DYNAMIC-STOCHASTIC SIMULATION OF CANCELLOUS BONE-RESORPTION

A stochastic simulation of cancellous bone resorption was developed an d applied to a simple two-dimensional lattice structure representing t he vertebral body, The simulation is based upon the concept of a basic multicellular unit (BMU) where net resorption (-Delta B.BMU) is consi dered at bone/marrow surfaces, The cancellous bone structure is define d as a binary matrix with the size of the pixels corresponding to a sq uare element of approximately 20 mu m dimension, The simulation consid ers both the probability that any surface pixel will be activated into a BMU and, if activated, the length of the resorption cavity, The rel ationship between relative stiffness and density for the simulation wa s predicted by finite element analysis, The stochastic simulation was iterated eight times with the mechanical properties assessed after eac h stage, Perforation of a single trabeculae was first observed at step 2, the structure completely lacking connectivity and mechanical integ rity by step 8, The slope of the stiffness-porosity graph was greater than unity for the first five steps, but thereafter approached zero be cause the structure had lost connectivity and effectively collapsed, T he eight-step simulation was repeated five times and demonstrated that , although the stiffness/density relationships were similar at the ext remes of density, the dependence of stiffness upon density varied, Thi s clearly demonstrates the stochastic nature of the simulation upon ca ncellous bone structure, and is probably indicative of a significant d ependence of mechanical integrity upon perforation effects. (C) 1998 b y Elsevier Science Inc. All rights reserved.