Gliomas, the most common primary brain tumors, are diffusive and highly invasive. The standard treatment for tumors consists of a combination surgery, radiation therapy chemotherapy. Over past few years, mathematical models have been applied to study untreated treated tumors. In an effort improve strategies, we consider simple spatio-temporal model, based on proliferation diffusion, that incorporates effects radiotherapeutic chemotherapeutic treatments. We different schedules therapy,...

Tumor oxygenation status is considered one of the important prognostic markers in cancer since it strongly influences response cells to various treatments; particular, radiation therapy. Thus, a proper and accurate assessment tumor oxygen distribution before treatment may highly affect outcome treatment. The heterogeneous nature hypoxia, mainly influenced by complex microenvironment, often makes its quantification very difficult. usual methods used measure hypoxia are biomarkers...

Tumors cannot grow beyond a certain size (about 1–2 mm in diameter) through simple diffusion of oxygen and other essential nutrients into the tumor. Angiogenesis, formation blood vessels from pre-existing vessels, is crucial observed step, which tumor obtains its own supply. Thus, strategies that interfere with development this vasculature, known as anti-angiogenic therapy, represent novel approach to controlling growth. Several pre-clinical studies have suggested currently available...

The theory of viscoelasticity appears to play a central role in the description materials which exhibit time dependent stress—strain behavior. Various like polymers, some soft biological tissues, and various foods have been already successfully modeled as nonlinear viscoelastic materials.The literature these application areas is replete with different, seemingly unconnected models. aim present paper review classical models provide unifying framework using continuum mechanics formalism.

Abstract The use of multigrid methods in complex fluid flow problems is recent and still under development. In this paper we present a method for the incompressible Navier‐Stokes equations. distinctive features are pressure‐correction as smoother novel continuity‐preserving manner grid coarsening. shear‐driven cavity problem used test case to demonstrate efficiency method.

Brain tissue exhibits viscoelastic behaviour. If loading times are substantially short, static tests not sufficient to determine the complete behaviour of material, and dynamic test methods more appropriate. The concept complex modulus elasticity is a powerful tool for characterizing frequency domain materials. On other hand, it well known that classical models can be generalized by means fractional calculus describe In this paper, Zener model investigated in order brain tissue. fitted...

Abstract A local mode Fourier analysis is used to assess the suitability of SIMPLE pressure‐correction algorithm act as a smoother in multigrid method. The necessary ellipticity Navier‐Stokes equations and their discrete representation are established. theoretical compared with practical results.

Abstract Objective: In recent years, support has increased for the notion that a subpopulation of brain tumour cells in possession properties typically characteristic stem is responsible initiating and maintaining tumour. Unravelling details cell (BTSC) hierarchy, as well interactions these with various therapies, will be essential design optimal treatment strategies. Materials methods: Motivated by this, we have developed mathematical model BTSC hypothesis may aid characterization tumours,...

Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing proliferative and migrative potentials of species. Spatial temporal disturbances lead to adverse hazardous microenvironments for cellular systems reflected in phenotypic heterogeneity within system. In this paper, we study effect on invasive capability species, or mutants, structured grids (in particular, square lattices) under influence site-dependent random proliferation addition...