PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Becky Halpenny.

Title:"Population Dynamics Modeling of Heterotypic Cell Aggregations and Related Parameter Identification Problems"
Seminar:Ph.D. Thesis Defense
Speaker:Yanping Ma/Advisers: Qiang Du & Cheng Dong
Cancer has been one of the leading causes of death around the world for decades, and metastasis, the spread of the tumor cells from the primary site to other locations in the body via the lymphatic system or through the blood stream, is responsible for most of the cancer deaths. Massive experimental studies have been done in these areas. The work of this thesis brings together the experimental, numerical, and mathematical studies on the step of polymorphonuclear neutrophils (PMNs) tethering to the vascular endothelial cells (EC), and the subsequent melanoma cell emboli formation in a nonlinear shear flow, both of which are important in tumor cell extravasations from the circulation during metastasis. The primary focus of this work is the development of mathematical models of heterotypic aggregation between PMNs and melanoma cells in the near-wall region of an in vitro parallel-plate flow chamber. We applied a population balance model based on the Smoluchowski coagulation equation to study the process, and then simulated in vivo cell-substrate adhesion from the vasculatures by combining mathematical modeling and numerical simulations with experimental observations. A new coagulation kernel was proposed. We developed a multiscale near-wall aggregation model, which to the best of our knowledge, was the first one that could incorporate the effects of both cell deformation and general ratios of heterotypic cells on the cell aggregation process. Quantitative agreement was found between numerical predictions and in vitro experiments. The effects of factors, including: intrinsic binding molecule properties, near-wall heterotypic cell concentrations, and cell deformations on the coagulation process, were discussed. Sensitivity analysis has been done, and the reaction coefficient along with the critical bond number on the aggregation process was recommended as the most critical variables. We could design some more experimental studies about them. The success of mathematical modeling not only depends on the theoretical model development, but also crucially relies on the accuracy of parameter estimations. Following the comparisons between numerical simulations and experimental results, it is reasonable to propose that the parameters in our model, instead of being constants over time, could be modeled by functions with stochastic uncertainties. The latter half of this thesis focused on the application of the Bayesian framework to the parameter identification problems for the models we proposed earlier, and hence, provided quantitative instead of purely qualitative analyses for the inverse problems. We adopted the Bayesian framework studied in literatures, and theoretically verified the assumptions for our specific models. Moreover, we successfully found the maximum a posteriori estimator (MAP estimator) for the parameters following variational methods, and estimated the sensitivity of the parameters with respect to the data using high dimensional numerical integration methods. Our work thus offered a systematic parameter identification tool specially tailored to our models.

Room Reservation Information

Room Number:MB106
Date:08 / 05 / 2011
Time:09:00am - 11:00am