Search Advanced

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 4: 1061-1083. doi: 10.3934/mbe.2011.8.1061
Previous Article Next Article

A mathematical model of the compression of a spinal disc

  • 1.
    Calgary Board of Education, Calgary, AB T2G 2L9
  • 2.
    School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623-5801
  • Received: 01 January 2010 Accepted: 29 June 2018 Published: 01 August 2011

  • MSC : Primary: 74F10, 74L15, 92C10; Secondary: 92B05.

  • A model is developed of the stress-strain response of an intervertebral disc to axial compression. This is based on a balance of increased intradiscal pressure, resulting from the compression of the disc, and the restraining forces generated by the collagen fibres within the annulus fibrosus. A formula is derived for predicting the loading force on a disc once the nucleus pressure is known. Measured material values of L3 and L4 discs are used to make quantitative predictions. The results compare reasonably well with experimental results.

    Citation: Matthias Ngwa, Ephraim Agyingi. A mathematical model of the compression of a spinal disc[J]. Mathematical Biosciences and Engineering, 2011, 8(4): 1061-1083. doi: 10.3934/mbe.2011.8.1061

    Related Papers:

    [1] Ming Huang, Wenfei Dong, Yingjie Sun, Baowen He . Two dimensional automatic active shape model of degenerative disc repaired by low-intensity laser. Mathematical Biosciences and Engineering, 2021, 18(4): 4358-4371. doi: 10.3934/mbe.2021219
    [2] Rui Zhu, Yuhang Chen, Qianqian Yu, Siqing Liu, Jianjie Wang, Zhili Zeng, Liming Cheng . Effects of contusion load on cervical spinal cord: A finite element study. Mathematical Biosciences and Engineering, 2020, 17(3): 2272-2283. doi: 10.3934/mbe.2020120
    [3] Huihao Wang, Kuan Wang, Zhen Deng, Xiaofei Li, Yi-Xian Qin, Hongsheng Zhan, Wenxin Niu . Effects of facet joint degeneration on stress alterations in cervical spine C5–C6: A finite element analysis. Mathematical Biosciences and Engineering, 2019, 16(6): 7447-7457. doi: 10.3934/mbe.2019373
    [4] Lorena Bociu, Giovanna Guidoboni, Riccardo Sacco, Maurizio Verri . On the role of compressibility in poroviscoelastic models. Mathematical Biosciences and Engineering, 2019, 16(5): 6167-6208. doi: 10.3934/mbe.2019308
    [5] Jiyu Sun, Yueming Wang, Shujun Zhang, Yunhai Ma, Jin Tong, Zhijun Zhang . The mechanism of resistance-reducing/anti-adhesion and its application on biomimetic disc furrow opener. Mathematical Biosciences and Engineering, 2020, 17(5): 4657-4677. doi: 10.3934/mbe.2020256
    [6] David Iron, Adeela Syed, Heidi Theisen, Tamas Lukacsovich, Mehrangiz Naghibi, Lawrence J. Marsh, Frederic Y. M. Wan, Qing Nie . The role of feedback in the formation of morphogen territories. Mathematical Biosciences and Engineering, 2008, 5(2): 277-298. doi: 10.3934/mbe.2008.5.277
    [7] Aftab Ahmed, Javed I. Siddique . The effect of magnetic field on flow induced-deformation in absorbing porous tissues. Mathematical Biosciences and Engineering, 2019, 16(2): 603-618. doi: 10.3934/mbe.2019029
    [8] Jinyi Tai, Chang Liu, Xing Wu, Jianwei Yang . Bearing fault diagnosis based on wavelet sparse convolutional network and acoustic emission compression signals. Mathematical Biosciences and Engineering, 2022, 19(8): 8057-8080. doi: 10.3934/mbe.2022377
    [9] Yongli Yan, Tiansheng Sun, Teng Ren, Li Ding . Enhanced grip force estimation in robotic surgery: A sparrow search algorithm-optimized backpropagation neural network approach. Mathematical Biosciences and Engineering, 2024, 21(3): 3519-3539. doi: 10.3934/mbe.2024155
    [10] Giovanna Guidoboni, Alon Harris, Lucia Carichino, Yoel Arieli, Brent A. Siesky . Effect of intraocular pressure on the hemodynamics of the central retinal artery: A mathematical model. Mathematical Biosciences and Engineering, 2014, 11(3): 523-546. doi: 10.3934/mbe.2014.11.523
  • A model is developed of the stress-strain response of an intervertebral disc to axial compression. This is based on a balance of increased intradiscal pressure, resulting from the compression of the disc, and the restraining forces generated by the collagen fibres within the annulus fibrosus. A formula is derived for predicting the loading force on a disc once the nucleus pressure is known. Measured material values of L3 and L4 discs are used to make quantitative predictions. The results compare reasonably well with experimental results.


  • This article has been cited by:

    1. Aurica Truţa, Felicia Aurora Cristea, Mariana Arghir, The Influence of Brush Cutters Vibrations on Human Body, 2013, 8-9, 2234-991X, 445, 10.4028/www.scientific.net/AEF.8-9.445
    2. Sébastien DEMERS, Sylvie NADEAU, Abdel-Hakim BOUZID, Analytical evaluation of stresses and displacements of an intervertebral disc, 2017, 12, 1880-9863, 16-00675, 10.1299/jbse.16-00675
  • Reader Comments
  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2700) PDF downloads(509) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog