AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting
of the American Society of Biomechanics
Clemson University, South Carolina
September 24-27, 1997
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| AMERICAN SOCIETY OF BIOMECHANICS
Presented at the Twenty-First Annual Meeting |
Cortical bone defects, such as surgical screw holes or osteotomies can result in post-operative complications, such as bone fracture leading to failure. An understanding of the effective' strain field around a circular hole in cortical bone is necessary for predicting situations in which the bone may fail, as well as for developing computational algorithms based on effective mechanical measures for predicting adaptive modeling and remodeling of bone in response to local damage. The purpose of the research described herein was, then, to experimentally describe the variations in the surface strain field surrounding a hole in a cortical bone plate using a novel laser speckle-based technique.
A non-imaging, laser speckle-based, strain-rate measurement technique that is sensitive to scale-size dependencies on strain rate was employed to measure directly the variations in the local strain field in the vicinity of a circular hole in a mandibular cortical bone plate undergoing a dynamic tensile load. Intact specimens (without a circular defect) were also examined using the same technique. Estimates of the Young's modulus of the intact samples were made based on the ratio of the imposed stress rates and the strain rates as measured via the laser speckle technique. As a means of confirming the modulus estimates (and by extension, the strain rate estimates), the intact specimens were also subjected to 3-point bending tests and the moduli of each sample was estimated by this means. Care was taken in all tests to keep the stress level well below the yield stress of cortical bone.
The effects of surgical hole defects have been studied by many authors, both experimentally (e.g. Brooks et al., 1970; Zioupos et al., 1995) and theoretically (Zioupos et al., 1995). Previous work on the development of the laser speckle technique employed herein has demonstrated that it is sensitive to scale size dependencies on strain rate (Duncan et al., 1994). Scale size is defined as the separation between the individual light scatterers in the bone samples. Modifications to the technique of Duncan et al., (1994) have proven successful in evaluating surface strains in cortical bone taken from the mid-diaphysis of porcine femurs (Kirkpatrick et al., in press). The present work combines the approaches of Duncan et al. (1994) and Kirkpatrick et al. (in press) to investigate the local mechanical effects of a round hole drilled into a cortical bone plate.
Five rectangular cortical bone samples were machined under constant irrigation from the corpus of a bovine mandible. At no time, either during the machining nor testing, were the samples allowed to dry. Each sample was subjected to dynamic tensile testing twice; once intact and once with a circular defect drilled through the center. The samples were tested in a direction parallel to the long axis of the mandible. In addition, the intact specimens were subjected to 3-point bending tests. The tensile testing was conducted in a custom micro-tensile testing machine. Strain rates were measured directly via the laser speckle technique as described by Duncan et al. (1994) and Kirkpatrick et al. (in press). Briefly, this technique samples the back-scattered light from the bone samples as they are sequentially illuminated by laser light from equal, but opposite illumination angles. The back-scatter is recorded by a linear array CCD camera and the sequential exposures from each illumination angle are placed into stacked-speckle histories' which are spatio-temporal displays of the sequential, one-dimensional exposures stacked into a two dimensional array such that position (pixel number) is given by the abscissa and time (as set by the sample interval) is given by the ordinate (Figure 1). The tilt of the structure of Fig. 1 is related to the strain rate. The rate of speckle pattern shift was determined by performing a 2-D frequency transform on a portion of the data of Fig. 1 (defined by the arrows). This transform results in a focused image' in the frequency domain, the slope of which is microns per second, or the time rate of speckle pattern shift. Any statistically significant curvature in this focused image indicates a scale-size dependence on strain rate. By differencing the rate as seen from the two illumination angles, the rigid body motion, out-of-plane, and rotational terms are eliminated. Thus the technique is sensitive only to in-plane strain rates.
The mean modulus for the intact specimens as determined by 3-point bending was 17.65(±0.22)GPa and that determined by the speckle technique was 17.37(±0.21)GPa. There was no statistical difference between the two means. In no cases was there determined to be a scale size dependence on strain rate for the intact specimens.
In all of the drilled samples a scale-size dependence on strain rate was found. The mean strain rate variation due to the presence of the hole was 1.75(±0.65):1. This variation in strain rate reflects the fact that the circular hole acts as a stress concentrator, locally varying the effective strain rates.
The Young's moduli determined in this study are in good agreement with published data on mandibular cortical bone (Dechow et al., 1993). This indicates that the speckle technique was successful in characterizing the mechanical properties of intact bone. The strain rate variation found due to the stress concentrator is similar to that found by Brooks et al. (1970) on drilled whole bones in torsion. The fact that neither the present study nor that of Brooks et al. conforms with the predictions of linear elasticity theory reflects the fact bone is an anisotropic material with properties of an orthotropic or transversely isotropic material. The results presented here can be applied towards the development of damage-based (re)modeling algorithms.
Brooks, D.B. et al. J. Bone Jt. Surg., 52, 507- 514, 1970.
Duncan, D.D. et al. Appl. Opt., 33, 5177-5186, 1994.
Dechow, P.C. et al. Am. J. Phys. Anthro., 90, 291-306, 1993.
Kirkpatrick, S.J. et al. J. Biomed. Mater. Res. in press.
Zioupos, P. et al. Phil. Trans. Roy. Soc. Lond. B, 347, 383-396, 1995.
