Asymptotic Self-Similar Blow-Up Profile for Three-Dimensional Axisymmetric Euler Equations Using Neural Networks.

Whether there exist finite-time blow-up solutions for the 2D Boussinesq and the 3D Euler equations are of fundamental importance to the field of fluid mechanics. We develop a new numerical framework, employing physics-informed neural networks, that discover, for the first time, a smooth self-similar blow-up profile for both equations. The solution itself could form the basis of a future computer-assisted proof of blow-up for both equations. In addition, we demonstrate physics-informed neural networks could be successfully applied to find unstable self-similar solutions to fluid equations by constructing the first example of an unstable self-similar solution to the Córdoba-Córdoba-Fontelos equation. We show that our numerical framework is both robust and adaptable to various other equations.

Liver transplant with controlled donors after circulatory death with normothermic regional perfusion and brain dead donors: A multicenter cohort study of transfusion, one-year graft survival and mortality.

BACKGROUND: Controlled donation after circulatory death (cDCD) has expanded the donor pool for liver transplantation (LT). However, transfusion requirements and perioperative outcomes should be elucidated. The aim of this multicenter study was to assess red blood cell (RBC) transfusions, one-year graft and patient survival after LT after cDCD with normothermic regional perfusion (NRP) compared with donors after brain death (DBD). METHODS: 591 LT carried out in ten centers during 2019 were reviewed. Thromboelastometry was used to manage coagulation and blood product transfusion in all centers. Normothermic regional perfusion was the standard technique for organ recovery. RESULTS: 447 patients received DBD and 144 cDCD with NRP. Baseline MCF Extem was lower in the cDCD group There were no differences in the percentage of patients (63% vs. 61% p = 0.69), nor in the number of RBC units transfused (4.7 (0.2) vs 5.5 (0.4) in DBD vs cDCD, p = 0.11. Twenty-six patients (6%) died during admission for LT in the DBD group compared with 3 patients (2%) in the cDCD group (p = 0.15). To overcome the bias due to a worse coagulation profile in cDCD recipients, matched samples were compared. No differences in baseline laboratory data, or in intraoperative use of RBC or one-year outcome data were observed between DBD and cDCD recipients. CONCLUSIONS: cDCD with NRP is not associated with increased RBC transfusion. No differences in graft and patient survival between cDCD and DBD were found. Donors after controlled circulatory death with NRP can increasingly be utilized with safety, improving the imbalance between organ donors and the ever-growing demand.