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Nonlinear tubular organ modeling and analysis for tracheal angioedema by swelling-morphoelasticity

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Abstract

We study one of the important human tubular organs, the trachea, under deformation caused by the disease angioedema. This pathology can suddenly increase the volume of the trachea and cause serious breathing difficulty. Two popular theories, the swelling theory and morphoelasticity theory, which generalize classical hyperelasticity to study material deformation under internal volume change, are integrated into a single model to study tracheal angioedema. Computational modeling results from various combinations of swelling and morphoelasticity are compared to exhibit the difference and similarity of the two theories in modeling tracheal angioedema. Nonlinear behaviors of the tubular radius changes are also illustrated to show how the trachea luminal size alteration depends on the swelling/growth parameters and their effect on modifying tissue stiffness. The possibility of complete tracheal channel closure is also studied to understand if it is possible for the angioedema to close the airway. This article serves as an exemplary study on nonlinear deformation behaviors of human tubular organs with multiple layers.

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Notes

  1. Force-free boundary conditions are different from traction-free boundary conditions. The force-free boundary condition means the integration of traction over the related boundary is annihilated.

  2. The main features of swelling theory are in (2.5) and (2.8). We call it volume-specified theory to avoid confusion with the incompressible theory. Also notice that (2.5) is always satisfied in the analysis, different from compressible theory in the fact that \(\text {det}{\mathbf {F}}\) can change after computation.

  3. These values were calculated from experimental data via justified mathematical formulas. See [33].

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Acknowledgements

Pak-Wing Fok is supported by a Simons Foundation Collaboration Grant #282579. Kun Gou is grateful to the 2018 Texas A&M University-San Antonio Research Council Grant and the College of Arts and Sciences Summer Faculty Research Fellowship.

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Authors and Affiliations

  1. Department of Science and Mathematics, Texas A&M University-San Antonio, San Antonio, TX, 78224, USA

    Kun Gou

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Pak-Wing Fok

  3. School of Computing and Mathematics, Keele University, Staffordshire, ST5 5BG, UK

    Yibin Fu

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  1. Kun Gou
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  2. Pak-Wing Fok
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Correspondence to Kun Gou.

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Gou, K., Fok, PW. & Fu, Y. Nonlinear tubular organ modeling and analysis for tracheal angioedema by swelling-morphoelasticity. J Eng Math 112, 95–117 (2018). https://doi.org/10.1007/s10665-018-9967-5

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  • DOI: https://doi.org/10.1007/s10665-018-9967-5

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