A POROELASTIC-SWELLING FINITE-ELEMENT MODEL WITH APPLICATION TO THE INTERVERTEBRAL DISC

The swelling process that occurs in soft tissue is incorporated into a poroelastic finite element model. The model is applied to a spinal segment consisting of two vertebrae and a single intervertebral disc. The theory is an extension of the poroelastic theory developed by Biot7 and the model is an adaptation of an axisymmetric poroelastic finite element model of the intervertebral disc by Simon.45,46 The model is completely three-dimensional although the results presented here assume symmetry about the sagittal plane. The theory is presented in two stages. First the development of the poroelastic theory. Following this, the effects of swelling caused by osmotic pressure are developed and expressed as a modification of the constitutive law and initial stresses. In the case of the disc, this pressure is produced mainly by the fixed negative charges on the proteoglycans within the disc. In this development we assume that the number of fixed charges remains constant over time and that the distribution of mobile ions has reached equilibrium. The variations over time in osmotic pressure, and thus in swelling effects are therefore only dependent on the initial state and the change in water content. Variations of the swelling effects caused by changes in mobile ion concentrations will be the subject of a future paper.47 The results reported in this article illustrate the dramatic effect of swelling on the load carrying mechanisms in the disc. The authors believe it is likely that this will have important useful implications for our understanding not only of normal disc function, but also of abnormal function, such as disc degeneration, herniation, and others.