The use of proficiency tests (PTs) in an analytical inorganics laboratory is an essential part of assuring clients the laboratory is producing accurate results. In the first part of this two-part series, we examined the ways in which contaminants can alter the results in a detrimental fashion in regard to proficiency testing and laboratory audits. In Part II, we examine the actual planning, running, and reporting of a PT scheme and the possible impact of error and contamination.

A proficiency test (PT) scheme does not start only upon opening the ampule or bottle to test the sample. The steps that lead up to the actual testing can play an important role in the success or failure of a testing scheme. As was discussed in the previous column, standards, calibrations, and maintenance are all important components in reducing error and contamination even before the first sample is placed on the instrument. Once the laboratory and all its contributing standards and equipment are ready, it is time to turn the attention to the actual PT sample.

The proper handing and processing of a PT sample can be critical in passing a PT test. For calendar-based PTs, one needs to check for shipping dates and delays, which could affect the quality of the PT. Upon receipt of the PT sample, open the package and check its condition. Report any damage to samples or if they have been thermally compromised. The first step after receiving and accepting the PT shipment is to check all of the handling and safety instructions to ensure that the samples are kept at their optimal conditions.

Some materials may require temperature control whereas others may have instructions on how to handle the sample during preparation or give information regarding the possible range of values for the PT. Once the PT is in-house, fresh chemicals and standards should be prepared and all calculations should be rechecked. Check PT instructions for methods and report results (that is, online, by phone, or by mail), and the correct reporting formats that are acceptable (that is, correct weight or concentration notations).

Take special note of any sample preparation procedures or method notes that are to be employed with that PT scheme. Any differences between your normal sample preparation and the PT preparation and analysis should be discussed with the quality manager. Otherwise, all differences in sample preparation because of the matrix or material should reveal the deviations or additions to prepare the sample that differ from routine preparation.

Once a PT has been analyzed, the data is reported back to the PT provider for analyses and final acceptance. The PT provider often has multiple methods for evaluating the data based on the type of PT that is being analyzed and the governing bodies under which the PT scheme is intended. Some accreditation or standards organizations offer documentation and tables for the reporting of PT results, whereas other PT results are entered into programs to create results from programmed algorithms and statistics.

ISO guidelines (ISO 13528) have two basic methods for the statistical evaluation of proficiency tests: the 

-value is most commonly used in interlaboratory comparisons where the laboratories report their uncertainty calculations (equation 3).

-value between 1 and -1 are considered successful and in agreement with the reference values. Results with 

-values greater than one or less than -1 are considered not successful and disagree with the reference values, which should trigger a corrective action.

-score can also be conducted within interlaboratory comparisons without an uncertainty calculation, but the 

-score assumes all samples reported are from the same population, batch, or sampling; therefore, all samples have the same uncertainty. The most practical of the statistical functions for chemical and biological analyses is the 

The results are calculated after the outliers are removed or are obtained from robust statistics. 

-scores less than two are considered successful and in agreement with accepted values. Scores between two and three are considered suspect whereas scores greater than three are unsuccessful and disagree with the accepted results.

Once scores are compared against the reference values and are assigned passing or failing scores, those scores are reported to the laboratories. Scores can either reflect individual scores for individual analysts or they can reflect the overall laboratory proficiency. In many cases, one unsuccessful score does not necessarily mean that the entire laboratory fails the PT scheme. One or more assessed failures in key practices or tests can cause a laboratory performance to be deemed unsatisfactory or multiple failures submitted in one PT round. Multiple consecutive failures for an analysis can also result an unsatisfactory rating. Results of a particular analysis may be deemed suspect if a clear bias or trend towards unsatisfactory results is apparent, including consistent bias over one standard deviation above or below the assigned values. Even if the results themselves are passing, the PT results can be considered unsatisfactory if there is a clear and measured bias. All failures or unsatisfactory results should be directed towards root cause analysis and corrective actions as dictated by that laboratories’ quality management system (QMS).

In the event that an analyst or laboratory fails a PT test, there should be a procedure for a comprehensive review of the processes, preparation, and analyses involved, along with a plan of action to correct the problems found. First, a root cause analyses is conducted to identify and document the problem. Then, a decision is made whether the problem was because of an error or a systematic defect that needs to be corrected. In cases of error, a full corrective action may not be required, but instead, a retraining for that analyst or laboratory. If a root cause analysis finds deficiencies within a system, then a corrective action is devised to remedy the issue. A retesting of a corrected system must be conducted to determine if the correction was successful.

Some of the points of review should include the laboratory processes and all internal quality control data. Points to reexamine during a system and procedure review for a PT failure include:

Sample storage and handling—were all requirements met?

Preparation—did the preparation process differ between normal samples and the PT samples?

Instrumentation and equipment—does the deficiency lie within the system, and can it be corrected with replacement, repair, or recalibration?

Environment—were all materials and equipment kept at the correct temperature?

Controls—were all the standards, QC samples, and controls within expiration? Were samples and standards prepared fresh or were new standards opened?

Calibrations—are all the dilutions correct and within the correct dynamic range for the system? Were all the calculations correct and documented including unit conversions?

Are there sources of contamination that may have caused the deviation in results?

Sources of Laboratory Contamination and Error

It is hard to imagine that such tiny amounts of contamination can dramatically change laboratory values. In most cases, the root of that contamination can be traced to a common source. The most common sources of contamination, in addition to the previously discussed volumetric labware, are water, reagents, laboratory environment, and personnel.

Water is one of the most basic yet most essential laboratory components. There are many types, grades, and intended uses for water. Inferior quality water can cause a host of problems from creating deposits in labware or inadvertently increasing a target element or element concentration in solution.

The actual type of water produced by a commercial laboratory water filtration system can vary in pH, solutes, and soluble silica. Critical analytical processes should always require a minimum quality of American Society for Testing and Materials International (ASTM) Type I water. All trace analysis should be conducted with the highest purity water. Analysts who use certified reference materials (CRMs) and perform quantitative analysis need to use quality water to prevent contaminating their CRMs, standards, PTs, and samples with inferior quality water.

Another source of contamination are all the chemicals used in sample processing. Just as in the case of water, there are several types or grades of chemicals, reagents, acids, and solvents. Some designations are set forth by standards set by national or international organizations other types or grades of material are designated by individual manufacturers based on intended use. Some grades are general laboratory grades with intended use for noncritical applications, whereas other grades high in purity and low in contaminants are designated for more critical analyses.

For example, consider acids, which by their very nature are oxidizers and many of the strongest acids are used in the processing of samples for inorganic analysis. Common acids in digestion and dissolution, such as perchloric acid, hydrofluoric acid, sulfuric acid, hydrochloric acid, and nitric acid, are commercially available in several grades from general laboratory or reagent grade to high purity trace metal grade. Acid grades often reflect the number of distillations the acid undergoes for purification before bottling. The more an acid is distilled, the higher the purity of the acid. These high purity acids have the lowest amount of elemental contamination but can become very costly.

To reduce contamination, it is recommended that high purity acids be used to dilute and prepare standards and samples when possible. In addition to using pure acid, it is important that the chemist check the certificate of the acid under analysis to identify the elemental contamination levels present in the acid.

All laboratories believe they observe a respectable level of laboratory cleanliness. Most chemists recognize there are inherent levels of contamination present in all laboratories. A common belief is that the tiny amounts of environmental and laboratory contamination cannot profoundly change the analytical results. Spex conducted a test where nitric acid was distilled in both a clean room and a normal preparation laboratory. The nitric acid distilled in the regular laboratory had considerable amounts of aluminum, calcium, iron, sodium, and magnesium contamination not found to the same degree as in the clean room.

Laboratory air also can contribute to the contamination of samples and standards. Common sources of air and particulate matter contamination are from surfaces and building materials. Surface contaminants can be found in dust and rust on shelves, equipment, and furniture. Dust contains many different earth elements such as sodium, calcium, magnesium, manganese, silicon, aluminum, and titanium. Dust can also contain elements from human activities (Ni, Pb, Zn, Cu, and As).

Laboratory personnel can add their own contamination from laboratory coats, makeup, perfume, and jewelry. Many other common elements can be brought in as contamination from personal care products. Even sweat and hair can cause elevated levels of sodium, calcium, potassium, lead, magnesium, and other ions. If a laboratory is seeing an unusually elevated level of cadmium or other heavy metals in the samples, it could be from cigarettes, pigments, or batteries. If the levels of lead are out of range, contamination can be from paint, cosmetics, and hair dyes (Table II).

Even with clean laboratory practices in place, erroneous results can often find their way into sample analysis. To eliminate some of these spurious results, replication of blanks and sample dilutions can be employed. The blank results should be averaged, and the sample run or PT values can either be minimally selected or averaged. The difference between the two values can then be plotted against a curve established against two more standards. A minimum of two standard points can be used if the chance of contamination is minimal, such as in the case of rare or uncommon elements. Additional standard points should be considered if the potential for contamination is high with common elements, such as aluminum, sodium, and magnesium. Multiple aliquots of blanks and dilutions can also be employed to further minimize analytical uncertainty.

As we have discussed, PTs are a necessary and helpful tool in the QMS system arsenal of a laboratory; but they do have limitations and misuses. In PT schemes where interlaboratory tests are used to establish values, there is often a retrospective aspect to the tests. These tests take time and have very time-critical periods for analyses in order for the results to be included in the data set. In many cases, the PTs available only include a small subset of analytes or matrices that a laboratory will analyze on a routine basis, meaning only those types of samples or target analytes are covered by the PT, whereas the others remain unmonitored.

There are often routine samples or analyses not reflected by the PT schemes either because the PT available is in a different sample format or matrix than the one routinely evaluated. For example, if a laboratory tests pesticides in plant extracts with alcohol-based matrices (for example, tinctures), but the PT is pesticide in oil extract or plant material, then the PT doesn’t completely reflect the state of the preparation routine to that laboratory.

Another problem or limitation of a PT is that it only indicates when a problem is present but does not provide any information in regard to the root cause of the problem. PT should not be used as a substitute for quality controls within a laboratory. Conversely, a successful PT study result does not indicate competence in other laboratory areas of testing.

PTs serve to measure the ongoing proficiency of independent laboratories through interlaboratory comparison of test results for the same characterized material. PT participation is often stipulated by the regulatory authority overseeing laboratories operations or an accrediting body to which laboratories comply, or sometimes both authorities concurrently. It is best to consider the laboratories accreditation goals and regulatory requirements when determining the schedule and budget for PTs participation. It is best to perform PTs at least annually to monitor laboratory performance during a twelve-month period. Longer stretches without PTs participation could negatively impact timely identification of nonconformance and delay implementation of effective corrective action. PTs are useful as tools to verify continuous improvement, resolve or monitor effective corrective actions, and demonstrate training and competency for laboratory analysts. PTs are a multipurpose external quality assessment tool and should be an integral part of the laboratory QMS.

(1) International Organization for Standardization. (2010). 

Conformity Assessment – General Requirements For Proficiency

(2) International Organization for Standardization. (2017). 

General Requirements For the Competence of Testing and Calibration Laboratories

. www.usp.org/proficiency-testing (accessed June 2022)

(4) NSI Laboratory Solutions, Proficiency Testing. www.nsilabsolutions.com/proficiency-testing/ (accessed June 2022).

(5) Spex CertiPrep Webinar, Clean Laboratory Techniques. https://www.spexcertiprep.com/webinar/clean-laboratory-techniques (accessed June 2022).

(6) American Society for Testing and Materials. (2018). 

(7) Spex Knowledge Base for white papers on dilutions, calibrations, and standards. www.spex.com/KnowledgeBase/AppNotesWhitepaper (accessed June 2022).

Articles

Column: Atomic Perspectives

Understanding the proper ways to plan, run, and report proficiency tests will help you avoid errors and contamination.

A Look at Inorganic Analyses, Proficiency Tests, and Best Practices, Part II

In this column, we begin to examine variations of the multiple linear regression (MLR) algorithm that confer special properties on the model the algorithm produces. We also present a critique of the use of derivatives in calibration models and some “real world” validation of a topic we discussed previously.

As promised (or threatened?) in our previous column on the topic of data transforms, we examine transformations of spectral data that have the goal of improving calibration performance. Here, however, not all transformations are designed to produce that result specifically, although that often occurs subject to the algorithm used. Similarly, although 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 used. This column is based on the talk given at the Gold Medal Award session when that award was presented to your columnists (1).

The need for data transformations did not develop in isolation. Nobody sat down one day and mused “Gee, I wonder if I could change these spectra I collected from my samples into other spectra, and what would happen if I did?” In isolation, such musing is pointless. Rather, the need or desire to change, or modify the spectra in a set, mainly grew out of the desire to improve analytical calibration performance and the need to be able to transfer calibration models between instruments and have them perform adequately well on the instrument to which the model was transferred. A particular need was for a calibration model to give the same answer when the same sample was measured a second time even when the sample was “repacked” (that is, removed from the sample holder and then replaced in it). The typical behavior of samples under those conditions is presented in Figure 1.

Thus, the question of data transformation is a subset of the questions revolving around the issues dealing with calibration transfer. We discussed the topic of calibration transfer previously and listed the various ways that goal can be (and has been) discussed by ourselves (2–8) as well as others. A good sampling of these methods can be found in the various “Theory and Application” articles referenced in the literature (9).

The ability to transfer calibrations between instruments certainly requires the hardware to be compatible, and we previously discussed that requirement as well (4,5). The reader also needs to consider the work done by Peter Griffiths (described in a later column of this subseries), wherein he explains how to convert spectra measured on an Fourier transform infrared (FT-IR)-based spectrometer to the equivalent spectra that would be obtained from a dispersive spectrometer, and vice versa.

However, the long history of calibration transfer when applied to near-IR (NIR) data indicated that having the hardware matching between two instruments is not always sufficient to ensure that a calibration developed on one instrument will perform comparably when used in conjunction with a different instrument, even one of the same make and model. One reason why that may occur is explained in our previous column (10). However, the figure in that previous column also illustrated a different point—when the data are highly correlated, the performance of almost any calibration model can be equivalent despite the wide differences of the actual calibration coefficients. It even becomes unclear as to whether the calibrations are “the same” or not. For this reason, data transforms are sometimes applied so that not only the calibration models perform similarly, but that they will do so when the models utilize the same (or nearly the same) calibration coefficients.

To avoid belaboring this issue, we concentrate on various data transformations that have been developed and applied, both by ourselves and other scientists. We avoid including the “derivative” transform (d

), the most common data transform used in NIR practice for several reasons. One reason is that this transform has been extensively discussed, both by others and by ourselves. We also avoid extensive discussion of the basic multiple linear regression (MLR) calibration algorithm for the same reason (11–20). Several chapters (4–7, 21, and 55–59) in the eponymous book based on this series of columns also discusses this derivative transform extensively (21).

Another reason is that, as the title of this column indicates, we are concentrating on data transforms that are used in conjunction with instruments that measure spectra at a limited number of discrete wavelengths (that is, interference filter-based instruments). Derivative transforms are not suited to such data because the use of a limited number of discrete wavelengths limits how closely together the wavelengths can be. Therefore, this occurrence forces the algorithm to violate the fundamental operation required by the definition of a “derivative”, that Δ

The whole concept of describing “derivatives” in connection with measured spectroscopic data is fraught with complications. Although never discussed in the chemometric literature or in the spectroscopic literature, the mathematical definition of a derivative is:

When applied to actual measured data that are typically digitized values from the measurement by an instrument, however, Δ

, for that matter) can never be zero, and the mathematical operation of taking the data to the limit of lim Δ

→0 can never actually be performed because in digitized data, there must always be a minimum difference of at least one digital bit between two successive numbers. However, the mathematics community has examined the issues that arise when data is digitized. One fundamental issue that needs to be dealt with is nomenclature: the term “derivative” should not be used in conjunction with digitized data. The mathematics community has replaced the term “derivative” (and “differential equations”) with the more accurate terms “differences” and corresponding “difference equations” (22) when digitized data is being considered. The spectroscopic and chemometric communities would do well to follow that lead.

Other Problematic Issues in Using “Derivatives”

One of the first things we learned about derivatives in calculus I after the basic concept and nomenclature was the property of the derivative that, if the data is multiplied by any constant, then the derivative of that data is multiplied by the same constant. In itself, this rule is not a problem because a computer will make the correct calculation for the data given, but when a “derivative” data transform is applied to a set of NIR calibration data, then the common claim that the “derivative” data transform “corrects for offset and scale differences between spectra” becomes inaccurate. “Scale” differences would automatically be included in the computation of the calibration coefficients.

A more serious problem arises when automated search algorithms are used to select the wavelength and the Δ (wavelength) representing the intended “derivative.” Because the underlying absorbance bands are usually nonlinear functions of the actual physical properties they are intended to represent, the application of linear mathematical algorithms introduced errors into the results obtained. These errors would typically be small, but we never really know in any particular case how severe this effect would be. For example, we would like to think that doubling the Δ (wavelength) would double the computed “derivative” (or at least the numerator term, especially in those software packages that do not perform the division by Δ

), but this outcome rarely occurs. We examined this situation in the past and presented the results (12–16), which showed that the accumulation of errors included the creation of artifacts (artificial spectral features that do not represent any actual physical phenomena).

Computing a calibration model based on “derivative” (actually difference) values produced a model that is effectively the same as a restricted version of MLR that is no longer a true least squares model that would be obtained from the original spectral data. Let us see how this comes about: Let 

 represent the various original spectral readings, and the corresponding model 

. If, instead of computing a model based on the original data values, we convert the original spectral data to their differences (

), the resulting model for the differences becomes:

 are the differences of the original spectra data, this equation is actually equal to:

or, upon expanding the parenthesized terms:

Therefore, the calibration model expressed by equation 3 can be seen to have the same nominal form as a true least squares model, but it is not a true least squares model because the coefficients of 

 are restricted to being the negatives of the coefficients of 

. Therefore, they do not attain their true least squares values. Thus, we can expect that a model based on differences would be less accurate than a true least squares model; therefore, one would be better off to perform MLR on the original spectral data.

A common template followed by many modern applications papers is to collect data, perform calibration and validation calculations with and without the application of a hypothesized “repack correction” algorithm, compute the standard error of predictions (SEPs) corresponding to the two sets of calculations, and, if the SEP corresponding to the use of the repack correction algorithm is smaller than the SEP obtained without that “correction,” conclude that the “correction” is in fact performing its intended function. There are several problems with this scenario, any of which could negate the validity of the procedure.

SEP is indeed an important statistic for evaluating calibration performance, but it is being misused and misinterpreted when applied to the individual pieces of variance that contribute to the total error (such as the repack error). Because repack represents only a small fraction of the total error, true changes in the value of the error because the application of a “correction” procedure can be easily overwhelmed by changes in other (larger) error sources in the overall procedure, which can lead to false conclusions regarding the role of the correction procedure.

A better approach is to collect appropriate data and use the statistical procedure of analysis of variance (ANOVA) to directly calculate the contribution of repack variation (error) to the Total Error Sum of Squares of the calibration process, which can be done without and with the use of the correction procedure. The ANOVA would then directly provide values for the repack error that can legitimately be compared. However, this comparison is not a simple “is A > B?” comparison. Because this procedure involves the comparison of variances, a statistical 

-test is necessary to properly compare the variances and determine if the procedure using the “repack correction” provides a statistically significant decrease in the repack error compared to the value obtained without the correction.

A still better approach is similar to the one above, but instead of calculating the contribution to the total error of the calibration, it is only necessary to determine the change in the readings when a sample is repacked. These changes can be averaged over the samples in the sample set (watch out for the signs of the changes for each sample!) again, with and without the correction procedure. This procedure is preferred because it can be performed using the statistical 

-test. Again, no conclusion can be drawn unless the reduction in the amount of repack variation is statistically significant.

We’ve decided to not discuss the most popular and common data transform and (arguably) one of the most common calibration algorithms. We will find out what that calibration algorithm is beginning in our next session, where we will start to examine alternate data transform methodologies including an algorithm that will make an MLR model based on data with special characteristics immune to the effect of repack.

For starters, even though we did not discuss the MLR algorithm itself, there are a large number of algorithms based on variations of the MLR algorithm. These variations give the resulting calibration model special properties in addition to the least squared error property that the basic MLR algorithm provides. In the following discussions, 

 is the absorbance of ith ingredient at the 

 is the concentration of the analyte, and 

Where and how and why does this arise? Statisticians have examined this case in detail, a good example discussion can be examined in chapter 19 of reference (23), dealing with mixture designs of experiments, particularly on pages 409–414. Mathematically, this forces the model to pass through the origin of the coordinate system. The authors point out that, because the sum of the ingredients in a mixture always equals 1 (unity), the dimensionality of the data from a mixture is always at least one fewer than the number of ingredients. Because of this rule, one cannot simply model the response variable (the constituent in an MLR model) using the compositions or, equivalently, an optical measurement representing those ingredient compositions, which is because of the fact that σ (ingredients) = 1 creates a perfect intercorrelation between the ingredients. Therefore, attempts to perform MLR on such data will inevitably result in a divide-by-zero error when performing the matrix inversion operation during the calibration.

One obvious way to break the intercorrelation between the ingredients is to leave one of the variables out of the calculations. This strategy will succeed (unless the data contains some other correlations between two or more of the remaining ingredients), but has some drawbacks:

The calculations cease to be objective. Particularly at the beginning of a study, there are no objective ways available for guidance as to which ingredient (or ingredients) to omit, and then the choice of which ingredient to leave out of the calculations becomes subjective.

The ingredient removed from the calculations may be a key predictor variable, so that removing its contributions to the data set will result in suboptimal results.

To avoid the issue raised by the previous point (b), it will become necessary to perform trial calibrations, wherein each of the ingredients is successively removed from the data set, which would require increasing the amount of computation by a factor of at least 

 is the number of ingredients in the mixture.

Draper and Smith (23) present an extensive discussion of this situation and propose that instead of removing any of the variables representing the ingredients from the calculations, the mathematics of the least square approach should be modified to remove the constant term from the model; that is, instead of the model being expressed as:

This change was not completely original to Draper and Smith but represents the consensus of the statistical community at that time.

Note that equation 5 is not simply equation 4 with the 

 term erased. It certainly looks like that, but the difference can be better appreciated by considering the normal equations from the two different approaches. The normal equations resulting from equation 4 (standard MLR) is:

In shorthand matrix notation, solving equation 6 for the values of the coefficients is expressed by the equation:

while the normal equations resulting from equation 5 (missing 

Interestingly, solving equation 8 for the coefficients results in the same matrix equation:

as for the previous conditions. The differences come from the construction of the equations (and matrices) themselves, to start with.

Equations 7 and 9 both come from performing the same operations on their respective models: they compute differences between the actual and predicted values from the model, sum the squares of the differences, then take derivatives with respect to each variable, and set the derivatives equal to zero. However, by eliminating the constant term, the matrix on the right-hand side of equation 8 loses an entire row and column compared to equation 6. Thus, even though what remains is the same as in equation 6, there is a whole group of computations that are not performed when the matrix is inverted, which affects all the subsequent results. Thus, the result of eliminating these computations cannot be replaced simply by eliminating 

 from equation 1. The reason is that including the otherwise omitted computation results in different values for all the coefficients other than 

The formation and properties of least squares models without 

 is discussed extensively in the statistics literature (23) as well as in the NIR literature (see Chapter 12 in (24)), a book on which some of this discussion is based). Here, we present it simply as another alternative way to calibrate NIR spectrometers. We think it is one of the many explorations performed by the early NIR practitioners and, although ignored, is worthy of further examination by the NIR community like in the case of several of the algorithms we examined here. In our next column on this topic, we will present and discuss another “simple” variation of MLR by adding the requirement that 

Several years back, we wrote a series of columns examining classical least squares (CLS) analysis of liquid mixtures, culminating in a study where we demonstrated that volume fractions were the proper units in which to measure concentrations to use when calibrating spectroscopic instruments used for quantitative analysis of liquids (25). These results were also published in the formal literature (26) as well as Chapters 90–100 and 107–111 in the eponymous book (21). In these publications, we also conjectured that the use of volume fractions as the measure of “concentration” was also the solution to the “mystery” of the nonlinearity of Beer’s law. It has been well-known since the time that August Beer declared that absorbance was proportional to concentration that the relationship was true only for low concentrations of a solute (and correspondingly low values of absorbance), and that departures from that proportionality were observed when the concentration exceeded a defined threshold (which depended on the solute). Our conjecture, which was based on the additional fact that the various units that chemists used to express concentration (molarity, molality, weight fraction, mg/mL) are not all linearly related to each other, was that the same effect (use of an incorrect measure for “concentration”) was also the cause of the nonlinearity observed when various solutions were measured spectroscopically, and that use of volume fractions as the concentration measure should correct the nonlinearity observed in this situation as well. This conjecture was investigated by a group of European scientists (27), who confirmed that expressing “concentration” as volume fractions provided a graph with a linear relationship between concentration and absorbance, and other measures of concentration resulted in a nonlinear relationship. Additionally, Thomas Meyerhofer has studied and published extensively concerning the optical behavior of liquid mixtures, with a view to relating that behavior, and the linearity of the relationships to underlying fundamental physical properties (index of refraction, polarizability) of the ingredients as well as extensive previous work (28–30; in reference [30], Meyerhofer demonstrates that Beer's Law follows from the fundamental physics when concentrations are expressed as volume fractions).

NY/ NJ Section of the Society for Applied Spectroscopy Gold Medal Award

 (accessed May 2022). https://eas.org/2020/?p=5502

(9) E.W. Ciurczak, B. Igne, J. Workman Jr., and D.A. Burns, eds., 

Handbook of Near-Infrared Analysis, Fourth Edition in Practical Spectroscopy Series

 (CRC Press imprint of Taylor & Francis Group, Boca Raton, FL, 2021), pp. 808.

 (Elsevier, Amsterdam, The Netherlands, 2nd ed., 2018).

 (Addison-Wesley Publishing Co., Inc., Reading, MA, 1st ed., 1963).

 (John Wiley & Sons, New York, NY, 3rd ed., 1998).

 (CRC Press; Boca Raton, FL, 4th ed., 2021).

(26) H. Mark, R. Rubinovitz, D. Heaps, P. Gemperline, D. Dahm, and K. Dahm, 

(27) H.Y.M. Yan, Z. Xiong, H. Siesler, L. Qi, and G. Zhang, 

(29) T. Meyerhofer, S. Pahlow, and J. Popp, 

(30) T. Meyerhofer, I. Oleksii, A. Kutsyk, and J. Popp, 

Columns: Chemometrics in Spectroscopy

We examine variations of the multiple linear regression (MLR) algorithm confer special properties on the model that the algorithm produces and critique the use of derivatives in calibration models.

Data Transforms in Chemometric Calibrations: Simple Variations of MLR, Part 2

The contents of Pb, Hg, As, Cr, Fe, Cu, Ba, and Cd in five traditional Mongolian medicines (Garidi-5, Susi-7, Yihe-12, Zadi- 5, and Alatanaru-5) were determined by X-ray fluorescence (XRF) spectroscopy. The results were compared with those obtained by inductively coupled plasma–mass spectrometry (ICP-MS). According to the fundamental parameter (FP) approach in XRF, the response signal value was converted into the element content value using computer software. The method was stable and fast, not requiring pretreatment processes. When the content of metal elements was below 2.0 mg/kg, the relative standard deviation (RSD) of the precision test was between 5.49–20.0%. When the content was above 2.0 mg/kg, the RSD of the precision test was less than 4.96%. The limits of quantitation (LOQ) of As, Cd, and Pb were all below 0.1 ppm, the limits of quantitation of Cr, Cu, Ba, and Hg were below 1 ppm, and the limit of quantitation of Fe was 1.525 ppm. The standard addition method was used in the accuracy test, and the recoveries of the other seven elements were all within 85–130% except Hg. Because Hg was easy to volatilize, the recoveries were low but above 68.4%.

Mongolian medicine is the crystallization of Mongolian traditional nomadic culture, which was created, accumulated, and selected by the Mongolian people in the long-term practice of fighting against nature and disease for thousands of years. As one of the four major minority medicine systems in China, Mongolian medicine has an unique style (1). Garidi-5, Susi-7, Yihehari-12, Zadi-5, and Alatanaru-5 are commonly used in Mongolian medicine. Garidi-5 (2) comes from what is known as the “Four Medical Classics.” It is composed of musk, processed 

. Susi-7 (3) also comes from the “Four Medical Classics,” which is comprised of bear gall, 

. Yihehari-12 (4) is comprised of 12 herbs, including black ice flakes, Digda, Elecampane (

Rhizoma nardostachyos (Nardostachys jatamansi)

 (dried cattle gallstones). Zadi-5 (5) comes from the classic work 

. Alatanaru-5 (6) comes from the classic works of Mongolian medicine, such as 

Study of Mongolian Medicine Prescriptions

), trogopterori faces extract powder, and black ice flakes. Mongolian medicine is good at using animal medicine, mineral medicine, or animal medicine and plant medicine after calcination and processing, such as black ice flakes, trogopterori faces, Gypsum fibrosum, beef gall powder, bear gall, processed 

, and processed wood turtle seed. These factors increase the chance of introducing heavy metal elements harmful to the human body into drugs. In recent years, the development of Mongolian medicine has been affected by many aspects, including the low quality standard of Mongolian medicine, and its safety and effectiveness can not be guaranteed scientifically and systematically (7). The detection and quantitative analysis of heavy metals in Mongolian medicine is an important guarantee for medication safety. In modern Mongolian medicine production and processing, because of the production technology, processing technology, origin environment, and other factors, the heavy metal content is easy to exceed the standard. This study showed the difference between the XRF method and inductively coupled plasma–mass spectrometry (ICP-MS), with the results revealing that XRF spectroscopy was fast, accurate, and simple, making it the more effective method in controlling the limit of heavy metal elements in Mongolian medicine.

In recent years, as more precision scientific instruments are used in the quality research of drugs, new methods for determining heavy metal content emerge. The most commonly used methods are ICP-MS (8–11) and atomic absorption spectrometry (AAS) (12–14). However, ICP-MS requires that the must be digested first, which may lead to incomplete digestion and error, and the digestion conditions need to be accurately controlled, so the operation is difficult. AAS cannot carry out multielement analysis at the same time, and the light source must be changed when determining specific elements, which greatly reduces the efficiency of analysis. The X-ray fluorescence (XRF) method is favored by analysts because of its nondestructive analysis, simple sample preparation, environmental friendliness, and fast analysis speed. It has a broad application prospect in the quality control of heavy metals in ethnic medicine. In this study, we used high sensitive XRF combined with a fundamental parameter (FP) method to analyze eight heavy metal elements, such as lead, mercury, arsenic, chromium, iron, copper, barium, and cadmium in five traditional Mongolian medicine prescriptions, including Garidi-5 (GRD-5), Susi-7 (SS-7), Yihe-12 (YH-12), Zadi-5 (ZD-5) and Alatanaru-5 (ALT-5). The results were compared with those obtained by ICP-MS, and the applicability and feasibility of XRF method was verified.

A Phecda-He XRF spectrometer (Beijing Ancoren Technology Co, Ltd), an Angilent 7900 ICP-MS instrument (Agilent Technology Co., Ltd), a MARS6 microwave digester (CEM), a Milli-Q Ultrapure water machine (Millipore), and a tablet machine (Tianjin Keqi Hi Tech Co., Ltd) were used for this study. Boric acid was also used as the analytical reagent.

The Boric acid edge pressing method was used by measuring approximately 4 g of the Mongolian medicine sample powder (all fine powder passing through 60 mesh sieve) into the grinding tool and pressing the tablet with the boric acid edging method. The pressure was set at 20 MPa, the pressure holding time was 60 s, and the sample diameter was 30 mm. Figure 1 shows what the Mongolian sample powder looked like after sample preparation was completed.

Because the excitation energy of different elements was different, three excitation conditions were used for the test. The test conditions are shown in Table I.

The appropriate amount of arsenic, lead, copper, iron, cadmium, chromium, barium, and mercury reference materials were prepared in a series of standard solutions of 0.10, 0.50, 1.00, 2.50, 5.00, 10.0, 25.0, 50.0, and 100.0 ng/mL, respectively.

The sample preparation method was performed as follows: 0.1 g of the sample was weighed accurately before 5 mL of nitric acid and 1 mL of hydrogen peroxide was added. The solution was allowed to soak overnight before being digested according to the following digestion procedure: it was heated for 6 min, then held for 5 min at a temperature of 110 °C, heated for 6 min, held for 5 min at a temperature of 140 °C, heated for 6 min, held for 5 min at a temperature of 180 °C, heated for 15 min, and finally held for 10 min at a temperature of 210 °C.

When determining iron, 1.0 mL of the above solution was absorbed and placed in a 100 mL volumetric flask before being diluted with water. The volume was fixed to the scale, shaken, and then precisely absorbed 1.0 mL of the solution, which was then placed in a 10 mL volumetric flask. The solution was then diluted with water before being shaken, after which then there was a wait for determination.

The testing conditions were as follows: the sample lifting rate was 0.4 mL/min. The radio frequency (RF) power was 1550 W. The atomization chamber temperature was 2 °C. The helium velocity in collision reaction tank was 0.4 mL/min. The internal standard was a virtual reality system comprised of scandium, indium, lithium, and bismuth. The acquisition mode was a combination of quantitative and rapid scanning.

The basic parameter method is a comprehensive calculation of the X-ray generation, monochromation, sample excitation, and detector reception process. From the X-ray generation, the filtering of the primary X-ray, and the interaction between the X-ray and the sample (fluorescence effect and scattering effect) to the response of X-ray detector, there were several parameters, such as X-ray parameters, monochromatic parameters, optical path parameters, interaction parameters between elements in the sample, and detector parameters. The core content of the basic parameter method is to calculate the whole process from the X-ray incident to the sample at a certain incident angle to the X-ray emission from the sample at a certain exit angle to obtain accurate X-ray energy spectrum.

The single energy X-ray incident on the sample (uniform sample or multilayer coating sample) excites the primary and secondary fluorescence X-ray and scattering X-ray produced by the elements in the sample. According to the principle of X-ray and substance interaction and the basic parameter database of X-ray and substance interaction, the monochromatic X-ray incident on the sample can be calculated. The continuous spectrum of incident X-ray can be divided into many fractions according to the energy, and each fraction can be calculated as monochromatic X-rays, namely numerical integration. Because of the need for numerical integration of the continuous spectrum, the amount of calculation for multiple iterations is large when quantifying unknown samples. Therefore, by optimizing the program design, the calculation time is significantly shortened.

According to the parameters of each step, the theoretical calculation spectrum of the whole process of X-ray generation and reception is calculated. The element content (and coating thickness) of the unknown sample is taken as the unknown parameters. The calculated spectrum is fitted with the actual spectrum collected by the detector, and the error between the calculated spectrum and the measured spectrum is minimized through iteration. During the fitting process, the content of each element changes continuously. When the fitting is complete, the content of each element does not change, which is the quantitative value. The obtained parameters are used as the element content (or coating thickness) of the unknown sample.

In the process of testing, the spectra of each element under different energy conditions are shown in Figure 2.

To conduct the precision test, the right amount of Mongolian medicine powder was taken and the sample was pressed according to the “boric acid edge pressing method,” before testing it on the XRF spectrometer. Each sample was determined six times. The results after fitting by the basic parameter method are shown in Table II. The results show that the precision was between 5.49–20.0% when the content of the metal elements was less than 2.0 mg/kg, and less than 4.96% when the content was more than 2.0 mg/kg. The precision of this method can meet the analysis requirements.

There were two methods for determining the LOD and LOQ—the background method and the repeated method. The LOD is usually determined by repeated determination. The LOD was calculated as LOD = 3×. For the RSD of the blank signal, the LOQ was calculated as LOQ = 10×. The RSD of the blank signal was calculated as the RSD of 11 repeated determinations of the blank sample. The results were shown in Table III. The results showed that the high sensitive XRF method had a low LOQ for heavy metals, which could meet the requirements of limit control analysis of heavy metals in drug quality standards.

Mongolian medicine samples with known contents of heavy metal elements were taken. Eight types of element reference materials were added to the samples, and the results were tested on a XRF spectrometer. The recovery rate was calculated by which the accuracy of the method was expressed. The results are shown in Table IV. Because mercury was easy to volatilize, the recovery rate was less than 70% but more than 68.4%. The recovery rates of the other seven elements were within 85–130%. The results show that the accuracy of the method is optimal.

According to the test conditions under “1.3.3,” the response values of each metal element series standard solution were determined one at a time, and the standard curve of each element was fitted by the least square method. The results are shown in Table V. The results revealed that there was a good linear relationship between the response value and the concentration of eight metal elements, including arsenic, lead, copper, iron, cadmium, chromium, barium, and mercury. The RSD of the intermediate concentration standard solution was less than 2.67% after repeated determination was performed five times, which showed that the precision of the method was optimal. The digestion solution with the known content was then taken, and an appropriate amount of each element standard material solution was added. The recovery rate of the method was calculated, which was between 85–130%, and that indicated that the accuracy of the method was good. In addition, the stability of the sample was also investigated. When the digested solution was placed at room temperature for 24 hr, the response value did not change significantly, which indicated that the digested solution was stable at room temperature.

The contents of eight heavy metals in Mongolian medicine were determined by ICP-MS method. The results were compared with those by XRF method, and the differences between the two methods were tested. The results are shown in Table VI. In addition, the results of cadmium in Zadi-5 and mercury in Yihe-12 are significantly different in the two methods; the other results were in the acceptable range. The results showed that both methods could determine the contents of the eight metal elements in question accurately. On the premise of ensuring the accuracy and precision of the determination, the XRF method is more rapid, simple, and nondestructive than ICP-MS, which makes it the more ideal method for analyzing heavy metals.

XRF spectroscopy has been widely used in the field of inorganic analysis, such as art identification, archaeology, agricultural product safety, environment, energy, mineral exploration, and electronic materials (15–20). In recent years, the XRF method has been widely used in analyzing and evaluating elements in traditional Chinese medicine because of its fast, convenient, and online analysis (21–25). In the past decade, the breakthrough of several core technologies has led to the rapid development of energy dispersive XRF (ED-XRF) spectroscopy, including silicon drift detector (SDD) technology with a high resolution and count rate. Monochromatic focusing excitation technology can greatly reduce the background interference and improve the intensity of the elemental fluorescence signal. Newer X-ray tubes can greatly improve the focal spot size, radiation flux, and stability. The breakthrough and development of these core hardware technologies extended the ability of XRF to analyze elements from the previous major elements to trace elements, and meet the requirements of many heavy metal detection limit specified in the quality standards of traditional Chinese medicines.

A single wavelength excitation ED-XRF spectrometer uses hyperboloid curved crystal focusing technology, a high-resolution detector, a micro focal spot end window X-ray tube, and other core technologies. In this study, this technology was first applied to the analysis of metal elements in ethnic compound pharmaceutical preparations. The detection limit and quantitation limit reached sub-ppm levels, and the quantitation limits of arsenic, cadmium, mercury, and lead—the most stringent drug limit—reached 0.039, 0.051, 0.135, and 0.075 mg/kg levels.

Traditional Chinese medicine and ethnic medicines have the characteristics of wide distribution and variety. For XRF quantitative analysis of trace heavy metal elements, in addition to the detection limits of the hardware, a software quantitative algorithm also has challenges. If the traditional influence coefficient method is used to make the standard curve, it cannot deal with the fact that the matrix of various types of traditional Chinese medicine is inconsistent, and quantitative deviation caused by the matrix effect is bound to exist. In this experiment, the complete basic parameter method was used to investigate the quantitative accuracy and its adaptability. Based on the theoretical calculation of XRF from the generation of X-ray tube to the detection of detector, the basic parameter method eliminates the influence of matrix effects and the absorption enhancement effect between elements. The systematic error correction can be carried out by a small number of standard samples to achieve the purpose of quantifying unknown elements and adapting to all types of samples. With the increasing demand for sensitive, trace, real-time and efficient information data, high-sensitivity XRF spectroscopy with its unique advantages will occupy an important position in the quality control and the research and development of Mongolian medicines.

This work was supported by the open project of the Inner Mongolia Key Laboratory of Human Genetic Diseases Research. This work was also supported by the construction project of the Key Laboratory of Chifeng University (CFXYZD202008).

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 is with Chifeng University, in Chifeng, China. 

 is with Shenyang Pharmaceutical University, in Shenyang, China. 

 are with Beijing Ancoren Technology Co. Ltd., in Beijing, China. Direct correspondence to: 

Peer-Reviewed Research

In this study, X-ray fluorescence (XRF) spectroscopy was used to analyze heavy metals in five traditional Mongolian medicines, and the results were compared to those obtained using ICP-MS.

Comparative Study of Heavy Metals Analysis in Mongolian Medicines Based on High Sensitivity X-ray Fluorescence Spectroscopy and ICP-MS

Space target recognition is of great importance for maintaining aerospace safety and national security. When observing a space target, owing to the low spatial resolution of ground-based observation equipment, each pixel in a hyperspectral image might represent a mixture of several different materials. Hyperspectral unmixing is a process used to extract the endmembers and their corresponding abundances from hyperspectral data. Unfortunately, most existing methods cannot make full use of the available spatial information data. The paper proposes a new local manifold sparse regularized unmixing model based on similarity regularized nonnegative matrix factorization (SRNMF). To exploit the spatial information of the vis-NIR (approximately 400–2500 nm) hyperspectral image of a space target, image segmentation is introduced to generate similar local regions. These local regions are generated adaptively, and pixels within each region have similar abundance sparseness. Simulation experiments validated the high efficiency and precision of the proposed algorithm, which should also be suitable for other spectral analysis applications.

A space target in the aerospace field usually refers to a man-made spacecraft or item of space debris orbiting the earth outside the limit of the atmosphere (1). With the rapid development of modern science and technology, increasing numbers of satellites are being sent into space, and Earth’s orbital space is becoming increasingly crowded. Therefore, the study of space objects is becoming of greater importance.

Owing to the spatial distance limitation, a ground-based observer cannot identify a space target through direct observation of local information. However, differences in the reflection spectra of the various materials comprising the surface composition of a space target provide unique spectral information that allows identification of space targets (2). Spectral analysis can be used to analyze the composition of space objects and the proportions of the different constituent space materials, allowing identification of space targets. With the rapid development of satellite and remote sensing technology, hyperspectral imaging has received increased attention because its numerous spectral bands can provide greater information for spectral analysis (3). However, owing to spatial resolution limitations, mixed pixels are commonly found in hyperspectral images, the existence of which can markedly affect the results of spectral analysis. Therefore, the goal of hyperspectral unmixing is to decompose mixed pixels into the constituent materials, called 

, and to determine their corresponding fractional abundances (4,5). Most existing hyperspectral separation methods are based on linear mixed models that assume mixed pixels are linear combinations of endmembers. In general, conventional algorithms for hyperspectral unmixing involve two steps—endmember extraction and mixed-pixel decomposition. Common endmember extraction algorithms include vertex component analysis (VCA). After endmember extraction, relevant abundance maps are usually obtained using fully constrained least squares (FCLS) analysis.

Nonnegative matrix factorization (NMF) is a statistical method typically used for hyperspectral unmixing. The NMF approach decomposes a data matrix into two low-rank matrices with nonnegative constraints. However, it should be noted that standard NMF methods might not guarantee solution uniqueness; thus, the decomposition result usually depends on the initialization (6). Constraints on endmembers and abundances have been exploited and used in NMF applications. Minimum volume constrained NMF (MVCNMF) (7) exploits the convex geometry information of mixed pixels and adds a volume constraint to NMF. In the case of low signal noise, although the performance of the MVCNMF algorithm is superior, MVCNMF cannot handle large data sets because of the large amount of computational overhead. Recently, owing to the sparse distribution of spatial materials, sparse constraints have been added to NMF to generate unique solutions that lead to improved results, such as L1 sparsity NMF (8) and L1/2 sparsity NMF (9).

In this paper, the SRNMF unmixing model is proposed, incorporating a spatial group sparsity regularizer and a sparse measure function regularizer into an NMF-based unmixing process. Thus, the SRNMF is able to explore the spatial information and the sparse structure of hyperspectral images. In addition, because of the high similarity between neighboring pixels in the hyperspectral data, simple linear hierarchical clustering (SLIC) is used to describe the similarity. The SLIC can obtain a number of meaningful homogeneous regions of the spectra that are spatially adjacent to each other. The paper considers the sparse spatial distribution of the target material and the spatial information, and introduces sparse regularizers to represent the spatial information. Integration of both the spatial structure information and the sparse properties means SRNMF can obtain improved unmixing results in comparison with other popular unmixing algorithms.

The linear mixed model, as a straightforward and efficient way to represent mixed pixels, assumes that the spectral response of a pixel is a linear combination of all the pure spectral signatures (endmembers) present in the pixel (10). Mathematically, if we let 

 denote a hyperspectral data matrix that consists of 

 bands, then the linear mixed model for each pixel can be written as follows:

 is the number of endmember signatures in the scene, 

 is the measured value of the reflectance at spectral band 

 represents the error term for spectral band 

A model based on similarity regularized nonnegative matrix factorization (SRNMF) can be used in space exploration and national security applications to exploit the spatial information in an image of a space target.

July 2022

A Look at Inorganic Analyses, Proficiency Tests, and Best Practices, Part II

Data Transforms in Chemometric Calibrations: Simple Variations of MLR, Part 2

Comparative Study of Heavy Metals Analysis in Mongolian Medicines Based on High Sensitivity X-ray Fluorescence Spectroscopy and ICP-MS

Simulation of an Algorithm for Space Target Materials Identification Based on vis-NIR Hyperspectral Data

Analysis of Serum from Acute Leukemia Patients Using Surface-Enhanced Raman Spectroscopy (SERS)