Improving in Situ Electrode Calibration with Principal Component

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Improving in Situ Electrode Calibration with Principal Component Regression for Fast-Scan Cyclic Voltammetry Douglas R. Schuweiler,† Christopher D. Howard,‡ Eric S. Ramsson,§ and Paul A. Garris*,† †

Illinois State University, Normal, Illinois 61790, United States Oberlin College, Oberlin, Ohio 44074, United States § Grand Valley State University, Allendale, Michigan 49401, United States ‡

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ABSTRACT: Fast-scan cyclic voltammetry with a carbon-fiber microelectrode is an increasingly popular technique for in vivo measurements of electroactive neurotransmitters, most notably dopamine. Calibration of these electrodes is essential for many uses, but it is complicated by the many factors that affect an electrode’s sensitivity when it is implanted in neural tissue. Experienced practitioners of fast-scan cyclic voltammetry are well aware that an electrode’s sensitivity to dopamine depends on both the size and shape of the electrode’s background waveform. In vitro electrode calibration is still the standard method, although a strategy for in situ calibration based on the size of the electrode’s background waveform has previously been published. We reasoned that the accuracy and transferability of in situ calibration could be improved by using principal component regression to capture information contained in the shape of the background waveform. We use leave-one-out cross-validation to estimate the ability of this strategy to predict unknown electrodes and to compare its performance with that of the total-background-current strategy. The principal-component-regression strategy has significantly greater predictive performance than the total-background-current strategy, and the resulting calibration models can be transferred across independent laboratories. Importantly, multivariate quality-control statistics establish the applicability of the strategy to in vivo data. Adoption of the principal-componentregression strategy for in situ calibration will improve the interpretation of in vivo fast-scan cyclic voltammetry data.

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some being broken before calibration.7 Chronically implanted electrodes are cemented to the skull, which makes extraction more difficult and has led to calibration before implantation.4 However, the validity of these calibrations is questionable because of electrode fouling in the brain and likely differences between in vitro and in vivo environments that could affect CFM sensitivity. These concerns have led to the pursuit of an in situ calibration method.7 During FSCV, the voltage applied to the CFM during a potential scan is rapidly ramped from a bias potential, which generates a large current known as the background waveform. The background waveform contains contributions from nonfaradaic currents caused by charging of the electrode double-layer, as well as faradaic currents from electroactive functional groups covalently bonded to the CFM surface and electroactive species present near the CFM surface.8 The background waveform is subtracted from waveforms collected in the presence of the analyte to reveal analyte faradaic currents and the voltammogram (i.e., current versus potential relationship) for analyte identification. CFMs with larger surface areas have larger background waveforms, which positively correlate

any measurement techniques rely on multivariate analyses to identify and quantify analytes.1 Spectra produced during spectrophotometry are a canonical example. For accuracy, care must be taken during calibration, which relates spectral amplitude to analyte concentration. The applicability of a calibration model is typically limited to a particular experimental setup and time window.2 In spectrophotometry, for example, optics of instruments differ, and performance of a spectrophotometer changes over time (e.g., as the lamp ages). Fast-scan cyclic voltammetry (FSCV) with a carbon-fiber microelectrode (CFM) is an increasingly popular analytical technique for monitoring electroactive neurotransmitters because of its nanomolar sensitivity, micrometer spatial resolution, and subsecond temporal resolution.3 Recently, this technique has been improved by using chronically implanted electrodes for months-long recordings in awake animals.4 Analogous to spectrophotometry and similar to other in vivo electrochemical techniques, FSCV suffers from changes in electrode sensitivity during experiments and different sensitives across equipment and electrode types.5,6 CFMs are calibrated for the neurotransmitter dopamine (DA) by exposure to a known concentration in vitro. Acutely implanted electrodes are typically calibrated after extraction from the brain, but the fragility of these electrodes results in © XXXX American Chemical Society

Received: July 19, 2018 Accepted: October 18, 2018 Published: October 18, 2018 A

DOI: 10.1021/acs.analchem.8b03241 Anal. Chem. XXXX, XXX, XXX−XXX

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Analytical Chemistry with DA sensitivity.7,9 This correlation has been leveraged for an in situ electrode-calibration strategy that predicts sensitivity on the basis of the size of the background waveform, referred to here as the total-background-current (TBC) strategy.7 A number of factors affect the size and shape of the background waveform and DA sensitivity. For example, acutely implanting a CFM in the brain affects sensitivity via electrode fouling.6 More recently it has been demonstrated that CFM fouling increases CFM impedance, decreases CFM sensitivity, and alters both the size and shape of the background waveform.10 Furthermore, DA sensitivity depends on the presence of hydroxyl functional groups covalently linked to the surface of the carbon fiber.11 Increases in the concentration of these hydroxyl groups result from redox reactions generated by the potential scan typically used in vivo, and this alters the shape of the background waveform by changing faradaic currents.8 Often, CFMs are pretreated by applying the potential scan at an increased frequency to purposefully cause an increase in hydroxyl groups and sensitivity, whereas the shape of the background waveform is used to monitor the progress of this change.12 In addition to factors affecting the CFM, changes to the Ag/AgCl reference electrode also occur with implantation and affect the shape of the background waveform as well as the DA sensitivity by causing a shift in the applied potential.13 Although these changes affect the size of the background waveform and DA sensitivity, we reasoned that the shape of the background waveform likely carries additional information about these changes that could be used to improve the predictive performance of in situ calibration. We sought to improve the accuracy of in situ calibration by utilizing information about the shape of the background waveform. To predict DA sensitivity, we employed principal component regression (PCR) with leave-one-out crossvalidation (LOOCV). Used here to analyze waveform shape, PCR is well-known in FSCV neurochemical applications as a chemometrics approach for resolving individual analytes from multianalyte signals.14,15 LOOCV estimates the predictive performance of a regression model without independent validation data sets.10 We also assessed three different strategies for calibration transfer across laboratories: uncorrected, slope- and bias-corrected, and robust.2 Here we demonstrate that the PCR strategy better predicts DA sensitivity than the TBC strategy and generates calibration models that transfer across laboratories and are valid in vivo.

set B contained glass- and epoxy-sealed electrodes from our laboratory calibrated after extraction from brain tissue using various pieces of equipment over a period of years. Data set C contained newly constructed, glass-sealed electrodes from an independent laboratory. Data set D contained glass- and paraffin-sealed electrodes from another independent laboratory. All data sets were collected using Ag/AgCl reference electrodes. The electrodes of data sets A and B used a bismuth alloy to make electrical contract between the carbon fiber and the lead, whereas those of data sets C and D used 1 M KCl. The electrodes of data sets A, B, and C used AS4 carbon fibers, whereas those of data set D used T-650 carbon fibers. Further details on electrode construction are available in the SI. Data Collection. Data set A contained data from 24 newly constructed fused-silica electrodes. To collect the data, the CFM and reference electrodes were positioned in a custom electrochemical cell. The CFM was held at −0.4 V versus the reference electrode. The current was recorded while applying a triangle waveform (60 Hz, −0.4 to 1.3 V and back at 400 V s−1) with an EI-400 potentiostat (Ensman Instrumentation, Bloomington, IN) controlled by TarHeel CV software (ESA, Chelmsford, MA), until the background waveform appeared stable. The triangle-waveform frequency was reduced to 10 Hz, and data collection began after the background waveform again appeared stable. A syringe pump (Fisher Scientific, Pittsburgh, PA) injected a continuous stream of buffer over the tip of the CFM at a rate of 3 mL min−1. A 10 s bolus injection of the 1 μM buffered DA solution was accomplished with an airactuated HPLC manual sample-injection system (Rheodyne, Cotati, CA). Data were digitally filtered with a fourth order Bessel 2 kHz low-pass filter. Background waveforms were collected approximately 1 s before exposing the electrode to DA. When consecutive multiple background waveforms were analyzed, they were collected approximately 1 to 3 s prior to DA exposure. DA sensitivity was determined as the background-subtracted current at its peak oxidation potential 3 s after the signal approached the asymptote. Data set B contained data from 19 glass-sealed electrodes calibrated immediately after extraction from urethane-anesthetized rats following an in vivo FSCV experiment reported elsewhere 17 and 12 epoxy-sealed electrodes calibrated immediately after extraction from freely behaving rats following an in vivo FSCV experiment.19 The calibrations were performed as described for the fused-silica electrodes. However, various pieces of equipment were used, including other potentiostats, syringe pumps, and sample-injection systems. Data set C contained data from 29 newly constructed, glasssealed electrodes collected using similar methods. Notable differences include the use of Tarheel HDCV recording software (UNC, Chapel Hill, NC), and a gravity-fed microfluidics device. Data set D contained data collected using Demon Voltammetry (Wake Forest Baptist Medical Center, Winston-Salem, NC), and the details are reported elsewhere.18,20 Data were included from five newly constructed, glass-sealed electrodes and the same five electrodes after they had been dipped in paraffin and cleaned with xylene. These data were collected using a gravity-fed microfluidics device. Data set D also contained data from five newly constructed electrodes that were sealed with paraffin and calibrated using a Petri dish and a pipet.

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EXPERIMENTAL SECTION Chemicals. All chemicals were purchased from SigmaAldrich Company (St. Louis, MO), unless otherwise noted. All chemicals were used without further purification. In vitro experiments were conducted in physiological buffer (11.5 mM Tris HCl, 140 mM NaCl (Fisher Scientific, Pittsburgh, PA), 3.25 mM KCl, 1.2 mM CaCl2·2H2O, 1.25 mM NaH2PO4 (Fisher Scientific, Pittsburgh, PA), 1.2 mM MgCl2, 2 mM Na2SO4) adjusted to pH 7.4 with 0.5 N NaOH (Acros Organics, Morris Plains, NJ). A 10 mM stock solution of dopamine HCl was prepared in 0.15 N HClO4 and diluted to 1 μM in room-temperature buffer immediately before use. Buffered DA solutions were discarded after 2 h. All aqueous solutions were prepared with ultrapure water (Barnstead GenPure system; Thermo Scientific, Waltham, MA). Electrodes. Electrodes and their data were separated into four different data sets. Data set A contained newly constructed fused-silica electrodes from our laboratory. Data B

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Figure 1. Total background current as a significant predictor of DA sensitivity: (A) example background waveforms with a linear relationship between total background current and sensitivity, (B) linear regression of sensitivity on total background current, (C) slope describing the relationship between observed sensitivities and sensitivities predicted from the total background current, and (D) example background waveforms without a linear relationship between total background current and sensitivity. The colors of the points correspond to the colors of the example background waveforms.

respectively; z = −0.74, p = 0.459).7 Next, we predicted sensitivity using the regression equation from our implementation of the TBC strategy, y = 53.90x − 9.54, where y is the predicted sensitivity (nA/μM) and x is TBC (mA). Finally, we plotted predicted versus observed sensitivity and fit a line through these data and the intercept (Figure 1C). The slope of this line was not significantly different from 1.00 (slope = 0.95, t[22] = −1.0374, p = 0.311), which is similar to the results from previous work.7 Thus, TBC is a significant predictor of DA sensitivity, as previously demonstrated. PCR Strategy for Predicting Sensitivity. Electrodes with similar TBCs but differently shaped background waveforms can have different sensitivities, whereas ones with different TBCs can have the same sensitivity (Figure 1D). We reasoned that the prediction of sensitivity could be improved by capturing information contained in the shape of the background waveform, and thus we assessed the use of PCR for predicting DA sensitivity. Details regarding a MatLab implementation of the PCR algorithm are presented in the SI (Figure S-1). PCR is a combination of principal component analysis (PCA), which extracts information from the waveform shape as principal components (PCs), and inverse leastsquares regression (ILR), which then predicts the dependent variable, CFM sensitivity, using PCs as the independent variable. Mean-centered PCA generates n − 1 PCs that are recombined in varying amounts to explain all of the variance in the background waveforms contained in the data set.21 However, in most cases only a small number of PCs are needed to capture signal variance, and the remaining PCs capture

Statistics. PCR was implemented as previously described.21 Q statistics were calculated as previously described.22 Meng’s z test was used to compare correlated correlation coefficients.23 Two-sample Kolmogorov−Smirnov (KS) tests were used to compare distributions. Fisher’s z transformation was used when comparisons involved an average correlation coefficient.24 All analyses were conducted in MatLab R2015b (MathWorks, Natick, MA). Plots were generated in SigmaPlot 12.5 (Systat Software Inc., San Jose, CA).

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RESULTS AND DISCUSSION TBC Strategy for Predicting Sensitivity. The previously established in situ calibration strategy was implemented as a multiple linear regression with parameters for TBC and switching potential.7 Here we focused on developing an in situ calibration strategy implemented with data from electrode calibrations for DA using the most commonly employed switching potential. For our data, the TBC strategy thus reduces from a multiple linear regression to a linear regression relating only TBC to DA sensitivity. However, as shown below, similar results are obtained without including a parameter for switching potential. We first implemented the TBC strategy using data set A, generated in our laboratory. Observed sensitivity was regressed on TBC, which was calculated by summing the absolute value of the current recorded at each point in the background waveform. This analysis produced a significant correlation between sensitivity and TBC (R = 0.80, F[1,24] = 38.97, p < 1 × 10−5; Figure 1A,B), which was not significantly different from the previously reported value (R = 0.80 and R = 0.86, C

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the observed sensitivities onto the TBCs, and then using the resulting regression equation to predict the sensitivity of the excluded electrode. By generating n TBC calibration models, the predicted sensitivities were collected for each electrode in a data set when it was unknown. The predicted sensitives from all data sets were regressed onto the observed sensitivities using a single OLSR (Figure 2A). We also applied the PCR

noise. Thus, a necessary step is determining which PCs contain signals and should therefore be included in the ILR. PC selection can be conceptualized as a trade-off between transferability and accuracy.16,25 Including fewer PCs results in a model that is more transferable with less predictive performance, whereas including too many PCs results in model overfitting with high predictive performance for the training set but less transferability to unknown data. Most selection methods are based on how well the PCs capture the variance in the training data set. PCs are first ordered according to the amount of variance that they explain, and k PCs are selected on the basis of a predetermined criterion (e.g., scree plots, Malinowski’s F test, or percent cumulative variance). However, although not always applicable, the LOOCV used here is advantageous because it estimates PC performance at predicting the dependent variable (i.e., sensitivity) rather than the variance explained in the training set.16,21 A disadvantage of LOOCV is computational complexity.16,21 For k PCs, LOOCV involves iteratively treating each electrode as an unknown by excluding it from the training set. PCA is performed on this training set, followed by ILR of the observed sensitivities from the remaining electrodes onto the amount of each of the k PCs contained in their background waveforms. This ILR generates a calibration model that is used to predict the sensitivity for the excluded electrode. After generating n calibration models, the predicted sensitivities have been collected for each electrode when it is unknown and k PCs were included. These predictions are compared to the observed sensitivities using ordinary least-squares regression (OLSR). This LOOCV process is repeated for each possible k, and after generating n × k calibration models, the final calibration model is determined by selecting k to maximize predictive performance. Predictive performance is maximized by different criteria, with the most popular being minimization of the root-meansquared error (RMSE, also called the standard error of the regression) or an equivalent statistic (i.e., mean-squared error or predicted-residual-error sum of squares).16,21 However, local and global minima for RMSE and equivalent statistics are often observed for cases where selection of the global minimum results in too many PCs and consequently model overfitting. For this reason, it is not unusual to find examples where a local minimum with fewer PCs is subjectively picked.16,26 Maximization of adjusted R2 addresses this issue.16,26 Adjusted R2 penalizes models that contain predictor variables that do not increase fit by more than chance, which limits model overfitting by excluding PCs containing noise. The subjectivity involved in PC selection using RMSE and equivalent statistics is thus resolved, because the global maximum for adjusted R2 is an objective criterion. For our data sets, the adjusted R2 global maximum typically corresponded with an RMSE local minimum, further supporting its utility for PC selection (Figure S-2). Comparing the Predictive Performances of the Strategies. A wide variety of electrode-construction methods and recording hardware and software are currently employed for FSCV. In order to provide an overall comparison of TBC and PCR strategies, we assessed the predictive performance of each strategy for four data sets collected in three laboratories (see the Experimental Section for details). We first assessed the predictive performance of the TBC strategy by performing an LOOCV of each data set’s TBC model. This analysis involved iteratively excluding each electrode from its data set, regressing

Figure 2. Significantly better predictive performance of the PCR strategy across laboratories. (A) TBC strategy applied to all four data sets. (B) PCR strategy applied to all four data sets. All insets have the same axes.

strategy to each data set. Predicted sensitivities for the electrodes were already determined during the LOOCV used for PC selection while analyzing each data set. These predicted sensitivities were also regressed onto the observed sensitivities using a single OLSR (Figure 2B). For these OLSRs, perfect predictive performance is indicated by a slope at unity, an intercept at the origin, and a correlation coefficient at unity (y = 1.00x + 0.00, R = 1.00). The OLSR estimating the predictive performance of the TBC strategy indicated a significant predictive ability (R = 0.89, F[1,97] = 369.77, p < 1 × 10−34; Figure 2A). However, the intercept for the TBC strategy was significantly different from the origin (intercept = 5.64, t[97] = 3.37, p = 0.001), and the slope was significantly less than unity (slope = 0.81, t[97] = −4.57, p < 0.0001). The OLSR estimating the predictive performance of the PCR strategy also had a significant correlation coefficient (R = 0.97, F[1,97] = 1300.217, p < 1 × 10−57; Figure 2B). The intercept for the PCR strategy was not significantly different from the origin (intercept = 1.95, t[99] = 1.89, p = 0.061), although the slope was significantly different from unity (slope = 0.93, t[97] = −2.72, p = 0.008). A comparison of the OLSRs for the two strategies revealed D

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Figure 3. Significantly better results from transferring a PCR calibration model across independent laboratories than from developing a TBC calibration model for each independent laboratory. (A) TBC strategy applied to data from independent laboratories (data sets C and D). (B) PCR strategy applied to data sets C and D. (C) Calibration model built by applying the PCR strategy to all the electrodes from our laboratory (data sets A and B). (D) Uncorrected transfer of the calibration model from our electrodes to electrodes from independent laboratories. (E) Slope- and biascorrected transfer of the calibration model. (F) Robust-calibration-transfer strategy applied to data sets C and D. All insets have the same axes.

strategy, referred to here as uncorrected transfer, has demonstrated success in spectroscopy only when instrumentation is identical. With instrumentation differences across laboratories, calibration transfer is currently executed with three different types of strategies. Corrected transfer modifies the predictions from the uncorrected transfer by applying a slope and bias adjustment to force the OLSR to produce a line with an intercept at the origin and a slope at unity. Robust transfer generates calibration models by including measurements from multiple laboratories. The final strategy involves the use of mathematical approaches to adjust the raw data so that the signals produced by different laboratories are more correlated. We only investigated uncorrected, corrected, and robust transfer strategies, because implementation of the final strategy would require collecting background waveforms from the same set of electrodes in different laboratories, and the fragility of these electrodes renders this strategy impractical. As a baseline for statistical comparisons between transfer strategies, we present the combined OLSR results for the TBC and PCR strategies when data set C is used to predict data set C and data set D is used to predict data set D. The OLSR estimating the predictive performance of the TBC strategy indicated a significant correlation (R = 0.77, F[1,42] = 62.504, p < 0.001; Figure 3A). As before, the intercept for the TBC strategy was significantly different from the origin (intercept = 18.29, t[42] = 6.91, p < 1 × 10−7), and the slope was significantly less than unity (slope = 0.63, t[42] = −7.81, p < 1 × 10−8). The OLSR estimating the predictive performance of the PCR strategy also indicated a significant correlation (R = 0.93, F[1,42] = 270.95, p < 1 × 10−19; Figure 3B). The intercept for the PCR strategy was not significantly different from the origin

significantly different correlation coefficients and slopes but not intercepts (z = −6.05, p < 1 × 10−8; t[194] = −2.48, p = 0.014; and t[194] = 1.88, p = 0.062, respectively). A histogram of the errors in the predicted sensitivities, expressed as absolute percent differences from the observed sensitivities, is displayed in the insets of the OLSR plots. The mean absolute percentage error (MAPE) for the TBC strategy was 25.47%, and the median error was 18.79% (inset, Figure 2A). The MAPE for the PCR strategy was 14.78%, and the median error was 11.32% (inset, Figure 2B). A KS test revealed a significant difference in the error distributions of the TBC and PCR strategies (D[99,99] = 0.26, p = 0.001). Thus, analyses of regression parameters and error distributions indicate that the PCR strategy has significantly greater predictive performance than the TBC strategy for the data collected in the three laboratories. We also assessed the predictive performance of the TBC and PCR strategies for each of the four data sets independently (Figure S-3). The PCR strategy had significantly better predictive performance than the TBC strategy for data sets A, B, and D. Both strategies performed similarly for data set C. Surprisingly, the TBC strategy failed for data set D. Detailed results are presented in the SI. Assessing Uncorrected Calibration Transfer of the PCR Strategy. Calibration transfer is an active area of research, particularly within spectroscopy, that seeks to develop methods for the generation of multivariate calibration models that accurately predict sensitivities across various pieces of equipment.2 The simplest strategy for calibration transfer is to directly apply a calibration model developed in one laboratory to data from another laboratory. However, this E

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indicated a significant correlation (R = 0.84, F[1,42] = 110.90, p < 1 × 10−12). By design, the intercept for the correctedtransfer strategy was not significantly different from the origin (intercept = 0.00, t[42] = 0.00, p > 0.999), and the slope was not significantly different from unity (slope = 1.00, t[42] = 0.00, p = 0.999). Additionally, the corrected calibration transfer produced an MAPE of 31.70%, and the median error was 17.05% (inset, Figure 3E). A KS test revealed that the correction also significantly improved the distribution of errors compared with the uncorrected model (D[44,44] = 0.32, p = 0.012). A comparison of OLSRs for corrected-transfer and baselineTBC strategies revealed significantly different intercepts and slopes but not correlation coefficients (t[84] = 2.50, p = 0.014; t[84] = −2.89, p = 0.005; and z = −1.28, p = 0.199, respectively). OLSRs for corrected-transfer and baseline-PCR strategies did not indicate significantly different intercepts and slopes but revealed significantly different correlation coefficients (t[84] = 0.90, p = 0.370; t[84] = −1.10, p = 0.273; and z = 2.69, p = 0.007, respectively). KS tests did not indicate significant differences between error distributions for corrected-transfer and either baseline-TBC (D[44,44] = 0.09, p = 0.649) or -PCR (D[44,44] = 0.11, p = 0.567) strategies. Taken together, these results indicate that although performance was significantly worse than that of the baseline-PCR strategy, the bias- and slope-corrected transfer of the PCR calibration model from our electrodes to electrodes from independent laboratories had significantly better performance than a TBC calibration model built from and applied to the independent data sets. Additionally, the corrected-transfer strategy results in an OLSR with an intercept at the origin and a slope at unity, values reflecting perfect predictive performance. Although corrected transfer requires in vitro calibration of electrodes on the equipment to which the model is to be transferred, it performed better than uncorrected transfer. Assessing Robust Calibration Transfer. The robustcalibration-transfer strategy is based on building a PCR calibration model using data from all of the laboratories to which the model will be applied.2 Although more complicated than uncorrected or corrected transfer, robust transfer models are less sensitive to differences in instrumentation across laboratories and within a single laboratory over time. Per uncorrected and corrected transfer, robust transfer was applied to data sets C and D (Figure 3F). The OLSR estimating the predictive performance of robust transfer indicated a significant correlation (R = 0.90, F[1,42] = 186.45, p < 1 × 10−16). The intercept for robust transfer was significantly different from the origin (intercept = 7.55, t[42] = 3.20, p = 0.003), and the slope was significantly different from unity (slope = 0.90, t[42] = −3.58, p = 0.001). A comparison of OLSRs for robust-transfer and baseline-TBC strategies revealed significantly different intercepts, slopes, and correlation coefficients (t[84] = 2.08, p = 0.040; t[84] = −2.47, p = 0.016; and z = −2.81, p = 0.005, respectively). OLSRs for robust-transfer and baseline-PCR strategies did not indicate significantly different intercepts, slopes, or correlation coefficients (t[84] = −0.44, p = 0.649; t[84] = 0.34, p = 0.735; and z = 1.13, p = 0.257, respectively). Robust transfer produced an MAPE of 21.89%, and the median error was 17.16% (inset, Figure 3F). KS tests did not indicate significant differences between error distributions for robusttransfer and either baseline-TBC (D[44,44] = 0.09, p = 0.649) or -PCR (D[44,44] = 0.09, p = 0.649) strategies.

(intercept = 5.83, t[42] = 1.91, p = 0.063), but the slope was significantly different from unity (slope = 0.88, t[42] = −2.34, p = 0.024). A comparison of the OLSRs for the two strategies revealed significantly different correlation coefficients, intercepts, and slopes (z = −4.072, p < 0.0001; t[84] = 2.26, p < 0.0001; and t[84] = −2.55, p = 0.013, respectively). The TBC strategy produced an MAPE of 30.04%, and the median error was 18.29% (inset, Figure 3A). The PCR strategy produced an MAPE of 20.67%, and the median error was 16.62% (inset, Figure 3B). A KS test did not indicate a significant difference in error distributions (D[44,44] = 0.16, p = 0.328). To generate the PCR calibration model to be transferred we pooled the data collected in our laboratory (data sets A and B). The OLSR estimating the predictive performance of the PCR strategy resulted in selecting eight PCs for the combined data set (Figure S-2E). The OLSR indicated a significant correlation (R = 0.93, F[1,53] = 335.88, p < 1 × 10−23; Figure 3C). However, the intercept was significantly different from the origin (intercept = 1.70, t[53] = 2.35, p = 0.022), and the slope was significantly different from unity (slope = 0.88, t[53] = 2.53, p = 0.015). For this combined data set, the PCR strategy produced an MAPE of 12.52%, and the median error was 9.08% (inset, Figure 3C). We first tested uncorrected transfer, which has the advantage of being the simplest of the strategies, because it requires no data from the laboratory to which the model will be transferred. We applied the calibration model generated from our laboratory (data sets A and B, see above) to the data sets obtained from two independent laboratories (data sets C and D). The OLSR for the uncorrected transfer indicated a significant correlation (R = 0.84, F[1,42] = 110.90, p < 1 × 10−12; Figure 3D). However, the intercept was significantly different from the origin (intercept = 15.11, t[42] = 7.57, p < 1 × 10−8), and the slope was significantly different from unity (slope = 0.35, t[42] = −18.69, p < 1 × 10−21). This calibration transfer produced an MAPE of 30.81%, and the median error was 30.85% (inset, Figure 3D). Comparison of the OLSRs for uncorrected-transfer and baseline-TBC strategies revealed significantly different slopes but not intercepts or correlation coefficients (t[84] = −3.92, p < 0.001; t[84] = −0.64, p = 0.526; and z = 1.23, p = 0.217, respectively). A comparison of the OLSRs for uncorrectedtransfer and baseline-PCR strategies indicated significantly different slopes, intercepts, and correlation coefficients (t[84] = −6.04, p < 1 × 10−7; t[84] = 2.54, p = 0.013; and z = −2.66, p = 0.008, respectively). KS tests indicated significant differences between error distributions for uncorrected-transfer and either baseline-TBC (D[44,44] = 0.30, p = 0.021) or -PCR (D[44,44] = 0.45, p < 0.001) strategies. The results of these analyses indicate that the uncorrectedtransfer strategy has significantly worse predictive performance than both the baseline-PCR and -TBC strategies. Indeed, the regression plot reveals a consistent underestimation of the sensitivity for electrodes with higher observed sensitivities. However, this can be compensated for by applying slope- and bias-correction to the predicted values, as described next. Assessing Slope- and Bias-Corrected Calibration Transfer. For corrected transfer, the slope and bias of the uncorrected transfer (0.35 and 15.11, respectively; Figure 3D) are used to correct predicted sensitivities generated by the transferred PCR calibration model (corrected = (prediction − intercept)/slope; Figure 3E).2 The OLSR estimating the predictive performance of the corrected-transfer strategy F

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Analytical Chemistry Unlike uncorrected- and corrected-transfer strategies, robust transfer produced results that were not significantly different from the baseline-PCR strategy on any parameter and were significantly different from the baseline-TBC strategy on all parameters. Thus, robust transfer appears preferable for constructing calibration models for transfer across independent laboratories. Although robust transfer requires in vitro calibration of electrodes in each different laboratory and subsequent PCR-model development, the number of samples necessary from each laboratory most likely will be reduced compared with developing separate laboratory-specific calibration models. Importantly, the more successful calibrationtransfer methods presented here (i.e., corrected and robust transfer) require in vitro calibration of electrodes in the laboratory to where the model is to be transferred. This ensures that data will be available to assess predictive performance of the transferred calibration model. Assessing the Effect of Noise on the PCR Strategy. FSCV recordings are susceptible to random high-frequency noise that could potentially impact the predictive performance of the PCR strategy. In order to determine if a single laboratory’s calibration model generates stable predictions despite high-frequency noise, we repeated the PCR strategy on all the electrodes from our laboratory (data sets A and B), but we included 20 consecutive background waveforms for each electrode. All 20 background waveforms were excluded from the training data set during LOOCV. Despite having 20 times as many data points, eight PCs were again selected, and the results of the OLSR analysis were exactly the same as before (MAPE = 12.52%, R = 0.93, intercept = 1.70, slope = 0.88; Figure S-4; compare with Figure 3C). Thus, the PCR strategy provides stable predictions, and the accuracy of the prediction does not appear to be influenced by random high-frequency noise. Importantly, this indicates that in practice, no special care is necessary for selecting background waveforms free of artifacts from random high-frequency noise. Applying the PCR Strategy to in Vivo Data. The background waveform of an electrode is different prior to, during, and after implantation in the brain (Figure 4A).10 We used the Q statistic22 to determine if the PCR calibration strategy had validity in vivo. These are the same Q statistics that the FSCV field has adopted for quality control of chemometrics using PCR.14,15 The Q value is the sum of squared residuals that are unaccounted for by the PCA model. Qα indicates the threshold value at which a Q value is significantly larger than noise, estimated from the training data set PCs that are not retained. In practice, if the Q value for a background waveform exceeds the Qα value, then the background waveform contains putative signals not accounted for by the model, and the PCR calibration model should not be used to estimate sensitivity from that background waveform. We calculated Q values for 50 background waveforms collected in vivo, 25 from glass-sealed electrodes implanted in anesthetized rats, and 25 from epoxy-sealed electrodes implanted in awake rats.17,19 CFMs were subjected to the same cycling procedures as those used for in vitro measurements, and the background waveforms were collected at the end of the experiment. None of these Q values exceeded the Qα determined from the calibration model containing all the electrodes from our lab (data sets A and B, Figure 4B). It is important to note that some of the electrodes used to generate in vivo background waveforms did not contribute in vitro waveforms to the training data set. Thus, the PCR strategy

Figure 4. PCR strategy applied to in vivo data: (A) example electrode showing the difference between in vivo and in vitro background waveforms and (B) Q values for in vivo background waveforms from different electrodes.

appears applicable to in situ data collected from both anesthetized and freely behaving rats even when using unknown electrodes. To minimize drift before conducting FSCV experiments, CFMs are given time to stabilize. However, some drift still occurs especially at early times. We used data previously recorded in an anesthetized rat across a 2 h period17 to determine how electrode drift influences predicted sensitivities in vivo. As above, the PCR model generated from data sets A and B was used to calibrate background waveforms collected during the first 5 min when some drift was occurring and the final 5 min with minimal drift (Figure 5). Drift is indicated by broad features in the pseudocolor plot of backgroundsubtracted voltammograms. We also calculated the mean ± SEM from five in vitro calibrations conducted after the CFM was extracted from the brain. Results demonstrate that electrode drift minimally influenced predicted sensitivities for the CFM. Additionally, results demonstrate that the predicted sensitivities were stable when the electrode was stable, excluding transient DA release evoked by electrical stimulation (≈0 and 115 min). Electrode drift has been linked to changes in CFM surface chemistry, and these changes in surface chemistry have been linked to changes in DA sensitivity, which suggests that CFM sensitivity may have changed over the course of the experiment, albeit negligibly.8,11 Unfortunately, determining the effect of in vivo drift on electrode sensitivity is technically difficult, and we are unaware of any existing publications where this has been attempted. Most importantly and taken together with the insensitivity of this calibration strategy to highfrequency noise (Figure S-4), these results indicate that most if G

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local minima would be made subjectively for each of the analyses. Given this limitation and on the basis of previous analyses, we used eight PCs for each analysis. We also consider this the best estimate for the number of PCs for analyses involving subsets of this data set, because it was the same number of PCs indicated from the LOOCV of the data set. These results indicate that the predictive performance of our strategy begins to asymptote when about 40 electrodes have been included. Thus, the data necessary to implement our strategy could be collected by a single individual in 1 day if it is not already available. However, it is important for FSCV practitioners to bear in mind that more exemplars are required for in situ calibration than for chemometric analyses using PCR. In addition to determining the necessary training set size, this analysis further validates the ability of the PCR strategy to predict the sensitivity of unknown electrodes, and it indicates that the success of this strategy is not restricted to a particular training set. Consider the case when 40 electrodes are randomly selected for inclusion in the training set. First, the average correlation coefficient for training sets including only 40 electrodes is not significantly different from the correlation coefficient for the LOOCV of the PCR strategy on the full training set (R = 0.89 and R = 0.93, respectively; z = 1.08; p = 0.280). However, the average correlation coefficient is significantly different from the correlation coefficient for the LOOCV of the TBC strategy (R = 0.89 and R = 0.81, respectively; z = −2.12; p = 0.034). Second, although no measures were taken to prevent the random selection of identical 40-electrode training sets, the number of possible combinations exceeds 1 × 1013 which ensures that most, if not all, of the 1000 training sets were different. Limitations. We have not yet extended the PCR strategy to predicting the sensitivities of multiple analytes and multiple waveforms. The previously reported TBC in situ calibration strategy was able to account for different waveforms with a single model, but different analytes required different models.7 Conversely, the PCR strategy would require different models for different waveforms, but it may be possible to determine the sensitivities for different analytes for one waveform with a single model. The success of this possibility will depend on the ability of the PCs to predict the sensitivity to the additional analytes.

Figure 5. Effects of in vivo electrode drift on the sensitivity predicted using the PCR strategy. Top: pseudocolor plots displaying serial background-subtracted cyclic voltammograms at the beginning and end of the in vivo experiment (x-axis: time, y-axis: applied potential, zaxis: recorded current). Bottom: changes in the electrode’s predicted sensitivity over time. The red lines show the mean ± SEM of the electrode’s observed sensitivity in vitro following the experiment.

not all in vivo background waveforms collected during an experiment will produce an acceptable predicted sensitivity. Determining the Necessary Training-Set Size. We sought to determine how many electrodes need to be calibrated for the training data set in order to generate accurate predictions. To accomplish this, we randomly selected a set of electrodes from data sets A and B to include in the training set, varying the number from 10 to 50 in increments of 5 electrodes, and we determined the ability of the training set to predict the observed sensitivity for a different randomly selected set of 5 electrodes. We performed this analysis 1000 times for each number of electrodes included in the training data set and calculated the correlation coefficients and MAPEs (Figure 6). We were unable to determine the number of PCs to retain for each analysis individually, because adjusted R2 requires the number of electrodes being predicted to be greater than the maximum number of PCs, and selection of the RMSE

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CONCLUSION Using PCR to capture information contained in the shape of an electrode’s background waveform produces significantly better predictions of DA sensitivity than using the size of the background waveform alone, per the TBC strategy. Although the PCR strategy performs best for a relatively homogeneous set of electrodes, it can be generalized to more variable data, transferred across laboratories, and applied to in situ data in a quality-controlled manner using Q statistics. These features are particularly useful, because they enable the possibility of an in situ calibration standard for the DA FSCV field. Although calibration transfer produces acceptable results for this analysis, it is important to acknowledge that we are not weighing in on its use for chemometrics and that there may be important differences between the applications of PCR for chemometrics and in situ calibration. Additionally, the PCR calibration strategy we describe is a multivariate analysis that is not limited to FSCV data, and it could potentially be adapted to other techniques. Returning to

Figure 6. Predictive accuracy of the PCR strategy beginning to asymptote with a training set size of 40 electrodes: (A) mean correlation coefficient for different training set sizes and (B) mean MAPE for different training set sizes. Error bars represent the standard deviations. H

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(5) Acciaroli, G.; Vettoretti, M.; Facchinetti, A.; Sparacino, G. Biosensors 2018, 8, No. e24. (6) Logman, M. J.; Budygin, E. A.; Gainetdinov, R. R.; Wightman, R. M. J. Neurosci. Methods 2000, 95, 95−102. (7) Roberts, J. G.; Toups, J. V.; Eyualem, E.; McCarty, G. S.; Sombers, L. A. Anal. Chem. 2013, 85, 11568−11575. (8) Mitchell, E. C.; Dunaway, L. E.; McCarty, G. S.; Sombers, L. A. Langmuir 2017, 33, 7838−7846. (9) Rodeberg, N. T.; Sandberg, S. G.; Johnson, J. A.; Phillips, P. E. M.; Wightman, R. M. ACS Chem. Neurosci. 2017, 8, 221−234. (10) Meunier, C. J.; Roberts, J. G.; McCarty, G. S.; Sombers, L. A. ACS Chem. Neurosci. 2017, 8, 411−419. (11) Roberts, J. G.; Moody, B. P.; McCarty, G. S.; Sombers, L. A. Langmuir 2010, 26, 9116−9122. (12) Fortin, S. M.; Cone, J. J.; Ng-Evans, S.; McCutcheon, J. E.; Roitman, M. F. Current Protocols in Neuroscience 2015, 70, 7.25.1− 7.25.20. (13) Hashemi, P.; Walsh, P. L.; Guillot, T. S.; Gras-Najjar, J.; Takmakov, P.; Crews, F. T.; Wightman, R. M. ACS Chem. Neurosci. 2011, 2, 658−666. (14) Keithley, R. B.; Wightman, R. M.; Heien, M. L. TrAC, Trends Anal. Chem. 2009, 28, 1127−1136. (15) Keithley, R. B.; Wightman, R. M.; Heien, M. L. TrAC, Trends Anal. Chem. 2010, 29, 110. (16) Wehrens, R. Chemometrics with R: multivariate data analysis in the natural sciences and life sciences; Springer: Berlin, 2011. (17) Schuweiler, D. R.; Athens, J. M.; Thompson, J. M.; Vazhayil, S. T.; Garris, P. A. Behav. Brain Res. 2018, 336, 191−203. (18) Ramsson, E. S.; Cholger, D.; Dionise, A.; Poirier, N.; Andrus, A.; Curtiss, R. PLoS One 2015, 10, No. e0141340. (19) Schuweiler, D. R.; Athens, J. M.; Thompson, J. M.; Vazhayil, S. T.; Garris, P. A. Amphetamine affects reward-related behavior but not reward-evoked dopamine signals. Presented at the 45th Society for Neuroscience Meeting, Washington, DC, Oct 17−21, 2015; Poster 316.09/J39. (20) Ramsson, E. S. BioTechniques 2016, 61, 269−271. (21) Kramer, R. Chemometric techniques for quantitative analysis; CRC Press: Boca Raton, FL, 1998. (22) Jackson, J. E.; Mudholkar, G. S. Technometrics 1979, 21, 341− 349. (23) Meng, X.-L.; Rosenthal, R.; Rubin, D. B. Psychological Bulletin 1992, 111, 172−175. (24) Strube, M. J. Journal of Applied Psychology 1988, 73, 559−568. (25) Xie, Y. L.; Kalivas, J. H. Anal. Chim. Acta 1997, 348, 19−27. (26) Joliffe, I. T. Principal Components in Regression Analysis. In Principal Component Analysis, 2nd ed; Springer Series in Statistics; Springer: New York, 2010; pp 167−198. (27) Khaydukova, M.; Medina-Plaza, C.; Rodriguez-Mendez, M. L.; Panchuk, V.; Kirsanov, D.; Legin, A. Sens. Actuators, B 2017, 246, 994−1000.

the canonical example of spectrophotometry, the analytical strategy we describe is analogous to using the spectra obtained from a spectrophotometer blank solution to predict calibration factors for a species of interest, although we are unaware if this has been attempted. This calibration strategy may have utility for any technique where the instrumentation produces a background response and features of the background response are correlated with the instrument’s sensitivity to a species of interest. For example, this strategy could improve the calibration of potentiometric electrodes from voltammetricelectrode data in multisensor systems.27 In the same vein, it may be possible to improve the in situ calibration of enzymelinked biosensors, such as those used for continuous bloodglucose monitoring, by adding a voltammetric electrode to the device.5

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.8b03241.

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Electrode construction, OLSRs comparing the predictive performances of the two strategies for each data set, flowchart detailing the PCR-strategy workflow, comparison of adjusted R2 and RMSE for the selection of k, significantly better predictive performance by the PCR strategy for three of the four data sets tested, and random high-frequency noise not affecting the PCR strategy (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: 309-438-2664. ORCID

Douglas R. Schuweiler: 0000-0003-1967-7161 Author Contributions

D.R.S. conceived and designed the analyses, P.A.G. and D.R.S. wrote the paper, D.R.S. collected data sets A and B, C.D.H. collected data set C, and E.S.R. collected data set D. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Beta Lambda chapter of Phi Sigma and the School of Biological Sciences at Illinois State University.

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REFERENCES

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DOI: 10.1021/acs.analchem.8b03241 Anal. Chem. XXXX, XXX, XXX−XXX