The curvature of the lumbar spine plays a critical role in maintaining spinal function, stability, weight distribution, and load transfer. We have developed a mathematical model of the lumbar spine curve by introducing a novel mechanism: minimization of the elastic bending energy of the spine with respect to two biomechanical parameters: dimensionless lumbosacral spinal curvature c LS and dimensionless curvature increment along the spine CI. While most of the biomechanical studies focus on a particular segment of the spine, the distinction of the presented model is that it describes the shape of the thoracolumbar spine by considering it as a whole (non-locally) and thus includes interactions between the different spinal levels in a holistic approach. From radiographs, we have assessed standard geometrical parameters: lumbar lordosis LL, pelvic incidence PI, pelvic tilt PT, sacral slope ψ0 and sagittal balance parameter SB = sagittal vertical axis (SVA)/sacrum-bicoxofemoral distance (SFD) of 42 patients with lumbar spinal stenosis (SS) or degenerative spondylolisthesis (SL) and 21 radiologically normal subjects. SB statistically significantly correlated with model parameters c L5 (r = -0.34, p = 0.009) and -CI (r = 0.33, p = 0.012) but not with standard geometrical parameters. A statistically significant difference with sufficient statistical power between the patients and the normal groups was obtained for c LS, CI, and SB but not for standard geometrical parameters. The model provides a possibility to predict changes in the thoracolumbar spine shape in surgery planning and in assessment of different spine pathologies.

Department of Mechanics Biomechanics and Mechatronics Faculty of Mechanical Engineering Czech Technical University Prague Technicka 4 CZ166 07 Prague 6 Czech Republic

Department of Orthopaedic Surgery University Medical Centre Ljubljana Zaloška 9 SI 1000 Ljubljana Slovenia

Institution for Higher Education for Physiotherapy Fizioterapevtika Slovenska cesta 58 SI 1000 Ljubljana Slovenia

Surgical Centre Rožna Dolina Rožna dolina cesta 4 45 SI 1000 Ljubljana Slovenia

University of Ljubljana Faculty of Electrical Engineering Laboratory of Physics Tržaška 25 SI 1000 Ljubljana Slovenia

University of Ljubljana Faculty of Health Sciences Laboratory of Clinical Biophysics Zdravstvena 5 SI 1000 Ljubljana Slovenia

University of Ljubljana Faculty of Medicine Vrazov trg 2 SI 1000 Ljubljana Slovenia

See more in PubMed

Yaroub S., Hamandi S.J., Mohson K. Kinematic analysis of L4-L5 spinal segment with spondylolysis and different types of grade 1 spondylolisthesis: a nonlinear finite element study. Acta Bioeng. Biomech. 2022;24:177–186. PubMed

Weiqi L., Peiming Z., Feihong G. Biomechanical characterization of bilateral pedicle screw internal fixation combinations on lumbar vertebrae. Acta Bioeng. Biomech. 2023 doi: 10.37190/ABB-02315-2023-03. DOI

Zou X., Yang H., Fu S., Deng C., et al. A novel surgical management for pediatric patients with irreducible atlantoaxial dislocation: transoral intraarticular cage distraction and fusion with C-JAWS staple fixation. Front Surg. 2022;9 doi: 10.3389/fsurg.2022.1054695. PubMed DOI PMC

Jiang Y., Cui X., Ji W., Li J., et al. Novel uniplanar pedicle screw systems applied to thoracolumbar fractures: a biomechanical study. Front. Bioeng. Biotechnol. 2023;11(11) doi: 10.3389/fbioe.2023.1172934. PubMed DOI PMC

Wendt K., Nau C., Jug M., Pape H., et al. ESTES recommendation on thoracolumbar spine fractures. Eur. J. Trauma Emerg. Surg. 2023 doi: 10.1007/s00068-023-02247-3. PubMed DOI PMC

Meszaros-Beller L., Hammer M., Riede J.M., Pivonka P., Little J.P., Schmitt S. Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution. Biomech. Model. Mechanobiol. 2023;22:669–694. doi: 10.1007/s10237-022-01673-3. PubMed DOI PMC

Liu Y., Zhang Q., Ji N., Wang J., Li J., et al. Stability simulation analysis of targeted puncture in L4/5 intervertebral space for PELD surgery. Front Bioeng Biotechnol Sec Biomech. 2024;11 doi: 10.3389/fbioe.2023.1298914. PubMed DOI PMC

Mac-Thiong J.M., Labelle H., Charlebois M., Huot M.P., de Guise J.A. Sagittal plane analysis of the spine and pelvis in adolescent idiopathic scoliosis according to the coronal curve type. Spine. 2003;28:1404–1409. doi: 10.1097/01.BRS.0000067118.60199. PubMed DOI

Labelle H., Roussouly P., Berthonnaud E., Transfeldt E., et al. Spondylolisthesis, pelvic incidence, and spinopelvic balance: a correlation study. Spine. 2004;29:2049–2054. doi: 10.1097/01.brs.0000138279.53439.cc. PubMed DOI

Abelin-Genevois K. Sagittal balance of the spine. Orthop Traumatol Surg Res. 2021;107 doi: 10.1016/j.otsr.2020.102769. PubMed DOI

Yang B.P., Yang C.W., Ondra S.L. A novel mathematical model of the sagittal spine. Spine. 2007;32:466–470. doi: 10.1097/01.brs.0000255207.44141.e9. PubMed DOI

Wang T., Wang H., Liu H., Ma L., Liu F.Y., Ding W.Y. Sagittal spinopelvic parameters in 2-level lumbar degenerative spondylolisthesis: a retrospective study. Medicine (Baltim.) 2016;95 doi: 10.1097/MD.0000000000005417. PubMed DOI PMC

Barrey C., Jund J., Noseda O., Roussouly P. Sagittal balance of the pelvis-spine complex and lumbar degenerative diseases. A comparative study about 85 cases. Eur. Spine J. 2007;16:1459–1467. doi: 10.1007/s00586-006-0294-6. PubMed DOI PMC

Sirbu E., Onofrei R.R., Szasz S., Susan M. Predictors of disability in patients with chronic low back pain. Arch. Med. Sci. 2023;19:94–100. doi: 10.5114/aoms.2020.97057. PubMed DOI PMC

Li Y., Zhang S., Shu P. Global burden of neck pain in 204 countries from 1990–2019. Arch. Med. Sci. 2023;19:1811–1821. doi: 10.5114/aoms/170962. PubMed DOI PMC

Ambrosio L., Vadala G., Russo F., Sakai D., Denaro V. Editorial: new perspectives and innovative techniques in contemporary spine surgery. Front Surg Sec Orthop Surg. 2023;10 doi: 10.3389/fsurg.2023.1220181. PubMed DOI PMC

Dorsi M.J., Buchanan P., Vu C., Bhandal H.S., et al. Pacific Spine and Pain Society (PSPS) evidence review of surgical treatments for lumbar degenerative spinal disease: a narrative review. Pain Ther. 2024 doi: 10.1007/s40122-024-00588-4. PubMed DOI PMC

Harrison D.E., Cailliet R., Harrison D.D., Janik T.J., Holland B. Reliability of centroid, Cobb, and Harrison posterior tangent methods: which to choose for analysis of thoracic kyphosis. Spine. 2001;26:E227–E234. doi: 10.1097/00007632-200106010-00002. PubMed DOI

Vrtovec T., Pernuš F., Likar B. A review of methods for quantitative evaluation of spinal curvature. Eur. Spine J. 2009;18(2009):593–607. doi: 10.1007/s00586-009-0913-0. PubMed DOI PMC

Harrison D.D., Cailliet R., Janik T.J., Troyanovich S.J., Harrison D.E., Holland B. Elliptical modeling of the sagittal lumbar lordosis and segmental rotation angles as a method to discriminate between normal and low back pain subjects. J. Spinal Disord. 1998;11:430–439. PubMed

Janik T.J., Harrison D.D., Cailliet R., Troyanovich S.J., Harrison D.E. Can the sagittal lumbar curvature be closely approximated by an ellipse? J. Orthop. Res. 1998;16:766–770. doi: 10.1002/jor.1100160620. PubMed DOI

Berthonnaud E., Dimnet J., Roussouly P., Labelle H. Analysis of the sagittal balance of the spine and pelvis using shape and orientation parameters. J. Spinal Disord. Tech. 2005;18:40–47. doi: 10.1097/01.bsd.0000117542.88865.77. PubMed DOI

Patel P., Arutyunyan G., Plusch K., Vaccaro A., Jr., Vaccaro A. A review of cervical spine alignment in the normal and degenerative spine. J Spine Surgery. 2020;6:106–123. https://jss.amegroups.org/article/view/4910 PubMed PMC

Aita I., Wadano Y., Yabuki T. Curvature and range of motion of the cervical spine after laminaplasty. JBJS. 2000;82:1743. doi: 10.2106/00004623-200012000-00008. PubMed DOI

Lin S., Zhou F., Sun Y., et al. The severity of operative invasion to the posterior muscular-ligament complex influences cervical sagittal balance after open-door laminoplasty. Eur. Spine J. 2015;24:127–135. doi: 10.1007/s00586-014-3605-3. PubMed DOI

Li X.Y., Wang Y., Zhu W.G., Kong C., Lu S.B. Impact of cervical and global spine sagittal alignment on cervical curvature changes after posterior cervical laminoplasty. J. Orthop. Surg. Res. 2022;17:521. doi: 10.1186/s13018-022-03421-w. PubMed DOI PMC

Kim D., Davis D.D., Menger R.P. StatPearls [Internet] StatPearls Publishing; Treasure Island (FL): 2024 Jan. Spine sagittal balance.https://www.ncbi.nlm.nih.gov/books/NBK534858/ [Updated 2023 Aug 14] Available from: PubMed

Kuhta M., Bošnjak K., Vengust R. Failure to maintain segmental lordosis during TLIF for one-level degenerative spondylolisthesis negatively affects clinical outcome 5 years postoperatively: a prospective cohort of 57 patients. Eur. Spine J. 2019;28:745–750. doi: 10.1007/s00586-019-05890-w. PubMed DOI

Legaye J., Duval-Beaupère G., Hecquet J., Martyet C. Pelvic incidence: a fundamental [pelvic parameter for three-dimensional regulation of spinal sagittal curves. Eur. Spine J. 1998;7:99–103. doi: 10.1007/s005860050038. PubMed DOI PMC

Wu Z.M., Ji X.Q., Lian K., Liu J.T. Analysis of the relationship between modic change and spinopelvic parameters in the sagittal plane. Med. Sci. Mon. Int. Med. J. Exp. Clin. Res. 2020;26 doi: 10.12659/MSM.919667. PubMed DOI PMC

Barrey C., Pinheiro-Franco J.L., Le-Huec J.C., Perrin G., Roussouly P. Advanced Concepts in Lumbar Degenerative Disk Disease. Springer; Berlin: 2016. Compensatory mechanisms contributing to the maintenance of sagittal balance in degenerative diseases of the lumbar spine; pp. 725–737.

Imai N., Suzuki H., Sakagami A., Hirano Y., Endo N. Correlation of the anatomical sacral slope with pelvic incidence in female patients with developmental hip dysplasia: a retrospective cross-sectional study. J. Orthop. Surg. Res. 2020;15:486. doi: 10.1186/s13018-020-02022-9. PubMed DOI PMC

Tanguay F., Mac-Thiong J.M., De Guise J.A., Labelle H. Relation between the sagittal pelvic and lumbar spine geometries following surgical correction of adolescent idiopathic scoliosis. Eur. Spine J. 2007;16:531–536. doi: 10.1007/s00586-006-0238-1. PubMed DOI PMC

Hay O., Hershkovitz I., Rivlin E. Spine curve modeling for quantitative analysis of spinal curvature. Annu Int Conf IEEE Eng Med Biol Soc. 2009:6356–6359. doi: 10.1109/IEMBS.2009.5333263. PubMed DOI

Zawadka M., Smolka J., Skublewska-Paszkowska M., Lukasik E., et al. Relationship of lumbar-hip kinematics during trunk flexion and sex, body mass index, and self-reported energy expenditure: a cross-sectional analysis. Acta Bioeng. Biomech. 2023;25:55–64. doi: 10.37190/ABB-02211-2023-03. DOIFig: PubMed DOI

Chen Y., Shen Y., Wang K., Qi Y., Niu W., Wang Y. Mechanical analysis of deep tissue injury during sitting in patients with spinal cord injury via parametric finite element model. Biomech. Model. Mechanobiol. 2022;21:1573–1584. doi: 10.1007/s10237-022-01607-z. PubMed DOI

Fiebert I., Kistner F., Gissendanner C., Dasilva C. Text neck: an adverse postural phenomenon. Work. 2021;69:1261–1270. doi: 10.3233/WOR-213547. PubMed DOI

Rajaee S.S., Bae H.W., Kanim L.E., Delamarter R.B. Spinal fusion in the United States: analysis of trends from 1998 to 2008. Spine. 2012;37:67–76. doi: 10.1097/BRS.0b013e31820cccfb. PubMed DOI

Wai G., Rusli W., Ghouse S., Kieser D.C., Kedgley A., Newel N. Statistical shape modelling of the thoracic spine for the development of pedicle screw insertion guides. Biomech. Model. Mechanobiol. 2023;22:123–132. doi: 10.1007/s10237-022-01636-8. PubMed DOI PMC

Hao J., Tang X.S., Jiang N., Wang H., Jiang J. Biomechanical stability of oblique lateral interbody fusion combined with four types of internal fixations: finite element analysis. Front Bioeng Biotechnol Sec Biomech. 2023;11 doi: 10.3389/fbioe.2023.1260693. PubMed DOI PMC

Xu Z., Zheng Q., Zhang L., Chen R., Li Z., Xu W. Biomechanical evaluation of different oblique lumbar interbody fusion constructs: a finite element analysis. BMC Muscoskel. Disord. 2024;25:97. doi: 10.1186/s12891-024-07204-8. PubMed DOI PMC

Le Huec J.C., Thompson W., Mohsinaly Y., Barrey C., Faundez A. Sagittal balance of the spine. Eur. Spine J. 2019;28:1889–1905. doi: 10.1007/s00586-019-06083. PubMed DOI