State-of-the-art of finite element modelling of the human spine to study the impact of vibrations: a review. (English) Zbl 1542.65165
Summary: Exposure to vibration can be harmful to the spinal column, which can cause injury to the spine and related tissues by jolting and compressing the spinal column’s vertebrae. Long-term exposure to vibration can lead to problems with the spinal column, including stenosis, herniated discs, and degenerative disc disease (degeneration of the intervertebral discs). Vibration can exacerbate muscle strains, sprains, and pre-existing back problems. To date, experimental studies on vibrations have been limited to simple human dummies, which cannot determine its effects on exposed critical organs such as the human spine. However, with computational modelling, it is possible to not only study the effects of vibrations on the realistic spine geometry, but also allow the assignment of biofidelic material properties, loads and boundary conditions. This work aims to comprehensively review computational models studying the various segments of the spinal column and the effects of spinal vibrations. This study is anticipated to lead to a better understanding of the state-of-the-art spine modelling and computational complexities associated with spinal geometry development, material modelling, and finite-element modelling with vibrational loads, and also highlights the gaps and essential future research prospects.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 92C20 | Neural biology |
| 92-10 | Mathematical modeling or simulation for problems pertaining to biology |
| 74L15 | Biomechanical solid mechanics |
References:
| [1] | Sandover, J., “Behaviour of the spine under shock and vibration: a review,” Clin Biomech (Bristol, Avon), vol. 3, no. 4, pp. 249-256, 1988. DOI: . |
| [2] | Johanning, E., “Diagnosis of Whole-Body Vibration Related Health Problems in Occupational Medicine,” J. Low Frequency Noise, Vibration Active Control, vol. 30, no. 3, pp. 207-220, 2011. Sep. DOI: . |
| [3] | Griffin, M. J. and Erdreich, J., “Handbook of Human Vibration,” J. Acoust. Soc. Am., vol. 90, no. 4, pp. 2213-2213, 1991. DOI: . |
| [4] | Bovenzi, M., “Disorders of the human spine caused by occupational exposure to whole-body vibration,” Noise Vibr. Worldwide, vol. 30, no. 7, pp. 19-24, 1999. DOI: . |
| [5] | Ramirez, D. Z. M., Strike, S. and Lee, R., “Vibration transmission of the spine during walking is different between the lumbar and thoracic regions in older adults,” Age Ageing, vol. 46, no. 6, pp. 982-987, 2017. DOI: . |
| [6] | Wilder, D. G., Woodworth, B. B., Frymoyer, J. W. and Pope, M. H., “Vibration and the Human Body,” Vibration and the human spine.” Spine, vol. 7, no. 3, pp. 243-254, 1982. |
| [7] | Seidel, H., “On the relationship between whole-body vibration exposure and spinal health risk,” Ind. Health, vol. 43, no. 3, pp. 361-377, 2005. DOI: . |
| [8] | Wilder, D. G., “The biomechanics of vibration and low back pain,” Am. J. Ind. Med., vol. 23, no. 4, pp. 577-588, 1993. DOI: . |
| [9] | Hinz, B., Menzel, G., Blüthner, R. and Seidel, H., “laboratory testing of operator seat vibration with 37 subjects—critical comment on ISO/DIS 7096,” J. Sound Vib., vol. 215, no. 4, pp. 977-988, Aug. 1998. DOI: . |
| [10] | Amiri, S., Naserkhaki, S. and Parnianpour, M., “Effect of whole-body vibration and sitting configurations on lumbar spinal loads of vehicle occupants,” Comput. Biol. Med., vol. 107, no. August 2018, pp. 292-301, 2019. DOI: . |
| [11] | Morgado Ramírez, D. Z., Strike, S. and Lee, R. Y. W., “Measurement of transmission of vibration through the human spine using skin-mounted inertial sensors,” Med. Eng. Phys., vol. 35, no. 5, pp. 690-695, May 2013. DOI: . |
| [12] | Hinz, B., Seidel, H., Menzel, G. and Blüthner, R., “Effects related to random whole-body vibration and posture on a suspended seatwith and without backrest,” J. Sound Vib., vol. 253, no. 1, pp. 265-282, May 2002. DOI: . |
| [13] | Seidel, H., “Myoelectric reactions to ultra-low frequency and low-frequency whole body vibration,” Eur. J. Appl. Physiol. Occup. Physiol., vol. 57, no. 5, pp. 558-562, May 1988. DOI: . |
| [14] | Blüthner, R., Hinz, B., Menzel, G. and Seidel, H., “Back muscle response to transient whole-body vibration,” Int. J. Ind. Ergon, vol. 12, no. 1-2, pp. 49-59, Aug. 1993. DOI: . |
| [15] | Blüthner, R., Seidel, H., Hinz, B. and Schust, M., “Timing of back muscles during whole-body vibration with transients – its significance for the internal spinal load,” J. Low Frequency Noise, Vibr. Active Control, vol. 17, no. 4, pp. 215-226, Dec. 1998. DOI: . |
| [16] | Blüthner, R., Seidel, H. and Hinz, B., “myoelectric response of back muscles to vertical random whole-body vibration with different magnitudes at different postures,” JSV, vol. 253, no. 1, pp. 37-56, May 2002. DOI: . |
| [17] | Dong, R. C. and Guo, L. X., “Effect of muscle soft tissue on biomechanics of lumbar spine under whole body vibration,” Int. J. Precis. Eng. Manuf, vol. 18, no. 11, pp. 1599-1608, 2017. DOI: . |
| [18] | Tiemessen, J. H., Hulshof, C. T. J. and Frings-Dresen, M. H. W., “Low back pain in drivers exposed to whole body vibration: analysis of a dose-response pattern,” Occup. Environ. Med., vol. 65, no. 10, pp. 667-675, Oct. 2008. DOI: . |
| [19] | Hedman, T. P. and Fernie, G. R., “Mechanical response of the lumbar spine to seated postural loads,” Spine (Phila Pa 1976), vol. 22, no. 7, pp. 734-743, Apr. 1997. DOI: . |
| [20] | Brinckmann, P., Biggemann, M. and Hilweg, D., “Prediction of the compressive strength of human lumbar vertebrae,” Clin. Biomech., vol. 4 no. Suppl. 2, pp. iii-27, Jan. 1989. DOI: . |
| [21] | Hansson, T., Roos, B. and Nachemson, A., “The bone mineral content and ultimate compressive strength of lumbar vertebrae,” Spine, vol. 5, no. 1, pp. 46-55, 1980. DOI: . |
| [22] | Seidel, H., et al., “On the health risk of the lumbar spine due to whole-body VIBRATION—THEORETICAL approach, experimental data and evaluation of whole-body vibration,” JSV, vol. 215, no. 4, pp. 723-741, Aug. 1998. DOI: . |
| [23] | Issever, H., Aksoy, C., Sabuncu, H. and Karan, A., “Vibration and its effects on the body,” Med. Princ. Pract., vol. 12, no. 1, pp. 34-38, 2003. DOI: . |
| [24] | Bovenzi, M., Schust, M. and Mauro, M., “An overview of low back pain and occupational exposures to whole-body vibration and mechanical shocks,” Med. Lav., vol. 108, no. 6, pp. 419-433, 2017. DOI: . |
| [25] | McGill, S. M., “The biomechanics of low back injury: implications on current practice in industry and the clinic,” J. Biomech., vol. 30, no. 5, pp. 465-475, 1997. DOI: . |
| [26] | Troup, J. D. G., “Driver’s back pain and its prevention. A review of the postural, vibratory and muscular factors, together with the problem of transmitted road-shock,” Appl. Ergon., vol. 9, no. 4, pp. 207-214, 1978. DOI: . |
| [27] | Bazrgari, B., Shirazi-Adl, A. and Kasra, M., “Computation of trunk muscle forces, spinal loads and stability in whole-body vibration,” J. Sound Vib., vol. 318, no. 4-5, pp. 1334-1347, 2008. DOI: . |
| [28] | Dupuis, H., Zerlett, G., Heidelberg, B. and York, N., The Effects of Whole-Body Vibration. |
| [29] | Drerup, B., Granitzka, M., Assheuer, J. and Zerlett, G., “Assessment of disc injury in subjects exposed to long-term whole-body vibration,” Eur. Spine. J., vol. 8, no. 6, pp. 458-467, 1999. DOI: . |
| [30] | Iatridis, J. C., Nicoll, S. B., Michalek, A. J., Walter, B. A. and Gupta, M. S., “Role of biomechanics in intervertebral disc degeneration and regenerative therapies: what needs repairing in the disc and what are promising biomaterials for its repair?,” Spine J., vol. 13, no. 3, pp. 243-262, 2013. DOI: . |
| [31] | Waters, T., Rauche, C., Genaidy, A. and Rashed, T., “A new framework for evaluating potential risk of back disorders due to whole body vibration and repeated mechanical shock,” Ergonom., vol. 50, no. 3, pp. 379-395, 2007. DOI: . |
| [32] | Ayari, H., Thomas, M., Doré, S. and Serrus, O., “Evaluation of lumbar vertebra injury risk to the seated human body when exposed to vertical vibration,” J. Sound Vib., vol. 321, no. 1-2, pp. 454-470, 2009. DOI: . |
| [33] | Magnusson, M. L., Pope, M. H., Hulshof, C. T. J. and Bovenzi, M., “Development of a protocol for epidemiological studies of whole-body vibration and musculoskeletal disorders of the lower back,” J. Sound Vib., vol. 215, no. 4, pp. 643-651, 1998. DOI: . |
| [34] | Van Der Houwen, E. B., Baron, P., Veldhuizen, A. G., Burgerhof, J. G. M., Van Ooijen, P. M. A. and Verkerke, G. J., “Geometry of the intervertebral volume and vertebral endplates of the human spine,” Ann. Biomed. Eng., vol. 38, no. 1, pp. 33-40, Jan. 2010. DOI: . |
| [35] | Guo, L. X., Teo, E. C., Lee, K. K. and Zhang, Q. H., “Vibration characteristics of the human spine under axial cyclic loads: effect of frequency and damping,” Spine, vol. 30, no. 6, pp. 631-637, Mar. 2005. DOI: . |
| [36] | Mo, F., et al., “A neuromuscular human body model for lumbar injury risk analysis in a vibration loading environment,” Comput. Methods Programs Biomed., vol. 232, pp. 107442, 2023. DOI: . |
| [37] | Wilder, D. G. and DrMedSc, M. H. P., “Epidemiological and aetiological aspects of low back pain in vibration environments an update,” Clin. Biomech., vol. 11, no. 2, pp. 61-73, 1996. DOI: . |
| [38] | Patterson, F., Miralami, R., Tansey, K. E., Prabhu, R. K. and Priddy, L. B., “Deleterious effects of whole-body vibration on the spine: a review of in vivo, ex vivo, and in vitro models,” Anim. Model Exp. Med., vol. 4, no. 2, pp. 77-86, 2021. DOI: . |
| [39] | Byeon, J. H., et al., “Degenerative changes of spine in helicopter pilots,” Ann. Rehabil. Med., vol. 37, no. 5, pp. 706-712, 2013. DOI: . |
| [40] | El-Rich, M., Shirazi-Adl, A. and Arjmand, N., “Muscle activity, internal loads, and stability of the human spine in standing postures: combined model and in vivo studies,” Spine, vol. 29, no. 23, pp. 2633-2642, Dec. 2004. DOI: . |
| [41] | Smit, T. H., “The use of a quadruped as an in vivo model for the study of the spine - Biomechanical considerations,” Eur. Spine J., vol. 11, no. 2, pp. 137-144, Apr. 2002. DOI: . |
| [42] | Ghezelbash, F., Shahvarpour, A., Larivière, C. and Shirazi-Adl, A., “Evaluating stability of human spine in static tasks: a combined in vivo-computational study,” Comput. Methods Biomech. Biomed Engin., vol. 25, no. 10, pp. 1156-1168, 2022. DOI: . |
| [43] | Alapan, Y., İnceoğlu, S. and Goel, V. K., “Computational modeling of the spine,” Benzel’s Spine Surg. Tech. Complicat. Avoid. Manag. vol. 1-2, pp. 305-311.e2. Jan. 2017, DOI: . |
| [44] | Fagan, M. J., Julian, S. and Mohsen, A. M., “Finite element analysis in spine research,” Proc. Inst. Mech. Eng H., vol. 216, no. 5, pp. 281-298, May 2002. DOI: . |
| [45] | Xin, H. and Diao, H., “Computational biomechanical modelling of the spine,” Comput. Model. Biomech. Biotribology Musculoskelet. Syst. Biomater. Tissues, pp. 577-597, Jan. 2021. DOI: . |
| [46] | Fung, Y.-C., “The application of biomechanics to the understanding of injury and healing.” In Accidental injury: biomechanics and prevention, pp. 1-11. New York, NY: Springer New York, 1993. DOI: |
| [47] | “Biomechanics of spine stabilization,” AJNR Am. J. Neuroradiol., vol. 23, no. 7, pp. 1261, 2002. Accessed: may 20, 2023. [Online]. Available:/pmc/articles/PMC8185725/ |
| [48] | Espinoza Orías, A. A., He, J. and Wang, M., “Biomechanical testing of the intact and surgically treated spine,” Exp. Methods Orthop. Biomech., pp. 133-147, Jan. 2017. DOI: . |
| [49] | Noailly, J. and Lacroix, D., “Finite element modelling of the spine,” Biomater. Spinal Surg., pp. 144-234e, Jan. 2012. DOI: . |
| [50] | Kramer, P. A., Hammerberg, A. G. and Sylvester, A. D., “Modeling the spine using finite element models: considerations and cautions,” Spinal Evol. Morphol. Funct. Pathol. Spine Hominoid Evol., pp. 387-400, Jan. 2019. DOI: . |
| [51] | Kurutz, M., Oroszváry, L., Kurutz, M. and Oroszváry, L., “Finite element modeling and simulation of healthy and degenerated human lumbar spine,” Finite Elem. Anal. - from Biomed. Appl. Ind. Dev, Mar. 2012. DOI: . |
| [52] | Lu, Y. M., Hutton, W. C. and Gharpuray, V. M., “The effect of fluid loss on the viscoelastic behavior of the lumbar intervertebral disc in compression,” J. Biomech. Eng., vol. 120, no. 1, pp. 48-54, 1998. DOI: . |
| [53] | Belytschko, T., Kulak, R. F., Schultz, A. B. and Galante, J. O., “Finite element stress analysis of an intervertebral disc,” J. Biomech., vol. 7, no. 3, pp. 277-285, May 1974. DOI: . |
| [54] | Brekelmans, W. A. M., Poort, H. W. and Slooff, T. J. J. H., “A new method to analyse the mechanical behaviour of skeletal parts,” Acta Orthop. Scand., vol. 43, no. 5, pp. 301-317, 1972. DOI: . |
| [55] | Knapik, G. G., Mendel, E., Bourekas, E. and Marras, W. S., “Computational lumbar spine models: a literature review,” Clin. Biomech., vol. 100, pp. 105816, 2022. DOI: . |
| [56] | Ellingson, B. M., Salamon, N. and Holly, L. T., “Imaging techniques in spinal cord injury,” World Neurosurg., vol. 82, no. 6, pp. 1351-1358, Dec. 2014. DOI: . |
| [57] | Hussain, S., et al., “Modern diagnostic imaging technique applications and risk factors in the medical field: a review,” Biomed. Res. Int., vol. 2022, pp. 1-19, 2022. DOI: . |
| [58] | Naoum, S., Vasiliadis, A. V., Koutserimpas, C., Mylonakis, N., Kotsapas, M. and Katakalos, K., “Finite element method for the evaluation of the human spine: a literature overview,” J. Funct. Biomater., vol. 12, no. 3, pp. 43, Jul. 2021. DOI: . |
| [59] | Mosekilde, L., “Vertebral structure and strength In vivo and In vitro,” Calcif. Tissue Int., vol. 53 Suppl 1, no. S1, pp. S121-S126, Feb. 1993. DOI: . |
| [60] | Jung, H. J., et al., “Quality of life in patients with osteoporotic vertebral compression fractures,” J. Bone Metab., vol. 24, no. 3, pp. 187-196, 2017. DOI: . |
| [61] | Melton, L. J., “Adverse outcomes of osteoporotic fractures in the general population,” J. Bone Miner. Res., vol. 18, no. 6, pp. 1139-1141, 2003. DOI: . |
| [62] | Deschênes, S. and De Guise, J., “Wavelet-based automatic segmentation of the vertebral bodies in digital radiographs,” ICASSP, IEEE Int. Conf. Acoust. Speech Signal Process. - Proc, vol. 4, 2002. DOI: . |
| [63] | Silva, M. J., Keaveny, T. M. and Hayes, W. C., “Load sharing between the shell and centrum in the lumbar vertebral body,” Spine vol. 22, no. 2, pp. 140-150, Jan. 1997. DOI: . |
| [64] | Higgins, K. B., Sindall, D. R., Cuitino, A. M. and Langrana, N. A., “Biomechanical alterations in intact osteoporotic spine due to synthetic augmentation: finite element investigation,” J Biomech Eng, vol. 129, no. 4, pp. 575-585, Aug. 2007. DOI: . |
| [65] | Whyne, C. M., Hu, S. S. and Lotz, J. C., “Burst fracture in the metastatically involved spine: development, validation, and parametric analysis of a three-dimensional poroelastic finite-element model,” Spine (Phila Pa 1976), vol. 28, no. 7, pp. 652-660, Apr. 2003. DOI: . |
| [66] | Cappetti, N., Naddeo, A., Pellegrino, A., Solitro, G. F. and Naddeo, F., “Parametric model of lumbar vertebra,” Dall’Idea al Prod. la Rappresent. come Base per lo Svilupp. e L’innovazione, vol. CD, no. January 2007. p. CD—file. |
| [67] | Zhou, S. H., McCarthy, I. D., McGregor, A. H., Coombs, R. R. H. and Hughes, S. P. F., “Geometrical dimensions of the lower lumbar vertebrae – analysis of data from digitised CT images,” Eur. Spine J., vol. 9, no. 3, pp. 242-248, 2000. DOI: . |
| [68] | Falcinelli, C. and Whyne, C., “Image-based finite-element modeling of the human femur,” Comput. Methods Biomech. Biomed. Engin., vol. 23, no. 14, pp. 1138-1161, 2020. DOI: . |
| [69] | Lessmann, N., van Ginneken, B., de Jong, P. A. and Išgum, I., “Iterative fully convolutional neural networks for automatic vertebra segmentation and identification,” Med. Image Anal., vol. 53, pp. 142-155, Apr. 2019. DOI: . |
| [70] | Michael Kelm, B., et al., “Spine detection in CT and MR using iterated marginal space learning,” Med. Image Anal., vol. 17, no. 8, pp. 1283-1292, Dec. 2013. DOI: . |
| [71] | Suzani, A., Rasoulian, A., Seitel, A., Fels, S., Rohling, R. N. and Abolmaesumi, P., “Deep learning for automatic localization, identification, and segmentation of vertebral bodies in volumetric MR images,” Proceedings Volume 9415, Medical Imaging 2015: Image-Guided Procedures, Robotic Interventions, and Modeling, vol. 9415, pp. 269-275, Mar. 2015. DOI: . |
| [72] | Jakubicek, R., Chmelik, J., Jan, J., Ourednicek, P., Lambert, L. and Gavelli, G., “Learning-based vertebra localization and labeling in 3D CT data of possibly incomplete and pathological spines,” Comput. Methods Programs Biomed., vol. 183, pp. 105081, Jan. 2020. DOI: . |
| [73] | Dickerson, D. A., Sander, E. A. and Nauman, E. A., “Modeling the mechanical consequences of vibratory loading in the vertebral body: microscale effects,” Biomech. Model Mechanobiol., vol. 7, no. 3, pp. 191-202, 2008. DOI: . |
| [74] | Galbusera, F., Neidlinger-Wilke, C. and Wilke, H. J., “Biomechanics of the spine,” in Spine Phenotypes. London, UK: Elsevier, 2023. https://www.sciencedirect.com/book/9780128128510/biomechanics-of-the-spine |
| [75] | Adams, M. A., Bogduk, N., Burton, K. and Dolan, P., The Biomechanics of Back Pain. Elsevier, 2012. p. 345. |
| [76] | Stokes, I. A. F. and Gardner-Morse, M., “A database of lumbar spinal mechanical behavior for validation of spinal analytical models,” J. Biomech., vol. 49, no. 5, pp. 780-785, Mar. 2016. DOI: . |
| [77] | Schmidt, H., Bashkuev, M., Galbusera, F., Wilke, H. J. and Shirazi-Adl, A., “Finite element study of human lumbar disc nucleus replacements,” Comput. Methods Biomech. Biomed. Engin., vol. 17, no. 16, pp. 1762-1776, 2014. DOI: . |
| [78] | Castro, A. P. G. and Lacroix, D., Computational Modelling of the Intervertebral Disc: A Case-Study for Biomedical Composites. 2nd ed. Elsevier Ltd., 2017, DOI: . |
| [79] | Malandrino, A., Noailly, J. Ô. and Lacroix, D., “Numerical exploration of the combined effect of nutrient supply, tissue condition and deformation in the intervertebral disc,” J. Biomech., vol. 47, no. 6, pp. 1520-1525, Apr. 2014. DOI: . |
| [80] | Wills, C. R., Malandrino, A., Van Rijsbergen, M., Lacroix, D., Ito, K. and Noailly, J., “Simulating the sensitivity of cell nutritive environment to composition changes within the intervertebral disc,” J. Mech. Phys. Solids, vol. 90, pp. 108-123, May 2016. DOI: . |
| [81] | Castro, A. P. G., et al., “Long-term creep behavior of the intervertebral disk: comparison between bioreactor data and numerical results,” Front. Bioeng. Biotechnol., vol. 2, no. NOV, pp. 56, Nov. 2014. DOI: . |
| [82] | Ferguson, S. J., Ito, K. and Nolte, L. P., “Fluid flow and convective transport of solutes within the intervertebral disc,” J. Biomech., vol. 37, no. 2, pp. 213-221, Feb. 2004. DOI: . |
| [83] | Hussain, M., Natarajan, R. N., An, H. S. and Andersson, G. B. J., “Progressive disc degeneration at C5-C6 segment affects the mechanics between disc heights and posterior facets above and below the degenerated segment: A flexion-extension investigation using a poroelastic C3-T1 finite element model,” Med. Eng. Phys., vol. 34, no. 5, pp. 552-558, Jun. 2012. DOI: . |
| [84] | Schmidt, H., et al., “Computational biomechanics of a lumbar motion segment in pure and combined shear loads,” J. Biomech., vol. 46, no. 14, pp. 2513-2521, Sep. 2013. DOI: . |
| [85] | Schroeder, Y., Huyghe, J. M., Van Donkelaar, C. C. and Ito, K., “A biochemical/biophysical 3D FE intervertebral disc model,” Biomech. Model. Mechanobiol., vol. 9, no. 5, pp. 641-650, Oct. 2010. DOI: . |
| [86] | Van Den Broek, P. R., Huyghe, J. M. and Ito, K., “Biomechanical behavior of a biomimetic artificial intervertebral disc,” Spine, vol. 37, no. 6, pp. E367-E373, Mar. 2012. DOI: . |
| [87] | Lin, H. S., Lui, Y. K., Ray, G. and Nikravesh, P., “Systems identification for material properties of the intervertebral joint,” J. Biomech., vol. 11, no. 1-2, pp. 1-14, Jan. 1978. DOI: . |
| [88] | Schmidt, H., Galbusera, F., Rohlmann, A. and Shirazi-Adl, A., “What have we learned from fi nite element model studies of lumbar intervertebral discs in the past four decades ?,” J. Biomech., vol. 46, no. 14, pp. 2342-2355, 2013. DOI: . |
| [89] | Showalter, B. L., et al., “Novel human intervertebral disc strain template to quantify regional three-dimensional strains in a population and compare to internal strains predicted by a finite element model,” J. Orthop. Res., vol. 34, no. 7, pp. 1264-1273, 2016. DOI: . |
| [90] | Cheung, J. T. M., Zhang, M. and Chow, D. H. K., “Biomechanical responses of the intervertebral joints to static and vibrational loading: A finite element study,” Clin. Biomech., vol. 18, no. 9, pp. 790-799, 2003. DOI: . |
| [91] | Yoganandan, N., Kumaresan, S. C., Liming, V., Pintar, F. A. and Larson, S. J., “Finite element modeling of the C4-C6 cervical spine unit,” Med. Eng. Phys., vol. 18, no. 7, pp. 569-574, 1996. DOI: . |
| [92] | Toosizadeh, N. and Haghpanahi, M., “Generating a finite element model of the cervical spine: estimating muscle forces and internal loads,” Sci. Iran, vol. 18, no. 6, pp. 1237-1245, Dec. 2011. DOI: . |
| [93] | Kleinberger, M., “Application of finite element techniques to the study of cervical spine mechanics,” SAE Tech. Pap, 1993. DOI: . |
| [94] | Clausen, J. D., Goel, V. K., Traynelis, V. C. and Scifert, J., “Uncinate processes and Luschka joints influence the biomechanics of the cervical spine: quantification using a finite element model of the C5-C6 segment,” J. Orthop. Res., vol. 15, no. 3, pp. 342-347, May 1997. DOI: . |
| [95] | P, L., A, N., B, S. and Claes, T., “Neck injuries in rear end collisions among front and rear seat occupants,” Proc. Int. Res. Counc. Biomech. Inj. Conf, vol. 16, pp. 319-325, 1988. http://www.safetylit.org/citations/index.php?fuseaction=citations.viewdetails&citationIds[]=citjournalarticle_247859_38 |
| [96] | Yoganandan, N., Kumaresan, S., Voo, L. and Pintar, F. A., “Finite Element Model of the Human Lower Cervical Spine: parametric Analysis of the C4-C6 Unit,” J. Biomech. Eng., vol. 119, no. 1, pp. 87-92, Feb. 1997. DOI: . |
| [97] | Merrill, T., Goldsmith, W. and Deng, Y. C., “Three-dimensional response of a lumped parameter head-neck model due to impact and impulsive loading,” J. Biomech., vol. 17, no. 2, pp. 81-95, Jan. 1984. DOI: . |
| [98] | Maurel, N., Lavaste, F. and Skalli, W., “A three-dimensional parameterized finite element model of the lower cervical spine, study of the influence of the posterior articular facets,” J. Biomech., vol. 30, no. 9, pp. 921-931, Sep. 1997. DOI: . |
| [99] | Panjabi, M. M., et al., “Mechanical properties of the human cervical spine as shown by three-dimensional load-displacement curves,” Spine, vol. 26, no. 24, pp. 2692-2700, Dec. 2001. DOI: . |
| [100] | Panzer, M. B., Fice, J. B. and Cronin, D. S., “Cervical spine response in frontal crash,” Med. Eng. Phys., vol. 33, no. 9, pp. 1147-1159, Nov. 2011. DOI: . |
| [101] | Erbulut, D. U., Zafarparandeh, I., Lazoglu, I. and Ozer, A. F., “Application of an asymmetric finite element model of the C2-T1 cervical spine for evaluating the role of soft tissues in stability,” Med. Eng. Phys., vol. 36, no. 7, pp. 915-921, Jul. 2014. DOI: . |
| [102] | Deng, Y. C. and Goldsmith, W., “Response of a human head/neck/upper-torso replica to dynamic loading—I. Physical model,” J. Biomech., vol. 20, no. 5, pp. 471-486, Jan. 1987. DOI: . |
| [103] | Saito, T., Yamamuro, T., Shikata, J., Oka, M. and Sutsumi, S., “Analysis and prevention of spinal column deformity following cervical laminectomy. I. Pathogenetic analysis of postlaminectomy deformities,” Spine, vol. 16, no. 5, pp. 494-502, 1991. DOI: . |
| [104] | Luo, Z. and Goldsmith, W., “Reaction of a human head/neck/torso system to shock,” J. Biomech., vol. 24, no. 7, pp. 499-510, Jan. 1991. DOI: . |
| [105] | Zafarparandeh, I., Erbulut, D. U., Lazoglu, I. and Ozer, A. F., “Development of a finite element model of the human cervical spine,” Turk. Neurosurg., vol. 24, no. 3, pp. 312-318, 2014. DOI: . |
| [106] | Kumaresan, S., Yoganandan, N. and Pintar, F. A., “Finite element analysis of the cervical spine: a material property sensitivity study,” Clin. Biomech., vol. 14, no. 1, pp. 41-53, Jan. 1999. DOI: . |
| [107] | Voo, L. M., Kumaresan, S., Yoganandan, N., Pintar, F. A. and Cusick, J. F., “Finite element analysis of cervical facetectomy,” Spine, vol. 22, no. 9, pp. 964-969, May 1997. DOI: . |
| [108] | Kumaresan, S., Yoganandan, N. and Pintar, F. A., “Finite element modeling approaches of human cervical spine facet joint capsule,” J. Biomech., vol. 31, no. 4, pp. 371-376, Apr. 1998. DOI: . |
| [109] | Östh, J., Brolin, K., Svensson, M. Y. and Linder, A., “A female ligamentous cervical spine finite element model validated for physiological loads,” J. Biomech. Eng., vol. 138, no. 6, pp. 061005, Jun. 2016. DOI: . |
| [110] | Camacho, D. L. A., Nightingale, R. W. and Myers, B. S., “Surface friction in near-vertex head and neck impact increases risk of injury,” J. Biomech., vol. 32, no. 3, pp. 293-301, Mar. 1999. DOI: . |
| [111] | Stemper, B. D., Kumaresan, S., Yoganandan, N. and Pintar, F. A., “Head-neck finite element model for motor vehicle inertial impact: material sensitivity analysis,” Biomed. Sci. Instrum., vol. 36, pp. 331-335, Jan. 2000. https://europepmc.org/article/med/10834254. |
| [112] | Meyer, F., Bourdet, N., Deck, C., Willinger, R. and Raul, J. S., “Human Neck Finite Element Model Development and Validation against Original Experimental Data,” SAE Tech. Pap, 2004. vol. 2004-Novem, no. November, Nov DOI: . |
| [113] | Cheng, X., Wang, T. and Pan, C., “Finite element analysis and validation of segments C2-C7 of the cervical spine,” Met. vol. 12, no. 12, pp. 2056, Nov. 2022. DOI: . |
| [114] | Yoganandan, N., Choi, H., Purushothaman, Y., Jebaseelan, D., Baisden, J. and Kurpad, S., “Effects of different severities of disc degeneration on the range of motion of cervical spine,” J Craniovertebr Junction Spine, vol. 11, no. 4, pp. 269-275, Oct. 2020. DOI: . |
| [115] | Cai, X. Y., et al., “Using finite element analysis to determine effects of the motion loading method on facet joint forces after cervical disc degeneration,” Comput. Biol. Med., vol. 116, pp. 103519, Jan. 2020. DOI: . |
| [116] | Cai, X. Y., YuChi, C. X., Du, C. F. and Mo, Z. J., “The effect of follower load on the range of motion, facet joint force, and intradiscal pressure of the cervical spine: a finite element study,” Med. Biol. Eng. Comput., vol. 58, no. 8, pp. 1695-1705, Aug. 2020. DOI: . |
| [117] | Sun, M. S., Cai, X. Y., Liu, Q., Du, C. F. and Mo, Z. J., “Application of Simulation Methods in Cervical Spine Dynamics,” J. Healthc. Eng., vol. 2020, pp. 7289648-12, 2020. DOI: . |
| [118] | Mimata, Y., Murakami, H., Sato, K. and Suzuki, Y., “Bilateral cerebellar and brain stem infarction resulting from vertebral artery injury following cervical trauma without radiographic damage of the spinal column: A case report,” Skeletal. Radiol., vol. 43, no. 1, pp. 99-105, Jan. 2014. DOI: . |
| [119] | Rao, R. D., Berry, C. A., Yoganandan, N. and Agarwal, A., “Occupant and crash characteristics in thoracic and lumbar spine injuries resulting from motor vehicle collisions,” Spine J., vol. 14, no. 10, pp. 2355-2365, Oct. 2014. DOI: . |
| [120] | Whitesides, T. E., Clinical Biomechanics of the Spine. 2nd ed., vol. 73, Lippincott, 1991. DOI: . |
| [121] | Aroeira, R. M. C., de, A. E., Pertence, M., Kemmoku, D. T. and Greco, M., “Three-dimensional geometric model of the middle segment of the thoracic spine based on graphical images for finite element analysis,” Res. Biomed. Eng., vol. 33, no. 2, pp. 97-104, May 2017. DOI: . |
| [122] | Lu, H., Zhang, Q., Ding, F., Wu, Q. and Liu, R., “Establishment and validation of a T12-L2 3D finite element model for thoracolumbar segments,” vol. 14, no. 3, pp. 1606-1615, 2022. |
| [123] | Wilcox, R. K., Allen, D. J., Hall, R. M., Limb, D., Barton, D. C. and Dickson, R. A., “A dynamic investigation of the burst fracture process using a combined experimental and finite element approach,” Eur. Spine J., vol. 13, no. 6, pp. 481-488, Oct. 2004. DOI: . |
| [124] | Wilcox, R. K., et al., “A dynamic study of thoracolumbar burst fractures,” J. Bone Joint Surg. Am., vol. 85, no. 11, pp. 2184-2189, 2003. DOI: . |
| [125] | “Dale“ Bass, C. R., et al., “Thoracic and lumbar spinal impact tolerance,” Accid. Anal. Prev., vol. 40, no. 2, pp. 487-495, Mar. 2008. DOI: . |
| [126] | Du, C., et al., “Biomechanical investigation of thoracolumbar spine in different postures during ejection using a combined finite element and multi-body approach,” Int. J. Numer. Method Biomed. Eng., vol. 30, no. 11, pp. 1121-1131, Nov. 2014. DOI: . |
| [127] | Ruan, J., El-Jawahri, R., Chai, L., Barbat, S. and Prasad, P., “Prediction and analysis of human thoracic impact responses and injuries in cadaver impacts using a full human body finite element model,” SAE Tech. Pap, Oct. 2003. DOI: . |
| [128] | Saha, S. and Roychowdhury, A., “Application of the finite element method in orthopedic implant design,” J. Long Term Eff. Med. Implants, vol. 19, no. 1, pp. 55-82, 2009. DOI: . |
| [129] | Campbell-Kyureghyan, N. H., “Computational modeling of the lumbar spine components : a review,” Int. J. Comput. Vis. Biomech, vol. 3, no. 1, 105816, 2017. |
| [130] | Orne, D. and Liu, Y. K., “A mathematical model of spinal response to impact,” J. Biomech., vol. 4, no. 1, pp. 49-71, 1971. DOI: . |
| [131] | Belytschko, T., Schwer, L. and Privitzer, E., “Theory and application of a three-dimensional model of the human spine,” Aviat. Space. Environ. Med., vol. 49, no. 1 Pt. 2, pp. 158-165, 1978. https://europepmc.org/article/med/623579 |
| [132] | Dietrich, M., Kedzior, K. and Zagrajek, T., “A Biomechanical Model of the Human Spinal System,” Proc. Inst. Mech. Eng. H, vol. 205, no. 1, pp. 19-26, 1991. DOI: . |
| [133] | Pankoke, S., Buck, B. and Woelfel, H. P., “Dynamic Fe model of sitting man adjustable to body height, body mass and posture used for calculating internal forces in the lumbar vertebral disks,” J. Sound Vib., vol. 215, no. 4, pp. 827-839, Aug. 1998. DOI: . |
| [134] | Ezquerro, F., Simón, A., Prado, M. and Pérez, A., “Combination of finite element modeling and optimization for the study of lumbar spine biomechanics considering the 3D thorax-pelvis orientation,” Med. Eng. Phys., vol. 26, no. 1, pp. 11-22, 2004. DOI: . |
| [135] | Xu, M., Yang, J., Lieberman, I. H. and Haddas, R., “Lumbar spine finite element model for healthy subjects: development and validation,” Comput. Methods Biomech. Biomed. Engin., vol. 20, no. 1, pp. 1-15, 2017. DOI: . |
| [136] | Breau, C., Shirazi-Adl, A. and de Guise, J., “Reconstruction of a human ligamentous lumbar spine using CT images-a three-dimensional finite element mesh generation,” Ann. Biomed. Eng., vol. 19, no. 3, pp. 291-302, May 1991. DOI: . |
| [137] | Chen, C. S., Cheng, C. K., Liu, C. L. and Lo, W. H., “Stress analysis of the disc adjacent to interbody fusion in lumbar spine,” Med. Eng. Phys., vol. 23, no. 7, pp. 483-491, Sep. 2001. DOI: . |
| [138] | Zander, T., Rohlmann, A., Klückner, C. and Bergmann, G., “Comparison of the mechanical behavior of the lumbar spine following mono- and bisegmental stabilization,” Clin. Biomech., vol. 17, no. 6, pp. 439-445, Jul. 2002. DOI: . |
| [139] | Park, W. M., Kim, K. and Kim, Y. H., “Effects of degenerated intervertebral discs on intersegmental rotations, intradiscal pressures, and facet joint forces of the whole lumbar spine,” Comput. Biol. Med., vol. 43, no. 9, pp. 1234-1240, Sep. 2013. DOI: . |
| [140] | Ayturk, U. M. and Puttlitz, C. M., “Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine,” Comput. Methods Biomech. Biomed. Engin., vol. 14, no. 8, pp. 695-705, Aug. 2011. DOI: . |
| [141] | Shirazi-Adl, A., “Nonlinear stress analysis of the whole lumbar spine in torsion—Mechanics of facet articulation,” J. Biomech., vol. 27, no. 3, pp. 289-299, Mar. 1994. DOI: . |
| [142] | Kong, W. Z., Goel, V. K. and Gilbertson, L. G., “Prediction of biomechanical parameters in the lumbar spine during static sagittal plane lifting,” J. Biomech. Eng., vol. 120, no. 2, pp. 273-280, Apr. 1998. DOI: . |
| [143] | Zander, T., Rohlmann, A., Calisse, J. and Bergmann, G., “Estimation of muscle forces in the lumbar spine during upper-body inclination,” Clin. Biomech., vol. 16, Suppl 1, pp. S73-S80, Jan. 2001. DOI: . |
| [144] | Little, J. P., De Visser, H., Pearcy, M. J. and Adam, C. J., “Are coupled rotations in the lumbar spine largely due to the osseo-ligamentous anatomy?—A modeling study,” Comput. Methods Biomech. Biomed. Engin., vol. 11, no. 1, pp. 95-103, 2008. Feb. DOI: . |
| [145] | Eberlein, R., Holzapfel, G. A. and Fröhlich, M., “Multi-segment FEA of the human lumbar spine including the heterogeneity of the annulus fibrosus,” Comput. Mech. vol. 34, no. 2, pp. 147-163, Apr. 2004. DOI: . · Zbl 1138.74370 |
| [146] | Schmidt, H., Galbusera, F., Rohlmann, A., Zander, T. and Wilke, H. J., “Effect of multilevel lumbar disc arthroplasty on spine kinematics and facet joint loads in flexion and extension: A finite element analysis,” Eur. Spine J., vol. 21, no. S5, pp. 663-674, Apr. 2012. DOI: . |
| [147] | Schmidt, H., et al., “Application of a new calibration method for a three-dimensional finite element model of a human lumbar annulus fibrosus,” Clin. Biomech., vol. 21, no. 4, pp. 337-344, May 2006. DOI: . |
| [148] | Guo, L. X. and Zhang, C., “Development and validation of a whole human body finite element model with detailed lumbar spine,” World Neurosurg., vol. 163, pp. e579-e592, Jul. 2022. DOI: . |
| [149] | Fan, W. and Guo, L. X., “Influence of different frequencies of axial cyclic loading on time-domain vibration response of the lumbar spine: A finite element study,” Comput. Biol. Med., vol. 86, pp. 75-81, Jul. 2017. DOI: . |
| [150] | Wu, C. C., et al., “Biomechanical role of the thoracolumbar ligaments of the posterior ligamentous complex: a finite element study,” World Neurosurg., vol. 112, pp. e125-e133, Apr. 2018. DOI: . |
| [151] | Fan, W. and Guo, L. X., “Biomechanical comparison of the effects of anterior, posterior and transforaminal lumbar interbody fusion on vibration characteristics of the human lumbar spine,” Comput. Methods Biomech. Biomed. Engin., vol. 22, no. 5, pp. 490-498, 2019. DOI: . |
| [152] | Dong, R. C., Guo, Q. J., Yuan, W., Du, W., Yang, X. H. and Zhao, Y. J., “The finite element model of seated whole human body for vibration investigations of lumbar spine in complex system,” IEEE Access, vol. 8, pp. 125046-125055, 2020. DOI: . |
| [153] | Verver, M., van Hoof, J., Oomens, C. W., van de Wouw, N. and Wismans, J. S. H., “Estimation of spinal loading in vertical vibrations by numerical simulation,” Clin. Biomech., vol. 18, no. 9, pp. 800-811, 2003. DOI: . |
| [154] | Biglari, H., Razaghi, R., Ebrahimi, S. and Karimi, A., “A computational dynamic finite element simulation of the thoracic vertebrae under blunt loading: spinal cord injury,” J. Braz. Soc. Mech. Sci. Eng., vol. 41, no. 2, pp. 1-8, Feb. 2019. DOI: . |
| [155] | Goel, V. K., Park, H. and Kong, W., “Investigation of vibration characteristics of the ligamentous lumbar spine using the finite element approach,” J. Biomech. Eng., vol. 116, no. 4, pp. 377-383, 1994. DOI: . |
| [156] | Kong, W. Z. and Goel, V. K., “Ability of the finite element models to predict response of the human spine to sinusoidal vertical vibration,” Spine, vol. 28, no. 17, pp. 1961-1967, 2003. DOI: . |
| [157] | Valentini, P. P., “Modeling human spine using dynamic spline approach for vibrational simulation,” J. Sound Vib., vol. 331, no. 26, pp. 5895-5909, 2012. DOI: . |
| [158] | Valentini, P. P. and Pennestrì, E., “An improved three-dimensional multibody model of the human spine for vibrational investigations,” Multibody Syst. Dyn., vol. 36, no. 4, pp. 363-375, 2016. DOI: . |
| [159] | Goel, V. and Park, H., “Investigation vibration characteristics ligamentous lumbar spine using finite element approach,”J Biomech Eng., vol. 116, no. 4, pp. 377-383, 1994. |
| [160] | Comer, C. M., White, D., Conaghan, P. G., Bird, H. A. and Redmond, A. C., “Effects of walking with a shopping trolley on spinal posture and loading in subjects with neurogenic claudication,” Arch. Phys. Med. Rehabil., vol. 91, no. 10, pp. 1602-1607, 2010. DOI: . |
| [161] | Huang, Y. P., et al., “Gait adaptations in low back pain patients with lumbar disc herniation: trunk coordination and arm swing,” Eur. Spine J., vol. 20, no. 3, pp. 491-499, 2011. DOI: . |
| [162] | Schmid, S., Stauffer, M., Jäger, J., List, R. and Lorenzetti, S., “Sling-based infant carrying affects lumbar and thoracic spine neuromechanics during standing and walking,” Gait Posture, vol. 67, pp. 172-180, 2019. DOI: . |
| [163] | Kim, Y. H., Khuyagbaatar, B. and Kim, K., “Recent advances in finite element modeling of the human cervical spine,” J. Mech. Sci. Technol., vol. 32, no. 1, pp. 1-10, 2018. DOI: . |
| [164] | Guo, L. X., Zhang, Y. M. and Zhang, M., “Finite element modeling and modal analysis of the human spine vibration configuration,” IEEE Trans. Biomed. Eng., vol. 58, no. 10, pp. 2987-2990, 2011. DOI: . |
| [165] | Guo, L. X. and Li, R., “Influence of vibration frequency variation on poroelastic response of intervertebral disc of lumbar spine,” J. Mech. Sci. Technol., vol. 33, no. 2, pp. 973-979, 2019. DOI: . |
| [166] | Boos, N. and Aebi, M., Spinal Disorders: Fundamentals of Diagnosis and Treatment. Berlin Heidelberg: Springer, 2008. DOI: . |
| [167] | Sukthankar, A., Nerlich, A. G. and Paesold, G., “Age-related changes of the spine,” Spinal Disord. Fundam. Diagnosis Treat., pp. 91-122, 2008. DOI: . |
| [168] | Ferguson, S. J. and Steffen, T., “Biomechanics of the aging spine,” Eur. Spine J., vol. 12, pp. S97-S103, 2003. DOI: . |
| [169] | Verma, S., Singh, G. and Chanda, A., “A novel finite element model for the study of harmful vibrations on the aging spine,” Comput. vol. 11, no. 5, pp. 93, May 2023. DOI: . |
| [170] | Castro, A. P. G., “Computational challenges in tissue engineering for the spine,” Bioengineering, vol. 8, no. 2, pp. 25, Feb. 2021. DOI: . |
| [171] | Wilmink, J. T., “The normal aging spine and degenerative spinal disease,” Neuroradiology, vol. 53, Suppl 1, pp. S181-S183, 2011. DOI: . |
| [172] | Natarajan, P., Fonseka, R. D., Kim, S., Betteridge, C., Maharaj, M. and Mobbs, R. J., “Analysing gait patterns in degenerative lumbar spine diseases: a literature review,” J. Spine Surg., vol. 8, no. 1, pp. 139-148, 2022. DOI: . |
| [173] | Seidel, H., “Selected health risks caused by long‐term, whole‐body vibration,” Am. J. Ind. Med., vol. 23, no. 4, pp. 589-604, 1993. DOI: . |
| [174] | Fan, R., Liu, J. and Liu, J., “Finite element investigation on the dynamic mechanical properties of low-frequency vibrations on human L2-L3 spinal motion segments with different degrees of degeneration,” Med. Biol. Eng. Comput., vol. 58, no. 12, pp. 3003-3016, Dec. 2020. DOI: . |
| [175] | Guo, L. X. and Teo, E. C., “Influence prediction of injury and vibration on adjacent components of spine using finite element methods,” J. Spinal. Disord. Tech., vol. 19, no. 2, pp. 118-124, Apr. 2006. DOI: . |
| [176] | Kurutz, M. and Oroszváry, L., “Finite element analysis of weightbath hydrotraction treatment of degenerated lumbar spine segments in elastic phase,” J. Biomech., vol. 43, no. 3, pp. 433-441, 2010. DOI: . |
| [177] | Guo, L. X. and Fan, W., “The effect of single-level disc degeneration on dynamic response of the whole lumbar spine to vertical vibration,” World Neurosurg., vol. 105, pp. 510-518, 2017. DOI: . |
| [178] | Aroeira, R. M. C., Pertence, A. E. M., Kemmoku, D. T. and Greco, M., “The effect of hypokyphosis on the biomechanical behavior of the adolescent thoracic spine,” J. Braz. Soc. Mech. Sci. Eng., vol. 40, no. 3, 2018. DOI: . |
| [179] | Matos, R., Fernandes, P. R., Matela, N. and Castro, A. P. G., “Lumbar intervertebral disc segmentation for computer modeling and simulation,” Comput. Methods Programs Biomed., vol. 230, pp. 107337, Mar. 2023. DOI: . |
| [180] | Chu, C., Belavý, D. L., Armbrecht, G., Bansmann, M., Felsenberg, D. and Zheng, G., “Fully automatic localization and segmentation of 3D vertebral bodies from CT/MR images via a learning-based method,” PLoS One, vol. 10, no. 11, pp. e0143327, Nov. 2015. DOI: . |
| [181] | Natalia, F., et al., “Development of Ground Truth Data for Automatic Lumbar Spine MRI Image Segmentation,” Proc. - 20th Int. Conf. High Perform. Comput. Commun. 16th Int. Conf. Smart City 4th Int. Conf. Data Sci. Syst. HPCC/SmartCity/DSS 2018, pp. 1449-1454. Jan. 2019. DOI: . |
| [182] | Bozic, K. J., Keyak, J. H., Skinner, H. B., Bueff, H. U. and Bradford, D. S., “Three-dimensional finite element modeling of a cervical vertebra: an investigation of burst fracture mechanism,” J Spinal Disord, vol. 7, no. 2, pp. 102-110, 1994. DOI: . |
| [183] | Silva, M. J., Keaveny, T. M. and Hayes, W. C., “Computed tomography-based finite element analysis predicts failure loads and fracture patterns for vertebral sections,” J. Orthop. Res., vol. 16, no. 3, pp. 300-308, 1998. DOI: . |
| [184] | Imai, K., Ohnishi, I., Bessho, M. and Nakamura, K., “Nonlinear finite element model predicts vertebral bone strength and fracture site,” Spine, vol. 31, no. 16, pp. 1789-1794, Jul. 2006. DOI: . |
| [185] | Eswaran, S. K., Gupta, A. and Keaveny, T. M., “Locations of bone tissue at high risk of initial failure during compressive loading of the human vertebral body,” Bone, vol. 41, no. 4, pp. 733-739, Oct. 2007. DOI: . |
| [186] | Buckley, J. M., Loo, K. and Motherway, J., “Comparison of quantitative computed tomography-based measures in predicting vertebral compressive strength,” Bone, vol. 40, no. 3, pp. 767-774, Mar. 2007. DOI: . |
| [187] | Dall’Ara, E., Pahr, D., Varga, P., Kainberger, F. and Zysset, P., “QCT-based finite element models predict human vertebral strength in vitro significantly better than simulated DEXA,” Osteoporos Int, vol. 23, no. 2, pp. 563-572, Feb. 2012. DOI: . |
| [188] | Pahr, D. H., Schwiedrzik, J., Dall’Ara, E. and Zysset, P. K., “Clinical versus pre-clinical FE models for vertebral body strength predictions,” J. Mech. Behav. Biomed. Mater, vol. 33, no. 1, pp. 76-83, May 2014. DOI: . |
| [189] | Costa, M. C., Eltes, P., Lazary, A., Varga, P. P., Viceconti, M. and Dall’Ara, E., “Biomechanical assessment of vertebrae with lytic metastases with subject-specific finite element models,” J. Mech. Behav. Biomed. Mater., vol. 98, pp. 268-290, Oct. 2019. DOI: . |
| [190] | Goel, V. K. and Clausen, J. D., “Prediction of load sharing among spinal components of a C5-C6 motion segment using the finite element approach,” Spine, vol. 23, no. 6, pp. 684-691, Mar. 1998. DOI: . |
| [191] | Yu, L. P., Qian, W. W., Yin, G. Y., Ren, Y. X. and Hu, Z. Y., “MRI assessment of lumbar intervertebral disc degeneration with lumbar degenerative disease using the pfirrmann grading systems,” PLoS One, vol. 7, no. 12, pp. e48074, Dec. 2012. DOI: . |
| [192] | Matthews, P. M. and Jezzard, P., “Functional magnetic resonance imaging,” J. Neurol. Neurosurg. Psychiatry, vol. 75, no. 1, pp. 6, 2004. DOI: . |
| [193] | Dall’Ara, E., et al., “Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation,” J. Mech. Behav. Biomed. Mater., vol. 25, pp. 23-32, Sep. 2013. DOI: . |
| [194] | Marchandise, E., Compère, G., Willemet, M., Bricteux, G., Geuzaine, C. and Remacle, J. F., “Quality meshing based on STL triangulations for biomedical simulations,” Numer. Methods Biomed. Eng., vol. 26, no. 7, pp. 876-889, Jul. 2010. DOI: . · Zbl 1197.92031 |
| [195] | Owen, S. J., Owen, S. J., White, D. R. and Tautges, T. J., “Facet-based surfaces for 3d mesh generation facet-based surfaces for 3D mesh generation,” 2002. [TA44] |
| [196] | Geuzaine, C. and Remacle, J. F., “Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities,” Numer. Meth Engin., vol. 79, no. 11, pp. 1309-1331, Sep. 2009. DOI: . · Zbl 1176.74181 |
| [197] | Szczerba, D., McGregor, R. and Székely, G., “High quality surface mesh generation for multi-physics bio-medical simulations,” Lect. Notes Comput. Sci. (Including Subser. Lect. Notes Artif. Intell. Lect. Notes Bioinformatics), vol. 4487 LNCS, pp. 906-913, 2007. DOI: . |
| [198] | Wang, C. S., Wang, W. H. A. and Lin, M. C., “STL rapid prototyping bio-CAD model for CT medical image segmentation,” Comput. Ind., vol. 61, no. 3, pp. 187-197, Apr. 2010. DOI: . |
| [199] | Wang, D., Hassan, O., Morgan, K. and Weatherill, N. P., “Enhanced remeshing from STL files with applications to surface grid generation,” Commun. Numer. Meth. Engng, vol. 23, no. 3, pp. 227-239, Mar. 2007. DOI: . · Zbl 1111.65016 |
| [200] | Zhang, Y., Bajaj, C. and Sohn, B. S., “3D finite element meshing from imaging data,” Comput. Methods Appl. Mech. Eng., vol. 194, no. 48-49, pp. 5083-5106, Nov. 2005. DOI: . · Zbl 1093.65019 |
| [201] | Camacho, D. L. A., Hopper, R. H., Lin, G. M. and Myers, B. S., “An improved method for finite element mesh generation of geometrically complex structures with application to the skullbase,” J. Biomech., vol. 30, no. 10, pp. 1067-1070, Oct. 1997. DOI: . |
| [202] | Ribeiro, N. S., Fernandes, P. C., Lopes, D. S., Folgado, J. O., … …Fernandes, P. R., “3-D Solid and finite element modeling of biomechanical structures-a software pipeline,” EUROMECH Solid, 2009. |
| [203] | Cook, R. D., Malkus, D. S., Plesha, M. E. and Witt, R. J. W., “Concept and Applications of Finite Element Analysis,” p. 733, 2002. https://www.wiley.com/en-us/Concepts+and+Applications+of+Finite+Element+Analysis |
| [204] | Ho-Le, K., “Finite element mesh generation methods: a review and classification,” Comput. Des., vol. 20, no. 1, pp. 27-38, Jan. 1988. DOI: . · Zbl 0661.65124 |
| [205] | Lederman, C., Joshi, A., Dinov, I., Van Horn, J. D., Vese, L. and Toga, A., “Tetrahedral mesh generation for medical images with multiple regions using active surfaces,” Proc IEEE Int Symp Biomed Imag., vol. 2010, pp. 436-439, 2010. DOI: . |
| [206] | Mohamed, A. and Davatzikos, C., “Finite element mesh generation and remeshing from segmented medical images,” 2004 2nd IEEE Int. Symp. Biomed. Imaging Macro to Nano, vol. 1, pp. 420-423, 2004. DOI: . |
| [207] | Burkhart, T. A., Andrews, D. M. and Dunning, C. E., “Finite element modeling mesh quality, energy balance and validation methods: A review with recommendations associated with the modeling of bone tissue,” J. Biomech., vol. 46, no. 9, pp. 1477-1488, May 2013. DOI: . |
| [208] | Singh, G. and Chanda, A., “Mechanical properties of whole-body soft human tissues: a review,” Biomed. Mater., vol. 16, no. 6, pp. 062004, Oct. 2021. DOI: . |
| [209] | Singh, G., Gupta, V. and Chanda, A., “Artificial skin with varying biomechanical properties,” Mater. Today Proc., vol. 62, pp. 3162-3166, 2022. DOI: . |
| [210] | Stemper, B. D., Board, D., Yoganandan, N. and Wolfla, C. E., “Biomechanical properties of human thoracic spine disc segments,” J. Craniovertebr Junction Spine, vol. 1, no. 1, pp. 18-22, Jan. 2010. DOI: . |
| [211] | Palaniswamy, M. and Yie, L. W., “Mechanical properties of the human vertebrae between normal, post corrective and post operative,” 2014 IEEE Int. Symp. Robot. Manuf. Autom. IEEE-ROMA2014, pp. 188-193, Oct. 2015. DOI: . |
| [212] | Karimi, A., Shojaei, A. and Tehrani, P., “Mechanical properties of the human spinal cord under the compressive loading,” J. Chem. Neuroanat., vol. 86, pp. 15-18, Dec. 2017. DOI: . |
| [213] | Wagnac, E., Arnoux, P. J., Garo, A., El-Rich, M. and Aubin, C. E., “Calibration of hyperelastic material properties of the human lumbar intervertebral disc under fast dynamic compressive loads,” J Biomech Eng, vol. 133, no. 10, pp. 101007, 2011. DOI: . |
| [214] | Sudres, P., et al., “Tensile mechanical properties of the cervical, thoracic and lumbar porcine spinal meninges,” J. Mech. Behav. Biomed. Mater., vol. 115, pp. 104280, 2021. Mar. DOI: . |
| [215] | Jiang, Y., Wang, Y. and Peng, X., “A visco-hyperelastic constitutive model for human spine ligaments,” Cell Biochem. Biophys., vol. 71, no. 2, pp. 1147-1156, 2015. DOI: . |
| [216] | Pintar, F. A., Yoganandan, N., Myers, T., Elhagediab, A. and Sances, A., “Biomechanical properties of human lumbar spine ligaments,” J. Biomech., vol. 25, no. 11, pp. 1351-1356, Nov. 1992. DOI: . |
| [217] | Picinbono, G., Delingette, H. and Ayache, N., “Non-linear and anisotropic elastic soft tissue models for medical simulation,” Proc. - IEEE Int. Conf. Robot. Autom, 2001. vol. 2, pp. 1370-1375, DOI: . |
| [218] | Courtney, T., Sacks, M. S., Stankus, J., Guan, J. and Wagner, W. R., “Design and analysis of tissue engineering scaffolds that mimic soft tissue mechanical anisotropy,” Biomaterials, vol. 27, no. 19, pp. 3631-3638, Jul. 2006. DOI: . |
| [219] | Cowin, S. C., “Mechanical properties of cortical bone and cancellous bone tissue,” in Bone Mechanics Handbook, CRC Press Inc., pp. 311-334, Sep. 2013. |
| [220] | Holzapfel, G. A., Gasser, T. C. and Ogden, R. W., “A new constitutive framework for arterial wall mechanics and a comparative study of material models,” J. Elast., vol. 61, no. 1/3, pp. 1-48, 2000. DOI: . · Zbl 1023.74033 |
| [221] | Holzapfel, G. A., “Nonlinear solid mechanics : a continuum approach for engineering,” p. 455, 2000. https://www.wiley.com/en-us/Nonlinear+Solid+Mechanics · Zbl 0980.74001 |
| [222] | Martins, P. A. L. S., Jorge, R. M. N. and Ferreira, A. J. M., “A comparative study of several material models for prediction of hyperelastic properties: application to silicone-rubber and soft tissues,” Strain, vol. 42, no. 3, pp. 135-147, Aug. 2006. DOI: . |
| [223] | Wilke, H. J., Neef, P., Caimi, M., Hoogland, T. and Claes, L. E., “New in vivo measurements of pressures in the intervertebral disc in daily life,” Spine, vol. 24, no. 8, pp. 755-762, Apr. 1999. DOI: . |
| [224] | Stadelmann, M. A., et al., “Integrating MRI-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc,” J. Mech. Behav. Biomed. Mater., vol. 85, pp. 37-42, Sep. 2018. DOI: . |
| [225] | Peng, X. Q., Guo, Z. Y. and Moran, B., “An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus,” J. Appl. Mech, vol. 73, no. 5, pp. 815-824, Sep. 2006. DOI: . · Zbl 1111.74590 |
| [226] | Kumaresan, S., Yoganandan, N., Pintar, F. A. and Maiman, D. J., “Finite element modeling of the cervical spine: role of intervertebral disc under axial and eccentric loads,” Med Eng Phys, vol. 21, no. 10, pp. 689-700, Dec. 1999. DOI: . |
| [227] | Guan, Y., et al., “Validation of a clinical finite element model of the human lumbosacral spine,” Med. Biol. Eng. Comput., vol. 44, no. 8, pp. 633-641, Aug. 2006. DOI: . |
| [228] | Yi Cai, X., et al., “Biomechanical effect of L4-L5 intervertebral disc degeneration on the lower lumbar spine: a finite element study,” Orthop. Surg., vol. 12, no. 3, pp. 917-930, Jun. 2020. DOI: . |
| [229] | Jones, A. C. and Wilcox, R. K., “Finite element analysis of the spine: towards a framework of verification, validation and sensitivity analysis,” Med. Eng. Phys., vol. 30, no. 10, pp. 1287-1304, Dec. 2008. DOI: . |
| [230] | Bilston, L. E. and Thibaultt, L. E., “The mechanical properties of the human cervical spinal cord in vitro,” Ann Biomed Eng, vol. 24, no. 1, pp. 67-74, 1996. DOI: . |
| [231] | Oakland, R. J., Hall, R. M., Wilcox, R. K. and Barton, D. C., “The biomechanical response of spinal cord tissue to uniaxial loading,” Proc. Inst. Mech. Eng H, vol. 220, no. 4, pp. 489-492, 2006. DOI: . |
| [232] | El Bojairami, I., El-Monajjed, K. and Driscoll, M., “Development and validation of a timely and representative finite element human spine model for biomechanical simulations,” Sci Rep, vol. 10, no. 1, pp. 21519, Dec. 2020. DOI: . |
| [233] | Khaniki, H. B., Ghayesh, M. H., Chin, R. and Amabili, M., A Review on the Nonlinear Dynamics of Hyperelastic Structures, vol. 110, Netherlands: Springer, 2022. DOI: . |
| [234] | Ogden, R., Non-linear elastic deformations. 1997. https://books.google.com/books?hl=en&lr=&id=2u7wCaojfbEC&oi=fnd&pg=PP1&ots=boKxO1ZwqZ&sig=fBVyjXuYh_JZnQWdWpfexVJuV0k |
| [235] | Nikkhoo, M., et al., “Development and validation of a geometrically personalized finite element model of the lower ligamentous cervical spine for clinical applications,” Comput. Biol. Med., vol. 109, pp. 22-32, Jun. 2019. DOI: . |
| [236] | Guo, Z. Y., Peng, X. Q. and Moran, B., “A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus,” J. Mech. Phys. Solids, vol. 54, no. 9, pp. 1952-1971, Sep. 2006. DOI: . · Zbl 1120.74634 |
| [237] | Eberlein, R., Holzapfel, G. A. and Schulze-Bauer, C. A. J., “An Anisotropic Model Annulus Tissue Enhanced Finite Element Analyses Intact Lumbar Disc Bodies,” vol. 4, no. 3, pp. 209-229, 2007. DOI: . |
| [238] | Groenen, K. H. J., et al., “Case-specific non-linear finite element models to predict failure behavior in two functional spinal units,” J. Orthop. Res., vol. 36, no. 12, pp. 3208-3218, Dec. 2018. DOI: . |
| [239] | Xie, F., Zhou, H., Zhao, W. and Huang, L., “A comparative study on the mechanical behavior of intervertebral disc using hyperelastic finite element model,” Technol. Health Care, vol. 25, no. S1, pp. 177-187, Jan. 2017. DOI: . |
| [240] | Jannesar, S., et al., “Compressive mechanical characterization of non-human primate spinal cord white matter,” Acta Biomater., vol. 74, pp. 260-269, Jul. 2018. DOI: . |
| [241] | Mooney, M., “A theory of large elastic deformation,” J. Appl. Phys, vol. 11, no. 9, pp. 582-592, Sep. 1940. DOI: . · JFM 66.1021.04 |
| [242] | Teo, E. C. and Ng, H. W., “Evaluation of the role of ligaments, facets and disc nucleus in lower cervical spine under compression and sagittal moments using finite element method,” Med. Eng. Phys., vol. 23, no. 3, pp. 155-164, Apr. 2001. DOI: . |
| [243] | Guan, Y., et al., “Moment-rotation responses of the human lumbosacral spinal column,” J. Biomech., vol. 40, no. 9, pp. 1975-1980, Jan. 2007. DOI: . |
| [244] | Dehghan-Hamani, I., Arjmand, N. and Shirazi-Adl, A., “Subject-specific loads on the lumbar spine in detailed finite element models scaled geometrically and kinematic-driven by radiography images,” Int. J. Numer. Method. Biomed. Eng., vol. 35, no. 4, pp. e3182, Apr. 2019. DOI: . |
| [245] | Rohlmann, A., Bauer, L., Zander, T., Bergmann, G. and Wilke, H. J., “Determination of trunk muscle forces for flexion and extension by using a validated finite element model of the lumbar spine and measured in vivo data,” J. Biomech., vol. 39, no. 6, pp. 981-989, Jan. 2006. DOI: . |
| [246] | Little, J. P., “The spine: biomechanics and subject-specific finite element models,” in DHM Posturography, pp. 287-293, Academic Press, Jan. 2019. DOI: . |
| [247] | Hansson, T., Magnusson, M. and Broman, H., “Back muscle fatigue and seated whole body vibrations: an experimental study in man,” Clin. Biomech., vol. 6, no. 3, pp. 173-178, Aug. 1991. DOI: . |
| [248] | Griffin, M. J., “The evaluation of vehicle vibration and seats,” Appl. Ergon., vol. 9, no. 1, pp. 15-21, Mar. 1978. DOI: . |
| [249] | Sandover, J., “The fatigue approach to vibration and health: is it a practical and viable way of predicting the effects on people?,” JSV, vol. 215, no. 4, pp. 699-721, Aug. 1998. DOI: . |
| [250] | Badilatti, S. D., Kuhn, G. A., Ferguson, S. J. and Müller, R., “Computational modelling of bone augmentation in the spine,” J. Orthop. Translat., vol. 3, no. 4, pp. 185-196, Oct. 2015. DOI: . |
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