A recent paper by Pendry et al (2006 Science 312 1780-2) used the coordinate invariance of Maxwell's equations to show how a region of space can be 'cloaked'-in other words, made inaccessible to electromagnetic sensingby surrounding it with a suitable (anisotropic and heterogenous) dielectric shield. Essentially the same observation was made several years earlier by Math. Res. Lett. 10 685-93, 2003 in the closely related setting of electric impedance tomography. These papers, though brilliant, have two shortcomings: (a) the cloaks they consider are rather singular; and (b) the analysis by Greenleaf, Lassas and Uhlmann does not apply in space dimension n = 2. The present paper provides a fresh treatment that remedies these shortcomings in the context of electric impedance tomography. In particular, we show how a regular near-cloak can be obtained using a nonsingular change of variables, and we prove that the change-of-variable-based scheme achieves perfect cloaking in any dimension n 2.

Objective. To study the osteogenic differentiation capacity of bone marrow-derived mesenchymal stem cells (BM-MSCs) from patients with ankylosing spondylitis (AS) and to investigate the mechanisms of abnormal osteogenic differentiation of BM-MSCs in AS.Methods. BM-MSCs from healthy donors (HDMSCs) and patients with AS (AS-MSCs) were cultured in osteogenic differentiation medium for 0-21 days, after which their osteogenic differentiation capacity was determined using alizarin red S and alkaline phosphatase assays. Gene expression levels of osteoblastic markers and related cytokines were detected by high-throughput quantitative reverse transcription-polymerase chain reaction. Enzyme-linked immunosorbent assay was performed to detect protein levels of bone morphogenetic protein 2 (BMP-2) and Noggin in the cell culture supernatant. The activation of Smad1/5/8 and MAPK signaling pathways was measured by Western blotting. The balance between BMP-2 and Noggin expression was regulated using lentiviruses encoding short hairpin RNA and exogenous Noggin, respectively, which enabled evaluation of how this balance affected osteogenic differentiation of AS-MSCs.Results. AS-MSCs outperformed HD-MSCs in osteogenic differentiation capacity. During osteogenic differentiation, AS-MSCs secreted more BMP-2 but less Noggin, accompanied by an overactivation of Smad1/5/ 8 and ERK-1/2. When the Noggin concentration was increased or BMP-2 expression was inhibited, the abnormal osteogenic differentiation of AS-MSCs was rectified. In addition, the balance between BMP-2 and Noggin secretion was restored.Conclusion. The results of this study demonstrate that an imbalance between BMP-2 and Noggin secretion induces abnormal osteogenic differentiation of AS-MSCs. These findings reveal a mechanism of pathologic osteogenesis in AS and provide a new perspective on inhibiting pathologic osteogenesis by regulating the balance between BMP-2 and Noggin.

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