Spatial Autocorrelation of Bone Material Stiffness and its Implications on Skeletal Toughness

A Computational analysis was performed on the spatial autocorrelation of the elastic modulus and its effects on skeletal toughness. This study utilized MATLAB to test our hypothesis that a clustered autocorrelation could increase toughness by comparing Moran's I to strain energy. Boundary conditions were applied at the bottom, and loads were applied at the top of a 30 X 30 element model. Homogeneous, random, checkerboarded, and clustered spatial autocorrelations were examined, with each autocorrelation corresponding to a specific range of Moran's I values. To compare the Moran's I's to the strain energy for different autocorrelations, 250 iterations were run. Multiple simulations were conducted, which incorporated padding. The padding was added on both the top and bottom rows of the model to simulate a distributed load across the autocorrelation. The padding would also ensure that the effects of the autocorrelation were not masked due to the high stress concentrations at those points. The simulations showed a positive correlation between the Moran's I and strain energy, supporting our hypothesis. The simulations also provided evidence that any microscale variations of the elastic modulus will increase toughness, making the material more resilient to fracture.