The effect of interphase stiffness on microstresses and macromechanical behavior has been investigated for transverse loading of an hexagonal-array unidirectional fiber composite. The interphase is modeled by a layer which resists radial extension and circumferential shear deformation. Taking advantage of the periodicity of the medium, the states of stress, and deformation in a basic cell have been analyzed numerically by the use of the boundary element method. The circumferential tensile stress along the matrix side of the interphase and the radial stress in the interphase have been analyzed for various values of the interphase parameters and the fiber volume ratio. The micromechanical results have also been used to determine the effect of interphase stiffness on the effective moduli. The calculated values have been compared with analytical results that were adjusted for interphase stiffness.
BackgroundCartilage degradation is a typical characteristic of arthritis. This study examined whether there was a subset of phagocytic chondrocytes that expressed the specific macrophage marker, CD163, and investigated their role in cartilage degradation.MethodsCartilage from the knee and temporomandibular joints of Sprague-Dawley rats was harvested. Cartilage degradation was experimentally-induced in rat temporomandibular joints, using published biomechanical dental methods. The expression levels of CD163 and inflammatory factors within cartilage, and the ability of CD163+ chondrocytes to conduct phagocytosis were investigated. Cartilage from the knees of patients with osteoarthritis and normal cartilage from knee amputations was also investigated.ResultsIn the experimentally-induced degrading cartilage from temporomandibular joints, phagocytes were capable of engulfing neighboring apoptotic and necrotic cells, and the levels of CD163, TNF-α and MMPs were all increased (P<0.05). However, the levels of ACP-1, NO and ROS, which relate to cellular digestion capability were unchanged (P>0.05). CD163+ chondrocytes were found in the cartilage mid-zone of temporomandibular joints and knee from healthy, three-week old rats. Furthermore, an increased number of CD163+ chondrocytes with enhanced phagocytic activity were present in Col-II+ chondrocytes isolated from the degraded cartilage of temporomandibular joints in the eight-week experimental group compared with their age-matched controls. Increased number with enhanced phagocytic activity of CD163+ chondrocytes were also found in isolated Col-II+ chondrocytes stimulated with TNF-α (P<0.05). Mid-zone distribution of CD163+ cells accompanied with increased expression of CD163 and TNF-α were further confirmed in the isolated Col-II+ chondrocytes from the knee cartilage of human patients with osteoarthritis, in contrast to the controls (both P<0.05).ConclusionsAn increased number of CD163+ chondrocytes with enhanced phagocytic activity were discovered within degraded joint cartilage, indicating a role in eliminating degraded tissues. Targeting these cells provides a new strategy for the treatment of arthritis.
We propose in this article a Bayesian sequential design using alpha spending functions to control the overall type I error in phase III clinical trials. We provide algorithms to calculate critical values, power, and sample sizes for the proposed design. Sensitivity analysis is implemented to check the effects from different prior distributions, and conservative priors are recommended. We compare the power and actual sample sizes of the proposed Bayesian sequential design with different alpha spending functions through simulations. We also compare the power of the proposed method with frequentist sequential design using the same alpha spending function. Simulations show that, at the same sample size, the proposed method provides larger power than the corresponding frequentist sequential design. It also has larger power than traditional Bayesian sequential design which sets equal critical values for all interim analyses. When compared with other alpha spending functions, O'Brien-Fleming alpha spending function has the largest power and is the most conservative in terms that at the same sample size, the null hypothesis is the least likely to be rejected at early stage of clinical trials. And finally, we show that adding a step of stop for futility in the Bayesian sequential design can reduce the overall type I error and reduce the actual sample sizes.
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