On a Projection Method for the Numerical Integration of Constitutive Equations Involving Large Inelastic and Incompressible Deformations

Finite deformation plasticity often involves the multiplicative split of the deformation gradient into an elastic and plastic part. Motivated by observations in physics, the plastic part is assumed to be volume preserving, i.e., the plastic part of the deformation gradient is unimodular. In order to not accumulate errors, in the best case, one fulfills this constraint exactly to obtain accurate results (see, e.g., [3]). While other approaches where pursued as well, many authors therefore adopted the use of the exponential map, which is a geometric integrator preserving the plastic incompressibility. However, it's computation is not straightforward and performing the eigenvalue decomposition and it's linearization for the exponential function is numerically elaborate. Therefore, in this work, a new approach which also exactly preserves the incompressibility constraint is developed. It makes use of a projection of all symmetric tensors onto the manifold of unimodular tensors. The proposed method is compared to models utilizing the exponential map in numerical experiments

Continuous thoracic epidural anesthesia improves gut mucosal microcirculation in rats with sepsis

Microcirculatory dysfunction contributes significantly to tissue hypoxia and multiple organ failure in sepsis. Ischemia of the gut and intestinal hypoxia are especially relevant for the evolution of sepsis because the mucosal barrier function may be impaired, leading to translocation of bacteria and toxins. Because sympathetic blockade enhances intestinal perfusion under physiologic conditions, we hypothesized that thoracic epidural anesthesia (TEA) may attenuate microcirculatory perturbations during sepsis. The present study was designed as a prospective and controlled laboratory experiment to assess the effects of continuous TEA on the mucosal microcirculation in a cecal ligation and perforation model of sepsis in rats. Anesthetized Sprague-Dawley rats underwent laparotomy and cecal ligation and perforation to induce sepsis. Subsequently, either bupivacaine 0.125% (n = 10) or isotonic sodium chloride solution (n = 9) was continuously infused via the thoracic epidural catheter for 24 h. In addition, a sham laparotomy was carried out in eight animals. Intravital videomicroscopy was then performed on six to ten villi of ileum mucosa. The capillary density was measured as areas encircled by perfused capillaries, that is, intercapillary areas. The TEA accomplished recruitment of microcirculatory units in the intestinal mucosa by decreasing total intercapillary areas (1,317 +/- 403 vs. 1,001 +/- 236 microm2) and continuously perfused intercapillary areas (1,937 +/- 512 vs. 1,311 +/- 678 microm2, each P < 0.05). Notably, TEA did not impair systemic hemodynamic variables beyond the changes caused by sepsis itself. Therefore, sympathetic blockade may represent a therapeutic option to treat impaired microcirculation in the gut mucosa resulting from sepsis. Additional studies are warranted to assess the microcirculatory effects of sympathetic blockade on other splanchnic organs in systemic inflammation