Evaluation of axial and flexural stresses in the vertebral body cortex and trabecular bone in lordosis and two sagittal cervical translation configurations with an elliptical shell model

Abstract

Background: Osteoarthritis and spinal degeneration are factors in neck and back pain. Calculations of stress in clinically occurring configurations of the sagittal cervical spine are rare. Objective: To calculate and compare combined axial and flexural stresses in lordosis versus cervical configurations in anterior and vertical sagittal head translated positions. Design: Digitized measurements from lateral cervical radiographs of 3 different shapes were used to calculate axial loads and bending moments on the vertebral bodies of C2-C7. Methods: An elliptical shell model was used to model horizontal cross-sections of the vertebral bodies of C2 through T1. Axial and flexural stresses were calculated with short compression block equations. Elliptical shell modeling permitted separation of stresses into cortical and inner medullary regions. Digitized radiographic points were used to create polynomials representing the shape of the sagittal cervical curvatures from C1 to T1. To calculate bending moments at each vertebral segment, moment arms from a vertical line through C1 were determined from digitizing. Results: Compared with the normal lordosis, stresses on the anterior vertebral body cortical margins of C5-T1 in the sagittal translated postures are compression rather than tension. At the posterior vertebral bodies in the anteriorly translated position and vertically translated postures, the stresses change from compression to tension at C5 through T1. In absolute value (ABS) compared with values at the same segments in a normal lordosis, the magnitude of the combined anterior stresses in the sagittal postures are higher at C5-C7 (eg, ABS[σ_straight/σ_normal] ≃ 1.25 to 4.25). Conclusions: Vertebral body stresses are reversed in direction at C5-T1 in sagittal translated postures compared to a normal lordosis. Stress analysis, with implications for bone remodeling, indicates that both sagittal head translation postures, anterior head carriage, and vertical head translation, are undesirable configurations in the cervical spine. (J Manipulative Physiol Ther 2002;25:391-401)

Introduction

Recently, health care providers have become interested in head posture in the sagittal plane, especially anterior head translation, which is termed head protrusion/protraction.1, 2, 3 In addition, a lordotic configuration in the sagittal plane has been reported to be an important indicator of good outcomes in cervical surgery,4, 5, 6, 7 whereas others have reported no significance.⁸ Regardless, loss of cervical lordosis will create changes in loading on the vertebrae and soft tissues.

Frassica et al⁹ have suggested 7 concepts that could assist the clinician in understanding normal and abnormal conditions of the human skeleton. Two of these are stress/strain and Wolff's law. Several types of pathologies can be attributed to abnormal loading of bone as consequences of Wolff's Law, eg. osteoarthritis.9, 10, 11, 12 According to Kissel and Youmans,¹³ asymptomatic osteophytes of the anterior cervical vertebral margins may occur in 30% of the population. It is also known that tension on the periosteum will result in osteoblastic activity (bone growth).¹⁴ Thus any change in stresses from compression to tension at the anterior or posterior vertebral margins may result in traction spurring on the vertebral body margins.

Because bone remodels to the applied stresses, it is desirable to determine the stresses borne by the cortex and the inner trabeculae (medullary region). One of the first models to separate the cortex and trabecular bone was by Belytschko et al¹⁵ in 1976 with a cylindrical shell model used for the lumbar vertebral body. Recently, Van der Perre and Lowet¹⁶ and a review by Hayes and Bouxsein¹⁷ discussed cylindrical shell models of the long bones and vertebral bodies. However, while the cross-section of thoracic vertebral bodies have been reported to be somewhat circular, the cervical and lumbar vertebral bodies have been reported to more closely resemble ellipses in cross-section.18, 19 Harrison et al²⁰ used an elliptical shell model to approximate cervical vertebral body stresses in kyphosis and S-configurations. They reported high stresses (10 times in magnitude) in cervical kyphotic regions.

Our approach is to apply an elliptical shell model for the cervical vertebral bodies' cross-sections to 3 examples of lateral cervical configurations to determine stresses in the cortex and trabecular bone. The first example will be a normal symmetrical cervical lordosis, defined as C1 directly vertical over T1. The second example will be a straight cervical curvature associated with vertical head translation, and the third example will be cervical lordosis with anterior head translation. From these 2 abnormal curvatures, axial and flexural stresses can be compared with the normal cervical configuration. It is hypothesized that vertebral body stresses will be increased in the sagittal translated configurations.