Multiple Time Scales Observed in Spontaneously Evolved Neurons … · 2020-04-11 · Multiple Time Scales Observed in Spontaneously Evolved Neurons on High-density CMOS Electrode

Multiple Time Scales Observed in Spontaneously Evolved Neurons onHigh-density CMOS Electrode Array

Eiko Matsuda1,7, Takeshi Mita2, Julien Hubert1, Mizuki Oka3,Douglas Bakkum4, Urs Frey5, Hirokazu Takahashi6 and Takashi Ikegami1

1Department of Arts and Sciences, the University of Tokyo, Tokyo, Japan,2Department of Mechano-informatics, the University of Tokyo, Tokyo, Japan,3Tsukuba University, Ibaraki, Japan, 4ETH Zurich, Department of Biosystems Science and Engineering, Basel, Switzerland,

5RIKEN Quantitative Biology Center, Kobe, Japan, 6Research Center for Advanced Science and Technology, the University of Tokyo, Tokyo, Japan,7JSPS research fellow, email: [email protected]

Abstract

Spontaneous evolution of neural cells was recorded around4-34 days in vitro (DIV) with high-density CMOS micro-electrode array, which enables detailed study of the spatio-temporal activity of cultured neurons. We used the CMOSarray to characterize 1) the evolution of activation patternsof each putative neurons, 2) the developmental change incell-cell interactions, and finally, 3) emergence of multipletimescales for neurons to exchange information with eachother. The results revealed not only the topology of the phys-ical connectivity of the neurons but also the functional con-nectivity of the neurons within different time scales. We fi-nally argued the relationship of the results with “functionalnetworks”, which interact with each other to support multiplecognitive functions in the mature human brain.

IntroductionHow can the gap between living and nonliving matter bebridged? Since 1987 when Artificial Life was launched byChristopher Langton, we have not answered this question.Rodney Brooks wrote in the paper (2001) that there are fourpossibilities why we still cannot make living machines: 1)An alife model is correct, but several parameters were setincorrectly; (2) an alife model needs more complexity; (3)we need more computational power; and (4) a new funda-mental law in addition to the laws of physics is needed. Inthis paper, we search for the possibility of (2) yet unrevealedlaws of neuro-dynamics, by studying cultivated neural cellson a glass plate.

Biological neurons are cultivated on a glass plate fromneural “seeds”. The seeds develop into either neural or gliacells. Neurons have cell bodies, axons, and numerous den-drites, which the neurons use to connect with each other. Aunique characteristic of the present study is that we recordthe action potential from neurons by using a CMOS arrayglass plate. As we will describe later, each CMOS is thesame size order of the neurons. Therefore, by using theCMOS array, we can potentially accurately record the timeseries of each neural firing. A remarkable aspect of this bi-ological neural network is the developmental process. Theentire time course of the growing process can be recorded

with the CMOS array. We analyze the time series data tocharacterize the developmental dynamics.

A disadvantage of this experiment is that we have no wayof designating which neurons connect to which. We thusmeasure the information transfer from the time series to inferthe neural connectivity. This method reveals not only thetopology of the physical connectivity of the neurons but alsothe functional connectivity of the neurons within differenttime scales. A finding in this paper is that growing biologicalneurons use different time scales to exchange informationwith each other.

The paper is organized as follows. In section of Materialsand Methods, the specifications of the CMOS array and thebiological conditions for the neural cells are provided. Themethod for cultivating cells and associated techniques arealso described. In section of Result and Discussion, the an-alyzed results are presented. The activation patterns of eachcell are quantified with inter-spike intervals (ISIs). Cell-cellinteraction is also inferred by transfer entropy (TE), whichreveals that multiple functional networks emerge from theneural original network. Finally, in section of Conclusion,the paper is summarized, and future work is discussed.

Materials and MethodsTo measure the electrical activity of cultured neurons, weused a high-density CMOS microelectrode array 1(Freyet al., 2010). The CMOS array is pictured in figure 1(a). This array is an emerging instrument for investigat-ing the spatio-temporal activity of cultured neurons in de-tail. The CMOS array has 11,011 recording sites with aninter-electrode distance of 18 µm, i.e., in the order of cellbody size, and a sampling rate of 20 kHz. This high spatio-temporal resolution allows precise recording of action po-tentials from the identified cell bodies of neurons. Usingthis high spatial resolution, we localized neural somata andrecorded their activity.

1All procedures were approved by the institutional committeeat the University of Tokyo, and were performed in accordance withthe Guiding Principles for the Care and Use of Animals in the Fieldof Physiological Science of the Japanese Physiological Society.

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This CMOS array is superior to conventional microelec-trode array (MEA) (Sun et al., 2010; Eytan and Marom,2006; van Pelt et al., 2004) in respect of spatio-temporalresolution: The locations of recording sites in conventionalMEAs are predetermined, with an inter-electrode distance of200 µm, so that it is difficult to identify signals from an indi-vidual cell, and neurons far from these recording sites are notincluded. Alternatively, optical imaging can be used to studythe Ca++ dynamics of any neuron of interest; however, thetemporal resolution is not high enough to characterize theaction potentials of each neuron.

Figure 1: High-density CMOS array (a) Appearance. (b)Interval of each electrodes is close to the cell body size.

Dissociated neural culture The neural cultures were pre-pared from the cerebral cortex of E18 (embryonic 18)Wistar rats. The cortex was triturated with trypsin anddissociated cells were plated and cultured on high-densityCMOS microelectrode arrays coated with polyethylen-imine and laminin. For the first 24 h, the cells were cul-tured in neurobasal medium containing 10% horse serum,0.5 mM GlutaMAX and 2% B-27 supplement. Afterthe first 24 h, half of the medium was replaced withgrowth medium in the form of Dulbecco’s modified Ea-gle’s medium with 10% horse serum, 0.5 mM GlutaMAX,and 1 mM sodium pyruvate. During the cell culturing,half of the medium was replaced once a week with thegrowth medium. The cultures were placed in an incuba-tor at 37 !C with an H2O-saturated atmosphere consistingof 95% air and 5% CO2. We prepared for two conditionswith different densities of neurons. The denser chips had35,000 cells plated, denoted as Chip#1D and Chip#2D,while the sparser ones had 14,000 cells, termed Chip#1Sand Chip#2S.

Recording of neural activity Neural activity wasrecorded with high-density CMOS microelectrodearrays. Before the neural somata activity was recorded,almost all of the 11,011 electrodes were scanned to obtainan electrical activity map with which we estimated thelocations of the somata. A scan session consisted of 95recordings; each recording was conducted for 60 sec withabout 110 electrodes that were selected randomly, whileavoiding overlap with already selected electrodes. An

electrical activity map was obtained from the scanneddata by calculating the average height of the spikes forevery electrode. We assumed that the neural somata werenear the local peaks in the Gaussian-filtered electricalactivity map. About 100 of the higher-level peaks wereselected, and then the nearest electrodes were selected forrecording. If the number of local peaks was fewer than126, then all the peaks were selected. The electrical ac-tivity of the selected electrodes was recorded for 30 min.All recordings were done at a 20-kHz sampling rate usingthe LimAda spike detection algorithm (Wagenaar et al.,2005) with a threshold of 5. Unexpected double-detectedspikes were removed from the data before the analysiswas conducted.

Results and DiscussionSimple observation of activity patternsFirst, we observed the activation patterns of the neurons byexamining the time series of the neural spikes. Figure 2shows examples of raster plots of Chip#1D and Chip#1S.Chip#2D and Chip#2S showed similar tendency to their re-spective counterparts (data not shown). The data plottedhere are a compressed version of the raw data with a dif-ferent bin-length, which is denoted by !t. Namely, thespikes within the same bin are regarded as one spike. If !tis smaller, the time series represents single spikes generatedfrom each single neuron, while a larger !t represents themacroscopic behavior created by an ensemble of neurons.In the figure 2, the data are plotted in !t = 0.6 ms and 100ms. At the top of each raster plot, the activation ratio is dis-played. We chose !t = 0.6 ms and 100 ms as the examplesby two reasons; a single spike of neurons lasts around 1 ms,while, observably from figure 2, synchronous activation ofneurons is detected around !t =10–100 ms. Therefore, wetook !t = 0.6 ms to capture interaction between individ-ual cells (microscopic), while !t = 100 ms is to observecollective activities generated from an ensemble of neurons(macroscopic).

As shown in figure 2(a) right, the Chip#1D neurons atdays in vitro 7 (DIV 7) are activated intermittently in syn-chronization. This activation pattern was burst synchroniza-tion, in which an ensemble of neurons has active and silentphases; in the active phase, synchronous activation of theneurons is intermittently observed. The burst synchroniza-tion is a typical activation pattern observed in cell cultures(Maeda et al., 1995). On the left of figure 2(a), the silentphase of the neural activation is magnified with !t = 0.6ms. Neural spikes are observed sparsely, which suggests thateach neurons was activated independently from others.

On the other hand, at the later stage (DIV 14) of theChip#1D, burst synchronization is not observed (figure 2(b) right). Instead, we observed each neurons shows dif-ferent activation patterns; i.e., some neurons were activated


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almost all the time, some showed spikes less often, and oth-ers remained silent. These neurons seem to be activated atdifferent frequencies. The left of figure 2(b) shows that, at!t = 0.6 ms, a single spike is followed by another, whichsuggests that one single spike can activates another. In con-trast, Chip#1S showed the burst synchronization throughoutthe entile recoding period (figure 2(c) and (d)).

To summarize the results thus far, burst synchronizationwas observed in two conditions; in the earlier developmen-tal stage of the dense cell condition, or in the sparse cellcondition. In those cases, any single spikes hardly activateanother. In the later stage of the dense cell condition, theneurons spiked at various frequencies, where single spikesinduce others.This tendency is explained by the maturity ofsynapses. At the earlier developmental stage, the synapsesare not mature; therefore, a single spike cannot activate an-other. Still, if the neurons send spikes at the same time (syn-chronous bursts), the signals become enough strong to ac-tivate each other. In contrast, at the later stage of develop-ment, the synapses were enough strong to transmit a singlespike from one neuron to another.

Single cell activity evaluated with ISIIn the next step of the analysis, we quantified the activationpatterns of each neuron. Therefore, we analyzed the inter-spike intervals (ISI) distribution of the neural activity. Fig-ure 3 (a) depicts examples of ISI distribution recorded fromputative single neurons cultured in Chip#1D. In the earlierculture stage (DIV 7; figure 3 (a) left), exponential decaywas observed, while the neurons tended to obey the powerlaw at DIV 14 (right figure). To quantify this tendency, weplotted the ISI frequency on a logarithmic scale, and we fitthe slope with a straight line by the least squared method. Ifthe ISI distribution follows the power law, the distributionshould be a straight line, so that the R-squared value is anindex of fitting the power law.

Figure 3(b) shows the average of the R-squared valuesover each neuron; the values tended to increase in Chip#1D,Chip#1S and Chip#2S. Especially, Chip#1D shows a drasticincrease at DIV 10, which suggests the neural activity be-came closer to the power law. Chip#2D also shows a higherR-squared value throughout the entire recording period. Therecordings for Chip#2D started from DIV 17, which ex-plains the result is similar to the later stage of Chip#1D.

The power law means that each neuron exhibited a widerange of ISIs. It may be related to the observation from theraster plots (figure 2), which showed that a wide range offrequencies between neurons were observed at the later de-velopment stage. To sum them up, a broader range of timescales likely emerges after synaptic maturation. However,from this ISI analysis, it is not possible to understand howthose cultured neurons interact with each other to generatethe activity patterns. In the next part, we then investigatedneuron connectivity.

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Figure 3: (a) Examples of the ISI distribution of neural activ-ity recorded in a cell on Chip#1D. The X and Y axes depictthe ISI logarithm and frequency respectively. The two fig-ures show the results for each 7 and 14 DIV. The estimatedexponents for DIV 7 and 14 are -1.40(0.57) and -3.77(0.57).The values inside the parentheses denote the R-squared val-ues of the regression lines. (b) Change in the R-squared val-ues with DIV. The R-squared value is obtained from a re-gression line fit to the ISI distribution, which is plotted ona logarithmic scale. When the R-squared value is closer to1.0, the ISI distribution is more likely to obey the power law.

Cell-cell interaction inferred with transfer entropyWe used transfer entropy (TE) to estimate the effectiveconnectivity for transferring information from one neuronto another. TE measures directed information transfer,which detects causal relationship between two time series(Schreiber, 2000; Lizier et al., 2011; Staniek and Lehnertz,2008; Bertschinger et al., 2008). For instance, higher TEfrom one neuron to another indicates that the first neuronstrongly affects the second. Therefore, TE enables us to findthe functional synaptic connectivity. We defined the TE, andthen applied it to artificial neural networks to ensure the va-lidity of TE to estimate effective connectivity. Finally, weapplied TE to the cultured neural cells to infer their topol-ogy.

Definition of transfer entropy Information is measuredwith Shannon entropy, which quantifies the amount of un-certainty associated with a system X . Specifically, Shan-non entropy of a system X is defined as:

H(X) = !!

x!Xp(x) log p(x), (1)


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Figure 2: Examples of the raster plot of the cultured neurons. The X axis denotes time (s). The Y axis represents the indexesof the recoding channel, where one channel can be considered as one neural cell. The subfigures at the top of the raster plotsshows the spike rate. (a) - (d) Results for Chip#1D and Chip#1S with different DIVs. !t = 0.6 ms (microscopic) and 100 ms(macroscopic).

where p(x) denotes the probability of x (x is an eventof X). To evaluate the dependency between X and Y ,mutual information (MI) is defined as follows:

MI(X,Y ) = H(X)!H(X|Y )

= H(Y )!H(Y |X). (2)

H(X|Y ) means conditional entropy, i.e., the uncertaintyof X when Y is known. Therefore, MI(X,Y ) suggestsa decrease in the uncertainty of X when Y is known.MI(X,Y ) measures the dependency between X and Y;so that this variable cannot quantify a causal relationshipbetween them.TE measures the causal relationship between X and Y bycalculating the past history. The TE from X to Y is de-noted by TX!Y , which is written as:

TX!Y = H(yn+1|y(k)n )!H(yn+1|y(k)n , x(l)n )

=!N"1

n=0 p(yn+1, y(k)n , x(l)

n ) log p(yn+1|y(k)n ,x(l)

n )

p(yn+1|y(k)n )

(3)

where n is the current time step, and y(k)t and x(l)t

are the past variables with length k and l respec-tively (i.e., y(k)t = {yn, yn"1, ...yn"k+1} and x(l)

n ={xn, xn"1, ...xn"k+1}). When the next step of Y (=yn+1) is conditioned from the past history of X (=x(l)n ), then H(yn+1|y(k)n , x(l)

n ) takes a smaller value thanH(yn+1|y(k)n ). If yn+1 is independently determined from

the past history of X , then the two components will havethe same value. Therefore, TEX!Y measures the causal-ity of X to Y .

Settings of artificial neural networks TE analysis wasfirst applied to a computational neural model. The modelwas built around Izhikevich neurons connected throughartificial synapses (Izhikevich, 2003). The Izhikevichneurons form a simple model of cortical neurons that isimplemented by a system of two differential equationsmodeling the membrane potential and the refractory pe-riod. When the membrane potential reaches a thresholdvalue (for instance, 30 mV), a spike is emitted. Thisspike is transferred to post-synaptic neurons through someshared synapses. The voltage on arrival is the originalspike strength, modulated by the efficacy of the synapses.For instance, an initial spike of 30 mV traveling on asynapse with an efficacy of 0.5 delivers a voltage of 15mV to the post-synaptic neuron. Every synapse has a de-lay of 1 ms between the time of emission and the arrivalof a spike.

The complete model is composed of seven neurons:four input neurons receiving randomly generated externalstimulations, two internal neurons and one output neu-ron. The parameters for the Izhikevich neurons corre-spond to the regular spiking model(a = 0.02, b = 0.2,c = !65mV and d = 6). Different types of connec-tivity patterns have been tested, ranging from fully inter-


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(a) Topology 1 (b) Topology 2

(c) Topology 3

Figure 4: Topology of the original network used in the com-puter simulation.

connected to sparse (figure 4 (a)–(c)). The strength of theconnection is randomly assigned based on uniform dis-tribution. Every update of the model represents a 0.1-msstep in time, which ensures the model’s mathematical sta-bility. The total duration of a test is 1000 s, which corre-sponds to 10,000,000 updates of the model.

Estimated connectivity of the artificial network Fromthe time series of the artificial neural activity, we cal-culated the TE from one neuron to another. Using theTE, we estimated the network structure of the artificialneurons. A synaptic connection from one to the other wasassumed when the TE between two neurons was higherthan the threshold. Then, we compared the topologyof the reconstructed network and the original networkshown in figure 4 (a)–(c). The number of false edges foreach topology is shown in figure 5. !t in this figure isthe same one as previously used, which represents thebin-length of the compressed time series. This figureshows that the optimal parameter set to reconstruct theoriginal topology depends on the dimension of the pastvariables (k and l) and !t.

The result ensures that the effective connectivity to trans-mit signals by TE is estimated. However, a good approx-imation depends on the dimension and time scale !t. Weused various !t to get a good approximation of the effec-tive connectivity in the cultured neurons.

Estimated connectivity of cultured neurons Figure 6shows some examples of the estimated network structureof neurons. This depicts the network of Chip #1D DIV 14with different !t (= 0.6 ms, 1 ms and 10 ms). An edge isdrawn if the TE from one neuron to another is higher thanthe threshold, which was set to 0.00001. The threshold isdetermined arbitrarily, but to display dynamical changein connectivity patterns. The first observation about thisfigure is that different topology is structured depending

(a) Topology 1

k=l=1k=l=2k=l=3

(b) Topology 2 (c) Topology 3

Figure 5: Number of false connections with different !tvalues. The threshold was set to 0.005.

on !t. As is shown with the artificial neural network,each connection may not have the same optimal !t toestimate connections. Based on (Oka and Ikegami, 2013),we used the optimal !t to understand the informationflow in the network.

!t = 0.6 ms !t = 1 ms !t = 10 ms

(a) Example of estimated connectivity

Figure 6: Examples of the network structure of the infor-mation flow obtained from TE. The data used here is fromChip#1D DIV 14. !t = 0.6 ms, 1 ms, and 10 ms. The TEthreshold to draw edges was set to 0.00001.

Optimal time scale to convey informationAs observed, the cell-cell interaction estimated from the TEanalyses depends on the time scale !t, so that we evaluatedthe optimal !t to estimate the network structure better. Wedefined the optimal !t as !t! that maximizes TE. !t! wascalculated for each directed pair of neurons. Informationwas considered to be transferred most effectively with the!t!. Therefore, the !t! exhibits effective synaptic connec-tivity from each neuron to another.

Figure 7 (a) and (b) depict !t! from one neuron to an-other in Chip#1D and Chip#1S respectively. Edges are


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drawn if TE at the !t! is larger than the threshold (=0.00001; same as the one used above). The color indicatesthe value of !t!, where red represents !t! smaller than 10ms and blue indicates larger. We defined !t! = 10 ms as athreshold to assign color, because burst activity was observ-ably detected with !t larger than 10 ms (figure 2). Here-after, we call !t > 10 ms “the smaller !t”, and !t ! 10ms “the larger !t”, where we divide the activity pattern intomicroscopic and macroscopic using this threshold. Addi-tionally, figure 8 shows the !t! distribution.

Figure 7 (a) and 8 (a) show that, at an earlier stage ofthe development of Chip #1D, a larger !t! is mainly ob-served. The number of the smaller !t! increases at DIV12, which means a causal relationship between each neu-rons is observed within a shorter period. This is consistentwith the observation in figure 2 (b) that a single spike acti-vates another neuron within a short period. For Chip#2D,a smaller !t! was observed throughout the entire record-ing period (figure 8(b)). Chip#2D was recorded beginningat DIV 17, which is relatively later compared with those ofthe other chips. That can explain why Chip#2D was similarto the later stage of Chip#1D.

Interestingly, the smaller !t! observed in Chip#1D andChip#2D coexisted with the larger !t! (figure 8 (a) and(b)). This suggests that neural activity occurs at a widerrange of time scales. Figure 7 (a) shows that the interven-ing neurons have red and blue edges, which implies mi-croscopic and macroscopic activity to exchange informa-tion with each other. However, the frequency of the smaller!t! in Chip#1S and Chip#2S was low throughout the en-tire recording period (figure 7(b), 8(c-d)). Still, similarly tothe result for the dense cell condition, as DIV increased, thenumber of the smaller !t! grew.

ConclusionWe characterized neural activity cultured on a high-densityCMOS array. The neurons showed different activation pat-terns depending on the density and age (days in vitro; DIV).The neurons did not receive external inputs, but still sponta-neously evolved. The neurons were cultured in two differentconditions, i.e., dense or sparse.

When the cell density was high, the neurons showed burstactivity first, and afterward, each neural cell activated at adifferent frequency (figure 2 (a), (b)). Some were activatedall the time, some showed spikes intermittently, and othersremained silent. The ISI distribution of each cell becamecloser to the power law as the DIV increased (figure 3),which suggests a single cell evolved to show a wider rangeof time scales. These results suggest that neural activity ex-hibits a wider range of time scales as the synapses mature.This tendency was shown clearly with TE (figure 7). At theearlier stage of development, TE was mainly optimized ata larger time scale, while, at the later stage, TE was alsooptimized at a smaller time scale (figure 8).

A mature human brain is a collection of functional net-works, each of which corresponds to a different cognitivefunction (Fair et al., 2009). In this paper, we insist that evena neural network on a glass plate spontaneously develops“functional networks”, which can be distinguished in termsof the time scale determined by effective information trans-fer. Without relevant sensory input, we cannot say the net-works are functional in the proper context of brain science;however, we speculate that the spontaneous development of“functional networks” is a candidate for the brain functionalnetwork. In future work, we will connect the neurons with anavigation robot to see how the functional networks actually“function” as cognitive modules.

AcknowledgementsThis work was supported by Grant-in-Aid for Scien-tific Research (Studies on Homeo-Dynamics with Culti-vated Neural Circuits and Embodied Artificial Neural Net-works; 24300080), Grant-in-Aid for Scientific Research(23680050), and Denso Corp. Eiko Matsuda thanks theJapan Society for the Promotion of Science for researchfunding.

ReferencesBertschinger, N., Olbrich, E., Ay, N., and Jost, J. (2008). Biosys-

tems, 91(2):331–34.

Eytan, D. and Marom, S. (2006). Dynamics and effective topologyunderlying synchronization in networks of cortical neurons.The Journal of Neuroscience, 26(33):8465–8476.

Fair, D. A., equal contributor, A. L. C., Power, J. D., Dosenbach,N. U. F., Church, J. A., Miezin, F. M., Schlaggar, B. L., andPetersen, S. E. (2009). Functional brain networks developfrom a“ local to distributed”organization. PLOS COMPU-TATIONAL BIOLOGY, 5:e1000381.

Frey, U., Sedivy, J., Heer, F., Pedron, R., Ballini, M., Mueller, J.,Bakkum, D. J., Hafizovic, S., Faraci, F. D., Greve, F., et al.(2010). Switch-matrix-based high-density microelectrode ar-ray in cmos technology. IEEE Journal of Solid-State Circuits,45(2):467–482.

Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEETransactions on Neural Networks, 14(6):1569–1572.

Lizier, J. T., Heinzle, J., Horstmann, A., John-Dylan, Haynes, andProkopenko, M. (2011). Multivariate information-theoreticmeasures reveal directed information structure and task rele-vant changes in fmri connectivity. Journal of ComputationalNeuroscience, 30(1):85–107.

Maeda, E., Robinson, H. P. C., and Kawana, A. (1995). The mech-anisms of generation and propagation of synchronized burst-ing in developing networks of cortical neurons. Journal ofNeuroscience, 15(10):6834–6845.

Oka, M. and Ikegami, T. (2013). Exploring default mode and in-formation flow on the web. PLOS ONE, 8(4):e60398.

Schreiber, T. (2000). Measuring information transfer. Phys RevLett, 85:464–464.


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Figure 7: Network structure obtained with !t! from one neuron to another. The TE threshold for drawing edges is also equalto 0.00001. The color indicates the value of !t!, where red represents a !t! smaller than 10 ms, and blue is for a larger !t!.

Staniek, M. and Lehnertz, K. (2008). Phys. Rev. Lett.,100(15):158101.

Sun, J.-J., Kilb, W., and Luhmann, H. J. (2010). Self-organizationof repetitive spike patterns in developing neuronal networksin vitro. European Journal of Neuroscience, 32:1289–1299.

van Pelt, J., Wolters, P. S., Corner, M. A., and Rutten, W.L. C. (2004). Long-term characterization of firing dy-namics of spontaneous bursts in cultured neural networks.IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING,51(11):2051–2062.

Wagenaar, D. A., DeMarse, T. B., and Potter, S. M. S. M. (2005).Meabench: A toolset for multi-electrode data acquisition andon-line analysis. In Conference Proceedings of 2nd Interna-tional IEEE EMBS Conference on Neural Engineering, pages518–521, Pasadena, CA.


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throughout the entire recoding periods. (c) (d) Smaller !t! is observed less often. Still, !t! decreases as DIV increases.


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Multiple Time Scales Observed in Spontaneously Evolved Neurons … · 2020-04-11 · Multiple Time Scales Observed in Spontaneously Evolved Neurons on High-density CMOS Electrode