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Automatic and Reliable Quantification of Tonic Dopamine Concentrations In Vivo Using a Novel Probabilistic Inference Method

Dysregulation of the neurotransmitter dopamine (DA) is implicated in several neuropsychiatric conditions. Multiple-cyclic square-wave voltammetry (MCSWV) is a state-of-the-art technique for measuring tonic DA levels with high sensitivity (<5 nM), selectivity, and spatiotemporal resolution. Currently, however, analysis of MCSWV data requires manual, qualitative adjustments of analysis parameters, which can inadvertently introduce bias. Here, we demonstrate the development of a computational technique using a statistical model for standardized, unbiased analysis of experimental MCSWV data for unbiased quantification of tonic DA. The oxidation current in the MCSWV signal was predicted to follow a lognormal distribution. The DA-related oxidation signal was inferred to be present in the top 5% of this analytical distribution and was used to predict a tonic DA level. The performance of this technique was compared against the previously used peak-based method on paired in vivo and post-calibration in vitro datasets. Analytical inference of DA signals derived from the predicted statistical model enabled high-fidelity conversion of the in vivo current signal to a concentration value via in vitro post-calibration. As a result, this technique demonstrated reliable and improved estimation of tonic DA levels in vivo compared to the conventional manual post-processing technique using the peak current signals. These results show that probabilistic inference-based voltammetry signal processing techniques can standardize the determination of tonic DA concentrations, enabling progress toward the development of MCSWV as a robust research and clinical tool.


Electrode fabrication
The carbon-fiber microelectrode design was modified from our previous studies [1][2] . Single carbon fibers (AS4, d = 7μm; Hexel, Dublin, CA) were isolated and inserted into silica tubings (20μM ID, 90μM OD, 10μM coat with polyimide; Polymicro Technologies, Phoenix, AZ) to manufacture the carbon-fiber microelectrodes. The connection between the carbon fiber and the silica tubings was sealed with polyamic acid (Sigma-Aldrich, St. Louis, MO). They were heated to 200˚C to polymerize the polyamic acid into a polyimide film. A silver-based conductive paste was then used to attach the silica tubing to a nitinol (Nitinol #1, an alloy of nickel and titanium; Fort Wayne Metals, IN) extension wire 1 . A polyimide tubing (0.0089"ID, 0.0134"OD, 0.00225" WT; Vention Medical, Salem, NH) was then used to insulate the nitinol wire and its attached carbon fiber except at the carbon fiber sensing part. We trimmed the exposed carbon fiber under a dissecting microscope to a length of approximately 50 μm. An Ag/AgCl reference electrode was prepared by chlorinating the exposed tip of a Teflon-coated silver wire (A-M systems, Inc., Sequim, WA) in saline with a 9 V dry cell battery.

Biological experiments protocol
Rats were housed in a AAALAC accredited vivarium (21º C, 45% humidity) with a 12 hr light-dark cycle (lights on at 0600 hr) with ad libitum access to food and water. They were anesthetized with urethane (1.6 g/kg, i.p.) and stabilized in a commercially available stereotaxic frame (David Kopf Instruments, Tujunga, CA) for the surgery. A longitudinal skin incision was made on the top of the head to expose the skull and three burr holes (0.5-1.0 mm diameter) were made for the implantation of a carbon-fiber microelectrode, a bipolar electrical stimulating electrode (Plastic One, MS303/2, Roanoke, VA, USA) and an Ag/AgCl reference electrode. The reference electrode was placed superficially in cortex contralateral to the carbon-fiber microelectrode and stimulating electrode site. Electrode coordinates were referenced by Watson and Paxinos rat brain atlas 3 based on flat-skull position using bregma and dura as reference points with coordinates anteroposterior S4 (AP), mediolateral (ML), and dorsoventral (DV). The carbon-fiber microelectrode was placed in the dorsomedial striatum (AP +1.0 mm; ML +2.5 mm; DV -4.5 to -5.5 mm) of the right hemisphere. The stimulating electrode was inserted ipsilaterally just above the medial forebrain bundle (MFB, AP -4.8; ML +1.0; DV -8.0 to -9.0). A train of bipolar pulses (2 ms pulse width, 200 μA, 60 Hz) using WINCS Harmoni electrometer was delivered for 2 seconds to identify the optimal dopamine (DA) release sites in the striatum. FSCV signal was synchronized with electrical stimulation by interleaving the intervals of stimulation during FSCV scans to prevent stimulation artefact 4 . Thus, electrical stimulation was not applied when the FSCV pulses (about 10ms) were delivered. The carbon-fiber microelectrode and the electrical stimulating electrode were gradually adjusted until a robust phasic DA signal was detected at the carbon-fiber microelectrode using FSCV. Immediately thereafter, we switched to MCSWV recording. The MCSWV waveform was applied at 0.1 Hz for the duration of recording. Stabilization of the recorded electrochemical signal was achieved in the first 10 minutes.

DA-kernel method
A threshold algorithm was applied to the post-calibration in vitro and in vivo DA response of MCSWV, where signals greater than cut-off level (60% of the peak current for the peak-based method; top 5 th percentile of the oxidation currents distribution for the probabilistic inference method) in the 2D voltammogram were given a logical value of 1, while others were given a logical value of 0 (yellow and red, respectively, in Figure 2B). The resulting mask was called the dopamine-kernel, i.e., DA-kernel. A DA-kernel was computed for a respective in vivo and postcalibration in vitro recording of each animal. We computed the DA-kernel and applied it to the 2D voltammogram by element-wise multiplication. This multiplication computation results in selecting the currents over the entire area of value 1 in DA-kernel; in other words, extracting closely DA-related signals. The results were then integrated and used to predict the DA concentration. This process was repeated for each 2D voltammogram to obtain the trend of DA over time ( Figure 2C).

Validation of analytical distribution
The lognormal distribution was used to estimate an analytical distribution of the post-calibration in vitro and in vivo DA response of MCSWV ( Figure 3). To assess if the empirical MCSWV data plausibly from the lognormal distribution, we performed a graphical method, a quantile-quantile (Q-Q) plot ( Figure S1 A and B). We could confirm that Q-Q points fall along a unity line in Q-Q plot for both in vitro and in vivo data of all six animals, which provides strong evidence that the empirical data fairly come from a lognormal distribution. We also compared the fitting of the empirical data with lognormal distribution to the fitting with a gamma distribution ( Figure S1C). The mean of RMSE (root mean squared error) of the theoretical distribution was lower using the lognormal function compared to using the gamma function, which shows the lognormal distribution greater estimator of the theoretical distribution of the DA response of MCSWV. Furthermore, we performed a likelihood ratio test of fitting S6 using the lognormal distribution against using the gamma distribution. This test supported that lognormal distribution is greater theoretical estimator (six electrodes in vitro post-calibrations: likelihood ratio statistics > 3.4 x 10 2 , P < 1.1 x 10 -10 ; six rats in vivo: likelihood ratio statistics > 45, P < 2.3 x 10 -9 ).

Generalized linear model
To estimate the DA concentrations, we fit regression models using the quadratic function (secondorder polynomial function) as where a, b, and c are real numbers and a≠0. This fitting regression model was implemented using the generalized linear mode (GLM). We used "fitglm" function in Matlab with the quadratic model. An individual GLM derived for each animal (thus, total six GLMs were generated in this study) was then used to predict DA concentrations The GLM was generated from in vitro post-calibration dataset. To compare the DA estimation methods (peak-based method vs probabilistic inference method), the full in vitro dataset was split into a training dataset (50% of the total in vitro MCSWV scans) and a test dataset (50% of the total in vitro MCSWV scans). Then, the GLM generated by the training dataset was used to predict DA concentrations for the test dataset including the 50% in vitro MCSWV scans as well as full in vivo MCSWV scans. To fit each GLM (total six models for six rats), we performed 5-fold cross-validation on the training set. We selected best-fitting parameters that returned the lowest cross-validated prediction error (measured as root mean squared error).
For the quadratic regression, in detail, we used in vitro MCSWV scans collected as the postcalibration procedure. The previous study demonstrated that the MCSWV responses to 50-1000 nM of DA were fitted well with quadratic function ( Figure 1C) 5 . Thus, we fitted the regression model (i.e. link function of GLM) using the quadratic function ("quadratic" in the options of Matlab fitglm function). The integration of the MCSWV oxidation currents which overlapped with the predetermined binary DA-kernel was then computed. In individual animals, the integrated oxidation currents were normalized according to the area of the DA-kernel. The resultant link function (i.e., a fitted quadratic model with equation 1) was used to predict DA concentrations of the test dataset. More precisely, the GLM-based quadratic regression allows the model (i.e., link function) to be related to the response/dependent variable (i.e., DA concentration), by allowing the magnitude of the variance for each DA measurement to be a function of the predictor/independent variable (i.e., the integration of the oxidation currents within the DA-kernel).

Testing cut-off levels generating DA-kernel
We repeated the estimation of in vivo tonic DA concentration shown in Figure 5B using three different cut-off levels, top 1-2, 5, and 10 % ( Figure S2). For two animals, the top 1% of analytical distribution was out of the range of empirical data. In those cases, the top 2% was used for the cut-off level to generate DA-kernel. The probabilistic inference method using the cut-off levels of top 1-10% showed significantly reduced variance in the tonic DA level prediction across animals compared to the peak-based method. The cut-off at top 1-2% appears to lose too much DArelated information in MCSWV responses and resulted in sparse predictions in tonic DA. Moreover, we could not find strong evidence that the cut-off of the top 5% is better than the cut-off of the top 10%. However, in the within-animal comparison, more animals demonstrated significantly reduced variance using the cut-off of the top 5% versus the top 10% (significantly reduced variance in 5 rats using the top 5% vs. 3 rats using the top 10%). The selection of DA-related information is crucial for DA level estimations not only in FSCV and MCSWV techniques 5-6 . The cut-off level of top 5th percentile may provide a statistically DA-related signal from the analytically estimated distribution and less arbitrary standard to determine the DA-kernel based on statistical model (Figure 3 and 4B). This is analogous to a one-sided statistical test with a 5% significance level 7 . Figure S2. The predicted in vivo tonic DA concentrations with three different cut-off levels.
Variance of the predicted mean tonic DA across rats was significantly lower in the probabilistic inference method compared to the peak-based method (Bartlett's test, *P < 0.05, **P < 0.01; mean in vertical bar ± SEM in box at log 10 scale). Filled circles indicate significantly lower variance of tonic DA predictions within single animal using the probabilistic inference method compared to the peak-based method (Bartlett's test , P < 0.05; open circles indicate non-significance in Bartlett's test).