# A forward dynamics simulation of human lumbar spine flexion predicting the load sharing of intervertebral discs, ligaments, and muscles

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## Abstract

Determining the internal dynamics of the human spine’s biological structure is one essential step that allows enhanced understanding of spinal degeneration processes. The unavailability of internal load figures in other methods highlights the importance of the forward dynamics approach as the most powerful approach to examine the internal degeneration of spinal structures. Consequently, a forward dynamics full-body model of the human body with a detailed lumbar spine is introduced. The aim was to determine the internal dynamics and the contribution of different spinal structures to loading. The multi-body model consists of the lower extremities, two feet, shanks and thighs, the pelvis, five lumbar vertebrae, and a lumped upper body including the head and both arms. All segments are modelled as rigid bodies. 202 muscles (legs, back, abdomen) are included as Hill-type elements. 58 nonlinear force elements are included to represent all spinal ligaments. The lumbar intervertebral discs were modelled nonlinearly. As results, internal kinematics, muscle forces, and internal loads for each biological structure are presented. A comparison between the nonlinear (new, enhanced modelling approach) and linear (standard modelling approach, bushing) modelling approaches of the intervertebral disc is presented. The model is available to all researchers as ready-to-use C/C++ code within our in-house multi-body simulation code *demoa* with all relevant binaries included.

## Keywords

Biomechanics Direct dynamics Multi-body model Impact Shock wave Computer simulation## Abbreviations

- IVD
Intervertebral disc

- MTC
Muscle–tendon complex

- MB
Multi-body

- FE
Finite element

- DOF
Degree of freedom

- CT
Computed tomography

- CE
Contractile element

- IVFE
Intervertebral flexion–extension

- ROM
Range of motion

- ALL
Anterior longitudinal ligament

- PLL
Posterior longitudinal ligament

- LF
Ligamentum flavum

- SSL
Supraspinal ligament

- ISL
Interspinal ligament

- RA
Rectus abdominis muscle

- EO
External oblique muscle

- IO
Internal oblique muscle

- PM
Psoas major muscle

- MF
Multifidus

- IT_m
Intertransversarii mediales

- LTpL
Longissimus thoracis pars lumborum

- IL
Iliocostalis lumborum pars lumborum

- C1–C7
Cervical vertebrae

- T1–T12
Thoracic vertebrae

- L1–L5
Lumbar vertebrae

- S1–S5
Sacral vertebrae

- Sagittal axis
Dorsal to ventral (\(=\!x\)-axis)

- Longitudinal axis
Caudal to cranial (\(=\!z\)-axis)

- Graphic primitive
Geometric primitive, describes the simplest geometric objects that the system can handle; in this model, the graphic primitives represent respective body segments

## Notes

### Acknowledgments

The authors would like to thank the German Research Foundation (DFG) for financial support of the project within the Cluster of Excellence in Simulation Technology (EXC 310/1) at the University of Stuttgart.

T.R. and S.S. have received funding from the (European Union) Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 246994.

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