Comparison of explicit finite element and mechanical simulation of the proximal femur during dynamic drop-tower testing
Introduction
It is estimated that each year over 1.6 million people suffer a hip fracture worldwide (Johnell and Kanis, 2006). Beyond its devastating effects on mobility and quality of life (Boonen et al., 2004, Ekstrom et al., 2009, Hallberg et al., 2004, Magaziner et al., 2003, Nevalainen et al., 2004, Osnes et al., 2004), this type of injury has been associated with increased risk of death (Cooper, 1997, Haleem et al., 2008). These fractures are often associated with a short, low trauma fall; with falls to the side having a high fracture rate (Parkkari et al., 1999). Current screening techniques based on areal bone mineral density (aBMD) measurements (Stone et al., 2003) are unable to identify the majority of people who sustain hip fractures. There is, therefore, a need to study the biomechanics of this problem with the ultimate goal of determining what predisposes a hip to fracture.
In sideways fall in-vitro experimental studies, forces have most often been applied using materials testing machines (Bouxsein et al., 1999, Cheng et al., 1997, de Bakker et al., 2009, Eckstein et al., 2004) with the actuator displacing the greater trochanter (GT) or femoral head in the medial–lateral direction while the shaft is supported. Constant loading rates of 0.1 m/s or lower have been generally used, while the impact speed associated with a sideways fall from standing is 3.0 m/s or higher (Feldman and Robinovitch, 2007, Robinovitch et al., 2004). This rate is beyond the reach of most current materials testing machines. Loading rate is important, however, as it has been shown to affect the mechanical properties of bone (Carter and Hayes, 1977, Courtney et al., 1994a, Linde et al., 1991). Given this rate dependency and the heterogeneity of the mechanical properties of bone, internal stress distributions could be different between dynamic and quasi-static loading, potentially resulting in different fracture patterns being created at different loading rates (Gilchrist et al., 2014). Testing femoral specimens at quasi-static loading rates in a classical sideways fall loading configuration, where the distal end of each specimen is allowed to rotate about a pivoting point (see e.g. Dragomir-Daescu et al., 2011, Grassi et al., 2012), ideally represents a statically determinant structural problem; this means that the reaction forces are independent of the bone׳s mechanical properties. When testing bones dynamically in the same configuration, the nature of the problem changes. Force equilibrium must take inertial forces into account, and these are ultimately tied to the stiffness and mass of the bone and surrounding anatomical structures, as well as the input energy.
Validated subject-specific Finite Element (FE) models based on X-ray computed tomography (CT) scans for studying the mechanics of the proximal femur have been extensively published (Bessho et al., 2007, Dragomir-Daescu et al., 2011, Duchemin et al., 2008, Grassi et al., 2012, Keyak, 2001, Keyak et al., 1998, Koivumaki et al., 2012, Schileo et al., 2008, Trabelsi et al., 2009, Trabelsi et al., 2011). These models have almost invariably followed a quasi-static structural approach and been validated against quasi-static experimental in-vitro models using local strains, overall stiffness of the bone and ultimate force as primary foci of validation. However, the recent introduction of drop-towers to simulate in-vitro the effect of a sideways fall on the mechanical response of the proximal human femur at realistic impact speeds (Fliri et al., 2013, Gilchrist et al., 2013), has opened up the possibility of comparing dynamic FE model predictions to the outcome of dynamic testing, which is the specific aim of the present study.
Section snippets
Experimental testing
The experimental setup and testing are described in detail in previous studies (Gilchrist et al., 2013, Gilchrist et al., 2014) and will only briefly be explained here for clarity. Sixteen fresh frozen proximal femora from 15 females and 1 male were obtained from a tissue donation bank (National Disease Research Interchange, Philadelphia, PA). Before testing, the specimens were imaged using two modalities: first they were scanned at 41 µm isotropic voxel size in an HR-pQCT scanner (XtremeCT,
Experimental testing
Force–time results for all 15 tests showed similar features (Fig. 4), including one or more small and short peaks – likely due to the impact of the bypass masses – followed by a steep rise in force up to the peak value.
Force–time response and force–displacement response comparison
The specimen force–time plots (Fig. 5) show similar relationships between the experimental and FE data, with the force rising at similar rates and times. However, there is a time delay in the FE model force trace compared to their corresponding experimental tests. The
Discussion
The aim of the present study was to compare FE model derived whole bone stiffness and force response to the outcome of experimentally simulated sideways falls occurring at realistic impact speeds. In general, we found statistically significant moderate correlations between the experimentally and computationally derived results for bone stiffness and energy absorption compared at equivalent displacements. No correlation was found between experimental and FEA derived force at equivalent
Conflict of interest
None.
Acknowledgement
Funding from the Natural Sciences and Engineering Research Council of Canada (NSERC RGPIN 288148-09) and the Swiss National Science Foundation (Project no. 205321_144435).
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