We consider a mono-dimensional two-velocities scheme used to approximate the solutions of a scalar hyperbolic conservative partial differential equation. We prove the convergence of the discrete solution toward the unique entropy solution by first estimating the supremum norm and the total variation of the discrete solution, and second by constructing a discrete kinetic entropy-entropy flux pair being given a continuous entropy-entropy flux pair of the hyperbolic system. We finally illustrate our results with numerical simulations of the advection equation and the Burgers equation.

Aortic blood pressure is a strong indicator to cardiovascular diseases and morbidity. Clinically, pressure measurements are done by inserting a catheter in the aorta. However, imaging techniques have been used to avoid the invasive procedure of catheterization. In this paper, we combined MRI measurements to a one-dimensional model in order to simulate blood flow in an aortic segment. Absolute pressure was estimated in the aorta by using MRI measured flow as boundary conditions and MRI measured compliance as a pressure law for solving the model. Model computed pressure was compared to catheter measured pressure in an aortic phantom. Furthermore, aortic pressure was estimated in vivo in three healthy volunteers.

Objectives: KEYNOTE-426 demonstrated statistically and clinically meaningful improvements in overall survival (OS), progression-free survival (PFS) and overall response rate (ORR) in ccmRCC subjects treated with P+A versus (vs) sunitinib. This NMA synthesized RCT evidence to indirectly compare the relative treatment effects of P+A vs other therapies. Methods: A systematic literature review identified RCTs of approved or investigational 1L treatments of mRCC. Fixed-effect Bayesian NMA was conducted to determine the relative efficacy of treatments; OS, PFS [hazard ratios (HRs)] and ORR (odds ratio [OR]) were presented with 95% credible intervals (CrIs). Results: 18 RCTs (total ITT population: 10,547) that evaluated 17 interventions were identified (10 evaluable for OS, 14 for PFS, 13 for ORR). P+A showed statistically significant OS benefit over 7 out of 9 interventions evaluated [ranging from interferon-alpha (IFN-a) (HR=0.43, 0.29-0.64) through bevacizumab (B) + IFN-a, B + temsirolimus (B+T), sunitinib, placebo, pazopanib to atezolizumab + bevacizumab (A+B) [HR=0.65, 0.43-0.99]. OS benefit favored P+A vs avelumab + axitinib (A+A) [HR=0.68, 0.43-1.09] and vs nivolumab + ipilimumab (N+I) [HR=0.75, 0.51-1.09], but was not statistically significant. P+A showed statistically significant PFS benefit over 11 out of 13 interventions evaluated [ranging from placebo (HR=0.26, 0.16-0.42) through sorafenib, IFN-a, axitinib, tivozanib, B+T, B+ IFN-a, pazopanib, atezolizumab, sunitinib to A+B (HR=0.77, 0.60-0.99)]; PFS benefit favored P+A over N+I [HR=0.81, 0.64-1.03] but was not statistically significant, and P+A showed no difference compared to A+A [HR=1.00, 0.76-1.32]. P+A showed statistically significant ORR benefit over 11 out of 12 interventions evaluated [ranging from placebo (OR=25.22, 7.93-110.97) , sorafenib, IFN-a, axitinib, B+T, B+ IFN-a, atezolizumab, A+B, sunitinib, pazopanib to N+I (OR=1.95, 1.35-2.82)]; results favored A+A over P+A [OR=0.86, 0.58-1.27], but were not statistically significant. Conclusions: These analyses suggest that P+A provides significant OS, PFS and ORR benefits when indirectly compared to majority of 1L ccmRCC treatments.