Glioblastoma of septum pellucidum

A rare case of glioblastoma multiforme (GBM) of septum pellucidum is being reported. There were symptoms of altered behaviour, memory and changes in sensorium. The MRI was suggestive of a tumour arising from the septum pellucidum. Glioblastomas arising from septum pellucidum are rare. While even a partial endoscopic excision of the more common pathology viz. colloid cyst is acceptable, only, a safe maximal excision of a highly malignant pathology like glioblastoma is an acceptable goal in order to give any benefit of surgical exploration to the patient

Dimensional reduction of a fractured medium for a two-phase flow

We consider a porous medium containing a single fracture, and identify the aperture to length ratio as the small parameter ɛ with the fracture permeability and the fracture porosity scaled as exponents of ɛ. We consider a two-phase flow where the flow is governed by the mass balance and the Darcy law. Using formal asymptotic approach, we derive a catalogue of reduced models as the vanishing limit of ɛ. Our derivation provides new models in a hybrid-dimensional setting as well as models which exhibit two-scale behaviour. Several numerical examples confirm the theoretical derivations and provide additional insight.publishedVersio

Modelling and well-posedness of evolutionary differential variational-hemivariational inequalities

In this paper, we study the well-posedness of a class of evolutionary variational-hemivariational inequalities coupled with a nonlinear ordinary differential equation in Banach spaces. The proof is based on an iterative approximation scheme showing that the problem has a unique mild solution. In addition, we established continuity of the flow map with respect to the initial data. Under the general framework, we consider two new applications for modelling of frictional contact with viscoelastic materials, where the friction coefficient $\mu$ depends on an external state variable $\alpha$ and the slip rate $|\dot{u}_\tau|$. In the first application, we consider Coulomb friction with normal compliance, and in the second, normal damped response. In both cases, we present a new first-order approximation of the Dieterich rate-and-state friction law

Splitting method for elliptic equations with line sources

In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is known to be non-standard as the line source causes the solution to be singular. Our main result is a splitting theorem for the solution; we show that the solution admits a split into an explicit, low regularity term capturing the singularity, and a high-regularity correction term $w$ being the solution of a suitable elliptic equation. The splitting theorem states the mathematical structure of the solution; in particular, we find that the solution has anisotropic regularity. More precisely, the solution fails to belong to $H^1$ in the neighbourhood of $\Lambda$, but exhibits piecewise $H^2$-regularity parallel to $\Lambda$. The splitting theorem can further be used to formulate a numerical method in which the solution is approximated via its correction function $w$. This approach has several benefits. Firstly, it recasts the problem as a 3D elliptic problem with a 3D right-hand side belonging to $L^2$, a problem for which the discretizations and solvers are readily available. Secondly, it makes the numerical approximation independent of the discretization of $\Lambda$; thirdly, it improves the approximation properties of the numerical method. We consider here the Galerkin finite element method, and show that the singularity subtraction then recovers optimal convergence rates on uniform meshes, i.e., without needing to refine the mesh around each line segment. The numerical method presented in this paper is therefore well-suited for applications involving a large number of line segments. We illustrate this by treating a dataset (consisting of $\sim 3000$ line segments) describing the vascular system of the brain

Application of data mining techniques in bioinformatics

With the widespread use of databases and the explosive growth in their sizes, there is a need to effectively utilize these massive volumes of data. This is where data mining comes in handy, as it scours the databases for extracting hidden patterns, finding hidden information, decision making and hypothesis testing. Bioinformatics, an upcoming field in today’s world, which involves use of large databases can be effectively searched through data mining techniques to derive useful rules. Based on the type of knowledge that is mined, data mining techniques [1] can be mainly classified into association rules, decision trees and clustering. Until recently, biology lacked the tools to analyze massive repositories of information such as the human genome database [3]. The data mining techniques are effectively used to extract meaningful relationships from these data.Data mining is especially used in microarray analysis which is used to study the activity of different cells under different conditions. Two algorithms under each mining techniques were implemented for a large database and compared with each other. 1. Association Rule Mining: - (a) a priori (b) partition 2. Clustering: - (a) k-means (b) k-medoids 3. Classification Rule Mining:- Decision tree generation using (a) gini index (b) entropy value. Genetic algorithms were applied to association and classification techniques. Further, kmeans and Density Based Spatial Clustering of Applications of Noise (DBSCAN) clustering techniques [1] were applied to a microarray dataset and compared. The microarray dataset was downloaded from internet using the Gene Array Analyzer Software(GAAS).The clustering was done on the basis of the signal color intensity of the genes in the microarray experiment. The following results were obtained:- 1. Association:- For smaller databases, the a priori algorithm works better than partition algorithm and for larger databases partition works better. 2. Clustering:- With respect to the number of interchanges, k-medoids algorithm works better than k-means algorithm. 3. Classification:- The results were similar for both the indices (gini index and entropy value). The application of genetic algorithm improved the efficiency of the association and classification techniques. For the microarray dataset, it was found that DBSCAN is less efficient than k-means when the database is small but for larger database DBSCAN is more accurate and efficient in terms of no. of clusters and time of execution. DBSCAN execution time increases linearly with the increase in database and was much lesser than that of k-means for larger database. Owing to the involvement of large datasets and the need to derive results from them, data mining techniques can be effectively put in use in the field of Bio-informatics [2]. The techniques can be applied to find associations among the genes, cluster similar gene and protein sequences and draw decision trees to classify the genes. Further, the data mining techniques can be made more efficient by applying genetic algorithms which greatly improves the search procedure and reduces the execution time