A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schr\"odinger equation

We present the results of a numerical experiment inspired by the semiclassical (zero-dispersion) limit of the focusing nonlinear Schroedinger (NLS) equation. In particular, we focus on the Gaussian semiclassical soliton ensemble, a family of exact multisoliton solutions obtained by repeatedly solving the initial-value problem for a particular sequence of initial data. The sequence of data is generated by adding an asymptotically vanishing sequence of perturbations to pure Gaussian initial data. These perturbations are obtained by applying the inverse-scattering transform to formal WKB approximations of eigenvalues of the associated spectral problem with a Gaussian potential. Recent results [Lee, Lyng, & Vankova, Physica D 24 (2012):1767--1781] suggest that, remarkably, these perturbations---interlaced as they are with the integrable structure of the equation---do not excite the acute modulational instabilities that are known to be present in the semiclassical regime. Here, we provide additional evidence to support the claim that these WKB-induced perturbations indeed have a very special structure. In particular, as a control experiment, we examine the evolution from a family of initial data created by an asymptotically vanishing family of analytic perturbations which are qualitatively indistinguishable from the WKB-induced perturbations that generate the Gaussian semiclassical soliton ensemble. We then compare this evolution to the (numerically computed) true evolution of the Gaussian and also to the evolution of the corresponding members of the semiclassical soliton ensemble. Our results both highlight the exceptional nature of the WKB-induced perturbations used to generate the semiclassical soliton ensemble and provide new insight into the sensitivity properties of the semiclassical limit problem for the focusing NLS equation

Sensitivity of MRI Tumor Biomarkers to VEGFR Inhibitor Therapy in an Orthotopic Mouse Glioma Model

MRI biomarkers of tumor edema, vascular permeability, blood volume, and average vessel caliber are increasingly being employed to assess the efficacy of tumor therapies. However, the dependence of these biomarkers on a number of physiological factors can compromise their sensitivity and complicate the assessment of therapeutic efficacy. Here we examine the response of these MRI tumor biomarkers to cediranib, a potent vascular endothelial growth factor receptor (VEGFR) inhibitor, in an orthotopic mouse glioma model. A significant increase in the tumor volume and relative vessel caliber index (rVCI) and a slight decrease in the water apparent diffusion coefficient (ADC) were observed for both control and cediranib treated animals. This contrasts with a clinical study that observed a significant decrease in tumor rVCI, ADC and volume with cediranib therapy. While the lack of a difference between control and cediranib treated animals in these biomarker responses might suggest that cediranib has no therapeutic benefit, cediranib treated mice had a significantly increased survival. The increased survival benefit of cediranib treated animals is consistent with the significant decrease observed for cediranib treated animals in the relative cerebral blood volume (rCBV), relative microvascular blood volume (rMBV), transverse relaxation time (T2), blood vessel permeability (Ktrans), and extravascular-extracellular space (νe). The differential response of pre-clinical and clinical tumors to cediranib therapy, along with the lack of a positive response for some biomarkers, indicates the importance of evaluating the whole spectrum of different tumor biomarkers to properly assess the therapeutic response and identify and interpret the therapy-induced changes in the tumor physiology

Essential role for mast cell tryptase in acute experimental colitis

Patients with inflammatory bowel disease (IBD) have increased numbers of human tryptase-β (hTryptase-β)-positive mast cells (MCs) in the gastrointestinal tract. The amino acid sequence of mouse mast cell protease (mMCP)-6 is most similar to that of hTryptase-β. We therefore hypothesized that this mMCP, or the related tryptase mMCP-7, might have a prominent proinflammatory role in experimental colitis. The dextran sodium sulfate (DSS) and trinitrobenzene sulfonic acid (TNBS) colitis models were used to evaluate the differences between C57BL/6 (B6) mouse lines that differ in their expression of mMCP-6 and mMCP-7 with regard to weight loss, colon histopathology, and endoscopy scores. Microarray analyses were performed, and confirmatory real-time PCR, ELISA, and/or immunohistochemical analyses were carried out on a number of differentially expressed cytokines, chemokines, and matrix metalloproteinases (MMPs). The mMCP-6–null mice that had been exposed to DSS had significantly less weight loss as well as significantly lower pathology and endoscopy scores than similarly treated mMCP-6–expressing mice. This difference in colitis severity was confirmed endoscopically in the TNBS-treated mice. Evaluation of the distal colon segments revealed that numerous proinflammatory cytokines, chemokines that preferentially attract neutrophils, and MMPs that participate in the remodeling of the ECM were all markedly increased in the colons of DSS-treated WT mice relative to untreated WT mice and DSS-treated mMCP-6–null mice. Collectively, our data show that mMCP-6 (but not mMCP-7) is an essential MC-restricted mediator in chemically induced colitis and that this tryptase acts upstream of many of the factors implicated in IBD