Energy-based stochastic control of neural mass models suggests time-varying effective connectivity in the resting state

Journal of Computational Neuroscience

Volumn 32, Issue 3, 2012, Pages 563-576

  Sotero, Roberto C ^a   Shmuel, Amir ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Connectivity matrix; Effective connectivity; Energy consumption; Neural mass models; Stochastic LQR; Time varying parameters model

Indexed keywords

BRAIN; COST FUNCTIONS; COSTS; ENERGY UTILIZATION; MATHEMATICAL TRANSFORMATIONS; STOCHASTIC CONTROL SYSTEMS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TIME DELAY; TIME VARYING CONTROL SYSTEMS;

CONNECTIVITY MATRIX; EFFECTIVE CONNECTIVITIES; ENERGY-CONSUMPTION; LINEAR QUADRATIC; NEURAL MASS MODELS; QUADRATIC REGULATORS; RESTING STATE; STOCHASTIC LINEAR QUADRATIC REGULATOR; STOCHASTICS; TIME-VARYING PARAMETER MODELS;

NEURONS;

ARTICLE; CELL POPULATION; ENERGY CONSUMPTION; ENERGY COST; EVOKED CORTICAL RESPONSE; LINEAR SYSTEM; NERVE CELL EXCITABILITY; NERVE CELL INHIBITION; NONLINEAR SYSTEM; PRIORITY JOURNAL; PROBLEM SOLVING; REST; STATISTICAL PARAMETERS; TASK PERFORMANCE; TIME;

EID: 84863879795     PISSN: 09295313     EISSN: 15736873     Source Type: Journal    
DOI: 10.1007/s10827-011-0370-8     Document Type: Article

References (69)

1. Aiello, L. C., & Wheeler, P. (1995). The expensive-tissue hypothesis: the brain and the digestive system in human and primate evolution. Current Anthropology, 36, 199-221.
2. Alle, H., Roth, A., & Geiger, J. R. (2009). Energy-efficient action potentials in hippocampal mossy fibbers. Science, 325, 1405-1408.
3. Ames, A. (2000). CNS energy metabolism as related to function. Brain Research Reviews, 34, 42-68.
4. Attwell, D., & Iadecola, C. (2002). The neural basis of functional brain imaging signals. Trends in Neurosciences, 25, 621-625. (Pubitemid 35356509)
5. Babajani, A., & Soltanian-Zadeh, H. (2006). Integrated MEG/EEG and fMRI model based on neural masses. IEEE Transactions on Biomedical Engineering, 53, 1794-1801. (Pubitemid 44285907)
6. Balasubramanian,V.,Kimber,D.,&Berry,M. J., II. (2001).Metabolically efficient information processing. Neural Computation, 13, 799-815. (Pubitemid 33594305)
7. Bennet, M. R., & Kearns, J. L. (2000). Statistics of synaptic release at nerve terminals. Progress in Neurobiology, 60, 545-606.
8. Blomquist, P., Devor, A., Indahl, U. G., Ulbert, I., Einevoll, G. T., & Dale, A. M. (2009). Estimation of thalamocortical and intracortical network models from joint thalamic single-eletrode and cortical laminar-electrode recordings in the rat barrel system. PLoS Computational Biology, 5, e1000328.
9. Brock, O., & Kavraki, L. (2001). Decomposition based motion planning: a framework for real time motion planning in high-dimensional configuration spaces. In IEEE International Conference on Robotics and Automation, 2, 1469-1474.
10. Chen, S., Li, X., & Zhou, X. Y. (1998). Stochastic linear quadratic regulators with indefinite control weight costs. SIAM Journal on Control and Optimization, 36, 1685-1702. (Pubitemid 128493568)
11. Chen, X., & Zhou, Y. (2004). Stochastic linear-quadratic control with conic control constraints on an infinite time horizon. SIAM Journal on Control and Optimization, 43, 1120-1150.
12. Chklovskii, D. B.,&Koukalov, A.A. (2004). Maps in the brain: what can we learn from them? Annual Review of Neuroscience, 27, 369-392.
13. Çimen, T. (2008). State-dependent Riccati equation (SDRE) control: A survey. In: Proc. of the 17th IFAC World Congress, Seoul, South Korea.
14. Clarke, D. D., & Sokoloff, L. (1999) Circulation and energy metabolism of the brain. In Agranoff, B. W., & Siegel, G. J. (eds), Basic neurochemistry. Molecular, cellular and medical aspects (6th edn) (pp. 637-670). Lippincott-Raven.
15. David, O., & Friston, K. J. (2003). A neural mass model for MEG/ EEG: coupling and neuronal dynamics. NeuroImage, 20, 1743-1755. (Pubitemid 37468280)
16. Deco, G., Jirsa, V. K., Robinson, P. A., Breakspear, M., & Friston, K. (2008). The dynamic brain: from spiking neurons to neural masses and cortical fields. PLoS Computational Biology, 4, e1000092.
17. Faugeras, O., Veltz, R., & Grimbert, F. (2009). Persistent neural states: stationary localized activity patterns in nonlinear continuous n-population, q-dimensional neural networks. Neural Computation, 21, 147-187.
18. Feng, J., & Tuckwell, H. C. (2003). Optimal control of neuronal activity. Physical Review Letters, 91, 018101.
19. Freeman, W. J. (1975). Mass action in the nervous system. New York: Academic.
20. Friston, K. (2010). The free-energy principle: a unified brain theory? Nature Reviews Neuroscience, 11, 127-138.
21. Friston, K., Kilner, J., & Harrison, L. (2006). A free energy principle for the brain. Journal of Physiology, Paris, 100, 70-87. (Pubitemid 44827686)
22. Gertsner, W., Kreiter, A. K., Markram, H., & Hertz, A. V. M. (1997). Neural codes: firing rates and beyond. PNAS, 94, 12740-12741. (Pubitemid 27518414)
23. Granger, C. W. J. (2008). Non-linear models: where do we go next-time varying parameters models? Studies in Nonlinear Dynamics & Econometrics, 12, 1-9.
24. Grimbert, F., & Faugeras, O. (2006). Bifurcation analysis of Jansen's neural mass model. Neural Computation, 18, 3052-3068. (Pubitemid 44879152)
25. Guigon, E., Baraduc, P., & Desmurget, M. (2008). Optimality, stochasticity, and variability in motor behaviour. Journal of Computational Neuroscience, 24, 57-68. (Pubitemid 351148251)
26. Hasenstaub, A., Otte, S., Callaway, E., & Sejnowski, T. J. (2010). Metabolic cost as a unifying principle governing neuronal biophysics. PNAS, 107, 12329-12334.
27. Heemels, W. P. M. H., Van Eijndhoven, S. J. L., & Stoorvogel, A. A. (1998). Linear quadratic regulator with positive controls. International Journal of Control, 70, 551-578. (Pubitemid 128552933)
28. Highman, N. J. (2008). Function of matrices: theory and computation. Philadelphia: Siam. Sociaty for Industrial and Applied Mathematics.
29. Hu, Y., & Zhou, X. Y. (2005). Constrained stochastic LQ control with random coefficients, and application to portfolio selection. SIAM Journal on Control and Optimization, 44, 444-466.
30. Jansen, B. H., & Rit, V. G. (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics, 73, 357-366.
31. Johnson, C. D. (1987). Limits of propriety for linear-quadratic regulator problems. International Journal of Control, 35, 1835-1846.
32. Kalman, R. E. (1960). Contributions to the theory of optimal control. Bol Soc Math Mexicana, 5, 102-119.
33. Karbowski, J. (2003). How does connectivity between cortical areas depend on brain size? Implications for efficient computations. Journal of Computational Neuroscience, 15, 347-356.
34. Katz, B., & Miledi, R. (1970). Membrane noise produced by acetylcholine. Nature, 226, 962-963.
35. Körding, K. P., & Wolpert, D. M. (2004). Bayesian integration in sensorimotor learning. Nature, 427, 244-247. (Pubitemid 38112039)
36. Körding, K. P., & Wolpert, D. M. (2006). Bayesian decision theory in sensorimotor control. Trends in Cognitive Sciences, 10, 319-326. (Pubitemid 44094227)
37. Laughlin, S. B. (2001). Energy as a constrain on the coding and processing of sensory information. Current Opinion in Neurobiology, 11, 475-480.
38. Laughlin, S. B., & Sejnowski, T. J. (2003). Communication in neuronal networks. Science, 301, 1870-1874. (Pubitemid 37221384)
39. Lennie, P. (2003). The cost of cortical computation. Current Biology, 13, 493-497.
40. Levy, W. B., & Baxter, R. A. (1996). Energy efficient neural codes. Neural Computation, 8, 531-543. (Pubitemid 126450623)
41. Lopes da Silva, F. H., Hoeks, A., Smits, H., & Zetterberg, L. H. (1974). Model of brain rhythmic activity. The alpha-rhythm of the thalamus. Kybernetik, 15, 27-37.
42. Maloney, L. T., & Mamassian, P. (2009). Bayesian decision theory as a model of human visual perception: testing Bayesian transfer. Visual Neuroscience, 26, 147-155.
43. Maloney, L. T., & Zhang, H. (2010). Decision-theoretic models of visual perception and action. Vision Research, 50, 2362-2374.
44. Martin, R. D. (1996). Scaling of the mammalian brain: the maternal energy hypothesis. News in Physiological Sciences, 11, 149-156.
45. Model, P. G., Highstein, S. M., & Bennett, M. V. L. (1975). Depletion of vesicles and fatigue of transmission at a vertebrate central synapse. Brain Research, 98, 209-228.
46. Montgomery, J. M., & Madison, D. V. (2004). Discrete synaptic states define a major mechanism of synaptic plasticity. TRENDS in Neuroscience, 27, 744-750. (Pubitemid 39488078)
47. Moran, R. J., Stephan, K. E., Kiebel, S. J., Rombach, N., O'Connor, W. T., Murphy, K. J., et al. (2008). Bayesian estimation of synaptic physiology from the spectral responses of neural masses. NeuroImage, 42, 272-284.
48. Niven, J. E. (2007). Brains, islands and evolution: breaking all the rules. Trends in Ecology & Evolution, 22, 57-59.
49. Niven, J. E., & Laughlin, S. B. (2008). Energy limitation as a selective pressure on the evolution of sensory systems. The Journal of Experimental Biology, 211, 1792-1804. (Pubitemid 351964926)
50. + - channels are predicted to reduce the metabolic cost of neural information in Drosophila photoreceptors. Proceedings of the Royal Society of London - Series B: Biological Sciences, 270, S58-S61.
51. Oksendal, B. (2003). Stochastic Differential Equations. Springer-verlag.
52. Pons, A. J., Cantero, J. L., Atienza, M., & Garcia-Ojalvo, J. (2010). Relating structural and functional anomalous connectivity in the aging brain via neural mass modeling. NeuroImage, 52, 848-861.
53. Raichle, M. E. (2010). Two views of brain function. Trends in Cognitive Sciences, 14, 180-190.
54. Sotero, R. C., Bortel, A., Martínez-Cancino, R., Neupane, S., O'Connor, P., & Shmuel, A. (2010). Anatomically-constrained effective connectivity within and among layers in a cortical column modeled and estimated from local field potentials. Journal of Integrative Neuroscience, 9, 355-379.
55. Sotero, R. C., & Martínez-Cancino, R. (2010). Dynamical mean field model of a neural-glial mass. Neural Computation, 22, 969-997.
56. Sotero, R. C., & Trujillo-Barreto, N. J. (2007). Modelling the role of excitatory and inhibitory neuronal activity in the generation of the BOLD signal. NeuroImage, 35, 149-165.
57. Sotero, R. C., & Trujillo-Barreto, N. J. (2008). Biophysical model for integrating neuronal activity, EEG, fMRI and metabolism. NeuroImage, 39, 290-309. (Pubitemid 350110533)
58. Sotero, R. C., Trujillo-Barreto, N. J., Iturria-Medina, Y., Carbonell, F., & Jiménez, J. C. (2007). Realistically coupled neural mass models can generate EEG rhythms. Neural Computation, 19, 478-512.
59. Spiegler, A., Kiebel, S. J., Atay, F. M., & Knösche, T. R. (2010). Bifurcation analysis of neural mass models: impact of extrinsic inputs and dendritic time constants. NeuroImage, 52, 1041-1058.
60. Todorov, E. (2005). Stochastic optimal control and estimation methods adapted to the noise characteristics of the sensorimotor system. Neural Computation, 17, 1084-1108.
61. Todorov, E., Li, W., & Pan, W. (2005). From task parameters to motor synergies: a hierarchical framework for approximately optimal feedback control of redundant manipulators. Journal of Robotic Systems, 22, 669-710.
62. Tomás-Rodríguez, M., & Banks, S. P. (2010). Linear, Time-varying Approximations to Nonlinear Dynamical Systems with Applications in Control and Optimization. Lecture Notes in Control and Information Sciences. New York: Springer.
63. Torrealdea, F. J., Sarasola, C., & d'Anjou, A. (2009a). Energy consumption and information transmission in model neurons. Chaos, Solitons and Fractals, 40, 60-68.
64. Torrealdea, F. J., Sarasola, C., d'Anjou, A., Moujahid, A., & Velez de Mendizabal, N. (2009b). Energy efficiency of information transmission by electrically coupled neurons. Bio Systems, 97, 60-71.
65. Turelli, M. (1977). Random environments and stochastic calculus. Theoretical Population Biology, 12, 140-178.
66. Valdés-Sosa, P. A., Sanchez-Bornot, J. M., Sotero, R. C., Iturria-Medina, Y., Bosch-Bayard, J., Carbonell, F., et al. (2009). Model driven EEG/fMRI fusion of brain oscillations. Human Brain Mapping, 30, 2701-2721.
67. Wilson, H. R., & Cowan, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12, 1-24.
68. Wonham, W. M. (1968). On a matrix Riccati equation of stochastic control. SIAM Journal on Control and Optimization, 6, 312-326.
69. Zetterberg, L. H., Kristiansson, L., & Mossberg, K. (1978). Performance of a model for a local neuron population. Biological Cybernetics, 31, 15-26. (Pubitemid 9043104)