Significant advances in the functional analysis of musculoskeletal systems require the development of modelling techniques with improved focus, accuracy and validity. This need is particularly visible in the fields, such as palaeontology, where unobservable parameters may lie at the heart of the most interesting research questions, and where models and simulations may provide some of the most innovative solutions. Here, we report on the development of a computational modelling method to generate estimates of the mechanical properties of vertebral bone across two living species, using elderly human and juvenile porcine specimens as cases with very different levels of bone volume fraction and mineralization. This study is presented in two parts; part I presents the computational model development and validation, and part II the virtual loading regime and results. This work paves the way for the future estimation of mechanical properties in fossil mammalian bone.
Load and displacement data for finite element models of human and pig vertebrae
Six porcine and four human cadaveric vertebrae were imaged using micro computed tomography (μCT) (Scanco μCT80, Scanco Medical, Switzerland) at a voxel size of 0.074 mm. Species-specific threshold values were then applied to segment the images of all of the specimens of each species. Each set of segmented images was then imported into an image processing software tool (ScanIP, Simpleware Ltd, Exeter) and downsampled to a resolution of 1 x 1 x 1 mm using an averaging method that allowed for partial volume effects. Each downsampled voxel represented the average of the binary segmented voxels within it and therefore the greyscale value of the downsampled voxel represented the BV/TV value of that region of the underlying bone. For all of the specimens, the regions were then imported into a FE meshing tool (ScanFE, Simpleware Ltd, Exeter) and a FE model of the vertebra and two end-caps was generated. An element size of approximately 1 mm was used because this had previously been shown to be sufficient for vertebral stiffness evaluation in specimens of a similar size and under similar conditions. A combination of hexahedral and tetrahedral linear elements were used to represent the vertebral geometry; in total each model contained between 200,000 and 400,000 elements. The cement region was assigned an elastic modulus of 2.45 GPa. Each element within the bone was assigned an elastic modulus based on BV/TV value derived from the downsampled voxel grayscale. All of the models were imported into a finite element software package (ABAQUS CAE version 6.9-1, Simulia Corp, USA). The models were solved and the specimen stiffness determined. To normalize for size, the ‘apparent modulus’ was also determined by multiplying the stiffness by the vertebral height and dividing by the cross sectional area. All the models were processed and the predicted vertebral stiffness was determined.
KRB_et_al_KCalculations.xlsx
Modelled stiffness and apparent modulus of porcine and human vertebral models for 5 loading modes
Six porcine and four human cadaveric vertebrae were imaged using micro computed tomography (μCT) (Scanco μCT80, Scanco Medical, Switzerland) at a voxel size of 0.074 mm. Species-specific threshold values were then applied to segment the images of all of the specimens of each species. Each set of segmented images was then imported into an image processing software tool (ScanIP, Simpleware Ltd, Exeter) and downsampled to a resolution of 1 x 1 x 1 mm using an averaging method that allowed for partial volume effects. Each downsampled voxel represented the average of the binary segmented voxels within it and therefore the greyscale value of the downsampled voxel represented the BV/TV value of that region of the underlying bone. For all of the specimens, the regions were then imported into a FE meshing tool (ScanFE, Simpleware Ltd, Exeter) and a FE model of the vertebra and two end-caps was generated. An element size of approximately 1 mm was used because this had previously been shown to be sufficient for vertebral stiffness evaluation in specimens of a similar size and under similar conditions. A combination of hexahedral and tetrahedral linear elements were used to represent the vertebral geometry; in total each model contained between 200,000 and 400,000 elements. The cement region was assigned an elastic modulus of 2.45 GPa. Each element within the bone was assigned an elastic modulus based on BV/TV value derived from the downsampled voxel grayscale. All of the models were imported into a finite element software package (ABAQUS CAE version 6.9-1, Simulia Corp, USA). The models were solved and the specimen stiffness determined. To normalize for size, the ‘apparent modulus’ was also determined by multiplying the stiffness by the vertebral height and dividing by the cross sectional area. All the models were processed and the predicted vertebral stiffness was determined. A series of virtual tests was then undertaken on the models generated with the species-specific threshold and the linear conversion factor. First, the height of the upper cement endcap was adjusted in all cases to be 40 % of the vertebral body height to ensure the loading point was always the same relative distance from the vertebra. The load was then applied to five positions equally spaced between the anterior and the posterior extent of the vertebral body. In each case, the model was solved and the vertebral stiffness determined as the load divided by the displacement at the point where the load was applied.
KRB_et_al_LoadingMode-PorcineHuman.xlsx
