Improved Microplastic Identification from Simultaneously Collected Photothermal Infrared and Raman Spectra Using Multiview Conformal Prediction

Abstract

Microplastics (MPs) have been documented in urban and remote locations across the globe. Further identification and quantification of MPs are required to determine how widespread they are in the environment. One of the most popular chemometric methods for identifying microplastics (MPs) is database matching, in which an unknown spectrum is compared with reference library spectra by calculating likeness scores. Threshold minima determine if the score is high enough to consider the reference spectrum as a potential match, yet these thresholds are frequently set arbitrarily. There is a growing consensus that MP identification should involve multiple measurement techniques, but statistically robust methods to relate multiple database matching scores are lacking. Herein, multiview conformal prediction (MVCP) incorporates two views (i.e., photothermal infrared (PTIR) and Raman spectra) to calculate multidimensional thresholds for MP identification with statistical confidence. The chemical identities returned for an unknown particle have a statistical assurance that one of the identities is the correct match based on a user-defined uncertainty parameter. The average number of potential matches returned by MVCP was closer to one chemical identitythe ideal number of identities returnedwhen compared to single-view CP methods that used either the PTIR or Raman spectra. Moreover, MVCP was less affected than its single-view counterparts when one of the two spectra was difficult, or impossible, to identify. To show the utility of MVCP for real-world samples, an ambient particle sample with MPs deposited on it was used to demonstrate that an MVCP threshold at 73% theoretical confidence maximized the fraction of MP particles correctly identified as plastic (0.80 ± 0.07), while limiting the fraction of non-MP environmental particles misidentified as plastic (0.10 ± 0.06). This initial application of MVCP to spectroscopy demonstrates the benefits of utilizing multiple spectral methods with data analysis routines for identifying MPs with statistical confidence.

Introduction

Microplastics (MPs) have become an increasing concern due to the rising prevalence of mismanaged plastic waste in the environmentthe extent of which is largely uncertain. , Pieces of plastic between 1 and 5000 μm in size are considered MPs, and they can be created intentionally (often for commercial products) or by the breakdown of larger pieces of plastic. These particles must be identified chemically as visual methods are limited to particles >50 μm, − with some studies recommending additional chemical validation for any MPs < 2 mm in size. A growing number of spectroscopy and mass spectrometry techniques are being used to identify MPs in field studies as they provide information on the molecular structure of polymers, − which aids in distinguishing the polymers from other organic and inorganic species. −

For vibrational spectroscopy techniques specifically, there are many commercial − and in-house ,− reference libraries available to help identify MPs from unknown infrared (IR) and Raman spectra using database matching. Hit Quality Index (HQI), a general term for similarity metrics, can be used to calculate a score between the unknown spectrum and a reference library spectrum. , Returned HQI scores are often between 0 and 1 (though they are sometimes reported as 0–1000 or 0–100%), , meaning the spectra are either entirely dissimilar or a perfect match, respectively. Once all of the scores between the unknown spectrum and corresponding reference library spectra are calculated and tabulated, the highest scores are returned to the user as potential matches (also known as labels) for the unknown particle.

The final decision on whether these labels are a correct match can be difficult as HQI scores between the lowest and highest possible values are often arbitrary and carry no inherent significance. , The scores are highly dependent upon a number of variables such as the metrics used to calculate HQI scores, the particle types included in the reference library, and the MP particle type. ,, Moreover, most commercial database matching software systems do not make their data analysis routines public, making direct comparisons between HQI scores calculated from different software systems challenging. Many researchers have worked around these issues by selecting a minimum threshold value above which the HQI score is considered high enough for the reference library and unknown spectra to be a potential match. , Methods for selecting a threshold have largely been ambiguous processes based on qualitative observations or the precedent of previous publications, resulting in researchers selecting threshold values ranging anywhere from 0.6 to 0.8or not reporting a threshold value at all. Given that thresholds are not comparable between different database matching methods yet significantly affect match accuracy, ,, a data-driven approach that determines thresholds with statistical confidence values is crucial to accurately and efficiently determine MP identities.

Conformal prediction (CP) is statistical approach used to establish thresholds for similarity metrics that carried a theoretical confidence guarantee (i.e., the probability that the correct match was returned) for returned labels for an unknown spectrum. Generally, CP is a statistical method that calculates a threshold based on a calibration data set which can then be used for unknown data sets. , Clough et al. utilized CP to either return potential matches for an unknown particle’s spectrum in a prediction set or return an empty prediction set if none of the scores surpassed the data-driven threshold. CP not only outperformed a commonly used commercial database matching software for MPs, but the method could also be optimized and employed for environmental plastic identification. However, the use of CP to identify plastics was limited to one spectral input, despite it being established that the combination of IR and Raman spectroscopy can further enhance the certainty of MP identification. ,,

Optical photothermal infrared (O-PTIR) spectroscopy systems provide an advantage for particle identification as they simultaneously collects photothermal infrared (PTIR) and Raman spectra for individual particles by utilizing a pump–probe mechanism, where the pump is a tunable scanning mid-IR laser and the probe is a visible laser. − In addition to collecting two spectra for each particle, this technique circumvents the size resolution of traditional Beer’s Law-based IR measurements, which are practically limited to detecting MP particles > ∼20 μm in size. , The size resolution for O-PTIR depends upon the probe laser (532 nm), not the pump laser (∼3–10 μm), and is advantageous for detecting MP particles down to the submicron size range. ,,, Among the few studies combining IR and Raman spectra, Böke et al. proposed plotting the HQI scores from PTIR and Raman in a two-dimensional score space. However, it was noted the range HQI scores for the correct label was as low as 0.3. Developing a method that can establish reliable thresholds and return labels with statistical confidence values is critical for identifying MPs with multiple spectral inputs.

To achieve the goal of aggregating multiple methods, we used a special case of conformal score aggregation (CSA), called multiview conformal prediction (MVCP), in which multiple models are obtained from different views of the same object. This adaptation leverages the spectral inputs from O-PTIR+Raman while using preexisting theoretical properties, such as confidence guarantees, that have already been established with CSA. Herein, we apply MVCP to the case of PTIR and Raman spectra collected from one individual particle. This enables the use of PTIR and Raman to identify MP particles with quantified statistical confidence. PTIR and Raman spectra collected from samples containing both MP and non-MP particle types (<10 μm in size), were used to calibrate and establish an envelope threshold. The efficiency and robustness of this technique was then compared with traditional, single-view CP methods that only considered either the PTIR or Raman spectra independently. Finally, MVCP was applied to an additional data set of aerosolized MP particles impacted on an ambient particle sample (without MPs) to determine the method’s capability to differentiate MP particles from other non-MP particles in an environmental sample.

Materials and Methods

Laboratory-Generated and Ambient Samples

Detailed information regarding sample preparation and spectral collection parameters can be found in Parham et al. Briefly, three samples (named MPs-Only, MPs+Standards, and MPs+Ambient) were generated by impacting aerosol particles onto microscopy substrates for analysis. For the MPs-Only sample, three MP particle typeshigh-density polyethylene (HDPE), polypropylene (PP), and polystyrene (PS)were sequentially aerosolized and impacted onto an aluminum-coated silicon wafer. This process was repeated along with non-MP particle typesammonium sulfate (AS), sodium nitrate (SN), and sucrose (SCR)for the MPs+Standards sample. Finally, the MPs+Ambient sample was made with MP particle types impacted onto a sample of ambient atmospheric particles.

Computer-Controlled Optical Photothermal Infrared and Raman (CC-O-PTIR+Raman) Analysis

All samples were analyzed with Photothermal Spectroscopy Corp.’s mIRage CC-O-PTIR+Raman to simultaneously collect PTIR and Raman spectra for individual particles. A tunable IR quantum cascade laser (mIRcat-QT, 120 mW maximum power, 1% duty cycle, 100 kHz pulse rate, 100 ns pulse width) scanned through a wavenumber range of 948–1860 and 2698–3002 cm^–1. A particle’s photothermal expansion was detected by changes in the elastic scattering of a continuous-wave 532 nm probe laser (200 mW power) by a photodiode. PTIR spectral collection parameters included a 20% IR laser power, 5% visible laser power, and 10 coaveraged scans. The inelastic scattering from the visible laser was also used to collect Raman spectra simultaneously for each particle. Raman spectral collection parameters included a 600 groove/mm grating, 15 s delay time (in case of fluorescence), 30 s integration time, and 3 coaveraged scans. The featurefindIR module (within the PTIR Studios software) was used to automate the detection and spectral collection of particles in a field-of-view image based on parameters such as particle size and contrast between particles.

Reference Library Generation and Manual Matching of Experimental Spectra

Samples of each MP and non-MP particle type (i.e., HDPE, PP, PS, AS, SN, and SCR) were individually prepared and analyzed with CC-O-PTIR+Raman. These spectra were then used to create averaged reference library spectra for each of the MP and non-MP particle types. Note that no spectra from the ambient particles were included due to the diversity and complexity of chemical species in ambient particles. For this work, the data sets collected from these samples for the reference library were reassessed and used individually (i.e., not averaged together) to maximize the number of high-quality PTIR and Raman spectra that could be used for database matching.

Each spectrum from the MPs-Only, MPs+Standards, and MPs+Ambient samples was then compared to the in-house reference library to manually identify the unknown particles based on their individual PTIR and Raman spectra as well as considering both together. These manually assigned labels were used as the ground truth for method calibration and accuracy calculations in this work. In addition to the MP and non-MP particle types, other categories were included as follows: ambient particles (AMB), mixture (MIX) of distinct chemical signatures from two or more particle types, unsorted (UNS) spectra where the peaks present were not characteristic of a particle type or the Raman spectrum was dominated by fluorescence or saturation, and low signal (LOW) where no peaks were present in the spectrum. Each sample used labels relevant to the particle types used; for example, possible labels assigned to unknown spectra in the MPs-Only sample included HDPE, PP, PS, MIX, UNS, and LOW.

Spectral Preprocessing

For this study, the raw spectra from the samples and reference library were preprocessed in-house using Python. Note that all spectra shown herein have been preprocessed unless otherwise indicated. The PTIR spectra were automatically calibrated in PTIR Studios, and the spectra were interpolated such that all wavenumbers were aligned between the sample and reference library spectra and could be used for database matching. The spacing of the wavenumbers remained 2 cm^–1 before and after interpolation. Although interpolating the PTIR spectra was not strictly necessary for these spectra, it was included as part of the workflow for consistency between the PTIR and Raman spectra. The PTIR spectra were then truncated to the wavenumber ranges of 981–1799 and 2721–2965 cm^–1 to remove regions of high noise due to laser chip transitions (see Section S1 and Figure S1.1 for more details). Finally, the spectra were normalized using the standard normal variate (SNV) transformation. ,

The Raman spectra had to be calibrated manually, so the spectra were first baseline-corrected using Zhao et al.’s fifth-order iPolyModFit. This method was shown to improve fluorescence background removal for Raman spectra with low signal-to-noise ratios compared to the commonly used multipolynomial fitting method. The spectra were then normalized using the SNV transformation, calibrated using a 520 cm^–1 peak from an internal silicon standard that was collected daily, and interpolated to ensure the wavenumbers aligned between the reference library spectra and sample spectra. The interpolation additionally modified the spacing of wavenumbers from 3 cm^–1 to 2 cm^–1. Note that the Raman spectra were collected over a range of 480–3762 cm^–1, though some ranges were slightly extended and changed the wavenumber values. These variances made interpolation necessary for the Raman spectra. Similar to the PTIR spectra, the Raman spectra were truncated to 601–1849 and 2751–3499 cm^–1 to exclude the low variance and low specificity regions, which could influence automated spectral matching.

Database Matching with the Normalized Nearest Neighbor $(\widetilde{\mathit{N}N})$ Similarity Metric

Database matching involves calculating the likeness between an unknown spectrum and a collection of reference spectra from a library. Figure a shows example PTIR and Raman spectra for an unknown particle with the reference library spectra below them. Note that these reference library PTIR and Raman spectra are not inherently correlated with each othermeaning that they were not necessarily retrieved from the same particle (see the reference library section above for more information). Additionally, database matching was conducted independently for the particle’s PTIR and Raman spectra.

1.

Experimental outline for labeling unknown spectra. (a) Database matching for the PTIR and Raman spectra (pink and green traces, respectively) of an unknown particle. The gray traces underneath are the top-matching spectra for each particle type with their respective $\widetilde{NN}$ scores (i.e., HQI scores) next to them. The resulting single-view CP methods for (b) the PTIR $\widetilde{NN}$ scores and (c) the Raman $\widetilde{NN}$ scores are shown with the returned prediction sets based on the methods’ theoretical confidence percentages. (d) The results from the MVCP method, utilizing both PTIR and Raman $\widetilde{NN}$ scores, with the returned prediction sets shown based on the theoretical confidence percentage. Note that each numbered point in (b), (c), and (d) corresponds with the particle types denoted in (a).

HQI scores were calculated using the nearest neighbor (NN) similarity metric (eq ), which not only takes into account the similarity between an unknown and reference library spectrum, but also whether the unknown spectrum is more similar to other particle types in the reference library. Additionally, it has been shown that the NN similarity metric is more selective than the commonly used Pearson’s Correlation Coefficient (PCC) metric.

$$N{N}_y=\frac{\underset{\mathrm{r}\mathrm{e}\mathrm{f}}{\min }\{|x-x_{\mathrm{r}\mathrm{e}\mathrm{f}}|:y_{\mathrm{r}\mathrm{e}\mathrm{f}}=y\}}{\underset{\mathrm{r}\mathrm{e}\mathrm{f}}{\min }\{|x-x_{\mathrm{r}\mathrm{e}\mathrm{f}}|:y_{\mathrm{r}\mathrm{e}\mathrm{f}}\ne y\}}$$ 1a

$$\widetilde{NN}=1-e^{-\frac{N{N}_y}{\tau }}$$ 1b

In the numerator for NN _y , the minimum distance between the unknown spectrum, x, and all reference spectra, x _ref, for a specific the label (y _ref = y) is calculated. This value is then divided by the minimum distance between spectrum x and every reference spectrum x _ref that does not correspond to the label of interest (i.e., y _ref ≠ y). For example, if the NN similarity metric was calculated for an unknown spectrum and HDPE was the label of interest, then the Euclidean distance between the unknown spectrum and the closest HDPE reference spectrum would be calculated. This value would then be divided by the Euclidean distance between the unknown spectrum and the closest reference library spectrum of any particle type that is not HDPE. The resulting score, NN _HDPE, would be specific to the HDPE label, and this calculation would be repeated for the other potential labels in the reference library.

Given that the initial NN similarity metric could be any value greater than 0, it can be normalized so that the output value is between 0 and 1 and can be interpreted as an HQI score (eq ). This transformation is negatively monotonic (i.e., when the similarity metric increases, the normalized similarity metric will strictly decrease) and is introduced solely to improve interpretability, meaning it will not affect the resulting confidence or prediction sets returned by the CP methods. For this study, an exponential function with a constant τ was used to generate this normalized NN similarity metric $(\widetilde{NN})$ , which will herein be referred to as an $\widetilde{NN}$ score. These scores were scaled (τ = 1.4427) such that $\widetilde{NN}$ ≈ 0.5 when the first and second nearest neighbors were the same distance from the unknown spectrum. $\widetilde{NN}$ was more than 0.5 only when the label in question was truly the nearest neighbor to the unknown spectrum, whereas when $\widetilde{NN}$ was less than 0.5, it signified a different label was the nearest neighbor (Figure S1.2). Using the example spectra from Figure a, this normalization caused the top $\widetilde{NN}$ scores for each particle type to be lower than what may be typically expected for an HQI score.

Conformal Prediction (CP)

Unlike traditional database matching methods, which seek to assign one label to an unknown spectrum, conformal prediction (CP) returns prediction sets containing however many labels that have scores surpassing a data-determined threshold (i.e., a threshold calculated from a calibration set). The advantage of this CP threshold is that the returned prediction set has a confidence guarantee that the correct match is in the prediction set based on the user-defined theoretical confidence percentage. For example, if a user sets a threshold with 80% theoretical confidence, then all prediction sets returned have an 80% guarantee that the correct label (if the correct label is in the reference library) is returned in the prediction set (Section S2.1).

An important characteristic of CP is that the confidence guarantees require relatively weak distributional assumptions of the calibration spectra. Whereas other statistical approaches (such as the bootstrap method , ) give guarantees that are only asymptotically validmeaning the data set should be near-infinite in sizeCP gives guarantees even when the data set’s score distribution is not Gaussian in shape and finite. However, it is crucial to note that CP assumes the calibration set used is representative of the sample, meaning the score distributions between the calibration and unknown sample are the same. Thus, if a particle type is not included in the calibration set, then the theoretical confidence guarantees provided by CP do not extend to this type of particle. Figure b and c show the prediction sets returned for the PTIR and Raman spectra’s respective CP methods based on a range of theoretical confidences. The differences between the calculated CP (PTIR) and CP (Raman) quantiles and $\widetilde{NN}$ scores mean the prediction sets returned will not always agree.

Multiview Conformal Prediction (MVCP)

Unlike single-view machine learning methods, multiview machine learning aims to solve prediction problems when different (often nonoverlapping) representations of the same underlying “object” are observed. In this case, our “object” is an unidentified particle and it is being represented via the $\widetilde{NN}$ scores for its PTIR and Raman spectra. Thus, MVCP is similar to its single-view counterpart in that it utilizes a threshold to determine what particle type labels are returned in the prediction sets based on a user-defined theoretical confidence value (Section S2.2). However, this boundary is no longer a single number; instead, it is two-dimensional in a score space. The score space encompassed by the boundary, called an envelope, returns labels whose combined scores from multiple views (treated as x and y coordinates) are within it. As shown in Figure d, the example particle’s $\widetilde{NN}$ scores are now plotted in a two-dimensional score space, and the envelopes cover a wider area of the score space as their theoretical confidence increases. Correspondingly, more potential matches are returned as the envelope increases in size. Although MVCP is used with two views in this work, it is important to note that it could be leveraged for a collection of n viewsin which case the threshold would be n-dimensional.

The challenge with creating an envelope is that there is no canonical ordering of points in higher-dimensional score spaces. For example, if given the $\widetilde{NN}$ scores for the PTIR spectra of 50 particles, a user could easily order these particles from having the highest to lowest scores. However, there is no clear way to order these particles when also considering their Raman $\widetilde{NN}$ scores. Thus, the envelope must be constructed using directional quantiles, meaning the distributional information on the calibration points are assessed over several directions in the score space, to address the multiple views. An example of this process to generate the shape of an envelope is shown in Figure . A range of angles originating from the maximum point of the score space (PTIR $\widetilde{NN}$ = 1.0 and Raman $\widetilde{NN}$ = 1.0) are evaluated. Each angle is assessed by projecting the calibration data points orthogonally onto a line such that the points are represented by only one dimension, and this projection’s score distribution is used to calculate the threshold at the user’s desired theoretical coverage. By projecting the data points back to a one-dimensional space across different directions (i.e., angles), the weights of the multiple views’ scores on the overall distribution also change. This means a projection along the x-axis or y-axis would be 100% weighted toward the PTIR or Raman $\widetilde{NN}$ scores, respectively, and a projection at a 45° angle between these two axes would be equally weighted between the PTIR and Raman $\widetilde{NN}$ scores. For each envelope calibration, 400 projection directions were evaluated. The threshold at the user’s selected theoretical confidence is then calculated based on this new distribution of scores. Once the individual threshold windows are calculated at each angle, their overlapping areas are used to create the two-dimensional envelope.

2.

Method for generating MVCP envelope and boundary. In total, 400 projections were assessed to determine the shape of the envelope, but only four projections are shown for visual simplicity.

The size of the envelope may need to be adjusted after establishing the envelope shape since the data points had to transform from their original positions to make the directional quantile, and the actual coverage of the envelope may be different for the distribution of the calibration points in the two-dimensional score space. Thus, only 24% of the calibration data determines the shape of the envelope while the remaining 76% of the calibration data adjusts the size of the envelope based on the calculated empirical coverage of these data points (Figure S2.1).

A sensitivity analysis for this split for the calibration subsets, along with the number of projections used to determine the envelope during calibration, is shown in Figures S3.1 and S3.2. The number of projections did not greatly impact prediction set size, empirical confidence, or the overall shape of the envelope, but it is still recommended to use a large number of projections to decrease the potential impact of calibration set size and randomly selected locations of projections. Parameters outside of these can be adjusted in the Python script as well, which is available for open access on GitHub (https://github.com/eochoarv/MVCP/tree/main). A full list of user-selected parameters for the database matching and CP methods is provided in the accompanying user guide. Users are directed to Clough et al. for a recommended workflow when first using the script.

Calibration and Test Data Sets for Single-View CP and MVCP Experiments

In this study, calibration and test spectral data sets were generated with the combined manually labeled particle spectra from the MPs-Only and MPs+Standards samples. To investigate the performance of the single-view CP and MVCP methods, these spectra were filtered based on how challenging the unknown particles were to manually identify based on their respective PTIR and Raman spectra. Spectral Dataset #1 (n = 321) included particles with the most straightforward manual identification: the PTIR and Raman spectra both had an MP or non-MP label and were not mixtures (i.e., neither spectrum was labeled MIX, UNS, or LOW). Additionally, the Raman spectra did not exhibit fluorescence or saturation. Spectral Dataset #2 (n = 209) included particles where one spectrum had an MP or non-MP label and the other did not (i.e., this other spectrum was labeled UNS or LOW). Mixtures were not included in this data set, and Raman spectra that exhibited saturation or fluorescence were included regardless of whether they had an MP or non-MP label. Although expert judgment was used to identify these particles, calibration and evaluation of the CP methods are ultimately dependent upon these manual assignments. It is common practice to use manually assigned identities as a ground truth data set, and it is acknowledged that the following experimental framework is working to reproduce these expert decision boundaries.

As a more rigorous test of robustness, a separate data set was generated by augmenting some of the spectra from Spectral Dataset #1 with noise. For this test, Gaussian noise (see Section S1.3) was added to investigate the effect of spectral noise on the single-view CP and MVCP methods and push their limitations for particle identification. Spectral Dataset #1 was thus split into three subsets: one subset contained half of the particles from Spectral Dataset #1 (n = 161) and was left unchanged, one subset contained a quarter of the particles (n = 80) with their PTIR spectra augmented with Gaussian noise, and the last subset contained a quarter of the particles (n = 80) with their Raman spectra augmented with Gaussian noise (Figure S1.3). For clarity, the first subset will be referred to herein as Spectral Dataset #1: Unchanged Subset, and the other two subsets will be jointly referred to as Spectral Dataset #1: Noise-Added Subsets.

All data sets or subsets used for an experiment were evaluate using Monte Carlo cross-validation, , which is a method that assesses prediction models by randomly splitting a data set between calibration and test sets n-times and using the results for quantitative comparisons. In this study, the data set used for each experiment was split 84% and 16% between calibration and test data, respectively. These fractions for the split favored the calibration set to produce more accurate estimations of the envelope’s performance during the calibration phase. Although the coverage guarantee holds regardless of the calibration data set’s size, there is an impact on the empirical confidence observed. Larger calibration data sets lead to higher precision (i.e., empirical confidence has less error associated with it). In practice, users should include as much data as is reasonable in the calibration set. The calibration data was first run through the database matching algorithm. The top score of the correct polymer type for each PTIR and Raman spectrum was plotted in a distribution for their respective measurements, and quantiles were then calculated based on their respective distributions. The database matching process was then repeated with the test spectra, but this time the scores were plotted along the axis of their corresponding method and used to determine which potential matches were returned in the prediction sets based on the quantiles established. This process was repeated 100 times for each experiment.

Results and Discussion

Comparing Thresholds between Single-View CP and MVCP Methods

One of the ways that MVCP utilizes dual information from PTIR and Raman is by creating an envelope with both spectral inputs. Figure shows the histograms of these top $\widetilde{NN}$ values for their respective single-view CP methods for Spectral Dataset #1 and Spectral Dataset #2. For this work, the histograms are shown as a visual representation of the one-dimensional spread of data, which is why the thresholds are plotted irrespective of the bin edges. The 95% quantiles for CP (PTIR) and CP (Raman), shown as dashed lines, were nearly identical values of $\widetilde{NN}$ = 0.44 and 0.42, respectively. Although these thresholds are low relative to other thresholds previously used, , they are a result of the $\widetilde{NN}$ scores being scaled so the data points could be interpreted based on which quadrant of the score space they resided in (Section S1.2).

3.

An example calibration with resulting thresholds for the three CP methods. The histograms for the top $\widetilde{NN}$ scores of the correct particle type are shown for the PTIR and Raman CP methods (pink and green, respectively). Their corresponding quantiles at 95% theoretical confidence are denoted with dashed lines that intercept with the PTIR or Raman $\widetilde{NN}$ axes. The spread of these PTIR and Raman scores for each particle are plotted underneath the histograms, with the MVCP envelope at 95% theoretical confidence shown in gold.

The MVCP envelope at 95% theoretical confidence extends past the overlapping region from the single-view CP thresholds. However, the convex shape of the envelope covers a different area of the score space than the rectangular shape of the single-view CP quantiles, which may affect what potential matches are returned for unknown spectra. For example, the left-hand side of the envelope exceeds the CP (PTIR) threshold, but it does not cover a large fraction of the score space within the CP (Raman) threshold. The shared information between the two spectroscopy techniques creates a unique threshold that interacts with labels differently than when considering one of the single-view CP quantiles or the region where the two quantiles overlap.

Performance Evaluation for Single-View CP and MVCP Methods

One trade-off of CP methods is the number of potential matches returned in a prediction set increases as the confidence (and thus the probability of the prediction set containing the correct label) increases, which would require manual analysis to decide between the returned labels. Therefore, it is critical to evaluate a CP method’s efficiency over a range of theoretical confidence values to choose a threshold that does not return too many labels, especially when using reference libraries with tens or hundreds of available labels that could be returned. This evaluation is shown in Figure a, where the average prediction set size is used as a metric of a CP method’s efficiency using Spectral Dataset #1 and Spectral Dataset #2. The MVCP and CP (Raman) methods dramatically increase from ∼1 to ∼4 labels after 95% theoretical confidence. CP (PTIR)’s average set size is already close to 2 labels at 95% theoretical confidence and reaches as high as 5 labels (out of 6 labels total in the reference library) at 100% theoretical confidence. The 95% theoretical confidence value was thus selected to establish thresholds for all experiments in this work (excluding the assessment of the MPs+Ambient sample) as it maximizes the theoretical confidence guarantee range while keeping the average set size close to one label, thus minimizing the amount of uncertainty (i.e., the need for manual verification of potential matches) associated with the prediction sets returned.

4.

(a) The averaged prediction set sizes compared with the inputted theoretical confidence value for CP (PTIR), CP (Raman), and MVCP. (b) The calculated empirical confidence (top panel) and box-and-whisker plots of average prediction set size (bottom panel) for each split at 95% theoretical confidence (n = 100). Error bars shown for the empirical confidence represent the standard deviation. Filled points in the box plots signify outliers.

Further comparison shows that MVCP has a higher efficiency than either of the single-view CP methods in most cases (Figure a). MVCP overall has the lowest average prediction set size of 1.1 ± 0.1 labels at 95% theoretical confidence, though its range overlaps with CP (Raman)’s average prediction set size (1.3 ± 0.1 labels). The average prediction set size for CP (PTIR), which is 1.8 ± 0.2 labels, is significantly higher than MVCP. Despite these differences, the majority of prediction sets on average had a set size of 1 label for each method at 95% theoretical coverage (Figure S5.1).

These trends between the three CP methods (i.e., CP (PTIR), CP (Raman), and MVCP) are even more pronounced in Figure b, where the spread of the average prediction set sizes over 100 splits at 95% theoretical confidence is shown with box-and-whisker plots. MVCP still maintains the lowest median among the three methods (CP (PTIR) median: 1.82 labels; CP (Raman) median: 1.52 labels; MVCP median: 1.32 labels). Although CP (Raman) has a smaller range overall than MVCP (CP (Raman) range: 0.65 labels, MVCP range: 1.93 labels), it is largely due to MVCP’s lowest quantile extending to ∼1 labelthe target prediction set size in this casewhereas the lowest average prediction set size for CP (Raman) is limited to 1.29 labels. CP (PTIR) has the highest median and widest range of labels (median: 1.82 labels, range: 1.26 labels). Although Figure shows trends in the average prediction set sizes across 100 splits, the median and range for each prediction set returned from a selected split can also be returned (Figure S5.2). At 95% theoretical confidence, the largest prediction set returned for MVCP contained 2 labels, whereas CP (PTIR) and CP (Raman) reached set sizes of 6 and 5 labels, respectively. This closer look at returned prediction sets shows that CP (Raman) and CP (PTIR) reach larger set sizes at lower theoretical confidence values, signifying MVCP’s continuous efficiency over a wide range of potential theoretical confidence values.

The three methods are still accurate and precise despite the differences in their prediction set sizes, as shown by the calculated average empirical confidence in Figure b. Empirical confidence is a metric used for CP methods to calculate the fraction of prediction sets containing the correct label (which is the manually assigned label) during testing (Section S4.1). It should be noted that empirical confidence is not affected by set size; rather, it only evaluates if the correct label was returned for a test spectrum. All three methods have 95% empirical confidence with a standard deviation of 2–3%, indicating that MVCP’s higher efficiency does not come at the cost of accuracy.

The benefits of having two spectral inputs to distinguish between particle types can also be observed at the single-particle level. Utilizing the complementary nature of O-PTIR and Raman spectra has been shown to improve manual identification of pristine MP particles, especially in size ranges <10 μm where particles often have lower signal, and this improvement extends to computational analysis of unknown particles as well. Figure shows PTIR and Raman spectra from two example particles in Spectral Dataset #2 (i.e., the data set of particles where one of their spectra was not easily identifiable). In Figure a, an unknown particle has a Raman spectrum with clear peaks that visually agree with a reference library spectrum for HDPE. The Raman spectrum’s $\widetilde{NN}$ score of 0.56 for HDPE corroborates this likeness, and the score is high enough to indicate that HDPE has closer agreement with the unknown spectrum than neighboring labels. Indeed, Figure b shows HDPE is the only label to pass the CP (Raman) threshold. The PTIR spectrum in Figure a, on the other hand, is clearly only noise. Its corresponding $\widetilde{NN}$ score for HDPE ( $\widetilde{NN}$ = 0.48) is close to 0.5, indicating that it is about the same Euclidean distance from the unknown spectrum as another label in the reference library. In fact, all PTIR $\widetilde{NN}$ scores for the six labels are between 0.47 and 0.51, and the resulting prediction set contains all six labels. In this case, the MVCP envelope only passes HDPE and excludes all other labels due to the added information from the Raman spectrum.

5.

(a) PTIR and Raman spectra for an example HDPE particle and the top-matching reference library HDPE spectra in dark gray below. (b) Top HQI scores for each particle type with the example particle’s spectra compared with the CP method’s thresholds. A similar structure was used for an example PS particle’s (c) spectra and (d) HQI scores. Note the region from 800 to 1800 cm^–1 in the Raman spectrum for (c) is not shown as the signal was saturated.

Raman spectra can also suffer from spectral quality issues, especially when peaks are overwhelmed by fluorescence or saturation. Figure c shows an example PS particle with part of its Raman spectrum saturated. The signal in the fingerprint region exhibited a sharp increase and a gradual decline after baseline correction, and this region was removed from the figure for visual clarity. Similar to the previous example, all six labels pass the CP (Raman) threshold in Figure d. The PTIR spectrum for the PS particle has clear agreement with the PS reference spectrum, and this agreement is further supported by the PS label’s relatively high $\widetilde{NN}$ score of 0.64. Now the CP (PTIR) and MVCP methods only return the PS label.

Although these examples present extreme cases where MVCP returns 1 label and one of the single-view CP methods returns all labels, it did occur for 4 ± 2 and 0.6 ± 0.7 particles in Spectral Dataset #2 for CP (PTIR) and CP (Raman), respectively (Table S5.1, Table S5.2, and Figure S5.3). When comparing returned MVCP prediction sets containing 1 label to their single-view CP counterparts, CP (PTIR) returned over half of these prediction sets with >1 label (14 ± 4 particles) and CP (Raman) had 5 ± 2 prediction sets with >1 label. These example cases along with the particle-by-particle comparisons of prediction set size clearly exhibit MVCP’s use of a two-dimensional score space to return correct matches for unknown particles even when one of the spectra cannot be identified based on a similarity metricthus reducing the uncertainty of this method by returning smaller prediction sets. Moreover, utilizing two complementary spectral inputs further ensures the identification of MP particles that could otherwise be overlooked if only one of the spectroscopy methods were used.

Robustness Assessment Based on Spectral Identification Capability

The robustness of MVCP is further demonstrated by the quantitative comparisons between spectra based on how readily they can be identified. The earlier results from the combined Spectral Dataset #1 and Spectral Dataset #2 (see Figure b) are now shown separated by data set in Figure a. For the particles in Spectral Dataset #1, the spread of average prediction set sizes for the single-view CP and MVCP methods has a median near 1 label with narrow ranges. On the other hand, the particles that were harder to manually identify using both the PTIR and Raman spectra (Spectral Dataset #2) subsequently have much higher median set sizesespecially for CP (PTIR) (CP (PTIR) median: 3.0 labels, CP (Raman) median: 1.5 labels, MVCP median: 1.2 labels). The empirical confidence shows that all methods for both types of spectra are statistically within bounds for 95% accuracy, which is the target as 95% theoretical coverage was still used to establish the thresholds.

6.

Empirical confidence (top panel) and spread of average prediction set sizes over 100 splits (bottom panel) for (a) Spectral Dataset #1 (n = 321) and Spectral Dataset #2 (n = 209) as well as (b) Spectral Dataset #1: Unchanged Subset (n = 161) and Spectral Dataset #1: Noise-Added Subsets (n = 160). Error bars shown for the empirical confidence represent the standard deviation. Filled points in the box plots signify outliers.

The stark difference between CP (PTIR) and the other two methods in the results for Spectral Database #2 is likely due to the number of particles with PTIR spectra labeled as LOW and Raman spectra labeled as an MP or non-MP (n = 124). These particles could lead to an increase in the uncertainty of the CP (PTIR) method during calibration and testing, causing a slightly lower threshold (Figure ) and higher average prediction set sizes (Figures and a). The influence of these PTIR spectra on the calibration and performance of the CP (PTIR) method is thus observed through the higher number of potential matches in the prediction sets increasing the uncertainty of the sets overall.

The limits of the single-view CP and MVCP methods were investigated further by augmenting subsets of spectra in Spectral Dataset #1 with Gaussian noise. The results for the CP methods when calibrated and tested with Spectral Dataset #1: Unchanged Subset and Spectral Dataset #1: Noise-Added Subsets are shown in Figure b. As expected, the addition of Gaussian noise to the augmented subsets increased the overall root-mean-square (rms) noise of the spectra, as shown with an example PP particle in Figure S1.4. The unchanged subset has similar metrics to Spectral Dataset #1 shown in Figure a, though this unchanged subset has an even narrower range of average prediction set sizes, with the widest range being 0.1 labels. Meanwhile, the noise-added subset can be seen to greatly affect the single-view CP methods. Indeed, the median for CP (PTIR) increased to 1.92 labels (range: 1.53–2.46 labels), and CP (Raman) also increased to a median of 1.68 labels (range: 1.46–1.99 labels). Only MVCP remained relatively unaffected as its median stayed near 1 and its range was still relatively small (1.04–1.18 labels)thus maintaining a lower uncertainty in its returned prediction sets. All three methods surprisingly show a slight increase in empirical confidence (CP (PTIR): 0.962 ± 0.007, CP (Raman): 0.97 ± 0.01, MVCP: 0.964 ± 0.009), which may be due to the smaller number of data points in the subsets when compared to Spectral Dataset #1 and Spectral Dataset #2. The adaptability of MVCP to these noisier spectra demonstrates the advantage of multiple spectra when working with a variety of particles and pushing the limits of MP detection and identification.

MVCP Method Validation with MPs+Ambient Sample

To probe the capabilities of MVCP for environmental MP studies, the method was applied to a controlled experiment where HDPE, PP, and PS particles were impacted on top of an ambient aerosol particle sample on a gridded silicon substrate. A selected grid cell was analyzed after the environmental sample was first collected (no MP particles were identified from the ambient particle spectra), and the same grid cell was reanalyzed after MP impaction. The particles from the MPs+Ambient sample were then used as a test data set to determine the most appropriate threshold for MVCP.

The results from this experiment were treated as a binary classification so the data analysis routine could be assessed using common metrics for models. In particular, only the three MP types were used as potential labels for database matching, and only MP particles from Spectral Dataset #1 and Spectral Dataset #2 were used for the envelope calibration. The calibration data was randomly split 100 times between the two calibration subsets, to account for differences in the envelope’s shape and size, and the averaged metrics were calculated. Test particles from the MPs+Ambient sample were considered correctly identified if 1) one or more labels were returned for MP particles and 2) no labels were returned for ambient or unidentified particles (i.e., ambient, no identifiable peaks, or unsorted). Figure a shows performance metrics for this binary classification as a function of theoretical confidence. True positive rate (TPR) was defined as the fraction of prediction sets that contained a label for an MP particle. Conversely, the fraction of prediction sets returned with an MP label for an ambient, no identifiable peaks, or unsorted particle was defined as the false positive rate (FPR). For simplicity, particle mixtures were not considered for the TPR and FPR. These two rates were then used to calculate an F₁ score, which is frequently used as an accuracy metric for a model (Section S4.2).

7.

(a) The false positive rate (FPR), true positive rate (TPR) and F₁ score compared over theoretical confidence. (b) Empirical confidence and (c) prediction set size as a function of theoretical confidence. A dotted line denotes the threshold at 73% theoretical confidence, which was selected by the criterion of a 10% maximum FPR. The values of each metric are shown in light gray. The shaded area around traces represents standard deviation.

The priority for this study was to minimize the number of false positives to reduce prediction set size, so the threshold was established at 73% theoretical confidence to ensure the average FPR did not exceed 0.10 (FPR = 0.10 ± 0.06). This threshold also coincides with the peak in the F₁ score (0.76 ± 0.05)which indicates the number of true positives is greater than the sum of false positives and false negatives. The TPR is also fairly high (0.80 ± 0.07), which is further corroborated by the selectivity of the PP and PS particles (Figure S6.1). The HDPE test particles had more HDPE labels outside of the envelope while other MP labels were within the envelope, which contributes to lowering the TPR fraction. These metrics could be considered satisfactory by general standards for models, but they indicate lower performance compared to other data analysis routines employed for MP identification. ,

Although these results show the potential of using MVCP in environmental analysis, more can be done to improve the overall performance of the data analysis routine. Fortunately, this routine can be assessed with tools from the MVCP method. The performance of the selected envelope itself should be evaluated first using the average empirical confidence and prediction set size in Figure b and c, respectively. The empirical confidence, which only considers if the correct MP label is returned, is higher on average than the target confidence for this threshold (0.78 ± 0.07). In terms of efficiency, the prediction sets for the MP particles should ideally return 1 label and all other particle types should not have a label returned, so the target prediction set size should reflect the fraction of MP particles (n = 71) within all particles analyzed (n = 253), which was ∼0.28. The average prediction set size at 73% theoretical confidence is 0.30 ± 0.05, which is in good agreement with the target set size. It should be noted that this fraction of MPs is much higher than what would be expected in an ambient atmospheric sample. A recent modeling study from Evangelou et al. compiled results from 76 studies and computed an average global MP concentration of 31 particles m^–3, which is many orders of magnitude lower than typical ambient aerosol number concentrations. Regardless, these performance metrics signify the capability of MVCP to not only identify MPs, but also its capacity to differentiate MPs from ambient particles.

Given that the MVCP envelope is performing well, the score space and envelopes used for MVCP can be employed to evaluate database matching with the ambient and unidentified particles. The $\widetilde{NN}$ scores of the MP labels for ambient particles (AMB) or particles with no peaks in their spectra (LOW) are clustered in the center of the score space (Figure S6.1), indicating the database matching method employed did not have the correct label to identify the particles. In fact, one of the primary reasons why an envelope with higher theoretical confidence (e.g., 95% theoretical confidence) was not selected was due to MP labels being returned for a majority of the AMB and LOW particles (Figure S6.1). More MP particles, and even some particle mixtures, could be captured, but it would also result in more misidentifications of ambient or unidentified particles and thus increasing analysis time during manual verification of the returned prediction sets. Utilizing the MVCP envelope to contextualize results from database matching with multiple spectral inputs is advantageous for determining areas of improvement.

Although non-MP particle types were deliberately excluded from the reference library to employ a binary classification, restricting the reference library and calibration set to only pristine MPs limits the use of this envelope and confidence guarantee to samples beyond the one evaluated in this work. A confidence guarantee assumes the unknown particles will have the same distribution of scores as those used in the calibration set (i.e., the same particle types are in the unknown and calibration sets), meaning the envelope used for the MPs+Ambient sample would only be valid if a future user intended to identify pristine HDPE, PS, or PP particles in their sample. The reference library would also need to include any particle types that are expected in an unknown sample. Studies have shown that expanding reference libraries to contain more particle types encountered in an environmental sample, as well as natural polymeric species and aged plastic particles, improves database matching and HQI scores. ,,, In other words, the reference libraries and calibration sets employed in this study would not be sufficient on their own for calibrating a CP threshold to identify MPs in environmental samples, but they could be used to augment existing reference libraries and calibration sets. Additional guidelines are available for determining calibration set size, and it is recommended to include as many particle types expected in a sample as possible.

Methods beyond traditional database matching could further improve the identification of these chemically complex particles. Statistical and deep-learning , methods have shown potential for identifying MPs under nonpristine conditions (e.g., weathering and particle mixtures). MVCP can adapt to these improvements to data analysis routines, making the amenable nature of MVCP a powerful tool for quantitatively evaluating the overall performance of MP identification workflows and enhancing them.

Conclusions

This study demonstrated the potential for MVCP to identify MPs by assessing HQI scores from PTIR and Raman spectra with statistical confidence. By treating the $\widetilde{NN}$ scores from individual particles as coordinates in a score space, the information between these two inputs was shared to calculate multidimensional regions that generalize the thresholds used in the one-dimensional case. This envelope allowed MVCP to maintain accuracy while returning fewer labels than its single-view counterparts (CP), as well as be less susceptible to particle misidentification when one of the spectra was difficult to identify or could not be identified. Although this method is designed to work with any combination of analysis methods employed with database matching, it is implied that these chemical inputs are collected from the same particle. The mIRage instrument that provides O-PTIR+Raman has a distinct advantage as it simultaneously collects PTIR and Raman spectra for individual particles, thus enhancing the simplicity and throughput of multitechnique analysis. Directly comparing the two spectral inputs with these CP methods quantitatively demonstrates the benefits of using both types of spectra for MP identification.

MVCP was also shown to differentiate between MP and environmental non-MP particles, and metrics for binary classification models combined with CP performance metrics to determine the best-performing threshold. Minimizing misidentification of ambient or unidentified particles as MPs was emphasized in this study, but this did result in a few MP particles not being identified. Although the overall performance of MVCP was positive, we recommend incorporating additional particle types encountered in environmental samples (e.g., natural inorganic and organic materials, natural polymers, oxidized MPs, particle mixtures, etc.) before implementing it broadly across field data sets. Improvements to data analysis routines, such as the spectral preprocessing pipeline and the method used for determining scores of likeness, could be further assessed using sensitivity studies as well as the statistical confidence provided by the MVCP or single-view CP methods. Such advancements paired with reporting statistical confidence for targeted analysis of MPs will ensure confidence in MP identification and contextualize results between MP studies.

Associated images and data for all figures in the main text and Supporting Information are publicly available at the University of MichiganDeep Blue Data. The Python script used to run MVCP and a corresponding user guide can be found on GitHub (https://github.com/eochoarv/MVCP/tree/main).

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsmeasuresciau.6c00002.

• Truncating PTIR spectra and calculating rms noise, relationship between initial NN similarity metric and $\widetilde{NN}$ score, creation of Spectral Dataset #1: Unchanged Subset and Spectral Dataset #1: Noise-Added Subsets, example particle spectra and MVCP scores when augmented with Gaussian noise, confidence guarantees for single-view CP and MVCP methods, adjusting the size of the MVCP envelope during calibration, sensitivity analysis for parameters used in the MVCP method, empirical confidence calculations, F₁ score calculation, number of prediction sets and empirical confidence compared by prediction set size, percentiles of prediction set sizes compared across the CP methods from a select split of data, heat maps of prediction set sizes compared between the CP methods, and comparison of MVCP labels for MPs+Ambient sample separated by particle type (PDF)

R.L.P. and E.O.R. contributed equally to this work. R.L.P. conceptualization, data curation, formal analysis, investigation, methodology, visualization, validation, writingoriginal draft, writingreviewing and editing; E.O.R. conceptualization, data curation, formal analysis, investigation, methodology, software, visualization, validation, writingreview and editing; A.M.A. conceptualization, visualization, methodology, investigation, writingreviewing and editing; M.E.C. conceptualization, visualization, writingreview and editing; Y.P. writingreview and editing; A.J.M. project administration, funding acquisition, writingreview and editing; A.T. conceptualization, project administration, funding acquisition, methodology, writingreview and editing, supervision, visualization; A.P.A. conceptualization, project administration, funding acquisition, methodology, visualization, writingreview and editing, supervision.

The authors declare no competing financial interest.