Motion sensitivity analysis of retinal ganglion cells in mouse retinausing natural visual stimuli

Federico Wadehn1, Konrad Schieban1 and Konstantin Nikolic2

Abstract— One of the major objectives in functional studiesof the retina is the understanding of neural circuits andidentification of the function of involved nerve cells. Instead ofstimulating the retina with light patterns of simple geometricalshapes, we analyze the response of retinal ganglion cells ofmouse retina to a black and white movie containing a naturalscenery. By correlating measured spike trains with a metricfor the velocity of a visual scene, PV0 cells were found tobe direction selective, whereas PV5 cells did not show anysensitivity to motion.

I. INTRODUCTION

One major task in neuroscience is the understanding of neuralcircuits and identification of the function of pertaining nervecell. The retina is a light-sensitive neural tissue on the backof the eye, counted as part of the central nervous system. Itsneural circuitry consists of a layered structure of differentcells, the function of which, is still not well understood. Thepurpose of the retina is to process a high dimensional inputsignal, e.g. a visual scene, into a discrete sequence of neuralspikes. Photons absorbed by the photoreceptors can induceaction potentials, which are sequentially relayed through thedifferent layers of the retina, to be finally transmitted to theretinal ganglion cells, whose axons form the optic nerve,which connects to the visual cortex.

The goal of this work is to propose a method to identifymotion sensitivity of retinal cells and to expose interestingfindings of motion sensitivity of eight different retinal gan-glion cell types in mice. Feedback does exist in the retinalcircuitry [1], but our approach for functional identification ofretinal cells examines sequential processing of inputs, sincemost of the information-flow in the retina is unidirectional,opposed to the bidirectional information-flow in the cerebralcortex [2].

Successful approaches aimed at functional understandingof neurons can be classified into two groups. On the onehand there are model-based approaches, which assume forinstance a linear-nonlinear-Poisson spiking model [3] andtry to identify the different parts of the model using white-noise as input stimulus. Algorithms like the spike triggeredaverage and spike triggered covariance are then employedto extract the linear receptive fields [4], [5]. Other, moreexperimental approaches, have been based on projections ofsimple geometrical shapes such as bright or dark spots ontothe retina [2], [6]. It has been shown in [6] that specific types

1Department of Information Technology and Electrical Engineering,ETH Zurich, Switzerland {wadehnf,skonrad}@ee.ethz.ch

2Institute of Biomedical Engineering, Imperial College London, UKk.nikolic@imperial.ac.uk

of retinal ganglion cells fired, when projecting an increasingblack circle onto the retina, which in nature could correspondto an approaching object or in the case of rodents to apredator [2], [6]. Natural scenes, on the other hand, are muchmore involved and feature a higher variety in contrast, shapesand light intensity. Considering that the retinal circuitryevolved in a natural environment, it is instructive to studythe spiking response of various neurons as a response tonatural stimuli as presented in this work.

This paper is structured as follows: In section II wedescribe the data used for our experiments and outline theproposed correlation analysis and in section III we presentresults on motion sensitivity of different retinal ganglioncells.

II. MATERIALS AND METHODS

Electrophysiological neural spike measurements of eightgenetically different types of retinal ganglion cells wererecorded as described in [7], using mouse retinas of theso called Paravalbumin-Cre x Thy1-Stop-EYFP mouse line.A black and white movie with 256 grayscale values wasprojected onto the retina and the spiking behavior of differentretinal ganglion cells, called PV0 up to PV7, was recordedusing a patch clamp [2], [8].

The video was obtained by mounting a digital camera ona cat’s head and making the cat walk around in a field,to obtain the natural scenery a mouse is usually exposedto under daylight. Note that most frame movements occurin the horizontal plane and only few rotational movementsof the camera are presents. Furthermore zooming effectswere not an issue due to the high frame rate compared tothe cat’s walking speed. The grayscale video of the naturalscene with a frame rate of 25 frames per second consists of499 bitmap raster graphic images. Image processing and theimplementation of the correlation algorithm was performedin MATLAB R2014a, using MATLAB’s computer visionsystem toolbox. In total, 37 measurements of retinal ganglioncells of the different PV classes were used in our correlationanalysis. The total number of measured cells of each classand the total number of spikes when projecting the movieonto the retina is shown in Table I. Note that PV3 cellswere excluded from the analysis due to their extremely sparsespiking behavior, which does not allow a sensible statisticalanalysis. Figure 1 shows the spike trains of a PV0 and aPV2 cell during the projection of the movie onto the retina.It can be seen that the firing frequency of the distinct classesof retinal ganglion cells differs significantly.

Cell PV0 PV1 PV2 PV4 PV5 PV6 PV7# Cells 2 10 9 5 7 2 2# Spikes 1579 1063 309 645 3791 5499 312

TABLE I: Parameters of the electrophysiological recordings of 37retinal ganglion cells

0 100 200 300 400 500

Spik

esPV

0(a

.u.)

0 100 200 300 400 500Frame number

Spik

esPV

2(a

.u.)

Fig. 1: Spike trains of different retinal ganglion cells (PV0, PV2)responding to the same visual stimulus. The spiking rate as responseto the same stimulus differs strongly between different retinalganglion cell classes.

A. MOTION SENSITIVITY ANALYSIS

When using uncorrelated white noise input stimuli for areceptive field analysis as performed in [4], [9], often amere averaging of the input preceding a spike is used toidentify relevant inputs for the analyzed receptive field. Theassumption of uncorrelated inputs can hardly be supportedwhen using natural stimuli, such as consecutive movieframes. Thus, techniques like spike triggered average [4]would provide biased results. Therefore, when working withcorrelated inputs, one can resort to a Bayesian analysis,taking into consideration the prior distribution of the inputand comparing it to the input distribution preceding neuralspikes.

When trying to identify the function of specific cells byprojecting simple geometrical shapes onto the retina as in[6], [10], it is straightforward to define the type of motionthe object performed. Finding a metric to describe how theenvironment is changing in natural scenes is more involved.

Image sequences have large parts around the center, whichare similar from frame to frame and only shifted in aparticular direction. This motion reflects how the visual inputto the eyes changes due to head and eye movements. Weassumed that the displacement of an image’s center is agood metric to describe the velocity in a natural scene. Todetermine the displacement profile of the center, we useda template matching algorithm. A square around the centerof the current frame was chosen to be the template to belooked for in the subsequent frame. The displacement is

determined by finding the maximum of the two-dimensionalcross-correlation function. To get whitened images for anunbiased cross-correlation, we subtract the mean grayscalevalue and divide by the standard deviation.

Sw(m,n) = (S(m,n)−µS)/√

Var(S) (1)

Tw(m,n) = (T (m,n)−µT )/√

Var(T ) (2)

d(x,y) =M−1

∑m=0

N−1

∑n=0

Sw(m,n) ·Tw(m− x,n− y) (3)

With −(L− 1) ≤ x ≤ M− 1 and −(L− 1) ≤ y ≤ N − 1,where L is the side length of the quadratic template in pixels,M and N the number of pixels of the frame and µ the meangrayscale value of the image S or template T respectively.Positioning the center of both the template and the image inthe origin, the estimated displacement vector c ∈ R2, wherethe center has moved is

c = argmaxx,y

d(x,y) (4)

Figure 2 shows the displacement of the center from oneimage to the next.

Fig. 2: On the left, the current frame is displayed with the squareindicating the center. On the right, the next frame is shown andthe position where the center has moved, found with the templatematching algorithm

The number of pixels as well as the shape of the templateinfluence the displacement profile. Small template sizes ofa few pixels in each direction are noise-sensitive, whereasvery large template sizes lead to inaccurate displacementestimates. Having had movie frames of size 320× 240,we found that choosing a 100× 100 template results insmooth trajectories. Less than 2% of the displacements werefound to be outliers and manually adjusted. The horizontaldisplacement profile of the movie for the first 180 frames isshown in Figure 3.

With the displacement profile and the neural spike trainsof 37 retinal ganglion cells we performed the correlationanalysis. The prior distribution of x- and y-displacements isapproximated with the sample distribution using histogramswith a bin size of 3 pixels. The conditional distributionof x- and y-displacements preceding spikes was computedseparately for each delay from 0 up to 5 frames (i.e. 0 ms -200 ms) and then averaged to get the transient response ofthe retinal ganglion cells. It has been shown in [2] that retinalganglion cells within the same class have a similar spiking

0 30 60 90 120 150 180

−10

10

30

Frame number

∆x

[Pix

el]

Fig. 3: Displacement profile of the center

behavior. Therefore spike trains of retinal ganglion cellsin the same class were lumped together to get an averageconditional input distribution. The distribution is computedas:

p(input ∈ bin i ) =#inputs in bin itotal # of inputs

(5)

For the prior distribution, the input is the full displace-ment profile and for the conditional distribution, only thedisplacement of the center preceding a spike. The absolutedifference of the two histograms, if not vanishing, indicatesthe specific motion sensitivity of the considered cell class.This approach is inspired by the spike triggered average [4],but by considering the prior distribution of the input, wecorrect for the fact that our input is not white noise, butstrongly correlated.

The L1 distance ∆p between the prior input distributionand the conditional input distribution is computed as follows:

∆p = ∑input|p(input)− p(input|spike)| (6)

We further analyzed the correlation between the spike trainsof different PV cells and the angle θ of the motion of thetemplate’s center, defined as: θ = atan2(∆y/∆x), as shown inFigure 6. Moreover, we examined the dependency betweenthe minimal neural response and the displacement of theimage center.

III. RESULTS

The prior distribution of the vertical and horizontal dis-placements are shown in blue and the distribution of thedisplacement profile preceding a spike p(input|spike) isshown in red (cf. Figure 4). For PV0 cells the horizontaldisplacement profile of inputs preceding a spike is shifted tothe left (c.f. Figure 4 a), compared to the prior displacementprofile, which indicates that PV0 cells preferentially fire upondetection of horizontal motion. The close match of the twohistograms in Figure 4 (c) and (d) indicates that PV5 cellsdo not preferentially fire upon horizontal or vertical motion.

In Figure 5 the clustering behavior of the absolute differ-ences of the prior distribution and the conditional distributionallows insights on direction and motion sensitivity. If theabsolute differences of the prior and conditional input distri-bution for horizontal and vertical motion form a cluster witha high value, the cell can be assumed to be motion sensitive,but not direction selective. On the other hand if the cluster

−30 −20 −10 0 10 20 30 400

0.1

0.2

0.3

x-Displacement [pixel]

Prob

abili

tyPV

0

Figure 4a

p(x)p(x|spike)

−30 −20 −10 0 10 20 30 40y-Displacement [pixel]

Figure 4b

p(y)p(y|spike)

−30 −20 −10 0 10 20 30 400

0.1

0.2

0.3

x-Displacement [pixel]

Prob

abili

tyPV

5

Figure 4c

p(x)p(x|spike)

−30 −20 −10 0 10 20 30 40y-Displacement [pixel]

Figure 4d

p(y)p(y|spike)

Fig. 4: Histograms of horizontal and vertical displacement for PV0and PV5 retinal ganglion cell. From the shift between the blue andred histograms in Figure 4 (a), it can be inferred that PV0 has aparticularity strong direction selectivity.

0 1 2 3 4 5 6 7

PV cell

∆p

(a.u

.)

x y |x| |y|

Fig. 5: Absolute difference of prior and conditional input distribu-tion for PV0 up to PV7 cells

is widely spread, the cells can be assumed to be directionselective to either horizontal or vertical motion. PV0 cellswere found to be direction selective, which manifests itselfby a large absolute difference between the prior and posteriordistribution as shown in Figure 5, especially for horizontaldisplacements. PV1, PV4 and PV7 cells, on the other hand,do not seem to have a preferred input direction, but arenonetheless more sensitive to motion than PV5 cells.

The polar plots in Figure 6 (a) show displacement distri-butions of natural input stimuli and inference of nerve cells’selectivity to directed motion (i.e. probability of getting aspike if the scene moves in the direction θ). The delay rep-resents the latency between the onset of motion and spiking,expressed in number of time bins (40 ms each). The two PV7cells show a strong preference for certain directions, whenaveraging up the conditional input distributions precedinga spike as described in the previous section (e.g. for thefirst PV7 cell the highest probability of spiking is along adirection of approximately 32◦). A similar result has beenobtained for PV0 cells, but other cell types did not showsuch a strong preferential direction. Furthermore, for PV0the spiking probability as a function of the angle does notchange, when the delay parameter changes. However this

Fig. 6: (a) Polar plots of the probability distribution p(θ) forthe scene movement directions (blue), and conditional distributionp(spike|θ) (red) for two PV7 cells and one PV0 cell. (b) Conditionalprobability of firing for a specific frame to frame shift and delay(resolution: 1 pixel = 3.75 µm). (c) Relationship between the frameshift which produces minimal response and the size of the dendriticfield for PV cells.

was not true for other cells, when the delay was changedthe direction changed as well. This could be due to thedifferences in the memory of different cells [2].

Another interesting insight is shown in Figure 6 (b) and(c) where we analyzed the minimal response of differentretinal ganglion cell classes to absolute displacements ofthe image’s center. The frame shift, which gives minimalresponse, shows good correlation with the dendritic treediameter (c.f. Figure 6 (c)). It seems that when frame-to-frame movement is about the size of the cells’ receptive field,the cell is the least sensitive.

IV. DISCUSSION

The methods presented in this paper form a basis formotion sensitivity analysis of retinal cells performed byextracting dynamic information from visual scenes like dis-placement profiles and correlating these quantities with thespiking data of neurons.

Several parameters have to be considered in this analysis.It is important to ensure that the measurements are longenough to obtain statistically significant results, since dif-ferent neurons display a very different spiking frequency asshown in Figure 1. Knowledge of the delay between theinput exposure and the time to peak of the neural activity of aspecific neuron is furthermore fundamental for the reliabilityof the results. A further inquiry on the influence of theframe rate on the spiking behavior of neurons would be alsobenficial.

In [2], motion sensitivity of PV0-PV7 cells has beenexamined by projecting black and white spots onto theretina. In alignment with our analysis PV0 cells were foundto be direction selective, whereas PV5 cells did not show

significant sensitivity to motion. It has been shown in [2]that different retinal ganglion cells have varying delays inthe time to peak. For instance PV5 cells were coined asfast reacting cells with a time to peak of around 50 ms,whereas the other PV cells showed greater delays above100 ms before firing. Correlation analysis, is as the namesuggests, only an analysis of correlations and does not implya functional link nor does it explain causation. Therefore,the neuron’s main function could be to react to a quantitycorrelated with the linear displacement, such as the rotationor approaching motion as described in [6].

V. CONCLUSIONS AND FUTURE WORK

In this work, we showed that besides the classical projec-tion of geometric shapes on the retina, also natural scenesprove to be a helpful tool to analyze neurons in the retina.Using the displacement of the image center as a possiblemetric for movements in a natural scene, a Bayesian analysisof the spiking behavior was performed.

With more measurements of neural spike trains comingup in future, this simple correlation analysis between thedisplacement profiles in images and the spiking behavior ofcells can be used as a first step in the analysis of the responseof retinal cells to movements. The correlation analysis canalso be extended to include other parameters such as lightintensity, contrast changes, accelerations and rotations of theimage center. A further step could include tools stemmingfrom information theory, such as analyzing the mutual infor-mation of the spike train and the displacement profile, whichwould not only capture first order statistics, but also highermoments.

ACKNOWLEDGEMENTS

The authors thank Dr. B. Roska of Friedrich MiescherInstitute and Dr. T. Viney from Oxford University for theexperimental data and interesting discussions.

ETHICS APPROVAL

All animal procedures were performed in accordancewith standard ethical guidelines (European CommunitiesGuidelines on the Care and Use of Laboratory Animals,86/609/EEC). The study was approved by the VeterinaryDepartment of the Canton of Basel-Stadt (Kantonales Vet-erinaramt, Postfach 264, 4025 Basel, Switzerland, documentno. 2105).

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