ABSTRACT
For micelles, "shape" is prominent in rheological computations of fluid flow, but this "shape" is often expressed too informally to be useful for rigorous analyses. We formalize topological "shape equivalence" of micelles, both globally and locally, to enable visualization of computational fluid dynamics. Although topological methods in visualization provide significant insights into fluid flows, this opportunity has been limited by the known difficulties in creating representative geometry. We present an agile geometric algorithm to represent the micellar shape for input into fluid flow visualizations. We show that worm-like and cylindrical micelles have formally equivalent shapes, but that visualization accentuates unexplored differences. This global-local paradigm is extensible beyond micelles.
ABSTRACT
This study involves the mathematical modelling of long-term HIV dynamics. The proposed model is able to predict the entire trajectory of the disease: initial viremia in the early weeks of the infection, latency, and progression to AIDS; a range spanning approximately ten years. The model outcomes were compared to clinical data and significant agreement was achieved. The formulated model considers all important population compartments including macrophages, latently-infected CD4+ T-cells, and cytotoxic T-lymphocytes (CTLs), an attempt which in many respects is novel in the area of HIV modelling. The ranges of the model parameters and initial conditions were obtained from literature, and their values were determined in this work directly by fitting published clinical data. Furthermore, the simulation results emphasize the importance of macrophages in HIV infection and progression to AIDS and show a clear correlation between the level of CTLs and HIV progression. The ability of the model to correlate analytical data gives credibility to its predictions, a fact that will be exploited in future research in modelling immunological and pharmacological avenues of treatment.
