Physical Sciences and Mathematics Commons^™

Stochastic Calculations For Computation Of Radiation Effects And Cell Survivability Under Voltage Pulsing, Madhuri Ganapathiraju

Electrical & Computer Engineering Theses & Dissertations

Statistical computations are an important tool for the analysis of stochastic phenomena and processes that are characterized by variability. Biological systems (e.g., cells, tissues etc.) are perfect examples wherein response to a given external stimulus can be varied and needs to be adequately considered. The Monte Carlo method of analysis has now been recognized as the most effective way of treating stochastic variability.

This thesis uses Monte Carlo based simulations to probe two problems that require the quantification and modeling of effects caused by energy deposition onto biological matter from external sources. One problem involves the probabilistic study of the …

Radical Impact Of Change In Actions And Confidence Index On Reverse Decision Making An Application Based Study, Swatee Trimbak Paithankar

Engineering Management & Systems Engineering Theses & Dissertations

While making decisions under uncertainty, people are often unaware of the logical approach to form the decision process. It is assumed that collecting details, analyzing and evaluating data is enough to make 'proper' decisions. However, past research in the decision making arena has significantly validated that there exists a class of decision problems which is complex, ill-structured and not defined to the level where decision makers can draw logical conclusions based on existing traditional decision approaches. RDM (reverse decision making), one of the novel approaches of decision making under conditions of uncertainty, has shown potential towards addressing some of these …

Mathematical Models Of Prevascular Tumor Growth By Diffusion, Sophia A. Maggelakis

Mathematics & Statistics Theses & Dissertations

A study of several complementary mathematical models that describe the early, prevascular stages of solid tumor growth by diffusion under various simplifying assumptions is presented. The advantage of these models is that their degree of complexity is relatively low, which ensures fairly straightforward comparisons with experimental or clinical data (as it becomes available), yet they are mathematically sophisticated enough to capture the main biological phenomena of interest.

The tumor growth and cell proliferation rate are assumed to depend on the local concentrations of nutrients and inhibitory factors. The effects of geometry and spatially non-uniform inhibitor production and non-uniform nutrient consumption …