Low delay connection strength estimation of time-variant neuronal network with Kalman filter
-
1
The University of Tokyo, Japan
Brain-computer interface (BCI) has many future applications to enrich people’s life, though that of current BCI technology is limited. To improve interactive functions of BCI, it is important to extract information efficiently from brain activities. Estimating current state of a brain is helpful to extract information. In this study, we aim to estimate current state of a neuronal network from extracellular potentials recorded with microelectrode array (MEA). As an indicator of the brain state, we focus on synaptic connection strengths between neurons because the synaptic weights is a key for determining the network activity patterns which generate brain functions.
We have developed an estimation method of synaptic connection strengths from spike trains by maximum likelihood estimation (MLE) [1]. In the previous method, estimations must be calculated from a certain time width of spike trains for accuracy of the estimation. Long time width leads to long time delay because the estimations are calculated repeatedly after the data acquisition completed. In this study, we propose a new method with improved accuracy and time delay of the estimation by using Kalman filter which is a method for estimating state of a time-variant system from observation values with uncertainty. With Kalman filter, even if uncertainty of MLE value increased to shorten time delay, accurate connection strengths are expected to be estimated. In the Kalman filter method, observation steps and prediction steps are repeated to estimate the current state. In an observation step, an MLE value was observed and was merged with the current estimation by assuming a normal distribution whose mean equals the MLE value and whose variance equals the variance of MLEs. In a prediction step between the observations, the estimations were changed according to Song’s spike-timing-dependent plasticity (STDP) rule [2]. By these procedures, the observing and changing were merged considering uncertainty to obtain estimations with short time delay and high accuracy in every time.
For an evaluation of the proposed method, we conducted a simulation experiment. In this experiment, connection strengths were estimated from simulated spike trains, and were compared with true values. First, spike trains and synaptic strengths were generated as follows. Membrane potentials of neurons were simulated by Euler’s method with time step of 0.2 ms, using Izhikevich simple neuron model [3] and alpha function synaptic connection model. Synaptic connections changed according to Song’s STDP rule. Second, connection strengths were estimated from data of various length with both the previous and proposed methods. Spike trains which were generated by the simulation were recorded and were used to estimate connection strengths. Root mean square errors (RMSEs) of estimated connection strengths and true connection strengths were calculated. In order to evaluate relationships of time delay and estimation accuracy, RMSEs of the proposed method were compared with that of the previous method by changing the length of data for calculating MLEs. The result showed that the proposed method kept high estimation accuracy when the time width got short, while that of the previous method decreased. The result indicated that the proposed method could estimate connection strength with higher accuracy and shorter time delay compared to the previous method.
For verifying whether the proposed method is applicable to actual neurons, we estimated connection strengths from the activities of rat cortical neurons cultured on MEAs, and compared the results with physiological knowledge. Neurons were dissected from Wistar rat cortical tissues and were cultured on MEAs with 64 electrodes of an 8x8 square pattern. Extracellular potential was recorded for 60 min at 40 - 44 days in vitro (DIV). Spike trains were extracted from the extracellular potential to estimate connection strengths by the proposed method. By comparing estimations at two different times, probabilities of plasticity occurrence were calculated as probabilities that two estimations differed by more than a certain threshold by using reproductive property of normal distribution. First, ratio of neurons which showed plasticity was calculated. The result showed that the ratio of neurons which showed plasticity was 1.2%. Previous study reported that cultured neurons of rat cortex reached stable state after approximately 20 DIV [4, 5], which is consistent with our result. Second, relationships between ratio of neurons which showed plasticity and time length between two estimations were evaluated. The result showed that the ratio of neurons which showed plasticity increased as time passed, which is consistent with the physiological observation that synaptic connections of actual neurons are thought to change as time passes. These results indicated that the proposed method could estimate physiologically appropriate connection strengths and detect synaptic plasticity from activities of actual neurons.
In conclusion, we proposed a new method to estimate connection strengths from spike trains with short time delay and high estimation accuracy by merging a MLE method of a previous study and STDP rule by Kalman filter. The simulation experiment showed that the proposed method could estimate connection strengths with short time delay and high accuracy. The proposed method was applied to spike trains measured from neurons cultured on MEA, showing that the proposed method could estimate physiologically appropriate connection strengths and detect synaptic plasticity from actual neurons. Taken together, our new method is useful to estimate current state of a living neuronal network with higher accuracy.
References
[1] T. Isomura, A. Takeuchi, K. Shimba, K. Kotani, Y. Jimbo : ”Connection-Strength Estimation of Neuronal Networks by Fitting for Izhikevich Model”, Electrical Engineering in Japan, Vol.187, No.4, pp.42-50(2014)
[2] S. Song, K. Dayan, and L. F. Abbott : “Competitive Hebbian learning through spike-timing-dependent synaptic plasticity”, Nature Neuroscience, Vol.3，No.9 (2010)
[3] E. M. Izhikevich : “Simple model of spiking neurons”, IEEE Transactions on Neural Networks, Vol.14，Issues 6 (2003)
[4] H. Kamioka, E. Maeda, Y. Jimbo, H. P. C. Robinson, and A. Kawana : “Spontaneous periodic synchronized bursting during formation of mature patterns of connections in cortical cultures”, Neuroscience Letters, Vol.206，Issues 2-3, pp.109-112 (1996)
[5] S. Watanabe, Y. Jimbo, H. Kamioka, Y. Kirino, A. Kawana : “Development of low magnesium-induced spontaneous synchronized bursting and GABAergic modulation in cultured rat neocortical neurons”, Neuroscience Letters, Vol.210，Issues 1, pp.41-44 (2003)
Keywords:
Synaptic connections,
parameter estimation,
Kalman filter,
STDP,
time-variant
Conference:
MEA Meeting 2018 | 11th International Meeting on Substrate Integrated Microelectrode Arrays, Reutlingen, Germany, 4 Jul - 6 Jul, 2018.
Presentation Type:
Poster Presentation
Topic:
Neural Networks
Citation:
Asahina
T,
Shimba
K,
Sakai
K,
Kotani
K and
Jimbo
Y
(2019). Low delay connection strength estimation of time-variant neuronal network with Kalman filter.
Conference Abstract:
MEA Meeting 2018 | 11th International Meeting on Substrate Integrated Microelectrode Arrays.
doi: 10.3389/conf.fncel.2018.38.00121
Copyright:
The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers.
They are made available through the Frontiers publishing platform as a service to conference organizers and presenters.
The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated.
Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed.
For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions.
Received:
16 Mar 2018;
Published Online:
17 Jan 2019.
*
Correspondence:
Mr. Takahiro Asahina, The University of Tokyo, Bunkyō, Tokyo-to, Japan, asahina@neuron.t.u-tokyo.ac.jp