Encyclopedia of Computational Neuroscience

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| Editors: Dieter Jaeger, Ranu Jung

Computational Models of Neural Retina

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DOI: https://doi.org/10.1007/978-1-4614-7320-6_652-2



Computational models of the neural retina are extremely useful in the understanding of normal and abnormal retinal responses to light. They can also be for investigating retinal responses to artificial stimuli such as electrical stimulation by a vision prosthesis. Depending on the aims, complexities, and physiological assumptions on which the model is based, computational models of the retina may be classified into six broad types: single-compartment, morphologically realistic, block-compartment, discrete-neuronal network, continuum, and empirical models of retinal function.


The retina is an elaborate architecture of neurons interconnected through gap junctions and synapses. At the outer retina, an array of rod and cone photoreceptors converts the incident light to neural responses. These signals then pass through approximately ten types of cone and one type of rod...

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  1. Abbas SY, Hamade KC, Yang EJ, Nawy S, Smith RG, Pettit DL (2013) Directional summation in non-direction selective retinal ganglion cells. PLoS Comput Biol 9:e1002969PubMedPubMedCentralCrossRefGoogle Scholar
  2. Abramian M, Lovell NH, Morley JW, Suaning GJ, Dokos S (2011) Activation of retinal ganglion cells following epiretinal electrical stimulation with hexagonally arranged bipolar electrodes. J Neural Eng 8:035004PubMedCrossRefPubMedCentralGoogle Scholar
  3. Abramian M, Lovell NH, Habib A, Morley JW, Suaning GJ, Dokos S (2014) Quasi-monopolar electrical stimulation of the retina: a computational modelling study. J Neural Eng 11:025002PubMedCrossRefPubMedCentralGoogle Scholar
  4. Aidley DJ (1979) The physiology of excitable cells. Cambridge University Press, CambridgeGoogle Scholar
  5. Al Abed A, Lovell NH, Suaning GJ, Dokos S (2013) A continuum neuronal tissue model based on a two-compartmental representation of cells. Conf Proc IEEE Eng Med Biol Soc 2013:6543–6546PubMedPubMedCentralGoogle Scholar
  6. Alqahtani A, Al Abed A, Guo TR, Lovell NH, Dokos S (2017) A Continuum model of electrical stimulation of multi-compartmental retinal ganglion cells. Conf Proc IEEE Eng Med Biol Soc 2017: 2716–2719Google Scholar
  7. Altman KW, Plonsey R (1990) Point-source nerve bundle stimulation – effects of fiber diameter and depth on simulated excitation. IEEE Trans Biomed Eng 37:688–698PubMedCrossRefPubMedCentralGoogle Scholar
  8. Aoyama T, Kamiyama Y, Usui S (2005) Simulation analysis of receptive-field size of retinal horizontal cells by ionic current model. Vis Neurosci 22:65–78PubMedCrossRefPubMedCentralGoogle Scholar
  9. Arguello E, Silva R, Huerta M, Castillo C (2013) New trends in computational modeling: a Neuroid-based retina model. Conf Proc IEEE Eng Med Biol Soc 2013:4561–4564PubMedPubMedCentralGoogle Scholar
  10. Baccus SA, Olveczky BP, Manu M, Meister M (2008) A retinal circuit that computes object motion. J Neurosci 28:6807–6817PubMedPubMedCentralCrossRefGoogle Scholar
  11. Baden T, Berens P, Franke K, Roson MR, Bethge M, Euler T (2016) The functional diversity of retinal ganglion cells in the mouse. Nature 529:345–350PubMedPubMedCentralCrossRefGoogle Scholar
  12. Barriga-Rivera A, Guo TR, Yang CY, Al Abed A, Dokos S, Lovell NH, Morley JW, Suaning GJ (2017) High-amplitude electrical stimulation can reduce elicited neuronal activity in visual prosthesis. Sci Rep 7:42682PubMedPubMedCentralCrossRefGoogle Scholar
  13. Baylor DA, Hodgkin AL, Lamb TD (1974) Reconstruction of the electrical responses of turtle cones to flashes and steps of light. J Physiol 242:759–791PubMedPubMedCentralCrossRefGoogle Scholar
  14. Berry MJ 2nd, Brivanlou IH, Jordan TA, Meister M (1999) Anticipation of moving stimuli by the retina. Nature 398:334–338PubMedCrossRefPubMedCentralGoogle Scholar
  15. Boinagrov D, Loudin J, Palanker D (2010) Strength-duration relationship for extracellular neural stimulation: numerical and analytical models. J Neurophysiol 104:2236–2248PubMedPubMedCentralCrossRefGoogle Scholar
  16. Boinagrov D, Pangratz-Fuehrer S, Suh B, Mathieson K, Naik N, Palanker D (2012) Upper threshold of extracellular neural stimulation. J Neurophysiol 108:3233–3238PubMedPubMedCentralCrossRefGoogle Scholar
  17. Bomash I, Roudi Y, Nirenberg S (2013) A virtual retina for studying population coding. PLoS One 8:e53363PubMedPubMedCentralCrossRefGoogle Scholar
  18. Borg-Graham LJ (2001) The computation of directional selectivity in the retina occurs presynaptic to the ganglion cell. Nat Neurosci 4:176–183PubMedCrossRefPubMedCentralGoogle Scholar
  19. Borst A, Flanagin VL, Sompolinsky H (2005) Adaptation without parameter change: dynamic gain control in motion detection. Proc Natl Acad Sci U S A 102:6172–6176PubMedPubMedCentralCrossRefGoogle Scholar
  20. Brindley GS (1956) The passive electrical properties of the frog’s retina, choroid and sclera for radial fields and currents. J Physiol 134:339–352PubMedPubMedCentralCrossRefGoogle Scholar
  21. Cai CF, Liang PJ, Zhang PM (2007) A simulation study on the encoding mechanism of retinal ganglion cell. Lect N Bioinformat 4689: 470–479Google Scholar
  22. Cao X, Sui XH, Lyu Q, Li LM, Chai XY (2015) Effects of different three-dimensional electrodes on epiretinal electrical stimulation by modeling analysis. J Neuroeng Rehabil 12:73PubMedPubMedCentralCrossRefGoogle Scholar
  23. Carras PL, Coleman PA, Miller RF (1992) Site of action potential initiation in amphibian retinal ganglion cells. J Neurophysiol 67:292–304PubMedCrossRefPubMedCentralGoogle Scholar
  24. Cho A, Ratliff C, Sampath A, Weiland J (2016) Changes in ganglion cell physiology during retinal degeneration influence excitability by prosthetic electrodes. J Neural Eng 13:025001PubMedPubMedCentralCrossRefGoogle Scholar
  25. Chua J, Nivison-Smith L, Fletcher EL, Trenholm S, Awatramani GB, Kalloniatis M (2013) Early remodeling of Muller cells in the rd/rd mouse model of retinal dystrophy. J Comp Neurol 521:2439–2453PubMedCrossRefPubMedCentralGoogle Scholar
  26. Cottaris NP, Elfar SD, Iezzi R, Abrams GW (2005) How the retinal network reacts to epiretinal stimulation to form the prosthetic visual input to the cortex: computational modeling of a degenerated retina. Invest Ophthalmol Vis Sci 46:S74–S90Google Scholar
  27. Curlander JC, Marmarelis VZ (1987) A linear spatiotemporal model of the light-to-bipolar cell system and its response characteristics to moving bars. Biol Cybern 57:357–363PubMedCrossRefPubMedCentralGoogle Scholar
  28. Dokos S, Suaning GJ, Lovell NH (2005) A bidomain model of epiretinal stimulation. IEEE Trans Neural Syst Rehabil Eng 13:137–146PubMedCrossRefPubMedCentralGoogle Scholar
  29. Dreosti E, Esposti F, Baden T, Lagnado L (2011) In vivo evidence that retinal bipolar cells generate spikes modulated by light. Nat Neurosci 14:951–952PubMedPubMedCentralCrossRefGoogle Scholar
  30. Enciso G, Rempe M, Dmitriev AV, Gavrikov KE, Terman D, Mangel SC (2010) A model of direction selectivity in the starburst amacrine cell network. J Comput Neurosci 28:567–578PubMedPubMedCentralCrossRefGoogle Scholar
  31. Felsen G, Dan Y (2005) A natural approach to studying vision. Nat Neurosci 8:1643–1646PubMedCrossRefPubMedCentralGoogle Scholar
  32. Fohlmeister JF (2009) A nerve model of greatly increased energy-efficiency and encoding flexibility over the Hodgkin-Huxley model. Brain Res 1296:225–233PubMedPubMedCentralCrossRefGoogle Scholar
  33. Fohlmeister JF, Miller RF (1997a) Impulse encoding mechanisms of ganglion cells in the tiger salamander retina. J Neurophysiol 78:1935–1947PubMedCrossRefPubMedCentralGoogle Scholar
  34. Fohlmeister JF, Miller RF (1997b) Mechanisms by which cell geometry controls repetitive impulse firing in retinal ganglion cells. J Neurophysiol 78:1948–1964PubMedCrossRefPubMedCentralGoogle Scholar
  35. Fohlmeister JF, Coleman PA, Miller RF (1990) Modeling the repetitive firing of retinal ganglion cells. Brain Res 510:343–345PubMedCrossRefPubMedCentralGoogle Scholar
  36. Fohlmeister JF, Cohen ED, Newman EA (2010) Mechanisms and distribution of ion channels in retinal ganglion cells: using temperature as an independent variable. J Neurophysiol 103:1357–1374PubMedPubMedCentralCrossRefGoogle Scholar
  37. Freed MA (2000) Parallel cone bipolar pathways to a ganglion cell use different rates and amplitudes of quantal excitation. J Neurosci 20:3956–3963PubMedPubMedCentralCrossRefGoogle Scholar
  38. Freed M (2001) Parallel cone bipolar pathways to a ganglion cell use different rates and amplitudes of quantal excitations. Invest Ophthalmol Vis Sci 42:S519–S519Google Scholar
  39. Freed MA, Smith RG, Sterling P (1992) Computational model of the on-alpha ganglion-cell receptive-field based on bipolar cell circuitry. Proc Natl Acad Sci U S A 89:236–240PubMedPubMedCentralCrossRefGoogle Scholar
  40. Freeman DK, Rizzo JF, Fried SI (2011) Encoding visual information in retinal ganglion cells with prosthetic stimulation. J Neural Eng 8:035005PubMedPubMedCentralCrossRefGoogle Scholar
  41. Fried SI, Munch TA, Werblin FS (2002) Mechanisms and circuitry underlying directional selectivity in the retina. Nature 420:411–414PubMedCrossRefPubMedCentralGoogle Scholar
  42. Gollisch T, Meister M (2010) Eye smarter than scientists believed: neural computations in circuits of the retina. Neuron 65:150–164PubMedPubMedCentralCrossRefGoogle Scholar
  43. Greenberg RJ, Velte TJ, Humayun MS, Scarlatis GN, De Juan E, Jr. (1999) A computational model of electrical stimulation of the retinal ganglion cell. IEEE Trans Biomed Eng 46:505–514PubMedCrossRefPubMedCentralGoogle Scholar
  44. Guo T, Tsai D, Suaning GJ, Lovell NH, Dokos S (2012) Modeling normal and rebound excitation in mammalian retinal ganglion cells. Conf Proc IEEE Eng Med Biol Soc 2012:5506–5509PubMedPubMedCentralGoogle Scholar
  45. Guo T, Tsai D, Morley JW, Suaning GJ, Lovell NH, Dokos S (2013a) Cell-specific modeling of retinal ganglion cell electrical activity. Conf Proc IEEE Eng Med Biol Soc 2013:6539–6542PubMedPubMedCentralGoogle Scholar
  46. Guo T, Tsai D, Morley JW, Suaning GJ, Lovell NH, Dokos S (2013b) Influence of cell morphology in a computational model of ON and OFF retinal ganglion cells. Conf Proc IEEE Eng Med Biol Soc 2013:4553–4556PubMedPubMedCentralGoogle Scholar
  47. Guo T, Tsai D, Sovilj S, Morley JW, Suaning GJ, Lovell NH, Dokos S (2013c) Influence of active dendrites on firing patterns in a retinal ganglion cell model. Conf Proc IEEE Eng Med Biol Soc 2013:4557–4560PubMedPubMedCentralGoogle Scholar
  48. Guo T, Yang CY, Tsai D, Muralidharan M, Suaning GJ, Morley JW, Dokos S, Lovell NH (2018) Closed-loop efficient searching of optimal electrical stimulation parameters for preferential excitation of retinal ganglion cells. Front Neurosci 12:168PubMedPubMedCentralCrossRefGoogle Scholar
  49. Guo T, Tsai D, Yang CY, Al Abed A, Twyford P, Fried SI (2019) Mediating retinal ganglion cell spike rates using high-frequency electrical stimulation. Front Neurosci 13:413PubMedPubMedCentralCrossRefGoogle Scholar
  50. Halupka KJ, Shivdasani MN, Cloherty SL, Grayden DB, Wong YT, Burkitt AN, Meffin H (2017) Prediction of cortical responses to simultaneous electrical stimulation of the retina. J Neural Eng 14:016006PubMedCrossRefPubMedCentralGoogle Scholar
  51. Hamer RD, Nicholas SC, Tranchina D, Lamb TD, Jarvinen JLP (2005) Toward a unified model of vertebrate rod phototransduction. Vis Neurosci 22:417–436PubMedPubMedCentralCrossRefGoogle Scholar
  52. Hennig MH, Worgotter F (2007) Effects of fixational eye movements on retinal ganglion cell responses: a modelling study. Front Comput Neurosci 1.  https://doi.org/10.3389/Neuro.10/002.2007
  53. Hennig MH, Funke K, Worgotter F (2002) The influence of different retinal subcircuits on the nonlinearity of ganglion cell behavior. J Neurosci 22:8726–8738PubMedPubMedCentralCrossRefGoogle Scholar
  54. Henriquez CS (1993) Simulating the electrical behavior of cardiac tissue using the Bidomain model. Crit Rev Biomed Eng 21:1–77PubMedPubMedCentralGoogle Scholar
  55. Herrmann R, Heflin SJ, Hammond T, Lee B, Wang J, Gainetdinov RR, Caron MG, Eggers ED, Frishman LJ, McCall MA, Arshavsky VY (2011) Rod vision is controlled by dopamine-dependent sensitization of rod bipolar cells by GABA. Neuron 72:101–110PubMedPubMedCentralCrossRefGoogle Scholar
  56. Herz AVM, Gollisch T, Machens CK, Jaeger D (2006) Modeling single-neuron dynamics and computations: a balance of detail and abstraction. Science 314:80–85PubMedCrossRefPubMedCentralGoogle Scholar
  57. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544PubMedPubMedCentralCrossRefGoogle Scholar
  58. Hood DC, Shady S, Birch DG (1993) Heterogeneity in retinal disease and the computational model of the human-rod response. J Opt Soc Am A 10:1624–1630PubMedCrossRefPubMedCentralGoogle Scholar
  59. Hosoya T, Baccus SA, Meister M (2005) Dynamic predictive coding by the retina. Nature 436:71–77PubMedCrossRefPubMedCentralGoogle Scholar
  60. Jackman SL, Babai N, Chambers JJ, Thoreson WB, Kramer RH (2011) A positive feedback synapse from retinal horizontal cells to cone photoreceptors. PLoS Biol 9:e1001057PubMedPubMedCentralCrossRefGoogle Scholar
  61. Jeng J, Tang S, Molnar A, Desai NJ, Fried SI (2011) The sodium channel band shapes the response to electric stimulation in retinal ganglion cells. J Neural Eng 8:036022PubMedPubMedCentralCrossRefGoogle Scholar
  62. Joarder SA, Abramian M, Suaning GJ, Lovell NH, Dokos S (2011) A continuum model of retinal electrical stimulation. J Neural Eng 8:066006PubMedCrossRefPubMedCentralGoogle Scholar
  63. Jones BW, Marc RE (2005) Retinal remodeling during retinal degeneration. Exp Eye Res 81:123–137PubMedCrossRefPubMedCentralGoogle Scholar
  64. Juusola M, Weckstrom M, Uusitalo RO, Korenberg MJ, French AS (1995) Nonlinear models of the first synapse in the light-adapted fly retina. J Neurophysiol 74:2538–2547PubMedCrossRefPubMedCentralGoogle Scholar
  65. Kalloniatis M, Nivison-Smith L, Chua J, Acosta ML, Fletcher EL (2016) Using the rd1 mouse to understand functional and anatomical retinal remodelling and treatment implications in retinitis pigmentosa: a review. Exp Eye Res 150:106–121PubMedCrossRefPubMedCentralGoogle Scholar
  66. Kameneva T, Meffin H, Burkitt AN (2011) Modelling intrinsic electrophysiological properties of ON and OFF retinal ganglion cells. J Comput Neurosci 31:547–561PubMedCrossRefPubMedCentralGoogle Scholar
  67. Kameneva T, Maturana MI, Hadjinicolaou AE, Cloherty SL, Ibbotson MR, Grayden DB, Burkitt AN, Meffin H (2016) Retinal ganglion cells: mechanisms underlying depolarization block and differential responses to high frequency electrical stimulation of ON and OFF cells. J Neural Eng 13:016017PubMedCrossRefPubMedCentralGoogle Scholar
  68. Kamiyama Y, Ogura T, Usui S (1996) Ionic current model of the vertebrate rod photoreceptor. Vis Res 36:4059–4068PubMedCrossRefPubMedCentralGoogle Scholar
  69. Keat J, Reinagel P, Reid RC, Meister M (2001) Predicting every spike: a model for the responses of visual neurons. Neuron 30:803–817PubMedCrossRefPubMedCentralGoogle Scholar
  70. Klaassen LJ, Sun ZY, Steijaert MN, Bolte P, Fahrenfort I, Sjoerdsma T, Klooster J, Claassen Y, Shields CR, Ten Eikelder HMM, Janssen-Bienhold U, Zoidl G, McMahon DG, Kamermans M (2011) Synaptic transmission from horizontal cells to cones is impaired by loss of connexin hemichannels. PLoS Biol 9:e1001107PubMedPubMedCentralCrossRefGoogle Scholar
  71. Kourennyi DE, Liu XD, Hart J, Mahmud F, Baldridge WH, Barnes S (2004) Reciprocal modulation of calcium dynamics at rod and cone photoreceptor synapses by nitric oxide. J Neurophysiol 92:477–483PubMedCrossRefPubMedCentralGoogle Scholar
  72. Lamb TD, Pugh EN Jr (1992) A quantitative account of the activation steps involved in phototransduction in amphibian photoreceptors. J Physiol 449:719–758PubMedPubMedCentralCrossRefGoogle Scholar
  73. Lee SC, Ishida AT (2007) Ih without Kir in adult rat retinal ganglion cells. J Neurophysiol 97:3790–3799PubMedPubMedCentralCrossRefGoogle Scholar
  74. Loizos K, Lazzi G, Lauritzen JS, Anderson J, Jones BW, Marc R (2014) A multi-scale computational model for the study of retinal prosthetic stimulation. Conf Proc IEEE Eng Med Biol Soc 2014:6100–6103Google Scholar
  75. Loizos K, Ramrakhyani AK, Anderson J, Marc R, Lazzi G (2016) On the computation of a retina resistivity profile for applications in multi-scale modeling of electrical stimulation and absorption. Phys Med Biol 61:4491–4505PubMedPubMedCentralCrossRefGoogle Scholar
  76. Loizos K, Marc R, Humayun M, Anderson JR, Jones BW, Lazzi G (2018) Increasing electrical stimulation efficacy in degenerated retina: stimulus waveform design in a multiscale computational model. IEEE Trans Neural Syst Rehabil Eng 26:1111–1120PubMedPubMedCentralCrossRefGoogle Scholar
  77. Luo YH, Da Cruz L (2014) A review and update on the current status of retinal prostheses (bionic eye). Br Med Bull 109:31–44PubMedCrossRefPubMedCentralGoogle Scholar
  78. Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382:363–366PubMedCrossRefPubMedCentralGoogle Scholar
  79. Marc RE, Jones BW, Watt CB, Anderson JR, Sigulinsky C, Lauritzen S (2013) Retinal connectomics: towards complete, accurate networks. Prog Retin Eye Res 37:141–162PubMedPubMedCentralCrossRefGoogle Scholar
  80. Margolis DJ, Detwiler PB (2011) Cellular origin of spontaneous ganglion cell spike activity in animal models of retinitis pigmentosa. J Ophthalmol 2011:pii: 507037Google Scholar
  81. Martinek J, Stickler Y, Reichel M, Mayr W, Rattay F (2008) A novel approach to simulate Hodgkin-Huxley-like excitation with COMSOL multiphysics. Artif Organs 32:614–619PubMedCrossRefPubMedCentralGoogle Scholar
  82. Masland RH (2001) The fundamental plan of the retina. Nat Neurosci 4:877–886PubMedCrossRefPubMedCentralGoogle Scholar
  83. Masland RH (2012) The neuronal organization of the retina. Neuron 76:266–280PubMedPubMedCentralCrossRefGoogle Scholar
  84. Matteucci PB, Chen SC, Tsai D, Dodds CWD, Dokos S, Morley JW, Lovell NH, Suaning GJ (2013) Current steering in retinal stimulation via a quasimonopolar stimulation paradigm. Invest Ophthalmol Vis Sci 54:4307–4320PubMedCrossRefPubMedCentralGoogle Scholar
  85. Maturana MI, Kameneva T, Burkitt AN, Meffin H, Grayden DB (2013) The effect of morphology upon electrophysiological responses of retinal ganglion cells: simulation results. J Comput Neurosci.  https://doi.org/10.1007/s10827-013-0463-7PubMedPubMedCentralCrossRefGoogle Scholar
  86. Maturana MI, Apollo NV, Garrett DJ, Kameneva T, Cloherty SL, Grayden DB, Burkitt AN, Ibbotson MR, Meffin H (2018) Electrical receptive fields of retinal ganglion cells: influence of presynaptic neurons. PLoS Comput Biol 14:e1005997PubMedPubMedCentralCrossRefGoogle Scholar
  87. McCormick DA, Shu Y, Yu Y (2007) Neurophysiology: Hodgkin and Huxley model – still standing? Nature 445:1060–1063CrossRefGoogle Scholar
  88. Mennerick S, Zenisek D, Matthews G (1997) Static and dynamic membrane properties of large-terminal bipolar cells from goldfish retina: experimental test of a compartment model. J Neurophysiol 78:51–62PubMedCrossRefPubMedCentralGoogle Scholar
  89. Miller RF, Stenback K, Henderson D, Sikora M (2002) How voltage-gated ion channels alter the functional properties of ganglion and amacrine cell dendrites. Arch Ital Biol 140:347–359PubMedPubMedCentralGoogle Scholar
  90. Miller RF, Staff NP, Velte TJ (2006) Form and function of ON-OFF amacrine cells in the amphibian retina. J Neurophysiol 95:3171–3190PubMedCrossRefPubMedCentralGoogle Scholar
  91. Nivison-Smith L, Sun D, Fletcher EL, Marc RE, Kalloniatis M (2013) Mapping kainate activation of inner neurons in the rat retina. J Comp Neurol 521:2416–2438PubMedPubMedCentralCrossRefGoogle Scholar
  92. O’Brien BJ, Isayama T, Richardson R, Berson DM (2002) Intrinsic physiological properties of cat retinal ganglion cells. J Physiol 538:787–802PubMedPubMedCentralCrossRefGoogle Scholar
  93. Oesch N, Euler T, Taylor WR (2005) Direction-selective dendritic action potentials in rabbit retina. Neuron 47:739–750PubMedCrossRefPubMedCentralGoogle Scholar
  94. Ogura T, Satoh TO, Usui S, Yamada M (2003) A simulation analysis on mechanisms of damped oscillation in retinal rod photoreceptor cells. Vis Res 43:2019–2028PubMedCrossRefPubMedCentralGoogle Scholar
  95. Pillow JW, Paninski L, Uzzell VJ, Simoncelli EP, Chichilnisky EJ (2005) Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model. J Neurosci 25:11003–11013PubMedPubMedCentralCrossRefGoogle Scholar
  96. Pillow JW, Shlens J, Paninski L, Sher A, Litke AM, Chichilnisky EJ, Simoncelli EP (2008) Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature 454:995–U37PubMedPubMedCentralCrossRefGoogle Scholar
  97. Poznanski RR (1992) Modelling the electrotonic structure of starburst amacrine cells in the rabbit retina: a functional interpretation of dendritic morphology. Bull Math Biol 54:905–928PubMedCrossRefPubMedCentralGoogle Scholar
  98. Publio R, Oliveira RF, Roquea AC (2006) A realistic model of rod photoreceptor for use in a retina network model. Neurocomputing 69:1020–1024CrossRefGoogle Scholar
  99. Publio R, Oliveira RF, Roque AC (2009) A computational study on the role of gap junctions and rod I-h conductance in the enhancement of the dynamic range of the retina. PLoS One 4:e6970PubMedPubMedCentralCrossRefGoogle Scholar
  100. Publio R, Ceballos CC, Roque AC (2012) Dynamic range of vertebrate retina ganglion cells: importance of active dendrites and coupling by electrical synapses. PLoS One 7:e48517PubMedPubMedCentralCrossRefGoogle Scholar
  101. Qin W, Hadjinicolaou A, Grayden DB, Meffin H, Burkitt AN, Ibbotson MR, Kameneva T (2017) Single-compartment models of retinal ganglion cells with different electrophysiologies. Network 28:74–93PubMedCrossRefPubMedCentralGoogle Scholar
  102. Rattay F, Resatz S (2004) Effective electrode configuration for selective stimulation with inner eye prostheses. IEEE Trans Biomed Eng 51:1659–1664PubMedCrossRefPubMedCentralGoogle Scholar
  103. Rattay F, Resatz S, Lutter P, Minassian K, Jilge B, Dimitrijevic MR (2003) Mechanisms of electrical stimulation with neural prostheses. Neuromodulation 6:42–56PubMedCrossRefPubMedCentralGoogle Scholar
  104. Resatz S, Rattay F (2004) A model for the electrically stimulated retina. Math Comput Model Dyn Syst 10:93–106CrossRefGoogle Scholar
  105. Ristanovic D, Milosevic NT, Jelinek HF, Stefanovic IB (2009) Mathematical modelling of neuronal dendritic branching patterns in two dimensions: application to retinal ganglion cells in the cat and rat. Biol Cybern 100:97–108PubMedCrossRefPubMedCentralGoogle Scholar
  106. Robson JG, Frishman LJ (1995) Response linearity and kinetics of the cat retina: the bipolar cell component of the dark-adapted electroretinogram. Vis Neurosci 12:837–850PubMedCrossRefPubMedCentralGoogle Scholar
  107. Robson JG, Frishman LJ (1996) Photoreceptor and bipolar-cell contributions to the cat electroretinogram: A kinetic model for the early part of the flash response. J Opt Soc Am A Opt Image Sci Vis 13:613–622PubMedCrossRefPubMedCentralGoogle Scholar
  108. Rockhill RL, Daly FJ, Macneil MA, Brown SP, Masland RH (2002) The diversity of ganglion cells in a mammalian retina. J Neurosci 22:3831–3843PubMedPubMedCentralCrossRefGoogle Scholar
  109. Roska B, Meister M (2014) The retina dissects visual scenes into distinct features. In: Werner JS, Chalupa LM (eds) The new visual neurosciences. MIT Press, LondonGoogle Scholar
  110. Roth BJ, Wikswo JP (1994) Electrical-stimulation of cardiac tissue – a Bidomain model with active membrane-properties. IEEE Trans Biomed Eng 41:232–240PubMedCrossRefPubMedCentralGoogle Scholar
  111. Saglam M, Hayashida Y, Murayama N (2009) A retinal circuit model accounting for wide-field amacrine cells. Cogn Neurodyn 3:25–32PubMedCrossRefPubMedCentralGoogle Scholar
  112. Schachter MJ, Oesch N, Smith RG, Taylor WR (2010) Dendritic spikes amplify the synaptic signal to enhance detection of motion in a simulation of the direction-selective ganglion cell. PLoS Comput Biol 6:e1000899PubMedPubMedCentralCrossRefGoogle Scholar
  113. Schiefer MA, Grill WM (2006) Sites of neuronal excitation by epiretinal electrical stimulation. IEEE Trans Neural Syst Rehabil Eng 14:5–13PubMedCrossRefPubMedCentralGoogle Scholar
  114. Shah S, Levine MD (1996a) Visual information processing in primate cone pathways. I. A model. IEEE Trans Syst Man Cybern B Cybern 26:259–274PubMedCrossRefPubMedCentralGoogle Scholar
  115. Shah S, Levine MD (1996b) Visual information processing in primate cone pathways. II. Experiments. IEEE Trans Syst Man Cybern B Cybern 26:275–289PubMedCrossRefPubMedCentralGoogle Scholar
  116. Sheasby BW, Fohlmeister JF (1999) Impulse encoding across the dendritic morphologies of retinal ganglion cells. J Neurophysiol 81:1685–1698PubMedCrossRefPubMedCentralGoogle Scholar
  117. Shirahata T (2008) Simulation of rabbit A-type retinal horizontal cell that generates repetitive action potentials. Neurosci Lett 439:116–118PubMedCrossRefPubMedCentralGoogle Scholar
  118. Shirahata T (2011) The effect of variations in sodium conductances on pacemaking in a dopaminergic retinal neuron model. Acta Biol Hung 62:211–214PubMedCrossRefPubMedCentralGoogle Scholar
  119. Sivyer B, Williams SR (2013) Direction selectivity is computed by active dendritic integration in retinal ganglion cells. Nat Neurosci 16:1848–1856PubMedCrossRefPubMedCentralGoogle Scholar
  120. Smith RG (1995) Simulation of an anatomically defined local circuit: the cone-horizontal cell network in cat retina. Vis Neurosci 12:545–561PubMedCrossRefPubMedCentralGoogle Scholar
  121. Smith RG, Vardi N (1995) Simulation of the Aii Amacrine cell of mammalian retina – functional consequences of electrical coupling and regenerative membrane-properties. Vis Neurosci 12:851–860PubMedCrossRefPubMedCentralGoogle Scholar
  122. Smith RG, Freed MA, Sterling P (1986) Microcircuitry of the dark-adapted cat retina – functional architecture of the rod cone network. J Neurosci 6:3505–3517PubMedPubMedCentralCrossRefGoogle Scholar
  123. Steffen MA, Seay CA, Amini B, Cai YD, Feigenspan A, Baxter DA, Marshak DW (2003) Spontaneous activity of dopaminergic retinal neurons. Biophys J 85:2158–2169PubMedPubMedCentralCrossRefGoogle Scholar
  124. Tabata T, Ishida AT (1996) Transient and sustained depolarization of retinal ganglion cells by Ih. J Neurophysiol 75:1932–1943PubMedCrossRefPubMedCentralGoogle Scholar
  125. Taylor GC, Coles JA, Eilbeck JC (1995) Mathematical-modeling of weakly nonlinear pulses in a retinal neuron. Chaos, Solitons Fractals 5:407–413CrossRefGoogle Scholar
  126. Teeters J, Jacobs A, Werblin F (1997) How neural interactions form neural responses in the salamander retina. J Comput Neurosci 4:5–27PubMedCrossRefPubMedCentralGoogle Scholar
  127. Traub RD, Contreras D, Cunningham MO, Murray H, Lebeau FE, Roopun A, Bibbig A, Wilent WB, Higley MJ, Whittington MA (2005) Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts. J Neurophysiol 93:2194–2232PubMedCrossRefPubMedCentralGoogle Scholar
  128. Trenholm S, Awatramani GB (2015) Origins of spontaneous activity in the degenerating retina. Front Cell Neurosci 9:277PubMedPubMedCentralCrossRefGoogle Scholar
  129. Tsai D, Chen S, Protti DA, Morley JW, Suaning GJ, Lovell NH (2012) Responses of retinal ganglion cells to extracellular electrical stimulation, from single cell to population: model-based analysis. PLoS One 7:e53357PubMedPubMedCentralCrossRefGoogle Scholar
  130. Tsai D, Morley JW, Suaning GJ, Lovell NH (2017) Survey of electrically evoked responses in the retina – stimulus preferences and oscillation among neurons. Sci Rep 7:13802PubMedPubMedCentralCrossRefGoogle Scholar
  131. Tukker JJ, Taylor WR, Smith RG (2004) Direction selectivity in a model of the starburst amacrine cell. Vis Neurosci 21:611–625PubMedCrossRefPubMedCentralGoogle Scholar
  132. Twyford P, Cai C, Fried S (2014) Differential responses to high-frequency electrical stimulation in ON and OFF retinal ganglion cells. J Neural Eng 11:025001PubMedPubMedCentralCrossRefGoogle Scholar
  133. Usui S, Mitarai G, Sakakibara M (1983) Discrete nonlinear reduction model for horizontal cell response in the carp retina. Vis Res 23:413–420PubMedCrossRefPubMedCentralGoogle Scholar
  134. Usui S, Ishihara A, Kamiyama Y, Ishii H (1996a) Ionic current model of bipolar cells in the lower vertebrate retina. Vis Res 36:4069–4076PubMedCrossRefPubMedCentralGoogle Scholar
  135. Usui S, Kamiyama Y, Ishii H, Ikeno H (1996b) Reconstruction of retinal horizontal cell responses by the ionic current model. Vis Res 36:1711–1719PubMedCrossRefPubMedCentralGoogle Scholar
  136. Vallerga S, Covacci R, Pottala EW (1980) Artificial cone responses – a computer-driven hardware model. Vis Res 20:453–457PubMedCrossRefPubMedCentralGoogle Scholar
  137. van Elburg RA, van Ooyen A (2010) Impact of dendritic size and dendritic topology on burst firing in pyramidal cells. PLoS Comput Biol 6:e1000781PubMedPubMedCentralCrossRefGoogle Scholar
  138. van Hateren JH, Snippe HP (2007) Simulating human cones from mid-mesopic up to high-photopic luminances. J Vis 7:1–11PubMedCrossRefPubMedCentralGoogle Scholar
  139. Velte TJ, Masland RH (1999) Action potentials in the dendrites of retinal ganglion cells. J Neurophysiol 81:1412–1417PubMedCrossRefPubMedCentralGoogle Scholar
  140. Velte TJ, Miller RF (1995) Dendritic integration in ganglion cells of the mudpuppy retina. Vis Neurosci 12:165–175PubMedCrossRefPubMedCentralGoogle Scholar
  141. Velte TJ, Miller RF (1997) Spiking and nonspiking models of starburst amacrine cells in the rabbit retina. Vis Neurosci 14:1073–1088PubMedCrossRefPubMedCentralGoogle Scholar
  142. Victor JD (1987) The dynamics of the cat retinal X-cell center. J Physiol 386:219–246PubMedPubMedCentralCrossRefGoogle Scholar
  143. Victor JD (1988) The dynamics of the cat retinal Y-cell subunit. J Physiol 405:289–320PubMedPubMedCentralCrossRefGoogle Scholar
  144. Vigh J, Banvolgyi T, Wilhelm M (2000) Amacrine cells of the anuran retina: morphology, chemical neuroanatomy, and physiology. Microsc Res Tech 50:373–383PubMedCrossRefPubMedCentralGoogle Scholar
  145. Werginz P, Fried SI, Rattay F (2014) Influence of the sodium channel band on retinal ganglion cell excitation during electric stimulation – a modeling study. Neuroscience 266:162–177PubMedPubMedCentralCrossRefGoogle Scholar
  146. Werginz P, Benav H, Zrenner E, Rattay F (2015) Modeling the response of ON and OFF retinal bipolar cells during electric stimulation. Vis Res 111:170–181PubMedCrossRefPubMedCentralGoogle Scholar
  147. Wohrer A, Kornprobst P (2009) Virtual retina: a biological retina model and simulator, with contrast gain control. J Comput Neurosci 26:219–249PubMedCrossRefPubMedCentralGoogle Scholar
  148. Wong RC, Cloherty SL, Ibbotson MR, O’Brien BJ (2012) Intrinsic physiological properties of rat retinal ganglion cells with a comparative analysis. J Neurophysiol 108:2008–2023PubMedCrossRefPubMedCentralGoogle Scholar
  149. Yang CY, Lukasiewicz P, Maguire G, Werblin FS, Yazulla S (1991) Amacrine cells in the tiger salamander retina: morphology, physiology, and neurotransmitter identification. J Comp Neurol 312:19–32PubMedCrossRefPubMedCentralGoogle Scholar
  150. Yang CY, Tsai D, Guo T, Dokos S, Suaning GJ, Morley JW, Lovell NH (2018) Differential electrical responses in retinal ganglion cell subtypes: effects of synaptic blockade and stimulating electrode location. J Neural Eng 15:046020PubMedCrossRefPubMedCentralGoogle Scholar
  151. Yin S, Lovell NH, Suaning GJ, Dokos S (2010) A continuum model of the retinal network and its response to electrical stimulation. Conf Proc IEEE Eng Med Biol Soc 2010:2077–2080PubMedPubMedCentralGoogle Scholar
  152. Yin S, Lovell NH, Suaning GJ, Dokos S (2011) Continuum model of light response in the retina. Conf Proc IEEE Eng Med Biol Soc 2011:908–911PubMedPubMedCentralGoogle Scholar
  153. Zhang YF, Kim IJ, Sanes JR, Meister M (2012) The most numerous ganglion cell type of the mouse retina is a selective feature detector. Proc Natl Acad Sci U S A 109:E2391–E2398PubMedPubMedCentralCrossRefGoogle Scholar

Authors and Affiliations

  1. 1.Graduate School of Biomedical EngineeringUniversity of New South WalesSydneyAustralia

Section editors and affiliations

  • Nigel H. Lovell
    • 1
  1. 1.Graduate School of Biomedical EngineeringUNSW AustraliaSydneyAustralia