A convolutional network to deconvolve calcium traces, living in an embedding space of statistical properties

As mentioned before (here and here), the spikefinder competition was set up earlier this year to compare algorithms that infer spiking probabilities from calcium imaging data. Together with Stephan Gerhard, a PostDoc in our lab, I submitted an algorithm based on convolutional networks. Looking back at the few days end of April when we wrote this code, it was a lot of fun to work together with Stephan, who brought in his more advanced knowledge on how to optimize and refactor Python code and how to explore hyper-parameter spaces very efficiently. In addition, our algorithm performed quite well and ranked among the top submissions. Other high-scoring algorithms were submitted by Ben Bolte, Nikolay Chenkov/Thomas McColgan, Thomas Deneux, Johannes Friedrich, Tim Machado, Patrick Mineault, Marius Pachitariu, Dario Ringach, Artur Speiser and their labs.

The detailed results of the competition will be covered and discussed very soon in a review paper (now on bioRxiv), and I do not want to scoop any of this. The algorithm, which is described in the paper in more detail, goes a bit beyond a simple convolutional network. In simple words, the algorithm creates a space of models. Then, the algorithm chooses a location in this space for the current task based on statistical properties of the calcium imaging data that are to be analyzed. The idea of this step is that it will allow the model to generalize to datasets that it has not seen before.

The algorithm itself, which we wrote in Python3.6/Keras, should be rather straightforward to test with the Jupyter notebook that is provided or the plain Python file. We do not intend to publish the algorithm in a dedicated paper since everything will be described in the review paper, and the algorithm is already published on Github. It should be pretty self-explanatory and easy to set up (if not, let me know!).

So if you have some calcium imaging data that you would like to deconvolve, and if you want to get some hands-on experience with small-scale deep learning methods, this is your best chance …

I also was curious how some random calcium imaging traces of mine would look like after deconvolution based on my network. Sure, there is no spiking ground truth for these recordings, but one can still look at the results and immediately see whether it is a complete mess or something that looks more or less realistic. Here is one example from a very nice calcium recording that I did in 2016 in the dorsal telencephalon of an adult zebrafish using this 2P microscope. The spiking probabilities (blue) seem to be realistic and very reliable, but the recording quality was also extremely good.

I was also curious about the performance of the algorithm for somebody else’s data as input. The probably most standardized calcium imaging dataset for mice that there is can be retrieved from the Allen Brain Observatory. Fluorescence traces can be accessed via the Allen SDK (yet another Jupyter notebook to start with). I deconvolved 20 traces each 60 min of recording @ 30 Hz framerate, which took me in total ca. 20 min (on a normal CPU, no GPU!). Let me show you some examples of calcium traces (blue) and the corresponding deconvolved spiking probability estimates (orange) for a couple of neurons; x-axis is time in seconds, y-axis is scaled arbitrarily:

Overall, the deconvolved data clearly seem to be less noisy than most of the predictions from the Spikefinder competition, probably due to better SNR of the calcium signal. False positives from the baseline are not very frequent. There are still some small most likely unwanted bumps, depending on the noisiness of the respective recorded neuron. For very strong calcium responses, the network sometimes tends to overdo the deconvolution, leading to a kind of slight negative overshooting of the spiking probability, or, put differently, ringing of the deconvolution filter. This could have been fixed by forcing the network to give back only positive values, but the results also look pretty fine without this fix.

Of course, if you want to try out your own calcium imaging data with this algorithm, I’d be happy to see the results! And if you are absolutely not into Python yet and don’t want to install anything before seeing some first results, you can also send me some of your calcium imaging traces for a quick test run.