Finite element analysis of fibrous tissue morphogenesis : a study of the osteogenic index with a biphasic approach

The development of tissues in the skeleton is a complex process beginning with mesenchymal cells in a blastema and finishing with some ''equilibrium'' tissue suited to the mechanical function required for the particular skeletal part. The process involves differentiation of the pluripotent mesenchymal cells into those that form the particular equilibrium tissue, e.g., chondrocytes for cartilage or osteoblasts for bone, Several philosophers in the previous century have hypothesized that the process is not just genomic, but that mechanical factors play a part in determining the pathway which is followed [1]. Nonetheless, very little is)let known about the mechanical events that underlie the tissue formation process. Based on an idea proposed by the German orthopaedic surgeon . Pauwels [2] concerning the relative influence of hydrostatic and shear stresses, it has been proposed by Carter [3] that the tendency for fibrous connective tissue, cartilage, or bone to be formed could be captured by an osteogenic index (1) OI = (i=1)Sigma(c) n(i) (S-i + kD(i)) where S and D denote the cyclic octahedral shear stress and hydrostatic stress respectively, k is a constant weight factor, n(i) is the number of loading cycles of a particular loading condition, and c is the number of such different loading conditions. Representing the tissue as an elastic and isotropic solid, finite element models have been developed to analyze the morphogenetic behavior of tissues [3-5]. It has been suggested that this kind of modeling approach is able to describe features of fracture repair and chondrogenesis [3] and ligament [4] and tendon [5] tissue phenotype. Despite the convenience of the elastic approach, it is clear that the tissue itself is a material containing both solid and fluid constituents (called a biphasic material), The solid phase is mainly a certain type of collagen mixed with proteoglycans, whereas the fluid phase consists of blood and interstitial fluid, Since the cells that undergo differentiation (mesenchymal cells) are contained in the fluid until such time as they become precursors for tissue forming cells [6], it seems worthwhile to ask whether or not a model derived from the fundamental biphasic nature of the tissue would lead us toward a better understanding of the phenomenon of tissue development. To investigate this idea, rue generated a finite element model of peri-prosthetic tissue formation observed in an animal experiment, using both elastic and biphasic [7] finite element analyses, The animal experiments analyzed in this investigation have been reported in the doctoral dissertation of Soballe [8], The osteogenic index was calculated in the gap between implant aml bone, using both linear elastic and biphasic tissue models. Since the fluid phase moves relative to the solid, it is possible that the osteogenic stimulus might arise as a result of fluid motion. To investigate this, the velocity of fluid relative to sold phase was calculated, Results are compared to the histological results reported by Soballe [8]. Finally, some discussion of how a morphogenic stimulus might really arise is given