Novel human intervertebral disc strain template to quantify regional three-dimensional strains in a population and compare to internal strains predicted by a finite element model

Abstract

Tissue strain is an important indicator of mechanical function, but is difficult to noninvasively measure in the intervertebral disc. The objective of this study was to generate a disc strain template, a 3D average of disc strain, of a group of human L4-L5 discs loaded in axial compression. To do so, magnetic resonance images of uncompressed discs were used to create an average disc shape. Next, the strain tensors were calculated pixel-wise by using a previously developed registration algorithm. Individual disc strain tensor components were then transformed to the template space and averaged to create the disc strain template. The strain template reduced individual variability while highlighting group trends. For example, higher axial and circumferential strains were present in the lateral and posterolateral regions of the disc, which may lead to annular tears. This quantification of group-level trends in local 3D strain is a significant step forward in the study of disc biomechanics. These trends were compared to a finite element model that had been previously validated against the disc-level mechanical response. Depending on the strain component, 81-99% of the regions within the finite element model had calculated strains within one standard deviation of the template strain results. The template creation technique provides a new measurement technique useful for a wide range of studies, including more complex loading conditions, the effect of disc pathologies and degeneration, damage mechanisms, and design and evaluation of treatments. © 2015 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1264-1273, 2016.

Keywords: finite element model; image registration; internal disc strain; intervertebral disc mechanics; magnetic resonance imaging.

Figure 1

Disc strain template creation process. First, MR images of individual discs are acquired and subject strain maps are calculated (A). Next, the MR images are used to create a disc anatomical template (B). The transformations from the subject discs to the template are saved (T₁, T₂, …, T_n). Those transformations are used to transform the subject disc strains to the template space, which are then averaged to create the disc strain template (C). Although images shown are two-dimensional, the process was completed using three-dimensional data.

Figure 2

(A) A segmentation image (colored) overlays one of the individual disc images (grayscale) used to create the template. (B) The same segmentation from (A) overlays the template, demonstrating that the individual disc is notably larger than the template. (C) The individual disc segmentation is transformed to the template. The transformed mask matches the outer contour of the template and original features of the original mask are preserved, including the diagonal lines between the annular regions, indicating a reasonable transformation between the individual disc and the template.

Figure 3

Circumferential and radial basis vectors for a local disc coordinate system. Defining the strain in local coordinate system facilitates transformation of strain tensors from the subjects to the template and interpreting results in the context of disc coordinate system.

Figure 4

Midaxial (A), midcoronal (B), and midsaggital (C) slices of the disc anatomical template. The annulus approximately the mid-third of axial region of the disc was divided into five regions (anterior, anterolateral, lateral, posterolateral, and posterior). The lower lateral side of the template was more poorly defined than the upper lateral side (A), because the original images had lower signal-to-noise and contrast-to-noise ratios in the lower lateral side as it was further away from the RF coil. As a result, this side was not included in the strain analysis.

Figure 5

Midaxial disc slices showing the first invariant of the Lagrangian strain tensor of four of the seven individual discs (A) and the template (B). The negative values indicate decreased volume, which is consistent with the applied compression load. The template does not have the invariant peaks evident in many of the samples (e.g., the peaks located at arrows in Discs 2 and 3). The template preserved general trends, such as higher invariants in the lateral and posterior regions (e.g., the regions of blue-green shading in the template marked with *).

Figure 6

Boxplots of the voxel strain distributions in the five annular regions for the axial (A), circumferential (B), and radial (C) strain components. The data represents the average strain values for all of the voxels within the regions as defined in Figure 4. Midaxial slices of the strain template are also shown. Solid lines are significant differences between means of the seven subject discs transformed to the template space (p<0.05), and dotted lines are trends (p<0.1).

Figure 7

Comparison of voxel distributions axial (A), circumferential (B), and radial (C) strain components between the inner and outer annulus of the strain template. In most regions, there was minimal difference and no statistical difference between the inner and outer annulus. # indicates trend of difference between means of the seven subject discs transformed to the template (p<0.1).

Figure 8

Comparison of the disc template created in this study (red) and the finite element model geometry, which were created using different samples and methods (blue). The template and shape model are similar in both shape and size. The shapes differed in that the disc anatomical template had peaks along the outer rim of the inferior and superior edges that were not evident in the FEM geometry (see arrows in midcoronal and midsagittal views).

Figure 9

Midaxial slices of the strain template (A) and finite element model (B). The difference of the FEM from the template mean is also shown in terms of the standard deviation at each voxel (C). The strains predicted by the FEM are within one standard deviation for the majority of the annulus in all three strain components. The greatest difference between the FEM and template is in the peak radial strains in the posterior region (arrow).

Figure 10

Comparison of mean template strains and finite element model strains in the mid-third of the disc. The boxplots represent range of strain values found in the voxels within each annular region. Median strains between the template and finite element model are within 0.2–2.5% strain for all compared regions except for the axial component in the anterolateral and lateral regions and the radial component in the posterior region, which have a difference in median strain of 3.8–6.0% strain (*).