Finite Element Modelling Methodology
Finite element models were created based on the µCT scan data using Simpleware ScanIP (2021.03, Synopsis, USA) for segmentation and FE meshing. Abaqus (2017, Dassault Systèmes, France) was used for solving.
Segmentation
Methodology was based on previous studies and optimisation using porcine tissue [1]. The μCT background was first binarised, using a fixed threshold across all specimens, and was then downsampled to 0.164 mm3, such that the resulting voxel greyscale was proportional to the bone volume fraction (BV/TV). The downsampling made the image data more manageable to manipulate in computer memory. Binarisation of the uCT image data meant that changes to the density of the none mechanical aspects of the bone, the fluid components, had no influence on the resultant material properties of the elements in the FE models.
Meshing
Meshing utilised a target element edge length of 1 mm following previous mesh density sensitivity analyses [1]. When the number of elements was doubled from that used, the change in stiffness was between 1.5–3.3% for the models. Initial mesh density was based on tests of the graft - host interaction, with a relatively high mesh density required at the contact interface for the models to reliably solve.
Osteochondral grafts were defined using the surfaces tools in Simpleware ScanIP to match the experimental graft diameter, 6.5 mm, and graft length, 10 mm. The surfaces, when compared to segmented masks allowed for translation and rotation to the correct location and orientation based on the post-graft harvest scan. The voxel rendering options were used to aid the alignment, using the upper cartilage surface as the position of the top surface part. The cylinders describing each graft were meshed using tetrahedral elements, with the same target edge length of 1 mm. A 1 mm edge length produced a mesh with approximately 8032 elements, doubling the mesh density gave a difference in push-in force of 0.2% and using quadratic tetrahedral elements gave a difference of 0.6% while taking approximately 10 times as long to solve.
Similarly, Simpleware ScanIP surfaces were used to describe the holes (6.35 mm diameter), using the post-test scan to set the correct alignment and position and the pre-test scan to assign the correct material properties of the surrounding region. Contact surfaces were defined between the surface mesh, and the host bone and cartilage so that the mesh describing the hole had a high-quality contact surface.
Material Properties
Material properties for the endcaps used a Young’s modulus of 2.45 GPa and a Poisson’s ratio of 0.3. Bone materials were modelled as an isotropic linear elastic material, where the Young’s modulus of each element was proportional to the uCT scan intensity of each voxel using a linear conversion factor. The relationship between the Young’s modulus of each element and the bone density of the underlying voxel was optimised to minimise the root mean square difference between the FE-predicted stiffness and corresponding experimentally-derived stiffness values of the six specimens. This calibration process was performed using the opti4abq optimisation toolbox [2]. A hyperelastic, neo-Hookean material property was used for the host and graft cartilage, bulk modulus K = 16.67 MPa and shear modulus G = 1.37 MPa. This was based on a cartilage property calibration of a previous study [3].

[1] Day GA, Cooper RJ, Jones AC, Mengoni M, Wilcox RK. 2022 Development of robust finite element models to investigate the stability of osteochondral grafts within porcine femoral condyles. J. Mech. Behav. Biomed. Mater. 134, 105411. (doi:10.1016/j.jmbbm.2022.105411)
[2] M. Mengoni. opti4Abq (V 2.0), a Generic python Code to Run Abaqus in an Optimisation Loop (2017), 10.5281/zenodo.580475
[3] R.J. Cooper, A. Liu, G.A. Day, V.N. Wijayathunga, L.M. Jennings, R.K. Wilcox, A.C. Jones. Development of robust finite element models of porcine tibiofemoral joints loaded under varied flexion angles and tibial freedoms. J. Mech. Behav. Biomed. Mater., 109 (2020), 10.1016/j.jmbbm.2020.103797