Research Papers

The Path to Deliver the Most Realistic Follower Load for a Lumbar Spine in Standing Posture: A Finite Element Study

[+] Author and Article Information
Han Zhang

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai, 200072, China

Weiping Zhu

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai, 200072, China
e-mail: wpzhu@shu.edu.cn

1Corresponding author.

Manuscript received March 14, 2018; final manuscript received December 26, 2018; published online January 31, 2019. Assoc. Editor: Eric A. Kennedy.

J Biomech Eng 141(3), 031010 (Jan 31, 2019) (10 pages) Paper No: BIO-18-1139; doi: 10.1115/1.4042438 History: Received March 14, 2018; Revised December 26, 2018

A spine is proven to be subjected to a follower load which is a compressive load of physiologic magnitude acting on the whole spine. The path of the follower load approximates the tangent to the curve of the spine in in vivo neutral standing posture. However, the specific path location of the follower load is still unclear. The aim of this study is to find out the most realistic location of the follower load path (FLP) for a lumbar spine in standing. A three-dimensional (3D) nonlinear finite element model (FEM) of lumbosacral vertebrae (L1-S1) with consideration of the calibrated material properties was established and validated by comparing with the experimental data. We show that the shape of the lumbosacral spine is strongly affected by the location of FLP. An evident nonlinear relationship between the FLP location and the kinematic response of the L1-S1 lumbosacral spine exists. The FLP at about 4 and 3 mm posterior to the curve connecting the center of the vertebral bodies delivers the most realistic location in standing for healthy people and patients having low back pains (LPBs), respectively. Moreover, the “sweeping” method introduced in this study can be applicable to all individualized FEM to determine the location of FLP.

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Grahic Jump Location
Fig. 1

Finite element model for lumbosacral vertebrae L1-S1 and L4-L5 intervertebral disk

Grahic Jump Location
Fig. 2

Follower load is applied by connector elements in lumbosacral vertebrae L1-S1 bilaterally. Black bold lines represent the connecter elements that located at initial curve. Every pair of connector element passes through the center of each vertebral body on both sides in the sagittal plane. Five pairs of connector elements in each segment are connected head to tail.

Grahic Jump Location
Fig. 3

The range of FLP in neutral standing position. The FLP were swept and evaluated from 10 mm posterior (P10) and 5 mm anterior (A5) to the geometrical center of each lumbar vertebra (initial path).

Grahic Jump Location
Fig. 4

The shape of lumbosacral spine for different location of FLP. (a) Total ROM of lumbosacral spine L1-S1 from P10 (−10.0 mm) to A5 (5.0 mm). (b) Sum of absolute values for IVRs in each level from P10 to A5. The fitted curves of the numerical calculated results and in vivo measured values were also given.

Grahic Jump Location
Fig. 5

(a)–(e) The influence of different location of the FLP between IVR and IDP in each disk. The left longitudinal axis of each figure represented the influence of the position of FLP on the IVR. The right longitudinal axis of each figure represented the influence of the position of FLP on the IDP. The fitted curves of the numerical calculated results of IDP and IVR, as well as in vivo measured values, were also given.

Grahic Jump Location
Fig. 6

The ANN was divided into four regions with specific local weight factors (μa, μal, μpl, and μp)

Grahic Jump Location
Fig. 7

The calibrated stress–strain curves for four regions of fibers and an experimental data [33]

Grahic Jump Location
Fig. 8

The calibrated stress–strain curves for all ligaments of FEM in comparison with an experimental measured data [35]

Grahic Jump Location
Fig. 9

Comparison of the FE model calculated and in vitro experiment [11] rotations in the lumbar spine (L1-5) for flexion-extension (left), lateral bending (middle), and axial rotation (right) under pure moments of 2.5, 5, and 7.5 N·m. The ranges of the in vitro study results were also given.

Grahic Jump Location
Fig. 10

The calculated rotations in the lumbar spine (L1-5) for lateral bending, flexion-extension, and axial rotation under pure moments of 7.5 N·m and a 280 N pre-follower load plus 7.5 N·m. The ranges of the in vitro study results were given.

Grahic Jump Location
Fig. 11

Intradiskal pressure predictions of the model in pure compression

Grahic Jump Location
Fig. 12

The maximum outward DB predictions under axial compression of 500 N and pure unconstraint moments of 7.5 N·m in flexion, lateral bending, and axial rotation



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