Tissue-level Strain Research Articles

A model for strain amplification in the actin cytoskeleton of osteocytes due to fluid drag on pericellular matrix

A model is presented that provides a resolution to a fundamental paradox in bone physiology, namely, that the strains applied to whole bone (i.e., tissue level strains) are much smaller (0.04–0.3 percent) than the strains (1–10 percent) that are necessary to cause bone signaling in deformed cell cultures (Rubin and Lanyon, J. Bone Joint Surg. 66A (1984) 397–410; Fritton et al., J. Biomech. 33 (2000) 317–325). The effect of fluid drag forces on the pericellular matrix (PM), its coupling to the intracellular actin cytoskeleton (IAC) and the strain amplification that results from this coupling are examined for the first time. The model leads to two predictions, which could fundamentally change existing views. First, for the loading range 1–20 MPa and frequency range 1–20 Hz, it is, indeed, possible to produce cellular level strains in bone that are up to 100 fold greater than normal tissue level strains (0.04–0.3 percent). Thus, the strain in the cell process membrane due to the loading can be of the same order as the in vitro strains measured in cell culture studies where intracellular biochemical responses are observed for cells on stretched elastic substrates. Second, it demonstrates that in any cellular system, where cells are subject to fluid flow and tethered to more rigid supporting structures, the tensile forces on the cell due to the drag forces on the tethering fibers may be many times greater than the fluid shear force on the cell membrane.

Convergence behavior of high-resolution finite element models of trabecular bone.

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

Bone Regeneration and Fracture Healing

The relation between physical forces and the processes of bone regeneration and healing remains incompletely understood. Gaps in understanding of these processes stem in part from models that produce inadequate amounts of new bone for study. Bone created through the use of distraction osteogenesis provides an attractive substrate for the study of mechanical forces and their effects on bone formation because this technique produces large volumes of new bone in a controlled fashion. The optimal mechanical environment in which bone formation occurs clinically has not been fully determined. In laboratory studies, however, the mechanical environment can be manipulated, and resultant changes in bone formation can be measured. To investigate how changes in strain environment influence patterns of bone formation, a bilateral New Zealand White rabbit model of bilateral distraction osteogensis was implemented. When a stiffener was applied to the external distractor, computation analyses predicted a sevenfold to eightfold decrease in all strain measures. These reductions in gap strains appeared to induce significant decreases in bone volume fraction and mean trabecular thickness. When osteotomies were created at a 30 degrees angle to the bony axis to generate more shear within the gap tissue, changes in the distribution of gap strains and resultant new bone architecture were observed. Specific correlations between changes in tissue level strains and the pattern of bone regeneration were seen in both experiments. These results provide direct in vivo evidence that pluripotential gap tissues are sensitive to their physical surroundings. Mechanisms responsible for this sensitivity might include vascularity, stem cell supply, and scaffolding architecture. The process of bone formation in distraction osteogenesis appears to be related to bone formation processes associated with more common conditions. The distraction osteogenesis model described suggests a mechanism for bone formation that seems applicable to other more common processes associated with bone formation, including fracture healing and impaired fracture healing.

Strain Concentrations Surrounding an Ellipsoid Model of Lacunae and Osteocytes

Direct cell sensing of tissue matrix strains is one possible signaling mechanism for mechanically mediated bone adaptation. We utilized homogenization theory lo estimate bone tissue matrix strains surrounding osteocytes using two sets of models. The first set of models estimated the strain levels surrounding the lacunae and canaliculi, taking into account variations in lamellar properties. The second set estimated strain levels in the osteocyte and the surrounding matrix for different cellular mechanical properties. The results showed that the strain levels found in and surrounding osteocytes, 1700 to 2700 microstrain (denoted as μe; 1 =.0001% strain), were significantly greater than the trabecular tissue level strains of [1325 μe, 287 μe, 87 μe] used for model input. Variation in lamellar properties did not affect strain levels, except at lamellar boundaries. Strain in and surrounding the osteocyte was not significantly affected by cellular stiffness ranging between 28 and 28,000 Pascals (Pa). Strain levels surrounding lacunae and canaliculi were approximately equivalent.