High dimensional model representation is under active development as a set of quantitative model assessment and analysis tools for capturing high-dimensional input-output system behavior based on a hierarchy of functions of increasing dimensions. The HDMR component functions are optimally constructed from zeroth order to higher orders step-by-step. This paper extends the definitions of HDMR component functions to systems whose input variables may not be independent. The orthogonality of the higher order terms with respect to the lower order ones guarantees the best improvement in accuracy for the higher order approximations. Therefore, the HDMR component functions are constructed to be mutually orthogonal. The RS-HDMR component functions are efficiently constructed from randomly sampled input-output data. The previous introduction of polynomial approximations for the component functions violates the strictly desirable orthogonality properties. In this paper, new orthonormal polynomial approximation formulas for the RS-HDMR component functions are presented that preserve the orthogonality property. An integrated exposure and dose model as well as ionospheric electron density determined from measured ionosonde data are used as test cases, which show that the new method has better accuracy than the prior one.

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.

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Background Induced pluripotent stem cells (iPSCs) can generate epithelial stem cells (EpSCs) as seed cells for skin substitutes to repair skin defects. Here, we investigated the effects of a human acellular amniotic membrane (hAAM) combined with iPSC-derived CD200 + /ITGA6 + EpSCs as a skin substitute on repairing skin defects in nude mice. Methods Human urinary cells isolated from a healthy donor were reprogrammed into iPSCs and then induced into CD200 + /ITGA6 + epithelial stem cells. Immunocytochemistry and RT-PCR were used to examine the characteristics of the induced epithelial stem cells. iPSC-derived EpSCs were cultured on a hAAM, and cytocompatibility of the composite was analyzed by CCK8 assays and scanning electron microscopy. Then, hAAMs combined with iPSC-derived EpSCs were transplanted onto skin defects of mice. The effects of this composite on skin repair were evaluated by immunohistochemistry. Results The results showed that CD200 + /ITGA6 + epithelial stem cells induced from iPSCs displayed the phenotypes of hair follicle stem cells. After seeding on the hAAM, iPSC-derived epithelial stem cells had the ability to proliferate. After transplantation, CD200 + /ITGA6 + epithelial stem cells on the hAAM promoted the construction of hair follicles and interfollicular epidermis. Conclusions These results indicated that transplantation of a hAAM combined with iPS-derived EpSCs is feasible to reconstruct skin and skin appendages, and may be a substantial reference for iPSC-based therapy for skin defects.