Construction of C 2 Pythagorean-hodograph interpolating splines by the homotopy method

The complex representation of polynomial Pythagorean-hodograph (PH) curves allows the problem of constructing a C 2 PH quintic “spline” that interpolates a given sequence of points p 0 , p 1 ,..., p N and end-derivatives d 0 and d N to be reduced to solving a “tridiagonal” system of N quadratic equations in N complex unknowns. The system can also be easily modified to incorporate PH-spline end conditions that bypass the need to specify end-derivatives. Homotopy methods have been employed to compute all solutions of this system, and hence to construct a total of 2 N +1 distinct interpolants for each of several different data sets. We observe empirically that all but one of these interpolants exhibits undesirable “looping” behavior (which may be quantified in terms of the elastic bending energy , i.e., the integral of the square of the curvature with respect to arc length). The remaining “good” interpolant, however, is invariably a fairer curve-having a smaller energy and a more even curvature distribution over its extent-than the corresponding “ordinary” C 2 cubic spline. Moreover, the PH spline has the advantage that its offsets are rational curves and its arc length is a polynomial function of the curve parameter.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41719/1/10444_2005_Article_BF02124754.pd

Iodinated contrast agents in patients with myasthenia gravis : a retrospective cohort study

Currently, it has not been satisfactorily established, whether modern low-osmolality iodinated contrast agents (ICAs) used in computed tomography (CT) studies are a risk factor for exacerbation of myasthenic symptoms. The rate of acute adverse events as well as delayed clinical worsening up to 30 days were analyzed in 73 patients with confirmed myasthenia gravis (MG) who underwent contrast-enhanced CT studies and compared to 52 patients who underwent unenhanced CT studies. One acute adverse event was documented. 12.3% of MG patients experienced a delayed exacerbation of symptoms after ICA administration. The rate of delayed severe exacerbation was higher in the contrast-enhanced group. Alternative causes for the exacerbation of MG-related symptoms were more likely than ICA administration in all cases. ICA administration for CT studies in MG patients should not be withheld if indicated, but patients particularly those with concomitant acute diseases should be carefully monitored for exacerbation of symptoms.(VLID)354446

Lower serum cholesterol levels as a risk factor for critical illness polyneuropathy: a matched case–control study

Abstract Critical illness polyneuropathy (CIP) is a frequent and underdiagnosed phenomenon among intensive care unit patients. The lipophilic nature of neuronal synapses may result in the association of low serum cholesterol levels with a higher rate of CIP development. We aimed to investigate this issue in critically ill patients. All cases diagnosed with CIP in our tertiary care hospital between 2013 and 2017 were 1:1 matched with controls without the condition by age, sex, and ICD diagnoses. The main risk factors examined were the differences in change between initial and minimum serum total cholesterol levels, and minimum serum total cholesterol levels between matched pairs. Other predictors were serum markers of acute inflammation. We included 67 cases and 67 controls (134 critically ill patients, 49% female, 46% medical). Serum total cholesterol levels decreased more profoundly in cases than controls (median: −74 (IQR −115 to −24) vs. −39 (IQR −82 to −4), median difference: −28, 95% CI [−51, −5]), mg/dl). Minimum serum total cholesterol levels were lower in the cases (median difference: −24, 95% CI [−39, −9], mg/dl). We found significant median differences across matched pairs in maximum serum C-reactive protein (8.9, 95% CI [4.6, 13.2], mg/dl), minimum albumin (−4.2, 95% CI [−6.7, −1.7], g/l), decrease in albumin (−3.9, 95% CI [−7.6, −0.2], g/l), and lowest cholinesterase levels (−0.72, 95% CI [−1.05, −0.39], U/l). Subsequently, more pronounced decreases in serum total cholesterol levels and lower minimum total cholesterol levels during critical care unit hospitalizations may be a risk factor for CIP

Nuclear β-Catenin Induces an Early Liver Progenitor Phenotype in Hepatocellular Carcinoma and Promotes Tumor Recurrence

Transforming growth factor-β cooperates with oncogenic Ras to activate nuclear β-catenin during the epithelial to mesenchymal transition of hepatocytes, a process relevant in the progression of hepatocellular carcinoma (HCC). In this study we investigated the role of β-catenin in the differentiation of murine, oncogene-targeted hepatocytes and in 133 human HCC patients scheduled for orthotopic liver transplantation. Transforming growth factor-β caused dissociation of plasma membrane E-cadherin/β-catenin complexes and accumulation of nuclear β-catenin in Ras-transformed, but otherwise normal hepatocytes in p19ARF−/− mice. Both processes were inhibited by Smad7-mediated disruption of transforming growth factor-β signaling. Overexpression of constitutively active β-catenin resulted in high levels of CK19 and M2-PK, whereas ablation of β-catenin by axin overexpression caused strong expression of CK8 and CK18. Therefore, nuclear β-catenin resulted in dedifferentiation of neoplastic hepatocytes to immature progenitor cells, whereas loss of nuclear β-catenin led to a differentiated HCC phenotype. Poorly differentiated human HCC showed cytoplasmic redistribution or even loss of E-cadherin, suggesting epithelial to mesenchymal transition. Analysis of 133 HCC patient samples revealed that 58.6% of human HCC exhibited strong nuclear β-catenin accumulation, which correlated with clinical features such as vascular invasion and recurrence of disease after orthotopic liver transplantation. These data suggest that activation of β-catenin signaling causes dedifferentiation to malignant, immature hepatocyte progenitors and facilitates recurrence of human HCC after orthotopic liver transplantation