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A Two-Phase Model for Mucosal Aggregation and Clearance in the Human Tear Film

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Recent Advances in Mechanics and Fluid-Structure Interaction with Applications

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

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Abstract

This study aims to computationally identify the detailed mechanisms of the adhesion process of mucin and foreign bodies in the human tear film subject to the blinking motion of eyelid. The results give us a clue about the role of mucus as a protective agent for the ocular surface and its role in diseases such as dry eye syndrome (DES). We propose a multi-phase model which models the tear film as an inhomogeneous fluid comprising of a mixture of an aqueous layer in which mucin particles are exponentially distributed in the direction normal to corneal surface. We model the mucin adherence to any immersed foreign object, and its overall clearance through the blinking motion of the eyelid. The motions of mucin in the flow are solved by a force balance equation which accounts for the macroscopic interactions between the fluid and the body. The clearance rates of the foreign particle are explored under various conditions with different varying mechanical properties of mucin such as its adhesion force, distribution profile, as well as its viscosity. Our parametric study shows that a condition for higher clearance rate requires (i) greater mucin population in the entire region of tear film, i.e., larger viscosity, (ii) an optimal mucin distribution profile, and (iii) normal physiologic adhesion force between mucin and immersed particles.

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Notes

  1. 1.

    So if m refers to a single mucin strand, M = n wrap m where n wrap is a critical number which depends upon the dimension of mucin. See Sect. 2.2.2 for more discussion on this point.

  2. 2.

    This assumption is made to side-step the issue of having as many as 104 mucin particles in the simulation to see an increase in aggregate size, as modeled by Eq. (19).

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Acknowledgements

AV dedicates this work to his dear friend and co-author Bong Jae Chung who was an essential part of this project. Bong Jae was working hard on finding collaborators who could help provide experimental support for this work at the time of his untimely passing. I fondly remember all the wonderful discussions about this project and his excitement about all the questions that lay ahead that we planned to work on. BM, a former graduate student of Dr. Chung, remembers countless lessons he instilled in those who knew him, his immeasurable dedication to teaching, and his ever willingness to give his time to students and foster the growth of new ideas.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Montclair State University, Montclair, NJ, USA

    Bong Jae Chung & Brandon Martinez

  2. Department of Mathematics, Department of Physics and Astronomy, Complex Fluids Laboratory, Montclair State University, Montclair, NJ, USA

    Ashwin Vaidya

Authors
  1. Bong Jae Chung
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  2. Brandon Martinez
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  3. Ashwin Vaidya
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Correspondence to Ashwin Vaidya .

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Editors and Affiliations

  1. Department of Mathematics and CIMA, University of Évora, Évora, Portugal

    Fernando Carapau

  2. Department of Mathematics, Montclair State University, Montclair, NJ, USA

    Ashwin Vaidya

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Chung, B.J., Martinez, B., Vaidya, A. (2022). A Two-Phase Model for Mucosal Aggregation and Clearance in the Human Tear Film. In: Carapau, F., Vaidya, A. (eds) Recent Advances in Mechanics and Fluid-Structure Interaction with Applications. Advances in Mathematical Fluid Mechanics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-14324-3_16

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