Fig 1.
Overlapping electrical images of 24 neurons (different colors) over the MEA, aligned to onset of spiking at t = 0.5ms.
Each trace represents the time course of voltage at a certain electrode. For each neuron, traces are only shown in the electrodes with a strong enough signal. Only a subset of neurons visible on the MEA are shown, for better visibility.
Fig 2.
Visual inspection of traces reveals the difficulty of the problem.
First column: templates of spiking neurons. Second to fourth columns: responses of one (A) or two (B) cells to electrical stimulation at increasing stimulation amplitudes as recorded in the stimulating electrode (first rows) or a neighboring, non-stimulating electrode (third rows). If the stimulation artifact is known (gray traces) it can be subtracted from raw traces to produce a baseline (second and fourth rows) amenable for template matching: traces with spike(s) (colored) match, on each electrode, either a translation of a template (A and B) or the sum of different translations of two or more templates (B). As reflected by the activation curves (fifth column) for strong enough stimuli spiking occurs with probability close to one, consistent with the absence of black traces in the rightmost columns.
Fig 3.
Properties of the electrical stimulation artifact revealed by TTX experiments.
(A) local, electrode-wise properties of the stimulation artifacts. Overall, magnitude of the artifact increases with stimulation strength (different shades of blue). However, unlike non-stimulating electrodes, where artifacts have a typical shape of a bump around 0.5 ms (fourth column), the case of the stimulating electrode is more complex: besides the apparent increase in artifact strength, the shape itself is not a simple function of stimulating electrode (first and second rows). Also, for a given stimulating electrode the shape of the artifact is a complex function of the stimulation strength, changing smoothly only within certain stimulation ranges: here, responses to the entire stimulation range are divided into three ranges (first, second, and third column) and although traces within each range look alike, traces from different ranges cannot be guessed from other ranges. (B) stimulation artifacts in a neighborhood of the stimulating electrode, at two different stimulus strengths (left and right). Each trace represents the time course of voltage at a certain electrode. Notice that stimulating electrode (blue) and non-stimulating electrodes (light blue) are plotted in different scales.
Table 1.
Summary of relevant notation.
Fig 4.
Examples of learned GP kernels.
A Left: inferred kernels Kt, Ke, Ks in the top, center, and bottom rows, respectively. Center: corresponding stationary auto-covariances from the Matérn(3/2) kernels (Eq 4). Right: corresponding unnormalized ‘gamma-like’ envelopes dα,β (Eq 5). The inferred quantities are in agreement with what is observed in Fig 3B: first, the shape of temporal term dα,β reflects that the artifact starts small, then the variance amplitude peaks at ∼.5 ms, and then decreases rapidly. Likewise, the corresponding spatial dα,β indicates that the artifact variability induced by the stimulation is negligible for electrodes greater than 700 microns away from the stimulating electrode. B Same as A), but for the stimulating electrode. Only temporal kernels are shown, for two inter-breakpoint ranges (first and second rows, respectively).
Fig 5.
Example of neural activity and artifact inference in a neighborhood of the stimulating electrode.
Left: Two recordings in response to a 2.01 μA stimulus. Center: estimated artifact (as the stimulus doesn’t change, it is the same for both trials). Right: Difference between raw traces and estimated artifact, with inferred spikes in color. In the first trial (above) one spiking neuron was detected, while in trial 2 (below) three spiking neurons were detected. The algorithm separates the artifact A and spiking activity s effectively here.
Fig 6.
Population results from thirteen retinal preparations reveal the efficacy of the algorithm.
A. Trial-by-trial wise performance of estimators broken down by the the four types of stimulation considered (total number of trials 1,713,233, see Table 1 S1 Text for details). B. Trial-by-trial wise performance of estimators to perturbations of real data (only single-electrode): five trials per stimulus for trial subsampling, every other stimulus for amplitude subsampling and σ = 20 for noise injection. C,D. Amplitude-series wise performance of estimators. C: false omission rate (FOR = FN/(FN+TP)), false discovery rate (FDR = FP/(FP+TP)), and error rate based on the 4,045 available amplitude series (see Table 2 S1 Text for details); D: comparison of activation thresholds (human vs. kernel-based algorithm). E. Performance measures (trial-by-trial) broken down by distance between neuron and stimulating electrode. F. Trial-by-trial error as a function of EI peak strength across all electrodes (only kernel-based). A Spearman correlation test revealed a significant negative correlation. G. Error as a function of number of iterations in the algorithm. H. For the true positives, histogram of the differences of latencies between human and algorithm. I. Computational cost comparison of the three methods for the analysis of single-electrode scans, with 20 to 25 (left) or 50 (right) trials per stimulus.
Fig 7.
Filtering (Eq 10) leads to a better, less spike-corrupted artifact estimate in our simulations.
A effect of filtering on traces for two non-stimulating electrodes, at a fixed amplitude of stimulation (2.2μA). A1,A3 raw traces, A2,A4 filtered traces. Notice the two main features of the filter: first, it principally affects traces containing spikes, a consequence of the localized nature of the kernel in Eq 2. Second, it helps eliminate high-frequency noise. B through simulations, we showed that filtering leads to improved results in challenging situations. Two filters—only smoothing and localization + smoothing—were compared to the omission of filtering. In all cases, to rule out that performance changes were due to the extrapolation estimator, extrapolation was done with the naive estimator. B1 results in a less challenging situation. B2 results in the heavily subsampled (nj = 1) case. B3 results in the high-noise variance (σ2 = 10) case.
Fig 8.
Kernel-based extrapolation (Eq 11) leads to more accurate initial estimates of the artifact.
A comparison between kernel-based extrapolation and the naive estimator, the artifact at the previous amplitude of stimulation. For a non-stimulating (first row) and the stimulating (second row) electrode, left: artifacts at different stimulus strengths (shades of blue), center: differences with extrapolation estimator (Eq 11), right: differences with the naive estimator. B comparison between the true artifact (black), the naive estimator (blue) and the kernel-based estimator (light blue) for a fixed amplitude of stimulus (3.1μA) on a neighborhood of the stimulating electrode. C Through simulations we showed that extrapolation leads to improved results in a challenging situation. Kernel-based extrapolation was compared to naive extrapolation. C1 results in a less challenging situation. C2-C3 results in the case where the artifact is multiplied by a factor of 3 and 5, respectively.
Fig 9.
Analysis of responses of neurons in a neighborhood of the stimulating electrode.
A Spatial configuration: stimulating electrode (blue/yellow annulus) and four neurons on its vicinity. Soma of green neuron and axon of pink neuron overlap with stimulating electrode. B Activation curves (solid lines) along with human-curated and algorithm inferred spike probabilities (gray and colored circles, respectively) of all the four cells. Stimulation elicited activation of green and pink neurons; however, the two other neurons remained inactive. C Raster plots for the activated cells, with responses sorted by stimulation strength in the y axis. Human and algorithm inferred latencies are in good agreement (gray and colored circles, respectively). Here, direct somatic activation of the green neuron leads to lower-latency and lower-threshold activation than of the pink neuron, which is activated through its axon.
Fig 10.
Electrical receptive field of a neuron.
A spatial representation of the soma (black circle) and axon (black line) over the array. Electrodes where stimulation was attempted are represented by circles, with colors indicating the activation threshold in the case of a successful activation of the neuron within the stimulation range. B For those cases, activation curves (solid lines) are shown along with with human and algorithm inferred spike frequencies (gray and colored circles, respectively). Large circles indicate the activation thresholds represented in A. In this case, much of the activity is elicited through axonal stimulation, as there is a single electrode close to the soma that can activate the neuron. Human and algorithm are in good agreement.
Fig 11.
Analysis of differential responses to single (A) and two-electrode (B) stimulation.
Gray and colored dots indicate human and algorithm inferences, respectively. In both cases activation of the two neurons is achieved. However, shape of activation curves is modulated by the presence of a current with the same strength and opposite polarity in a neighboring electrode (yellow/blue annulus in B): indeed, in this case bipolar stimulation leads to an enhanced ability to activate the pink neuron without activating the green neuron. The algorithm is faithfully able to recover the relevant activation thresholds.
Fig 12.
Large-scale analysis of the stimulation of a population of parasol cells.
For each neuron, one or more stimulating electrodes in a neighborhood of neural soma were chosen for stimulation. A Receptive fields colored by the lowest achieved stimulation threshold (black if activation was not achieved). B Inferred somas (big black circles) of the neurons labeled A-E in A), showing which electrodes were chosen for stimulation (small circles) and whether activation was achieved (colors). C Activation curves (solid lines) of the neurons in B for the successful activation cases. Gray and colored dots represent human and algorithm results, respectively, and large circle indicates stimulation thresholds.