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Fractional calculus for respiratory mechanics: Power law impedance, viscoelasticity, and tissue heterogeneity

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  • Ionescu, Clara
  • Kelly, James F.

Abstract

This paper presents a synopsis of fractional calculus tools for characterising respiratory mechanics. A discussion on power law impedance, viscoelasticity and tissue heterogeneity is made based on morphological and structural properties of lungs. Although targeted towards respiratory system applications, these tools can serve as a basis for modelling other biological structures as well. The paper underlines the importance of characterising the viscoelastic properties of the respiratory tissue and its time-varying properties as a function of disease progress. Perspectives are suggested for developing models able to mimic disease progression and understand treatment effects for better therapeutic management.

Suggested Citation

  • Ionescu, Clara & Kelly, James F., 2017. "Fractional calculus for respiratory mechanics: Power law impedance, viscoelasticity, and tissue heterogeneity," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 433-440.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:433-440
    DOI: 10.1016/j.chaos.2017.03.054
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    References listed on IDEAS

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    1. B. Mauroy & M. Filoche & E. R. Weibel & B. Sapoval, 2004. "An optimal bronchial tree may be dangerous," Nature, Nature, vol. 427(6975), pages 633-636, February.
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    Cited by:

    1. Templos-Hernández, Diana J. & Quezada-Téllez, Luis A. & González-Hernández, Brian M. & Rojas-Vite, Gerardo & Pineda-Sánchez, José E. & Fernández-Anaya, Guillermo & Rodriguez-Torres, Erika E., 2021. "A fractional-order approach to cardiac rhythm analysis," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Abdelkawy, M.A. & Lopes, António M. & Babatin, Mohammed M., 2020. "Shifted fractional Jacobi collocation method for solving fractional functional differential equations of variable order," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Tabatabaei, S. Sepehr & Dehghan, Mohammad Reza & Talebi, Heidar Ali, 2022. "Real-time prediction of soft tissue deformation; a non-integer order modeling scheme and a practical verification for the theoretical concept," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    4. Rodríguez-Cuadrado, Javier & San Martín, Jesús, 2021. "Fractal equilibrium configuration of a mechanically loaded binary tree," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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