Research Papers

Evaluation and Prediction of Human Lumbar Vertebrae Endplate Mechanical Properties Using Indentation and Computed Tomography

[+] Author and Article Information
Ravi R. Patel

Department of Mechanical Engineering,
University of Colorado Denver,
Campus Box 112,
P.O. Box 173364,
Denver, CO 80217
e-mail: Ravi.patel@ucdenver.edu

Andriy Noshchenko

Department of Orthopedics,
University of Colorado,
Anschutz Medical Campus,
13001 E 17th Avenue, Building 500,
Mail Stop 432,
Aurora, CO 80045
e-mail: Andriy.Noshchenko@ucdenver.edu

R. Dana Carpenter

Department of Mechanical Engineering,
University of Colorado Denver,
Campus Box 112,
P.O. Box 173364,
Denver, CO 80217
e-mail: Dana.carpenter@ucdenver.edu

Todd Baldini

Department of Orthopedics,
University of Colorado,
Anschutz Medical Campus,
13001 E 17th Avenue, Building 500,
Mail Stop 432,
Aurora, CO 80045
e-mail: Todd.baldini@ucdenver.edu

Carl P. Frick

Department of Mechanical Engineering,
College of Engineering and Applied Science,
University of Wyoming,
Dept. 3295, 1000 E. University Avenue,
Laramie, WY 82071
e-mail: cfrick@uwyo.edu

Vikas V. Patel

Department of Orthopedics,
University of Colorado,
Anschutz Medical Campus,
12631 E. 17th Avenue,
Academic Office 1, Room 4602,
Denver, CO 80045
e-mail: Vikas.patel@ucdenver.edu

Christopher M. Yakacki

Department of Mechanical Engineering,
University of Colorado Denver,
Campus Box 112,
P.O. Box 173364,
Denver, CO 80217
e-mail: Chris.yakacki@ucdenver.edu

1Corresponding author.

Manuscript received February 9, 2018; final manuscript received May 7, 2018; published online June 21, 2018. Assoc. Editor: James C Iatridis.

J Biomech Eng 140(10), 101011 (Jun 21, 2018) (9 pages) Paper No: BIO-18-1082; doi: 10.1115/1.4040252 History: Received February 09, 2018; Revised May 07, 2018

Current implant materials and designs used in spinal fusion show high rates of subsidence. There is currently a need for a method to predict the mechanical properties of the endplate using clinically available tools. The purpose of this study was to develop a predictive model of the mechanical properties of the vertebral endplate at a scale relevant to the evaluation of current medical implant designs and materials. Twenty vertebrae (10 L1 and 10 L2) from 10 cadavers were studied using dual-energy X-ray absorptiometry to define bone status (normal, osteopenic, or osteoporotic) and computed tomography (CT) to study endplate thickness (μm), density (mg/mm3), and mineral density of underlying trabecular bone (mg/mm3) at discrete sites. Apparent Oliver–Pharr modulus, stiffness, maximum tolerable pressure (MTP), and Brinell hardness were measured at each site using a 3 mm spherical indenter. Predictive models were built for each measured property using various measures obtained from CT and demographic data. Stiffness showed a strong correlation between the predictive model and experimental values (r = 0.85), a polynomial model for Brinell hardness had a stronger predictive ability compared to the linear model (r = 0.82), and the modulus model showed weak predictive ability (r = 0.44), likely due the low indentation depth and the inability to image the endplate at that depth (≈0.15 mm). Osteoporosis and osteopenia were found to be the largest confounders of the measured properties, decreasing them by approximately 50%. It was confirmed that vertebral endplate mechanical properties could be predicted using CT and demographic indices.

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Grahic Jump Location
Fig. 1

Cartesian map of the indentation sites across the vertebral endplate. Indentation sites were defined relative to percentages of the dimensions of the vertebral endplate.

Grahic Jump Location
Fig. 2

(a) Overall indentation protocol where E is the Oliver–Pharr modulus assessment at the endplate surface; stiffness is the load at 1 mm of probe displacement (N/mm); maximum load was defined as the peak of the load–displacement curve. (b) Oliver–Pharr indentation protocol where S is the unloading stiffness of the curve (N/mm), Pmax is the maximum load achieved in this loading step (10 N), and hm is the maximum indentation depth (displacement) reached in this step (mm).

Grahic Jump Location
Fig. 3

Representative load–displacement curves for Oliver–Pharr measurements for specimens within the top 10% (404 MPa), top 25% (208 MPa) and bottom 50% (106 MPa) of all test data

Grahic Jump Location
Fig. 4

Representative stiffness curves for the Common spinal cage materials and vertebral endplates. The two bottom curves are representative of the top 10% of tested endplates and the top 50%, respectively. PEEK and cortical bone are shown to be significantly stiffer than even the stiffest endplates.

Grahic Jump Location
Fig. 7

Correspondence between predicted apparent modulus and apparent modulus measured from indentation testing. Apparent Oliver–Pharr modulus was modeled using endplate density, presence of endplate defects, and patient weight. Modulus was modeled using the equation E = −71.35 + 1.57X1 + X2 − 0.092X3, where E is the linear approximation Oliver–Pharr modulus (MPa); X1 is the patient weight (kg); X2 is the presence of an endplate defect or herniation parameter (yes/no = ±19.3), and X3 is the endplate mineral density (mg/mm3). The linear model showed a correlation of R2 = 0.19.

Grahic Jump Location
Fig. 6

Correspondence between predicted hardness and hardness measured from indentation testing. Brinell hardness was modeled as a linear and polynomial model using endplate density, endplate thickness, the presence of and endplate defect, and patient weight. The linear fit used the equation yBH = −2.9 + 0.002X1 + 0.0011X2 + 0.008X4, where yBH is the linear approximation of Brinell hardness, X1 is the endplate mineral density (mg/mm3), X2 is the endplate thickness (μm), X3 is the presence of an endplate defect or herniation (yes/no = ±0.1), and X4 is patient weight (kg). The polynomial fit was described by the equation YBH = 0.06 + 0.85 yBH + 0.36 (yBH − 0.98)2, where YBH is the polynomial approximation of Brinell hardness, and yBH is the linear approximation obtained from the first equation. The linear fit showed a correlation of R2 = 0.64 while the polynomial fit showed a correlation of 0.68 with the measured hardness values.

Grahic Jump Location
Fig. 5

Correspondence between the predictive stiffness model and stiffness measured from indentation testing. Stiffness was modeled as a function of endplate thickness, endplate density, adjacent cancellous bone density, existence of endplate defects, and patient age according to Eqs. (6) and (7). The stiffness model showed a correlation of R2 = 0.72 with the measured endplate stiffness from indentation.



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