Research Papers

Relative Nucleus Pulposus Area and Position Alter Disk Joint Mechanics

[+] Author and Article Information
Bo Yang, Colin Um

Department of Mechanical Engineering,
University of California Berkeley,
Etcheverry Hall,
Berkeley, CA 94720

Yintong Lu

Department of Mathematics,
University of California Berkeley,
Evans Hall,
Berkeley, CA 94720

Grace D. O'Connell

Department of Mechanical Engineering,
University of California Berkeley,
Etcheverry Hall,
Berkeley, CA 94720;
Department of Orthopaedic Surgery,
University of California,
San Francisco, CA 94142
e-mail: g.oconnell@berkeley.edu

1Corresponding author.

Manuscript received June 19, 2018; final manuscript received February 17, 2019; published online March 25, 2019. Assoc. Editor: David Corr.

J Biomech Eng 141(5), 051004 (Mar 25, 2019) (11 pages) Paper No: BIO-18-1287; doi: 10.1115/1.4043029 History: Received June 19, 2018; Revised February 17, 2019

Aging and degeneration of the intervertebral disk are noted by changes in tissue composition and geometry, including a decrease in nucleus pulposus (NP) area. The NP centroid is positioned slightly posterior of the disk's centroid, but the effect of NP size and location on disk joint mechanics is not well understood. We evaluated the effect of NP size and centroid location on disk joint mechanics under dual-loading modalities (i.e., compression in combination with axial rotation or bending). A finite element model (FEM) was developed to vary the relative NP area (NP:Disk area ratio range = 0.21–0.60). We also evaluated the effect of NP position by shifting the NP centroid anteriorly and posteriorly. Our results showed that compressive stiffness and average first principal strains increased with NP size. Under axial compression, stresses are distributed from the NP to the annulus, and stresses were redistributed toward the NP with axial rotation. Moreover, peak stresses were greater for disks with a smaller NP area. NP centroid location had a greater impact on intradiscal pressure during flexion and extension, where peak pressures in the posterior annulus under extension was greater for disks with a more posteriorly situated NP. In conclusion, the findings from this study highlight the importance of closely mimicking NP size and location in computational models that aim to understand stress/strain distribution during complex loading and for developing repair strategies that aim to recapitulate the mechanical behavior of healthy disks.

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Grahic Jump Location
Fig. 1

(a) Seven models with different geometric descriptions for the nucleus pulposus (NP: purple), and, therefore, the annulus fibrosus (AF), which contained 20 lamellae in all models. In series I (shown in the first and second rows), the effect of NP size was evaluated. In series II (third row), the effect of NP position was evaluated by creating either an anterior or posterior shift in the location of the NP centroid with respect to the control model (see Table 1). Inset: Midsagittal cross section of the control model. The whole disk joint model included the AF (teal), cartilaginous endplates (CEPs, red), and boney endplates (gray). (b) Stress–stretch of AF fibers from six regions. A: anterior, L: lateral, P: posterior, O: outer, I: inner. Material parameters were calibrated using data from single lamellae tensile tests [35].

Grahic Jump Location
Fig. 2

Model validation results. (a) Results for the control model were compared to experimental data for normalized disk height change under axial compression [40,44,45]. (b) Load–displacement curves for bending and axial rotation without a compressive preload were shown for the control model (black lines, NP:Disk area ratio = 0.28, 5% posterior NP centroid offset). Model simulation results were compared to experimental results from the literature [42,43]. (c) Toe-region and linear-region stiffness for bending and axial rotation without a compressive preload were shown for the control model and compared to experimental results [4143]. Error bar in (a) and (c) represents one standard variation while error bar in (b) represents range of the test result.

Grahic Jump Location
Fig. 3

(a) Compressive load (pressure) versus the change in disk height under load normalized to the original disk height. (b) Normalized compressive stiffness (stiffness × disk height/disk area) of the toe- and linear-region versus NP:Disk area ratio. (c) The change in disk height under compression decreased nonlinearly with an increase in NP:Disk area ratio. (d) Percentage of NP support under 0.48 MPa compression, which was calculated as the ratio of NP support divided by applied axial compressive load. Relative NP support increased with NP:Disk area ratio. Dashed lines in (b) and (d) represent a fit line with equation aside.

Grahic Jump Location
Fig. 4

(a) Torque versus angular displacement for the control model under bending and rotation, with the reference configuration defined as the moment after axial compression was applied. Simulations were performed with (blue lines) or without (gray lines) a compressive preload. (b) Disk joint stiffness under bending with a compressive preload. Disk joint stiffness under flexion, extension, and lateral bending varied little with an increase in NP:Disk area ratio. Rotational stiffness decreased slightly with a larger NP area. “+” in the legend represents inclusion of a compressive preload. Dashed lines in B represent a fit line with equation aside.

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Fig. 5

Pressure distribution at the mid-disk height (i.e., midtransverse plane) and midsagittal plane for the 0.21 (smallest) and 0.60 (largest) NP:Disk models under compression, bending, and rotation. For lateral bending, midcoronal plane pressure distributions are presented instead of the midsagittal plane. + represents inclusion of a compressive preload before bending was applied.

Grahic Jump Location
Fig. 6

(a) Pressure distribution along the mid-disk height from the posterior to the anterior of the midsagittal plane under 0.48 MPa axial compression. Average pressure in the (b) NP and (c) AF under compression, bending, or rotation with respect to NP:Disk area ratio. Average first principal strain for the (d) NP and (e) AF under compression, bending, or rotation with respect to NP:Disk area ratio. Figures 5(b)5(e) share the same legend, where + represents inclusion of a compressive preload.

Grahic Jump Location
Fig. 7

Strain distribution of the first principal strain at the mid-disk height (i.e., midtransverse plane) for the 0.21 and 0.60 NP: Disk models under compression-only loading and compression with bending or rotation. + represents inclusion of a compressive preload before bending was applied

Grahic Jump Location
Fig. 8

(a) Pressure distribution along the mid-disk height under 0.48 MPa axial compression. Pressure distribution in the midsagittal plane for models in compression with (b) 6.5 deg flexion and (c) 4 deg extension. All data are displayed with the posterior AF on the left side and the anterior AF on the right side.



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