This month’s column focuses on the applicability of inductively coupled plasma–optical emission spectroscopy (ICP-OES) fitted with a high efficiency nebulizer as a real-world alternative to ICP–mass spectrometry (ICP-MS) for certain applications. It is well-recognized that ICP-MS is the most widely used and recommended technique for ultra trace element analysis because it offers extremely high sensitivity. However, if the necessary sensitivity is achieved, an ICP-OES instrument can be a viable option because it is simpler to operate and less costly to maintain than an ICP-MS instrument. In this study, the sensitivity of ICP-OES was significantly enhanced by using a highly efficient yet robust sample introduction system. The increased efficiency was accomplished by employing an external impact surface positioned close to the nebulizer gas orifice at an optimized angle. The robustness by a non-concentric design was achieved by separating the gas and sample channels throughout the entire body of the nebulizer. The results of applying this approach to the ICP-OES analysis of a select group of sample matrices and meeting the required challenging detection limits are demonstrated.

Generally, inductively coupled plasma–mass spectrometry (ICP-MS) and inductively coupled plasma–optical emission spectroscopy (ICP-OES) are complementary techniques; each has its benefits and limitations. Although ICP-MS is more sensitive, ICP-OES can handle approximately 10 times higher amounts of total dissolved solids (TDS). This corresponds to the lower dilution factors applied in the ICP-OES analyses. When calculated on the undiluted sample basis, the detection limits may end up being comparable to the detectability power achieved by ICP-MS. Even though modern ICP-MS instrumentation is said to allow direct analysis of samples with up to 25% of TDS without prior dilution, such analysis is accomplished by employing a carrier gas dilution module. Because the samples are still being diluted online by the argon carrier gas within the sample introduction module of the ICP-MS rather than externally by the aqueous diluent in many cases, the detection limits are not practically improved.

The ability of ICP-OES to handle a higher amount of TDS alone is usually not enough to meet the application requirements for the minimum detectable levels. That is why a key factor was to achieve the necessary sensitivity level by focusing on the sample introduction area. Introduced in 1976 (1), the most commonly used Meinhard or concentric nebulizers are usually selected when the lowest detection limits are required (2,3). A significant sensitivity boost is offered by ultrasonic nebulization and desolvating nebulizer systems, but both accessories are quite complex in operation, add significant costs, and the results depend on the different volatilities of some analyte species formed.

To meet the demand for increased sensitivity, the selected approach focused on improving nebulization efficiency by utilizing a principle like the one applied in the Babington V-Groove type nebulizer, introduced by Giess, McKinnon, and Knight in 1981, and named GMK after its three authors (3). A non-concentric design includes a glass impact bead located next to the gas nozzle. The quality of the initially created aerosol is significantly improved because finer particles were produced because of the impact action (3).

Exploring this principle further, the increase of the nebulization efficiency of the OptiMist Vortex nebulizer was accomplished by employing an external impact surface positioned very close to the gas orifice at an optimized angle. The sample channel’s internal diameter (i.d.) was kept relatively large at approximately 0.75 mm. The gas and sample channels were separated throughout the entire body of the nebulizer, which, in combination with a large sample channel i.d., provides resistance to blockages. Unlike the GMK design, which relies solely on gravity force, a thin film is formed on the surface of the OptiMist Vortex similar to the thin film induction nebulizer (3.4). This facilitates gas–liquid interaction and more efficient energy transfer. Because fine aerosol is deflected by the impact surface, the nebulizer is oriented at approximately 90° to the vertical plane within the spray chamber (Figure 1).

This design in combination with a baffled cyclonic spray chamber provides an enhancement of the ICP-OES sensitivity on average by about a factor of two as compared to the most efficient concentric nebulizers. The density of the aerosol is illustrated in Figure 2.

The suggested approach applies to a wide range of sample types. Here are some selected examples where challenging detection limits were required.

Trace analysis of high-purity materials is one such application area. Some of the elements of interest (for example, calcium, magnesium, manganese, sodium, and potassium) can be detected at the single parts per trillion (ppt) range by modern, axially viewed ICP-OES spectrometers. However, the analysis for a few of the difficult analytes, such as bismuth, tellurium, selenium, and antimony, usually need more sensitive graphite furnace atomic absorption (GFAA) or ICP-MS (5,6).

High-purity metals, such as indium, copper, and aluminum, are widely used by the semiconductor industry. The purity levels are more demanding, requiring 99.999%, 99.9999%, or even higher. To meet such high purity grade requirements, the impurities have to be analyzed at extremely low levels of 0.5 ppm in the solid material.

In this study, the analysis of high-purity copper was performed on an axially viewed ICP-OES instrument (Spectro Arcos). Additional gas flow was introduced through the special adapter attached between the spray chamber and the torch to reduce the sample deposition within the torch injector. To minimize the dilution factor, the samples were prepared as a 5% copper solution. Then, 0.500 g of the copper sample was digested with 5.0 mL of 50% v/v trace metal grade nitric acid and brought up to the 10 mL volume to a final dilution factor of 20. The calibration was made with fully matrix-matched standards using high-purity copper digested the same way and spiked at the different levels of 20, 200, and 2000 ppb.

Examples of the calibration curves for critical elements bismuth, tellurium, selenium, and antimony, are shown in Figure 3.

The detection limits were estimated in a single ppb range in the 5% copper solution, which corresponds to 0.06 to 0.100 ppm in the solid copper matrix.

Another challenging application for ICP- OES is related to the recent developments in the field of medical and recreational use of hemp or cannabis products, which created the need for testing these products for toxic elements. Maximum allowable limits (MAL) for these toxic elements are currently set by the individual states where cannabis is legal. For example, in California, Colorado, and Massachusetts, the required levels for arsenic, cadmium, mercury, and lead, referred to as the “big four,” are extremely low, so ICP-MS became the widely used and recommended analytical technique for this application.

From the analytical point of view hemp and cannabis are plants with unique chemical composition. This example was selected because the suggested approach can apply to any analyses involving plants, botanicals, environmental, or food materials where low detection limits are required.

It has been shown that the sensitivity needed to meet the MAL for the four toxic elements in cannabis products can be reached by ICP-OES with an ultrasonic nebulizer (7). However, as already mentioned, it complicates the analysis, makes it more difficult to run on a routine basis, and makes the analysis more costly.

The suggested analytical approach included the combination of the following three key components:

High-efficiency sample introduction system described earlier that improves instrument detection power by approximately a factor of two.

Digestion and sample preparationmethodology optimized for reaching maximum completeness of the organic matrix decomposition at a minimum dilution factor.

Creative approach to close matrix-matching of the calibration standards.

Of the four toxic elements to be detected at the low level, arsenic and lead were the most challenging for two reasons: the ICP-OES instrument detection limits were in the single ppb range and both analytes were affected by spectral interferences from the matrix components.

The preliminary experiments helped to identify the main sources for the interferences: residual carbon, which still remained in the digested samples, and calcium, which is a typical component found in the plant materials at a relatively high concentration. The effect of the residual carbon presence on the most sensitive arsenic 189.0 nm analytical line is shown in Figure 4. Calcium is known to create a stray light, which elevates the overall background in the spectral region below 250 nm and usually is taken into account by background correction.

Compensating for carbon spectral interference was critical. To reduce the residual carbon content, the optimization of the digestion methodology was focused on reaching the maximum possible completeness of the organic sample matrix decomposition. This is usually accomplished by conducting the digestion step at the highest possible temperature. Considering that a relatively significant sample size of 1.00 g has to be used to minimize the final dilution factor, the digestion temperature was set at 230 °C with 20 min to safely reach the target temperature and keep it for 15 min. Samples were digested in the MARS 6 Closed Vessel Microwave Digestion System (CEM Corporation) using the manufacturer-recommended recipe: 10 mL of concentrated nitric acid plus 0.3 mL of concentrated HCl to keep mercury stable. The samples and standards were prepared gravimetrically for better accuracy. Digestates were brought up to a final weight of 15 g (Figure 5).

It is common for plant samples to contain small amounts of silicon, which forms a small amount of Silica precipitate as shown in Figure 5. Usually, the samples have to be filtered to prevent the blockages common for concentric-type nebulizers (2,3). As described earlier, the utilized nebulizer has a relatively large sample channel i.d. at approximately 0.75 mm, which allowed elimination of the time-consuming and quite often costly filtration step.

The content of the residual carbon in the samples, digested by the described procedure, was estimated by ICP-OES analysis at less than 2% (approximately 1150 ppm), indicating a relatively good level of decomposition completeness (8). However, even that amount of carbon in the digested samples resulted in a high bias of approximately 4–5 ppb for arsenic if analyzed against the calibration standards without carbon.

That is why the addition of carbon along with calcium estimated at 600 ppm to closely matrix match the calibration standards was necessary to compensate for such interferences and improve the accuracy of the results. The matrix composition of the calibration standards following the reagents digestion recipe included 33% HNO

/2% HCl acids mixture, 1150 ppm carbon as (potassium hydrogen phthalate) KHP, and 600 ppm of calcium. Because the vast majority of the acids were consumed during the digestion step, for practical purposes the amount of acids used for matrix matching can be decreased.

Analyses were carried out on two ICP-OES spectrometers with different designs of the optical systems: Agilent Technologies 5800 (System #1) and an axially viewed Spectro Arcos instrument (System #2). The operating parameters were optimized on each instrument for the maximum sensitivity of arsenic, which generally favors lower nebulizer flow and higher RF power setting. The examples of the calibration curves from both instruments with matrix-matched standards at 0, 1, 5, and 10 ppb and two times lower concentrations for mercury are shown in Figure 6.

The calibration data showed that the lowest point at 1 ppb in the matrix-matched standard is clearly separated on the calibration curves for all the elements, including the most challenging arsenic and lead.

The sensitivity potential of the developed methodology was evaluated by the results of the digested samples spiked at the levels approaching the instrument detection limits. The recoveries for the 1 ppb (0.5 ppb for mercury) spike were in the range of 60–140%, whereas 2 ppb (1 ppb for mercury) spike was recovered between 84–115%.

The three sigma detection limits determined on both systems from 7–10 measurements of the matrix-matched blank were within the range from 0.07 ppb (for cadmium) to 1.5–2.0 ppb (for arsenic and lead) or 0.001 μg/g to 0.03 μg/g on a dry sample base. This shows that the estimated detection limits in the range 0.001–0.03 μg/g are well below the strictest regulatory limits (MAL) defined by the state of California for inhalable cannabis and hemp products which are in the range 0.1–0.5 μg/g (Table I).

The results of the hemp samples analysis performed on both ICP-OES instruments are shown in Table II.

The described applications of high-purity materials and cannabis plant material show that the ICP-OES if configured correctly for high sensitivity can be a viable, attractive, less expensive, and reliable alternative to ICP-MS. In addition, because of its robustness, the methodology can be applied to areas where high productivity and high sample throughput are required, including environmental, food, specialty chemicals, and other sample matrices.

This work was funded by Inorganic Ventures and Texas Scientific Products. We gratefully acknowledge Ben Turner from Tru-Harvest Farms for providing the hemp samples, Sam Heckle at CEM Corporation, Spectro Ametek, and Dion Tsourides at Pure Lithium, as well as Mike Booth, Madeline Gozzi, and Olivia Forbes at Inorganic Ventures, for their support, recommendations, and assistance.

(1) Meinhard , J. The Concentric Glass Nebulizer. 

Inductively Coupled Plasmas in Analytical Atomic Spectrometry, 

2nd Ed. John Wiley & Sons, 2nd Ed. 1996. p 225.

Nebulization Systems in Sample Introduction Systems in ICP-MS and ICP-OES; 

(4) Leikin, S.; Sweat, S. Analytical Nebulizer. US 11,378,518 B2, 2022.

(5) Sugiyama, N. Analysis of Ultratrace Impurities in High Purity Copper using the Agilent 8900 ICP-QQQ. 2018. 

https://www.agilent.com/cs/library/applications/application_cu-impurities-icp-ms-8900-5994-0383en-us-agilent.pdf

(6) Merrifield, R.; Stephan, C. Measurement of Impurities in High-Purity Copper Concentrate Using the NexION 5000 ICP-MS.2021. 

http://resources.perkinelmer.com/lab-solutions/resources/docs/APP-Measurement-of-Impurities-in-High-Purity-Copper-Concentrate-NexION5000-ICP-MS-159845.pdf

(7) Davis, D.; Long, K.; Masone, J.; Firmin, P. Analysis of “The Big Four” Heavy Metals in Cannabis by USN-ICP-OES. 2015. 

https://www.ssi.shimadzu.com/sites/ssi.shimadzu.com/files/pim/pim_document_file/ssi/applications/application_note/15153/ICP%20Application%20-%20Analysis%20of%20Heavy%20Metals%20in%20Cannabis%20by%20USN-ICP-OES.pdf

(8) Wasilewska, M.; Goessler, W.; Zischka, Maichin, B.; Knapp, G. Efficiency of Oxidation in Wet Digestion Procedures and Influence from the Residual Organic Carbon Content on Selected Techniques for Determination of Trace Elements. J

Articles

A new sample introduction method improves ICP-OES for ultratrace element analysis. An explanation of how this ICP-OES compares to ICP-MS analysis is also provided.

ICP-OES as a Viable Alternative to ICP-MS for Trace Analysis: Meeting the Detection Limits Challenge

In this column, we examine a variation of the MLR algorithm that reduces sensitivity to repack variations in the special case that the absorbance at all wavelengths used in the calibration model undergo the same change when repacked.

Correction to past columns: We apologize to those of our readers who have no difficulty in counting beyond 1 even without their computers. Your authors, on the other hand, seem to have run into some difficulties in that regard, even WITH our computers. The first two parts of this “Data Transforms” sub‐series were published in the February 2022 and July 2022 issues of Spectroscopy (1,2). However, both columns designated themselves “Part 1” of the sub‐series in print; this has been corrected for the online versions as denoted in the reference section.

As mentioned in our previous column (2) on the topic of data transforms, here we examine transformations of spectral data that have the goal of improving calibration performance. Not all transformations, however, are designed specifically to produce that result, although that often occurs as a “side effect” to the algorithm used. Similarly, while some data transforms can be applied to the data independently of the calibration algorithm used to create the ultimate calibration model, some transforms are more usefully applied before a particular calibration algorithm is applied. This column is based on the talk given at the 2020 Gold Medal Award session at EAS when that award was conferred on your columnists (3).

What does this mean, and why would we want to do it?

For most of its existence, and especially in the early days of modern NIR analysis, the technology has been applied to solid samples. Not just solid blocks of material, but granulated materials and powders. Powders have at least one distinctive characteristic: it can never achieve an exact repeat spectral reading when you re-measure a sample. The reason for that characteristic is very simple: the multitude of small particles in a powdered sample cannot be exactly reproduced because the particles are in different places and in different orientations, and therefore interact differently with the illuminating beam upon performing the re-reading. The resulting effect on the spectral data is that readings at different wavelengths are offset by uncontrolled and uncontrollable amounts, giving spectral displays that are similar to each other, but different in the details. These offsets are variously called the “Particle size Effect”, or the “Repack Effect”, in the literature. Numerous examples of this effect can be seen in the Applications sections of any of the editions of the 

 (4), or prior editions, as well as in other texts dealing with this subject, and applications articles in specialized journals. There is even an example in the previous column in this sub-series (2). These offsets are in addition to, independent of, and often larger than the variations in the spectra due to differences in the composition of the samples.

We present the analogy of a thermometer: before you can use a thermometer to make measurements of temperature, it must be calibrated. In the case of a thermometer, it is typically calibrated by putting it in an ice bath where you know the temperature is zero degrees C, and mark that point on the scale. Then you put it in a steam bath where you know the temperature is 100 degrees C, and put a mark on the scale corresponding to that. Now you can use the thermometer to read any temperature between those values, and with care and luck, even slightly beyond the marks. In order to do all that, however, you must also make some assumptions about the behavior of the thermometer, particularly that the thermometer reading is a linear function of the actual temperature.

So it is with NIR. Although somewhat more complicated to perform, the underlying concept and process is the same. Any instrument reading is meaningless in isolation. To give it meaning we have to somehow relate the instrument readings, represented by the spectra of the samples, to accurately known composition values. The process is somewhat more complicated than calibrating a thermometer, but the concept is 

the same: we need to have both the instrument readings (spectral data values) and the known (or “actual”) values of the composition variables in order to determine the relationships between them.

It doesn’t really matter what the original purpose of collecting the data is, as long as you wind up with all of it (spectra and composition). The original purpose of collecting a “prediction (or “validation”) set”, for example, is usually to verify the accuracy of the calibration model being used. In order to do that, you need to have accurate values for the composition of the samples (at least for the analyte of interest) so you can make the comparison. Then you can compare the instrument “predictions” to the known analyte values, and determine (in a “statistical” sense) the accuracy of the calibration model. But when you have both the spectra and the known analyte values, you can work the same data the other way and use the data to describe the relationships between them; that’s the NIR calibration process.

But NIR spectra, especially of particulate solid samples, have a complication that a thermometer doesn’t have. Because of the randomness inherent in the nature of particulate samples, oftentimes you can get a different set of spectral readings from two different portions of the same sample (as a result of the repack effect), even though they both correspond to the same sample composition.

For as long as NIR has been a popular analytical technique, that effect has shown up as differences in the predicted values of the analyte when the different portions were measured, a consequence of the differences in the measured spectra. Ever since Karl Norris described the new technology that we now know as modern NIR analysis, the community has sought an algorithm that would give the same predicted value for an analyte even in the face of the spectral differences that result from measuring two different portions of the same sample.

A typical example of the repack effect is shown in Figure 2 of our previous column (2). It is noteworthy that the spectral variations due to the repack phenomenon are systematic across the spectrum, but the magnitude of the effect varies both with wavelength and with the absorbance of the sample. Attempts to derive mathematical descriptions of these variations from first principles based on properties of the sample have, in general, been unsuccessful, despite many scientists attacking that problem for over 100 years (see [5,6], Kortum [7], Wendlandt, et al. [8], recently by Dahm [9] and more recently by Meyerhofer [10] [the “Dahm” reference also includes a nice review of the field over the years]).

The problem with having a sample set that exhibits repack variation is that when the data is included in a calibration model, such as in this generalized case:

 is the concentration of analyte computed by the model; 

 are the calibration coefficients. The different absorbance values result in different predicted values for portions of the same sample.

The standard solution of these equations, that results in the standard MLR algorithm, is achieved by converting the equations to matrix formulation:

, the calibration coefficients (in shorthand notation – see chapter 4 in [11] and the solution here is expressed in compact matrix notation:

The repack effect exhibits itself as a change in the value of C computed from spectra where the absorbances change due to the purely physical action of the sample being repacked into the sample cup: 

where the primed variables represent the absorbances and predicted concentration values calculated after the sample was repacked.

Therefore, for any sample subject to the effect of repack, a different value of the analyze will be computed for the two cases, even though they represent the same sample. Subtracting the result of one set of readings from the other, we obtain:

 represents the change in absorbance at the ith wavelength (that is 

), due to the changes in the sample surface attendant upon the repacking. The desire, therefore, is to create calibration models that not only would allow instruments to accurately analyze future samples (“unknown” samples at the time the calibration model was being generated), but that would also resist changes in the predicted analytical values when the sample was repacked during routine measurements. For this purpose, many ad hoc data transforms were applied to spectral data sets. Out of all that empirical work, certain data transforms became popular, primarily transforms involving spectral “derivatives” (dA/dλ). In particular, “second derivative” transforms (d

) came to be used to a large extent. This was not because anyone demonstrated any special merit to that data transform, but simply because instrument manufacturers and software manufacturers built it into their calibration software, and it worked “well enough”. After all, given several values of SEP, one of them has to be the smallest. But spectral derivatives have another problem: they can be used when continuous (or at least quasi-continuous spectra are available), but see the critique of the “derivative” transform in our previous column (2), and in any case, “derivatives” cannot be calculated when readings at separated individual wavelengths are measured, such as when instruments with fixed interference filters are used to select the wavelengths.

There is a special case of equation 7 that is of interest here, which provides an alternative to the use of spectral derivatives. It rarely happens exactly, but there are cases where it happens closely enough that the various ∆

 are all approximately equal. When this occurs, and the approximation of the variations to uniformity are sufficiently close, then we can replace all the ∆

 to represent the change in absorbance due to repack, as shown in equation 8. Arguably, this approach is not so much a transformation of the data as it is a modification of the MLR algorithm. The data does indeed get modified, but the changes are internal to the algorithm, and the modified data are normally not made accessible outside the program. Of course, anyone who can write their own calibration software can implement any variation they would like. Note that we configure the equation to illustrate the use of three wavelengths in the calibration model. Three wavelengths are sufficient to demonstrate the desired pedagogical requirements without overloading the process with excess symbology and confusion.

We can now factor the right-hand side of equation 8 as follows:

and in this case, if the sum of the calibration coefficients in equation 8 (excluding 

 is also zero, which means that there is no change to the computed analytical value of analyte concentration regardless of any changes of the spectra due to the repack effect.

This result can be used in a number of different ways. First, and simplest, once the standard regression calculations have been performed and the calibration coefficients have been determined, the coefficients can be added together, and the sum reported. This has been previously proposed and designated as the Index of Systematic Variation (see pages 57 and/or 98 in [12]). It serves as an indicator of the sensitivity of the predictions from the model to variations due to repack.

Second, we can seek mathematical ways to compute calibration coefficients that comprise a model that has that property. In addition to being least-square estimators of the reference values of the analyte, the coefficients sum to zero. This is a special case of a more 

general mathematical concept of applying constraints to the solution of a defined problem. This concept was devised by the Italian mathematician Joseph-Louis Lagrange (1736–1813) (13). Lagrange is famous for many contributions to mathematics, including defining what are now known as the five Lagrangian points of stability in astronomy (special solutions to the “three-body problem”). He also developed the concept and use of what is now called the Lagrange Multiplier. There are general approaches to implementing the concept, which are described in appropriate books on mathematics; for an example, see reference 14. But this column is neither a book on advanced mathematics nor a general discussion of the use and application of constraints, so we will just go directly to the discussion of how we apply those concepts to creating a calibration model whose coefficients sum to zero, in order to minimize the effect of repack on NIR readings.

Taylor (14) devotes an entire section of his book (starting on page 193) to finding solutions to various types of problems subject to constraints. The objective we have here, which is to find NIR calibration coefficients such that the sum of the coefficients equals zero, is addressed through the use of what is known as the Lagrange method of undetermined multipliers, which is discussed on page 198 (14). To implement this, we start with equation 8, and form the sum of squares to be minimized as is normally done:

Again, note that we couch our discussion in terms of a three-wavelength model, although the extension to any number of wavelengths is straightforward.

)= 0) to that sum of squares in the following form:

where λ represents the undetermined Lagrange multiplier. Note that our use of λ here should not be confused with our previous use of λ to indicate wavelengths. Mathematicians are not spectroscopists! A key aspect of using this formulation of adding the constraint in the form used to the sum-of-squares calculation, is that since 

 will ultimately be equal to zero, adding that expression to the sum of squares does not change or otherwise affect that sum of squares.

From this point on, we minimize the sum of squares by following the usual procedure of taking the derivative with respect to each of the variables, including λ, and then setting those derivatives equal to zero, just as we did with equation 3 to form the usual regression equations. The resulting matrix equation, corresponding to equation 6 in reference 2 (not the equation 6 in this column) is:

The procedure for deriving equation 12 is described in full detail in chapter 12 of reference 4.

Note several key points about equation 12:

The constraint added a row and a column to the [ATA] matrix, in addition to adding a row to each of the other two matrices in equation 12.

The upper-left-hand portion of the [ATA] matrix in equation 12 is the same as equation 6 in reference (4). This section represents the Least-Square calculation of the coefficients.

The last row and last column of the [ATA] matrix in Equation 12 represent the inclusion of the constraint.

The 1’s are each multiplied by the corresponding 

’s, and their sum must equal the last entry of the [CAT] matrix on the LHS of equation 12, which is zero. Equation 12 represents a set of simultaneous equations that need to be solved. Since one of the equations included as one of the simultaneous equations is the one that specifies (from equation 9) Σ

 = 0, then the solution to the simultaneous equations includes the values of 

 that are not only the least-square estimators, but also meet the condition that Σ

 = 0 are contingent on the absorbances of all the wavelengths in the model varying in a coordinated manner, that is, any changes must be in the same direction and by the same amount. By that definition, then, random noise will not be rejected.

One question remains: what is the meaning of λ? There are several on-line discussions of the Lagrange method, some of which discuss the significance and meaning of λ (13,15).

Some of the explanations are somewhat dismissive of this: “The value of λ isn’t really important to determining if the point is a maximum or a minimum so often we will not bother with finding a value for it” (15).

Others give a mathematical explanation, not addressing the physical meaning of the value of lambda as it pertains to the problem stated. For example, “λk is the rate of change of the quantity being optimized as a function of the constraint parameter. As examples,
in Lagrangian mechanics the equations of motion are derived by finding stationary points of the action, the time integral of the difference between kinetic and potential energy” (13).

Neither of those explanations is particularly useful to us. Sometimes the meaning of a variable becomes clear when that variable is provisionally assigned an extreme value, just for the purpose of elucidating its meaning and significance. On the other hand, if we examine equation 11 closely, we notice that λ multiplies Σ

i. Here we can apply a general procedure that enables us to gain insight to the meaning of mathematical quantities. The “trick” is to consider taking a property to an extreme value to see what happens. Thus, in our current case we consider setting λto zero. If λ = 0 then the sum of the coefficients is immaterial, since the product withλ is zero and has no effect on the value of the computation. In other words, if λ = 0, then the constraint disappears, and the result of the computation is the same as that of the corresponding unconstrained problem. Non-zero values for λ then, indicate the strength of the constraint. If λ is small, then the values of the sum of squares of the 

 will be their least square values. If λ is large, then values of the coefficients will be dominated by the constraint, and the sum of the coefficients will equal zero regardless of the ability of the coefficients to accurately predict the values of the constituent. Hopefully, the data will be such that a good compromise can be made. Our experience, though limited, has shown this to be the case.

(1) Mark, H.; Workman, J. Data Transforms in Chemometric Calibrations: Application to Discrete-Wavelength Models, Part 1: The Effect of Intercorrelation of the Spectral Data. 

 (2), 16–18, 54. DOI: 10.56530/spectroscopy.wp6284b9

(2) Mark, H.; Workman, J. Data Transforms in Chemometric Calibrations: Simple Variations of MLR, Part 2. 

 (7), 14–19. DOI: 10.56530/spectroscopy.cg7965x1

(3) The New York/New Jersey Section of the Society for Applied Spectroscopy. 

 The New York/New Jersey Section of the Society for Applied Spectroscopy 2023. https://nysas.org/past-gold-medal-winners/ (accessed 2023-08-14)

(4) Ciurczak, E. W.; Igne, B.; Workman, J.; Burns, D. 

, 4th Edition; CRC Press, 2021, pp. 9–43.

(5) Schuster, A. XXII. The influence of radiation on the transmission of heat. 

 (26), 243–257. DOI: 10.1080/14786440309462919

(6) Schuster, A. Radiation through a foggy atmosphere. 

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Reflectance Spectroscopy: Principles, Methods, Applications

Interpreting Diffuse Reflectance and Transmittance: A Theoretical Introduction to Absorption Spectroscopy of Scattering Materials

(10) Meyerhofer, T. G.; Oleksii, I.; Kutsyk, A.; Popp, J. Beyond Beer’s Law: Quasi-Ideal Binary Liquid Mixtures. 

 (1), 92–104. DOI: 10.1177/00037028211056293

Chemometrics in Spectroscopy, 2nd edition

Principles and Practice of Spectroscopic Calibration

 Wikipedia 2023. https://en.wikipedia.org/wiki/Lagrange_multipliers (accessed 2023-08-14)

 Paul Dawkins 2023. https://tutorial.math.lamar.edu/classes/calciii/lagrangemultipliers.aspx (accessed 2023-08-14)

There is a variation of the MLR calibration algorithm that can reduce sensitivity to repacked sample measurements. We explore that MLR method here in detail.

Data Transforms in Chemometric Calibrations: Variation in MLR, Part 3: Reducing Sensitivity to Repack Σbi = 0

The William F. Meggers Award was established in 1970 to honor its namesake, referred to by the National Institute of Standards and Technology on their website as “Dean of American Spectroscopists,” for his notable contributions to that field. This year’s recipient, Johannes Pedarnig of the Institute of Applied Physics at Johannes Kepler University (Linz, Austria) has recently investigated the optical emission of plasma on industrial steel samples utilizing laser ablation-spark discharge-optical emission spectroscopy (LA-SD-OES) and laser-induced breakdown spectroscopy (LIBS). Pedarnig spoke to 

 about this work as well as what winning the Meggers Award means to him.

In a recent paper (1), you discuss utilizing laser ablation-spark discharge-optical emission spectroscopy (LA-SD-OES) and laser-induced breakdown spectroscopy (LIBS) to overcome the matrix effect in the elemental analysis of steel. Why is the elemental analysis of steel important and what are the advantages of these specific analytical techniques?

Steel is a high-tech material with one of the largest volumes of production of all technical materials. Almost 2000 million tons of crude steel have been produced worldwide in 2021. The development of new (and optimized) grades of steel is a continuously ongoing process. Today, more than 3500 different grades are available. The steel grades have very different materials properties depending on the chemical composition and the production processes. Typically, more than 90 weight% of steel is made up by iron, up to 2 wt% is carbon, and the rest is covered by many other chemical elements. As the steel properties are critically depending on composition, the chemical element analysis of the produced material is crucial to ensure the targeted steel materials specifications are met.

The main advantage of laser-induced breakdown spectroscopy (LIBS) for the analysis of steel is the versatility of this technique. LIBS can be deployed in the field under harsh conditions and fast measurements can be performed that are otherwise not possible. One example is LIBS measurements of steel inline of the production process, which has been reported by several groups. This is useful to analyze and check the composition of the liquid steel and of the slag layer before the material is casted and further processed. The versatility of LIBS comes (often) at the cost of lower element sensitivity and laboratory-based techniques may have orders of magnitude lower (better) limits of detection than LIBS. A further disadvantage of LIBS (and of many other analytical techniques) is the potential matrix effect. The signal measured for a specific chemical element is not only depending on the concentration of the analyte, but also on the other elements in the material. The new LA-SD-OES technique combines LIBS with a second step for plasma excitation and this has enabled us to reduce the detrimental matrix effect in the element analysis of steel.

What made you decide to use these specific techniques to achieve accurate and rapid analysis of steel?

Laser-based spectroscopy techniques have a unique selling point when it comes to the analysis of steel in production, as no other technique is available to measure inline the chemical composition of liquid steel (temperature around 1500 °C). We have performed several research projects and inline measurement campaigns together with our industrial partner, voestalpine Stahl.

What are some of the limitations with current techniques being used to perform steel analysis?

The major limitation with standard techniques such as spark optical emission spectroscopy (OES) and X-ray fluorescence (XRF) spectroscopy is the offline measurement. Steel samples have to be taken, cooled down, sent to a laboratory, and measured. All this is slowing down the production process and the time required for element analysis may prevent from adjustment of the composition of the liquid steel.

Please summarize your findings in your research and describe what was most surprising or exciting about it.

We found that the slag layer, which is formed in steel production, and which is covering the steel liquid, can be chemically analyzed by a “calibration-free (CF)” LIBS method. We can determine the concentration of the major oxides in slag down to a concentration of about 1 wt% without measuring any reference material for calibration of the LIBS device. It was exciting for us to see that a physical model can be used to evaluate the optical emission spectra of laser-induced plasma and to determine the complex oxide composition of slags via this so-called CF-LIBS model.

Were there any specific unexpected limitations or challenges you encountered in your work?

Yes, there were several unexpected challenges. For instance, the temperature in the steel plant may vary from below 0 °C to above 30 °C. A high-resolution spectrometer, even if it is “temperature stabilized”, may not cope with large temperature variations and the measured spectra may be useless if this parameter is not precisely controlled.

Can you please summarize the feedback that you have received from others regarding your efforts?

Our papers on LIBS and LA-SD-OES are frequently cited, and we are invited to conferences; we are taking this as stimulating feedback from our colleagues worldwide.

What are the next steps in this research?

One of our next steps is the diversification to measure other materials as well. In a preliminary study we found that LA-SD-OES performs well for the analysis of technical polymers, significantly better than LIBS does. And of course, we will go one with the spectroscopy and chemical element analysis of steel and other metals.

What does your being named the recipient of the Meggers Award mean to you professionally? Personally?

Well, receiving this prestigious Meggers Award is a great honor for my research group and for me personally. It shows us that our research work is anticipated and appreciated. Furthermore, I am expecting this Award to boost our co-operation with industries and to support the raising of research funds.

(1) Grünberger, G.; Ehrentraut, V.; Eschlböck-Fuchs, S.; Hofstadler, J.; Pissenberger, A.; Pedarnig, J. D. Overcoming the Matrix Effect in the Element Analysis of Steel: Laser Ablation-Spark Discharge-Optical Emission Spectroscopy (LA-SD-OES) and Laser-Induced Breakdown Spectroscopy (LIBS). 

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A recent investigation of the optical emission of plasma on industrial steel samples using LA-SD-OES and LIBS revealed new findings about the oxide composition of the slag layer.

Overcoming the Matrix Effect in the Elemental Analysis of Steel: An Interview with 2023 Meggers Award Winner Johannes Pedarnig

Gallstone formation inside the gallbladder is a serious disease and causes health problems. To create preventative measures, it is crucial to examine the composition of gallstones and identify the minerals that are responsible for their pathogenesis. In the present work, we have employed laser-induced breakdown spectroscopy (LIBS)-based elemental studies in combination with partial least squares discriminative analyses (PLS-DA). Energy dispersive X-ray spectroscopy (EDX) was also applied to quantify the elements in the different parts (core and surface) of the gallstones. Fourier transform infrared (FT-IR) spectroscopy was used to classify the gallstone samples. Spectral studies using the LIBS and EDX techniques revealed the presence of trace and toxic elements in the center part of gallstones in higher amounts than that from surface parts. The EDX study also revealed that the elemental distribution is quite heterogenous, and their distribution is random. The EDX method revealed that the center (core) part of the stone samples contained the presence of numerous heavy and toxic elements such as arsenic (As), cadmium (Cd), mercury (Hg), lead (Pb), and nickel (Ni).

Gallstone disease is a severe health problem that affects millions of people globally. Gallstone production takes years in vivo, and it is difficult to investigate such processes from nucleation to consolidation (1,2). The mechanical irritation of the stones on the gallbladder tissues makes it one of the most painful disorders. Surprisingly, gallstone disease has become more common in children and adults over the last few decades. Adults are the subject of the great majority of reports (2). Gallstone disease is now treated solely by surgically removing the gallbladder. As a result, the disease has a significant impact on children. The primary job of the gallbladder is to concentrate bile by absorbing water and salt. It increases the concentration of impermeable solutes in hepatic bile by a factor of two.

The pathophysiology of gallstones is still unknown. Changes in hepatic bile composition, biliary glycoprotein, infection, age, genetics, sex, oestrogens, dietary variables, geographical distribution, and liver cirrhosis are all factors that may contribute to the formation of gallstones (2–5). Gallstones have a complex chemical composition. As a result, determining the major and trace elements present in the gallstones is critical. On the other hand, toxic elements are known to be exceedingly dangerous even at very low concentrations. Therefore, reliable elemental studies are needed to aid in the clarification and identification of effective treatment and management.

Gallstones of different compositions have a variety of color appearances. Gallstones are mostly comprised of organic components like cholesterol, bilirubin, bile acid, and fatty acid. According to their composition, there are three basic types of gallstones seen in patients: cholesterol type (cholesterol-rich); pigment type (bilirubin and calcium bilirubinate rich); and mixed type, which is the combination of cholesterol and bilirubin (6).

Many studies showed the presence of toxic elements, such as chromium, lead, nickel, cadmium, and arsenic in some of these stones, possibly as a result of people’s exposure to pollution, industrial waste, and smoking. Some research showed that toxic metals, such as chromium, lead, and cadmium, found in drinking water accumulate in the biliary system, eventually leading to gall

bladder stones. The growth in heavy metal toxicity has been linked to the gallbladder and other organ cancers (7). In some studies of gallstones, the authors used some techniques like X-ray fluorescence (XRF) and neutron activation analysis to show that the elements like calcium (Ca), sodium (Na), chlorine (Cl), potassium (K), magnesium (Mg), manganese (Mn), iron (Fe), phosphorus (P), copper (Cu), lead (Pb), titanium (Ti), zinc (Zn), aluminum (Al), nickel (Ni), and chro- mium (Cr) are the main constituents of gallstones (8).

Over the last few decades, a lot of research has been done to see how the accumulation and lack of particular elements in the human viscera cause disease. Many researchers are currently focused more on the elemental analysis of gallstones to detect the constituents and the presence of trace and toxic metal elements to understand their pathogenesis (9–11). For determining major and trace elements in gallstones, several analytical methods have been used, including atomic absorption spectrometry (AAS), particle-induced X-ray emission (PIXE), energy dispersive X-ray spectroscopy (EDX), wavelength dispersive X-ray fluorescence (WDXRF), inductively coupled plasma–optical emission spectrometry (ICP-OES), and laser-induced breakdown spectroscopy (LIBS).

LIBS is a well-known spectrochemical technique based on spectral analysis of radiation released by a micro-plasma created on the target surface by a laser pulse. The relative simplicity of the LIBS principle makes it incredibly appealing for a wide range of applications (1,12). The first analytical application of laser-plasma on surfaces, and therefore the origin of LIBS, occurred in 1962–1963. LIBS has been used in a wide range of applications and has a number of advantages over other well-known spectrochemical techniques. There is minimal or no sample preparation is required in LIBS.

Gazili and others (13) performed LIBS and photoacoustic spectroscopy (PAS) for the compositional analysis of gallstones. They classified the gallstones used in their study based on the organic and inorganic components presents in the samples and discriminate the gallstone samples using principal component analysis (PCA). For the first time, Singh and others (14) performed the variational analysis of gallstone samples using LIBS. They analyzed the variation in elemental composition from the center to the surface of the gallstones.

In numerous applications, including forensic evidence analysis and biomaterial identification, statistical approaches have been applied to analyze spectroscopic data. In some research publications, LIBS and chemometric approaches were used to test the feasibility of some biomaterial identification. Improved use of statistical approaches like PLS-DA is likely to play a big role in LIBS-based biological sample discrimination. PLS-DA is a type of multivariate analysis that identifies and maps interrelationships between data sets.

In the present work, we used LIBS to perform a comprehensive screening of the major and trace elements contained in the gallstone samples. The relative profiling of the com- ponents qualitatively present in the gallstone samples was done using the intensity ratio approach. For a better understanding of the characteristic variation of gallstone samples, the chemometric multivariate approach PLS-DA was applied to the LIBS data.

The gallstone samples were provided by the Department of Nephrology, Opal Hospital, in Varanasi, India, after surgical treatment of the patients. In the present study, five gallstones were used for the investigations. The stones were first washed thoroughly with doubly distilled water to get rid of blood or any other possible impurities and then dried at room temperature. The stones were observed microscopically and found of different colors (as can be seen from Figure 1a–f). During the visual examination, the surface and center portion of gallstones were also found to have a different appearance in color (Figure 1). The center parts were observed to be dark brown or black in coloration, whereas the colors of the surface parts varied, ranging from white to off white to yellow. This shows the different portions of major and minor chemical compositions. The center parts and surface parts of the stones were carefully removed. For convenience, the samples were coded G1, G2, G3, G4, G5, and G6. G5 and G6 represent the center and surface parts of a gallstone. The dried stone samples were crushed into fine powder using mortar and pestle and then analyzed using LIBS, EDX, and FT-IR spectroscopy.

A LIBS experimental setup RT100-EC instrument (Applied Spectra, Inc.) was used to record the LIBS spectra of the various gallstone samples. A laser source, sample stage, spectrometer with detector system, and plasma collection optics were the main components of the arrangement. The stone sample was put on a translational stage, and the plasma was created by focusing a Q-switched Nd:YAG laser operating at 1064 nm wavelength on the sample using a 15-cm focal length lens. The laser pulse energy, pulse repetition rate, and pulse duration were tuned at 17 mJ/pulse, 5 Hz, and 10 ns respectively to produce the best signal-to-background and signal-to-noise ratios. A five-channel charge-coupled device (CCD) spectrometer having approximately a 0.1 nm spectral resolution with 187–887 nm coverage was used to record the data. The size of the laser spot on the surface of the sample was 100 μm in diameter, which was measured by the LIBS instrument T100-EC from Applied Spectra, Inc. For each sample, 20 line scans were taken, and these 20 scans were then averaged to predict our LIBS results and to avoid the fluctuations because of shot-to-shot variation.

The chemical compositions of gallstones were recorded using a Hitachi SU 8010 cold field emission scanning electron microscope (SEM). EDX attachment provided the elemental composition of trace and toxic elements present in the different parts of the gallstone samples.

FT-IR spectroscopy has been used to characterize the gallstone samples. The surface parts of the stones were found rich in cholesterol, and the center parts were found rich in bilirubin using FT-IR spectroscopy. The contents of cholesterol and bilirubin were observed in varying amount in gallstones of different colors, and thus, the stones were categorized as mixed type gallstones.

Relative Concentrations of Elements in Gallstones (G1–G6) Using LIBS

LIBS spectra of gallstone samples (G1–G6) were recorded at optimized experimental conditions in the spectral region 187–887 nm. The spectra were recorded using twenty laser line scans. Identification of the atomic and ionic lines present in the LIBS spectra of gallstone samples were carried out by NIST database (15) and “Identification of Molecular Spectra” by Pearse and Gaydon (16). 

The detected elements were Al, Mg, Fe, silicon (Si), Mn, Ca, K, P, Na, Cu, Ti, strontium (Sr), and Zn.

The intensities of the spectral lines of the elements detected in the gallstone samples were significantly different in different gallstones. The intensity of the atomic emission lines of LIBS spectra was directly proportional to the concentrations of the elements present in the samples and therefore reflect the concentrations of the elements present in the gallstones (17). The relative LIBS concentration ratios were measured and indicated by the bar graph shown in Figures 2a–b. Because Ca is the major element detected in all the gallstones, the Ca line at 396.8 nm has been taken as the internal reference line for comparing the intensities of spectral lines of minor constituent elements in the stones (as can be seen from Figures 2a–b). We have chosen the resonance line of ionic Ca at 396.8 nm for taking the intensity ratio because it is free from the self-absorption effect. It can be seen that the concentrations of elements Fe, Ti, Mn, Al, Na, K, Mg, and Si are different in different stone samples. Figure 4 clearly shows that the concentration variations of these elements.

Gallstones can easily be identified by the presence of molecular Swan bands of C

] present in their LIBS spectra. LIBS spectra of gallstones (Figure 3) show the presence of C

 Swan bands at 468.4, 469.7, and 471.5 nm. The occurrence of C

 swan bands is directly related to sputtering from the cholesterol and possible hydrocarbons present in the gallstones (18).

LIBS Analysis of Center Part (G5) and Surface Part (G6) of Gallstone Sample

We have analyzed the center part (G5) and surface part (G6) of a gallstone sample using LIBS. The typical LIBS spectra of center and surface parts are shown in Figure 3 in the wavelength region 200–225 nm, 278–286 nm, 320–345 nm, and 400–475 nm. It can be seen from Figure 3 that the concentrations of the mineral elements Ca, Zn, P, Fe, Mg, Si, Cu, and Ti were found higher in center part than that of the surface parts. To reduce the shot-to-shot fluctuations, each LIBS spectrum was obtained as the average of 50 laser shots and to ensure the reliability of the LIBS data.

The FT-IR results showed the presence of bilirubin in center parts of the stones than that of the surface parts, whereas the LIBS study revealed the presence of higher level of Cu in center part than that of the surface parts. This clearly shows that Cu in the form of copper bilirubinate plays an important role in the formation of the pigmented parts of the black and brown color (Figure 1, gallstone G5) inside the core region of gallstones. Our finds are well supported by the studies performed on gallstones using the technique UV-visible (UV-vis) and time-of-flight secondary ion mass spectrometry (ToF-SIMS) (19).

Partial Least-Square Discriminative Analysis (PLS-DA) Modeling of LIBS to Distinguish Gallstones 

According to our FT-IR study, we have observed that the amount of cholesterol and bilirubin is different in different gallstone samples and hence, their color is different. Our LIBS studies on gallstones revealed that the concentrations of elements are also different in these different gallstones. Also, in the center part, the elements were observed in higher concentration than that of surface parts. Therefore, the nature of gallstones was found to be heterogeneous. Using PLS-DA modeling of LIBS data, we attempted to classify them based on their elemental composition so that we could distinguish the gallstone based on their elemental composition.

We have performed PLS-DA statistical analysis on LIBS spectral data to model all the outcome variables simultaneously for gathering and interpreting the PLS factors. These PLS factors could be further used to obtain the relevant information about the varying characteristics of different sample groups because of their slightly different chemical compositions. The whole data has been represented by a data matrix 

 which includes wavelengths as variables for the total “

” number of LIBS spectra. It has been modeled for 

 = 10239 wavelengths ranging from 200–900 nm for 

 = 120 LIBS spectra corresponding to each sample groups G1, G2, G3, G4, G5, and G6. The class matrix, or category vector 

, comprised of different categories (G1, G2, G3, G4, G5, and G6) where 

 = 6 stands for the number of sample groups and 

 = 120 denoted the total number of spectral data values taken for each sample groups. The two data matrix 

 are modeled to get the new variables known as latent variables or PLS factors and are relevant to depict the maximum covariance of 

. These newly developed latent variables are found to be linear combination of old variables and are best suited to explain the maximum information of 

The interpretation of PLS-DA model gives two main outputs in the form of score and loading plots. Score plot reflects the clustering of sample groups in different quadrants whereas loading plot specifies the weight age of each variable on the basis of which sample groups cluster themselves in different quadrants of score plot of PLS-DA model. Each and every point or dot appeared in the clustering of sample groups in the score plot represents the variables of 

 data matrix that are best suited for the classification of the 

 matrix. The points or dots which are positioned closed to the sample groups are said to be positively correlated with that much sample group and the points, which positioned themselves near the origin line do not reflect any knowledge about the samples groups and cannot be used for the analysis purpose.

The prepared PLS-DA model can be analyzed by looking upon both score and loading plot simultaneously in which one depicts the grouping of sample groups in the form of variables in different quadrants of score plot and other defined the weightage of each variable in the grouping of different samples groups in score plot. Figure 4 shows the score plot of PLS factors 1 and 2 which can clearly presents the distinction view of the gallstones (G1–G6) based on their relative elemental contents and grouped with the similar ones. By looking into score and loading plots of PLS factors 1 and 2 (Figures 4–5), it has been seen that emission intensities of elements such as K and Na are responsible for the clustered G4 sample group in the last quadrant of score plot (Figure 4). Therefore, the sample group G4 includes the increasing contents of elements K and Na and decreasing contents of other elements.

By looking into both score and loading plots of PLS factor 1 compared to PLS factor 3 (Figure not shown in this article), we concluded about the G1 sample group as it is clustered itself in the first quadrant of the same score plot where both PLS factor 1 and PLS factor 3 are observed positive ones. From the loading plots of the same PLS factor 1 and PLS factor 3 (Figure not shown here), it has been noticed that O and N are the only variables that satisfy the criteria of having both PLS factor 1 and PLS factor 3 as positive ones. This observation indicates that the increasing trends of emission intensities of variables O and N and decreasing contents of other elements are responsible for clustering the G1 sample group in the first quadrant of score plot of PLS-DA. On switching to the G3 sample group in the score plot of PLS factor 1 compared to PLS factor 3, we saw that the G3 sample group clustered itself in the second quadrant where PLS factor 1 is negative and PLS factor 3 is positive. From the loading plot of PLS factor 1 compared to PLS factor 3 (Figure not shown here), it was found that the wavelength of elements such as Ca, Al, Sr, and Mn are having PLS factor 1 as negative and PLS factor 3 as positive. This implies that the increasing content of elements, such as Ca, Al, Sr, and Mn, are responsible to cluster the G3 group in second quadrant of the score plot of PLS factor 1 and PLS factor 3. The same sample group G3 is also clustered in the last quadrant of the score plot of PLS factor 3 and PLS factor 4, where PLS factor 3 is positive and PLS factor 4 is negative. From loading plots of PLS factor 3 and PLS factor 4 (Figure not shown here), it has been found that the emission intensities of elements, such as Ca, Mn, Cn, H, Sr, and Al, are responsible for clustering the G3 sample group. Therefore, the content of elements, such as Ca, Mn, Sr, Al, copernicium (Cn), and hydrogen (H), were found to be more in the G3 sample group than other sample groups. The sample group G2 is found to be clustered in the last quadrant of the score plot of PLS factor 2 and PLS factor 3 (Figure not shown here), where PLS factor 2 is positive and PLS factor 3 is negative. From the loading plot of the same PLS factor 2 and PLS factor 3 (Figure not shown here), it was found that only the wavelengths of elements, such as the C2 band, satisfied the similar criteria, and their increasing trends in G2 make it clustered in the last quadrant of PLS factor 2 and PLS factor 3. In a similar way, the behavior of the center and surface parts of sample groups G5 and G6 have also been predicted by ana- lyzing the score and loading plots of PLS factor 1 and PLS factor 4 (Figures not shown here).

The behavior of sample groups can also be interpreted by looking over the spotted areas of points along their aligning directions. If we assume gridlines 

 = 0 as imaginary lines, then the alignment of the sample groups in different quadrants will give us idea about how close the behavior of sample groups are on the basis of their similar characteristics. The same alignment of the two sample groups has been seen in score plot of PLS factor 1 and PLS factor 3, in which the G3 sample group is clustered in the second quadrant and sample group G2 is clustered in the last quadrant. This alignment of sample groups indicates the idea about their inverse behavior (that is, the variables that are found to be more in the G3 group, such as CN, Mn, Ca, Mg, H, Sr, and Al, are found to be least in the G2 sample group).

The validity of the prepared PLS-DA model has been examined by the classification accuracy of the model. The whole LIBS spectra have been divided into two groups in which one is for training the model and other is for testing the model. This model has been calibrated by considering 20 × 6 = 120 spectral values and tested by randomly choosing 5 × 6 = 30 data values. The leave-one-out (LOO) method was adopted for the cross-validation of the prepared PLS-DA model. The prediction accuracy has been plotted as a function of number of PLS factors included in the model and shown in Figure 6. It has been noticed that PLS factors 1–10 are sufficient to discriminate all the six sample groups (G1–G6) with the explained variance of approximately 96% shown in Figure 7. Therefore, we can conclude that based on the PLS-DA modeling of LIBS data, the different colors of gallstones samples were successfully discriminated based on their relative elemental contents, which are responsible for stone formation and color appearance. This kind of discrimination is not possible by other elemental analysis techniques, which proves the utility of chemometrics coupled with LIBS techniques.

EDX Analysis of Centre and Surface Parts of Gallstones

To verify our FT-IR and LIBS experimental data and also to quantify more numbers of heavy and toxic elements in gallstones, different parts (center as well as surface) were analyzed using the EDX technique. Different scans (scan 1 and scan 2) at two locations at the center and surface parts were carried out using EDX. The concentration (wt.%) of the heavy and toxic elements observed in center and surface parts are tabulated in Table I. The heavy and toxic elements detected were As, Cd, Pb, Hg, Sr, Ni, Cu, and Zn. From Table I, it can be seen that the concentrations of the elements at different locations (center as well as surface parts) were quite different, which indicates the heterogeneous distributions of the elements throughout the gallstones. For example, Sr has been observed in center region, which is absent at the surface parts during scan 2. Mercury (Hg) and nickel (Ni) were only observed in center region and absent at surface region. Overall, it has been found that the concentrations of the elements are higher in center part than that of surface parts, which is in good agreement with the LIBS elemental concentration of Ca, Mn, P, Cu, Zn, and Fe. Our findings are in good agreement with the results reported on gallstones using other techniques such as WDXRF and ToF-SIMS (10,19,21).

The main organic elemental composition of gallstones as observed by EDX was carbon (C), oxygen (O), and nitrogen (N), which shows the presence of cholesterol and bilirubin in gallstones and which have been detected using FT-IR spectroscopy. Hydrogen is not detected by EDX because hydrogen has no core electrons (20). The EDS analysis revealed that the gallstones contained 91.10% C (wt.%) and 4.49% O (wt.%). Nitrogen was present in the core region of gallstones and was absent from the surface parts. The presence of N indicates the presence of bilirubin in the core region and responsible for the black/brown color of core region. The ratio of carbon to oxygen (C:O) was 20:28, which coincides with pure cholesterol (C

O) composition after omitting the hydrogen (that is, C (83.1%)/O (4.14%) = 20.07.

The characterization of gallbladder stones using the fast and reliable techniques EDX and LIBS are advantageous compared to the traditional chemical analytical methods. The presence of cholesterol was confirmed using FT-IR spectroscopy as the major chemical constituent in gallstone. In addition, bilirubin, calcium carbonate, and calcium phosphate were also noticed in gallstones. Elemental analyses of gallstones were carried out using LIBS. The chemometric method PLS-DA coupled with LIBS data were successfully used to discriminate the gallstones under present study. EDX was used to analyze the heterogeneous distribution of heavy and toxic elements throughout the gallstones and data were well correlated with the LIBS data. High contents of heavy and toxic elements in the core region suggested the nucleation and growth of gallbladder stones. In conclusion, it is recommended that foods having high amount of cholesterol, low-fiber diets, and contaminated water intake having heavy and toxic elements should be avoided to minimize, which prevents the formation of gallstones.

Author V.K. Singh is much thankful to UGC-DAE CSR Kolkata Centre for partial financial support. Authors V. Bali, Y. Khajuria, N. Sharma, and V. K. Singh are also grateful to SMVD University, India, for providing the necessary facility and support.

(1) Singh, V.K.; Singh, V.; Rai, A.K. et al. Quantitative Analysis Of Gallstones Using Laser-Induced Breakdown Spectroscopy.

Understanding gallstone formation requires examining their elemental composition. Here, EDS and LIBS were used with PLS-DA to quantify elements found in human gallstones.

October 2023

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