Nonlinear hyperbolic systems: Non-degenerate flux, inner speed variation, and graph solutions

We study the Cauchy problem for general, nonlinear, strictly hyperbolic systems of partial differential equations in one space variable. First, we re-visit the construction of the solution to the Riemann problem and introduce the notion of a nondegenerate (ND) system. This is the optimal condition guaranteeing, as we show it, that the Riemann problem can be solved with finitely many waves, only; we establish that the ND condition is generic in the sense of Baire (for the Whitney topology), so that any system can be approached by a ND system. Second, we introduce the concept of inner speed variation and we derive new interaction estimates on wave speeds. Third, we design a wave front tracking scheme and establish its strong convergence to the entropy solution of the Cauchy problem; this provides a new existence proof as well as an approximation algorithm. As an application, we investigate the time-regularity of the graph solutions $(X,U)$ introduced by the second author, and propose a geometric version of our scheme; in turn, the spatial component $X$ of a graph solution can be chosen to be continuous in both time and space, while its component $U$ is continuous in space and has bounded variation in time.Comment: 74 page

Single-Cell Analyses of Prostate Cancer Liquid Biopsies Acquired by Apheresis

Item does not contain fulltextPurpose: Circulating tumor cells (CTCs) have clinical relevance, but their study has been limited by their low frequency.Experimental Design: We evaluated liquid biopsies by apheresis to increase CTC yield from patients suffering from metastatic prostate cancer, allow precise gene copy-number calls, and study disease heterogeneity.Results: Apheresis was well tolerated and allowed the separation of large numbers of CTCs; the average CTC yield from 7.5 mL of peripheral blood was 167 CTCs, whereas the average CTC yield per apheresis (mean volume: 59.5 mL) was 12,546 CTCs. Purified single CTCs could be isolated from apheresis product by FACS sorting; copy-number aberration (CNA) profiles of 185 single CTCs from 14 patients revealed the genomic landscape of lethal prostate cancer and identified complex intrapatient, intercell, genomic heterogeneity missed on bulk biopsy analyses.Conclusions: Apheresis facilitated the capture of large numbers of CTCs noninvasively with minimal morbidity and allowed the deconvolution of intrapatient heterogeneity and clonal evolution. Clin Cancer Res; 24(22); 5635-44. (c)2018 AACR

Gender-Related Differences in Presentation, Treatment, and Outcome of Patients With Atrial Fibrillation in Europe. A Report From the Euro Heart Survey on Atrial Fibrillation

Objectives: This study sought to investigate gender-related differences in patients with atrial fibrillation (AF) in Europe. Background: Gender-related differences may play a significant role in AF. Methods: We analyzed the data of 5,333 patients (42% female) enrolled in the Euro Heart Survey on Atrial Fibrillation. Results: Compared with men, the women were older, had a lower quality of life (QoL), had more comorbidities, more often had heart failure (HF) with preserved left ventricular systolic function (18% vs. 7%, p < 0.001), and less often had HF with systolic dysfunction (17% vs. 26%, p < 0.001). Among patients with typical AF symptoms (56% of women, 49% of men), there was no gender-related difference in the choice of rate or rhythm control. Among patients with atypical or no symptoms (44% of women, 51% of men), women less frequently underwent rhythm control (39% vs. 51%, p < 0.001) than did men. Women underwent less electrical cardioversion (22% vs. 28%, p < 0.001). Prescription of oral anticoagulants was identical (65%) in both genders. One-year outcome was similar except that women had a higher chance for stroke (odds ratio 1.83 in multivariable regression analysis, p = 0.019). Conclusions: Women with AF had more comorbidities, more HF with preserved systolic function, and a lower QoL than men. In the large group with atypical or no symptoms, women were treated appropriately more conservatively with less rhythm control than men. Women had a higher chance for stroke. Long-term QoL changes and other morbidities and mortality were similar. © 2007 American College of Cardiology Foundation

Antithrombotic treatment in real-life atrial fibrillation patients: a report from the Euro Heart Survey on Atrial Fibrillation

Aims To describe guideline adherence and application of different stroke risk strati. cation schemes regarding antithrombotic therapy in real-life atrial. brillation (AF) patients and to assess which factors influence antithrombotic management decisions.Methods and results The Euro Heart Survey enrolled 5333 AF patients in 35 countries, in 2003 and 2004. Prescription of antithrombotic drugs, especially oral anticoagulation (OAC), was hardly tailored to the patient's stroke risk pro. le as indicated by the joint guidelines of the American College of Cardiology, American Heart Association, and the European Society of Cardiology, ACCP guidelines, or CHADS(2) and Framingham risk scores. In multivariable analysis, only a limited number of the well-known stroke risk factors triggered OAC prescription. In contrast, less relevant factors, of which clinical type of AF and availability of an OAC monitoring outpatient clinic were the most marked, played a significant role in OAC prescription. Electrical cardioversions and catheter ablations clearly triggered OAC prescription, whereas pharmacological cardioversions even in the presence of stroke risk factors did not.Conclusion Antithrombotic therapy in AF is hardly tailored to the patient's stroke risk pro. le. Factors other than well-known stroke risk factors were significantly involved in antithrombotic management decisions. To facilitate this tailored treatment, guideline writers and physician educators should focus on providing one uniform and easy to use stroke risk strati. cation scheme