Method Development for the Quantitative Analysis of Multivitamin Supplements by Laser Ablation–Inductively Coupled Plasma–Mass Spectrometry (LA-ICP-MS)

We present the development and optimization of an analytical method based on Laser Ablation–Inductively Coupled Plasma–Mass Spectrometry (LA-ICP-MS) for the analysis of multivitamin dietary supplements. Samples were ground and mixed with a cellulose powder containing internal standard elements; the resulting powder was pressed into pellets. Two calibration strategies were compared: (1) using increasing mass fractions of cellulose powder fortified with multiple elements of interest and (2) matrix matching using a multivitamin reference material in addition to the multi-element cellulose powder. Laser and ICP-MS parameters were closely monitored to achieve optimal conditions for monitoring multiple elements in cellulose and multivitamins while reducing the variability between replicate measurements. An energy output of 0.5 J/cm2, a repetition rate of 30 Hz, and a He carrier gas flow rate of 800 mL/min provided the best compromise between sensitivity and reproducibility. These parameters produced the most similar ablation behavior between cellulose and a matrix-matched calibration strategy. The dissimilarities in ablation yield due to differences in focus on the surface of the samples were successfully corrected after normalizing to an internal standard, resulting in relative differences of less than 10%. The results from the two different calibration approaches were compared to those obtained from solution-based ICP-MS and Inductively Coupled Plasma–Optical Emission Spectroscopy (ICP-OES) analyses. For most multivitamins, both calibration methods (i.e., cellulose and matrix-matched calibrations) performed adequately for As, B, Co, Cr, Cu, Mg, Ni, Na, Pb, and Zn. Matrix-matched calibration additionally resulted in better recoveries for S and Fe. Overall, matrix-matched calibration resulted in better recoveries for more multivitamins in comparison with cellulose calibration.


Introduction
Multivitamins are consumed for a wide assortment of reasons such as to compensate for diets or eating habits that limit the intake of essential vitamins and nutrients. The National Center for Health Statistics reported that, among U.S. adults aged 20 and over, 57.6% used any dietary supplement in the past 30 days, with multivitamin-minerals being the most commonly used supplement (Mishra et al. 2021). It is estimated that one-third of all adults in the USA, and onequarter of children and adolescents consumes multivitamins (Cowan et al. 2018;Qato et al. 2018). Additionally, most pregnant women take multivitamins as a source of folic acid, iron, iodine, and vitamin D (Wong et al. 2019).
Research has shown that several mineral components are beneficial and necessary for the wellbeing of individuals (National Academies 2019). For example, iron is needed for growth and development, in the production of hemoglobin, and to make essential hormones. However, high levels of iron can cause an upset stomach, constipation, nausea, abdominal pain, vomiting, and fainting (National Institutes of Health 2021). Trace elements can also impact human health. Chromium, copper, zinc, selenium, iodine, and molybdenum are among the nutritional elements: toxic elements include arsenic, cadmium, lead, and mercury (Mehri 2020).
Monitoring nutritional and toxic elements in food, cosmetics, and multivitamins is part of the Food and Drug Administration's (FDA) mission to protect and promote public health. The companies selling these products are responsible to ensure that the labels meet all the requirements, including the accuracy of nutrient declarations. To assist in verifying that the nutrient contents are accurately listed, there is a great interest in methods that ensure that the labels for multivitamins are reflective of the actual contents of the product.
Determination of the elemental composition of foods and multivitamins typically involves acid decomposition followed by analysis using Inductively Coupled Plasma-Mass Spectrometry (ICP-MS) and/or Optical Emission Spectroscopy (ICP-OES) (Canbay and Doğantürk 2017;Cubadda 2004;Dolan et al. 2003;Kauffman et al. 2007;Krejčová et al. 2006;Marrero et al. 2013). Additionally, Square Wave Anodic Stripping Voltammetry, Neutron Activation Analysis, Flame Graphite Furnace Atomic Absorption Spectroscopy, and Electrothermal Atomic Absorption Spectrometry, among others, have been reported (Hight et al. 1993;Reis and Saiki 2009;Soltyk et al. 2003;Turk et al. 2013). Solution-based methods of analysis of multivitamin supplements require decomposition of the materials using perchloric, hydrofluoric, hydrochloric, and/or nitric acid followed by dilution of the samples. Such methods invariably involve extensive sample preparation, handling of toxic substances, and are time-consuming and labor-intensive. A review article published in 2011 describes the use of atomic spectroscopy in the pharmaceutical industry (Lewen 2011).
Direct analysis of solids by Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry (LA-ICP-MS) is widely accepted and constitutes a powerful analytical tool for numerous types of materials (Becker 2002;Gunther and Hattendorf 2005;Koch and Gunther 2011;Limbeck et al. 2015;Russo et al. 2002). Some benefits of LA-ICP-MS for food and supplement analysis include a smaller amount of sample required, fast sample exchange and high throughput, minimal carryover in comparison with liquid sample introduction, reduction of contamination and analyte loss that would otherwise occur during acid digestion, and minimal sample preparation requirements (Russo et al. 2002). One drawback of solid analysis by LA-ICP-MS is elemental fractionation, where the isotope or elemental ratio detected may not be entirely representative of the composition of the original sample (Limbeck et al. 2015). In terms of ablation behavior, elements fall into several distinct clusters in which they correlate well with each other during the ablation period; therefore, an element from the same cluster can be used as an internal reference for the rest of the elements in the same group, thus mitigating the quantitative discrepancies that result from fractionation (Longerich et al. 1996). A second drawback of LA-ICP-MS is the dissimilarity in the interaction between the laser beam and the sample surface observed with different matrices. This effect causes changes in the ablated mass in relation to the properties of the matrices in question (Kroslakova and Günther 2007). In addition, different matrices produce different particle size distributions of the laser ablation aerosol; larger particles are more difficult to vaporize, atomize, and ionize, leading to variations in ionization efficiency. A promising approach for quantification is the preparation of matrix-matched calibration standards using materials with the same matrix composition as the samples (Fitzpatrick et al. 2008;Miliszkiewicz et al. 2015;Perkins et al. 1991;Shaheen and Fryer 2011;Sinclair et al. 1998;Vanheuzen and Morsink 1991;Zhu et al. 2013).
Analytical methods of pharmaceuticals and multivitamin supplements by LA-ICP-MS are limited, especially studies in which solution and laser ablation ICP-MS complementary results are reported. The scarcity of laser ablation studies is mostly due to the lack of reference materials and matrixmatched calibration standards; only a few studies are available (Augusto et al. 2017;Bu et al. 2013;Lam and Salin 2004;Rudovica et al. 2014). Augusto et al. described the use of cellulose as a binder for creating pellets followed by LA-ICP-MS determination of nutrients and contaminants in food and supplements (Augusto et al. 2017). Bu et al. reported the analysis of six herbal products by LA and solution-based ICP-MS using the National Institute of Standards and Technology (NIST) Standard Reference Material (SRM®) 1573a (tomato leaf) as a one-point calibrant (Bu et al. 2013). Lam and Salin described the analysis of pharmaceutical tablets (10% and 20% Neusilin) by LA-ICP-MS and Laser Ablation-Inductively Coupled Plasma-Atomic Emission Spectroscopy (LA-ICP-AES) using a three-point calibration made of Neusilin at different concentrations (Lam and Salin 2004). Rudovika et al. reported the LA-ICP-MS analysis of elemental impurities in an active pharmaceutical ingredient using laboratory-made matrix calibration standards for quantification by adding inorganic salts at certain concentrations to the main pharmaceutical ingredient (Rudovica et al. 2014).
In this work, the development and optimization of an analytical method based on LA-ICP-MS that can be applied specifically to multivitamins is presented. The technique offers quick sample analysis without the use of corrosive acids and extensive sample preparation. Additionally, the analysis can be automated using a carousel autosampler. This method is especially useful for products such as multivitamin tablets which are resistant to nitric acid digestion and require the use of hydrofluoric and/or perchloric acids. The developed method aims to reduce the effects of fractionation and differences in ablation yield between different materials by creating a matrix-matched calibration and by normalization to an internal standard added to the samples.

Sample Preparation
Cellulose multi-element and internal standard powders were prepared by mixing a multi-element stock solution with a particle size ≤ 20-μm cellulose binder (3642, Spex, Metuchen, NJ). The multi-element stock solution concentrations are represented in Table S1 (left); this solution was prepared using 1000 and 10,000 μg/mL single-element ICP-MS standards (Inorganic Ventures, Christiansburg, VA) diluted to 1 L with 1% nitric acid. The stock was then mixed with approximately 450 g of cellulose powder and stirred for at least 1 h, filtered using vacuum filtration, and dried in an oven at 60 °C until most of the moisture evaporated. The resulting material was ground into a fine powder (i.e., approximately 20 μm, D50) using a knife mill (GM 300, Retsch, Haan, NRW, Germany). The multi-element standard powder was further characterized by solution-based ICP-MS and ICP-OES analysis after microwave-assisted acid digestion to determine the final concentration of each element in the powder, shown in Table S1 (right). The internal standard solution stock consisted of a solution of 5 μg/mL of Bi, Ge, Ir, Rh, Sc, and 10 μg/mL of Te and the internal standard powder material was prepared in the same way as the multielement powder. The cellulose blank was also characterized by solution-based ICP-MS, with no detected concentration above the limits of quantitation for the monitored elements.
The cellulose calibration standards were prepared by mixing the multi-element cellulose powder at increasing mass fractions with 2 g of internal standard and cellulose blank for a total mass of 4 g. The calibrants consisted of five to six standards with concentrations of up to 8 mg/kg for the trace elements (i.e., As, Cr, Co, Ni, Pb), and up to 80 mg/kg for the major elements (i.e., B, Cu, Fe, Mg, Na, S, and Zn). The matrix-matched calibration standards were prepared by mixing the multi-element cellulose powder at increasing concentrations with 1 g of multivitamin reference material VITA-1 (National Research Council NRC, Canada), 2 g of internal standard, and cellulose for a total mass of 4 g. For the matrix-matched calibration, the calibrants consisted of five to six standards with concentrations of up to 4 mg/kg in the pellets, for the trace elements. The concentrations of the major elements were predominantly determined by the VITA-1 reference material as these elements were present at much higher concentrations in the reference material than in the cellulose multi-element standard. The mass fraction ranges for the calibration standards are represented in the supplemental information (Table S2). The addition of the multivitamin reference material aimed to create calibration standards that matched the matrix of the unknown multivitamin samples.
Twelve multivitamins were locally purchased from retail stores; the list included the typical variety available to the public (i.e., general multivitamins for adults, iron-free and iron-rich, for age 50 + , and for men or women). Most multivitamins were tablets, and one was in the form of capsules. The twelve multivitamins were ground and mixed with 2 g of internal standard.
All samples and standards were separately ground using disposable grinding chambers (IKA, Wilmington, NC, USA) at 15,000 RPM for 3 min. A mass of approximately 300 mg from each homogenized sample was pressed into 13 mm by 1-mm pellets at 10 ton for 30 s using a pellet press (3613 13-mm pellet die set and 3635 X-Press, Spex Sample Prep, Metuchen, NJ, USA). The pellets were stored in a vacuum oven at approximately 40 °C prior to analysis to limit the absorption of moisture from the air.
The multivitamins, reference materials, and cellulose powders were analyzed by solution-based ICP-MS and ICP-OES following microwave acid digestion. Digestion was performed according to the method in FDA's Elemental Analysis Manual (EAM) Sect. 4.7 (Gray et al. 2020) using the ultraWAVE microwave digestion system (Milestone, Shelton, CT, USA) by adding 5 mL of concentrated nitric acid and 1 mL of hydrogen peroxide to PTFE digestion vessels containing 250-500 mg of sample. The digests were diluted to 50 mL resulting in a final acid concentration of 5% nitric acid and 0.5% hydrochloric acid. Additional dilutions were required prior to ICP-MS and ICP-OES analyses (i.e., 5 times for trace elements and 500 times for the major elements).
VITA-1 and VITB-1 (NRC, Canada), and NIST SRM 3280 (NIST, Gaithersburg, MD, USA) were used as reference materials. These materials served as quality control for solution and LA-ICP-MS analyses and for the creation of matrix-matched calibration standards (VITA-1). Although NIST SRM 3280 is no longer available, NIST SRM 3294 Multielement Tablets can be purchased instead.

Instrumentation
The pellets were ablated and analyzed using a 193-nm excimer-based laser ablation system (NWR193, Elemental Scientific Lasers LLC, Bozeman, MT, USA) coupled to an ICP-MS instrument (iCAP Q, Thermo Fisher Scientific, Waltham, MA, USA). The laser system was equipped with a small volume self-seal chamber. A carousel autosampler was used for a fully automated analysis of up to 20 samples at a time. The analysis of one sample took approximately 7 min (plus 1 min of purge and carrier gas stabilization). The ablated material was transported using He at 800 mL/ min. The carrier gas was then mixed with N 2 at 5 mL/min and Ar at 400 mL/min. The sample was finally introduced to the ICP-MS using a signal smoothing mixing chamber (NWR193, Elemental Scientific Lasers LLC, Bozeman, MT). The analysis was performed in Kinetic Energy Discrimination (KED) mode using 4.8 mL/min He as collision gas to minimize interferences. Table 1 describes the optimized parameters for LA-ICP-MS analysis. A 60 s "gas blank" (no ablation) and five 3-mm-long ablation lines were performed on each pellet.
The solution-based ICP-MS analyses were performed using Agilent 8800 (Agilent, Santa Clara, CA) and Element 2 (Thermo Scientific, Waltham, MA) systems. The sample was introduced to the tandem ICP-MS using 0.762-mm inner diameter PVC peristaltic pump tubing at 6 RPM. The solution was aspirated using a MicroMist nebulizer into a Peltierchilled Scott double-pass spray chamber (Glass Expansion, Port Melbourne, Victoria, Australia). Helium was used as the collision gas and oxygen as the reaction gas for selected isotopes (i.e., As and S), to mass-shift the analyte away from polyatomic interferences. Sample was introduced to the magnetic sector ICP-MS using a 0.762-mm inner diameter PVC peristaltic pump tubing at 3 RPM. The sample was aspirated using a MicroMist nebulizer into a Peltierchilled cyclonic spray chamber (Elemental Scientific Inc., Omaha, NE, USA). For both ICP-MS analyses, the internal standard solution ( 103 Rh) was mixed with the sample using 0.762-mm inner diameter PVC peristaltic pump tubing and a T-connector resulting in a 1:1 sample-to-internal standard ratio. The concentration of internal standard solution was approximately 2.5 ng/g Rh for the Agilent 8800 analyses and 2 ng/g Rh for the Element HR-ICP-MS analyses.
ICP-OES analyses were performed using the Agilent 5900 (Agilent Technologies, Inc., Santa Clara, CA) system. Samples were introduced into the plasma using 1.03-mm inner diameter PVC peristaltic pump tubing at 12 RPM. Sample solution was aspirated into a double-pass glass cyclonic spray chamber (Agilent Technologies, Inc., Santa Clara, CA) using a concentric glass nebulizer (SeaSpray) prior to introduction into the plasma. Nitrogen was used as the polychromator purge gas. Sc II 361.383 nm and In I 325.609 nm were used as internal standards for the ionic and atomic lines, respectively. The concentration of internal standard solution was 2 μg/g for scandium and 20 μg/g for indium. The internal standard solution was mixed with the sample using 1.03-mm inner diameter PVC peristaltic pump tubing and a T-connector resulting in a 1:1 sample-to-internal standard ratio.
Concentration results from both ICP-MS instruments and from ICP-OES were combined by finding an average value and the uncertainties propagated to find the concentration mean for all multivitamins. The recoveries from the multivitamin reference materials were used as quality controls for the digestion and for the ICP-MS and ICP-OES analyses. Additionally, Initial Calibration Verification standards (ICV) and Continuing Calibration Verification standards (CCV) were added to the analysis sequence every ten samples to monitor instrumental drift and the performance of the calibration across the sampling sequence. Acceptable ICV and CCV recoveries were those in the range of 90-110%. Acceptable reference material recoveries were those in the range of 80-120%. The multivitamin digests were diluted by a factor of 5 and 500, for trace and major elements, respectively. In addition, dilution/additional gas downstream from the spray chamber was needed to reduce the total dissolved solid concentration in the ICP-MS sampling. Solution-based ICP-MS and ICP-OES parameters are summarized in Table 2.

Data Processing
Following LA-ICP-MS analysis, the transient signal corresponding to the gas blank (no ablation) and five ablation lines was obtained using the ICP-MS data analysis software Qtegra (Qtegra, Version 2.10.4345.64, Thermo Scientific, Waltham, MA). The acquired transient data was exported to .csv files and processed using a custom R script (R Core Team 2021) (R version 1.3.959) and the R package "outliers" (Komsta 2015). The script was responsible for removing spikes from the signal using the Grubbs' test for outliers (at a significance, α = 0.0005), integrating the area for the signal and blank regions and subtracting the area of the blank from the signal. The integrated signal and blank areas consisted of 50 s of analysis time. Area ratios were obtained by normalizing each element's area by the internal standard (i.e., 13 C, 209 Bi, 193 Ir, 74 Ge, 103 Rh, 45 Sc, 125 Te). These ratios were averaged (n = 5) and plotted against the concentrations (ng/g) of the calibration standards in the pellets to create external calibration curves for each element. For elements present in the matrix-matching material (VITA-1) at high concentrations, a single-point calibration approach was applied instead using the highest calibration standard as the calibrant. The analytes calibrated using a single-point calibration were B, Cr, Cu, Fe, Mg, Na, S, and Zn. The mass fraction ranges for the calibration standards are represented in the supplemental information (Table S2).
The analytes reported for laser ablation analyses were those without unavoidable polyatomic and isobaric interferences and with solution concentrations above the limits of detection. For this reason, Cd, Hg, K, and Ca were not reported. Cd isotopes suffer interferences from molybdenum oxide polyatomics, which formed in the ICP from high Mo concentrations in most of the multivitamins (Begu et al. 2019). Hg was not determined above limits of detection in the solution analyses; therefore, it could not be compared to the LA-ICP-MS concentrations. K and Ca suffer interferences from Ar (May and Wiedmeyer 1998).

Results and Discussion
Different laser parameters were closely monitored to achieve optimal conditions for monitoring multiple elements in cellulose and multivitamins while reducing the variability between replicate measurements (%RSD). Table 1 summarizes the optimized parameters for the analysis of multivitamins by LA-ICP-MS. Parameters optimized included laser energy (fluence), repetition rate (frequency), and flow rates of the carrier and makeup gasses. The final optimized parameters were used for the LA-ICP-MS analysis of the twelve multivitamins. Additionally, an experiment was conducted to determine the effect of differences in focal points between pellets on the instrument signal.

Instrumental Parameters Optimization
The laser energy optimization was critical to minimize the differences in ablation between the cellulose and multivitamin pellets, thus reducing the impact of fractionation and matrix differences on the results. Figure 1 shows the signal intensity obtained after ablating at different energy outputs and the Relative Percent Difference (RPD) between the cellulose and NIST SRM 3280 pellets, for Rh. The error bars in Fig. 1 represent the standard deviation from five replicate measurements. Both pellets contained 2 g of internal standard; therefore, the concentration of Rh in the pellets was identical. The same trend was observed for all the other internal standard elements. A fluence of 0.5 J/cm 2 was selected for future experiments as it provided a smaller relative difference between the materials in terms of ablation yield, while still resulting in acceptable sensitivity for most analytes. The effect of laser repetition and He carrier gas flow rates were investigated to provide optimal sensitivity and lower repeatability between replicate measurements. Figure 2A shows the signal intensity at different repetition rates for lead ( 208 Pb), as an example. A frequency of 30 Hz was selected for further analyses as it resulted in higher signal intensity, adequate repeatability, and the removal of sufficient material for accurate LA-ICP-MS analyses for most of the elements monitored. Figure 2B shows the intensity counts and relative standard deviation (RSD) obtained for Pb at different flow rates. A flow rate of 800 mL/min of carrier He gas was selected for further analyses as it provided higher signal intensity and lower %RSD between the five replicates for most of the elements monitored.

Effect of Differences in Focal Point
Integration of a carousel autosampler allowed for automated and unattended LA-ICP-MS analysis of the pellets. The pellets (13-mm diameter and 1-mm width) were inserted in 3D-printed holders and placed on the carrousel wheel. The instrumental parameters for the analysis, including the z-position or focal point, were initially set for the first sample in a sequence of up to 20 samples. The surface focal point varied slightly between pellets due to microscopic height differences of the sample holders and variations in pellet thickness due to the nature of the materials. Typically, the largest observed difference in focal point was 100 μm, meaning that the surface of the sample appeared to be out of focus in either the positive or negative "z" directions by up to 100 μm. An experiment was designed to assess the effect of these focal point differences in the resulting signals.
The experiment consisted of 11 ablation lines on a multi-element cellulose pellet where the focal point was adjusted by lowering or raising the laser stage. The center line (i.e., 0 μm) was ablated at the best possible image focus on the surface of the pellet. The rest of the lines were ablated 20, 40, 60, 80, and 100 μm away from the focal point in both positive and negative "z" directions; for example, lines 5 and 7 were ablated at − 20 and + 20 μm away from the focal point, respectively. The signal intensity for each line were plotted for all elements before and after normalization to another element already present in the sample. Figure 3 shows the results of the focusing experiment for Pb before and after signal normalization. The graph shows the Relative Percent Difference (RPD) of the intensities with respect to the center focal point (zero μm out of focus) after lowering and raising the stage from − 100 to + 100 μm. Although the resulting signals varied considerably as the surface of the sample moved away from the center focal point, the dissimilarities in ablation yield were successfully corrected after normalizing to the internal standard element ( 103 Rh), resulting in RPD of less than 10%.

Internal Standard Selection
To select the most suitable internal standard for each analyte, seven isotopes were monitored: 13 C,209 Bi,74 Ge,193 Ir,103 Rh,45 Sc,and 125 Te. Figure 4 shows the experimentally determined and certified concentrations for As in pellets from reference materials VITB-1 and NIST SRM 3280 after normalization to the different internal standards and without internal standard normalization. In this case, tellurium was selected as the best internal standard for Ar for the analysis of multivitamins as it resulted in the highest accuracy for

Focal Point
Intensity Normalized Intensity both the reference materials as well as in commercial multivitamins. The error bars shown in Fig. 4 represent the standard deviation of five replicates (n = 5) for the laser ablation results, and the reported standard deviations for the certified values. Similar to As in Fig. 4, the selection of the internal standard for all the other analytes was accomplished by monitoring the recovery of the certified reference materials (and of the multivitamins in comparison to solution results) with each internal standard. The selection of the appropriate internal standard is essential to accurately quantify the elements in the samples. The use of internal standards was critical to mitigate the differences in ablation yield between the multivitamins and the calibration standards, to correct for focal differences between the different samples, and to compensate for variability in the signal intensity caused by the presence of matrix components and differences in ionization energies. The internal standard selection was dependent on the sample matrix; for example, in matrix-matched calibration, the best internal standard for Pb was found to be Rh, while C provided better recoveries for the reference materials and multivitamins when calibrating with cellulose. The internal standard elements used for each analyte, for both calibration strategies, are shown in Table 3.

Calibration and Quantitative Analysis
Two calibration strategies were compared for the analysis of multivitamins: (1) using increasing concentrations of cellulose powder fortified with multiple elements of interest and (2) matrix matching using a multivitamin reference material in addition to the cellulose multi-element powder. External calibration was applied with either single or multiple calibrants, depending on the analyte's concentration in the samples. In the cellulose calibration, the calibrants consisted of five to six standards with concentrations of up to 8 mg/kg for the trace elements and up to 80 mg/kg for the major elements, such as Mg. In the case of the matrixmatched calibration, the standards had concentrations of up to 4 mg/kg in the pellets for the trace elements. The two calibration ranges differed because of the amount of multielement powder added. In the case of the matrix-matched calibration, the maximum amount of multi-element powder that was added was 1 g, plus 1 g of VITA-1 and 2 g of internal standard for a total of 4 g. Concentrations of the major elements were predominantly those present in the VITA-1 reference material, which was used for creating the matrix-matched calibrants. Most of the major elements in the matrix-matched material were present at much higher concentrations than in the cellulose multi-element powder; therefore, an external multiple-point calibration curve was not feasible. In these cases, a single-point calibration approach was used instead. The analytes quantified with a single-point calibration included B, Cr, Cu, Fe, Mg, Na, S, and Zn. The mass fraction ranges for the calibration standards are represented in the supplemental information (Table S2). Figure 5 shows the calibration curves for As using cellulose (Fig. 5A) and matrix-matched calibration standards (Fig. 5B). The intensity ratios consist of the ratio of the analyte intensity to that of the internal standard element. The calibration curves were linear for all the monitored  trace elements with both calibrations. The major elements that fell outside the calibration curves, or that were already present at high concentrations in the multivitamin matrix (VITA-1), were calibrated using a single-point calibration using the highest standard as calibrant, after internal standard correction. Limits of detection (LOD) and limits of quantitation (LOQ) were estimated from the analyses of cellulose "blanks" (i.e., cellulose powder mixed with 2 g of internal standard without any of the elements of interest added). The LOD was calculated as 3 times the standard deviation of the blanks and the LOQ were calculated as 10 times the standard deviation of the blanks and are summarized in Table 3. Ten cellulose blank pellets were used for the LOD and LOQ calculations.
For most multivitamins, both calibrations performed adequately for the following elements: As, B, Co, Cr, Cu, Mg, Na, Ni, Pb, and Zn. Figure 6 shows the LA-ICP-MS determined concentrations of As in the twelve multivitamins for both calibrations, in comparison to the solution ICP results. The error bars represent the standard deviation from five replicate measurements for laser ablation and the propagated standard deviation from three digestion replicates analyzed by solution-based ICP-MS and ICP-OES. Table 4 summarizes the LA-ICP-MS determined concentrations for all the analytes for the twelve multivitamins by the different calibration approaches in comparison to the solution results.

Conclusions
We presented the development and optimization of an LA-ICP-MS analytical method for the analysis of multivitamins. This technique offers quick and automated sample analysis without the need for corrosive acids and extensive sample preparation. Integration of a carrousel autosampler allowed for automated and unattended analysis, resulting in high sample throughput. In comparison with the solution-based ICP-MS analysis, the laser ablation method was considerably quicker and simpler. The main notable advantage was the ability to analyze the samples without having to decompose them by acid digestion. In addition, the digests required two sets of dilutions (i.e., a 5 × dilution, for trace elements, and a 500 × dilution for the major elements), which was not only time consuming, but also generated large amounts of hazardous waste and involved the use of costly ICP-MS standards, high-purity concentrated acids, and consumables. The optimum energy output selected for the laser ablation analysis was 0.5 J/cm 2 which resulted in less differences in ablation between the two materials, without significantly sacrificing sensitivity. A repetition rate of 30 Hz and a carrier gas flow rate of 800 mL/min were determined to be optimum as they provided the best compromise between sensitivity and reproducibility. The dissimilarities in ablation yield due to differences in focal points were successfully corrected after normalizing to internal standard elements, resulting in relative differences of less than 10%. The use of internal standards was critical for some elements, such as As, for the accurate quantification of the multivitamins. The