Development of a validated glenoid trabecular density-modulus relationship

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Abstract

Incorporating subject-specific mechanical properties derived from clinical-resolution computed tomography data increases the accuracy of finite element models. Site-specific relationships between density and modulus are required due to variations in trabecular architecture and tissue density by anatomic location. Equations have been developed for many anatomic locations and have been shown to have excellent statistical agreement with empirical results; however, a shoulder-specific density-modulus relationship does not currently exist. This study used micro-finite element cores of glenoid trabecular bone and co-registered quantitative computed tomography finite element models to develop a validated glenoid trabecular density-modulus relationship. Micro finite element model tissue density was considered as either homogeneous or heterogeneous, scaled by CT-intensity. When heterogeneous tissue density was considered, near absolute statistical agreement was predicted in the co-registered QCT-derived finite element models. The validated relationships have also been adapted for use in whole bone scapular models and have the potential to dramatically increase the accuracy of clinical-resolution CT-derived shoulder finite element studies.

Introduction

Subject-specific finite element models (FEMs) are a valuable tool in biomechanical research. Highly correlated relationships exist between CT-intensity and bone mechanical properties, allowing for mechanical properties to be accurately modeled using clinical-resolution CT images (Knowles et al., 2016). These density-modulus relationships depend on bone architecture and mineralization, and are therefore site-specific (Helgason et al., 2008, Morgan et al., 2003). As such, previous studies have determined that anatomic site-specific and subject-specific modeling parameters increase the accuracy of FEMs derived with clinical-resolution scans (Campoli et al., 2013, Schileo et al., 2008, Schileo et al., 2007, Unnikrishnan et al., 2013). This allows for patient-specific computational modeling or development of population-based statistical shape models.

Most reported density-modulus relationships are determined from mechanical testing of small bone cores. Testing protocols have suffered from potentially high end-artifact errors due to specimen preparation, off-axis coring, and misrepresentation of boundary conditions (Chen et al., 2017). This may result in calculation of a transverse modulus, limiting the accuracy of previously developed relationships (Bayraktar et al., 2004, Helgason et al., 2008). Additionally, coring of trabecular bone samples inherently disturbs the outer trabeculae, reducing or eliminating these trabeculae's load carrying capacity. These side-artifacts have been suggested to greatly influence the determination of modulus, and subsequently density-modulus relationships. Ün et al. report implications for all modulus development, especially those with low density, and the correction factors developed within should be used to adjust previously developed moduli (Ün et al., 2006).

A possible additional source of error arises in relationship development due to systematic error in density measures (Knowles et al., 2016, Zioupos et al., 2008). Accurate bone density measurements are required as the initial input in density-modulus relationships, and therefore, the effect of variations in density measures between studies is difficult to elucidate. Direct relationships between computational derived density provided by quantitative computed tomography (QCT) and mechanical properties has the potential to minimize these errors and may optimize development of density-modulus relationships (Kopperdahl et al., 2002), and the associated material mapping accuracy.

Although recognized as an imminent need (Pomwenger et al., 2014), a validated density-modulus relationship specific to the shoulder does not exist, potentially limiting the accuracy of clinical-resolution derived shoulder finite element (FE) models. As such, previous FE studies of the scapular side of the shoulder have used density-modulus relationships developed for alternate anatomical locations. None of these studies have provided experimental validation of the FE results, limiting translation of outcomes and comparisons among studies. The objective of this study was to develop a validated glenoid trabecular density-modulus relationship using computational comparisons between micro-computed tomography (µ-CT) FEMs and co-registered QCT-FEMs.

Section snippets

Specimens and computed tomography scanning

Fourteen cadaveric scapulae (7 male, 7 female) were denuded of soft tissue. Each specimen was scanned with a cone-beam µ-CT scanner (Nikon XT H 225 ST, Nikon Metrology, NV) with the largest field of view (FOV) possible to capture the entire glenoid structure in the largest specimen. For consistency, uniform parameters were used for all subsequent specimens, regardless of specimen size. This resulted in a spatial resolution of 32 µm, which was less than one-fourth the mean trabecular thickness

Results

The trabecular-specific glenoid density-modulus relationships were E = 39940ρqct2.053, E = 29070ρqct1.816, E = 29302ρqct1.837, for the homogeneous tissue modulus OLS, FOLS, and LOG, respectively. For the heterogeneous tissue modulus, the relationship was E = 34800ρqct2.506. The OLS homogeneous relationship was corrected to E = 38780ρqct1.88. Only the OLS homogeneous relationship was corrected because it was the most accurate homogeneous density-modulus relationship. The heterogeneous

Discussion and conclusions

This study presented a new computational methodology for the development of density-modulus relationships using µ-CT and co-registered QCT derived FEMs. This allows for a direct comparison of the mechanical properties of trabecular architecture and density to be translated to linear isotropic QCT derived FEMs. Although only linear isotropic density-modulus material mapping was considered in this study, this methodology could potentially be translated to validate bone strength and fracture using

Acknowledgements

The authors would like to thank Shruthi Poolacherla for her assistance with data collection. Funding for this work was provided in part by a Lawson Health Research Institute Internal Research Fund Grant (#LRI7762117). Nikolas K. Knowles is supported in part by the Natural Sciences and Engineering Research Council of Canada and by a Transdisciplinary Bone & Joint Training Award from the Collaborative Training Program in Musculoskeletal Health Research at The University of Western Ontario.

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