IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v155y2022ics0960077921009875.html
   My bibliography  Save this article

Real-time prediction of soft tissue deformation; a non-integer order modeling scheme and a practical verification for the theoretical concept

Author

Listed:
  • Tabatabaei, S. Sepehr
  • Dehghan, Mohammad Reza
  • Talebi, Heidar Ali

Abstract

This paper presents a practical study to verify the concept of non-integer order dynamic behavior of multi-dimensional soft tissue deformation. The stress-strain relationship of soft tissue is of non-integer order. However, this concept needs to be proven. To this aim, the stress-strain relationship is combined with the mechanical equations describing a continuum body. Then, a set of differential equations are obtained modeling the body deformation. Next, the parameters of the model are calculated considering data extracted from an experimental study. The dynamic behavior of the tissue -which is required in the identification of the order- is then simulated using Abaqus. After estimating the order in an adaptive scheme, the non-integer order model and the proposed identification method are verified using some experimental test on a silicone-gel cube.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921009875
    DOI: 10.1016/j.chaos.2021.111633
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921009875
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111633?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. S. Sepehr Tabatabaei & Mohammad Javad Yazdanpanah & Sajad Jafari & Julien Clinton Sprott, 2014. "Extensions in dynamic models of happiness: effect of memory," International Journal of Happiness and Development, Inderscience Enterprises Ltd, vol. 1(4), pages 344-356.
    2. 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.
    3. Carrera, Y. & Avila-de la Rosa, G. & Vernon-Carter, E.J. & Alvarez-Ramirez, J., 2017. "A fractional-order Maxwell model for non-Newtonian fluids," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 276-285.
    4. Wang, Lei & Chen, Yi-Ming, 2020. "Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    5. Zafar, Zain Ul Abadin & Younas, Samina & Hussain, Muhammad Tanveer & Tunç, Cemil, 2021. "Fractional aspects of coupled mass-spring system," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Ali, Farhad & Iftikhar, Muhammad & Khan, Ilyas & Sheikh, Nadeem Ahmad, 2019. "Atangana–Baleanu fractional model for electro-osmotic flow of viscoelastic fluids," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 125-133.
    7. Coronel-Escamilla, Antonio & Gomez-Aguilar, Jose Francisco & Stamova, Ivanka & Santamaria, Fidel, 2020. "Fractional order controllers increase the robustness of closed-loop deep brain stimulation systems," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    8. Omar Naifar & Abdellatif Ben Makhlouf, 2021. "On the Stabilization and Observer Design of Polytopic Perturbed Linear Fractional-Order Systems," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-6, March.
    9. Tabatabaei, S. Sepehr & Talebi, H.A. & Tavakoli, M., 2017. "A novel adaptive order/parameter identification method for variable order systems application in viscoelastic soft tissue modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 447-455.
    10. Omar Naifar & Assaad Jmal & A. M. Nagy & Abdellatif Ben Makhlouf, 2020. "Improved Quasiuniform Stability for Fractional Order Neural Nets with Mixed Delay," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, November.
    11. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    12. Yu, Chunxiao & Zhang, Jie & Chen, Yiming & Feng, Yujing & Yang, Aimin, 2019. "A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 275-279.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Defoort, Michael & Boulaaras, Salah, 2021. "Predefined-time convergence in fractional-order systems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    3. Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. Cui, Yuhuan & Qu, Jingguo & Han, Cundi & Cheng, Gang & Zhang, Wei & Chen, Yiming, 2022. "Shifted Bernstein–Legendre polynomial collocation algorithm for numerical analysis of viscoelastic Euler–Bernoulli beam with variable order fractional model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 361-376.
    5. Kritika, & Agarwal, Ritu & Purohit, Sunil Dutt, 2020. "Mathematical model for anomalous subdiffusion using comformable operator," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    6. Pritam, Kocherlakota Satya & Sugandha, & Mathur, Trilok & Agarwal, Shivi, 2021. "Underlying dynamics of crime transmission with memory," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Singh, C.S. & Singh, Harendra & Singh, Somveer & Kumar, Devendra, 2019. "An efficient computational method for solving system of nonlinear generalized Abel integral equations arising in astrophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1440-1448.
    8. Partohaghighi, Mohammad & Akgül, Ali, 2021. "Modelling and simulations of the SEIR and Blood Coagulation systems using Atangana-Baleanu-Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    9. Ganji, R.M. & Jafari, H. & Baleanu, D., 2020. "A new approach for solving multi variable orders differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    10. Chatibi, Y. & El Kinani, E.H. & Ouhadan, A., 2019. "Variational calculus involving nonlocal fractional derivative with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 117-121.
    11. Muhammad, Yasir & Khan, Nusrat & Awan, Saeed Ehsan & Raja, Muhammad Asif Zahoor & Chaudhary, Naveed Ishtiaq & Kiani, Adiqa Kausar & Ullah, Farman & Shu, Chi-Min, 2022. "Fractional memetic computing paradigm for reactive power management involving wind-load chaos and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    12. Shiri, Babak & Baleanu, Dumitru, 2023. "All linear fractional derivatives with power functions’ convolution kernel and interpolation properties," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    13. Hosseininia, M. & Heydari, M.H., 2019. "Meshfree moving least squares method for nonlinear variable-order time fractional 2D telegraph equation involving Mittag–Leffler non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 389-399.
    14. Marasi, H.R. & Derakhshan, M.H., 2023. "Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 368-389.
    15. Kumar, Sachin & Pandey, Prashant, 2020. "Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    16. Ahmad, Shabir & Ullah, Aman & Arfan, Muhammad & Shah, Kamal, 2020. "On analysis of the fractional mathematical model of rotavirus epidemic with the effects of breastfeeding and vaccination under Atangana-Baleanu (AB) derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    17. Li, Yiqun & Wang, Hong, 2023. "A finite element approximation to a viscoelastic Euler–Bernoulli beam with internal damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 138-158.
    18. Zeid, Samaneh Soradi, 2019. "Approximation methods for solving fractional equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 171-193.
    19. Wang, Lei & Chen, Yiming & Cheng, Gang & Barrière, Thierry, 2020. "Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    20. Ahmed, Jawad & Khan, Masood & Ahmad, Latif, 2020. "Radiative heat flux effect in flow of Maxwell nanofluid over a spiraling disk with chemically reaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921009875. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.