Biomechanical stability of hernia-damaged abdominal walls.

Hernia occurs when the peritoneum and/or internal organs penetrate through a defect in the abdominal wall. Implanting mesh fabrics is a common way to reinforce the repair of hernia-damaged tissues, despite the risks of infection and failure associated with them. However, there is neither consensus on the optimum mesh placement within the abdominal muscles complex nor on the minimum size of hernia defect that requires surgical correction. Here we show that the optimum position of the mesh depends on the hernia location; placing the mesh on the transversus abdominis muscles reduces the equivalent stresses in the damaged zone and represents the optimum reinforcement solution for incisional hernia. However, retrorectus reinforcement of the linea alba is more effective than preperitoneal, anterectus, and onlay implantations in the case of paraumbilical hernia. Using the principles of fracture mechanics, we found that the critical size of a hernia damage zone becomes severe at 4.1 cm in the rectus abdominis and at larger sizes (5.2-8.2 cm) in other anterior abdominal muscles. Furthermore, we found that the hernia defect size must reach 7.8 mm in the rectus abdominis before it influences the failure stress. In other anterior abdominal muscles, hernia starts to influence the failure stress at sizes ranging from 1.5 to 3.4 mm. Our results provide objective criteria to decide when a hernia damage zone becomes severe and requires repair. They demonstrate where mesh should be implanted for a mechanically stable reinforcement, depending on the type of hernia. We anticipate our contribution to be a starting point for sophisticated models of damage and fracture biomechanics. For example, the apparent fracture toughness is an important physical property that should be determined for patients living with different obesity levels. Furthermore, relevant mechanical properties of abdominal muscles at various ages and health conditions would be significant to generate patient specific results.

Improvements to local projective noise reduction through higher order and multiscale refinements.

The broad spectrum characteristic of signals from nonlinear systems obstructs noise reduction techniques developed for linear systems. Local projection was developed to reduce noise while preserving nonlinear deterministic structures, and a second order refinement to local projection which was proposed ten years ago does so particularly effectively. It involves adjusting the origin of the projection subspace to better accommodate the geometry of the attractor. This paper describes an analytic motivation for the enhancement from which follows further higher order and multiple scale refinements. However, the established enhancement is frequently as or more effective than the new filters arising from solely geometric considerations. Investigation of the way that measurement errors reinforce or cancel throughout the refined local projection procedure explains the special efficacy of the existing enhancement, and leads to a new second order refinement offering widespread gains. Different local projective filters are found to be best suited to different noise levels. At low noise levels, the optimal order increases as noise increases. At intermediate levels second order tends to be optimal, while at high noise levels prototypical local projection is most effective. The new higher order filters perform better relative to established filters for longer signals or signals corresponding to higher dimensional attractors.

Time-dependent, irreversible entropy production and geodynamics.

We present an application of entropy production as an abstraction tool for complex processes in geodynamics. Geodynamic theories are generally based on the principle of maximum dissipation being equivalent to the maximum entropy production. This represents a restriction of the second law of thermodynamics to its upper bound. In this paper, starting from the equation of motion, the first law of thermodynamics and decomposition of the entropy into reversible and irreversible terms,(1) we come up with an entropy balance equation in an integral form. We propose that the extrema of this equation give upper and lower bounds that can be used to constrain geodynamics solutions. This procedure represents an extension of the classical limit analysis theory of continuum mechanics, which considers only stress and strain rates. The new approach, however, extends the analysis to temperature-dependent problems where thermal feedbacks can play a significant role. We apply the proposed procedure to a simple convective/conductive heat transfer problem such as in a planetary system. The results show that it is not necessary to have a detailed knowledge of the material parameters inside the planet to derive upper and lower bounds for self-driven heat transfer processes. The analysis can be refined by considering precise dissipation processes such as plasticity and viscous creep.