ANALYTIC APPROXIMATE SOLUTIONS FOR THE 1D AND 2D NONLINEAR FRACTIONAL DIFFUSION EQUATIONS OF FISHER TYPE
COMPTES RENDUS DE L ACADEMIE BULGARE DES SCIENCES
Authors: Ahmed, Hoda F.
Abstract
In this paper, analytical approximate solutions for solving the one dimensional (1D) and two dimensional (2D) fractional time diffusion equations of Fisher type (FTDEFT) are given via the Laplace variational iteration method (LVIM). The proposed method is a combination of two powerful methods; Laplace transform (LT) and variational iteration method (VIM). The achieved solutions are given as a speedily convergent series with simply computable terms. The suggested technique is effective and easy to implement. The proposed technique is tested by introducing three different examples. These examples include the 1D fractional time Fisher equation, the fractional time Burger- Fisher equation and the 2D generalized fractional time Fisher type equation. The obtained solutions demonstrate the accuracy of the proposed method when compared with the exact solutions or the numerical solutions in the existing literature. The conclusion of the study exposes that the LVIM is computationally very effective and accurate to analyze nonlinear fractional differential equations. Also with this method, the nature of results can be scanned when the fractional derivative factors are varied.
Clinical significance of epithelial-mesenchymal transition-related markers expression in the micrometastatic sentinel lymph node of NSCLC
CLINICAL & TRANSLATIONAL ONCOLOGY
Authors: Lafuente-Sanchis, A.; Olmo, A.; Carretero, J.; Alcacer Fernandez-Coronado, J.; Estors-Guerrero, M.; Martinez-Hernandez, N. J.; Cremades, A.; Zuniga, A.; Alcacer, J.; Farras, R.; Cuenca, M.; Galbis-Caravajal, J. M.
Abstract
Objectives Metastatic lymph node affectation is the main prognostic factor in localised lung cancer. However, the pathological study of lymph nodes reveals tumour relapse for 20% of patients after oncological curative surgery. Recently, EMT (epithelial-mesenchymal transition) has been established as one of the main factors related to lymphatic dissemination and metastasis. This study evaluated the prognostic value of EMT-related gene expression in micrometastatic sentinel lymph nodes (SLN) of non-small cell lung cancer (NSCLC) patients. Methods The presence of genes CDH1, CDH2, VIM, TWIST1, SNAI1, SNAI2, ZEB1, and ZEB2 in mRNA was analysed in tumours and in the SLN of NSCLC patients for whom surgery was planned for treatment. The significant association between the expression level of EMT-related markers and patients' clinicopathological characteristics and relapse was assessed. Results Of the 96 patients, 56 (58.33%) presented molecular micrometastasis in SLN, which showed higher CDH1, CDH2, and VIM expressions than non-micrometastatic ones. An association linking a low CDH1/CDH2 ratio in SLN with molecular micrometastasis, adenocarcinoma, and non-smoking patients was found. The multivariate Cox regression analysis proved the prognostic accuracy of the CDH1/CDH2 ratio in SLN. Conclusions The molecular EMT status of SLN could be used as an independent prognosis predictor in early stage NSLCL patients, and as a new tool to better stratify and predict patient outcomes.