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Bulletin of mathematical biology
Feb 19, 2025;87 (4): 45.

Influence of Contact Lens Parameters on Tear Film Dynamics.

Darshan Ramasubramanian, Jos�� Luis Hern��ndez-Verdejo, Jos�� Manuel L��pez-Alonso
Author Information
  1. Darshan Ramasubramanian: Faculty of Optics and Optometry, Complutense University of Madrid, Madrid, Spain.
  2. Jos�� Luis Hern��ndez-Verdejo: Faculty of Optics and Optometry, Complutense University of Madrid, Madrid, Spain.
  3. Jos�� Manuel L��pez-Alonso: Faculty of Optics and Optometry, Complutense University of Madrid, Madrid, Spain. jmlopez@ucm.es.
PMID: 39969699 DOI: 10.1007/s11538-025-01425-1

Abstract

This study employs a computational model to simulate the dynamics of tear fluid and tear film in conjunction with contact lens motion, examining the interplay between diverse contact lens characteristics-such as material, design, and dimensions-and key ocular factors like dry eye conditions, corneal size, and blink rate. These interactions are critical for customising lens fit to maximise wearer comfort. Utilising optical measurements from a single participant, the study integrates data on tear meniscus size, blink velocity, and palpebral fissure height with sixteen different contact lens parameters, including Young's modulus, thickness, diameter, and curvature. Correlation analyses were conducted to determine the impact of these parameters on the dynamics of the tear fluid and overall tear film. Results show that the diameter and Young's modulus of the contact lens significantly influence pre-lens tear film thickness, with robust, statistically significant correlations. In contrast, lens thickness and base curve showed minimal impact, as evidenced by weak and non-significant correlations. These findings underscore the critical roles of lens diameter and Young's modulus in enhancing the stability and distribution of tear fluid, thereby improving wearer comfort and advancing contact lens design.

Keywords

Contact lens design Correlation analysis Tear film dynamics Tear fluid Wearer comfort

References

  1. Anderson DM, Corsaro M, Horton J et al (2021) Tear film dynamics with blinking and contact lens motion. Math Med Biol J IMA 38:355���395. https://doi.org/10.1093/imammb/dqab010 [DOI: 10.1093/imammb/dqab010]
  2. Berrar D, Dubitzky W (2013) Bootstrapping. In: Dubitzky W, Wolkenhauer O, Cho K-H, Yokota H (eds) Encyclopedia of systems biology. Springer, New York, New York, NY, pp 158���162
  3. Bowman AW, Azzalini A (1999) Applied smoothing techniques for data analysis: the kernel approach with s-plus illustrations. J Am Stat Assoc 94:982
  4. Braun RJ (2003) Modelling drainage of the precorneal tear film after a blink. Math Med Biol 20:1���28. https://doi.org/10.1093/imammb/20.1.1 [DOI: 10.1093/imammb/20.1.1]
  5. Braun RJ (2012) Dynamics of the tear film. Annu Rev Fluid Mech 44:267���297. https://doi.org/10.1146/annurev-fluid-120710-101042 [DOI: 10.1146/annurev-fluid-120710-101042]
  6. Braun RJ, King-Smith PE (2007) Model problems for the tear film in a blink cycle: single-equation models. J Fluid Mech 586:465���490. https://doi.org/10.1017/S002211200700701X [DOI: 10.1017/S002211200700701X]
  7. Braun RJ, King-Smith PE, Begley CG et al (2015) Dynamics and function of the tear film in relation to the blink cycle. Prog Retin Eye Res 45:132���164. https://doi.org/10.1016/j.preteyeres.2014.11.001 [DOI: 10.1016/j.preteyeres.2014.11.001]
  8. Capote-Puente R, Bautista-Llamas M-J, S��nchez-Gonz��lez J-M (2023) Tear film dynamics between low and high contact lens dry eye disease questionnaire (CLDEQ-8) score with a Lehfilcon A silicone hydrogel water gradient contact lens: a non-invasive methodology approach. Diagnostics 13:939. https://doi.org/10.3390/diagnostics13050939 [DOI: 10.3390/diagnostics13050939]
  9. Chauhan A, Radke CJ (2001) Modeling the vertical motion of a soft contact lens. Curr Eye Res 22:102���108. https://doi.org/10.1076/ceyr.22.2.102.5521 [DOI: 10.1076/ceyr.22.2.102.5521]
  10. Dunn AC, Tichy JA, Urue��a JM, Sawyer WG (2013) Lubrication regimes in contact lens wear during a blink. Tribol Int 63:45���50. https://doi.org/10.1016/j.triboint.2013.01.008 [DOI: 10.1016/j.triboint.2013.01.008]
  11. Espinosa J, Domenech B, V��zquez C et al (2018) Blinking characterization from high speed video records. Application to biometric authentication. PLoS ONE 13:e0196125. https://doi.org/10.1371/journal.pone.0196125 [DOI: 10.1371/journal.pone.0196125]
  12. Fink BA, Hill RM, Carney LG (1992) Influence of rigid contact lens base curve radius on tear pump efficiency. Optom vis Sci 69:60
  13. Garh��fer G, Dos Santos VA, Stegmann H et al (2020) The association between tear film thickness as measured with OCT and symptoms and signs of dry eye disease: a pooled analysis of 6 clinical trials. JCM 9:3791. https://doi.org/10.3390/jcm9113791 [DOI: 10.3390/jcm9113791]
  14. Hart SM, McGhee EO, Urue��a JM et al (2020) Surface gel layers reduce shear stress and damage of corneal epithelial cells. Tribol Lett 68:106. https://doi.org/10.1007/s11249-020-01344-3 [DOI: 10.1007/s11249-020-01344-3]
  15. Heryudono A, Braun RJ, Driscoll TA et al (2007) Single-equation models for the tear film in a blink cycle: realistic lid motion. Math Med Biol 24:347���377. https://doi.org/10.1093/imammb/dqm004 [DOI: 10.1093/imammb/dqm004]
  16. Hsiao C-J, Tung H-C, Tien C et al (2023) The influence of large-diameter multifocal contact lens on ocular surface, visual quality, and visual function for presbyopic adults with dry eye syndromes. Sci Rep 13:19444. https://doi.org/10.1038/s41598-023-46732-6 [DOI: 10.1038/s41598-023-46732-6]
  17. Hulley SB (ed) (2013) Designing clinical research, 4th edn. Wolters Kluwer/Lippincott Williams & Wilkins, Philadelphia
  18. Iyamu E, Enobakhare O (2019) pH and osmolality of pre-corneal tear film and commercially available artificial tears
  19. Jones MB, Please CP, McElwain DLS et al (2005) Dynamics of tear film deposition and draining. Math Med Biol J IMA 22:265���288. https://doi.org/10.1093/imammb/dqi012 [DOI: 10.1093/imammb/dqi012]
  20. Jones MB, Fulford GR, Please CP et al (2008) Elastohydrodynamics of the eyelid wiper. Bull Math Biol 70:323���343. https://doi.org/10.1007/s11538-007-9252-7 [DOI: 10.1007/s11538-007-9252-7]
  21. Kaur P, Stoltzfus J, Yellapu V (2018) Descriptive statistics. Int J Acad Med 4:60. https://doi.org/10.4103/IJAM.IJAM_7_18 [DOI: 10.4103/IJAM.IJAM_7_18]
  22. Kim H-Y (2013) Statistical notes for clinical researchers: assessing normal distribution (2) using skewness and kurtosis. Restor Dent Endod 38:52. https://doi.org/10.5395/rde.2013.38.1.52 [DOI: 10.5395/rde.2013.38.1.52]
  23. Kim E, Saha M, Ehrmann K (2018) Mechanical properties of contact lens materials. Eye Contact Lens Sci Clin Pract 44:S148���S156. https://doi.org/10.1097/ICL.0000000000000442 [DOI: 10.1097/ICL.0000000000000442]
  24. King-Smith E, Fink B, Hill R et al (2004) The thickness of the tear film. Curr Eye Res 29:357���368. https://doi.org/10.1080/02713680490516099 [DOI: 10.1080/02713680490516099]
  25. Kohn MA, Senyak J (2024) Sample size calculators for designing clinical research���correlation sample size. https://www.sample-size.net/ . Accessed 9 Nov 2024
  26. Kosloff D, Tal-Ezer H (1993) A Modified chebyshev Pseudospectral method with an O(N-1) time step restriction. J Comput Phys 104:457���469. https://doi.org/10.1006/jcph.1993.1044 [DOI: 10.1006/jcph.1993.1044]
  27. Kwon K-A, Shipley RJ, Edirisinghe M et al (2013) High-speed camera characterization of voluntary eye blinking kinematics. J R Soc Interface 10:20130227. https://doi.org/10.1098/rsif.2013.0227 [DOI: 10.1098/rsif.2013.0227]
  28. Lee W-H, Seo J-M, Hwang J-M (2017) The analysis of eye blinking pattern using high-frame-rate camera. 2017 39th annual international conference of the IEEE engineering in medicine and biology society (EMBC). IEEE, Seogwipo, pp 1509���1512
  29. Lee JH, Kim CH, Choe CM, Choi TH (2020) Correlation analysis between ocular surface parameters with subjective symptom severity in dry eye disease. Korean J Ophthalmol 34:203���209. https://doi.org/10.3341/kjo.2019.0133 [DOI: 10.3341/kjo.2019.0133]
  30. Lo���pez-Alonso JM (2002) Bad pixel identification by means of principal components analysis. Opt Eng 41:2152. https://doi.org/10.1117/1.1497397 [DOI: 10.1117/1.1497397]
  31. L��pez-Alonso JM, Alda J, Bernab��u E (2002) Principal-component characterization of noise for infrared images. Appl Opt 41:320. https://doi.org/10.1364/AO.41.000320 [DOI: 10.1364/AO.41.000320]
  32. Maki KL, Ross DS (2014) A new model for the suction pressure under a contact lens. J Biol Syst 22:235���248. https://doi.org/10.1142/S021833901440004X [DOI: 10.1142/S021833901440004X]
  33. Martin DK, Holden BA (1986) Forces developed beneath hydrogel contact lenses due to squeeze pressure. Phys Med Biol 31:635���649. https://doi.org/10.1088/0031-9155/31/6/005 [DOI: 10.1088/0031-9155/31/6/005]
  34. Mas D, Domenech B, Espinosa J et al (2010) Noninvasive measurement of eye retraction during blinking. Opt Lett 35:1884. https://doi.org/10.1364/OL.35.001884 [DOI: 10.1364/OL.35.001884]
  35. McNamara NA, Polse KA, Brand RJ et al (1999) Tear mixing under a soft contact lens: effects of lens diameter. Am J Ophthalmol 127:659���665. https://doi.org/10.1016/S0002-9394(99)00051-3 [DOI: 10.1016/S0002-9394(99)00051-3]
  36. Miot HA (2018) Correlation analysis in clinical and experimental studies. J Vasc Bras 17:275���279. https://doi.org/10.1590/1677-5449.174118 [DOI: 10.1590/1677-5449.174118]
  37. Muntz A, Subbaraman LN, Sorbara L, Jones L (2015) Tear exchange and contact lenses: a review. J Optom 8:2���11. https://doi.org/10.1016/j.optom.2014.12.001 [DOI: 10.1016/j.optom.2014.12.001]
  38. Ng SC (2017) Principal component analysis to reduce dimension on digital image. Proc Comput Sci 111:113���119. https://doi.org/10.1016/j.procs.2017.06.017 [DOI: 10.1016/j.procs.2017.06.017]
  39. Nichols JJ, King-Smith PE (2003) Thickness of the pre- and post-contact lens tear film measured in vivo by interferometry. Invest Ophthalmol vis Sci 44:68. https://doi.org/10.1167/iovs.02-0377 [DOI: 10.1167/iovs.02-0377]
  40. Nichols JJ, King-Smith PE (2004) The impact of hydrogel lens settling on the thickness of the tears and contact lens. Invest Ophthalmol vis Sci 45:2549. https://doi.org/10.1167/iovs.04-0149 [DOI: 10.1167/iovs.04-0149]
  41. Paranjpe V, Phung L, Galor A (2019) The tear film: anatomy and physiology. In: Guidoboni G, Harris A, Sacco R (eds) Ocular fluid dynamics. Springer International Publishing, Cham, pp 329���345
  42. Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065���1076
  43. Perez J, Espinosa J, Domenech B et al (2011) Blinking kinematics description through non-invasive measurement. J Mod Opt 58:1857���1863. https://doi.org/10.1080/09500340.2011.554898 [DOI: 10.1080/09500340.2011.554898]
  44. Raj A (2016) Anterior segment optical coherence tomography for tear meniscus evaluation and its correlation with other tear variables in healthy individuals. JCDR. https://doi.org/10.7860/JCDR/2016/18717.7722 [DOI: 10.7860/JCDR/2016/18717.7722]
  45. Sanju��n AM, L��pez-Alonso JM (2021) Caracterizaci��n de movimientos oculares mediante flujo ��ptico velocim��trico. In: Sampedro AG, Gimeno IB, Cobija MJL, et al (eds) Temas actuales en optometr��a SIYO 2021. Universidad de Valencia, pp 45���55
  46. Saravanan C (2010) Color image to grayscale image conversion. 2010 second international conference on computer engineering and applications. IEEE, Bali Island, Indonesia, pp 196���199
  47. Schober P, Boer C, Schwarte LA (2018) Correlation coefficients: appropriate use and interpretation. Anesth Analg 126:1763���1768. https://doi.org/10.1213/ANE.0000000000002864 [DOI: 10.1213/ANE.0000000000002864]
  48. Shampine LF, Reichelt MW (1997) The MATLAB ODE suite. SIAM J Sci Comput 18:1���22. https://doi.org/10.1137/S1064827594276424 [DOI: 10.1137/S1064827594276424]
  49. Stapleton F, Tan J (2017) Impact of contact lens material, design, and fitting on discomfort. Eye Contact Lens Sci Clin Pract 43:32���39. https://doi.org/10.1097/ICL.0000000000000318 [DOI: 10.1097/ICL.0000000000000318]
  50. The MathWorks Inc. (2021) MATLAB version: 23.2.0.2459199 (R2023b). https://www.mathworks.com . Accessed 8 Nov 2023
  51. The MathWorks Inc. (2023a) Kernel Distribution���MATLAB & Simulink. https://www.mathworks.com/help/stats/kernel-distribution.html . Accessed 24 Apr 2024
  52. The MathWorks Inc. (2023b) Kernel smoothing function estimate for univariate and bivariate data���MATLAB ksdensity. https://www.mathworks.com/help/stats/ksdensity.html#References . Accessed 8 Aug 2024
  53. The MathWorks Inc. (2023) Correlation coefficients���MATLAB corrcoef. https://www.mathworks.com/help/stats/corr.html?s_tid=doc_ta . Accessed 24 Apr 2024
  54. The MathWorks Inc. (2023c) Bootstrap Sampling���MATLAB bootstrp. https://www.mathworks.com/help/stats/bootstrp.html#mw_cdd50063-8fd8-41ed-af6f-c53071293b4f . Accessed 5 Nov 2024
  55. Thielicke W, Stamhuis EJ (2014) PIVlab���towards user-friendly, affordable and accurate digital particle image velocimetry in MATLAB. J Open Res Softw 2:30. https://doi.org/10.5334/jors.bl [DOI: 10.5334/jors.bl]
  56. Tiffany JM (1991) The viscosity of human tears. Int Ophthalmol 15:371���376. https://doi.org/10.1007/BF00137947 [DOI: 10.1007/BF00137947]
  57. Tiffany JM, Winter N, Bliss G (1989) Tear film stability and tear surface tension. Curr Eye Res 8:507���515. https://doi.org/10.3109/02713688909000031 [DOI: 10.3109/02713688909000031]
  58. Trefethen LN (2000) Spectral methods in MATLAB. Society for Industrial and Applied Mathematics, Oxford, England
  59. Upadhyaya A, Khan S, Sahay P et al (2020) Pentacam���a corneal tomography system. Delhi J Ophthalmol 31:90
  60. Wang J, Fonn D, Simpson TL, Jones L (2003) Precorneal and pre- and postlens tear film thickness measured indirectly with optical coherence tomography. Invest Ophthalmol vis Sci 44:2524. https://doi.org/10.1167/iovs.02-0731 [DOI: 10.1167/iovs.02-0731]
  61. William Thielicke (2021a) PIVlab���particle image velocimetry (PIV) tool with GUI. https://pivlab.blogspot.com/ . Accessed 9 Nov 2023a
  62. William Thielicke (2021b) PIVlab���Digital Particle Image Velocimetry Tool for MATLAB. https://in.mathworks.com/matlabcentral/fileexchange/27659-pivlab-particle-image-velocimetry-piv-tool-with-gui . Accessed 9 Nov 2023b
  63. Young G, Hall L, Sulley A et al (2017) Inter-relationship of soft contact lens diameter, base curve radius, and fit. Optom vis Sci 94:458���465. https://doi.org/10.1097/OPX.0000000000001048 [DOI: 10.1097/OPX.0000000000001048]

Grants

  1. 956274/HORIZON EUROPE Framework Programme

MeSH Term

Tears
Humans
Models, Biological
Blinking
Dry Eye Syndromes
Computer Simulation
Mathematical Concepts
Elastic Modulus
Contact Lenses
Cornea
Contact Lenses, Hydrophilic
Journal Article
Article has an altmetric score of 2

Word Cloud

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