Computing the Maximum Volume Inscribed Ellipsoid of a Polytopic Projection

We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic projection. It is well-known that deriving an explicit description of a projected polytope is NP-hard. Our approach does not require an explicit description of the projection, and can easily be generalized to find a maximally sized convex body of a polytopic projection. Our obtained MVE is an inner approximation of the projected polytope, and its center is a centralized relative interior point of the projection. Since FME may produce many redundant constraints, we apply an LP-based procedure to keep the description of the projected polytopes at its minimal size. Furthermore, we propose an upper bounding scheme to evaluate the quality of the inner approximations. We test our approach on a simple polytope and a color tube design problem, and observe that as more auxiliary variables are eliminated, our inner approximations and upper bounds converge to optimal solutions

AAV plasmid DNA simplifies liver-directed in vivo gene therapy: comparison of expression levels after plasmid DNA-, adeno-associated virus- and adenovirus-mediated liver transfection

Background Successful liver gene therapy depends on efficient gene transfer techniques and long-lasting gene expression after successful transfer. Over the last decades, important progress has been made with the introduction of viral vectors using animal models, although their use is hampered by a complex and costly preparation compared to the simple and cost-effective preparation of plasmid DNA. These problems become even more critical when considering the application of viral vectors in human gene therapy and gene therapy trials. In a previous study, we were able to show that the hydrodynamics-based gene transfer of plasmid-DNA, containing the adeno-associated-virus specific inverted terminal repeats (AAV-ITR), prolongs gene expression in the liver, although it remained unclear whether plasmid gene transfer could achieve similar expression levels compared to viral-vector gene transfer. Methods Rat livers were transfected in-vivo with AAV-ITR-containing plasmid-DNA using a modified hydrodynamics-based procedure. Expression levels were monitored thereafter and compared with expression levels after viral-vector gene transfer. Results A high and stable long-term expression was achieved after in vivo transfection of rat livers with AAV-ITR-containing plasmids. The expression course resembled that after AAV-mediated gene transfer, and the expression was at least as high, and lasted as long, compared to recombinant AAV-mediated gene transfer. Conclusions We consider AAV-ITR-containing plasmids as a simple and cost-effective alternative to recombinant viral vectors, especially for liver-directed gene therapy in rodents. With ongoing progress in gene transfer methods for naked DNA, these plasmids may also become a successful alternative to recombinant viral vectors in human gene therapy. Copyright (C) 2010 John Wiley & Sons, Ltd