2014, 11(2): 343-361. doi: 10.3934/mbe.2014.11.343

Distributed, layered and reliable computing nets to represent neuronal receptive fields

1. 

Facultad de Informática, Universidad Politécnica de Madrid (UPM), Spain

2. 

Instituto Universitario de Ciencias y Tecnologías Cibernéticas, Universidad de Las Palmas de Gran Canaria, Spain, Spain

Received  September 2012 Revised  April 2013 Published  October 2013

Receptive fields of retinal and other sensory neurons show a large variety of spatiotemporal linear and non linear types of responses to local stimuli. In visual neurons, these responses present either asymmetric sensitive zones or center-surround organization. In most cases, the nature of the responses suggests the existence of a kind of distributed computation prior to the integration by the final cell which is evidently supported by the anatomy. We describe a new kind of discrete and continuous filters to model the kind of computations taking place in the receptive fields of retinal cells. To show their performance in the analysis of different non-trivial neuron-like structures, we use a computer tool specifically programmed by the authors to that effect. This tool is also extended to study the effect of lesions on the whole performance of our model nets.
Citation: Arminda Moreno-Díaz, Gabriel de Blasio, Moreno-Díaz Jr.. Distributed, layered and reliable computing nets to represent neuronal receptive fields. Mathematical Biosciences & Engineering, 2014, 11 (2) : 343-361. doi: 10.3934/mbe.2014.11.343
References:
[1]

H. B. Barlow, Summation and inhibition in the frog's retina, J. Physiol., 119 (1953), 69-88.

[2]

G. de Blasio, A. Moreno-Díaz and R. Moreno-Díaz, Bioinspired computing nets for directionality in vision, Computing, 94 (2012), 449-462. doi: 10.1007/s00607-012-0186-z.

[3]

G. de Blasio, A. Moreno-Díaz, R. Moreno-Díaz, Jr. and R. Moreno-Díaz, New biomimetic neural structures for artificial neural nets, in Computer Aided Systems Theory - EUROCAST 2011: 13th International Conference, Las Palmas de Gran Canaria, Spain, February 6-11, 2011, Revised Selected Papers, Part I, Lecture Notes in Computer Science, 6927, Springer, Berlin-Heidelberg, 2011, 25-31. doi: 10.1007/978-3-642-27549-4_4.

[4]

W. Feller, An Introduction to Probability Theory and its Applications. Vol. I, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968.

[5]

S. B. Frost, S. Barbay, K. M. Friel, E. J. Plautz and R. J. Nudo, Reorganization of remote cortical regions after ischemic brain injury: A potential substrate for stroke recovery, J. Neuriphysiol., 89, (2003), 3205-3214.

[6]

P. Hammond, Contrasts in spatial organization of receptive fields at geniculate and retinal levels: Centre-surround and outer-surround, J. Physiol., 228, (1973), 115-137.

[7]

H. Hochstadt, The Functions in Mathematical Physics, Second edition, Dover Publications, Inc., New York, 1986.

[8]

D. H. Hubel and T. N. Wiesel, Anatomical demonstration of columns in the monkey striate cortex, Nature, 221 (1969), 747-750.

[9]

H. Kolb, How the retina works, American Scientist, 91 (2003), 28-35.

[10]

S. W. Kuffler, Discharge patterns and functional organization of mammalian retina, J. Neurophysiol., 16 (1953), 37-68.

[11]

K. N. Leibovic, Principles of brain function: Information processing in convergent and divergent pathways, in Progress in Cybernetics and Systems, Vol. VI (eds. Pichler and Trappl), Hemisphere, Washington, D.C.-London, 1982, 91-99.

[12]

C. Y. Li, Y. X. Zhou, X. Pei, F. T. Qiu, C. Q. Tang and X. Z. Xu, Extensive disinhibitory region beyond the classical receptive field of cat retinal ganglion cells, Vision Res., 32 (1992), 219-228.

[13]

M. London and M. Häusser, Dendritic computation, Annu. Rev. Neurosci., 28 (2005), 503-532. doi: 10.1146/annurev.neuro.28.061604.135703.

[14]

P. Marmarelis and K. I. Naka, Non-linear analysis and synthesis of receptive field responses in the catfish retina. I. Horizontal cell-ganglion chains, J. Neuriphysiol., 36 (1973), 605-618.

[15]

P. Marmarelis and K. I. Naka, Non-linear analysis and synthesis of receptive field responses in the catfish retina. II. One input white noise analysis, J. Neuriphysiol., 36 (1973), 619-633.

[16]

D. Marr, Vision, W. H. Freeman and Company, San Francisco, 1982.

[17]

W. S. McCulloch, Embodiments of Mind, MIT Press, Cambridge, MA, 1988.

[18]

R. Moreno-Díaz, An Analytical Model of the Group 2 Ganglion Cell in the Frog'S Retina, Report, Massachusetts Institute of Technology, Instrumentation Laboratory, 1965, 33-34.

[19]

R. Moreno-Díaz and G. de Blasio, Systems methods in visual modelling, Systems Analysis Modelling Simulation, 43 (2003), 1159-1171. doi: 10.1080/02329290310001600255.

[20]

R. Moreno-Díaz and G. de Blasio, Systems and computational tools for neuronal retinal models, in Computer Aided Systems Theory - EUROCAST 2003, Lecture Notes in Computer Science, 2809, Springer, Berlin-Heidelberg, 2003, 494-505. doi: 10.1007/978-3-540-45210-2_45.

[21]

R. Moreno-Díaz, Jr., Computación Paralela y Distribuida: Relaciones Estructura-Función en Retinas, Ph.D thesis, Universidad de Las Palmas de Gran Canaria, 1993.

[22]

R. Moreno-Díaz, Jr. and K. N. Leibovic, On some methods in neuromathematics (or the development of mathematical methods for the description of structure and function in neurons), in From Natural to Artificial Neural Computation, Lecture Notes in Computer Science, Vol. 930/1995, 1995, 209-214.

[23]

C. L. Passaglia, D. K. Freeman and J. B. Troy, Effects of remote stimulation on the modulated activity of cat retinal ganglion cells, The Journal of Neuroscience, 29 (2009), 2467-2476. doi: 10.1523/JNEUROSCI.4110-08.2009.

[24]

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. Flannery, Numerical Recipes: The Art of Scientific Computing, $3^{rd}$ edition, Cambridge University Press, Cambridge, 2007.

[25]

R. W. Rodieck, Quantitative analysis of cat retinal ganglion cell response to visual stimuli, Vision Res., 5 (1965), 583-601. doi: 10.1016/0042-6989(65)90033-7.

[26]

R. W. Rodieck and J. Stone, Response of cat retinal ganglion cells to moving visual patterns, J. Neurophysiol., 28 (1965), 819-832.

[27]

G. Schweigart and U. T. Eysel, Activity-dependent receptive field changes in the surround of adult cat visual cortex lesions, European Journal of Neuroscience, 15 (2002), 1585-1596. doi: 10.1046/j.1460-9568.2002.01996.x.

[28]

I. Segev, What do dendrites and their synapses tell the neuron? J. Neurophysiol., 95 (2006), 1295-1297. doi: 10.1152/classicessays.00039.2005.

[29]

T. Shou, W. Wang and H. Yu, Orientation biased extended surround of the receptive field of car retinal ganglion cells, Neuroscience, 98 (2000), 207-212.

[30]

P. Sterling, The ganglion receptive field, in The Retinal Basis of Vision (eds. J. Toyoda, et al.), Elsevier Science, 1999, 163-169.

[31]

G. Szegö, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, RI, 1959.

[32]

Y. Tokutake and M. A. Freed, Retinal ganglion cells - spatial organization of the receptive field reduces temporal redundancy, European Journal of Neuroscience, 28 (2008), 914-923. doi: 10.1111/j.1460-9568.2008.06394.x.

[33]

J. B. Troy and T. Shou, The receptive fields of cat retinal ganglion cells in physiological and pathological states: where we are after half a century of research, Progress in Retinal and Eye Research, 21 (2002), 263-302. doi: 10.1016/S1350-9462(02)00002-2.

[34]

M. Van Wyk, W. R. Taylor and D. I. Vaney, Local edge detectors: A substrate for fine spatial vision at low temporal frequencies in rabbit retina, The Journal of Neurosci., 26 (2006), 13250-13263.

[35]

M. Van Wyk, H. Wässle and W. R. Taylor, Receptive field properties of ON- and OFF-ganglion cells in the mouse retina, Visual Neurosci., 26 (2009), 297-308.

[36]

F. Werblin, A. Jacobs and J. Teeters, The computational eye, Spectrum IEEE, 33 (1996), 30-37. doi: 10.1109/6.490054.

show all references

References:
[1]

H. B. Barlow, Summation and inhibition in the frog's retina, J. Physiol., 119 (1953), 69-88.

[2]

G. de Blasio, A. Moreno-Díaz and R. Moreno-Díaz, Bioinspired computing nets for directionality in vision, Computing, 94 (2012), 449-462. doi: 10.1007/s00607-012-0186-z.

[3]

G. de Blasio, A. Moreno-Díaz, R. Moreno-Díaz, Jr. and R. Moreno-Díaz, New biomimetic neural structures for artificial neural nets, in Computer Aided Systems Theory - EUROCAST 2011: 13th International Conference, Las Palmas de Gran Canaria, Spain, February 6-11, 2011, Revised Selected Papers, Part I, Lecture Notes in Computer Science, 6927, Springer, Berlin-Heidelberg, 2011, 25-31. doi: 10.1007/978-3-642-27549-4_4.

[4]

W. Feller, An Introduction to Probability Theory and its Applications. Vol. I, Third edition, John Wiley & Sons, Inc., New York-London-Sydney, 1968.

[5]

S. B. Frost, S. Barbay, K. M. Friel, E. J. Plautz and R. J. Nudo, Reorganization of remote cortical regions after ischemic brain injury: A potential substrate for stroke recovery, J. Neuriphysiol., 89, (2003), 3205-3214.

[6]

P. Hammond, Contrasts in spatial organization of receptive fields at geniculate and retinal levels: Centre-surround and outer-surround, J. Physiol., 228, (1973), 115-137.

[7]

H. Hochstadt, The Functions in Mathematical Physics, Second edition, Dover Publications, Inc., New York, 1986.

[8]

D. H. Hubel and T. N. Wiesel, Anatomical demonstration of columns in the monkey striate cortex, Nature, 221 (1969), 747-750.

[9]

H. Kolb, How the retina works, American Scientist, 91 (2003), 28-35.

[10]

S. W. Kuffler, Discharge patterns and functional organization of mammalian retina, J. Neurophysiol., 16 (1953), 37-68.

[11]

K. N. Leibovic, Principles of brain function: Information processing in convergent and divergent pathways, in Progress in Cybernetics and Systems, Vol. VI (eds. Pichler and Trappl), Hemisphere, Washington, D.C.-London, 1982, 91-99.

[12]

C. Y. Li, Y. X. Zhou, X. Pei, F. T. Qiu, C. Q. Tang and X. Z. Xu, Extensive disinhibitory region beyond the classical receptive field of cat retinal ganglion cells, Vision Res., 32 (1992), 219-228.

[13]

M. London and M. Häusser, Dendritic computation, Annu. Rev. Neurosci., 28 (2005), 503-532. doi: 10.1146/annurev.neuro.28.061604.135703.

[14]

P. Marmarelis and K. I. Naka, Non-linear analysis and synthesis of receptive field responses in the catfish retina. I. Horizontal cell-ganglion chains, J. Neuriphysiol., 36 (1973), 605-618.

[15]

P. Marmarelis and K. I. Naka, Non-linear analysis and synthesis of receptive field responses in the catfish retina. II. One input white noise analysis, J. Neuriphysiol., 36 (1973), 619-633.

[16]

D. Marr, Vision, W. H. Freeman and Company, San Francisco, 1982.

[17]

W. S. McCulloch, Embodiments of Mind, MIT Press, Cambridge, MA, 1988.

[18]

R. Moreno-Díaz, An Analytical Model of the Group 2 Ganglion Cell in the Frog'S Retina, Report, Massachusetts Institute of Technology, Instrumentation Laboratory, 1965, 33-34.

[19]

R. Moreno-Díaz and G. de Blasio, Systems methods in visual modelling, Systems Analysis Modelling Simulation, 43 (2003), 1159-1171. doi: 10.1080/02329290310001600255.

[20]

R. Moreno-Díaz and G. de Blasio, Systems and computational tools for neuronal retinal models, in Computer Aided Systems Theory - EUROCAST 2003, Lecture Notes in Computer Science, 2809, Springer, Berlin-Heidelberg, 2003, 494-505. doi: 10.1007/978-3-540-45210-2_45.

[21]

R. Moreno-Díaz, Jr., Computación Paralela y Distribuida: Relaciones Estructura-Función en Retinas, Ph.D thesis, Universidad de Las Palmas de Gran Canaria, 1993.

[22]

R. Moreno-Díaz, Jr. and K. N. Leibovic, On some methods in neuromathematics (or the development of mathematical methods for the description of structure and function in neurons), in From Natural to Artificial Neural Computation, Lecture Notes in Computer Science, Vol. 930/1995, 1995, 209-214.

[23]

C. L. Passaglia, D. K. Freeman and J. B. Troy, Effects of remote stimulation on the modulated activity of cat retinal ganglion cells, The Journal of Neuroscience, 29 (2009), 2467-2476. doi: 10.1523/JNEUROSCI.4110-08.2009.

[24]

W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. Flannery, Numerical Recipes: The Art of Scientific Computing, $3^{rd}$ edition, Cambridge University Press, Cambridge, 2007.

[25]

R. W. Rodieck, Quantitative analysis of cat retinal ganglion cell response to visual stimuli, Vision Res., 5 (1965), 583-601. doi: 10.1016/0042-6989(65)90033-7.

[26]

R. W. Rodieck and J. Stone, Response of cat retinal ganglion cells to moving visual patterns, J. Neurophysiol., 28 (1965), 819-832.

[27]

G. Schweigart and U. T. Eysel, Activity-dependent receptive field changes in the surround of adult cat visual cortex lesions, European Journal of Neuroscience, 15 (2002), 1585-1596. doi: 10.1046/j.1460-9568.2002.01996.x.

[28]

I. Segev, What do dendrites and their synapses tell the neuron? J. Neurophysiol., 95 (2006), 1295-1297. doi: 10.1152/classicessays.00039.2005.

[29]

T. Shou, W. Wang and H. Yu, Orientation biased extended surround of the receptive field of car retinal ganglion cells, Neuroscience, 98 (2000), 207-212.

[30]

P. Sterling, The ganglion receptive field, in The Retinal Basis of Vision (eds. J. Toyoda, et al.), Elsevier Science, 1999, 163-169.

[31]

G. Szegö, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, RI, 1959.

[32]

Y. Tokutake and M. A. Freed, Retinal ganglion cells - spatial organization of the receptive field reduces temporal redundancy, European Journal of Neuroscience, 28 (2008), 914-923. doi: 10.1111/j.1460-9568.2008.06394.x.

[33]

J. B. Troy and T. Shou, The receptive fields of cat retinal ganglion cells in physiological and pathological states: where we are after half a century of research, Progress in Retinal and Eye Research, 21 (2002), 263-302. doi: 10.1016/S1350-9462(02)00002-2.

[34]

M. Van Wyk, W. R. Taylor and D. I. Vaney, Local edge detectors: A substrate for fine spatial vision at low temporal frequencies in rabbit retina, The Journal of Neurosci., 26 (2006), 13250-13263.

[35]

M. Van Wyk, H. Wässle and W. R. Taylor, Receptive field properties of ON- and OFF-ganglion cells in the mouse retina, Visual Neurosci., 26 (2009), 297-308.

[36]

F. Werblin, A. Jacobs and J. Teeters, The computational eye, Spectrum IEEE, 33 (1996), 30-37. doi: 10.1109/6.490054.

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