Rank estimation and the multivariate analysis of in vivo fast-scan cyclic voltammetric data

Abstract

Principal component regression has been used in the past to separate current contributions from different neuromodulators measured with in vivo fast-scan cyclic voltammetry. Traditionally, a percent cumulative variance approach has been used to determine the rank of the training set voltammetric matrix during model development; however, this approach suffers from several disadvantages including the use of arbitrary percentages and the requirement of extreme precision of training sets. Here, we propose that Malinowski's F-test, a method based on a statistical analysis of the variance contained within the training set, can be used to improve factor selection for the analysis of in vivo fast-scan cyclic voltammetric data. These two methods of rank estimation were compared at all steps in the calibration protocol including the number of principal components retained, overall noise levels, model validation as determined using a residual analysis procedure, and predicted concentration information. By analyzing 119 training sets from two different laboratories amassed over several years, we were able to gain insight into the heterogeneity of in vivo fast-scan cyclic voltammetric data and study how differences in factor selection propagate throughout the entire principal component regression analysis procedure. Visualizing cyclic voltammetric representations of the data contained in the retained and discarded principal components showed that using Malinowski's F-test for rank estimation of in vivo training sets allowed for noise to be more accurately removed. Malinowski's F-test also improved the robustness of our criterion for judging multivariate model validity, even though signal-to-noise ratios of the data varied. In addition, pH change was the majority noise carrier of in vivo training sets while dopamine prediction was more sensitive to noise.

Figure 1

Histograms of the estimated rank of A) Case I and B) Case II training sets. White and black represent rank determined by the 99.5% cumulative variance method and Malinowski’s F-test, respectively. C) Histogram of the estimated rank of Case III training sets.

Figure 2

Comparison of effective cyclic voltammograms in a representative Case I training set. A) Original dopamine cyclic voltammograms containing all PCs before factor selection. B) Original pH change cyclic voltammograms containing all PCs before factor selection. C) Dopamine cyclic voltammograms from A) constructed using only the PCs retained by the 99.5% cumulative variance method (n = 5 PCs). D) pH change cyclic voltammograms from B) constructed using only the PCs retained by the 99.5% cumulative variance method (n = 5 PCs). E) Dopamine cyclic voltammograms from A) constructed using only the PCs retained by Malinowski’s F-test (n = 2 PCs). F) pH change cyclic voltammograms from B) constructed using only the PCs retained by Malinowski’s F-test (n = 2 PCs).

Figure 3

RMS noise removed by the 99.5% cumulative variance method (99.5% C.V.) and Malinowski’s F-test for all of the Case I training sets. Error bars represent SEM. White bars represent noise from dopamine secondary PCs and black bars represent noise from pH change secondary PCs. Two stars and three stars represent P < 0.01 and P < 0.001 significance, respectively.

Figure 4

Cyclic voltammetric representation of the secondary PCs from each method of factor selection for a representative Case II training set. A) Secondary PCs of the dopamine cyclic voltammograms determined by the 99.5% cumulative variance method (PCs 3–10). B) Secondary PCs of the pH change cyclic voltammograms determined by the 99.5% cumulative variance method (PCs 3–10). C) Secondary PCs of the dopamine cyclic voltammograms determined by Malinowski’s F-test (PCs 5–10). D) Secondary PCs of the pH change cyclic voltammograms determined by Malinowski’s F-test (PCs 5–10). E) The difference of secondary PCs between methods for the dopamine cyclic voltammograms (PCs 3–4). F) The difference of secondary PCs between methods for the pH change cyclic voltammograms (PCs 3–4).

Figure 5

Histograms of Q_α values of A) Case I and B) Case II training sets. White and black represent the rank determined by the 99.5% cumulative variance method and Malinowski’s F-test, respectively. C) Histogram of Q_α values of Case III training sets.

Figure 6

Comparison of stimulated release predicted by PCR using primary PCs determined with both methods of factor selection for a representative Case I training set. A) Color plot representation of in vivo cyclic voltammograms collected in a freely-moving rat. The pink bar indicates a stimulation given to the animal to evoke dopamine release and pH changes (60 Hz, 24 pulses, 125 μA). The white dashed line indicates the oxidation potential of dopamine. B) Current versus time trace at the oxidation potential of dopamine showing a convoluted response with pH changes. C) Dopamine concentration predicted by PCR using the primary PCs determined by the 99.5% cumulative variance method (blue) and Malinowski’s F-test (red). D) pH change predicted by PCR using the primary PCs determined by the 99.5% cumulative variance method (blue) and Malinowski’s F-test (red).

Figure 7

Dopamine release predicted by PCR during an ICSS experiment using primary PCs determined with both methods of factor selection for a Case I training set. Time 0 s represents cue presentation and the pink bar represents the stimulation. The blue and red traces are average (error bars representing SEM) dopamine concentrations predicted using the primary PCs from the 99.5% cumulative variance method (rank = 4) and Malinowski’s F-test (rank = 2), respectively. The black trace is an average dopamine concentration predicted using Malinowski’s F-test without pH in the training set. The green bar represents a significant difference in concentrations predicted when pH was excluded from the training set (one-way ANOVA, p < 0.05).