A Model for Intervertebral Disk Shape Variation in a Population Including the Effect of Degeneration

Abstract

Introduction While IVD strain can be measured, the stress distribution within the disk is dependent on the IVD's material properties and its geometry and must be calculated. The IVD geometry remains incompletely characterized. Prior whole-disk models have been constructed from single IVDs. While this approach ensures that the geometry has a physiological basis, the degree to which results from a single IVD shape can be generalized to the entire population is uncertain. The primary objective of this study, therefore, was to develop a quantitative representation of IVD shape for the population. The approach incorporates a representative average IVD shape from multiple individuals and uses principal components analysis (PCA) to partition the variability of IVD shape into a small number of orthogonal modes of variation. These modes of variation can be adjusted parametrically. Since IVD shape is expected to change with degeneration, each mode of variation was correlated with degeneration grade to isolate degeneration-related shape variability from normal variability between individuals. Materials and Methods Magnetic Resonance Imaging Total 14 postmortem, agarose embedded L3-L4 motion segments (13 M, 1 F - age 69 ± 12 years - Pfirrmann grade 3.3 ± 0.8) underwent MRI (7T Siemens scanner - custom RF coil) using a 3D FLASH sequence (TE/TR = 3.7/9 ms) with ∼200 mm isotropic resolution.1 Image SegmentationBefore segmentation, the MRI images underwent intensity inhomogeneity correction, 50% downsampling, and Gaussian smoothing. Segmentation of the intervertebral disk was done in SNAP.2 The intensity-based region competition active contour tool was used to provide an initial segmentation. Errors in the automatic result were corrected by manual slice-by-slice segmentation. Shape Quantification The shape model was created by PCA of the disk segmentations.3 To make the images amenable to PCA, they were embedded as signed distance functions.3 The mean of the signed distance functions represents the average disk shape, with the residual shape variability captured as offsets from the mean signed distance function. These residuals were analyzed by PCA to produce a new 13-dimensional orthonormal basis for IVD shape. Each basis vector represents a different mode of shape variation. The basis vectors were ordered by the amount of variability that they capture from the original dataset. Following PCA, each disk in the dataset was projected into the new basis as a linear combination of the mean shape and the shape variation basis vectors. To determine which basis vectors represented degeneration-related shape variation, the projection coefficients were then correlated to Pfirrmann grade. Finally, to supplement the PCA-derived representation, the disk shapes were summarized by geometric measures: width, (left to right), depth (anterior-posterior distance at the mid-sagittal plane), height (averaged over the entire IVD), and axial-plane area. Results The first basis vector M1 represented an order of magnitude more variance than any other basis vector. Relative to M1, the second basis vector M2 captured 11% as much variance; M3, 9%; M4, 7%; M5, 5%; M6, 3%. Basis vectors 7 to 13 captured less than 2% as much variance as basis vector M1. Given the low variances associated with basis vectors M2 to M13 relative to basis vector M1, it is possible to represent IVD shape by the basis vector M1 coefficient w1 alone and still capture the majority of the population's IVD shape variation. Examination of the shapes produced by adding and subtracting one standard deviation of basis vector M1 from the mean shape reveals that basis vector M1 primarily controls lateral disk bulging, with little change in disk height. The basis vector M1 was also the only basis vector to show a significant correlation to degeneration as measured by Pfirrmann grade. None of the basis vectors were significantly correlated with age. Conclusion The objective of obtaining a low-dimensional representation of IVD shape was met. IVD shape variation was dominated by a single lateral bulging-related component, which was also correlated to degeneration grade. The low dimensionality of the shape representation makes it amenable to human manipulation, permitting straightforward modeling of a representative sampling of IVD shapes for example, for finite element analysis. The shape representation can also be used directly as a shape before Bayesian image segmentation of low-detail IVD images, for example, in vivo MRI. Further work is required to establish causation between degeneration and shape changes. Acknowledgment NIH grant R01 AR05005. I confirm having declared any potential conflict of interest for all authors listed on this abstract Yes Disclosure of Interest None declared Pfirrmann CW, et al. Spine 2001;26:1873 Yushkevich PA, et al. NeuroImage 2006;31:1116 Tsai A, et al. IEEE Transaction Medical Imaging 2003;22:137