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 cLS 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 cL5 (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 cLS, 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

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