Journal of Engineering Mathematics

, Volume 112, Issue 1, pp 95–117 | Cite as

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

  • Kun Gou
  • Pak-Wing Fok
  • Yibin Fu


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.


Angioedema Growth Hyperelasticity Morphoelasticity Swelling Trachea 



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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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Science and MathematicsTexas A&M University-San AntonioSan AntonioUSA
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA
  3. 3.School of Computing and MathematicsKeele UniversityStaffordshireUK

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