Abstract
Introduction
Density-modulus relationships are often used to map the mechanical properties of bone based on CT- intensity in finite element models (FEMs). Although these relationships are thought to be site-specific, relationships developed for alternative anatomic locations are often used regardless of bone being modeled. Six relationships are commonly used in finite element studies of the shoulder; however, the accuracy of these relationships have yet to be compared. This study compares each of these six relationships ability to predict apparent strain energy density (SEDapp) in trabecular bone cores from the glenoid.
Methods
Quantitative-CT (QCT) (0.625 mm isotropic voxels), and µ-CT scans (0.032 mm isotropic voxels) were obtained for fourteen cadaveric scapulae (7 male, 7 female). Micro finite element models (µ-FEMs) were created from 98 virtual ‘cores’ using direct conversion to hexahedral elements. Two µ-FEM cases were considered: homogeneous tissue modulus of 20 GPa, and heterogeneous tissue modulus scaled by CT intensity of the µ-CT images (196 models). Each µ- FEM model was compressively loaded to 0.5% apparent strain and apparent strain energy density (SEDapp) was calculated. Additionally, each of the six density-modulus relationships were used to map heterogeneous material properties to co- registered QCT-derived models (588 models in total). The loading and boundary conditions were replicated in the QCT-FEMs and the SEDapp was calculated and compared to the µ-FEM SEDapp. To account for more samples than donors, restricted maximum likelihood estimation (REML) linear regression compared µ-FEM SEDapp and QCT-FEM SEDapp for each relationship.
Results
When considering comparisons between QCT-FEMs and µ-FEMs with a homogeneous tissue modulus, near absolute statistical agreement (Y=X) was observed between the µ-FEMs and the QCT-FEMs using the Morgan et al. (2003) pooled relationship. Not surprisingly, due to the similarity between the two relationships, the Gupta & Dan (2004) and Carter and Hayes (1977) models showed near identical REML linear regression fit parameters. All relationships other than the Morgan et al. (2003) pooled relationship, greatly underestimated the µ-FEM apparent strain energy density (SEDapp) when considering a homogeneous tissue modulus in the µ-FEMs. The same result with the pooled relationship did not hold true when heterogeneous tissue modulus was considered in the µ-FEMs. The Büchler et al., (2002) relationship most accurately predicted the SEDapp for this comparison. Interestingly, the Gupta & Dan (2004) and Carter and Hayes (1977) relationships again showed near identical REML linear regression fit parameters.
DISCUSSION
This study compared six common density-modulus relationships used to map mechanical properties of bone in shoulder FE studies. It was found that when considering a homogeneous tissue modulus for µ-FEMs, relationships pooled from alternative anatomic locations may accurately predict the mechanical properties of glenoid trabecular bone. However, when considering a heterogeneous tissue modulus, this did not hold true. Further studies to determine if these relationships can be translated to whole bones may provide insight into the predictive capabilities of using pooled density-modulus equations in the mapping of mechanical properties in future FEMs of the shoulder.
