volume | PIER Journals

Abstract

New electromagnetic models for the rods and cones that are the photoreceptors at the back of the retina are developed and simulated in order to explain the roles of dimension, geometrical structure, directional sensitivity and visual pigments of the photoreceptors in the reception of visible light. The rods and cones are modeled as uniform and quasi-tapered helical antennas, respectively. The results of the model study show that if the model antennas have the original photoreceptor cell dimensions, the frequency responses of the model antennas and the spectral sensitivities of the photoreceptors would be very close to each other. In addition, it's observed that the spectral sensitivities of L, M and S cones are broadband over the visible light spectrum, and there are secondary peaks beside main peaks in the spectral sensitivity curves of the cones, because of the conical shape of the cones. It's also observed that there is only one main peak in the spectral sensitivity curves of the rods, because of the uniform and cylindrical shape of the rods. Finally, an array of the novel modeled antennas is also discussed to be used in biomedical applications of artificial retinal photoreceptors in medicine, although the main scope is not designing artificial retinal photoreceptor prosthesis.

1. Sheppard, J. J., Human Color Perception: A Critical Study of the Experimental Foundation, American Elsevier, 1968.

2. Tessier-Lavigne, M., "Phototransduction and information processing in the retina," Principles of Neural Science Prentice-Hall, Connecticut, 3 edition, E. R. Kandel, J. H. Schwartz, and T. M. Jessell (eds.), Prentice-Hall, Connecticut, 1991.

3. Wassle, H., "Colour vision --- A patchwork of cones," Nature, Vol. 397, No. 6719, 473-475, 1999.
doi:10.1038/17216

4. Feynman, R. P., R. B. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. 1, Chapter 35, 36, Addison-Wesley, 1989.

5. Baylor, D., "Transduction in retinal photoreceptor cells," Sensory Transduction: Society of General Physiologists --- 45th Annual Symposium, Vol. 47, D. P. Corey and S. D. Roper, Rockefeller University Press, New York, 1992.

6. Young, T., "The Bakerian lecture: On the theory of light and colours," Philosophical Trans. Roy. Soc. Lond., Vol. 92, 12-48, 1802.
doi:10.1098/rstl.1802.0004

7. Rushton, W. A. H., "A cone pigment in the protanope," J. Physiol., Vol. 168, No. 2, 345-359, 1963.

8. Marks, W. B., W. H. Dobelle, and E. F. Macnichol Jr., "Visual pigments of single primate cones," Science, Vol. 143, No. 3611, 1181-1182, 1964.
doi:10.1126/science.143.3611.1181

9. Baylor, D. A., B. J. Nunn, and J. L. Schnapf, "The photocurrent, noise and spectral sensitivity of rods of the monkey Macaca fascicularis," J. Physiol., Vol. 357, 575-607, December 1984.

10. Nathans, J., D. Thomas, and D. S. Hogness, "Molecular genetics of human color vision: Genes encoding blue, green, and red pigments," Science, Vol. 232, No. 4747, 193-202, 1986.
doi:10.1126/science.2937147

11. Nathans, J., T. P. Piantanida, R. L. Eddy, T. P. Shows, and D. S. Hogness, "Molecular genetics of inherited variation in human color vision," Science, Vol. 232, No. 4747, 203-210, 1986.
doi:10.1038/325439a0

12. Schnapf, J. L., T. W. Kraft, and D. A. Baylor, "Spectral sensitivity of human cone photoreceptors," Nature, Vol. 325, No. 6103, 439-441, 1987.
doi:10.1083/jcb.105.5.2267

13. Eckmiller, M. S., "Cone outer segment morphogenesis: Taper change and distal invaginations," J. Cell Biol., Vol. 105, No. 5, 2267-2277, 1987.

14. Palmer, S. E., Vision Science: Photons to Phenomenology, MIT Press, 1999.

15. Miller, D., The Wisdom of the Eye, Academic Press, 2000.
doi:10.1016/j.visres.2006.03.019

16. Roberts, N. W., "The optics of vertebrate photoreceptors: Anisotropy and form birefringence," Vision Res., Vol. 46, No. 19, 3259-3266, 2006.
doi:10.1016/S0042-6989(97)00151-X

17. Warrant, E. J. and D.-E. Nilsson, "Absorption of white light in photoreceptors," Vision Res., Vol. 38, No. 2, 195-207, 1998.

18. Kraus, J. D. and R. J. Marhefka, Antennas for All Applications, McGraw-Hill, 2002.

19. Enoch, J. M., "Nature of the transmission of energy in the retinal receptors," J. Opt. Soc. Am., Vol. 51, No. 10, 1122-1126, 1961.

20. Enoch, J. M., "Optical properties of the retinal receptors," J. Opt. Soc. Am., Vol. 53, No. 1, 71-85, 1963.
doi:10.1016/S0042-6989(97)00291-5

21. Pask, C. and A. Stacey, "Optical properties of retinal photoreceptors and the Campbell effect," Vision Res., Vol. 38, No. 7, 953-961, 1998.
doi:10.1109/TMAG.2007.915299

22. Hajiaboli, A. and M. Popovie, "FDTD analysis of light propagation in the human photoreceptor cells," IEEE Trans. Magnetics, Vol. 44, No. 6, 1430-1433, 2008.

23. Gouras, P., Principles of Neural Science, 3 Ed., E. R. Kandel, J. H. Schwartz, and T. M. Jessell (eds.), Prentice-Hall, 1991.

24. Wald, G., "Blue-blindness in the normal fovea," J. Opt. Soc. Am., Vol. 57, No. 11, 1289-1301, 1967.
doi:10.1016/S0042-6989(98)00029-7

25. Logvinenko, A. D., "On derivation of spectral sensitivities of the human cones from trichromatic colour matching functions," Vision Res., Vol. 38, No. 21, 3207-3211, 1998.
doi:10.1109/TAP.1982.1142897

26. Lee, K.-F., P.-F.Wong, and K.-F. Larm, "Theory of the frequency responses of uniform and quasi-taper helical antennas," IEEE Trans. Antennas Propag., Vol. 30, No. 5, 1017-1021, 1982.

27. Grand, Y. L., Light, Colour and Vision, Chapman & Hall, 1968.

28. Kraus, J. D. and D. A. Fleisch, Electromagnetics with Applications, McGraw-Hill, 1999.
doi:10.1088/0031-9155/41/11/003

29. Gabriel, C., S. Gabriel, and G. Corthout, "The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues," Phys. Med. Biol., Vol. 41, No. 11, 2271-2293, 1996.

30. Canbay, C., Anten ve Propagasyon I, Yeditepe University Press, 1997.
doi:10.2528/PIERB07102001

31. Challa, R. K., D. Kajfez, J. R. Gladden, A. Z. Elsherbeni, and V. Demir, "Permittivity measurement with a non-standard waveguide by using TRL calibration and fractional linear data fitting," Progress In Electromagnetics Research B, Vol. 2, 1-13, 2008.
doi:10.2528/PIER06111204

32. Kumar, A., S. Sharma, and G. Singh, "Measurement of dielectric constant and loss factor of the dielectric material at microwave frequencies," Progress In Electromagnetics Research, Vol. 69, 47-54, 2007.
doi:10.1109/TAP.1980.1142322

33. King, H. E. and J. L. Wong, "Characteristics of 1 to 8 wavelength uniform helical antennas," IEEE Trans. Antennas Propag., Vol. 28, No. 2, 291-296, 1980.

34. Emerson, D. T., "The gain of an axial-mode helix antenna," The ARRL Antenna Compendium, Vol. 4, 64-68, 1995.
doi:10.1109/JRPROC.1948.232289

35. Sinclair, G., "Theory of models of electromagnetic systems," Proc. IRE, Vol. 36, No. 11, 1364-1370, 1948.

36. Brindley, G. S., Physiology of the Retina and Visual Pathway, Camelot Press, 1970.

37. Holcman, D. and J. I. Korenbrot, "Longitudinal diffusion in retinal rod and cone outer segment cytoplasm: The consequence of cell structure," Biophysical Journal, Vol. 86, No. 4, 2566-2582, 2004.
doi:10.1109/TAP.1979.1142033

38. Wong, J. L. and H. E. King, "Broadband quasi-taper helical antennas," IEEE Trans. Antennas Propag., Vol. 27, No. 1, 72-78, 1979.
doi:10.1049/ip-map:19970977

39. Nakano, H., N. Ikeda, and J. Yamauchi, "Quadrifilar conical helical antenna with travelling-wave current distribution," IEE Proc. --- Microwaves, Antennas and Propag., Vol. 144, No. 1, 53-55, 1997.
doi:10.1109/8.982460

40. Dobbins, J. A. and R. L. Rogers, "Folded conical helix antenna," IEEE Trans. Antennas Propag., Vol. 49, No. 12, 1777-1781, 2001.
doi:10.1163/156939307779378835

41. Seluk, A. and B. Saka, "A general method for the analysis of curved wire antennas," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 175-188, 2007.

42. Zhang, Y., J.Wang, Z. Zhao, and J. Yang, "The analysis of LPDA using MoM and transmission matrix," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 12, 1621-1633, 2007.
doi:10.2528/PIERB07102702

43. Shafieha, J. H., J. Noorinia, and C. Ghobadi, "Probing the feed line parameters in Vivaldi Notch Antennas," Progress In Electromagnetics Research B, Vol. 1, 237-252, 2008.
doi:10.2528/PIERB07110802

44. Rajabi, M., M. Mohammadirad, and N. Komjani, "Simulation of ultra wideband microstrip antenna using EPML-TLM," Progress In Electromagnetics Research B, Vol. 2, 115-124, 2008.

45. Yu, Y. K. and J. Li, "Analysis of electrically small size conical antennas," Progress In Electromagnetics Research Letters, Vol. 1, 85-92, 2008.
doi:10.2528/PIERL07112302

46. Chen, Y.-L., C.-L. Ruan, and L. Peng, "A novel ultra-wideband bow-tie slot antenna in wireless communication systems," Progress In Electromagnetics Research Letters, Vol. 1, 101-108, 2008.

47. Gao, G.-P., X.-X. Yang, J.-S. Zhang, and J.-X. Xiao, "A printed volcano smoke antenna for UWB and WLAN communications," Progress In Electromagnetics Research Letters, Vol. 4, 55-61, 2008.
doi:10.1109/8.53486

48. Kraft, U. R. and G. Mnich, "Main-beam polarization properties of modified helical antennas," IEEE Trans. Antennas Propag., Vol. 38, No. 5, 589-597, 1990.

49. Blieske, U., T. Doege, P. Gayout, M. Neander, D. Neumann, and A. Prat, "Light-trapping in solar modules using extra-white textured glass," Proc. 3rd World Conference on Photovoltaic Energy Conversion , Vol. 1, 188-191, Osaka, May 2003.
doi:10.1038/223526a0

50. Snyder, A. W. and P. A. V. Hall, "Unification of electromagnetic effects in human retinal receptors with three pigment colour vision," Nature, Vol. 223, No. 5205, 526-528, 1969.

51. Enoch, J. M. and G. A. Fry, "Characteristics of a model retinal receptor studied at microwave frequencies," J. Opt. Soc. Am., Vol. 48, No. 12, 899-911, 1958.
doi:10.1109/5.104213

52. Oughstun, K. E., "Pulse propagation in a linear, causally dispersive medium," Proc. IEEE, Vol. 79, No. 10, 1379-1390, 1991.
doi:10.2528/PIER97050700

53. Hillion, P., "Electromagnetic pulses in dispersive media," ProgressIn Electromagnetics Research, Vol. 18, 245-260, 1998.
doi:10.2528/PIER99062802

54. Margetis, D., "Pulse propagation in sea water: The modulated pulse," Progress In Electromagnetics Research, Vol. 26, 89-110, 2000.

55. Koester, J., "Voltage-gated ion channels and the generation of the action potential," Principles of Neural Science, 3 edition, E. R. Kandel, J. H. Schwartz, and T. M. Jessell (eds.), Prentice-Hall, Connecticut, 1991.
doi:10.1016/S0042-6989(01)00043-8

56. Roorda, A., A. B. Metha, P. Lennie, and D. R. Williams, "Packing arrangement of the three cone classes in primate retina," Vision Res., Vol. 41, No. 10, 1291-1306, 2001.
doi:10.1038/17383

57. Roorda, A. and D. R. Williams, "The arrangement of the three cone classes in the living human eye," Nature, Vol. 397, No. 6719, 520-522, 1999.
doi:10.1016/S0960-9822(00)00632-1

58. Lennie, P., "Color vision: Putting it together," Curr. Biol., Vol. 10, No. 16, 589-591, 2000.

59. Balanis, C. A., Antenna Theory, Analysis and Design, John Wiley & Sons, 1997.
doi:10.1016/S0074-7696(08)60181-3

60. Mariani, A. P., "The neuronal organization of the outer plexiform layer of the primate retina," Int. Rev. Cytol., Vol. 86, 285-320, 1984.
doi:10.1002/cne.902550103

61. Ahnelt, P. K., H. Kolb, and R. Pflug, "Identification of a subtype of cone photoreceptor, likely to be blue sensitive, in the human retina," J. Comp. Neurol., Vol. 255, No. 1, 18-34, 1987.
doi:10.1016/S0960-9822(02)01345-3

62. Laughlin, S. B., "Retinal function: Coupling cones clarifies vision," Curr. Biol., Vol. 12, No. 24, 833-834, 2002.

63. Enoch, J. M., "Response of a model retinal receptor as a function of wavelength," J. Opt. Soc. Am., Vol. 50, No. 4, 315-320, 1960.

64. Enoch, J. M., "Summated response of the retina to light entering different parts of the pupil," J. Opt. Soc. Am., Vol. 48, No. 6, 392-405, 1958.
doi:10.1109/JRPROC.1955.278072

65. Sensiper, S., "Electromagnetic wave propagation on helical conductors," Proc. IRE, Vol. 43, No. 2, 149-161, 1955.
doi:10.1126/science.1067996

66. Zrenner, E., "Will retinal implants restore vision?," Science, Vol. 295, No. 5557, 1022-1025, 2002.
doi:10.1002/(SICI)1098-2760(20000120)24:2<106::AID-MOP8>3.0.CO;2-K

67. Dean, Jr., R. N., P. C. Nordine, and C. G. Christodoulou, "3-D helical THz antennas," Microw. Opt. Tech. Lett., Vol. 24, No. 2, 106-111, 2000.

68. Billiet, R. L. and H. T. Nguyen, Ceramic-embedded microelectromagnetic device and method of fabrication thereof, U.S. Patent, Patent No: 6 693601, 2004.
doi:10.1088/0957-4484/16/5/017

69. Alda, J., J. M. Rico-Garcia, J. M. Lopez-Alonzo, and G. Boreman, "Optical antennas for nano-photonic applications," Nanotechnology, Vol. 16, No. 5, 230-234, 2005.
doi:10.1016/j.exer.2004.02.003

70. Liang, F.-Q., L. Green, C. Wang, R. Alssadi, and B. F. Godley, "Melatonin protects human retinal pigment epithelial (RPE) cells against oxidative stress," Exp. Eye Res., Vol. 78, No. 6, 1069-1075, 2004.

71. Gurney, P. W. V., "Is our ‘inverted’ retina really ‘bad design’?," Technical Journal–in-depth Journal of Creation, Vol. 13, No. 1, 37-44, 1999.
doi:10.1088/0031-9155/47/16/303

72. Preece, S. J. and E. Claridge, "Monte Carlo modelling of the spectral reflectance of the human eye," Phys. Med. Biol., Vol. 47, No. 16, 2863-2877, 2002.

Dr. Cahit Canbay

Dr. İlhami Ünal