A finite element study on the effects of follower load on the continuous biomechanical responses of subaxial cervical spine

Highlights

• The follower load path is optimized through a novel Rom-based method.

• A nonlinear logarithmic function is proposed to fit the rotation-moment data.

• The continuous biomechanical responses of the cervical spine were investigated.

• The follower load increases both the facet joint forces and intradiscal pressures.

• The follower load impacts the shape of Rom-moment curves in all anatomical planes.

Abstract

In spine biomechanics, follower loads are used to mimic the in vivo muscle forces acting on a human spine. However, the effects of the follower load on the continuous biomechanical responses of the subaxial cervical spines (C2-T1) have not been systematically clarified. This study aims at investigating the follower load effects on the continuous biomechanical responses of C2-T1. A nonlinear finite element model is reconstructed and validated for C2-T1. Six levels follower loads are considered along the follower load path that is optimized through a novel range of motion-based method. A moment up to 2 Nm is subsequently superimposed to produce motions in three anatomical planes. The continuous biomechanical responses, including the range of motion, facet joint force, intradiscal pressure and flexibility are evaluated for each motion segment. In the sagittal plane, the change of the overall range of motion arising from the follower loads is less than 6%. In the other two anatomical planes, both the magnitude and shape of the rotation-moment curves change with follower loads. At the neutral position, over 50% decrease in flexibility occurs as the follower load increases from zero to 250 N. In all three anatomical planes, over 50% and 30% decreases in flexibility occur in the first 0.5 Nm for small (≤100 N) and large (≥150 N) follower loads, respectively. Moreover, follower loads tend to increase both the facet joint forces and the intradiscal pressures. The shape of the intradiscal pressure-moment curves changes from nonlinear to roughly linear with increased follower load, especially in the coronal and transverse planes. The results obtained in this work provide a comprehensive understanding on the effects of follower load on the continuous biomechanical responses of the C2-T1.

Introduction

In order to better model the in vivo biomechanical responses of human spines in numerical simulation or in vitro experiments, many literature studies have demonstrated the importance of introducing muscle forces. However, by treating muscle forces as a simple concentrated offset load acting on cervical spines, cadaveric spinal specimens are typically found to buckle under a loading level far below those that are able to be carried out in vivo [1]. Such an apparent inconsistency calls for the more accurate modeling of muscle forces in the in vitro cervical spine tests [2,3,4].

Instead of using a simple concentrated end load, Patwardhan et al. [5] introduced a varying compressive force acting along the spinal axis, termed as the follower load. To reflect the muscle activation along the curved spinal axis, the follower load passes through the centers of rotation of the spinal segments and always be tangential to the spinal curve [[6], [7], [8]]. Under the follower load, each spinal motion segment is under pure compression. Therefore, its couplings with the spinal extension-flexion, lateral bending and axial rotation can be minimized. Patwardhan et al. [7] evaluated the lordosis angle change of six cervical spines under the application of the follower load. The lordosis angles were found to increase by less than 5° for the follower load of 250 N. In contrast, they increased by 15–20° when a concentrated compressive end load of 20–40 N is applied. For 21 lumbar spinal specimens, Patwardhan et al. [6] examined their lordosis angle changes. The average change of lumbar lordosis angles was less than 1° for the 1200 N follower load.

Since the proposal of the follower load concept, its effects on the biomechanical responses of cervical and lumbar spines have been examined in the literature. The range of motion (ROM) of spines in three anatomic planes is one of the most important biomechanical performances. In terms of 12 fresh-frozen cadaveric human cervical specimens, Bell et al. [9] considered the combined loading of a 100 N follower load and a 2 Nm bending moment in the sagittal plane. Although the maximum rotations were not affected in the sagittal plane, the inclusion of the follower load is found to significantly change the shape of the rotation-moment curve. Barrey et al. [10] calculated the rotations of 12 cadaveric human cervical specimens under the successive applications of a 50 N follower load and a 2 Nm moment load. The follower load was first applied, followed by the moment load. The rotation increases slightly in extension and flexion while decreases in both lateral bending and axial rotation. Cai et al. [11] also studied the rotations of cervical specimens. However, the moment load was applied before the follower load. Probably because of the reverse application order of the follower load and the moment load, these two works obtained different rotations for the lower C3–C7 cervical segments in lateral bending and axial rotation.

With regard to the effects of follower load on spinal flexibility and stiffness, Bell et al. [9] pointed out that the inclusion of the follower load leads to larger width and higher stiffness in the neutral zone of the cervical spine. Smit et al. [12] proposed a double sigmoidal function to reflect the S-shaped characteristics of the moment-rotation relation. Both the width and stiffness of the neutral zone of the spinal motion segment were defined. In terms of the experimental kinematics-moment data in the sagittal plane, Bell et al. [9] found that the application of the follower load significantly increased the neutral zone width and stiffness. However, no changes were identified for the stiffness in the elastic zone. Zhang et al. [13] modeled the intervertebral joint moment as a function of both the rotation and compressive load. They found that the inclusion of the follower load results in the increase of rotational stiffness throughout the spine.

In addition, the facet joint force and the intradiscal pressure have also been found to increase with the follower load [10,9,11]. By examining the contact performance of the lumbar spinal facet joints, Du et al. [14] reported that the application of the follower load tends to increase the facet joint force, contact area and contact pressure in extension. Polga et al. [15] measured the intradiscal pressure of thoracic intervertebral discs in vivo. They found that the intradiscal pressure is significantly influenced by body position and movement.

In view of the above literature reviews on the effects of the follower load, a few limitations can be identified. First, most in vitro experimental studies focused only on the changes of biomechanical responses in the sagittal plane with the application of the follower load. Second, no suitable fitting functions were proposed for analyzing the effects of the follower load on spinal flexibility and stiffness. Third, no optimization studies have been conducted for the loading path of the follower load prior to its application in simulation studies. Finally, existing studies only examined the endpoints of loading. No continuous biomechanical responses were analyzed for the entire extension-flexion, lateral bending and axial rotation motion path.

The primary goal of the present study is to comprehensively evaluate the effects of the follower load on the continuous biomechanical responses of the subaxial cervical spine. This cervical spine includes the relatively complete C2-T1 segments. All three motion paths, i.e., the extension-flexion, lateral bending and axial rotation, are considered in sufficient ranges. For this purpose, a detailed finite element model was reconstructed and validated for the entire subaxial cervical spine. Prior to the application of the follower load, an optimization is conducted on the follower load path on the basis of the ROM data. A few representative follower loads are superimposed with the moment load, separately considered in the sagittal, coronal and transverse planes. A nonlinear logarithmic function is then proposed to fit the resultant rotation-moment data. The flexibility-moment curve is determined for each motion segment. In terms of these analyses, the effects of the follower load on the continuous kinematics, flexibility, stiffness, facet joint force and intradiscal pressure are evaluated for each motion segment.