Visualization of Neuron Data
using Nonlinear Technic
Yoko Uwate and Yoshifumi Nishio

Marie Engelene J. Obien and Urs Frey

Dept. of E. E. Eng., Tokushima University
2-1 Minami-Josanjima Tokushima
770-8506 Japan
Email: {uwate, nishio}@ee.tokushima-u.ac.jp

MaxWell Biosystems
Mattenstrasse 26, Basel,4058 Switzerland
Email: {marie.obien, urs.frey}@mxwbio.com

Abstract— In our previous study, we have proposed the method
to use nonlinear time-series analysis to apply to neuronal data forvisualizing a characteristic of neurons. We set up three types ofneuron data which are observed at different days. By applying
three nonlinear time-series analysis, we confirmed that theyoungest neuron has strong activity and the neuronal behavior
settles down as the day goes on. In this study, we investigate theeffect of the delay parameter of attractor reconstruction of
nonlinear time-series analysis. From observed results, we can seethat the appropriate value of delay parameter exists to display
the network characteristics.

In this study, we focus on the delay parameter of attractor
reconstruction which is defined by Takens' theorem. The delay
parameter is important role for displaying the networkcharacteristics. By changing the delay parameters, we obtained
the different shapes of attractors in 3-dimensioanl space. Fromobserved results, we can see that the appropriate value of delay
parameter exists to display the network characteristics.
II.

A. Measurement Platform
We used a CMOS-based high-density microelectrode array(HD-MEA) system called MaxOne (MaxWell Biosystems,Basel, Switzerland) composed of 26,400 platinum electrodes ina regular grid format with 17.5 μm electrode center-to-center
distance (3,265 electrodes/mm2). Up to 1,024 electrodes could
be simultaneously recorded by routing the electrodes to lownoise read-out channels through a flexible switch-matrix
approach [5]. On-chip circuitry was used to amplify (0-78 dB
programmable gain), filter, and digitalize (10-bit, 20 kHz) therecorded signals. Online spike detection was performed by theMaxLab Live software (threshold: x5 RMS noise).

Keywords; neuron data, nonlinear time-series analysis

I.

INTRODUCTION

Understanding how brain circuits develop and operate is amajor goal for recent neuroscience project. Burst patterns
within neurons may have some important role for operating
information processing in a brain. Therefore, to develop
detecting and analyze burst pattern are investigated in various
fields [1]. Although it is important to study burst pattern inorder to make clear correlation and communication process
between neurons, unveiling a structure of the whole neuronal
network is also required. While, nonlinear time-series analysis
is a useful tool for characterizing about the dynamics behindobserved time-series data [2]. The neuronal data obtained fromliving neurons should be high-dimensional and dynamic data.
Then nonlinear time-series analysis matches well tocharacterize the neuronal data.

B. Cortical Cell Cultures
Primary cell cultures were prepared as described in Ref. [6]in accordance to Swiss Federal Laws on animal welfare.
Briefly, cells from embryonic day 18 Wistar rat cortices weredissociated in 2 ml of trypsin with 0.25~% EDTA (Invitrogen,California, USA) with trituration. The cultures weremaintained inside an incubator to control environmental
conditions in 1 ml of growth medium (partially replaced twiceper week).

Then, three techniques: attractor reconstruction, recurrenceplot and Lyapunov exponent are applied. In our previous study,
we focus on time-series data generated from spike time data ofneurons. The spike times are detected at each electrode withhigh-density microelectrode array (HD-MEA) system called
MaxOne [3]. There are 1024 electrodes in total and thesampling rate is 20kHz. The recording time is 60 seconds.
First, in order to figure out the characteristics of spike time, wedisplay the spike time as raster plot. Next, we change the spiketime data to time-series data depending on the spike rate atcertain range. Finally, we apply nonlinear time-series analysis
to three time-series data of neurons, which are measured byday 15, 20 and 30, respectively. By using computer
simulations, we confirm that the characteristics of neuron aredifferent between youngest and oldest neurons [4].

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NEURON DATA SET

C. HD-MEA Extracellular Recordings
The MaxOne HD-MEA recording setup was placed in arecording incubator (65~% humidity) for a control ofenvironmental conditions (5~% CO2). During experiments, theMaxOne chips were transferred to the recording incubator andcovered with sterilized lids to minimize media evaporation.
Figure 1 shows the raster plot obtained from Day 15, using1024 electrodes. Next, we calculate the spike rate at a certain
range, then time-series data is obtained as shown in Fig. 2.

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(a) tau=5.

(b) tau=10.

Fig. 1. Raster plot of neurons from 1024 electrode (Day 15).

(c) tau=20.

(d) tau=30.

(e) tau=40.

(f) tau=50.

Fig. 2. Time series data from all neurons (Day 15).
III.

SIMULATION RESULTS

The attractor of dynamical systems can be reconstructed
topologically in the embedding space from Takens' theorem[7]. The state vectors in the reconstructed m-dimensional
embedding space are defined byFig. 3. Attractor reconstruction.

REFERENCES[1]

where x(t) means a scalar time series and tau is the delay time.
Figure 3 shows the simulation results when neuronal timeseries data is embedded in 3-dimensional space by changing
the delay time tau. From these figures, we confirm that theneuron have a structure when the tau is fixed with smaller than20, because the orbit draws in certain range, does not move
about randomly. While, when the tau is set to larger than 30,
the behavior of the orbit is complex. To evaluate the network
characteristics, it is better to fix the delay parameter tau<20 toobtain the structure.

[2]
[3]

[4]

[5]

IV.

CONCLUSIONSIn this study, we changed the delay parameter of attractor
reconstruction. The delay parameter is important role fordisplaying the network characteristics. By changing the delayparameters, we obtained the different shapes of attractors in 3dimensioanl space. From observed results, we can see that theappropriate value of delay parameter exists to display thenetwork characteristics.

[6]

[7]

In the future works, we would like to calculate thecharacteristics of attractor reconstruction results, and to use
more different types of neuronal data. Applying classificationof neuronal data is also our future works.

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