Space-time reduced basis methods for parametrized unsteady Stokes equations

In this work, we analyse space-time reduced basis methods for the efficient numerical simulation of hemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite differences schemes are employed for the time integration of the resulting ordinary differential equation (ODE). Space-time reduced basis (ST-RB) methods extend the dimensionality reduction paradigm to the temporal dimension, projecting the full-order problem onto a low-dimensional spatio-temporal subspace. Our goal is to investigate the application of ST-RB methods to the unsteady incompressible Stokes equations, with a particular focus on stability. High-fidelity simulations are performed using the Finite Element (FE) method and BDF2 as time marching scheme. We consider two different ST-RB methods. In the first one - called ST-GRB - space-time model order reduction is achieved by means of a Galerkin projection; a spatio-temporal velocity basis enrichment procedure is introduced to guarantee stability. The second method - called ST-PGRB - is characterized by a Petrov--Galerkin projection, stemming from a suitable minimization of the FOM residual, that allows to automatically attain stability. The classical RB method - denoted as SRB-TFO - serves as a baseline for the theoretical development. Numerical tests have been conducted on an idealized symmetric bifurcation geometry and on the patient-specific one of a femoropopliteal bypass. The results show that both ST-RB methods provide accurate approximations of the high-fidelity solutions, while considerably reducing the computational cost. In particular, the ST-PGRB method exhibits the best performance, as it features a better computational efficiency while retaining accuracies in accordance with theoretical expectations.Comment: 30 pages (25 + 5 in appendix), 4 figures, 4 tables. To appear on SIAM Journal on Scientific Computing (SISC

674 insertional mutagenesis to identify mechanisms of cetuximab resistance in colorectal cancer

Anti-cancer drugs designed to target specific molecular pathways have shown an excellent therapeutic potential but also very poor long-term durability of tumor responses, mainly due to the outbreak of resistant clones among the residual neoplastic cell population. For that reason, understanding the molecular mechanisms underlying the onset of anti-cancer drug resistance (ACDR) is one of the major goals of clinical research. ACDR has been widely studied by DNA/RNA sequencing of primary human samples and several culprits identified. We have previously developed an approach based on lentiviral vector (LV)-induced insertional mutagenesis that allowed to identify the genes involved in lapatinib and erlotinib resistance on HER2+ human breast cancer cell lines and EGFR+ pancreatic cell line respectively. Here we took advantage of this platform to investigate ACDR genes in colorectal cancer (CRC). Cetuximab, anti-EGFR monoclonal antibody, is used as first line therapy in metastatic CRC, which results in prolonged survival of treated patients. However, nearly all patients relapse due to ACDR. We thus selected CRC cells sensitive to cetuximab deriving either from five microsatellite stable cell lines or from eight Patient Derived Xenografts (PDX), primary human CRC cells implanted subcutaneously into immunodeficient mice (NSG). To induce insertional mutagenesis we generated a luciferase-expressing LV harboring the SFFV enhancer/promoter in the long terminal repeats able to perturb the expression of genes nearby the integration site. As control, we used a non-genotoxic SIN-LV. We set up a collagenase IV-based disaggregation protocol that allows single-cell suspension and a serum-free culture condition to maintain the stemness of in vitro cultured cells. This protocol allowed to efficiently disaggregate and expand CRC cells in vitro as well as reach a LV copy number per cell ranging from 0.25 to 5.6. Luciferase gene expression was stable and allowed live-animal monitoring for up to 30 weeks after transplant. CRC-0069 and -0077 PDXs and NCI-H508 and HDC82 cell lines were transduced ex vivo and kept in vitro and/or transplanted in NSG mice. After in vitro or in vivo expansion of the transduced CRCs cetuximab treatment was applied. After an initial shrinking of the tumor mass in mice we observed ACDR in 3 out of 10 mice transplanted with NCI-H508 cells transduced with SFFV-LV and in none of the controls. Genomic DNA from resistant cells is being used for insertion site (IS) analysis to identify common IS, ACDR gene candidates. IS obtained from SIN-LV groups will be used to filter LV integration biases, whereas IS from SFFV-LV transduced cells but not treated with cetuximab will be used to filter mutations that provide a proliferative advantage unrelated to cetuximab treatment. We will validate the most promising candidates by LV-mediated overexpression and knockdown techniques. This approach could pave the way to perform insertional mutagenesis-based forward genetics studies on primary human samples