This paper presents a structured model of the dielectric properties of the corneal tissue at microwave frequencies, based on the fine structure and chemical composition of its constituents. This is accomplished by appropriately combining the known properties of tissue substructures using mixing rules, in order to obtain the effective macroscopic properties of the medium. The presented approach is multi-scale: it begins from the microscopic scale and derives the macroscopic properties after several scale-steps. The predictions of the model agree with the existing measured data in the literature. Verification and analysis of the model sensitivity to input parameters has been presented. The model is expected to find application in non-invasive medical sensing where it can relate dielectric response to pathological structural changes in the tissue. The model is also useful for the prediction of dielectric properties for high-frequency computational dosimetry, and for understanding the physical mechanisms behind the macroscopic dielectric behaviour in general.
"A Theoretical Model for the Frequency-Dependent Dielectric Properties of Corneal Tissue at Microwave Frequencies," Progress In Electromagnetics Research,
Vol. 137, 389-406, 2013. doi:10.2528/PIER12112510
1. Huang, K., X. B. Xu, L. P. Yan, and M. Zhang, "A new noninvasive method for determining the conductivity of tissue embedded in multilayer biological structure," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 6, 851-860, 2002. doi:10.1163/156939302X00192
2. Surowiec, A. J., S. S. Stuchly, J. R. Barr, and A. Swarup, "Dielectric properties of breast carcinoma and the surrounding tissues," IEEE Transactions on Biomedical Engineering, Vol. 35, 257-263, 1988. doi:10.1109/10.1374
3. Yan, L. P., K. M. Huang, and C. J. Liu, "A noninvasive method for determining dielectric properties of layered tissues on human back," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 13, 1829-1843, 2007.
4. Gabriel, C., "Dielectric properties of body tissues in the frequency range 10 Hz - 100 GHz,", IFAC (L'Istituto di Fisica Applicata Nello Carrara") Website,-2010, Available at: Hyperlink, http://niremf.ifac.cnr.it/tissprop, Accessed February 1, 2012.
5. Klemm, M. and G. Troester, "EM energy absorption in the human body tissues due to UWB antennas," Progress In Electromagnetics Research, Vol. 62, 261-280, 2006. doi:10.2528/PIER06040601
6. Zhang, M. and A. Alden, "Calculation of whole-body sar from a 100MHz dipole antenna," Progress In Electromagnetics Research, Vol. 119, 133-153, 2011. doi:10.2528/PIER11052005
7. Mohsin, S. A., "Concentration of the specific absorption rate around deep brain stimulation electrodes during MRI," Progress In Electromagnetics Research, Vol. 121, 469-484, 2011. doi:10.2528/PIER11022402
8. Otin, R. and H. Gromat, "Specific absorption rate computations with a nodal-based finite element formulation," Progress In Electromagnetics Research, Vol. 128, 399-418, 2012.
9. Theilmann, P. T., M. A. Tassoudji, E. H. Teague, D. F. Kimball, and P. M. Asbeck, "Computationally e±cient model for UWB signal attenuation due to propagation in tissue for biomedical implants," Progress In Electromagnetics Research B, Vol. 38, 1-22, 2012.
10. Basar, M. R., M. F. B. A. Malek, K. M. Juni, M. I. M. Saleh, M. S. Idris, L. Mohamed, N. Saudin, N. A. Mohd Affendi, and A. Ali, "The use of a human body model to determine the variation of path losses in the human body channel in wireless capsule endoscopy," Progress In Electromagnetics Research, Vol. 133, 495-513, 2013.
11. Gabriel, C., "Compilation of the dielectric properties of body tissues at RF and microwave frequencies,", Final Report Prepared for AFOSR/NL, 1996.
12. Walker, D. C., B. H. Brown, R. H. Smallwood, D. R. Hose, and D. M. Jones, "Modelled current distribution in cervical squamous tissue," Physiol. Meas., Vol. 23, 159-168.
13. Huclova, S., D. Erni, and J. Frohlich, "Modelling and validation of dielectric properties of human skin in the MHz region focusing on skin layer morphology and material composition," J. Physics D: Applied Physics, Vol. 45, 025301, 2012. doi:10.1088/0022-3727/45/2/025301
14. Singh, R. S., P. Tewari, J. L. Bourges, J. P. Hubschman, D. B. Bennett, Z. D. Taylor, H. Lee, E. R. Brown, W. S. Grundfest, and M. O. Culjat, "Terahertz sensing of corneal hydration," Proc. 32nd Annumal Int'l Conf., IEEE EMBS, 2010.
15. Spathmann, O., T. Fiedler, V. Hansen, M. Saviz, J. Streckert, M. Zang, M. Clemens, K. Statnikov, and U. Pfeiffer, "Attempts for exposure assessment in the THz frequency range using numerical computations," Proc. EMC Europe, Rome, Italy, 2012.
16. Gabriel, C., S. Gabriel, and E. Corthout, "The dielectric properties of biological tissues: I. Literature survey," Phys. Med. Biol., Vol. 41, 2231-2249, 1996. doi:10.1088/0031-9155/41/11/001
17. Gabriel, S., R. W. Lau, and C. Gabriel, "The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues," Phys. Med. Biol., Vol. 41, 2271-2293, 1996. doi:10.1088/0031-9155/41/11/003
18. Peyman, A., S. Holden, and C. Gabriel, "Measurement of the dielectric properties of biological tissues in vivo at microwave frequencies,", Mobile Telecommunications and Health Research Programme, RUM 3, Final Report, 2005.
19. Gabriel, S., R. W. Lau, and C. Gabriel, "The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz," Phys. Med. Biol., Vol. 41, 2251-2256, 1996. doi:10.1088/0031-9155/41/11/002
20. Remington, L. A., Clinical Anatomy of the Visual System, 3rd Edition, Butterworth Heinemann, Ed., Elsevier, 2012.
21. Hayashi, S., T. Osawa, and K. Tohyama, "Comparative observations on corneas, with special reference to Bowman's layer and Descemet's membrane in mammals and amphibians," J. Morphol., Vol. 254, No. 3, 247-258, 2002. doi:10.1002/jmor.10030
22. Kadler, K. E., D. F. Holmes, J. A. Trotter, and J. A. Chapman, "Collagen fibril formation," Biochem. J., Vol. 316, 1-11, 1996.
23. Hahnel, C., S. Somodi, D. G. Weiss, and R. F. Guthoff, "The keratocyte network of human cornea: A three-dimensional study using confocal laser scanning fluorescence microscopy," Cornea, Vol. 19, No. 2, 185-193, 2000. doi:10.1097/00003226-200003000-00012
24. Almubrad, T. and S. Akhtar, "Structure of corneal layers, collagen fibrils, and proteoglycans of tree shrew cornea," J. Molecular Vision, Vol. 17, 2283-2291, 2011.
25. Boote, C., S. Hayes, M. Abahussin, and K. M. Meek, "Mapping collagen organization in the human cornea: Left and right eyes are structurally distinct," IOVS, Vol. 47, 901-908, 2006.
26. Meek, K. M. and D. W. Leonard, "Ultrastructure of the corneal stroma: A comparative study," Biophys. J., Vol. 64, 273-280, 1993. doi:10.1016/S0006-3495(93)81364-X
27. Kim, J. H., K. Green, M. Martinez, and D. Paton, "Solute permeability of the corneal endothelium and Descemet's membrane," Exp. Eye Res., Vol. 12, 231-238, 1971. doi:10.1016/0014-4835(71)90143-6
28. Sihvola, A., "Mixing rules with complex dielectric coefficients," Subsurface Sensing Technologies and Applications, Vol. 1, 393-415, 2000. doi:10.1023/A:1026511515005
29. Gimsa, J., T. Muller, T. Schnelle, and G. Fuhr, "Dielectric spectroscopy of single human erythrocytes at physiological ionic strength: Dispersion of the cytoplasm," Biochem. J., Vol. 71, 495-506, 1996.
30. Wei, Y. Z. and S. Sridhar, "Dielectric spectroscopy up to 20 GHz of LiCl/H2O solutions," J. Chem. Phys., Vol. 92, 923-928, 1990. doi:10.1063/1.458074
31. Grant, H. E., "The dielectric method of investigating bound water in biological material: An appraisal of the technique," Bioelectromagnetics, Vol. 3, 17-24, 1982. doi:10.1002/bem.2250030106
32. Pekonen, O., K. Karkkainen, A. Sihvola, and K. Nikoskinen, "Numerical testing of dielectric mixing rules by FDTD method," Journal of Electromagnetic Waves and Applications, Vol. 13, No. 1, 67-87, 1999. doi:10.1163/156939399X01618
34. Peyman, A. and C. Gabriel, "Cole-Cole parameters for the dielectric properties of porcine tissues as a function of age at microwave frequencies," Phys. Med. Biol., Vol. 55, N413-N419, 2010. doi:10.1088/0031-9155/55/15/N02
35. Dawkins, A. W. J., C. Gabriel, R. J. Sheppard, and E. H. Grant, "Electrical properties of lens material at microwave frequencies," Phys. Med. Biol., Vol. 26, 1-9, 1981. doi:10.1088/0031-9155/26/1/002
36. Pottel, R., D. Adolph, and U. Kaatze, "Dielectric relaxation in aqueous solutions of some dipolar organic molecules," Berichte der Bunsengesellschaft fÄur physikalische Chemie, Vol. 79, 278-285, 1975. doi:10.1002/bbpc.19750790308
37. Kaatze, U., "On the existence of bound water in biological systems as probed by dielectric spectroscopy," Phys. Med. Biol., Vol. 35, 1663, 1990. doi:10.1088/0031-9155/35/12/006
38. Jay, L., A. Brocas, K. Singh, J. C. Kieffer, I. Brunette, and T. Ozaki, "Determination of porcine corneal layers with high spatial resolution by simultaneous second and third harmonic generation microscopy," Optics Expres., Vol. 16, 16284-16293, 2008. doi:10.1364/OE.16.016284
39. Michelacci, Y. M., "Collagens and proteoglycans of the corneal extracellular matrix," Brazillian J. of Medical and Biological Research, Vol. 36, 1037-1046, 2003. doi:10.1590/S0100-879X2003000800009
40. Leonard, D. W. and K. M. Meek, "Refractive indices of the collagen fibrils and extrafibrillar material of the corneal stroma," Biophys. J., Vol. 72, 1382-1387, 1997. doi:10.1016/S0006-3495(97)78784-8
41. Ameen, D. B., M. F. Bishop, and T. McMullen, "A lattice model for computing the transmissivity of the cornea and sclera," Biophys. J., Vol. 75, 2520-2531, 1998. doi:10.1016/S0006-3495(98)77697-0
42. Hahnel, C., S. Somodi, C. Slowik, D. G. Weiss, and R. F. Guthoff, "Fluorescence microscopy and three-dimensional imaging of the porcine corneal keratocyte network," Graefe's Arch. Clin. Exp. Ophthalmol., Vol. 235, 773-779, 1997. doi:10.1007/BF02332862
43. Liebe, H. J., G. A. Hufford, and T. Manabe, "A model for the complex permittivity of water at frequencies below 1 THz," Int'l J. Infrared and Millimeter Waves, Vol. 12, 659-675, 1991. doi:10.1007/BF01008897
44. Simeonova, M. and J. Gimsa, "The influence of the molecular structure of lipid membranes on the electric field distribution and energy absorption," Bioelectromagnetics, Vol. 27, 652-666, 2006. doi:10.1002/bem.20259
45. Doughty, M. J., W. Seabert, J. P. G. Bergmanson, and and, "A Descriptive and qualitative study of keratocytes of the corneal stroma of albino rabbits using transmission electron microscopy," Tissues and Cells, Vol. 33, 408-412, 2001. doi:10.1054/tice.2001.0195
46. Piersol, G. A., "Eye: Cornea," Human Anatomy, Including Structure and Development and Practical Considerations, Vol. II, 1913:1450, J. B. Lippincott Company, Philadelphia, 1919.