WO2022056347A1

WO2022056347A1 - Probabilistic inference for estimating tonic concentrations using multiple cyclic square wave voltammetry

Info

Publication number: WO2022056347A1
Application number: PCT/US2021/049994
Authority: WO
Inventors: Hojin SHIN; Kendall H. Lee; Yoonbae OH
Original assignee: Mayo Foundation For Medical Education And Research
Priority date: 2020-09-14
Filing date: 2021-09-13
Publication date: 2022-03-17

Abstract

Techniques are disclosed for obtaining a voltammogram for multiple-cyclic square wave voltammetry (MCSWV) performed in a first solution. Based on the voltammogram, a distribution of oxidation currents is generated. A first binary kernel is generated for the first solution that differentiates significant oxidation currents from insignificant oxidation currents in the first solution. A second binary kernel is obtained for a second solution, where the second binary kernel differentiates significant oxidation currents from insignificant oxidation currents in the second solution based on one or more sessions of MCSWV performed in the second solution. A known level of the analyte in the second solution is identified, and tonic level of the analyte in the first solution is estimated by comparing the first binary kernel for the first solution to the second binary kernel for the second solution, with reference to a known level of the analyte in the second solution.

Description

PROBABILISTIC INFERENCE FOR ESTIMATING TONIC CONCENTRATIONS USING MULTIPLE CYCLIC SQUARE WAVE VOLTAMMETRY

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application Serial No. 63/078,044, filed September 14, 2020. The disclosure of the prior application is considered part of, and is incorporated by reference in its entirety, into the disclosure of this application.

STATEMENT OF FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under NS112176 awarded by the National Institutes of Health. The government has certain rights in the invention.

BACKGROUND

[0003] Neurotransmitters are endogenous substances which act on extracellular postsynaptic receptors to generate functional changes in target cells. Therefore, it is important to understand changes in extracellular concentrations of these neurotransmitters to unravel the pathologic mechanisms of neurological disorders.

[0004] Dopamine (DA) is one such neurotransmitter that plays a critical role in the modulation of several functions, including motor control, motivation, cognition, reward- seeking behavior, and prolactin release. Transient or phasic DA release occurs in response to behaviorally relevant stimuli against a background of relatively slow changing tonic DA levels. There is an interplay between tonic DA levels and the intensity of phasic responses. Dysregulation of both phasic and tonic DA release has been associated with several neuropsychiatric conditions such as Parkinson’s disease (PD), addiction, mania, obsessive- compulsive disorder, and schizophrenia.

[0005] In vivo DA levels have been measured using microdialysis and voltammetry. In contrast to microdialysis in which extracellular fluid is sampled for offline analysis, voltammetric techniques allow the analyte to be measured in situ. The size of voltammetry microsensors and rapid sub-second sampling minimizes tissue damage and allows for high spatial and temporal resolution. Despite these advantages, electrochemical techniques have generally been limited to measurement of only phasic changes in analyte concentration.

[0006] While efforts have been made to estimate tonic DA concentrations in the brain, signal interpretation techniques that correlate the measured electrochemical signal to actual levels have not been standardized.

SUMMARY

[0007] This specification discloses systems, methods, devices, and other techniques involving application of multiple cyclic square wave voltammetry (MCSWV) for analytical quantification of analytes in a solution.

[0008] Electrochemical analyses, including both phasic and tonic DA concentration estimations, can involve measuring a target analyte in vivo, and then calibrating the measurement using in vitro standards by comparing peak oxidation currents. Electrochemical techniques can utilize either peak current and/or integration of oxidation currents for estimation of neurochemical concentration. In the peak current method, the spread of oxidation current is not fully considered; therefore, information dimensionality inherent in the observed oxidation response is lost. When using the integration method, significantly more information is considered for the concentration estimation, leading to higher sensitivity. However, the integration potential range is ordinarily set by the user, introducing potential bias in the resulting data.

[0009] A preferred tonic DA measurement technique referred to as multiple cyclic square-wave voltammetry (MCSWV) is described in PCT Publication No. W02020/041277, which is hereby incorporated by reference in its entirety. MCSWV enables extensive collection of oxidation current data and, therefore, enables a more thorough understanding of DA mechanisms in vivo. MCSWV utilizes an integration method to process and evaluate the measured oxidation current.

[0010] Some implementations of the subject matter disclosed herein include methods for estimating a tonic level of an analyte in a first solution. The method can include obtaining a voltammogram for one or more sessions of multiple-cyclic square wave voltammetry (MCSWV) performed in the first solution; generating, based on the voltammogram, a distribution of oxidation currents detected in the one or more sessions of MCSWV performed in the first solution; determining a threshold oxidation current for the first solution as the oxidation current that corresponds to a pre-defined cutoff in the distribution; generating a first binary kernel for the first solution that differentiates significant oxidation currents from insignificant oxidation currents in the first solution by mapping (1) oxidation currents in the voltammogram that do not meet the threshold oxidation current to a first binary value and (2) oxidation currents in the voltammogram that meet the threshold oxidation current to a second binary value, wherein the oxidation currents that do not meet the threshold oxidation current are deemed insignificant and the oxidation currents that do meet the threshold oxidation current are deemed significant; obtaining a second binary kernel for a second solution, wherein the second binary kernel differentiates significant oxidation currents from insignificant oxidation currents in the second solution based on one or more sessions of MCSWV performed in the second solution; identifying a known level of the analyte in the second solution; and estimating the tonic level of the analyte in the first solution by comparing the first binary kernel for the first solution to the second binary kernel for the second solution, with reference to the known level of the analyte in the second solution.

[0011] These and other implementations can further include one or more of the following features.

[0012] The voltammogram can indicate oxidation currents measured in the solution during the one or more sessions of MCSWV in the first solution as a function of (1) a staircase voltage representing a staircase component of a MCSWV waveform and (2) a square wave voltage representing a square wave component of the MCSWV waveform.

[0013] The one or more sessions of MCSWV for the first solution can be performed in vivo in a mammal.

[0014] The analyte can be a neurochemical such as dopamine or serotonin.

[0015] Generating the distribution of oxidation currents can include generating a probability density function (PDF) of a continuous random variable based on the voltammogram. The distribution of oxidation currents can be a lognormal distribution.

[0016] The pre-defined cutoff of the distribution can be in the 95th percentile of the distribution. The first binary value can be zero and the second binary value can be one. Estimating the tonic level of the analyte in the solution based on the identified areas in the binary kernel assigned the second binary value can include integrating the binary values of the identified areas in the binary kernel assigned the second binary value. [0017] The one or more sessions of MCSWV performed in the first solution can be performed in vivo in a subject, and the one or more sessions of MCSWV performed in the second solution are performed in vitro with respect to the subject.

[0018] The method can further include: obtaining a second voltammogram for the one or more sessions of MCSWV performed in the second solution; generating, based on the second voltammogram, a second distribution of oxidation currents detected in the one or more sessions of MCSWV performed in the second solution; determining a second threshold oxidation current for the second solution as the oxidation current that corresponds to the pre-defined cutoff in the second distribution; and generating the second binary kernel for the second solution by mapping (1) oxidation currents in the second voltammogram that do not meet the second threshold oxidation current to the first binary value and (2) oxidation currents in the voltammogram that meet the second threshold oxidation current to the second binary value, wherein the oxidation currents that do not meet the second threshold oxidation current are deemed insignificant and the oxidation currents that do meet the second threshold oxidation current are deemed significant. The threshold oxidation current for the first solution is different from the second threshold oxidation current for the second solution.

[0019] Estimating the tonic level of the analyte in the first solution comprises comparing a total area in the first binary kernel that represent significant oxidation currents to a total area in the second binary kernel that represent significant oxidation currents.

[0020] The estimated tonic level of the analyte in the first solution can be derived by applying a function that relates the total areas in the first and second binary kernels that represent significant oxidation currents and the known level of the analyte in the second solution. The function can include a generalized linear model.

[0021] The known level of the analyte in the solution can be a tonic level of the analyte in the second solution.

[0022] The estimated tonic level of the analyte in the first solution can be used in a closed-loop feedback system to adjust one or more parameters of electrical or magnetic stimulation (e.g., deep brain stimulation or transcranial magnetic stimulation) applied to a brain or cranial area of a subject, wherein the first solution is located in the brain of the subject.

[0023] The systems, methods, devices, and other techniques described herein provide an objective framework for defining integration limits of oxidation signals for DA estimations (e.g., “final” DA estimations). The framework can use analytical inference of DA signals based on statistical modelling of the MCSWV oxidation signal. In some applications, the disclosed techniques can achieve one or more advantages. For example, by employing an objective framework, the need for subjective integration limits set by user can be eliminated or reduced. Moreover, the techniques can enable post-processing analysis to consider more DA-related information available from the MCSWV signals. These techniques can also improve precision and reduce bias for reliable quantification of tonic DA concentrations in vivo.

[0024] Additional features and advantages of the disclosed techniques will be apparent to one of ordinary skill upon review of the entire disclosure, and the claims.

DESCRIPTION OF DRAWINGS

[0025] Figure 1 A depicts a schematic design of an example square waveform. FigurelB depicts an example multiple cyclic square wave, and a plot of tonic concentration measurement utilizing dopamine adsorption property. Figure 1C depicts, on the left, peak current of dopamine 1 pM at each cyclic square wave (CSW); at the middle, pseudo-color plot of difference between CSW #2 and #5 for 200 nM dopamine; on the right, MCSWV signal (i.e., integration of oxidation currents) correlates with tonic dopamine concentrations (n=4 electrodes).

[0026] Figure 2 A depicts an example three-dimensional voltammogram illustration of MCSWV oxidation currents with 200 nM DA in vitro (i.e., post-calibration). Figure 2B depicts a DA-kernel for the representative in vitro post-calibration recording shown in Figure 2Aand an in vivo recording. Figure 2C depicts an example of DA concentration predictions using the peakbased method for the post-calibration (left) and the in vivo recording (right). Arrows represents DA injection for post-calibration and nomifensine administration in vivo; dashed line indicates injected DA concentration in post-calibration. Figure 2D depicts distributions of the predicted DA concentrations during the first 40 and the last 15 min for the in vivo and in vitro postcalibration recordings in Figure 2C, respectively. Inset: enlarged x-axis scale matching to Figure 4D.

[0027] Figure 3 depicts distributions of MCSWV oxidation currents for the recordings shown in Figure 2D. Analytical lognormal distribution is shown in the respective curves. Vertical dashed line indicates the top 5th percentile of the respective analytical distribution; the cut-off level/threshold to separate the DA-related signal (i.e., higher than the cut-off) and potentially non-signal (i.e., lower than the cut-off) in the post-calibration, in vitro (i.e., the curve with the higher peak), and in vivo (i.e., the curve with the lower peak), respectively.

[0028] Figs. 4A-4D relate to processing DA-kemel and prediction by probabilistic inference method. Figure 4A depicts an example distribution of MCSWV oxidation currents with 200 nM DA in vitro using the same data shown in Figure 2A. DA-kernel was determined using the methods proposed in herein: thresholding by the top 5th percentile from the analytical distribution (gray line). Figure 4B depicts DA-kernels for the representative in vitro postcalibration recordings shown in Figure 4A and the in vivo recording. Figure 4C depicts an example of DA concentration predictions using the method in Figs. 4A and 4B for the postcalibration (left) and the in vivo recording (right). Arrow represents DA injection for postcalibration and nomifensine administration in vivo; dashed line indicates injected DA concentration in post-calibration. Figure 4D depicts distributions of the predicted DA concentrations during the first 40 and last 15 min for in vivo and in vitro post-calibration recordings in Figure 4C, respectively.

[0029] Figure 5A depicts coefficient of variation (CV) in the predicted DA concentrations for the in vitro post-calibration (n = 6 electrodes; mean in vertical bar ± SEM in box; peak-based method: 5.4 ± 1.5%; probabilistic inference method: 1.2 ± 0.4%; peak-based vs. probabilistic inference, paired t-test, t5 = 2.77, P = 0.039). Figure 5B depicts comparison of the predicted tonic DA concentrations in vivo (n = 6 rats). Variance of predicted tonic DA across rats was significantly lower in the probabilistic inference method compared to the peak-based method (Bartlett’ s test, %2 = 14.36, P = 1.5 x 10-4; mean in vertical bar ± SEM in box at loglO scale).

[0030] Figure 6 is a flowchart of an example process for quantifying a level of an analyte in a solution.

DETAILED DESCRIPTION

[0031] This specification discloses systems, methods, devices, and other techniques for quantifying tonic levels of an analyte in a solution using multiple cyclic square wave voltammetry (MCSWV). In some implementations, MCSWV can be applied to measure tonic levels of dopamine in the brain of a mammal. [0032] Performance of MCSWV can include locating an electrode in a solution, applying a multiple cyclic square waveform electrical stimulus to the solution, measuring an electrical current response to the electrical stimulus using the electrode that is located in the solution, and determining a level of an electroactive analyte (e.g., dopamine, serotonin, and/or other neurotransmitters) in the solution based on the electrical current response to the electrical stimulus. The following example implementation provides an improved method of quantifying results through an objective framework that employs probabilistic methods to compute dopamine (or other neurochemical/analyte) levels in vivo.

Example Implementation

MSCWV and in vivo experiments

[0033] This section describes novel techniques applied in relation to a study involving six male Sprague-Dawley rats weighing 250-350g. The rats were used for in vivo tonic DA recordings and were utilized for evaluation of an improved signal processing method as described herein. The rats were implanted with a stimulating electrode (PLASTIC ONE, MS303/2, Roanoke, VA) and carbon-fiber microelectrodes in the medial forebrain bundle (MFB; AP: -4.6, ML: +1.3, DV: -8) and dorsomedial striatum (AP: +1.2, ML: +2.0, DV: -4.5), respectively. An electrometer (WINCS HARMONI) was used to determine placement of the carbon-fiber electrode via MFB electrical stimulation during application of fast-scan cyclic voltammetry. Upon successful placement of both electrodes, as well as a reference electrode, a switch was made to the MCSWV recording (Figure 1). MCSWV recordings were then performed to measure tonic DA concentrations in the rat striatum at baseline and following pharmacological manipulation.

Peak-based method

[0034] In the peak-based method, the peak oxidation current of MCSWV is used to estimate DA concentrations for post-calibration (in vitro) and in vivo recordings (Figure 2). To analyze the oxidation current derived from MCSWV in vivo recordings, a two-dimensional voltammogram was constructed that resulted from from DA oxidation. Then, a binary matrix referred to as a dopamine (DA) “kernel” (see Figure 2B) was generated. Techniques for generating such a kernel are described further in (Oh, Y.; Heien, M. L.; Park, C.; Kang, Y. M.; Kim, J.; Boschen, S. L.; Shin, H.; Cho, H. U.; Blaha, C. D.; Bennet, K. E. Biosensors and Bioelectronics 2018, 121, 174-182), incorporated herein by reference in its entirety. The peak oxidation current value from the 2D-voltammogram was identified, and then a kernel cut-off level/threshold was computed as a pre-defined percentage of the peak oxidation current value. The pre-defined percentage can be subjectively or arbitrarily selected, e.g., 60%, although other percentages can also be applied (e.g., in the range 40% to 80%). Oxidation currents exceeding the kernel cut-off level were assigned a logical 1 value in the kernel, and oxidation currents not exceeding the cut-off level were assigned a logical 0 value in the kernel. DA oxidation current values (i.e., oxidation currents within the area of logical 1 in the kernel) were integrated to calculate total faradaic current derived from DA oxidation. An estimated level of tonic DA can then be computed based on the post-calibration in vitro recordings.

Probabilistic inference method

[0035] With the probabilistic-inference approach, a cut-off level for producing a DA- kernel is determined in an objective manner, rather than using an arbitrary percentage reduction of the peak oxidation current. To determine the kernel cut-off level of the MCSWV oxidation current according to the probabilistic inference method, a voltammogram of the oxidation current for each MCSWV scan collected for the peak-based method was generated and plotted (see Figs. 3 and 4A). A probability density function for a continuous random variable was predicted, which best describes the analytical distribution of oxidation currents. Lognormal probability function was determined to provide a best fit for the experimental MCSWV data in this study. From this analytical distribution, the threshold level of oxidation current that would best quantify DA was determined. In this example, the statistically significant portion (e.g., top 5th percentile) from the analytical distribution was set as the objective standard to determine the cut-off level for generating the DA-kernel (Figure 3 and 4B). In some applications, the statistically significant portion of the analytical distribution may be more or less than the top 5^th percentile, e.g., a percentile in the range top 10 to top 3 percentile (e.g., any percentile deemed statistically significant above 90 percent, 95 percent, 97 percent). Oxidation currents exceeding the statistically significant cut-off level were assigned a logical 1 and currents lower than the cut-off level were assigned a logical 0 in the DA-kernel respectively. Then DA oxidation current values (oxidation currents within the area of logical 1) were integrated to calculate total faradaic current derived from DA oxidation. This is analogous to a one-sided statistical test with 5% significance level (see Results below).

Estimation of DA concentrations

[0036] To estimate in vivo DA concentrations, a generalized linear model (GLM) was generated from a “training” dataset (e.g., MCSWV scan data collected during post-calibration in vitro recordings to train a GLM, in which DA level is known). A GLM suitable for this purpose is described, for example, in (Nelder, J. A.; Wedderburn, R. W. Journal of the Royal Statistical Society: Series A (General) 1972, 135, 370-384), which is hereby incorporated by reference in its entirety. Individual GLM derived for each animal was then used to predict DA concentrations for a MCSWV scan data classified as the “test” dataset (e.g., in vitro and in vivo data to test/predict DA concentrations, in which DA level is unknown). Single animal post-calibration in vitro recordings were performed and MCSWV scans were systematically divided into two groups, i.e., training versus test dataset. The in vitro training dataset trained GLM, while the in vitro test dataset was used to compare performance of the two methods; the in vitro test dataset was presumed as the recordings with unknown DA concentration. In the case of in vivo recordings, all data were classified as the test dataset. MCSWV scans of the training dataset were collected in vitro either with zero or 200 nM DA. The integration of the oxidation currents which overlapped with the DA-kernel in raw data, i.e., total faradaic current derived from DA oxidation, was then computed. In individual recordings, the integrated oxidation currents were normalized according to the area of the DA-kernel in order to remove variance related to size of the DA-kernel. In the GLM, thereafter, the integrated values of the oxidation currents were linked to zero or 200 nM DA concentrations based on the in vitro training dataset. The resultant linking information, i.e., link function of GLM, was used to predict DA concentrations in the test dataset. Here, the GLM-based linear regression allows the model, e.g., link function, to be related to the response/dependent variable (e.g., DA concentration), by allowing the magnitude of the variance for each DA measurement to be a function of the predictor/independent variable (e.g., the integration of the oxidation currents within the DA-kernel). This link function of GLM, determined by the in vitro training dataset, allowed us to predict DA concentrations of the test dataset collected with in vitro post-calibration and in vivo recordings. General principles ofMCSWV

[0037] MCSWV exploits the adsorption equilibrium of DA on the surface of the carbon- fiber microelectrode to determine tonic concentrations. This is described in further detail in (Oh, Y.; Heien, M. L.; Park, C.; Kang, Y. M.; Kim, J.; Boschen, S. L.; Shin, H.; Cho, H. U.; Blaha, C. D.; Bennet, K. E. Biosensors and Bioelectronics 2018, 121, 174-182) and (Heien, M. L.; Phillips, P. E.; Stuber, G. D.; Seipel, A. T.; Wightman, R. M. Analyst 2003, 128, 1413-1419), which are each incorporated herein by reference in their entirety.. Its waveform parameters have been optimized to enhance sensitivity and selectivity to DA as determined empirically with in vitro experiments. Briefly, MCSWV consists of five cyclic square waveforms, each consisting of square wave oscillations superimposed on a symmetric staircase waveform (Figure 1 A and IB). These waveforms are applied every 10 seconds (Figure IB). When DA adsorption reaches equilibrium, multiple voltage waveforms are applied in quick succession. Dynamic DA oxidation and reduction takes place with each waveform and the amount of oxidizable DA available to each subsequent waveform is decreased (Figure 1C). This is due to relatively rapid depletion of DA adsorbed on the surface, relatively slower depletion of DA in the diffusion compact layer immediately adjacent to the surface, and repulsion and diffusion of the positively charged DA oxidation product (dopamine-o-quinone) away from the carbon-fiber microelectrode as voltage continues to increase for a period of time after the DA oxidation potential is reached. The extent of decrease in oxidation signal with the series of voltage waveforms correlates with the DA concentration in the sample. A rest period after the application of each cycle of multiple waveforms allows time for re-establishment of the DA adsorption equilibrium (Figure IB). Figure 1C (mid panel) shows an MCSWV pseudo-color plot (converted to grayscale). Of the 4 oxidation-reduction peaks shown, the signal with the highest oxidation peak was deemed most sensitive for detecting DA concentration (Figure 2 A) and, therefore, the high values of DA oxidation current were used to estimate DA level.

Peak-based estimation ofMCSWV signal

[0038] In the peak-based method for post-processing ofMCSWV data to determine DA concentration, the 60% value of the peak oxidation current from post-calibration recordings, and in vivo (top plane in Figure 2A, a representative example for in vitro with 200 nM DA) were used respectively as the threshold to generate DA-kernels (Figure 2B). The oxidation currents within this DA-kernel (Figure 2B) were considered closely DA-related signals and then summated to determine the DA concentration of post-calibration in vitro data and in vivo. Then GLM was used to estimate the DA concentrations by linking the in vitro MCSWV dataset recorded with the known DA concentration, i.e., zero and 200 nM, to the dataset to be predicted with unknown DA concentration (details in Methods). As depicted in Figure 2B, the size and shape of DA-kemel in vivo appear different from DA-kernel in vitro. This is because the peak oxidation potential and overall oxidation patterns for in vitro and in vivo recordings are different. The in vitro DA-kernel is relatively compact compared to in vivo DA-kernel, because of a sharper DA oxidation current peak in former (Figure 2D). The peak-based method does not consider this difference and, therefore, appears to be resulted in a higher error in in vivo DA estimation based on the post-calibration in vitro. In Figure 2C and 2D, estimations of DA concentration using the peak-based method are shown for a representative in vivo and in vitro post-calibration dataset. The values of each oxidation current within the DA-kemels in Figure 2B were integrated and predicted the in vivo concentration based on the GLM trained by the in vitro post-calibration with zero and 200 nM of DA. The in vivo recordings utilizing the peak-based method estimated the tonic level of DA in the rat striatum to be approximately 1000 nM for this animal, which is 9 to 25-fold higher than previous reports.

Analytical distribution of MCSWV signal

[0039] For a more objective post-processing of MCSWV data, the analytical distribution was applied of the oxidation current in MCSWV pseudo-color plot to systematically determine an oxidation current cut-off for generating DA-kernels. A probability density function modeling the distribution of the oxidation current was determined and used to predict the DA concentration for the same dataset shown in Figure 2. The intensity distribution of oxidation current in MCSWV pseudo-color plot was observed to approximate a lognormal distribution (Figure 3 and 4A; in vitro: n = 6 electrodes, R2 = 0.95 ± 0.01; in vivo: n = 6 rats, R2 = 0.93 ± 0.02; goodness- of-fit tests, P < 10-10 for each fitting). We chose the top 5th percentile of each analytical distribution (in vivo and post-calibration in vitro) to select DA-related oxidation signals and infer the concentration of DA. Here, the analytical distribution is presumed to be the distribution under the null hypothesis that there is no relationship with DA. Given the null distribution, if an oxidation value exists in the one-sided critical area greater than 5% significance level, that value is presumed to be significantly different from the null population and thus, is identified as a threshold; it is analogous to a one-sided statistical test with 5% significance level 27. Accordingly, values above the threshold were classified as unit of ones in the binary DA-kernel. The cut-off levels for the DA-related signal, i.e., top 5th percentiles for in vivo and for in vitro, are shown for a representative dataset in Figure 3. These cut-off values were then used to create the DA kernels for further data analysis to estimate DA concentration.

Probabilistic inference method

[0040] Using the analytical distribution inferred for the distribution of MCSWV oxidation currents, we further analyzed the data as shown in Figure 2. Each in vivo and postcalibration in vitro dataset was analyzed to create a new DA-kernel based on the top 5th percentile cut-off of the analytical distribution (Figure 4A). Comparing the new DA-kernels (Figure 4B) with those obtained using the previous peak-based method (Figure 2B), we observed increased similarity in the shape and size of the in vivo and post-calibration in vitro DA-kernels. This is because the probabilistic inference method considers the shape of oxidation response which can be different between in vivo and post-calibration in vitro. This suggests error can be reduced when inferring tonic DA concentration in vivo from a post-calibration performed in a different environment, i.e., in vitro. Estimated DA concentration using the new DA-kernels showed significantly reduced values by a factor of 12 for in vivo measurements for the representative dataset (76.3 ± 0.2 nM, mean ± SEM; Figure 4D), compared to the peak-based analysis (1016.0 ± 1.9 nM, mean ± SEM; Figure 2D). This indicates the possibility of an overestimation of tonic DA with the peak-based method. In addition, the variability of measured DA concentration over a given period of time is reduced by a factor of 5, mainly as a result of generating a much sharper peak of tonic DA (Figure 4D) compared to that with the peak-based method (Figure 2D).

Increased precision for in vivo tonic dopamine level estimation

[0041] The reliability of DA concentration estimation between the probabilistic inference method and the peak-based method were compared. Figure 5A compares the variance of the predicted values of MCSWV responses to 200 pM DA over a 15-minute period for the postcalibration in vitro data shown in Figure 4D versus Figure 2D (n = 6 electrodes). Coefficient of variation (CV), a statistical assessment of the level of dispersion around the mean, was computed in each post-calibration in vitro data set for both methods. In both cases, the CV was relatively small among samples. The CV of the peak-based method found to be 5.4 ± 1.5%, mean ± SEM, and the CV for the probabilistic inference method found to be 1.2 ± 0.4%, mean ± SEM, which is significantly reduced compared to the peak-based method (paired t-test, t5 = 2.77, P = 0.039), demonstrating increased precision for DA recordings in vitro.

[0042] It was next sought to be determined if the probabilistic inference method reduces variance across animals in the prediction of in vivo tonic DA concentrations over a 40-min period shown in Figure 4D versus Figure 2D (Figure 5B, n = 6 rats). The predicted tonic DA levels in rat striatum were estimated to be 295.3 ± 146.8 nM, mean ± SEM, with the peak-based method and 90.2 ± 15.3 nM, mean ± SEM, with the probabilistic inference method. The two methods were not found to be significantly different in the mean of tonic DA levels (paired t-test, t5 = 1.11, P = 0.32), and the tonic values are in line with previous work by Oh et al. (2018) and Heien et al. (2017) in both methods. However, the probabilistic inference method demonstrated significantly reduced variance in DA prediction across animals (Bartlett’s test, %2 = 14.36, P = 1.5 x 10-4). This finding indicates that the probabilistic inference method can be a more precise and reliable method for determining in vivo tonic DA concentrations.

[0043] Increased precision, automation and objective quantification stemming from these techniques can be important not only for research purposes but also for clinical applications. Neurotransmitter concentrations, especially DA, is thought to correlate with and be involved in mechanism of various neuropsychiatric conditions like PD. It is thought that deep brain stimulation (DBS) in PD may act by altering the level of DA which can in turn be used as a biomarker for closed-loop feedback. For a robust closed-loop DBS system, it is imperative to have a reliable technique for objective quantification of the neurotransmitters/neurochemicals it uses as biomarkers. MCSWV and the data processing techniques described herein can aid in advancing the field of human tonic voltammetry.

Supplemental Study Information

[0044] Single carbon fibers (AS4, d = 7pm) were isolated and inserted into silica tubings (20pM ID, 90pM OD, lOpM coat with polyimide) to manufacture the carbon-fiber microelectrodes. The connection between the carbon fiber and the silica tubings was sealed with polyamic acid. 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 extension wire. A polyimide tubing (0.0089”ID, 0.0134”OD, 0.00225”) 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 pm. An Ag/AgCl reference electrode was prepared by chlorinating the exposed tip of a Teflon-coated silver wire in saline with a 9 V dry cell battery.

[0045] Rats were housed in a AAALAC accredited vivarium (21° 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 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 and an Ag/AgCl reference electrode. The reference electrode was placed superficially in cortex contralateral to the carbon- fiber microelectrode and stimulating electrode site. 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 pA, 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. 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, 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.

[0046] DA HC1 was dissolved in distilled water at a stock concentration of 1 mM and preserved in 0.1M perchloric acid. Samples from the stock solutions were diluted to the desired concentration with TRIS buffer (15mM tris, 3.25mM KC1, 140mM NaCl, 1.2mM CaC12, 1.25mM NaH2PO4, 1.2mM MgC12, and 2.0mM Na2SO4, with the pH adjusted to 7.4). Immediately after in vivo experiments, post-calibration was performed in vitro. The carbon-fiber microelectrode and reference electrode used for the in vivo experiment were placed in a beaker with TRIS buffer. MCSWV was applied for 10 minutes to stabilize the signal and DA was added to the beaker. A disposable pipette was used to mix the solutions. The recording was continued for approximately 15 minutes after addition of DA.

[0047] A threshold algorithm was applied to the post-calibration in vitro and in vivo DA response of M-CSWV, where signals greater than cut-off level (60% of the peak current for the peak-based method; top 5th 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-kemel. A DA-kemel was computed for a respective in vivo and post-calibration 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).

Example Method

[0048] Figure 6 is a flowchart of an example process for estimating a level of an analyte in a solution, e.g., a tonic level of a neurochemical such as dopamine in a brain fluid solution. At stage 602, a system (e.g., a computing system having one or more computers in one or more locations) obtains a voltammogram for one or more sessions of MCSWV performed in a first solution (e.g., in vivo). The first solution includes an electroactive analyte, but the concentration of the analyte in the first solution is unknown. A session of MCSWV corresponds to a period of time during which MCSWV was performed in the first solution. In some cases, the performance of MCSWV may be disjointed or interrupted, and the voltammogram can represent more than one session. At stage 604, the system analyzes the voltammogram, and from it, generates a distribution of oxidation currents detected in the one or more sessions of MCSWV. The oxidation currents can be modeled, for example, as a lognormal distribution. At stage 606, the system determines a threshold oxidation current for the first solution as the oxidation current that corresponds to a pre-defined cutoff in the distribution (e.g., the oxidation current corresponding to the top 5th percentile of oxidation current levels). At stage 608, the system converts to the voltammogram to a first binary kernel for the first solution. The first binary kernel differentiates statistically significant oxidation currents that correspond to oxidation signals related to the target analyte (e.g., dopamine) from statistically insignificant oxidation currents. The first binary kernel can be generated by mapping (1) oxidation currents in the voltammogram that do not meet the threshold oxidation current to a first binary value and (2) oxidation currents in the voltammogram that meet the threshold oxidation current to a second binary value. The oxidation currents that do not meet the threshold oxidation current are deemed insignificant and the oxidation currents that do meet the threshold oxidation current are deemed significant. At stage 610, a second binary kernel is obtained for a second solution. The second binary kernel differentiates significant oxidation currents from insignificant oxidation currents in the second solution based on one or more sessions of MCSWV performed in the second solution (e.g., in vitro). A known level of the analyte is identified in the second solution, and at stage 612, the system computes an estimation of the tonic level of the analyte in the first solution by comparing the first binary kernel for the first solution to the second binary kernel for the second solution, with reference to the known level of the analyte in the second solution. The concentration or tonic level of the analyte in the first solution can be computed using any of the techniques described herein, including integrating the areas of the significant oxidation currents in the first and second binary kernels, comparing the integrated values, and weighting according to the known level of the analyte in the second solution.

Computer-based Implementations

[0049] In some implementations, analyte measurements using the MCSWV techniques disclosed herein can involve computer-based systems, devices, and/or processes, such as to control parameters of the stimulation, to record data, to generate voltammogram plots, perform automated determination of cutoffs, generate kernels, and quantify analyte levels, and/or otherwise analyze data collected according to the disclosed techniques.

[0050] For such implementations, the computer-based aspects of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, in tangibly-embodied computer software or firmware, in computer hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented as one or more computer programs, i.e., one or more modules of computer program instructions encoded on a tangible non transitory program carrier for execution by, or to control the operation of, data processing apparatus. Alternatively or in addition, the program instructions can be encoded on an artificially generated propagated signal, e.g., a machinegenerated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a data processing apparatus. The computer storage medium can be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, or a combination of one or more of them. The computer storage medium is not, however, a propagated signal.

[0051] The term "data processing apparatus" encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit). The apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0052] A computer program (which may also be referred to or described as a program, software, a software application, a module, a software module, a script, or code) can be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and it can be deployed in any form, including as a stand alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program may, but need not, correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data, e.g., one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, e.g., files that store one or more modules, sub programs, or portions of code. A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0053] As used in this specification, an “engine,” or “software engine,” refers to a software implemented input/output system that provides an output that is different from the input. An engine can be an encoded block of functionality, such as a library, a platform, a software development kit (“SDK”), or an object. Each engine can be implemented on any appropriate type of computing device, e.g., servers, mobile phones, tablet computers, notebook computers, music players, e-book readers, laptop or desktop computers, PDAs, smart phones, or other stationary or portable devices, that includes one or more processors and computer readable media. Additionally, two or more of the engines may be implemented on the same computing device, or on different computing devices.

[0054] The processes and logic flows described in this specification can be performed by one or more programmable computers executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0055] Computers suitable for the execution of a computer program include, by way of example, can be based on general or special purpose microprocessors or both, or any other kind of central processing unit. Generally, a central processing unit will receive instructions and data from a read only memory or a random access memory or both. The essential elements of a computer are a central processing unit for performing or executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device, e.g., a universal serial bus (USB) flash drive, to name just a few.

[0056] Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0057] To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input. In addition, a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user; for example, by sending web pages to a web browser on a user's client device in response to requests received from the web browser.

[0058] Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification, or any combination of one or more such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network ("LAN") and a wide area network ("WAN"), e.g., the Internet.

[0059] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client- server relationship to each other.

[0060] While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any invention or of what may be claimed, but rather as descriptions of features that may be specific to particular embodiments of particular inventions. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0061] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0062] Particular embodiments of the subject matter have been described. Other embodiments are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve desirable results. As one example, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In certain implementations, multitasking and parallel processing may be advantageous.

Claims

CLAIMS What is claimed is:

1. A method for estimating a tonic level of an analyte in a first solution, comprising: obtaining a voltammogram for one or more sessions of multiple-cyclic square wave voltammetry (MCSWV) performed in the first solution; generating, based on the voltammogram, a distribution of oxidation currents detected in the one or more sessions of MCSWV performed in the first solution; determining a threshold oxidation current for the first solution as the oxidation current that corresponds to a pre-defined cutoff in the distribution; generating a first binary kernel for the first solution that differentiates significant oxidation currents from insignificant oxidation currents in the first solution by mapping (1) oxidation currents in the voltammogram that do not meet the threshold oxidation current to a first binary value and (2) oxidation currents in the voltammogram that meet the threshold oxidation current to a second binary value, wherein the oxidation currents that do not meet the threshold oxidation current are deemed insignificant and the oxidation currents that do meet the threshold oxidation current are deemed significant; obtaining a second binary kernel for a second solution, wherein the second binary kernel differentiates significant oxidation currents from insignificant oxidation currents in the second solution based on one or more sessions of MCSWV performed in the second solution; identifying a known level of the analyte in the second solution; and estimating the tonic level of the analyte in the first solution by comparing the first binary kernel for the first solution to the second binary kernel for the second solution, with reference to the known level of the analyte in the second solution.

2. The method of claim 1, wherein the voltammogram indicates oxidation currents measured in the solution during the one or more sessions of MCSWV in the first solution as a function of (1) a staircase voltage representing a staircase component of a MCSWV waveform and (2) a square wave voltage representing a square wave component of the MCSWV waveform.

3. The method of any of claims 1-2, wherein the one or more sessions of MCSWV for the first solution are performed in vivo in a mammal.

4. The method of any of claims 1-3, wherein the analyte is a neurochemical.

5. The method of claim 4, wherein the neurochemical is dopamine or serotonin.

6. The method of any of claims 1-5, wherein generating the distribution of oxidation currents comprises generating a probability density function of a continuous random variable based on the voltammogram.

7. The method of any of claims 1-6, wherein the distribution of oxidation currents is a lognormal distribution.

8. The method of any of claims 1-7, wherein the pre-defined cutoff in the distribution is the 95^th percentile of the distribution.

9. The method of any of claims 1-8, wherein the first binary value is zero and the second binary value is one.

10. The method of claim 9, wherein estimating the tonic level of the analyte in the solution based on the identified areas in the binary kernel assigned the second binary value comprises integrating the binary values of the identified areas in the binary kernel assigned the second binary value.

11. The method of any of claims 1-10, wherein the one or more sessions of MCSWV performed in the first solution are performed in vivo in a subject, and the one or more sessions of MCSWV performed in the second solution are performed in vitro with respect to the subject.

12. The method of any of claims 1-11, further comprising: obtaining a second voltammogram for the one or more sessions of MCSWV performed in the second solution; generating, based on the second voltammogram, a second distribution of oxidation currents detected in the one or more sessions of MCSWV performed in the second solution; determining a second threshold oxidation current for the second solution as the oxidation current that corresponds to the pre-defined cutoff in the second distribution; and generating the second binary kernel for the second solution by mapping (1) oxidation currents in the second voltammogram that do not meet the second threshold oxidation current to the first binary value and (2) oxidation currents in the voltammogram that meet the second threshold oxidation current to the second binary value, wherein the oxidation currents that do not meet the second threshold oxidation current are deemed insignificant and the oxidation currents that do meet the second threshold oxidation current are deemed significant.

13. The method of claim 12, wherein the threshold oxidation current for the first solution is different from the second threshold oxidation current for the second solution.

14. The method of any of claims 1-13, wherein estimating the tonic level of the analyte in the first solution comprises comparing a total area in the first binary kernel that represent significant oxidation currents to a total area in the second binary kernel that represent significant oxidation currents.

15. The method of claim 14, further comprising deriving the estimated tonic level of the analyte in the first solution by applying a function that relates the total areas in the first and second binary kernels that represent significant oxidation currents and the known level of the analyte in the second solution.

16. The method of claim 15, wherein the function comprises a generalized linear model.

17. The method of any of claims 1-16, wherein the known level of the analyte in the solution comprises a tonic level of the analyte in the second solution.

18. The method of any of claims 1-17, further comprising using the estimated tonic level of the analyte in the first solution to adjust one or more parameters of electrical or magnetic stimulation applied to a brain or cranial area of a subject, wherein the first solution is located in the brain of the subject.

19. A system, comprising: one or more processors; and one or more computer-readable media encoded with instructions that, when executed by the one or more processors, cause performance of any of the methods of claims 1-18.

20. One or more non-transitory computer-readable media having instructions stored thereon that, when executed by one or more processors, cause performance of any of the methods of claims 1-18.