NUMERICAL INSTABILITIES IN BONE REMODELING SIMULATIONS - THE ADVANTAGES OF A NODE-BASED FINITE-ELEMENT APPROACH

Long bone structure occurs in two distinct forms. The bone mass near t he joint is primarily found in a distributed, porous trabecular struct ure, while in the diaphyses a tubular cortical structure is formed. It seems likely that these two observed morphologies come about, at leas t in part, as a mechanical adaptation to the different mechanical dema nds in the two regions, Mathematical formulations of this dependency h ave been proposed, thus facilitating numerical simulations of bone ada ptation. Recently two types of discontinuities have been observed in t hese simulations. The first type (near-field) appears in areas near di stributed load application and is characterized by a 'checkerboard' pa ttern of density wherein adjacent remodeled elements alternate between low and high density. The second type of discontinuity (far-field) ap pears remote from the load application and is characterized by strut o r column-like regions of elements which become fully compact bone whil e adjacent regions are fully resorbed. In fact, the far-field disconti nuity is an accurate representation of bone physiology and morphology since it is consistent with the appearance of cortical bone in the dia physis. On the other hand, the near-field discontinuity, appears in a region where continuous distributions of intermediate apparent densiti es (trabecular bone) are expected. This finding may cause some to ques tion whether a single continuum formulation of bone remodeling can pre dict both discontinuous far-field behavior and continuous near-field b ehavior. We describe a node-based implementation of current continuum bone remodeling theories which eliminates the spurious near-field disc ontinuities and preserves the anatomically correct far-field discontin uities, thus indicating that a single biological process may be at wor k in forming and maintaining both far-field and near-field morphologie s.