Nonlinear weakly curved rod by Γ-Convergence

We present a nonlinear model of weakly curved rod, namely the type of curved rod where the curvature is of the order of the diameter of the cross-section. We use an approach analogous to the one for rods and curved rods and start from the strain energy functional of three dimensional nonlinear elasticity. We do not impose any constitutional behavior of the material and work in a general framework. To derive the model, by means of Γ-convergence, we need to set the order of strain energy (i.e., its relation to the thickness of the body h). We analyze the situation when the strain energy (divided by the order of volume) is of the order h 4. This is the same approach as the one used in Föppl-von Kármán model for plates and the analogous model for rods. The obtained model is analogous to Marguerre-von Kármán for shallow shells and its linearization is the linear shallow arch model which can be found in the literature

Trends and outcome of neoadjuvant treatment for rectal cancer: A retrospective analysis and critical assessment of a 10-year prospective national registry on behalf of the Spanish Rectal Cancer Project

Introduction: Preoperative treatment and adequate surgery increase local control in rectal cancer. However, modalities and indications for neoadjuvant treatment may be controversial. Aim of this study was to assess the trends of preoperative treatment and outcomes in patients with rectal cancer included in the Rectal Cancer Registry of the Spanish Associations of Surgeons. Method: This is a STROBE-compliant retrospective analysis of a prospective database. All patients operated on with curative intention included in the Rectal Cancer Registry were included. Analyses were performed to compare the use of neoadjuvant/adjuvant treatment in three timeframes: I)2006–2009; II)2010–2013; III)2014–2017. Survival analyses were run for 3-year survival in timeframes I-II. Results: Out of 14, 391 patients, 8871 (61.6%) received neoadjuvant treatment. Long-course chemo/radiotherapy was the most used approach (79.9%), followed by short-course radiotherapy ± chemotherapy (7.6%). The use of neoadjuvant treatment for cancer of the upper third (15-11 cm) increased over time (31.5%vs 34.5%vs 38.6%, p = 0.0018). The complete regression rate slightly increased over time (15.6% vs 16% vs 18.5%; p = 0.0093); the proportion of patients with involved circumferential resection margins (CRM) went down from 8.2% to 7.3%and 5.5% (p = 0.0004). Neoadjuvant treatment significantly decreased positive CRM in lower third tumors (OR 0.71, 0.59–0.87, Cochrane-Mantel-Haenszel P = 0.0008). Most ypN0 patients also received adjuvant therapy. In MR-defined stage III patients, preoperative treatment was associated with significantly longer local-recurrence-free survival (p < 0.0001), and cancer-specific survival (p < 0.0001). The survival benefit was smaller in upper third cancers. Conclusion: There was an increasing trend and a potential overuse of neoadjuvant treatment in cancer of the upper rectum. Most ypN0 patients received postoperative treatment. Involvement of CRM in lower third tumors was reduced after neoadjuvant treatment. Stage III and MRcN + benefited the most