Cancer stem cells (CSCs) have been identified in primary breast cancer tissues and cell lines. The CSC population varies widely among cancerous tissues and cell lines, and is often associated with aggressive breast cancers. Despite of intensive research, how the CSC population is regulated within a tumor is still not well understood so far. In this paper, we present a mathematical model to expl...

Sialic acid-binding immunoglobulin-type lectins (Siglecs) are a group of cell surface transmembrane receptors expressed on immune cells, and regulate immune balance in inflammatory diseases. Sepsis is a life-threatened inflammatory syndrome induced by infection, and the pathogenesis of sepsis includes immune dysregulation, inflammation, and coagulation disorder. Here, we reviewed the various ro...

A numerical scheme based on the finite volume approach is developed to solve a binary breakage population balance equation (PBE) nonuniform meshes. The key feature of new that it free common requirement redistributing particle mass neighboring pivots, its formulation simpler compared other methods such as cell average and fixed pivot techniques. produces accurate results for distribution first ...

Because of its relatively low tolerance to elevated temperatures, Macoma balthica (L.) may be one of the first important marine species in temperate coastal areas to suffer from a warming climate. For the last few decades, the abundance of the species in the Dutch Wadden Sea has been seriously declining. At lower latitudes, the southern edge of its range recently shifted several 100s of km to t...

Population balances play an important role in process and bioprocess engineering. They represent PDEs which are often multidimensional. The numerical solution of these is quite challenging in particular for high dimensional problems. For this reason the distribution dynamics are usually represented by the respective moments. As the corresponding dynamic moment equations can only be computed in ...

The paper deals with the convergence analysis of the cell average technique given by J. Kumar et al. [3] to solve the nonlinear aggregation population balance equations. Similarly to our previous paper Giri et al. [1], which considered the fixed pivot technique, the main emphasis here is to check the convergence for five different types of uniform and non-uniform meshes. First, we observed that...

This work presents the convergence of the cell average technique (J. Kumar et al., 2007, Powder Technology 179, 205-228) for solving breakage population balance equation. Similarly to our paper Kumar and Warnecke [5] of this series, we study convergence on four different types of meshes. A second order convergence is proved for uniform, locally uniform and non-uniform smooth meshes. Finally the...

Phenotypic cell-to-cell variability or cell population heterogeneity originates from two fundamentally different sources: unequal partitioning of cellular material at cell division and stochastic fluctuations associated with intracellular reactions. We developed a mathematical and computational framework that can quantitatively isolate both heterogeneity sources and applied it to a genetic netw...