Spinal disorders such as degenerative disc disease, cervical spondylosis, osteoarthritis, muscular imbalance, trauma to the cervical spine, etc., may affect normal cervical spine lordosis (Lippa and Cacciola, 2017, Le Huec et al., 2015). Amongst these, conditions such as trauma, degenerative disc disease etc., require surgical treatment involving the use of spinal fixation instrumentation such as plating systems and cages. The latter provides support and stability to the cervical spine during the post-surgery healing period. While the plating system is ideally desired to be patient-specific to preserve the cervical lordosis, volume manufacturing of such instrumentation requires them to be designed to a mean lordosis representative of a large population. In this respect, describing cervical lordosis as an engineering figure-of-merit is useful.

Several methods have been reported in the literature to access spinal alignment and curvature using X-ray or MRI radiographs, such as the Cobb angle, C2 slope, C7 slope, T1 slope, the cervical sagittal vertical axis (cSVA), etc. (Zhao (2020)) The Cobb angle is measured as the included angle between the two perpendiculars erected on the tangent lines drawn from the inferior end plates of the C2 and C7 vertebrae (Midde et al., 2017). The T1 slope is measured as the angle between a horizontal line and a tangent line drawn at the superior endplate of T1 (Chen et al., 2020). The cSVA is measured as the horizontal offset from the posterosuperior corner of C7 to the vertebral body of C2 (Shao et al., 2019, Wang et al., 2023).

Ishihara reported a cervical curvature index, which was calculated by drawing a line connecting the postero-inferior edge of the C2 and C7 bodies and by erecting four perpendicular line segments from each postero-inferior edge of the C3, C4, C5, and C6 vertebral bodies to the C2-C7 line. The cervical curvature index was calculated as a percentage of the sum of the lengths of four perpendicular segments divided by the height of the C2-C7 line segment (Takeshita et al., 2001).

Jackson’s physiological stress line method represents cervical lordosis as the angle subtended between lines drawn parallel to the posterior margins of the C2 and C7 bodies (Yokoyama et al., 2017).

Harrison’s posterior tangent method quantifies cervical lordosis by drawing tangent lines on the posterior surface of the vertebral body from C2 to C7 in the X-ray or MRI radiograph and summing up all the angles subtended by the adjacent tangent lines (Yaltirik and Yuceli, 2019).

While representing cervical lordosis as an index or an angle is adequate for clinical use, lordosis must be translated to an engineering figure-of-merit, such as the radius-of-curvature (RoC) for designing spinal instrumentation. Harrison et al. described one such study where they propose a least squares circular and elliptical modeling method applied along the path of the posterior cervical vertebral body corners from C2–C7 to estimate the RoC of the cervical spine from X-ray radiographs (Harrison et al., 2004).

In contrast to the methods published in the literature for quantifying cervical lordosis, the present work models the cervical spine as a geometrical construct as part of a unique ellipse. The latter is constructed using the mean estimates of the four descriptors related to the cervical spine, viz. Cobb angle, cervical sagittal vertical axis (cSVA), T1 slope, and cervical spinal arc length using meta-analysis. The cervical spinal arc length is taken as the arc length spanning from the inferior end plate of C2 to the superior end plate of T1 vertebral body. To the best of our knowledge, the representation of the cervical spine as a geometrical construct part of a unique ellipse has not been published previously. The applicability of the work for the design and manufacturing of spinal fixation instrumentation is discussed.