Topological Causal Analysis Reveals Two Stages of In Vitro neural Network Maturation: Network Expansion and Network Reinforcement

Document Type : Original Research

Author
Z. Naghdabadi
Department of Electrical Engineering, Sharif University of Technology, Tehran 1458889694, Iran.
Abstract
Background: topological data analysis (TDA) in neural network and its advantages over traditional graph theory methods by capturing higher-order relationships and complex structures within the brain examined in this research. TDA provides insights into cognitive processes by analyzing multi-scale interactions among neural activities and is increasingly utilized in both brain science and psychological research.

Methods: The methodology explores neural data from various sources, including multi-electrode arrays (MEAs), to study neural ensemble behaviors and connectivity. Additionally, it critiques existing methods like Granger causality analysis (GCA) for their limitations in interpreting neural data.

Results: According to our findings, the number of spiking activities and active channels rise from the 10th to the 60th day in vitro (DIV). Burst activities peaked between 30 and 50 DIV, while the firing rate in active channels continued to increase until 30 DIV. Furthermore, the average burst length exhibited a consistent rise until 50 DIV. However, the percentage of spikes involved in burst activities displayed a non-monotonic pattern, initially declining until 30 DIV and rising again in subsequent days. The fluctuations in average spike amplitudes can be attributed to factors such as the distance between neurons and electrodes, as well as the ongoing neuronal plasticity and migration.

Conclusion: In summary, TCA provides qualitative insights into network status based on quantitative metrics and established thresholds. While we focused on primary neuronal cells derived from rat cortices, MEA technology is versatile enough to monitor the developmental stages of any neuronal type, including those derived from human sources

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References
Barbey, A. K. (2018) ‘Network Neuroscience Theory of Human Intelligence’, Trends in Cognitive Sciences. Elsevier Ltd, 22(1), pp. 8–20. doi: 10.1016/j.tics.2017.10.001.
Bredon, G. E. (1993) Topology and Geometery. Available at: http://library1.nida.ac.th/termpaper6/sd/2554/19755.pdf.
Bullmore, E. and Sporns, O. (2009) ‘Complex brain networks: Graph theoretical analysis of structural and functional systems’, Nature Reviews Neuroscience, 10(3), pp. 186–198. doi: 10.1038/nrn2575.
Cadotte, A. J. et al. (2008) ‘Causal measures of structure and plasticity in simulated and living neural networks’, PLoS ONE, 3(10). doi: 10.1371/journal.pone.0003355.
Carlsson, G. (2009) Topology and data, Bulletin of the American Mathematical Society. doi: 10.1090/S0273-0979-09-01249-X.
Curto, C. (2017) ‘What can topology tell us about the neural code?’, Bulletin of the American Mathematical Society, 54(1), pp. 63–78. Available at: http://dx.doi.org/10.1090/bull/1554.
Dabaghian, Y. et al. (2012) ‘A Topological Paradigm for Hippocampal Spatial Map Formation Using Persistent Homology’, PLoS Computational Biology, 8(8). doi: 10.1371/journal.pcbi.1002581.
Expert, P. et al. (2019) ‘Editorial: Topological neuroscience’, Network Neuroscience, 3(3), pp. 653–655. doi: 10.1162/netn_e_00096.
Freeman (2018) ‘Network neuroscience’, Physiology & behavior, 176(1), pp. 139–148. doi: 10.1117/12.2549369.Hyperspectral.
Frega, M. et al. (2012) ‘Cortical cultures coupled to Micro-Electrode Arrays: A novel approach to perform in vitro excitotoxicity testing’, Neurotoxicology and Teratology. Elsevier Inc., 34(1), pp. 116–127. doi: 10.1016/j.ntt.2011.08.001.
Gracia-Tabuenca, Z. et al. (2019) ‘Topological Data Analysis reveals robust alterations in the whole-brain and frontal lobe functional connectomes in Attention-Deficit/Hyperactivity Disorder’, bioRxiv, 7(June). doi: 10.1101/751008.
Granger, C. W. J. (2008) ‘Investigating Causal Relations by Econometric Models and Cross-Spectral Methods’, in Essays in Econometrics vol II: Collected Papers of Clive W. J. Granger, pp. 31–47. doi: 10.1017/ccol052179207x.002.
Kim, H. J. (2011) ‘Isolation and Culture of Neurons and Astrocytes from the Mouse Brain Cortex’, 0, pp. 63–75. doi: 10.1039/9781849733014.
Lee, H. et al. (2017) ‘Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology’, Human Brain Mapping, 38(3), pp. 1387–1402. doi: 10.1002/hbm.23461.
Lloyd, E. K., Bondy, J. A. and Murty, U. S. R. (1978) ‘Graph Theory with Applications’, The Mathematical Gazette, 62(419), p. 63. doi: 10.2307/3617646.
Lonardoni, D. et al. (2017) ‘Recurrently connected and localized neuronal communities initiate coordinated spontaneous activity in neuronal networks’, PLoS Computational Biology, 13(7), pp. 1–27. doi: 10.1371/journal.pcbi.1005672.
Madhavan, R., Chao, Z. C. and Potter, S. M. (2007) ‘Plasticity of recurring spatiotemporal activity patterns in cortical networks.’, Physical biology, 4(3), pp. 181–93. doi: 10.1088/1478-3975/4/3/005.
Odawara, A. et al. (2016) ‘Physiological maturation and drug responses of human induced pluripotent stem cell-derived cortical neuronal networks in long-term culture’, Scientific Reports. Nature Publishing Group, 6(April), pp. 1–14. doi: 10.1038/srep26181.
Opitz, T., De Lima, A. D. and Voigt, T. (2002) ‘Spontaneous development of synchronous oscillatory activity during maturation of cortical networks in vitro’, Journal of Neurophysiology, 88(5), pp. 2196–2206. doi: 10.1152/jn.00316.2002.
Plenz, D. et al. (2011) ‘Multi-electrode Array Recordings of Neuronal Avalanches in Organotypic Cultures’, Journal of Visualized Experiments, (54), pp. 2–7. doi: 10.3791/2949.
Seth, A. K., Barrett, A. B. and Barnett, L. (2015) ‘Granger causality analysis in neuroscience and neuroimaging’, Journal of Neuroscience, 35(8), pp. 3293–3297. doi: 10.1523/JNEUROSCI.4399-14.2015.
Setia, H. and Muotri, A. R. (2019) ‘Brain organoids as a model system for human neurodevelopment and disease’, Seminars in Cell and Developmental Biology. Elsevier, 95(August 2018), pp. 93–97. doi: 10.1016/j.semcdb.2019.03.002.
Spira, M. E. and Hai, A. (2013) ‘Multi-electrode array technologies for neuroscience and cardiology’, Nature Nanotechnology. Nature Publishing Group, 8(2), pp. 83–94. doi: 10.1038/nnano.2012.265.
Sporns, O. (2018) ‘Graph theory methods: Applications in brain networks’, Dialogues in Clinical Neuroscience, 20(2), pp. 111–120. doi: 10.31887/DCNS.2018.20.2/OSPORNS.
Stokes, P. A. and Purdon, P. L. (2017) ‘A study of problems encountered in Granger causality analysis from a neuroscience perspective’, Proceedings of the National Academy of Sciences of the United States of America, 114(34), pp. E7063–E7072. doi: 10.1073/pnas.1704663114.
Valenza, G. et al. (2016) ‘Stochastic modeling of spontaneous bursting activity to simulate neural responses of in-vitro networks on multielectrode arrays’, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS, 2016-Octob, pp. 1616–1619. doi: 10.1109/EMBC.2016.7591022.
Wagenaar, D. A. et al. (2009) ‘Controlling Bursting in Cortical Cultures with Closed-Loop Multi- Electrode Stimulation’, Technology, 25(3), pp. 680–688. doi: 10.1523/JNEUROSCI.4209-04.2005.Controlling.
Wagenaar, D. A., Pine, J. and Potter, S. M. (2004) ‘Effective parameters for stimulation of dissociated cultures using multi-electrode arrays’, Journal of Neuroscience Methods, 138(1–2), pp. 27–37. doi: 10.1016/j.jneumeth.2004.03.005.
Wagenaar, D. A., Pine, J. and Potter, S. M. (2006) ‘An extremely rich repertoire of bursting patterns during the development of cortical cultures’, BMC Neuroscience, 7, pp. 1–18. doi: 10.1186/1471-2202-7-11.
West, D. B. (2009) ‘Introduction to graph theory’, Introduction to Graph Theory, pp. 1–144.
Wheeler, B. C., Nam, Y. and Wheeler, B. C. (2011) ‘In vitro microelectrode array technology and neural recordings.’, Critical ReviewsTM in Biomedical Engineering, 39(1), pp. 45–61. doi: 10.1615/CritRevBiomedEng.v39.i1.40.
Zhu, M. J. et al. (2020) ‘Identifying the pulsed neuron networks’ structures by a nonlinear Granger causality method’, BMC Neuroscience. BioMed Central, 21(1), pp. 1–9. doi: 10.1186/s12868-020-0555-z.