Abstract
Introduction
Subject-specific finite element models (FEMs) allow for a variety of biomechanical conditions to be tested in a highly repeatable manner. Accuracy of FEMs is improved by mapping density using quantitative computed tomography (QCT) and choosing a constitutive relationship relating density and mechanical properties of bone. Although QCT-derived FEMs have become common practice in contemporary computational studies of whole bones, many density-modulus relationships used at the whole bone level were derived using mechanical loading of small trabecular or cortical bone cores. These cores were mechanically loaded to derive an apparent modulus, which is related to each core's mean apparent or ash density. This study used these relationships and either elemental or nodal material mapping strategies to elucidate optimal methods for scapular QCT-FEMs.
Methods
Six cadaveric scapulae (3 male; 3 female; mean age: 68±10 years) were loaded within a micro-CT in a custom CT-compatible hexapod robot Pre- and post-loaded scans were acquired (spatial resolution = 33.5 µm) and DVC was used to quantify experimental full-field displacements (BoneDVC, Insigneo) (Figure 1).. Experimental reaction forces applied to the scapulae were measured using a 6-DOF load cell. FEMs were derived from corresponding QCT scans of each cadaver bone. These models were mapped with one of fifteen density-modulus relationships and elemental or nodal material mapping strategies. DVC-derived BCs were imposed on the QCT-FEMs using local displacement measurements obtained from the DVC algorithm. Comparisons between the empirical and computational models were performed using resultant reaction loads and full-field displacements (Figure 2).
Results and Discussion
Reaction forces predicted by the QCT-FEMs showed large percentage error variations across all specimens and density-modulus relationships with elemental material mapping. The percentage errors were as large as 899%, but as low as 3=57% for the different specimens. Similarly, when using a nodal material mapping strategy, percentage errors were as large as 965%, but as low as 4=59% for the different specimens (Figure 3).
For all specimens, minimal variation only occurred in the slope between the QCT-FEM and DVC displacements in the x and y directions for either elemental or nodal material mapping strategies. Slopes ranged from 0.86 to 1.06. This held true for 3 specimens in the z direction; however, for the remaining 3 specimens more pronounced variations occurred between the QCT-FEM and DVC displacements, dependent on density-modulus relationship. The r2 values were consistently between 0.82 and 1.00 for both material mapping strategies and density-modulus relationships for all three Cartesian components of displacement and all specimens.
Conclusions
The results suggest that QCT-FEMs using DVC derived boundary conditions can replicate experimental loading of cadaveric specimens. It was also shown that only slight variations exist when either elemental or nodal material mapping strategies are adopted. Given the recent advancements provided by DVC-derived BCs, this study provides a basis for a common methodology that can be implemented in future studies comparing similar outcomes in all anatomic locations. Expanding the current sample size has the potential to determine if a single density-modulus relationship can exist or if specimen or anatomic location-specific relationships should be utilized.
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