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Research Papers

Determination of Elastic Modulus in Mouse Bones Using a Nondestructive Micro-Indentation Technique Using Reference Point Indentation

[+] Author and Article Information
Ganesh Thiagarajan

Department of Civil and Mechanical Engineering,
University of Missouri-Kansas City,
350K Robert H. Flarsheim Hall,
5110 Rockhill Road,
Kansas City, MO 64110
e-mail: ganesht@umkc.edu

Mark T. Begonia

Department of Civil and Mechanical Engineering,
University of Missouri-Kansas City,
350K Robert H. Flarsheim Hall,
5110 Rockhill Road,
Kansas City, MO 64110

Mark Dallas, Nuria Lara-Castillo, JoAnna M. Scott, Mark L. Johnson

Department of Oral and Craniofacial Sciences,
School of Dentistry,
University of Missouri-Kansas City,
Room 3143, 650 E 25th Street,
Kansas City, MO 64108

1Corresponding author.

Manuscript received February 20, 2017; final manuscript received April 2, 2018; published online May 10, 2018. Assoc. Editor: David Corr.

J Biomech Eng 140(7), 071011 (May 10, 2018) (11 pages) Paper No: BIO-17-1076; doi: 10.1115/1.4039982 History: Received February 20, 2017; Revised April 02, 2018

The determination of the elastic modulus of bone is important in studying the response of bone to loading and is determined using a destructive three-point bending method. Reference point indentation (RPI), with one cycle of indentation, offers a nondestructive alternative to determine the elastic modulus. While the elastic modulus could be determined using a nondestructive procedure for ex vivo experiments, for in vivo testing, the three-point bending technique may not be practical and hence RPI is viewed as a potential alternative and explored in this study. Using the RPI measurements, total indentation distance (TID), creep indentation distance, indentation force, and the unloading slope, we have developed a numerical analysis procedure using the Oliver–Pharr (O/P) method to estimate the indentation elastic modulus. Two methods were used to determine the area function: (1) Oliver–Pharr (O/P—based on a numerical procedure) and (2) geometric (based on the calculation of the projected area of indentation). The indentation moduli of polymethyl methacrylate (PMMA) calculated by the O/P (3.49–3.68 GPa) and geometric (3.33–3.49 GPa) methods were similar to values in literature (3.5–4 GPa). In a study using femurs from C57Bl/6 mice of different ages and genders, the three-point bending modulus was lower than the indentation modulus. In femurs from 4 to 5 months old TOPGAL mice, we found that the indentation modulus from the geometric (5.61 ± 1.25 GPa) and O/P (5.53 ± 1.27 GPa) methods was higher than the three-point bending modulus (5.28 ± 0.34 GPa). In females, the indentation modulus from the geometric (7.45 ± 0.86 GPa) and O/P (7.46 ± 0.92 GPa) methods was also higher than the three-point bending modulus (7.33 ± 1.13 GPa). We can conclude from this study that the RPI determined values are relatively close to three-point bending values.

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Copyright © 2018 by ASME
Topics: Bone , Elastic moduli
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Figures

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Fig. 1

Comparison of destructive (to determine structural properties of the bone) versus nondestructive methods of determining the elastic modulus in bone

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Fig. 2

Reference Point Indentation instrument used along with the custom positioning fixture built for the study with the microscope (top) and the bone during the indentation process (bottom)

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Fig. 3

Reference point indentation indenter prior to indentation in PMMA block (Top left), indentation on mouse bones, which are held in place by grips (Top right) and a typical one cycle indentation curve output by the RPI instrument from which material parameters are determined

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Fig. 4

(a) First, microCT scanning and three-point bending are employed. (b) Second, the stiffness is obtained from the load–displacement data. (c) Third, BoneJ is used to realign microCT slices and obtain an average moment of inertia that is used for calculating the elastic modulus.

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Fig. 5

Scanning electron microscopy micrographs showing the indentation location and microcracks at (a) 100× and (b) 1000× on the TOPGAL ulna. A 2 N load was applied for 1cycle.

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Fig. 6

Comparison of elastic moduli obtained from (a) three-point bending and (b) O/P method

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Fig. 7

Analysis of elastic moduli of femurs from (a) HETcKO mice and (b) their littermate controls revealed no significant differences in the elastic moduli, regardless of the analysis technique applied

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Fig. 8

Comparison of moments of inertia for C57BL/6 femurs by age in (a) females and (b) males. Distance measurements correspond to the total length of the 7.6 mm span. Negative values correspond to the distal direction while positive value correspond to the proximal direction with respect to the midshaft.

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