The properties of chondrocyte membrane reservoirs and their role in impact-induced cell death.

Impact loading of articular cartilage causes extensive chondrocyte death. Cell membranes have a limited elastic range of 3-4% strain but are protected from direct stretch during physiological loading by their membrane reservoir, an intricate pattern of membrane folds. Using a finite-element model, we suggested previously that access to the membrane reservoir is strain-rate-dependent and that during impact loading, the accessible membrane reservoir is drastically decreased, so that strains applied to chondrocytes are directly transferred to cell membranes, which fail when strains exceed 3-4%. However, experimental support for this proposal is lacking. The purpose of this study was to measure the accessible membrane reservoir size for different membrane strain rates using membrane tethering techniques with atomic force microscopy. We conducted atomic force spectroscopy on isolated chondrocytes (n = 87). A micron-sized cantilever was used to extract membrane tethers from cell surfaces at constant pulling rates. Membrane tethers could be identified as force plateaus in the resulting force-displacement curves. Six pulling rates were tested (1, 5, 10, 20, 40, and 80 µm/s). The size of the membrane reservoir, represented by the membrane tether surface areas, decreased exponentially with increasing pulling rates. The current results support our theoretical findings that chondrocytes exposed to impact loading die because of membrane ruptures caused by high tensile membrane strain rates.

Should tendon and aponeurosis be considered in series?

Fibres, aponeuroses, and tendons are often considered mechanically "in series" in skeletal muscles. This notion has led to oversimplified calculations of fibre forces from tendon forces, to incorrect derivations of constitutive laws for aponeuroses, and to misinterpretations of the recovery of elastic energy in stretch-shortening cycles of muscles. Here, we demonstrate theoretically, using examples of increasing complexity, that tendon and aponeurosis are not in series in a muscle fibre-aponeurosis-tendon complex. We then demonstrate that assuming the tendon and aponeurosis to be in series can lead to the appearance of mechanical work creation in these passive viscoelastic structures, a result that is mechanically impossible. Finally, we explain the mechanical role of the incompressible muscle matrix in force transmission from fibres to aponeuroses and tendon, and emphasize that incompressibility necessitates the introduction of extra forces necessary to maintain this constraint. Unfortunately, this requirement eliminates, for all but the simplest cases, a theoretical approach of muscle modeling based on intuitive free-body diagrams.

An articular cartilage contact model based on real surface geometry.

Abnormal, excessive stresses acting on articular joint surfaces are speculated to be one of the causes for joint degeneration. However, articular surface stresses have not been studied systematically, since it is technically difficult to measure in vivo contact areas and pressures in dynamic situations. Therefore, we implemented a numerical model of articular surface contact using accurate surface geometries. The model was developed for the cat patellofemoral joint. We demonstrated that small misalignments of the patella relative to the femur change the joint contact mechanics substantially for a given external load. These results suggest that misalignment might be studied as one of the factors causing articular cartilage disorder and joint degeneration.

Vibrations of Euler's disk.

A model of a partially deformable Euler disk is presented that allows transverse vibrations to be treated with the techniques of classical analytical mechanics. The model clearly shows that the increasing audible frequency produced during motion can be directly related to the forcing effect of the reaction and the angular velocity of the contact point. The material of the disk seems to play a role in affecting the intensity and quality of the sound, but not its pitch. Moreover, the friction force grows rapidly with the decline of the disk, thus causing the slipping that is partially responsible for the abrupt end of the motion. The model also supports the conjecture [P. Kessler and O. M. O'Reilly, Regul. Chaotic Dyn. 7, 49 (2002)] that the vibrations themselves contribute to this phenomenon by causing a loss of contact with the surface at small angles of inclination.

Boundary conditions for hyperbolic systems of partial differentials equations.

An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids.

Aspects of skeletal muscle modelling.

The modelling of skeletal muscle raises a number of philosophical questions, particularly in the realm of the relationship between different possible levels of representation and explanation. After a brief incursion into this area, a list of desiderata is proposed as a guiding principle for the construction of a viable model, including: comprehensiveness, soundness, experimental consistency, predictive ability and refinability. Each of these principles is illustrated by means of simple examples. The presence of internal constraints, such as incompressibility, may lead to counterintuitive results. A one-panel example is exploited to advocate the use of the principle of virtual work as the ideal tool to deal with these situations. The question of stability in the descending limb of the force-length relation is addressed and a purely mechanical analogue is suggested. New experimental results confirm the assumption that fibre stiffness is positive even in the descending limb. The indeterminacy of the force-sharing problem is traditionally resolved by optimizing a, presumably, physically meaningful target function. After presenting some new results in this area, based on a separation theorem, it is suggested that a more fundamental approach to the problem is the abandoning of optimization criteria in favour of an explicit implementation of activation criteria.