A novel convergence enhancement method based on Online Dimension Reduction Optimization

Iterative steady-state solvers are widely used in computational fluid dynamics. Unfortunately, it is difficult to obtain steady-state solution for unstable problem caused by physical instability and numerical instability. Optimization is a better choice for solving unstable problem because steady-state solution is always the extreme point of optimization regardless of whether the problem is unstable or ill-conditioned, but it is difficult to solve partial differential equations (PDEs) due to too many optimization variables. In this study, we propose an Online Dimension Reduction Optimization (ODRO) method to enhance the convergence of the traditional iterative method to obtain the steady-state solution of unstable problem. This method performs proper orthogonal decomposition (POD) on the snapshots collected from a few iteration steps, optimizes PDE residual in the POD subspace to get a solution with lower residual, and then continues to iterate with the optimized solution as the initial value, repeating the above three steps until the residual converges. Several typical cases show that the proposed method can efficiently calculate the steady-state solution of unstable problem with both the high efficiency and robustness of the iterative method and the good convergence of the optimization method. In addition, this method is easy to implement in almost any iterative solver with minimal code modification

C5b-9 membrane attack complex formation and extracellular vesicle shedding in Barrett's esophagus and esophageal adenocarcinoma

The early complement components have emerged as mediators of pro-oncogenic inflammation, classically inferred to cause terminal complement activation, but there are limited data on the activity of terminal complement in cancer. We previously reported elevated serum and tissue C9, the terminal complement component, in esophageal adenocarcinoma (EAC) compared to the precursor condition Barrett’s Esophagus (BE) and healthy controls. Here, we investigate the level and cellular fates of the terminal complement complex C5b-9, also known as the membrane attack complex. Punctate C5b-9 staining and diffuse C9 staining was detected in BE and EAC by multiplex immunohistofluorescence without corresponding increase of C9 mRNA transcript. Increased C9 and C5b-9 staining were observed in the sequence normal squamous epithelium, BE, low- and high-grade dysplasia, EAC. C5b-9 positive esophageal cells were morphologically intact, indicative of sublytic or complement-evasion mechanisms. To investigate this at a cellular level, we exposed non-dysplastic BE (BAR-T and CP-A), high-grade dysplastic BE (CP-B and CP-D) and EAC (FLO-1 and OE-33) cell lines to the same sublytic dose of immunopurified human C9 (3 µg/ml) in the presence of C9-depleted human serum. Cellular C5b-9 was visualized by immunofluorescence confocal microscopy. Shed C5b-9 in the form of extracellular vesicles (EV) was measured in collected conditioned medium using recently described microfluidic immunoassay with capture by a mixture of three tetraspanin antibodies (CD9/CD63/CD81) and detection by surface-enhanced Raman scattering (SERS) after EV labelling with C5b-9 or C9 antibody conjugated SERS nanotags. Following C9 exposure, all examined cell lines formed C5b-9, internalized C5b-9, and shed C5b-9+ and C9+ EVs, albeit at varying levels despite receiving the same C9 dose. In conclusion, these results confirm increased esophageal C5b-9 formation during EAC development and demonstrate capability and heterogeneity in C5b-9 formation and shedding in BE and EAC cell lines following sublytic C9 exposure. Future work may explore the molecular mechanisms and pathogenic implications of the shed C5b-9+ EV