Research PaperStudy of indentation of a sample equine bone using finite element simulation and single cycle reference point indentation
Graphical abstract
Introduction
In large mammals such as humans or horses, bone health is an important topic given the critical role it plays in life. From human athletes or racehorses at risk of fracture, to medical professionals performing surgery or those investigating the influence of disease such as osteoporosis, determining the health of bone is an objective highly relevant to the health and quality of lives.
Bone is the main load bearing organ of vertebrate animals, making it a specific point of interest since the dawn of modern medicine. Bone can be classified into two main types, cortical (or compact) and trabecular (or spongy). Cortical bone takes the brunt of the forces involved in structural loading, and therefore will be the focus of study here, at the characteristic Haversian, or osteonal level. Cortical bone is a biological hierarchical composite material, with different structural configurations corresponding to different scales of length, as seen in Fig. 1.
The measurement and testing of cortical bone properties have been researched for decades, with a variety of approaches. Conventional mechanical testing such as axial loading in tension and compression, and beam bending in three or four-point load setups have been explored extensively (Currey, 2002, Currey, 1999, Currey, 1990, Burstein et al., 1972, An and Draughn, 2000, Simkin and Robin, 1973, Reilly and Burstein, 1975). Various indentation methods have been used as well, ranging from macro scale methods such as Vickers and Rockwell, to using Berkovich indenters with an atomic force microscope or nanoindentor. Most of these tests are performed at quasi-static to low loading rates. Additionally, mineral density and chemical composition investigations have been performed, with various correlations being made to elastic properties (Mullins et al., 2009, Zhang et al., 2010, Zhang et al., 2008, Rho et al., 1998, Zysset, 2009, Hoc et al., 2006, Mercer et al., 2006, Tai et al., 2006).
One significant complication in testing properties of bone is the question of in- or ex-vivo. This is a large barrier for testing of bone. Inside a living animal, bone is hydrated and constantly undergoing cellular driven microstructural processes. Over the years many investigators have made advances in non-invasive in-vivo testing of bone properties. In particular, x-ray based methods have been extensively developed and are used for testing bone mineral density and tissue composition (Mazess et al., 1990). Another non-invasive technique used is that of ultra-sound measurements, widely studied and generally focused on density and elastic modulus (Jeffcott et al., 1987), but also used to investigate other properties, for example, correlation with failure strength in equine cortical bone (Glade et al., 1986).
Recently, another minimally-invasive in-vivo technique is receiving attention in the medical community, called reference point indentation (RPI) developed by two of the present authors (Bridges et al., 2012, Gallant et al., 2012). A new hand-held reference point indentation instrument, the Osteoprobe®, utilizes a single rapid, dynamic, indentation, with maximum indentation distance being the primary variable (Randall et al., 2013). A focus on dynamic indentation is used since most naturally occurring large deformation events occur in bone under impact or rapid loading, such as a sports injury or in a transportation accident. Due to indentation’s inherent connection to hardness, pressure and strength, this avenue of testing bone tissue has gained interest as a simple method to test bone quality in a quantitative way. There is growing clinical and laboratory evidence that bone response can reveal critical information about bone health as a whole, with important implications for fracture risk (Farr et al., 2014, Zhang et al., 2010, Rho et al., 1998, Zysset, 2009).
The goal of the current study was to examine indentation of equine cortical bone, with finite element analysis and experimental validation. Material was obtained from the third metacarpal of a thoroughbred donor, and stress–strain relationships of a cortical bone sample were first obtained from conventional mechanical property tests. A finite element simulation procedure was developed for indentation analyses, incorporating a yield criterion in the simulation calibrated by tested mechanical properties, with different values in tension and compression. Experimental validation of the simulation procedure, using material from the same bone sample, was performed by determining the maximum depth of indentation with single cycle reference point indentation, and the profile and depth of the unloaded, permanent indentation with atomic force microscopy. Refinement of the finite element procedure by introduction of a type of damage through reduction of Young’s modulus was added to further increase accuracy in simulating the profile and depth of the unloaded, permanent indentation, post recovery. Utility of the validated simulation procedure was demonstrated through prediction of differing responses between two tips of indenters with varying sharpness with experimental validation. This study details the development of a finite element procedure which uses a Drucker–Prager yield criterion, calibrated through mechanical testing of the same material sample used in experimental validation, and with simple Young’s modulus reduction to address damage, to simulate the response of cortical bone under a single cycle type of reference point indentation. Concluding remarks are made as to the insights gained with regard to the mechanical properties and behaviors of the equine cortical bone.
Section snippets
Mechanical testing
Four-point bending and axial compression tests were performed on cortical bone samples using an instrumented MTS 810 Universal Test machine. Bone tissue was provided by Purdue University’s College of Veterinary Medicine, in the form of cross-sectional segments from the third meta-carpal bone. The two different mechanical test setups can be seen in Fig. 2a and b. Material preparation started with the equine third metacarpal cross-sections. Different sample geometries were created for the two
Results
In order to study the mechanical behavior of equine bone under single cycle reference point indentation, stress strain relationships were obtained from conventional mechanical testing, a finite element procedure was developed for indentation analyses, and simulation results were validated by experimentally determining both the maximum depth of indentation, and the profile and depth of the recovered, permanent indentation with atomic force microscopy.
Discussion and concluding remarks
The indentation and recovery of an equine cortical bone sample using a reference point indentation instrument have been analyzed by finite element simulation and validated by experiment, showing good agreement. Simulating the behavior of cortical bone under reference point indentation could become a necessary and important step in mechanistically linking clinical results of the method to bone mechanical properties related to the health of the bone. The simplicity of use of the single cycle
Acknowledgements
The authors would like to gratefully acknowledge funding by NSF through grant CMMI-1031244, and by NIH through grant RO1 GM055354. Additionally, the authors would like to acknowledge the support of the UC Santa Barbara Mechanical Engineering Department, the UC Santa Barbara Physics Department, and also thank Dr. Srinivasan Chandrasekar, of the Department of Industrial Engineering, Purdue University, for thoughtful guidance and discussion.
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