Dynamic Stochastic Simulation of Cancellous Bone Resorption

A stochastic simulation of cancellous bone resorption was developed and applied to a simple two-dimensional lattice structure representing the vertebral body. The simulation is based upon the concept of a basic multicellular unit (BMU) where net resorption (−ΔB.BMU) is considered at bone/marrow surfaces. The cancellous bone structure is defined as a binary matrix with the size of the pixels corresponding to a square element of approximately 20 μm dimension. The simulation considers both the probability that any surface pixel will be activated into a BMU and, if activated, the length of the resorption cavity. The relationship between relative stiffness and density for the simulation was predicted by finite element analysis. The stochastic simulation was iterated eight times with the mechanical properties assessed after each stage. Perforation of a single trabeculae was first observed at step 2, the structure completely lacking connectivity and mechanical integrity by step 8. The slope of the stiffness-porosity graph was greater than unity for the first five steps, but thereafter approached zero because the structure had lost connectivity and effectively collapsed. The eight-step simulation was repeated five times and demonstrated that, although the stiffness/density relationships were similar at the extremes of density, the dependence of stiffness upon density varied. This clearly demonstrates the stochastic nature of the simulation upon cancellous bone structure, and is probably indicative of a significant dependence of mechanical integrity upon perforation effects.