Memristive cellular automata for modeling of epileptic brain activity

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Cellular Automata (CA) is a nature-inspired and widespread computational model which is based on the collective and emergent parallel computing capability of units (cells) locally interconnected in an abstract brain-like structure. Each such unit, referred as CA cell, performs simplistic computations/processes. However, a network of such identical cells can exhibit nonlinear behavior and be used to model highly complex physical phenomena and processes and to solve problems that are highly complicated for conventional computers. Brain activity has always been considered one of the most complex physical processes and its modeling is of utter importance. This work combines the CA parallel computing capability with the nonlinear dynamics of the memristor, aiming to model brain activity during the epileptic seizures caused by the spreading of pathological dynamics from focal to healthy brain regions. A CA-based confrontation extended to include long-range interactions, combined with the recent notion of memristive electronics, is thus proposed as a modern and promising parallel approach to modeling of such complex physical phenomena. Simulation results show the efficiency of the proposed design and the appropriate reproduction of the spreading of an epileptic seizure.Peer ReviewedPostprint (author's final draft

Cellular automata and artificial brain dynamics

[EN] Brain dynamics, neuron activity, information transfer in brains, etc., are a vast field where a large number of questions remain unsolved. Nowadays, computer simulation is playing a key role in the study of such an immense variety of problems. In this work, we explored the possibility of studying brain dynamics using cellular automata, more precisely the famous Game of Life (GoL). The model has some important features (i.e., pseudo-criticality, 1/f noise, universal computing), which represent good reasons for its use in brain dynamics modelling. We have also considered that the model maintains sufficient flexibility. For instance, the timestep is arbitrary, as are the spatial dimensions. As first steps in our study, we used the GoL to simulate the evolution of several neurons (i.e., a statistically significant set, typically a million neurons) and their interactions with the surrounding ones, as well as signal transfer in some simple scenarios. The way that signals (or life) propagate across the grid was described, along with a discussion on how this model could be compared with brain dynamics. Further work and variations of the model were also examined.This work was partially supported by the European Union's Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under grant agreement no 316165. This work was done with the support of the Czech Science Foundation, project 17-17921S.Fraile, A.; Panagiotakis, E.; Christakis, N.; Acedo Rodríguez, L. (2018). Cellular automata and artificial brain dynamics. Mathematical and Computational Applications (Online). 23(4):1-23. https://doi.org/10.3390/mca23040075S123234TURING, A. M. (1950). I.—COMPUTING MACHINERY AND INTELLIGENCE. Mind, LIX(236), 433-460. doi:10.1093/mind/lix.236.433Sarkar, P. (2000). A brief history of cellular automata. ACM Computing Surveys, 32(1), 80-107. doi:10.1145/349194.349202Ermentrout, G. B., & Edelstein-Keshet, L. (1993). Cellular Automata Approaches to Biological Modeling. Journal of Theoretical Biology, 160(1), 97-133. doi:10.1006/jtbi.1993.1007Boccara, N., Roblin, O., & Roger, M. (1994). Automata network predator-prey model with pursuit and evasion. Physical Review E, 50(6), 4531-4541. doi:10.1103/physreve.50.4531Gerhardt, M., & Schuster, H. (1989). A cellular automaton describing the formation of spatially ordered structures in chemical systems. Physica D: Nonlinear Phenomena, 36(3), 209-221. doi:10.1016/0167-2789(89)90081-xZhu, M. F., Lee, S. Y., & Hong, C. P. (2004). Modified cellular automaton model for the prediction of dendritic growth with melt convection. Physical Review E, 69(6). doi:10.1103/physreve.69.061610KANSAL, A. R., TORQUATO, S., HARSH, G. R., CHIOCCA, E. A., & DEISBOECK, T. S. (2000). Simulated Brain Tumor Growth Dynamics Using a Three-Dimensional Cellular Automaton. Journal of Theoretical Biology, 203(4), 367-382. doi:10.1006/jtbi.2000.2000Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, 79(8), 2554-2558. doi:10.1073/pnas.79.8.2554TSOUTSOURAS, V., SIRAKOULIS, G. C., PAVLOS, G. P., & ILIOPOULOS, A. C. (2012). SIMULATION OF HEALTHY AND EPILEPTIFORM BRAIN ACTIVITY USING CELLULAR AUTOMATA. International Journal of Bifurcation and Chaos, 22(09), 1250229. doi:10.1142/s021812741250229xAcedo, L., Lamprianidou, E., Moraño, J.-A., Villanueva-Oller, J., & Villanueva, R.-J. (2015). Firing patterns in a random network cellular automata model of the brain. Physica A: Statistical Mechanics and its Applications, 435, 111-119. doi:10.1016/j.physa.2015.05.017Chialvo, D. R. (2010). Emergent complex neural dynamics. Nature Physics, 6(10), 744-750. doi:10.1038/nphys1803Priesemann, V. (2014). Spike avalanches in vivo suggest a driven, slightly subcritical brain state. Frontiers in Systems Neuroscience, 8. doi:10.3389/fnsys.2014.00108Langton, C. G. (1990). Computation at the edge of chaos: Phase transitions and emergent computation. Physica D: Nonlinear Phenomena, 42(1-3), 12-37. doi:10.1016/0167-2789(90)90064-vFriedman, N., Ito, S., Brinkman, B. A. W., Shimono, M., DeVille, R. E. L., Dahmen, K. A., … Butler, T. C. (2012). Universal Critical Dynamics in High Resolution Neuronal Avalanche Data. Physical Review Letters, 108(20). doi:10.1103/physrevlett.108.208102Kello, C. T. (2013). Critical branching neural networks. Psychological Review, 120(1), 230-254. doi:10.1037/a0030970Werner, G. (2007). Metastability, criticality and phase transitions in brain and its models. Biosystems, 90(2), 496-508. doi:10.1016/j.biosystems.2006.12.001Bak, P., Chen, K., & Creutz, M. (1989). Self-organized criticality in the ’Game of Life". Nature, 342(6251), 780-782. doi:10.1038/342780a0Hemmingsson, J. (1995). Consistent results on ‘Life’. Physica D: Nonlinear Phenomena, 80(1-2), 151-153. doi:10.1016/0167-2789(95)90071-3Nordfalk, J., & Alstrøm, P. (1996). Phase transitions near the «game of Life». Physical Review E, 54(2), R1025-R1028. doi:10.1103/physreve.54.r1025Ninagawa, S., Yoneda, M., & Hirose, S. (1998). 1ƒ fluctuation in the «Game of Life». Physica D: Nonlinear Phenomena, 118(1-2), 49-52. doi:10.1016/s0167-2789(98)00025-6Allegrini, P., Menicucci, D., Bedini, R., Fronzoni, L., Gemignani, A., Grigolini, P., … Paradisi, P. (2009). Spontaneous brain activity as a source of ideal1/fnoise. Physical Review E, 80(6). doi:10.1103/physreve.80.061914Fox, M. D., & Raichle, M. E. (2007). Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging. Nature Reviews Neuroscience, 8(9), 700-711. doi:10.1038/nrn2201Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., & Ilmoniemi, R. J. (2001). Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations. The Journal of Neuroscience, 21(4), 1370-1377. doi:10.1523/jneurosci.21-04-01370.2001Gilden, D., Thornton, T., & Mallon, M. (1995). 1/f noise in human cognition. Science, 267(5205), 1837-1839. doi:10.1126/science.7892611Bédard, C., Kröger, H., & Destexhe, A. (2006). Does the1/fFrequency Scaling of Brain Signals Reflect Self-Organized Critical States? Physical Review Letters, 97(11). doi:10.1103/physrevlett.97.118102Wolfram, S. (1983). Statistical mechanics of cellular automata. Reviews of Modern Physics, 55(3), 601-644. doi:10.1103/revmodphys.55.601“Life Universal Computer”http://www.igblan.free-online.co.uk/igblan/ca/Bagnoli, F., Rechtman, R., & Ruffo, S. (1991). Some facts of life. Physica A: Statistical Mechanics and its Applications, 171(2), 249-264. doi:10.1016/0378-4371(91)90277-jGarcia, J. B. C., Gomes, M. A. F., Jyh, T. I., Ren, T. I., & Sales, T. R. M. (1993). Nonlinear dynamics of the cellular-automaton ‘‘game of Life’’. Physical Review E, 48(5), 3345-3351. doi:10.1103/physreve.48.3345Huang, S.-Y., Zou, X.-W., Tan, Z.-J., & Jin, Z.-Z. (2003). Network-induced nonequilibrium phase transition in the «game of Life». Physical Review E, 67(2). doi:10.1103/physreve.67.026107Blok, H. J., & Bergersen, B. (1999). Synchronous versus asynchronous updating in the «game of Life». Physical Review E, 59(4), 3876-3879. doi:10.1103/physreve.59.3876Schönfisch, B., & de Roos, A. (1999). Synchronous and asynchronous updating in cellular automata. Biosystems, 51(3), 123-143. doi:10.1016/s0303-2647(99)00025-8Reia, S. M., & Kinouchi, O. (2014). Conway’s game of life is a near-critical metastable state in the multiverse of cellular automata. Physical Review E, 89(5). doi:10.1103/physreve.89.052123De la Torre, A. C., & Mártin, H. O. (1997). A survey of cellular automata like the «game of life». Physica A: Statistical Mechanics and its Applications, 240(3-4), 560-570. doi:10.1016/s0378-4371(97)00046-0Beer, R. D. (2004). Autopoiesis and Cognition in the Game of Life. Artificial Life, 10(3), 309-326. doi:10.1162/1064546041255539Beer, R. D. (2014). The Cognitive Domain of a Glider in the Game of Life. Artificial Life, 20(2), 183-206. doi:10.1162/artl_a_00125Yuste, S. B., & Acedo, L. (2000). Number of distinct sites visited byNrandom walkers on a Euclidean lattice. Physical Review E, 61(3), 2340-2347. doi:10.1103/physreve.61.2340Lachaux, J.-P., Pezard, L., Garnero, L., Pelte, C., Renault, B., Varela, F. J., & Martinerie, J. (1997). Spatial extension of brain activity fools the single-channel reconstruction of EEG dynamics. Human Brain Mapping, 5(1), 26-47. doi:10.1002/(sici)1097-0193(1997)5:13.0.co;2-pMcDowell, J. E., Kissler, J. M., Berg, P., Dyckman, K. A., Gao, Y., Rockstroh, B., & Clementz, B. A. (2005). Electroencephalography/magnetoencephalography study of cortical activities preceding prosaccades and antisaccades. NeuroReport, 16(7), 663-668. doi:10.1097/00001756-200505120-00002Holsheimer, J., & Feenstra, B. W. . (1977). Volume conduction and EEG measurements within the brain: A quantitative approach to the influence of electrical spread on the linear relationship of activity measured at different locations. Electroencephalography and Clinical Neurophysiology, 43(1), 52-58. doi:10.1016/0013-4694(77)90194-8Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117(4), 500-544. doi:10.1113/jphysiol.1952.sp004764Porooshani, H., Porooshani, A. H., Gannon, L., & Kyle, G. M. (2004). Speed of progression of migrainous visual aura measured by sequential field assessment. Neuro-Ophthalmology, 28(2), 101-105. doi:10.1076/noph.28.2.101.23739Hutsler, J. J. (2003). The specialized structure of human language cortex: Pyramidal cell size asymmetries within auditory and language-associated regions of the temporal lobes. Brain and Language, 86(2), 226-242. doi:10.1016/s0093-934x(02)00531-xWilson, H. R., & Cowan, J. D. (1972). Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophysical Journal, 12(1), 1-24. doi:10.1016/s0006-3495(72)86068-5Conway’s Game of Life. Examples of patternshttps://en.wikipedia.org/wiki/Conway%27s_Game_of_Life#Examples_of_patternsGardner, M. (1970). Mathematical Games. Scientific American, 223(4), 120-123. doi:10.1038/scientificamerican1070-120Packard, N. H., & Wolfram, S. (1985). Two-dimensional cellular automata. Journal of Statistical Physics, 38(5-6), 901-946. doi:10.1007/bf01010423Nunomura, A., Perry, G., Aliev, G., Hirai, K., Takeda, A., Balraj, E. K., … Smith, M. A. (2001). Oxidative Damage Is the Earliest Event in Alzheimer Disease. Journal of Neuropathology & Experimental Neurology, 60(8), 759-767. doi:10.1093/jnen/60.8.759Kitamura, T., Ogawa, S. K., Roy, D. S., Okuyama, T., Morrissey, M. D., Smith, L. M., … Tonegawa, S. (2017). Engrams and circuits crucial for systems consolidation of a memory. Science, 356(6333), 73-78. doi:10.1126/science.aam6808Anderson, P. W. (1972). More Is Different. Science, 177(4047), 393-396. doi:10.1126/science.177.4047.39