A 16-Gene Signature Distinguishes Anaplastic Astrocytoma from Glioblastoma

Anaplastic astrocytoma (AA; Grade III) and glioblastoma (GBM; Grade IV) are diffusely infiltrating tumors and are called malignant astrocytomas. The treatment regimen and prognosis are distinctly different between anaplastic astrocytoma and glioblastoma patients. Although histopathology based current grading system is well accepted and largely reproducible, intratumoral histologic variations often lead to difficulties in classification of malignant astrocytoma samples. In order to obtain a more robust molecular classifier, we analysed RT-qPCR expression data of 175 differentially regulated genes across astrocytoma using Prediction Analysis of Microarrays (PAM) and found the most discriminatory 16-gene expression signature for the classification of anaplastic astrocytoma and glioblastoma. The 16-gene signature obtained in the training set was validated in the test set with diagnostic accuracy of 89%. Additionally, validation of the 16-gene signature in multiple independent cohorts revealed that the signature predicted anaplastic astrocytoma and glioblastoma samples with accuracy rates of 99%, 88%, and 92% in TCGA, GSE1993 and GSE4422 datasets, respectively. The protein-protein interaction network and pathway analysis suggested that the 16-genes of the signature identified epithelial-mesenchymal transition (EMT) pathway as the most differentially regulated pathway in glioblastoma compared to anaplastic astrocytoma. In addition to identifying 16 gene classification signature, we also demonstrated that genes involved in epithelial-mesenchymal transition may play an important role in distinguishing glioblastoma from anaplastic astrocytoma.

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.