Failure in cartilaginous tissues. Jacques M. Huyghe 1* , C. Jongeneelen 1 , Y. Schroeder 1 , F. Kraaijeveld 1 , R. de Borst 2 , F.P.T. Baaijens 1 1 Department of Biomedical Engineering, Eindhoven University of Technology P.O. Box 513, 5600MB Eindhoven, Netherlands j.m.r.huyghe@tue.nl 2 Koiter Institute, Faculty of Aerospace Engineering, Delft University of Technology P.O. Box 5,2600AA Delft, Netherlands Summary: Cartilaginous tissues high load bearing capacity is explained by osmotic prestressing putting the collagen fiber re- inforcement under tension and the proteoglycan gel under compression. The osmotic forces are boosted by a further 50 % by the affinity of the collagen with the aquous solution. The high osmolarity of the tissue provides a strong protection against crack propagation. Degeneration results in degradation of the prestressing and hence to internal damage. 3D visualisation of a dis- continuity of the collagen struction of the disc is achieved by confocal laser scanning microscopy. The collagen and the cells are visualised by means of a two fluorescent probes. The discontinuity is shown to open and close depending on the osmotic loading of the tissue. The process of internal degradation is presently modelled using Partition of Unity method in a osmotically prestressed fluid-solid mixture. Introduction Unlike most biological tissues, cartilaginous tissues tissues has no blood perfusion. The cells of the tissue obtain nutrition and removal of waste materials through diffusion only. This fact implies that cartilaginous tissues renew themselves at a much lower rate than any other tissue in the human body. The capacity of cartilaginous tissues to withstand relatively high loads of several MPa during a lifetime of up to 100 years, is a noteworthy achievement, especially in view of its low stiff- ness, low renewal rate and high water content. Cartilaginous tissues consists of a fluid-filled extra-cellular matrix, in which living cells are sparsely dispersed. The mechanical function is highly dependent on the composition of the extra-cellular ma- trix, which primary consists of collagen fibrils and negatively charged proteoglycans. Due to the fixed charges of the pro- teoglycans (PGs), the cation concentration inside the tissue is higher than in the surrounding synovial fluid. This excess of ion particles leads to an osmotic pressure difference, which causes swelling of the tissue [4]. The fibrillar collagen network re- nucleus annulus laminates Figure 1: The intervertebral disc is a cartilaginous tissue con- necting two vertebrae in the spine. It consists of a gelatinous nucleus surrounded by a fibrous annulus. sists straining and swelling pressures. This combination makes cartilaginous tissue a unique, highly hydrated and pressurized tissue, enforced with a strained collagen network. It has been shown that the osmotic pressure inside cartilaginous tissues is much higher than would be expected based on its FCD [5, 2]. This is because part of the water in the tissue is absorbed by the collagen fibers. The proteoglycan molecules, because of their large size, are excluded from this intra-fibrillar space. This means that their effective concentrations are much higher in the extra-fibrillar space than if they were distributed uniformly throughout the entire matrix. Hence, the effective fixed charge density is higher than if computed from total tissue water con- tent. Wilson et al. [6] predict the depth dependent stress-strain curve of articular cartilage solely from its composition and the inclusion of the intrafibrillar/extrafibrillar water compartments and their associated osmotic pressures. A corresponding anal- ysis for intervertebral disc tissue (Fig. 1) demonstrates that in- trafibrillar water affects pressure distribution, osmolarity and stress within the disc substantially [3]. Confined compression and swelling experiments on canine intervertebral disc samples were performed and fitted by Huyghe et al [1] using the concept of intrafibrillar water as well. Fractures in the intervertebral disc A peculiar observation in intervertebral disc degeneration is the finding that human intervertebral discs develop fractures with age virtually independently from load to which they are sub- jected (Fig. 2). Concommitantly, the osmotic prestressing is decreasing. Wognum et al. [7] studied the opening of a crack in a numerical and physical model of the degenerated inter- vertebral disc. Degeneration was modelled as a progressive de- crease in osmotic presstressing. They demonstrate that, while the osmotic prestressing is decreasing, the overal fiber stress is decreasing as well, but the stress at the crack tip increases sharply, because the shrinking of the tissue induces opening of the crack. This phenomenon is intrinsically multiscale in nature and may explain the poor relationship between external loads and crack propagation. None of the models used by Wognum et al [7] considers the intrafibrillar water effect mentioned earlier, while experimental data suggest that 30 % of the water con- tained in the annulus is grabbed by the collagen and is not seen by the charges fixed to the proteoglycan chains. This suggests