SCALPEL: EXTRACTING NEURONS FROM CALCIUM IMAGING DATA

Abstract

In the past few years, new technologies in the field of neuroscience have made it possible to simultaneously image activity in large populations of neurons at cellular resolution in behaving animals. In mid-2016, a huge repository of this so-called "calcium imaging" data was made publicly available. The availability of this large-scale data resource opens the door to a host of scientific questions for which new statistical methods must be developed. In this paper we consider the first step in the analysis of calcium imaging data-namely, identifying the neurons in a calcium imaging video. We propose a dictionary learning approach for this task. First, we perform image segmentation to develop a dictionary containing a huge number of candidate neurons. Next, we refine the dictionary using clustering. Finally, we apply the dictionary to select neurons and estimate their corresponding activity over time, using a sparse group lasso optimization problem. We assess performance on simulated calcium imaging data and apply our proposal to three calcium imaging data sets. Our proposed approach is implemented in the R package scalpel, which is available on CRAN.

Keywords: Calcium imaging; cell sorting; clustering; dictionary learning; neuron identification; segmentation; sparse group lasso.

Fig. 1.

In (a), we display sample frames from the raw calcium imaging video described in the text in Section 4, and analyzed in greater detail in Section 6.2. We wish to construct a spatial map of the neurons, like that shown in (b). As a by-product, we will also obtain a crude estimate of the calcium trace for each neuron over time, as shown in (c).

Fig. 2.

A summary of the SCALPEL procedure, along with the results of applying each step to an example data set with 205 × 226 pixels and 3000 frames, described in the text in Section 4, and analyzed in greater detail in Section 6.2.

Fig. 3.

In (a), we display a single frame of the example calcium imaging video after performing the preprocessing described in Section 9 of the Supplementary Material [Petersen, Simon and Witten (2018)]. In (b), we show the binary image that results after thresholding using the negative of the 0.1% quantile of the video’s elements. In (c), we display the seven connected components from the image in (b) that contain at least 25 pixels.

Fig. 4.

Each column displays two pairs of preliminary dictionary elements with overall dissimilarities, as defined in (5), of 0.05, 0.1, 0.15, 0.2 and 0.25. For each preliminary dictionary element, the average thresholded fluorescence over time and the (zoomed-in) spatial map are shown. These results are based on the example calcium imaging video.

Fig. 5.

In (a), we display the dendrogram that results from applying prototype clustering to the example calcium imaging data set. Three different cutpoints are indicated: 0.05 (), 0.18 () and 0.4 (). In (b), we display the number of clusters that result from these three cutpoints. In (c)–(e), we show the refined dictionary elements that result from using these three cutpoints. For simplicity, we only display dictionary elements corresponding to clusters with at least five members.

Fig. 6.

In (a), we plot the spatial maps for the 29 elements of the final dictionary for the calcium imaging video considered in Section 6.2. In (b), we plot their estimated intracellular calcium concentrations corresponding to λ chosen via a validation set approach. In (c), we compare the outlines of the 29 dictionary elements from (a) to a heat map of the pixel-wise variance of the calcium imaging video. That is, we plot the variance of each pixel over the 3000 frames with whiter points indicating higher variance.

Fig. 7.

In (a), we see that one of the estimated neurons in a low-variance region in Figure 6(c) does correspond to a true neuron. In (b), we see a frame in which one of the estimated neurons was identified, though there does not appear to be a true neuron.

Fig. 8.

We display the estimated neurons that result from applying a competitor method, CNMF-E [Zhou et al. (2016)], to the calcium imaging video considered in Section 6.2 for (a) the default parameters c_min = 0.85 and α_min = 10, (b) the parameters c_min = 0.6 and α_min = 7 and (c) the parameters c_min = 0.5 and α_min = 3. The variation in darkness of the neurons estimated by CNMF-E is due to the fact that they take on continuous values compared to the binary masks produced by SCALPEL. In each plot the true neurons identified by SCALPEL are outlined in gray. Regardless of the tuning parameters used, CNMF-E yields a substantial number of false positives and false negatives.

Fig. 9.

We present the results for the calcium imaging video analyzed in Section 6.3.1. In (a), we plot the outlines of the neurons identified by the Allen Institute in blue, along with the outlines of the corresponding SCALPEL neurons in orange. In (b), we plot the 25 potential neurons uniquely identified by SCALPEL in color, along with the SCALPEL neurons also identified by the Allen Institute in gray. In (c), we provide evidence for four of the 25 unique neurons. Similar plots for all of the potential neurons uniquely identified by SCALPEL are available at www.ajpete.com/software.

Fig. 10.

We present the results for the calcium imaging video analyzed in Section 6.3.2. In (a), we plot the outlines of the neurons identified by the Allen Institute in blue, along with the outlines of the corresponding SCALPEL neurons in orange. Those shown in green are the Allen Institute neurons that appear to actually be a combination of two neurons. In (b), we plot the 94 potential neurons uniquely identified by SCALPEL in color, along with the SCALPEL neurons also identified by the Allen Institute in gray. In (c), we provide evidence for four of the 94 unique neurons. Similar plots for all of the potential neurons uniquely identified by SCALPEL are available at www.ajpete.com/software.

Fig. 11.

We illustrate the various noise scenarios that we consider for the simulated calcium imaging data described in Section 7.1. We vary the signal to spatially correlated noise (SSCN) ratio and the signal to independent noise (SIN) ratio. We show the simulated neurons truly active during a particular frame, along with the simulated data for that frame for each of the noise scenarios. The top row of frames has a variable strength of spatially correlated noise with a fixed strength of independent noise (SIN = 1.5), and the bottom row of frames has a variable strength of independent noise with a fixed strength of spatially correlated noise (SSCN = 1.5).

Fig. 12.

We illustrate the performance of SCALPEL () and CNMF-E [Zhou et al. (2016)] () in terms of the average sensitivity (percent of true neurons detected; shown as a solid line) and precision (percent of neurons detected that are true neurons; shown as a dashed line) for the simulated calcium imaging data described in Section 7.1. For both, 95% confidence intervals are shown. In (a), we consider the performance for a fixed signal to independent noise ratio of 1.5 and varying signal to spatially correlated noise ratio. In (b), we consider the performance for a fixed signal to spatially correlated noise ratio of 1.5 and varying signal to independent noise ratio. Note that CNMF-E was unable to initialize neurons in the presence of a high amount of independent noise, so the CNMF-E results are omitted for ratios of 0.5 and 1 in (b).

Fig. 13.

We present the sensitivity of SCALPEL’s performance to changes in the tuning parameters for the simulated calcium imaging data described in Section 7.1. In all panels, we plot the average sensitivity () and precision (), along with 95% confidence intervals, as a function of the tuning parameter value. The dashed line indicates the default value of the tuning parameter. In (a), we consider the value of the quantile threshold used to construct the preliminary dictionary in Step 1. In (b), we consider the value of the dissimilarity weight ω in Step 2. In (c), we consider the value of the dendrogram cutpoint in Step 2, as a proportion of ω = 0.2.