ABSTRACT Purpose: To determine independent predictors of inguinal lymph node (ILN) metastasis in patients with penile cancer. Patients and methods: We retrospectively analyzed all patients with penile cancer who underwent surgery at our medical center in the last ten years (n=157). Using univariate and multivariate logistic-regression models, we assessed associations with age, medical-history, phimosis, onset-time, number and maximum diameter of involved ILNs measured by imaging, pathological T stage, degree of tumor differentiation and/or cornification, lymphatic vascular infiltration (LVI), nerve infiltration, and ILN metastases. Interaction and stratified analyses were used to assess age, phimosis, onset time, number of ILNs, cornification, and nerve infiltration. Results: A total of 110 patients were included in the study. Multiple logistic regression analysis showed that the following factors were significantly correlated with ILN metastasis: maximum diameter of enlarged ILNs, T stage, pathological differentiation, and LVI. Among patients with a maximum ILN diameter ≥1.5cm, 50% had lymph node metastasis whereas 30.6% patients with a maximum ILN diameter <1.5cm showed LNM. Among 44 patients with stage Ta/T1, 10 showed ILN metastases, while 47.0% patients with stage T2 showed ILN metastases. Among 40 patients with highly differentiated penile-cancer, eight showed ILN metastasis, while 47.1% patients with low-to-middle differentiation showed ILN metastases. The rate of LNM was 33.3% in the LVI-free group and 64.3% in the LVI group. Conclusion: Our single-center results suggested that maximum ILN diameter, pathological T stage, pathological differentiation, and LVI were independent risk factors for ILN metastases.

In this paper, a strongly nonlinear coupled elliptic-parabolic system modelling a class of engineering problems with heat effect is studied. Existence of a weak solution is first established by Schauder fixed point theorem, where the coupled functions σ(s), k(s) are assumed to be bounded. The uniqueness of the solution is obtained by applying Meyers' theorem and assuming that σ(s), k(s) are Lipschitz continuous. The regularity of the solution is then analyzed in dimension d < 2 under the assumptions on σ(s), k(s) ∈ C2(R) and the boundedness of their derivatives of second order. Finally, the blow-up phenomena of the system are studied. Mathematical subject classification: 35J60, 35K55.

In this work, a stationary Stokes flow with thermal effects is studied both mathematically and numerically. First, existence, uniqueness and regularity of the weak solution of the problem are established. Next, finite element approximation to the problem, based on a fixed point algorithm, is proposed. Then, an error estimate between continuous solution and discrete one is obtained. Finally, some numerical tests are presented to confirm the theoretical results.