at 145 °C. Such a calibration leads to mass loss results with good correlation. If water content is to be measured, the calibration has to
For NIR calibrations for the different scatter plots (see below), the automatic optimisation of the software OPUS from Bruker with cross validation was used. This resulted in the selection of various wave number areas and different data pre-treatments. Statistical values like slope and RMSECV are indicated in the respective figures. The scatter plots based on mass loss by oven drying, residual water by Karl Fischer titration and on the difference are shown in Fig. 2. Not all of the eight samples were analysed by KFT, because the NIR and KFT measurements were to be done at the same time to avoid water uptake by the dried and hygroscopic product. The scatter plot for the difference contains nevertheless eight data points, because they are calculated as difference of the original water content minus mass loss on drying. The calibration based on water content minus mass loss includes negative values. This shows that the mass loss is not only caused by evaporation of water. Obviously, other substances, formed by degradation reactions, also contribute to the mass loss. This can be shown by near infrared (NIR) spectra (Fig. 3). The spectra show that the absorbance at the typical wavenumber area decreases only until a drying time of 20 min. Longer drying times, though leading to a mass loss, do not decrease the absorbance and, hence, not the water content of the sample. The corresponding scatter plots using a vacuum drying oven are shown in Fig. 4. In contrast to oven drying at 140 °C, not only the mass loss based calibration but also the water content based calibration is satisfactory. Consequently, a calibration based on water content minus mass loss is also possible. The mass loss is obviously caused by evaporation of water only. This is in correspondence with the fact that the mass loss and the remaining water content in the
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KFT = 4.07 g / 100 g
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3h 4 h 40 Time Water content of dried sample Loss of mass
Fig. 5. Loss of mass of Lasana with an original water content of 4.07 g/100 g after different drying times at 48 °C and 300 mbar and water content of the dried fractions.
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Fig. 6. NIR spectra of Lasana samples dried for various times at 48 °C and 300 mbar.
dried fraction after the various drying times sum up to the water content of the original sample (see Fig. 5). Fig. 5 also shows that the water is far from being completely evaporated even after a drying time of 48 h. The decrease of absorbance during the whole drying time in Fig. 6 underlines the fact that the dried samples still contain water, even after 48 h. 4. Conclusions Calibrations must be based on a primary method that really determines the entity which is to be measured by the secondary method. A calibration with good statistical parameters is not a guarantee for correct measurements; calibration lines are always mathematically possible, even when the chemical background is not reasonable and justified. Typical examples are shown here. Very often drying techniques are used to determine what is thought to be water content. The mass loss, however, which is the result of such analyses, is caused by all the compounds volatile under the drying conditions, including not only those originally contained in the sample but also those that are formed by chemical reactions during the drying process. NIR spectra depend on the molecules in the sample. The primary method used for calibration must either measure the same compound which is to be analysed by NIR spectrometry or there must a clear and unambiguous relation between the chemical composition and the sample property which is to be measured.
Such a relation does not necessarily exist between the water content of a substance and the mass loss it undergoes on drying. References First Commission directive of 13 November 1979 laying down Community methods of analysis for testing certain partly or wholly dehydrated preserved milk for human consumption (79/1067/EEC). ICC Standard 110/1, International Association for Cereal Science and Technology (1976). Determination of the moisture content of cereals and cereal products (Practical method), revised 1976. Isengard, H.-D. (1995). Rapid water determination in foodstuffs. Trends in Food Science and Technology, 6, 155–162. Isengard, H.-D. (2008). Water determination – Scientific and economic dimensions. Food Chemistry, 106, 1393–1398. Isengard, H.-D., Felgner, A., Kling, R., Reh, C.T. (2006). Water determination in dried milk: Is the international standard reasonable? In M. del Pilar Buera, J. WeltiChanes, P.J. Lillford, & H.R. Corti (Eds.), Water properties of food, pharmaceutical, and biological materials (pp. 631–637). USA: CRC Press, Taylor & Francis Group. ISBN: 0-8493-2993-0. Isengard, H.-D., & Schmitt, K. (1995). Karl Fischer titration at elevated temperatures. Mikrochimica Acta, 120, 329–337. Isengard, H.-D., & Striffler, U. (1992). Karl Fischer titration in boiling methanol. Fresenius’ Journal of Analytical Chemistry, 342, 287–291. Rückold, S., Isengard, H.-D., Hanss, J., & Grobecker, K. H. (2003). The energy of interaction between water and surfaces of biological reference materials. Food Chemistry, 82, 51–59. Rüegg, M., & Moor, U. (1987). Die Bestimmung des Wassergehaltes in Milch und Milchprodukten mit der Karl-Fischer-Methode, V. Die Wasserbestimmung von getrockneten Milchprodukten. Mitteilungen aus dem Gebiete der Lebensmitteluntersuchung und Hygiene, 78, 309–319. Scholz, E. (1984). Karl Fischer titration. Berlin, Heidelberg, New York, Tokyo: Springer-Verlag.
Contents lists available at ScienceDirect
Food Chemistry journal homepage: www.elsevier.com/locate/foodchem
The influence of the reference method on the results of the secondary method via calibration Heinz-Dieter Isengard a,*, Georg Merkh a, Kerstin Schreib a, Inga Labitzke a, Clément Dubois b a b
University of Hohenheim, Institute of Food Science and Biotechnology, D-70593 Stuttgart, Germany École Supérieure d’Agriculture d’Angers, F-49007 Angers Cedex 01, France
a r t i c l e
i n f o
Article history: Received 6 March 2009 Received in revised form 8 February 2010 Accepted 19 February 2010
Keywords: Calibration Reference methods Near infrared spectroscopy Water content Karl Fischer titration Drying techniques
a b s t r a c t Indirect methods have often the advantage to be non-invasive and very rapid. They can sometimes even be applied in-line or at-line. The disadvantage is that they do not measure the target property of the product directly but either another property that depends on the target property or the response of the product to a physical influence. In all these cases it is necessary to know the relationship of the target property and the measured property or the response, respectively. This relationship is often very complex and needs to be established empirically for samples with known properties which have been measured with a reference method. In other words, a calibration must be established. The future predictions depend completely on the calibration. This means that the calibration must be as correct as ever possible. Inadequate calibration leads to erroneous results, although the user of the method may not be aware of this fact. This is shown at the example of near infrared spectroscopy (NIRS) for water content determination. The Karl Fischer titration as a selective method and drying techniques as non-selective methods were used as reference methods. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction 1.1. Direct and indirect analytical methods Direct methods measure the property of the sample or the analyte as such. Direct methods are therefore also called primary methods and often serve as reference methods. Indirect methods measure a property of the sample that depends on the concentration or amount of the analyte. Indirect methods need therefore a connection or relation to a direct method (to which they are ‘‘referred”) in a way that the value measured allows a conclusion to the property of the sample or the concentration or the amount of the analyte (Isengard, 1995). Samples with a known property (analysed with a ‘‘reference” method) are measured with an indirect method and the value found is related to the ‘‘true” value. This is done for several concentrations or amounts. Thus, value pairs are obtained. These pairs (values obtained with the indirect method [ordinate] versus values obtained with the reference method [abscissa]) are plotted and a regression curve (mostly a straight line) is laid through these data points. This is the calibration line in the univariate case.
* Corresponding author. Tel.: +49 711 397 4670; fax: +49 711 397 4674. E-mail address: [email protected] (H.-D. Isengard). 0308-8146/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodchem.2010.02.051
Samples with unknown concentration can then be analysed with the indirect method, the unknown concentration is read from the calibration curve. When chemometric methods are applied, the analytical data points are calculated from many responses each (multivariate case). These values are often called ‘‘predicted values” and are plotted against the ‘‘true values” obtained by the reference method. The ideal line through this plot ‘‘predicted values” (ordinate) versus ‘‘true values” (abscissa) is a straight line with the gradient 1 (45°) running through the origin of the coordinate system. The scattering of the data points around this line (expressed by the regression coefficient) is a measure of the accuracy of the method expressed as standard error of calibration (SEC) for the calibration and standard error of prediction (SEP) for a validation set. The standard errors SEC and SEP are calculated by means of Eq. (1):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 sec xref i¼1 ðxi i Þ SEC or SEP ¼ n1
ð1Þ
where xsec are values for sample i measured by the secondary methi the valod, for instance by near infrared (NIR) spectrometry and xref i ues measured by the reference method derived from the calibration set (for SEC) or derived from the validation set for prediction (for SEP). If cross validation is applied the abbreviation RMSECV is used which stands for root mean square error of cross validation. In this case, n is used instead of n 1 in Eq. (1).
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The whole approach depends, however, on the ‘‘correctness” of the reference method, because it is always possible to draw a regression line through data points. For every analytical measurement, a corresponding concentration of the analyte will be found and even a high precision is no proof of accuracy. A possible error will not be detected because the results are based on the same wrong conditions and assumptions. It is therefore essential that the reference method be ‘‘correct”. The importance of this prerequisite is shown at the example of water content determination. 1.2. Water content determination The Karl Fischer titration (KFT) detects water selectively (Scholz, 1984), whereas oven methods determine mass loss under the applied conditions (other volatiles are also included and strongly bound water is not detected completely). NIR spectra depend on water content. NIR calibrations should therefore be based on a reference method that really determines water and nothing but water (like the Karl Fischer titration). Calibrations can, however, also be carried out on the basis of a drying technique. Multivariate calibration algorithms will always find a calibration model. Water content is referred to wet basis (mass of the sample analysed) throughout this article. 2. Materials and methods 2.1. Samples Wheat semolina was from Alb-Gold Teigwaren, Trochtelfingen, Germany. The particle size distribution of semolina with fine granulation was the following: >500 lm: <1%, 400–500 lm: 3–9%, 250–400 lm: 55–63%, 160–250 lm: 21–29%, <160 lm: 7–12%. The coarse-granulation semolina had the following size distribution: >630 lm: <2%, 500–630 lm: 14–20%, 400–500 lm: 32–40%, 200–400 lm: 41–49%, <200 lm: <2%. Drying results were obtained by drying three replicates of 3–5 g for 2 h at 130 °C, according to the corresponding ICC method (ICC, 1976). Karl Fischer titration was carried out for three replicates at the boiling point of methanol (Isengard & Schmitt, 1995; Isengard & Striffler, 1992) using the one-component technique with
Hydranal-Composite 5 as titrating agent and methanol as working medium. The titrating vessel was a multi-necked round-bottomed flask. Whey powder was received from Nestlé, Switzerland. Whey powder contains high amounts of lactose. Lactose exists in different forms. The a-anomer (monohydrate) is the more stable form at temperatures below 93 °C. It crystallises with one mole of water per mole lactose. At higher temperatures the anhydrous b-monomer is more stable. Lactose occurs also in amorphous form which may include small amounts of water. Depending on the production conditions dried dairy powders contain mixtures of these polymorphs. In addition to included water and water of crystallisation, the product usually contains small quantities of surface water. The usual drying temperature for moisture determination of dairy products in drying ovens is 102 °C (First Commission directive, 1979). At this temperature the water of crystallisation of alactose is not evaporated completely during the usual drying times (Isengard, Felgner, Kling, & Reh, 2006). The separation of this water fraction from the matrix needs a high energy input (Rüegg & Moor, 1987; Rückold, Isengard, Hanss, & Grobecker, 2003). After 2 h, the standard drying time, only a part of this water is detected. The consequence is that drying techniques yield results that differ more or less from the true water content. For this reason, the drying temperature was raised to 145 °C. As lactose occurs in practically all dairy products and is also used in the pharmaceutical industry, this problem affects a wide range of products, particularly those with high lactose content like whey powders or lactose itself. Usually the drying results are lower than water content. In special cases, however, they can be higher. This is possible if the lack in water detection is over-compensated by other volatile substances which are contained in special products or which are formed by decomposition of components during the drying process (Isengard, 2008). Drying results were obtained from duplicates. Titrations were carried out in five replicates using the two-component technique with Hydranal-Titrant 2 as titrating agent and a mixture of Hydranal-Solvent and formamide in a volume ratio of 2:1 at a temperature of 40 °C in a double-walled titration vessel. The baby food Lasana Dauermilch 1 produced by Humana Milchindustrie, Everswinkel, Germany, was bought in a local shop in Germany. It contains 10.1 g/100 g proteins, 56.5 g/100 g carbohydrates (of which are 0.1 g/100 g glucose, 41.2 g/100 g lactose,
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Water content minus gravimetric loss of mass in g / 100 g ("true value") Fig. 2. Scatter plots of NIR predictions versus true values based on mass loss by oven drying (above), water content (centre) and water content minus loss of mass (below) of Lasana dried at 140 °C for different times.
0.3 g/100 g maltose, 6.8 g/100 g dextrins and 8.1 g/100 g starch), 25.6 g/100 g lipids and minerals, trace elements and vitamins.
The original water content of Lasana Dauermilch 1 was 4.07 g/ 100 g, determined by Karl Fischer titration.
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Lasana Dauermilch 1, which contains much lactose, was dried in duplicates at 140 °C for 5, 10, 20, 40, 60, 120 and 180 min and the dried fractions analysed for residual water by Karl Fischer titration (same technique as for whey powder). Calibrations were established on the basis of the mass loss and on the basis of residual water determination. If the mass loss is caused only by evaporation of water originally contained in the sample, a calibration on the basis water content minus mass loss must be possible. The same procedure was carried out in a vacuum drying oven at a temperature of 48 °C and a pressure of 300 mbar (instead of 140 °C at normal pressure in a drying oven) and drying times of 15 min, 40 min, 1,5 h, 3 h, 4.67 h, 24 h and 48 h. The corresponding NIR calibrations were established for these techniques.
Fourier transform NIR spectrometer Vector 22/N from Bruker Optik, Ettlingen, Germany. For wheat semolina, three spectra were registered with 20 scans each by the reflectance technique using a rotating dish. Whey powder was measured taking three spectra with three scans each using reflectance. For wheat semolina and whey powder validation was based on the test set/validation set method. Baby food was measured registering one spectrum with 64 scans using reflectance through a transparent window at the bottom of the sample container. For baby food cross validation was applied.
3. Results and discussion 3.1. Wheat semolina
2.2. Karl Fischer titrations Karl Fischer titrations were carried out with volumetric titrators from Metrohm, Herisau, Switzerland: KF Titrino 701 for wheat semolina, KF Titrando 841 for whey powder and for baby food. Chemicals for Karl Fischer titration (Hydranal-Composite 5, Hydranal-Titrant 2, Hydranal-Solvent, methanol, formamide) were from Sigma–Aldrich, Seelze, Germany. 2.3. Drying techniques Products were dried in a drying oven FD 115 from Binder, Tuttlingen, Germany and in a vacuum drying oven VRTK from ElektroWärme, Aachen, Germany. Wheat semolina samples of lower water content were obtained by drying portions of the original sample in a drying oven at 90, 103, 110 and 130 °C for a couple of minutes. After thorough mixing and cooling to room temperature, the samples were stored in sealed flasks. Samples with higher water content than the original sample were received by storing them in a desiccator over water for several days, mixing them and storing them in sealed flasks. 2.4. NIR spectrometry NIR spectra for wheat semolina and whey powder were registered with a Fourier transform NIR spectrometer NIRVIS from Bühler, Uzwil, Switzerland (now represented by Büchi, Essen, Germany). Other NIR measurements were carried out using the
Coarse samples had water contents (KFT, sample size about 100 mg) from 8.05 g/100 g ± 0.03 g to 15.50 ± 0.08 g/100 g with relative standard deviations between 0.19% and 1.98%. Fine samples yielded values from 8.08 g/100 g ± 0.10 g/100 g to 15.48 g/ 100 g ± 0.13 g/100 g with relative standard deviations from 0.14% to 1.42%. The mass loss on drying for the coarse samples ranged from 7.87 g/100 g ± 0.16 g/100 g to 15.90 g/100 g ± 0.03 g/100 g with relative standard deviations from 0.09% to 3.19%. For fine samples the values were from 7.86 g/100 g ± 0.04 g/100 g to 15.05 g/100 g and the relative standard deviations from 0.03% to 0.64%. Calibrations were established for both granulations separately, based on both KFT as well as on oven drying. The calibrations for the two granulations were also combined. For the combined calibration the wave numbers from 4440 to 9000 cm1 were used. Partial least square regression (PLS) was applied. The data pretreatment for the KFT based calibration was First derivative Savitzky-Golay 9 points and normalisation to unit length 4440–9000. The number of primary factors was 5. The data pre-treatment for the oven based calibration was Multiplicative scatter correction (MSC) full 4440–9000, mean vector (5 0 0) and First derivative Savitzky–Golay 9 points. The number of primary factors was 3. The calibration set for oven drying contained 165 samples, the validation set 81 samples. The standard errors were SEC = 0.1212 and SEP = 0.1208. The regression coefficient was rcal = 0.9985 for the calibration set and rval = 0.9982 for the validation set. The slope of the calibration line was mcal = 0.9970 and mval = 0.9989 for the validation line. The so-called Q value which combines all
Fig. 3. NIR spectra of Lasana samples dried for various times at 140 °C.
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Water content minus gravimetric loss of mass in g / 100 g ("true value") Fig. 4. Scatter plots of NIR predictions versus true values based on vacuum oven drying (above), residual water content (centre) and water content minus loss of mass (below) of Lasana dried at 48 °C and 300 mbar for different times.
the statistical quality criteria of the method and is in the ideal case 1 was 0.9935.
The calibration set for Karl Fischer titration contained 168 samples and the validation set 72 samples. The standard errors were
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SEC = 0.1176 and SEP = 0.1181. The regression coefficient was rcal = 0.9983 for the calibration set and rval = 0.9985 for the validation set. The slope of the calibration line was mcal = 0.9967 and mval = 0.9918 for the validation line. The Q value was 0.9941. These values indicate that both the oven drying as well as the Karl Fischer titration can be used for calibration in an equivalent way. Obviously, the only material volatile material under the drying conditions is water.
be based on Karl Fischer titration. The temperature ranges for the liberation of water from lactose monohydrate and the degradation of the product overlap. Experiments showed that upon drying of the product at 102 °C the mass loss even after 4 h was only 2.30 g/100 g for a sample that contained 4.52 g/100 g according to KFT. It is not possible to choose a temperature at which water is evaporated completely without degradation of the product. Drying techniques cannot be applied to determine water content correctly in this type of product.
3.2. Whey powder 3.3. Baby food Lasana Dauermilch 1
Gravimetric loss of mass / residual water content in g / 100g
The calibration set for oven drying contained 14 samples, the validation set 7 samples. For the calibration the wave numbers from 4596 to 9996 cm1 were used. Partial least square regression (PLS) was applied. The data pre-treatment was Multiplicative scatter correction (MSC) full 4596–9996, mean vector (5 0 0). The number of primary factors was 11. The values for the calibration based on oven drying at 145 °C were the following: SEC = 0.2492, SEP = 0.2447, regression coefficient for calibration rcal = 0.9977, regression coefficient for validation rval = 0.9977, slope of calibration line mcal = 0.9955, slope for validation line mval = 0.9966, Q value 0.9244. These values let conclude that a calibration is possible. This is, however, only true if the mass loss on drying is really the property to be analysed. This calibration cannot at all be used if the water content is the target property. Whereas mass loss values of more than 12 g/100 g occurred, the maximum water content measured by Karl Fischer titration was approximately 4.5 g/100 g. The reason for this phenomenon is that the product continues to lose mass at the temperature applied for drying. This is depicted in Fig. 1. The dried product was analysed for water content by Karl Fischer titration after various drying times. After some time the residual water remains constant, although the mass loss still increases. The product obviously undergoes degradation, which can also be derived from a more and more darkening colour. Further analyses showed that the relatively constant water content found in the dried fractions is to a great extent due to water which was taken up by the hygroscopic material during handling (cooling in a desiccator and weighing and transfer into the titration vessel). It is not possible to determine the water content of this product by NIR spectrometry if the calibration is based on oven drying at 145 °C. Such a calibration leads to mass loss results with good correlation. If water content is to be measured, the calibration has to
For NIR calibrations for the different scatter plots (see below), the automatic optimisation of the software OPUS from Bruker with cross validation was used. This resulted in the selection of various wave number areas and different data pre-treatments. Statistical values like slope and RMSECV are indicated in the respective figures. The scatter plots based on mass loss by oven drying, residual water by Karl Fischer titration and on the difference are shown in Fig. 2. Not all of the eight samples were analysed by KFT, because the NIR and KFT measurements were to be done at the same time to avoid water uptake by the dried and hygroscopic product. The scatter plot for the difference contains nevertheless eight data points, because they are calculated as difference of the original water content minus mass loss on drying. The calibration based on water content minus mass loss includes negative values. This shows that the mass loss is not only caused by evaporation of water. Obviously, other substances, formed by degradation reactions, also contribute to the mass loss. This can be shown by near infrared (NIR) spectra (Fig. 3). The spectra show that the absorbance at the typical wavenumber area decreases only until a drying time of 20 min. Longer drying times, though leading to a mass loss, do not decrease the absorbance and, hence, not the water content of the sample. The corresponding scatter plots using a vacuum drying oven are shown in Fig. 4. In contrast to oven drying at 140 °C, not only the mass loss based calibration but also the water content based calibration is satisfactory. Consequently, a calibration based on water content minus mass loss is also possible. The mass loss is obviously caused by evaporation of water only. This is in correspondence with the fact that the mass loss and the remaining water content in the
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Fig. 6. NIR spectra of Lasana samples dried for various times at 48 °C and 300 mbar.
dried fraction after the various drying times sum up to the water content of the original sample (see Fig. 5). Fig. 5 also shows that the water is far from being completely evaporated even after a drying time of 48 h. The decrease of absorbance during the whole drying time in Fig. 6 underlines the fact that the dried samples still contain water, even after 48 h. 4. Conclusions Calibrations must be based on a primary method that really determines the entity which is to be measured by the secondary method. A calibration with good statistical parameters is not a guarantee for correct measurements; calibration lines are always mathematically possible, even when the chemical background is not reasonable and justified. Typical examples are shown here. Very often drying techniques are used to determine what is thought to be water content. The mass loss, however, which is the result of such analyses, is caused by all the compounds volatile under the drying conditions, including not only those originally contained in the sample but also those that are formed by chemical reactions during the drying process. NIR spectra depend on the molecules in the sample. The primary method used for calibration must either measure the same compound which is to be analysed by NIR spectrometry or there must a clear and unambiguous relation between the chemical composition and the sample property which is to be measured.
Such a relation does not necessarily exist between the water content of a substance and the mass loss it undergoes on drying. References First Commission directive of 13 November 1979 laying down Community methods of analysis for testing certain partly or wholly dehydrated preserved milk for human consumption (79/1067/EEC). ICC Standard 110/1, International Association for Cereal Science and Technology (1976). Determination of the moisture content of cereals and cereal products (Practical method), revised 1976. Isengard, H.-D. (1995). Rapid water determination in foodstuffs. Trends in Food Science and Technology, 6, 155–162. Isengard, H.-D. (2008). Water determination – Scientific and economic dimensions. Food Chemistry, 106, 1393–1398. Isengard, H.-D., Felgner, A., Kling, R., Reh, C.T. (2006). Water determination in dried milk: Is the international standard reasonable? In M. del Pilar Buera, J. WeltiChanes, P.J. Lillford, & H.R. Corti (Eds.), Water properties of food, pharmaceutical, and biological materials (pp. 631–637). USA: CRC Press, Taylor & Francis Group. ISBN: 0-8493-2993-0. Isengard, H.-D., & Schmitt, K. (1995). Karl Fischer titration at elevated temperatures. Mikrochimica Acta, 120, 329–337. Isengard, H.-D., & Striffler, U. (1992). Karl Fischer titration in boiling methanol. Fresenius’ Journal of Analytical Chemistry, 342, 287–291. Rückold, S., Isengard, H.-D., Hanss, J., & Grobecker, K. H. (2003). The energy of interaction between water and surfaces of biological reference materials. Food Chemistry, 82, 51–59. Rüegg, M., & Moor, U. (1987). Die Bestimmung des Wassergehaltes in Milch und Milchprodukten mit der Karl-Fischer-Methode, V. Die Wasserbestimmung von getrockneten Milchprodukten. Mitteilungen aus dem Gebiete der Lebensmitteluntersuchung und Hygiene, 78, 309–319. Scholz, E. (1984). Karl Fischer titration. Berlin, Heidelberg, New York, Tokyo: Springer-Verlag.