Research paperFinite element simulation of Reference Point Indentation on bone
Introduction
The mechanical properties of bone are generally measured using traditional materials testing approaches such as compression, tension, three or four point bending, and fracture toughness tests. The basic limitations of these methods are that they are ex-vivo and destructive. The Reference Point Indentation (RPI) technique was invented to allow in-vivo measurements of bone material properties, relevant to the risk of bone fracture (Hansma et al., 2006, Diez-Perez et al., 2010). The instrument utilizes a cyclic loading to indent cortical bone multiple times at the same location (Fig. 1). The force-vs-displacement response, generated by the RPI technique (Fig. 2), allows the calculation of ten RPI parameters. The ID1 and TID are the maximum indentation depths after the first and last cycle, respectively. The IDI is the indentation distance increase observed between the first and last cycles. The CID1 is the creep distance for the first loading cycle while the AvCID is the average of creep distances over all cycles. The US1 is the unloading slope calculated from the first loading cycle and the average of unloading slopes over all cycles is denoted by AvUS. The LS1 is the loading slope for the first loading cycle, AvLS is the average of loading slopes over all cycles and AvED is the energy dissipated over the third to last loading cycle. These RPI parameters are summarized in Table 1 for easy reference. The BioDent 1000™ RPI instrument (Active Life Scientific, Inc., Santa Barbara, CA) is an experimental device used to perform the RPI tests and utilizes a software which computes the RPI parameters.
The RPI technique has received considerable interest in the bone mechanics community. There have been nearly fifty journal papers published from several different perspectives since its invention in 2006. Some of these studies have focused on the development of the method (Hansma et al., 2006, Hansma et al., 2008), protocols (Setters and Jasiuk, 2014, Coutts et al., 2015, Jenkins et al., 2015), in vivo studies (Diez-Perez et al., 2010, Aref et al., 2013, Güerri-Fernández et al., 2013, Farr et al., 2014), and ex vivo studies (Randall et al., 2009, Gallant et al., 2013, Rasoulian et al., 2013, Bart et al., 2014, Granke et al., 2014, Hammond et al., 2014, Milovanovic et al., 2014, Beutel and Kennedy, 2015, Coutts et al., 2015, Granke et al., 2015, Hoffseth et al., 2015, Katsamenis et al., 2015). The RPI technique has also been utilized in dental studies (Yassen et al., 2014) and soft tissue research (Hansma et al., 2009, Tang et al., 2010, Tang et al., 2011, Cheng et al., 2014). An overview of the RPI technique is given in a recent review paper by Allen et al. (2015).
Based on these introductory studies on the RPI technique, the IDI has been identified as the most promising output of the RPI method. Diez-Perez et al. (2010) showed that the IDI correlates well with the incidence of fracture and was able to distinguish between normal and osteoporotic patients. Gallant et al. (2013) found that the IDI is inversely correlated with bone toughness obtained from three point bending and axial compression tests. Rasoulian et al. (2013) studied age-related changes in porcine femoral cortical bone and showed that the IDI decreases with age in developing bone. In their studies, Granke et al. (2014) demonstrated that the IDI provides the best correlation between yield stress and toughness. However, in general, it is still not well understood how the RPI parameters are related to the specific bone properties. Thus, there is a need for further studies on the interpretation of the RPI parameters before this technique can be more fully utilized in both research and clinical settings.
Computer simulations can provide additional insight into the RPI technique. To date, there has only been one computational study on the RPI method (Hoffseth et al., 2015), which simulated an indentation of the cortical bone using an Osteoprobe, another RPI device designed with clinical setting in mind. This instrument provides only one output, the bone material strength index (normalized indentation distance increase). Other related computational studies include simulations of nanoindentation of bone (Adam and Swain, 2011, Mullins et al., 2009, Zhang et al., 2010, Zhang et al., 2008, among others). A constitutive law that captures the isotropic viscoelastic-plastic response of bone was proposed by Zhang et al. (2008), and it was subsequently generalized to include damage (Zhang et al., 2010).
In this paper we simulate RPI on human cortical bone, mimicking the BioDent tests, using the finite element method (FEM) available in the commercial software Abaqus (V6.14). Our model utilizes the isotropic viscoelastic-plastic constitutive model proposed by Zhang et al. (2010) for human cortical bone. This constitutive law has eight material constants and we vary four of these constants: (Young׳s modulus, yield stress, and viscous and damage parameters). Additionally, experimental factors (indentation peak load, number of cycles, and indenter tip radius) are varied in the simulations. The force-vs-displacement response is obtained for each case, post-processed to calculate the RPI parameters, and compared with experimental results (Granke et al., 2014). The effects of the input variables on the RPI outputs are reported, and the relationship between the RPI parameters and the mechanical behavior of bone is investigated to gain a better understanding of the RPI technique.
Section snippets
Material model
The plastic damage model of Lubliner et al. (1989) is a general model that incorporates damage in materials and a subsequent reduction in elastic modulus under tensile and compressive strains. RPI performed on cortical bone will locally damage the bone sample, mainly due to compressive loading (Setters and Jasiuk, 2014). Therefore, damage due to tensile strains is neglected in this study.
Assuming continuum damage, where is the scalar damage variable, the effective stress in the medium is
Computational results
In this paper we investigated computationally the effect of various material and testing variables on the RPI parameters. The RPI technique has been used to measure bone material properties in-vivo to predict the risk of bone fracture (Hansma et al., 2006, Diez-Perez et al., 2010). However, the relationship between the RPI measured parameters and bone properties is still not well understood. To address this issue, we simulated the RPI on human cortical bone, mimicking BioDent tests. Cortical
Conclusions
The finite element method within Abaqus software V6.14 was used to simulate RPI on human cortical bone and provided new data on how the RPI parameters are related to the material constants used to represent human bone properties (Zhang et al., 2010). Simulation results are in good agreement with the experimental study of Granke et al. (2014).
The simulation results indicate that RPI parameters are sensitive to the material properties of human cortical bone. The unloading slopes were found to be
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Acknowledgments
The authors gratefully acknowledge support from the National Science Foundation (NSF), the CMMI Program Grant 09-27909 and the DMR Program Grant 15-07169. The findings, conclusions and recommendations expressed in this manuscript are those of the authors and do not necessarily reflect the views of the NSF.
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