Strong Morita Equivalence and Imprimitivity Theorems

The purpose of this thesis is to give an exposition of two topics, mostly following the books \cite{R & W} and \cite{Wil}. First, we wish to investigate crossed product $C^*$-algebras in its most general form. Crossed product $C^*$-algebras are $C^*$-algebras which encode information about the action of a locally compact Hausdorff group $G$ as automorphisms on a $C^*$-algebra $A$. One of the prettiest example of such a dynamical system that I have observed in the wild arises in the gauge-invariant uniqueness theorem \cite{Rae}, which assigns to every $C^*$-algebra $C^*(E)$ associated with a graph $E$ a \emph{gauge action} of the unit circle \T to automorphisms on $C^*(E)$. Group $C^*$-algebras also arise as a crossed product of a dynamical system. I found crossed products in its most general form very abstract and much of its constructions motivated by phenomena in a simpler case. Because of this, much of the initial portion of this exposition is dedicated to the action of a discrete group on a unital $C^*$-algebra, where most of the examples are given. I must admit that I find calculations of crossed products when one has an indiscrete group $G$ acting on our $C^*$-algebra daunting except under very simple cases. This leads to our second topic, on imprimitivity theorems of crossed product $C^*$-algebras. Imprimitivity theorems are machines that output (strong) Morita equivalences between crossed products. Morita equivalence is an invariant on $C^*$-algebras which preserve properties like the ideal structure and the associated $K$-groups. For example, no two commutative $C^*$-algebras are Morita equivalent, but $C(X) \otimes M_n$ is Morita equivalent to $C(X)$ whenever $n$ is a positive integer and $X$ is a compact Hausdorff space. Notice that Morita equivalence can be used to prove that a given $C^*$-algebra is simple. All this leads to our concluding application: Takai duality. The set-up is as follows: we have an action $\alpha$ of an abelian group $G$ on a $C^*$-algebra $A$. On the associated crossed product $A \rtimes_\alpha G$, there is a dual action \Hat{\alpha} from the Pontryagin dual \Hat{G}. Takai duality states that the iterated crossed product (A \rtimes_\alpha G) \rtimes \Hat{G} is isomorphic to A \otimes \calK(L^2(G)) in a canonical way. This theorem is used to show for example that all graph $C^*$-algebras are nuclear or to establish theorems on the $K$-theory on crossed product $C^*$-algebras

Simultaneous determination of wave speed and arrival time of reflected waves using the pressure-velocity loop

This is the post print version of the article. The official published version can be found at the link below.In a previous paper we demonstrated that the linear portion of the pressure–velocity loop (PU-loop) corresponding to early systole could be used to calculate the local wave speed. In this paper we extend this work to show that determination of the time at which the PU-loop first deviates from linearity provides a convenient way to determine the arrival time of reflected waves (Tr). We also present a new technique using the PU-loop that allows for the determination of wave speed and Tr simultaneously. We measured pressure and flow in elastic tubes of different diameters, where a strong reflection site existed at known distances away form the measurement site. We also measured pressure and flow in the ascending aorta of 11 anaesthetised dogs where a strong reflection site was produced through total arterial occlusion at four different sites. Wave speed was determined from the initial slope of the PU-loop and Tr was determined using a new algorithm that detects the sampling point at which the initial linear part of the PU-loop deviates from linearity. The results of the new technique for detecting Tr were comparable to those determined using the foot-to-foot and wave intensity analysis methods. In elastic tubes Tr detected using the new algorithm was almost identical to that detected using wave intensity analysis and foot-to-foot methods with a maximum difference of 2%. Tr detected using the PU-loop in vivo highly correlated with that detected using wave intensity analysis (r 2 = 0.83, P < 0.001). We conclude that the new technique described in this paper offers a convenient and objective method for detecting Tr, and allows for the dynamic determination of wave speed and Tr, simultaneously

Therapeutic efficacy of regulable GDNF expression for Huntington's and Parkinson's disease by a high-induction, background-free "GeneSwitch" vector.

Gene therapy is currently an irreversible approach, without possibilities to fine-tune or halt the expression of a therapeutic gene product. Especially when expressing neurotrophic factors to treat neurodegenerative disorders, options to regulate transgene expression levels might be beneficial. We thus developed an advanced single-genome inducible AAV vector for expression of GDNF, under control of the approved small molecule drug mifepristone. In the rat brain, GDNF expression can be induced over a wide range up to three hundred-fold over endogenous background, and completely returns to baseline within 3-4 weeks. When applied with appropriate serotype and titre, the vector is absolutely free of any non-induced background expression. In the BACHD model of Huntington's disease we demonstrate that the vector can be kept in a continuous ON-state for extended periods of time. In a model of Parkinson's disease we demonstrate that repeated short-term expression of GDNF restores motor capabilities in 6-OHDA-lesioned rats. We also report on sex-dependent pharmacodynamics of mifepristone in the rodent brain. Taken together, we show that wide-range and high-level induction, background-free, fully reversible and therapeutically active GDNF expression can be achieved under tight pharmacological control by this novel AAV - "Gene Switch" vector

AAV5-miHTT gene therapy demonstrates suppression of mutant huntingtin aggregation and neuronal dysfunction in a rat model of Huntington's disease.

Huntington's disease (HD) is a fatal progressive neurodegenerative disorder caused by a mutation in the huntingtin (HTT) gene. To date, there is no treatment to halt or reverse the course of HD. Lowering of either total or only the mutant HTT expression is expected to have therapeutic benefit. This can be achieved by engineered micro (mi)RNAs targeting HTT transcripts and delivered by an adeno-associated viral (AAV) vector. We have previously showed a miHTT construct to induce total HTT knock-down in Hu128/21 HD mice, while miSNP50T and miSNP67T constructs induced allele-selective HTT knock-down in vitro. In the current preclinical study, the mechanistic efficacy and gene specificity of these selected constructs delivered by an AAV serotype 5 (AAV5) vector was addressed using an acute HD rat model. Our data demonstrated suppression of mutant HTT messenger RNA, which almost completely prevented mutant HTT aggregate formation, and ultimately resulted in suppression of DARPP-32-associated neuronal dysfunction. The AAV5-miHTT construct was found to be the most efficient, although AAV5-miSNP50T demonstrated the anticipated mutant HTT allele selectivity and no passenger strand expression. Ultimately, AAV5-delivered-miRNA-mediated HTT lowering did not cause activation of microglia or astrocytes suggesting no immune response to the AAV5 vector or therapeutic precursor sequences. These preclinical results suggest that using gene therapy to knock-down HTT may provide important therapeutic benefit for HD patients and raised no safety concerns, which supports our ongoing efforts for the development of an RNA interference-based gene therapy product for HD

Combined use of Ventrain and S-Guide for Airway Management of Severe Subglottic Stenosis.

The airway management of a patient with severe tracheal stenosis depends on its severity, length, location, and type of surgery. Its management is complex and requires the collaboration of an experienced team of anaesthetist and ear, nose, and throat surgeon. We report an innovative combination of Ventrain™ and S-Guide™ for airway management of a planned endoscopic dilation of a severe subglottic stenosis in an adult patient. This new alternative may offer advantages over existing airway management techniques in similar cases

Intravaginal live attenuated Salmonella increase local antitumor vaccine-specific CD8(+) T cells.

We have recently reported that the intravaginal instillation of synthetic Toll-like receptor 3 (TLR3) or TLR9 agonists after a subcutaneous vaccination against human papillomavirus E7 highly increases (~5-fold) the number of vaccine-specific CD8(+) T cells in the genital mucosa of mice, without affecting E7-specific systemic responses. Here, we show that the instillation of live attenuated Salmonella enterica serovar Typhimurium similarly, though more efficiently (~15- fold), increases both E7-specific and total CD8(+) T cells in the genital mucosa. Cancer immunotherapeutic strategies combining vaccination with local immunostimulation with live bacteria deserve further investigations