Научная статья на тему 'Stability of spontaneous electrical activity of neural networks in vitro'

Stability of spontaneous electrical activity of neural networks in vitro Текст научной статьи по специальности «Медицинские технологии»

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Ключевые слова
neuronal cultures / neural networks / learning / spontaneous activity / cluster analysis / bursting activity analysis / нейрональные культуры / нейронные сети / обучение / спонтанная активность / кластерный анализ / анализ пачечной активности

Аннотация научной статьи по медицинским технологиям, автор научной работы — Ilya Sokolov, М Tatarintsev M.K., Khasanov R.Y., Azieva A.M., Makarenko E.Yu.

Using brain-computer interfaces, one can both read data from and transmit them to the brain. However, these data are only a set of sensor system signals and not the knowledge or experience. Neural networks are a basis for cognitive activity and can simulate processes similar to learning in vitro. In this work we tested the hypothesis of a neural network’s ability to learn by detecting deviations from its stereotypical activity and modifying them in a way that allows it to get rid of external electrical stimulation. Spontaneous activity of several neuronal cultures in vitro was analyzed by clustering method. The results showed that activity of untrained cultures remained stable for a long time, and external electrical stimulation led to switching between various spontaneous activity patterns.

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Похожие темы научных работ по медицинским технологиям , автор научной работы — Ilya Sokolov, М Tatarintsev M.K., Khasanov R.Y., Azieva A.M., Makarenko E.Yu.

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Устойчивость спонтанной электрической активности нейронных сетей in vitro

С помощью нейро-компьютерных интерфейсов можно как считывать информацию с мозга, так и передавать ее в мозг. Однако эта информация — сигналы сенсорных систем, а не знание и опыт. Нейронные сети, представляющие собой основу когнитивной деятельности, способны in vitro воспроизводить процессы, аналогичные обучению. В работе проверена гипотеза о том, что нейронная сеть реализует обучение путем обнаружения отклонения от своей стереотипной активности и модификации ее таким образом, чтобы избавиться от внешней электрической стимуляции. Спонтанная активность нескольких нейрональных культур in vitro была проанализирована методом кластеризации. Результаты показали, что активность необученных культур остается стабильной на протяжении длительного времени, а внешняя электрическая стимуляция приводит к переключению между паттернами спонтанной активности.

Текст научной работы на тему «Stability of spontaneous electrical activity of neural networks in vitro»

stability of spontaneous electrical activity of neural networks in vitro

Sokolov IS1,2 М Tatarintsev MK1>3, Khasanov RY1>4, Azieva AM1, Makarenko EYu2, Burtsev MS1A5

1 Department of Neurosciences, Kurchatov Complex of NBICS Technologies, National Research Centre Kurchatov Institute, Moscow, Russia

2 Department of Physiology, Biomedical Faculty,

Pirogov Russian National Research Medical University, Moscow, Russia

3 Department of NBIC Technologies, Faculty of Nano-, Bio-, Information and Cognitive Technologies, Moscow Institute of Physics and Technology (State University), Dolgoprudny, Russia

4 Department of Human and Animal Physiology, Faculty of Biology, Lomonosov Moscow State University, Moscow, Russia

5 National Research Nuclear University MEPhI, Moscow, Russia

Using brain-computer interfaces, one can both read data from and transmit them to the brain. However, these data are only a set of sensor system signals and not the knowledge or experience. Neural networks are a basis for cognitive activity and can simulate processes similar to learning in vitro. In this work we tested the hypothesis of a neural network's ability to learn by detecting deviations from its stereotypical activity and modifying them in a way that allows it to get rid of external electrical stimulation. Spontaneous activity of several neuronal cultures in vitro was analyzed by clustering method. The results showed that activity of untrained cultures remained stable for a long time, and external electrical stimulation led to switching between various spontaneous activity patterns.

Keywords: neuronal cultures, neural networks, learning, spontaneous activity, cluster analysis, bursting activity analysis

Funding: this work was supported by the Russian Science Foundation, grant no. 15-11-30014. Correspondence should be addressed: Ilya Sokolov

ul. Chertanovskaya, d. 49, k. 2, kv. 121, Moscow, Russia, 117534; ilsersokolov@gmail.com Received: 01.04.2016 Accepted: 07.04.2016

устойчивость спонтанной электрической активности нейронных сетей in vitro

И. С. Соколов1,2 М. К. Татаринцев1,3, Р. Ю. Хасанов1,4, А. М. Азиева1, Е. Ю. Макаренко2, М. С. Бурцев1,3,5

1 Отдел нейронаук, Курчатовский центр НБИКС-технологий, Национальный исследовательски центр «Курчатовский институт», Москва

2 Кафедра физиологии, медико-биологический факультет,

Российский национальный исследовательский медицинский университет имени Н. И. Пирогова, Москва

3 Кафедра НБИК-технологий, факультет нано-, био-, информационных и когнитивных технологий, Московский физико-технический институт (государственный университет), Долгопрудный

4 Кафедра физиологии человека и животных, биологический факультет, Московский государственный университет имени М. В. Ломоносова, Москва

5 Национальный исследовательский ядерный университет «МИФИ», Москва

С помощью нейро-компьютерных интерфейсов можно как считывать информацию с мозга, так и передавать ее в мозг. Однако эта информация — сигналы сенсорных систем, а не знание и опыт. Нейронные сети, представляющие собой основу когнитивной деятельности, способны in vitro воспроизводить процессы, аналогичные обучению. В работе проверена гипотеза о том, что нейронная сеть реализует обучение путем обнаружения отклонения от своей стереотипной активности и модификации ее таким образом, чтобы избавиться от внешней электрической стимуляции. Спонтанная активность нескольких нейрональных культур in vitro была проанализирована методом кластеризации. Результаты показали, что активность необученных культур остается стабильной на протяжении длительного времени, а внешняя электрическая стимуляция приводит к переключению между паттернами спонтанной активности.

Ключевые слова: нейрональные культуры, нейронные сети, обучение, спонтанная активность, кластерный анализ, анализ пачечной активности

Финансирование: работа выполнена при поддержке Российского научного фонда, грант № 15-11-30014. Для корреспонденции: Илья Сергеевич Соколов

117534, г Москва, ул. Чертановская д. 49, к. 2, кв. 121; ilsersokolov@gmail.com Статья поступила: 01.04.2016 Статья принята к печати: 07.04.2016

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In medicine, brain-computer interfaces are used for the development of neuroprostheses comparable to healthy organs in their responsiveness to user's mental commands [1-3]. Data can also be transmitted in the reverse direction, from the computer to the brain; for example, lost sensory functions, such as auditory [4] and visual [5], can be recovered using electrical stimulation. However, what's more challenging for a researcher is transmission of information as such, i.e., knowledge and experience. It has been shown that using multi-input/multi-output non-linear dynamic model allows for transmitting a certain spatiotemporal pattern detected in the hippocampus of one rat to the hippocampus of another rat, which leads to the statistically reliable alterations in the behavior of the second animal [6].

It is known that neuronal networks that form a basis for cognitive activity do not have a distinct location in brain structures, but are distributed throughout them [7, 8]. From that, a need to reprogram neuronal networks ensues. Publications on the patterns patterns of neuronal network spontaneous activity in vitro and on the methods of its external modification [9-13] prove that networks of dissociated primary neuronal cultures of cortical and hippocampal cells on multi-electrode arrays (MEAs) can control external stimulation by changing their activity on the selected experimental electrode. Such neuronal network learning was first demonstrated by Shahaf and Marom [14] and was successfully reproduced by other researchers thereafter [15-18].

As the network is gradually developing from the dissociated neuronal culture, it starts to exhibit spontaneous bioelectrical activity recorded by array electrodes. Thus, in the absence of external stimulation in the first days of culture growth, only single action potentials are registered, but after a while they cluster into bursts [19]. In this work we hypothesize that spontaneous burst activity comes down to a small number of stereotypical patterns, and cluster analysis can help identify one or several dominating patterns. Since the external stimulation breaks the existing activation sequence, the network changes its activity pattern to switch off stimulation and go back to the typical pattern. Then, cluster analysis performed after the stimulation (training) can detect the resumption of the initial activity pattern.

METHODS Cell cultures

Primary cell culture was prepared from the hippocampal tissue of newborn rats of C57BL/6 breed. Experimental animals used in the study were managed according to the guidelines specified in Order no. 267 of the Ministry of the Russian Federation, dated June 19, 2003, "On the approval of rules for good laboratory practice". The experiment was approved by the local Ethics Committee for Biomedical Research of the National Research Center "Kurchatov Institute" (protocol no. 1, dated July 9, 2015).

Cells were cultured on 60-channel multi-electrode arrays 60StimMEA200/30-ITO (Multichannel Systems, Germany). Prior to the experiment, plates were coated with poly-L-lysine for better cell adhesion. The initial culture density was 300,000 cells per mm3. Their dissociation was achieved by using 0.25 % trypsin (Invitrogen 25200-056, USA). Neuronal viability was maintained in NeurobasalTM culture medium (Invitrogen 21103-049) in the complex with the bioactive additive B27 (Invitrogen 17504-044), glutamin (Invitrogen 25030-024) and penicillin-streptomycin (Life Technologies 15140122, USA)

in GALAXY 170S incubator (New Brunswick Scientific, USA) under stable conditions: temperature of 37 °C, humidity of 100 % and 5 % CO2 air concentration. Glial cell growth was not inhibited, because glial cells were necessary to ensure long-term culture viability in vitro. Half of the medium volume was replaced every three days.

Bioelectrical cell activity was recorded with MEA1060-Up-BC-Standard system (Multichannel Systems). For data acquisition, the bundled software was used.

Dynamics of spontaneous burst activity were observed in two cultures. Recording was performed from the 4th day in vitro (DIV) until culture death. For further processing, we used data obtained in the interval between the onset and offset of burst activity. For training, one 24-DIV culture was used.

Protocol of neuronal culture training in vitro

1) 1-hour background recording of culture bioelectrical activity .

2) Stimulation by single bipolar rectangular pulses of ± 300 mV on each electrode (one at a time) to select the electrode that evoked the most intense culture response.

3) 5 stimulation cycles on the electrode selected in step 2. Every cycle consisted of a 5-minute series of rectangular pulses with 2-minute breaks. In every experiment, the pause between the pulses was adjusted so that every pulse could induce burst activity. Based on stimulation results, a recording electrode was chosen, for which electrical activity within 30-80 ms after the signal was the lowest.

4) 1-hour recording of culture spontaneous bioelectrical activity.

5) 20 training cycles. Training was considered successful if a twofold increase in the probability to record spike activity within the preset time interval on the electrode chosen in step 3 was observed. Training consisted of stimulation described in paragraph 3, given that as soon as the success criterion had been reached, stimulation was discontinued and a 2-minute break was provided.

6) 1-hour recording of culture spontaneous bioelectrical activity.

Detection of spikes and burst events

The initial signal was digitally processed by a second-order high-pass Butterworth filter with a passband of over 200 Hz, which allowed for the exclusion of low-frequency noise. Action potentials were detected if signal amplitude exceeded 4 standard deviations. In that case, the maximum amplitude was considered time of spike onset.

A burst event (burst) occurs on one electrode and is characterized by a short-term explosion-like impulse generation (0.1-3.0 s depending on culture age and its stocking density), and is usually accompanied by the low-frequency (1-5 Hz) signal component. Detection of bursts was based on the identification of the low-frequency component in a given interval and on spike detection in the vicinity of the component. Time when the first and the last spikes were generated was considered the burst onset and offset, respectively.

Population burst events are bursts that are observed simultaneously (with small delays of about 0.002-0.05 s) on more than a half of all active electrodes. The onset of the population burst is time of the first burst event onset.

Pattern analysis

As a feature Vk of a burst event, activation pattern was used [10]. Vector Vk dimensionality is equal to the number of active electrodes, i.e., electrodes on which at least one burst was observed:

={y

^start^i=0 = (Ck0---Ckr)<

where tk(i) represents activity onset on the ith electrode, and tkstart represents time of population burst event onset. If no activity was recorded on the electrode during a given burst, but it was present during other bursts, the corresponding vector component takes the averaged value of other vector components.

As a metric, Pearson correlation coefficient was used. For cluster analysis, the weighted pair-group method with arithmetic averaging was used [20].

To obtain clusters, distances between neighboring vectors in the ordered feature vector sequence were found; then, based on the obtained distances, threshold value th was computed. Neighboring vectors, the distances between which were less than the threshold value, formed clusters.

Threshold value th was computed as follows. We built the graph representing the dependence of the maximum distance (D) between clusters on the number of clusters (n) in the order of increasing. Thus,

th = D(argmax( d2D)+2), (2) dn2

where argmax is a function that computes the maximum value. RESULTS

Cluster analysis of spontaneous burst activity in two neuronal cultures of 10...30 DIV (fig. 1) showed that in both cases over 50 % burst activation patterns belonged to the same dominating

cluster (cluster 7 in fig. 1, А and cluster 5 in fig. 1, В). The majority of other population bursts (40 %) were distributed in two clusters that were equal in size, namely, clusters 6 and 9 (fig. 1, А) and clusters 4 and 6 (fig. 1, В). Dominating patterns of neuronal bursts were stable, despite of external factors related to medium replacements and to moving culture from the incubator to the recording device and back

In the neuronal network training experiment, electrode 22 was chosen for stimulation (see paragraph 2 of the training protocol); stimulation was terminated on electrode 12 (see paragraph 3 of the training protocol). A prerequisite for terminated stimulation was detection of 5 or more spikes in the interval of 50-80 ms after stimulation was applied.

Results of cluster analysis of spontaneous burst activity recorded at stages 1, 4 and 6 of the training protocol are presented in figure 2. Before stimulation was applied to the culture, population bursts were formed by two big clusters, namely, 15 and 18. After stimulation with no feedback (stage 4), the number of bursts decreased in clusters 15 and 18 and increased in clusters 2 and 4. After stimulation with feedback (stage 6), the number of bursts in dominating clusters 15 and 18 remained on the intermediate level. The rest of the activity shifted to cluster 3 from clusters 2 and 4.

The patterns of the dominating spontaneous burst activity registered before and after stimulation were different (fig. 3). In that respect, clusters 3 and 4 were alike, but both differed from clusters 15 and 18, which overlapped to a great extent. Cluster 2 combined features of both sets of clusters.

DISCUSSION

According to our hypothesis, spontaneous burst activity of neuronal networks in vitro must be characterized by self-organization and repetitive activity patterns. Our experiment and results obtained by other researchers [13, 21, 22] confirm

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2000

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20 30 40 50 Number of bursts, %

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Fig. 1. Clustering of spontaneous burst activity of two neuronal cultures in vitro with the following IDs: 3035 (A) and 3040 (C); percentage of bursts In clusters with the following IDs: 3035 (B) and 3040 (D). Bursts are presented as they appeared. Red dotted lines represent days of culture development

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that with culture growth, self-organization of neurons results in the emergence of the limited number of dynamic modes; each of those modes is characterized by its own activity pattern, i.e., an attractor. Thus, neurons in vitro can produce and maintain some activation sequence, which is necessary for memory trace retention.

We also made a supposition that patterns of spontaneous burst activity are resistant to external impact, including external electrical stimulation. Results of our study demonstrate that patterns do not depend on the presence of feedback during stimulation; what changes is the frequency of their occurrence. It allows us to make an assumption that in live neuronal networks, learning can be a result of variations of existing patterns with subsequent selection of a template used to solve

the "problem". In the protocol used in this study, the "problem" was identified by means of external stimulation that can be switched off to provide a solution.

CONCLUSIONS

Study of spontaneous burst activity of neuronal networks in vitro showed that dynamics of network activity come down to a small number of attractors. Changes in burst activity registered after applying external stimulation showed that the dominating attractor of spontaneous activity does not disintegrate, but the variety of patterns increases. We can assume that learning is mediated by switching between the existing dynamic attractors of neuronal activity.

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References

1. Velliste M, Perel S, Spalding MC, Whitford AS, Schwartz AB. Cortical control of a prosthetic arm for self-feeding. Nature. 2008 Jun 19; 453 (7198): 1098-101.

2. Wessberg J, Stambaugh CR, Kralik JD, Beck PD, Laubach M, Chapin JK, et al. Real-time prediction of hand trajectory by 7. ensembles of cortical neurons in primates. Nature. 2000 Nov 16;

408 (6810): 361-5. 8.

3. Serruya MD, Hatsopoulos NG, Paninski L, Fellows MR, Donoghue JP. Instant neural control of a movement signal. Nature. 2002 Mar 14; 416 (6877): 141-2. 9.

4. Shannon RV. Advances in auditory prostheses. Curr Opin Neurol. 2012 Feb; 25 (1): 61-6.

5. Fernandes RA, Diniz B, Ribeiro R, Humayun M. Artificial vision 10. through neuronal stimulation. Neurosci Lett. 2012 Jun 25; 519 (2): 122-8.

6. Hampson RE, Song D, Chan RH, Sweatt AJ, Riley MR, 11.

Gerhardt GA, et al. A nonlinear model for hippocampal cognitive prosthesis: memory facilitation by hippocampal ensemble stimulation. IEEE Trans Neural Syst Rehabil Eng. 2012 Mar; 20 (2): 184-97.

Josselyn SA, Kohler S, Frankland PW. Finding the engram. Nat Rev Neurosci. 2015 Sep; 16 (9): 521-34. Quiroga RQ, Mukamel R, Isham EA, Malach R, Fried I. Human single-neuron responses at the threshold of conscious recognition. Proc Natl Acad Sci U S A. 2008 Mar 4; 105 (9): 3599-604. Kermany E, Gal A, Lyakhov V, Meir R, Marom S, Eytan D. Tradeoffs and constraints on neural representation in networks of cortical neurons. J Neurosci. 2010 Jul 14; 30 (28): 9588-96. Raichman N, Ben-Jacob E. Identifying repeating motifs in the activation of synchronized bursts in cultured neuronal networks. J Neurosci Methods. 2008 May 15; 170 (1): 96-110. Shahaf G, Eytan D, Gal A, Kermany E, Lyakhov V, Zrenner C,

et al. Order-based representation in random networks of cortical neurons. PLoS Comput Biol. 2008 Nov; 4 (11): e1000228.

12. Xydas D, Downes JH, Spencer MC, Hammond MW, Nasuto SJ, Whalley BJ, et al. Revealing ensemble state transition patterns in multi-electrode neuronal recordings using hidden Markov models. IEEE Trans Neural Syst Rehabil Eng. 2011 Aug; 19 (4): 345-55.

13. Pimashkin A, Kastalskiy I, Simonov A, Koryagina E, Mukhina I, Kazantsev V. Spiking signatures of spontaneous activity bursts in hippocampal cultures. Front Comput Neurosci. 2011; 5: 46.

14. Shahaf G, Marom S. Learning in networks of cortical neurons. J Neurosci. 2001 Nov 15; 21 (22): 8782-8.

15. Marom S, Shahaf G. Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy. Q Rev Biophys. 2002 Feb; 35 (1): 63-87.

16. Li Y, Zhou W, Li X, Zeng S, Luo Q. Dynamics of learning in cultured neuronal networks with antagonists of glutamate receptors. Biophys J. 2007 Dec 15; 93 (12): 4151-8.

17. Stegenga J, Le Feber J, Marani E, Rutten WL. The effect of

Литература

1. Velliste M, Perel S, Spalding MC, Whitford AS, Schwartz AB. Cortical control of a prosthetic arm for self-feeding. Nature. 2008 Jun 19; 453 (7198): 1098-101.

2. Wessberg J, Stambaugh CR, Kralik JD, Beck PD, Laubach M, Chapin JK, et al. Real-time prediction of hand trajectory by ensembles of cortical neurons in primates. Nature. 2000 Nov 16; 408 (6810): 361-5.

3. Serruya MD, Hatsopoulos NG, Paninski L, Fellows MR, Donoghue JP. Instant neural control of a movement signal. Nature. 2002 Mar 14; 416 (6877): 141-2.

4. Shannon RV. Advances in auditory prostheses. Curr Opin Neurol. 2012 Feb; 25 (1): 61-6.

5. Fernandes RA, Diniz B, Ribeiro R, Humayun M. Artificial vision through neuronal stimulation. Neurosci Lett. 2012 Jun 25; 519 (2): 122-8.

6. Hampson RE, Song D, Chan RH, Sweatt AJ, Riley MR, Gerhardt GA, et al. A nonlinear model for hippocampal cognitive prosthesis: memory facilitation by hippocampal ensemble stimulation. IEEE Trans Neural Syst Rehabil Eng. 2012 Mar; 20 (2): 184-97.

7. Josselyn SA, Kohler S, Frankland PW. Finding the engram. Nat Rev Neurosci. 2015 Sep; 16 (9): 521-34.

8. Quiroga RQ, Mukamel R, Isham EA, Malach R, Fried I. Human single-neuron responses at the threshold of conscious recognition. Proc Natl Acad Sci U S A. 2008 Mar 4; 105 (9): 3599-604.

9. Kermany E, Gal A, Lyakhov V, Meir R, Marom S, Eytan D. Tradeoffs and constraints on neural representation in networks of cortical neurons. J Neurosci. 2010 Jul 14; 30 (28): 9588-96.

10. Raichman N, Ben-Jacob E. Identifying repeating motifs in the activation of synchronized bursts in cultured neuronal networks. J Neurosci Methods. 2008 May 15; 170 (1): 96-110.

11. Shahaf G, Eytan D, Gal A, Kermany E, Lyakhov V, Zrenner C, et al. Order-based representation in random networks of cortical neurons. PLoS Comput Biol. 2008 Nov; 4 (11): e1000228.

learning on bursting. IEEE Trans Biomed Eng. 2009 Apr; 56 (4): 1220-7.

18. le Feber J, Stegenga J, Rutten WL. The effect of slow electrical stimuli to achieve learning in cultured networks of rat cortical neurons. PloS One. 2010; 5 (1): e8871.

19. Wagenaar DA, Pine J, Potter SM. An extremely rich repertoire of bursting patterns during the development of cortical cultures. BMC Neurosci. 2006; 7: 11.

20. Sokal R, Michener C. A statistical method for evaluating systematic relationships. University of Kansas Science Bulletin. 1958; 38 (22): 1409-38.

21. Lebedev RD, Burtsev MS. Klasterizatsiya pachek spontannoy aktivnosti neyronal'noy kul'tury. In: Sbornik nauchnykh trudov Vserossiyskoy nauchno-tekhnicheskoy konferentsii «Neyroinformatika 2010» v 2-kh chastyakh. P. 1. Moscow: MEPhI; 2010. p. 296-303. Russian

22. Burtsev MS, Lebedev RD. Evolution of bursts onsets during the development of cortical cultures. FENS Abstr, vol. 5, 130.12, 2010.

12. Xydas D, Downes JH, Spencer MC, Hammond MW, Nasuto SJ, Whalley BJ, et al. Revealing ensemble state transition patterns in multi-electrode neuronal recordings using hidden Markov models. IEEE Trans Neural Syst Rehabil Eng. 2011 Aug; 19 (4): 345-55.

13. Pimashkin A, Kastalskiy I, Simonov A, Koryagina E, Mukhina I, Kazantsev V. Spiking signatures of spontaneous activity bursts in hippocampal cultures. Front Comput Neurosci. 2011; 5: 46.

14. Shahaf G, Marom S. Learning in networks of cortical neurons. J Neurosci. 2001 Nov 15; 21 (22): 8782-8.

15. Marom S, Shahaf G. Development, learning and memory in large random networks of cortical neurons: lessons beyond anatomy. Q Rev Biophys. 2002 Feb; 35 (1): 63-87.

16. Li Y, Zhou W, Li X, Zeng S, Luo Q. Dynamics of learning in cultured neuronal networks with antagonists of glutamate receptors. Biophys J. 2007 Dec 15; 93 (12): 4151-8.

17. Stegenga J, Le Feber J, Marani E, Rutten WL. The effect of learning on bursting. IEEE Trans Biomed Eng. 2009 Apr; 56 (4): 1220-7.

18. le Feber J, Stegenga J, Rutten WL. The effect of slow electrical stimuli to achieve learning in cultured networks of rat cortical neurons. PloS One. 2010; 5 (1): e8871.

19. Wagenaar DA, Pine J, Potter SM. An extremely rich repertoire of bursting patterns during the development of cortical cultures. BMC Neurosci. 2006; 7: 11.

20. Sokal R, Michener C. A statistical method for evaluating systematic relationships. University of Kansas Science Bulletin. 1958; 38 (22): 1409-38.

21. Лебедев Р. Д., Бурцев М. С. Кластеризация пачек спонтанной активности нейрональной культуры. В сборнике: Сборник научных трудов Всероссийской научно-технической конференции «Нейроинформатика 2010» в 2-х частях. ч. 1. М.: НИЯУ МИФИ; 2010. с. 296-303.

22. Burtsev MS, Lebedev RD. Evolution of bursts onsets during the development of cortical cultures. FENS Abstr, vol. 5, 130.12, 2010.

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