Finite element modeling and simulation study of solid-liquid biphase fiber-reinforced lumbar intervertebral disc_Journal of Biomedical Engineering

Authors：

GAO Yongchang ¹ , FU Yantao ¹ , CUI Qingfeng ¹ , CHEN Shibin ¹ ,  LIU Peng ² ,  LIU Xifang ²

1. National Engineering Laboratory for Highway Maintenance Equipment, Chang’an University, Xi’an 710064, P. R. China;
2. Honghui Hospital, Xi'an Jiaotong University, Xi’an 710054, P. R. China;

Corresponding author：

LIU Peng, Email: 13991814651@163.com; LIU Xifang, Email: lxfyg2006@126.com

Keywords：

Lumbar intervertebral disc; Finite element analysis; Solid-liquid biphasic; Fiber-reinforced; Fluid support ratio

DOI：

10.7507/1001-5515.202310021

Video：

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The lumbar intervertebral disc exhibits a complex physiological structure with interactions between various segments, and its components are extremely complex. The material properties of different components in the lumbar intervertebral disc, especially the water content (undergoing dynamic change as influenced by age, degeneration, mechanical loading, and proteoglycan content) - critically determine its mechanical properties. When the lumbar intervertebral disc is under continuous pressure, water seeps out, and after the pressure is removed, water re-infiltrates. This dynamic fluid exchange process directly affects the mechanical properties of the lumbar intervertebral disc, while previous isotropic modeling methods have been unable to accurately reflect such solid-liquid phase behaviors. To explore the load-bearing mechanism of the lumbar intervertebral disc and establish a more realistic mechanical model of the lumbar intervertebral disc, this study developed a solid-liquid biphasic, fiber-reinforced finite element model. This model was used to simulate the four movements of the human lumbar spine in daily life, namely flexion, extension, axial rotation, and lateral bending. The fluid pressure, effective solid stress, and liquid pressure-bearing ratio of the annulus fibrosus and nucleus pulposus of different lumbar intervertebral discs were compared and analyzed under the movements. Under all the movements, the fluid pressure distribution was closer to the nucleus pulposus, while the effective solid stress distribution was more concentrated in the outer annulus fibrosus. In terms of fluid pressure, the maximum fluid pressure of the lumbar intervertebral disc during lateral bending was 1.95 MPa, significantly higher than the maximum fluid pressure under other movements. Meanwhile, the maximum effective solid stress of the lumbar intervertebral disc during flexion was 2.43 MPa, markedly higher than the maximum effective solid stress under other movements. Overall, the liquid pressure-bearing ratio under axial rotation was smaller than that under other movements. Based on the solid-liquid biphasic modeling method, this study more accurately revealed the dominant role of the liquid phase in the daily load-bearing process of the lumbar intervertebral disc and the solid-phase mechanical mechanism of the annulus fibrosus load-bearing, and more effectively predicted the solid-liquid phase co-load-bearing mechanism of the lumbar intervertebral disc in daily life.

1.	韩聪, 赵耀东, 朱玲, 等. 基于腰椎间盘退变生物力学探讨腰椎间盘突出症发病机制. 中医临床研究, 2020, 12(1): 47-50.
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4.	Azril, Huang K Y, Hobley J, et al. Correlation of the degenerative stage of a disc with magnetic resonance imaging, chemical content, and biomechanical properties of the nucleus pulposus. Journal of Biomedical Materials Research Part A, 2023, 111(7): 1054-1066.
5.	Sengul E, Ozmen R, Demir T. The effects of pre-stressed rods contoured by different bending techniques on posterior instrumentation of L4-L5 lumbar spine segment: a finite element study. Proc Inst Mech Eng H, 2022, 236(7): 960-972.
6.	Yan M, Song Z, Kou H, et al. New progress in basic research of macrophages in the pathogenesis and treatment of low back pain. Frontiers in Cell and Developmental Biology, 2022, 10: 866857.
7.	Bardia A, Hovnanian M D, Brachtel E F, et al. Case 35-2018: a 68-year-old woman with back pain and a remote history of breast cancer. New England Journal of Medicine, 2018, 379(20): 1946-1953.
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12.	Rohlmann A, Zander T, Schmidt H, et al. Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method. Journal of Biomechanics, 2006, 39(13): 2484-2490.
13.	Park W M, Kim Y H, Lee S. Effect of intervertebral disc degeneration on biomechanical behaviors of a lumbar motion segment under physiological loading conditions. Journal of Mechanical Science and Technology, 2013, 27: 483-489.
14.	Yang B, O'Connell G D. Intervertebral disc swelling maintains strain homeostasis throughout the annulus fibrosus: a finite element analysis of healthy and degenerated discs. Acta Biomaterialia, 2019, 100: 61-74.
15.	Finley S M, Brodke D S, Spina N T, et al. FEBio finite element models of the human lumbar spine. Comput Methods Biomech Biomed Engin, 2018, 21(6): 444-452.
16.	高旭, 邢文华. 有限元分析法在脊柱外科领域的应用. 中国组织工程研究, 2023, 27(18): 2921.
17.	Liu Z, Wang H, Yuan Z, et al. High-resolution 3D printing of angle-ply annulus fibrosus scaffolds for intervertebral disc regeneration. Biofabrication, 2022, 15(1): 015015.
18.	Lu Y, Xiang J, Yin B, et al. Finite element comparative analysis on treatment of lumbar disc herniation by the oblique wrench method and the combination of traction, pressing, and oblique pulling. Chinese Journal of Tissue Engineering Research, 2023, 27(13): 2011.
19.	Heo M, Park S. Biphasic properties of PVAH (polyvinyl alcohol hydrogel) reflecting biomechanical behavior of the nucleus pulposus of the human intervertebral disc. Materials, 2022, 15(3): 1125.
20.	Zhou M, Huff R D, Abubakr Y, et al. Torque-and muscle-driven flexion induce disparate risks of in vitro herniation: a multiscale and multiphasic structure-based finite element study. J Biomech Eng, 2022, 144(6): 061005.
21.	Iatridis J C, Setton L A, Foster R J, et al. Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. Journal of Biomechanics, 1998, 31(6): 535-544.
22.	Johannessen W, Elliott D M. Effects of degeneration on the biphasic material properties of human nucleus pulposus in confined compression. Spine, 2005, 30(24): E724-E729.
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24.	Iatridis J C, Setton L A, Weidenbaum M, et al. Alterations in the mechanical behavior of the human lumbar nucleus pulposus with degeneration and aging. Journal of Orthopaedic Research, 1997, 15(2): 318-322.
25.	Iatridis J C, Weidenbaum M, Setton L A, et al. Is the nucleus pulposus a solid or a fluid? Mechanical behaviors of the nucleus pulposus of the human intervertebral disc. Spine, 1996, 21(10): 1174-1184.
26.	Ateshian G A, Rajan V, Chahine N O, et al. Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena. J Biomech Eng, 2009, 131(6): 061003.
27.	Holmes M H, Mow V C. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. Journal of Biomechanics, 1990, 23(11): 1145-1156.
28.	Pintar F A, Yoganandan N, Myers T, et al. Biomechanical properties of human lumbar spine ligaments. Journal of biomechanics, 1992, 25(11): 1351-1356.
29.	Wilke H J, Neef P, Caimi M, et al. New in vivo measurements of pressures in the intervertebral disc in daily life. Spine, 1999, 24(8): 755-762.
30.	Dreischarf M, Zander T, Shirazi-Adl A, et al. Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together. Journal of Biomechanics, 2014, 47(8): 1757-1766.
31.	Rohlmann A, Neller S, Claes L, et al. Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine. Spine, 2001, 26(24): E557-E561.
32.	Woldtvedt D J, Womack W, Gadomski B C, et al. Finite element lumbar spine facet contact parameter predictions are affected by the cartilage thickness distribution and initial joint gap size. J Biomech Eng, 2011, 133(6): 061009.
33.	林伟健, 李俊言, 陈瑱贤, 等. 正常和早期膝骨关节炎的软骨生物力学研究. 力学学报, 2021, 53(11): 3147-3156.
34.	Ateshian G A, Maas S, Weiss J A. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding. J Biomech Eng, 2010, 132(6): 061006.
35.	Zimmerman B K, Maas S A, Weiss J A, et al. A finite element algorithm for large deformation biphasic frictional contact between porous-permeable hydrated soft tissues. J Biomech Eng, 2022, 144(2): 021008.
36.	Sun Z, Sun Y, Lu T, et al. A swelling-based biphasic analysis on the quasi-static biomechanical behaviors of healthy and degenerative intervertebral discs. Comput Methods Programs Biomed, 2023, 235: 107513.

1. 韩聪, 赵耀东, 朱玲, 等. 基于腰椎间盘退变生物力学探讨腰椎间盘突出症发病机制. 中医临床研究, 2020, 12(1): 47-50.
2. Brissenden A J, Amsden B G. In situ forming macroporous biohybrid hydrogel for nucleus pulposus cell delivery. Acta Biomaterialia, 2023, 170: 169-184.
3. Hayashi K, Suzuki A, Abdullah Ahmadi S, et al. Mechanical stress induces elastic fibre disruption and cartilage matrix increase in ligamentum flavum. Scientific Reports, 2017, 7(1): 13092.
4. Azril, Huang K Y, Hobley J, et al. Correlation of the degenerative stage of a disc with magnetic resonance imaging, chemical content, and biomechanical properties of the nucleus pulposus. Journal of Biomedical Materials Research Part A, 2023, 111(7): 1054-1066.
5. Sengul E, Ozmen R, Demir T. The effects of pre-stressed rods contoured by different bending techniques on posterior instrumentation of L4-L5 lumbar spine segment: a finite element study. Proc Inst Mech Eng H, 2022, 236(7): 960-972.
6. Yan M, Song Z, Kou H, et al. New progress in basic research of macrophages in the pathogenesis and treatment of low back pain. Frontiers in Cell and Developmental Biology, 2022, 10: 866857.
7. Bardia A, Hovnanian M D, Brachtel E F, et al. Case 35-2018: a 68-year-old woman with back pain and a remote history of breast cancer. New England Journal of Medicine, 2018, 379(20): 1946-1953.
8. Samanta A, Lufkin T, Kraus P. Intervertebral disc degeneration-current therapeutic options and challenges. Frontiers in Public Health, 2023, 11: 1156749.
9. Łebkowski W J. Autopsy evaluation of the extent of degeneration of the lumbar intervertebral discs. Pol Merkur Lekarski, 2002, 13(75): 188-190.
10. Raj P P. Intervertebral disc: anatomy-physiology-pathophysiology-treatment. Pain Practice, 2008, 8(1): 18-44.
11. Kingma I, van Dieën J H, Nicolay K, et al. Monitoring water content in deforming intervertebral disc tissue by finite element analysis of MRI data. Magnetic Resonance in Medicine, 2000, 44(4): 650-654.
12. Rohlmann A, Zander T, Schmidt H, et al. Analysis of the influence of disc degeneration on the mechanical behaviour of a lumbar motion segment using the finite element method. Journal of Biomechanics, 2006, 39(13): 2484-2490.
13. Park W M, Kim Y H, Lee S. Effect of intervertebral disc degeneration on biomechanical behaviors of a lumbar motion segment under physiological loading conditions. Journal of Mechanical Science and Technology, 2013, 27: 483-489.
14. Yang B, O'Connell G D. Intervertebral disc swelling maintains strain homeostasis throughout the annulus fibrosus: a finite element analysis of healthy and degenerated discs. Acta Biomaterialia, 2019, 100: 61-74.
15. Finley S M, Brodke D S, Spina N T, et al. FEBio finite element models of the human lumbar spine. Comput Methods Biomech Biomed Engin, 2018, 21(6): 444-452.
16. 高旭, 邢文华. 有限元分析法在脊柱外科领域的应用. 中国组织工程研究, 2023, 27(18): 2921.
17. Liu Z, Wang H, Yuan Z, et al. High-resolution 3D printing of angle-ply annulus fibrosus scaffolds for intervertebral disc regeneration. Biofabrication, 2022, 15(1): 015015.
18. Lu Y, Xiang J, Yin B, et al. Finite element comparative analysis on treatment of lumbar disc herniation by the oblique wrench method and the combination of traction, pressing, and oblique pulling. Chinese Journal of Tissue Engineering Research, 2023, 27(13): 2011.
19. Heo M, Park S. Biphasic properties of PVAH (polyvinyl alcohol hydrogel) reflecting biomechanical behavior of the nucleus pulposus of the human intervertebral disc. Materials, 2022, 15(3): 1125.
20. Zhou M, Huff R D, Abubakr Y, et al. Torque-and muscle-driven flexion induce disparate risks of in vitro herniation: a multiscale and multiphasic structure-based finite element study. J Biomech Eng, 2022, 144(6): 061005.
21. Iatridis J C, Setton L A, Foster R J, et al. Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. Journal of Biomechanics, 1998, 31(6): 535-544.
22. Johannessen W, Elliott D M. Effects of degeneration on the biphasic material properties of human nucleus pulposus in confined compression. Spine, 2005, 30(24): E724-E729.
23. Natarajan R N, Williams J R, Andersson G B. Recent advances in analytical modeling of lumbar disc degeneration. Spine, 2004, 29(23): 2733-2741.
24. Iatridis J C, Setton L A, Weidenbaum M, et al. Alterations in the mechanical behavior of the human lumbar nucleus pulposus with degeneration and aging. Journal of Orthopaedic Research, 1997, 15(2): 318-322.
25. Iatridis J C, Weidenbaum M, Setton L A, et al. Is the nucleus pulposus a solid or a fluid? Mechanical behaviors of the nucleus pulposus of the human intervertebral disc. Spine, 1996, 21(10): 1174-1184.
26. Ateshian G A, Rajan V, Chahine N O, et al. Modeling the matrix of articular cartilage using a continuous fiber angular distribution predicts many observed phenomena. J Biomech Eng, 2009, 131(6): 061003.
27. Holmes M H, Mow V C. The nonlinear characteristics of soft gels and hydrated connective tissues in ultrafiltration. Journal of Biomechanics, 1990, 23(11): 1145-1156.
28. Pintar F A, Yoganandan N, Myers T, et al. Biomechanical properties of human lumbar spine ligaments. Journal of biomechanics, 1992, 25(11): 1351-1356.
29. Wilke H J, Neef P, Caimi M, et al. New in vivo measurements of pressures in the intervertebral disc in daily life. Spine, 1999, 24(8): 755-762.
30. Dreischarf M, Zander T, Shirazi-Adl A, et al. Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together. Journal of Biomechanics, 2014, 47(8): 1757-1766.
31. Rohlmann A, Neller S, Claes L, et al. Influence of a follower load on intradiscal pressure and intersegmental rotation of the lumbar spine. Spine, 2001, 26(24): E557-E561.
32. Woldtvedt D J, Womack W, Gadomski B C, et al. Finite element lumbar spine facet contact parameter predictions are affected by the cartilage thickness distribution and initial joint gap size. J Biomech Eng, 2011, 133(6): 061009.
33. 林伟健, 李俊言, 陈瑱贤, 等. 正常和早期膝骨关节炎的软骨生物力学研究. 力学学报, 2021, 53(11): 3147-3156.
34. Ateshian G A, Maas S, Weiss J A. Finite element algorithm for frictionless contact of porous permeable media under finite deformation and sliding. J Biomech Eng, 2010, 132(6): 061006.
35. Zimmerman B K, Maas S A, Weiss J A, et al. A finite element algorithm for large deformation biphasic frictional contact between porous-permeable hydrated soft tissues. J Biomech Eng, 2022, 144(2): 021008.
36. Sun Z, Sun Y, Lu T, et al. A swelling-based biphasic analysis on the quasi-static biomechanical behaviors of healthy and degenerative intervertebral discs. Comput Methods Programs Biomed, 2023, 235: 107513.

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Latest ArticlesFinite element modeling and simulation study of solid-liquid biphase fiber-reinforced lumbar intervertebral disc

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