Determination of Al in cake mix: Method validation and estimation of measurement uncertainty

An analytical method for the determination of Al in cake mix was developed. Acceptable values were obtained for the following parameters: linearity, detection limit - LOD (5.00 mg-kg-1) quantification limit - LOQ (12.5 mg-kg-1), the recovery assays values (between 91 and 102%), the relative standard deviation under repeatability and within-reproducibility conditions (<20.0%) and measurement uncertainty tests (<10.0%) The results of the validation process showed that the proposed method is fitness for purpose.


Introduction
Aluminum (Al) is the third most abundant element in the earth's crust and is also present in water and food. For over a century it has been recognized as a neurotoxic element [1].
One of the main routes of exposure to aluminum in the general population is food consumption, especially of those with food additives containing Al [2]. The Joint FAO/WHO Expert Committee on Food Additives evaluated the toxicity of Al and established the Provisional Tolerable Weekly Intake (PTWI) 2 mg Al / kg body weight per week, from all sources, including additives. As reported in sixty-seventh meeting, some population groups could exceed Al, especially children, due to the consumption of food additives containing aluminum added in its composition [3]. The aluminum content in food has been studied in several countries. However, in Brazil, there are few data addressing the Al concentration.
Considering the relevance of the Al presence in the diet of the population, the aim of this work is to present a detailed procedure for in-house method validation and evaluate the uncertainty sources for determining the levels of Al in cake mix by ICP OES. The analytical performance of the entire procedure, such as linearity, detection, limit, quantification limit, precision and accuracy were assessed statistically to evaluate the developed procedures.

Instrumentation
The acid digestion of cake mix samples was performed using a closed-vessel microwave system (Model D Start, Milestone, Italy). The device can work up to the power of 1000 W during the time set by the user, providing that a vessel does not exceed 100 bars pressure or 300°C.
The Table 1 summarizes the operating conditions used in ICP OES with radially viewed configuration (Optima 3000, Perkin Elmer, USA).

Contamination care
In order to prevent contaminations all operations were performed in a clean room ISO Class 7 equipped with islands of laminar flow ISO class 5. The materials used in the test consists of Teflon or polyethylene and were decontaminated with 10 % HNO3 for 24 hours, then washed with ultrapure water, dried and kept in laminar flow.

Digestion procedure
The digestion procedure for all samples was performed as in [4], [5] and [6]. Aliquots (0.2-0.3 g) of homogenized sample were digested with 3 mL of 65 % nitric acid (w·w −1 ) and 3 ml of high purity deionized water in a closed microwave. The heating program for digestion of the samples was previously optimized [6]. The samples were transferred to 50 mL volumetric flasks.

Calibration and sample analysis
Two sets of standards were used for calibration: one for low concentrations of Al (20 µg·L -1 to 200 µg·L -1 ). Analytical blanks were also prepared in order to evaluate the noise and zero adjustment instrumental, but were not included in the calculations. The calibration curves were assessed through ordinary least squares estimation, outlier detection and lack of fit tests [7].

Validation
The performance characteristics of the method were established by assays employing standards solutions, sample blanks and spiked samples. Linearity, matrix effects, lack of trueness (recovery), precision under repeatability and within-reproducibility conditions, detection and quantification limits were the parameters evaluated [8].
All the tests for linearity assumption were also done for these curves [7]. The slopes and intercepts were compared by t-test for a 0.05 after evaluation the assumption of homogeneity of variances. The standard addition method was used to check the matrix effects. Due to the absence certified reference material for matrix studied, the parameters lack of trueness and precision were estimated through recovery.
The recovery and precision were established by spiked samples in four different days, with three independent replicates at the same levels of linearity test. Blank samples were also prepared, in triplicate, for each curve. The values obtained were analyzed. The repeatability and withinreproducibility were estimated by ANOVA [7].
The theoretical detection limit (LD) and quantification limit (LQ) were estimated using the background equivalent concentration, and after were confirmed by testing the recovery and precision.

Measurement uncertainty
Uncertainties were estimated according to the Guide to the Expression of Uncertainty in Measurement [9]. Relevant sources for the uncertainty assessment have been divided into four groups: uncertainties associated with a) sample preparation, b) preparation of standard solutions, c) the analytical curve, d) method precision. To calculate the expanded uncertainty (U), a coverage factor (k) of 2 was used which corresponds to a 95 % interval for a normal probability distribution.

Validation of method
Outliers were removed before statistical tests. The results obtained for the linearity assessment are shown in Table 2. The assumptions that the errors are normally distributed, homoscedastic and independent were confirmed as proposed by [7].
All the regression assumptions were confirmed for the solvent and matrix-matched calibration curves. No significant matrix effects were detected when the slopes of the solvent and matrix-matched curves were compared. The Table 3 presents the estimated recovery, relative standard deviations under repeatability (RSDr) and within-reproducibility (RSDR). These recovery results were considered acceptable and demonstrated no lack of trueness of the validated method. For the first level were obtained RSDr and RSDR above than the respective critical values (14.7%) [8], these results indicate accuracy and precision of the method in the range above of 12.5 mg ·kg -1 .
The theoretical detection and quantification limits were estimated in 5.0 mg kg -1 and 12.5 mg kg -1 , respectively. They were confirmed by recovery experiments.
The measurement uncertainty of the method was estimated using the bottom-up approach. The Ishikawa diagram with the uncertainty sources of the measurement uncertainty of the analysis shown in Figure 1.   Percent values of the standard uncertainty contribution from each group of uncertainties to the standard uncertainty are shown in Figure 2. The uncertainties associated with the precision are the main contribution in the method. For the analyzed sample, whose Al concentration determined, was 34.6 mg·kg -1 , the value of expanded uncertainty (U) was 2.0 mg·kg -1 , which corresponds less than 10 % of the concentration value.

Conclusions
The method presented good results of selectivity, linearity, precision (repeatability and reproducibility), recovery and the expanded uncertainties. These results showed that the proposed method is fitness for purpose.