Time-dependent mechanical behaviour of the periodontal ligament.

The process of tooth displacement in response to orthodontic forces is thought to be induced by the stresses and strains in the periodontium. The mechanical force on the tooth is transmitted to the alveolar bone through a layer of soft connective tissue, the periodontal ligament. Stress and/or strain distribution in this layer must be derived from mathematical models, such as the finite element method, because it cannot be measured directly in a non-destructive way. The material behaviour of the constituent tissues is required as an input for such a model. The purpose of this study was to determine the time-dependent mechanical behaviour of the periodontal ligament due to orthodontic loading of a tooth. Therefore, in vivo experiments were performed on beagle dogs. The experimental configuration was simulated in a finite element model to estimate the poroelastic material properties for the periodontal ligament. The experiments showed a two-step response: an instantaneous displacement of 14.10 +/- 3.21 microns within 4 s and a more gradual (creep) displacement reaching a maximum of 60.00 +/- 9.92 microns after 5 h. This response fitted excellently in the finite element model when 21 per cent of the ligament volume was assigned a permeability of 1.0 x 10(-14) m4/N s, the remaining 97 per cent was assigned a permeability of 2.5 x 10(-17) m4/N s. A tissue elastic modulus of 0.015 +/- 0.001 MPa was estimated. Our results indicate that fluid compartments within the periodontal ligament play an important role in the transmission and damping of forces acting on teeth.

Why does intermittent hydrostatic pressure enhance the mineralization process in fetal cartilage?

The purpose of this study was to determine which factor is the most likely one to have stimulated the mineralization process in the in vitro experiments of Klein-Nulend et al. (Arth. Rheum., 29, 1002-1009, 1986), in which fetal cartilaginous metatarsals were externally loaded with an intermittent hydrostatic pressure, by compressing the gas phase above the culture medium. Analytical calculations excluded the possibility that the tissue was stimulated by changes in dissolved gas concentration, pH or temperature of the culture medium through compression of the gas phase. The organ culture experiments were also mechanically analyzed using a poroelastic finite element (FE) model of a partly mineralized metatarsal with compressible solid and fluid constituents. The results showed that distortional strains occurred in the region where mineralization proceeded. The value of this strain was, however, very sensitive to the value of the intrinsic compressibility modulus of the solid matrix (Ks). For realistic values of Ks the distortional strain was probably too small (about 2 microstrain) to have stimulated the mineralization. If the distortional strain was not the factor to have enhanced the mineralization process, then the only candidate variable left is the hydrostatic pressure itself. We hypothesize that the pressure may have created the physical environment enhancing the mineralization process. When hydrostatic pressure is applied, the balance of the chemical potential of water across cell membranes may be disturbed, and restored again by diffusion of ions until equilibrium is reached again. The diffusion of ions may have contributed to the mineralization process.

A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation.

Loosening of implants in bone is commonly associated with a development of fibrous interface tissues, due to interface gaps and a lack of mechanical stability. It has been postulated that the differentiation of these tissues to fibrocartilage or bone is governed by mechanical stimuli. The objective of our research is to unravel these relationships to the extent that the question whether an implant will loosen can be answered from initial conditions determined by implant and interface morphology, and functional loads. In this project we studied the hypothesis that distortional strain and interstitial fluid flow are the mechanical stimuli governing tissue differentiation. For that purpose, a biomechanical regulatory model was developed and used in association with a finite element code to simulate animal experiments with implants moving in bone. The similarities between the implant incorporation process found in the experiment and its simulation with the computer model demonstrate that our hypothesis is viable from a regulatory point of view.

A comparison of finite element codes for the solution of biphasic poroelastic problems.

The extent to which three finite element codes can solve problems in biphasic poroelasticity is examined. Both linear and non-linear (that is where the permeability of the material is a function of deformation) formulations are studied using the standard confined compression problem as an example. The results are compared, where possible, to the results of Spilker, Suh and Mow who first presented a solution to this problem for cartilage. The agreement is excellent for the linear case. For the non-linear case, the solutions do differ slightly; however, the difference would not appear to be significant.