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 se gment consisting of two vertebrae and a single intervertebral disc. Th e theory is an extension of the poroelastic theory developed by Biot7 and the model is an adaptation of an axisymmetric poroelastic finite e lement model of the intervertebral disc by Simon.45,46 The model is co mpletely three-dimensional although the results presented here assume symmetry about the sagittal plane. The theory is presented in two stag es. First the development of the poroelastic theory. Following this, t he effects of swelling caused by osmotic pressure are developed and ex pressed as a modification of the constitutive law and initial stresses . In the case of the disc, this pressure is produced mainly by the fix ed negative charges on the proteoglycans within the disc. In this deve lopment we assume that the number of fixed charges remains constant ov er time and that the distribution of mobile ions has reached equilibri um. The variations over time in osmotic pressure, and thus in swelling effects are therefore only dependent on the initial state and the cha nge in water content. Variations of the swelling effects caused by cha nges in mobile ion concentrations will be the subject of a future pape r.47 The results reported in this article illustrate the dramatic effe ct of swelling on the load carrying mechanisms in the disc. The author s believe it is likely that this will have important useful implicatio ns for our understanding not only of normal disc function, but also of abnormal function, such as disc degeneration, herniation, and others.