Three-dimensional spike localization and improved motion correction for Neuropixels recordings

Neuropixels ( NP ) probes are dense linear multi-electrode arrays that have rapidly become essential tools for studying the electrophysiology of large neural populations . Unfortunately , a number of challenges remain in analyzing the large datasets output by these probes . Here we introduce several new methods for extracting useful spiking information from NP probes . First , we use a simple point neuron model , together with a neural-network denoiser , to efficiently map single spikes detected on the probe into three-dimensional localizations . Previous methods localized individual spikes in two dimensions only ; we show that the new localization approach is significantly more robust and provides an improved feature set for clustering spikes according to neural identity ( “ spike sorting '' ) . Next , we denoise the resulting three-dimensional point-cloud representation of the data , and show that the resulting 3D images can be accurately registered over time , leading to improved tracking of time-varying neural activity over the probe , and in turn , crisper estimates of neural clusters over time . Open source code is available at https : //github . com/int-brain-lab/spikes_localization_registration.git . 1 Introduction . Neuropixels ( NP ) probes are dense linear multi-electrode arrays that enable the simultaneous observation of hundreds of neurons across multiple brain areas . Since their introduction in [ 13 ] ( see also [ 27 ] ) , they have rapidly become an essential neurotechnology , deployed in hundreds of labs around the world . A number of challenges remain in analyzing the large datasets output by these probes . The basic goal is “ spike sorting '' — i.e. , to detect action potentials ( “ spikes '' ) and assign these spikes to individual neurons . Despite significant effort in the field [ 4 , 12 , 21 , 27 ] , current spike sorters for NP data have trouble tracking temporally non-stationary data and accurately sorting small spikes [ 28 ] . One major advantage of NP probes is their spatial density : the high spatial resolution of electrodes on the probe implies that each extracellular spike will typically be detected at multiple sites , providing an opportunity to “ triangulate '' the location of each spike . If effective , this spike localization can be helpful for multiple downstream tasks : spike locations serve as useful low-dimensional summarizations of the high-dimensional spatiotemporal spiking signals , which can in turn be visualized and used as features for clustering and tracking as the probe undergoes small motion relative to the brain . Several spike sorting algorithms localize spikes using a simple center of mass ( CoM ) method . More precisely , for each waveform , they select a set of channels , and compute the weighted average of the selected channels ’ positions , where the weights are given by an estimate of the amplitude of the spike on each channel . This fast , cheap method gives informative location estimates for spikes in multi-electrode array ( MEA ) recordings where long dendritic or axonal signals are not prevalent [ 23 , 20 , 10 ] ( cf . the primate retina [ 17 ] , where long axonal signals make localization approaches less useful ) . However , by definition , the CoM approach localizes spikes inside the convex hull of the electrodes , which is especially problematic for Neuropixels recordings , due to the long and thin shape of the electrodes . Hurwitz et al . [ 11 ] propose an improved localization method that provides location 35th Conference on Neural Information Processing Systems ( NeurIPS 2021 ) . estimates that can lie outside of the probe , but the estimates are still ( like the CoM method ) restricted to the two-dimensional plane spanned by the electrode locations . In addition , several approaches have been developed for localizing templates ( averages over many spikes , post spike-sorting ) in three dimensions , using biophysical models of varying sophistication [ 26 , 25 , 8 , 5 ] . Finally , triangulation approaches based on point-source [ 6 , 15 ] or dipole models [ 19 ] have been proposed for smaller-scale tetrode recordings , in which spikes are only detected on four electrodes , limiting the resolution of the resulting localization in the case of small , noisy spiking units . In this paper , we build on this previous work , making four key contributions : 1 . We introduce a denoise-then-triangulate approach , based on a simple point neuron model , that localizes single spikes in three dimensions . 2 . This improved three-dimensional localization in turn enables better spatial clustering of distinct neural units characterized by unique action potential waveform shapes . 3 . Our localization further enables better motion estimation in recordings with drift . 4 . Our approach is robust to different probe geometries . We demonstrate its utility and performance in both Neuropixels 1.0 and 2.0 probes . 2 Methods . 2.1 Point neuron model . A neuron ’ s spike is the result of a quick change in its membrane potential due to the shift of its charged particles from one side of the membrane to the other . This movement of charge creates an electric field outside of the neuron [ 14 ] , and Neuropixels electrodes record the potential of this field , at multiple locations along the probe ( Fig . 1A ) . We use a simple point-source model for these voltage differences at distance r from the cell : V ' α√ b2 + r2 ' α r , where α represents the cell ’ s overall signal magnitude , and the parameter b is fixed independently of the cell . This point-source model has been previously applied in tetrode recordings [ 6 , 15 ] , and could be replaced with more detailed models ( dipole , ball-and-stick , etc ) if desired . 2.2 Spike denoising and collision suppression . The triangulation approach described below relies only on the amplitude of the spike on each electrode . In practice we measure this amplitude using the peak-to-peak ( PTP ) value ( maximum minus minimum voltage over a short temporal interval ) . In the presence of noise , the PTP is biased upwards ( since noise will increase the maximum and decrease the minimum signal ) , and this bias depends on the underlying signal strength ( the PTP of small spikes is more biased than large spikes ) . Furthermore , collisions from near-synchronous spike events are prevalent in dense multi-electrode data [ 17 ] , and even small collisions can lead to inaccurate location estimates if not accounted for properly . Therefore , it is critical to incorporate a denoising / collision-suppression step prior to triangulation . We use the neural net denoiser implemented in YASS [ 17 ] ( retrained on NP data ) , which takes advantage of the waveform ’ s spatiotemporal signature , to suppress both noise and collisions ( Note that simple image denoising methods such as [ 16 , 7 , 3 ] do not serve to suppress collisions , and are therefore less effective here. ) . Fig . 1B shows three examples of waveforms ( in blue ) and their denoised version ( in red ) . The neural net denoiser removes noise and collided spikes , allowing us to successfully estimate each spike ’ s PTP amplitude ; see the Appendix for further details . 2.3 Spike localization . Given the denoised PTP amplitudes obtained above , we can proceed with localizing the origin of each waveform with respect to the multiple electrodes on the NP probe . We will denote { x , y , z } the coordinates of the point neuron , and { xc , zc } the planar coordinates of each NP electrode , with yc set to zero by convention . Here we exploit the fact that each spike is detectable on multiple channels simultaneously : i.e. , we have multiple observations of the form ptpc ' α√b2+r2c = α√ ( x−xc ) 2+ ( z−zc ) 2+y2+b2 , and our goal is to infer x , y , z , and α . Thus , for each spike and selected set of channels C around the “ main '' channel for each spike ( i.e. , the channel with the largest PTP amplitude ) , we want to optimize : ∑ c∈C ( ptpc − α√ ( x− xc ) 2 + ( z − zc ) 2 + y2 ) 2 . See Appendix for full optimization details . ( One important note here : due to the planar NP electrode geometry , the sign of y is not recoverable , i.e. , we can ’ t infer whether a spike is in front of or behind the probe , even if we can infer the orthogonal distance from the probe plane . ) Fig . 1 ( C ) shows examples of inferred { x , z } locations of detected spikes in both NP1.0 and 2.0 probes ( which have different electrode layouts ) , colored by max PTP . Panel ( D ) shows an example of 3-d { x , y , z } localization for the NP2.0 data . 2.4 Point cloud to image denoising . The estimated localizations are a point cloud in continuous space ( Fig . 2A ) . To enable the use of image registration techniques , we convert the point cloud representation to an image representation by generating spatial histograms where pixel location and intensity capture the spatial coordinates of spikes and their mean amplitudes ( Fig . 2B ) , following [ 27 ] . Note that this image representation is sparse and resembles a speckled Poisson image [ 18 ] , due to the limited number of spikes that are captured in each spatial position . In order to compute more accurate motion estimates , it is crucial to appropriately denoise this image representation . We adopt a Poisson denoising technique [ 18 ] , with three steps . First , we apply the Anscombe root transformation [ 1 ] to the histogram . Second , we use a Gaussian denoiser ( e.g . Block-matching and 3D filtering [ 7 ] , or non-local means [ 3 ] ) on the transformed histogram image . Third , the denoised signal is obtained by applying an inverse transformation to the denoised transformed histogram . Fig . 2C demonstrates the output for one second of time-binned data : Poisson denoising yields a more continuous pixelwise representation of the spatial histograms , which satisfies the pixel-wise continuity assumptions of image registration algorithms [ 9 ] and enables a more robust estimate of displacement . 2.5 Motion inference and registration . Given a set of dense Poisson denoised localization images for each second of recording , we estimate relative motion between frames by treating the set of images as a time-series video and use image registration techniques . Several techniques have been recently introduced to infer motion in Neuropixels recordings . The method proposed in [ 27 ] follows a non-rigid template based approach , where an average image of localizations is used as an anchor to register individual localization images using a phase-correlation based displacement estimator [ 9 ] . In contrast , the method in [ 29 ] follows a decentralized non-rigid approach , treating each localization image as its own template performing decentralized pair-wise motion estimates . This method has been shown to be more robust than the template based approach and we utilize it here to infer displacement both within the NP plane ( z , x ) and orthogonal to this plane ( y ) for the localization images . For other methods that yield only planar localizations , we just estimate vertical ( z ) and horizontal displacement ( y ) . The motion estimates for un-denoised and Poisson denoised localization image sets are shown in Fig . 5D . Once we estimate motion estimates for each time frame , we then correct for motion by volumetrically ( or planarly ) translating each image by the negative of the local non-rigid displacement that is estimated for that frame at that location on the probe , bringing all frames into alignment . Example average images before and after alignment can be seen in Fig . 5H .

Summary: This paper proposes a novel spike sorting algorithm, specifically for dense arrays such as the NeuroPixels series of electrodes. This is an extensive and detailed report. The comparisons to other approaches are up-to-date and thorough. They present some nice analysis of electrode drift, showing that the new algorithm performs well. It is well written, clear, and includes extensive figures to illustrate the work and results. This is an excellent piece of work.