Browsing by Subject "mathematical model"
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Item Combination therapeutics of Nilotinib and radiation in Acute Lymphoblastic Leukemia as an effective method against drug resistance(2016-08) Penning, JacksonIn this work we combine in vitro experimentation with mathematical modeling to study the combined effect of the tyrosine kinase inhibitor nilotinib and ionizing radiation on acute lymphoblastic leukemia cells. We develop a mathematical model for the cell response to this combined therapy. This mathematical model is parameterized via cell viability experiments conducted at a variety of different levels of nilotinib concentration and radiation exposure. We use this parameterized mathematical model to predict cell viability at new levels of nilotinib concentration. These predictions are then compared with new sets of cell viability experiments. We then investigate the structure of optimal radiation dosing schedules under our mathematical model. Finally, the model is expanded to incorporate an additional toxicity constraint on healthy lymphoblast cells, further characterizing optimized treatment protocols.Item Development of a Mathematical Model to Predict the Role of Surface Runoff and Groundwater Flow in Overfertilization of Surface Waters(Water Resources Research Center, University of Minnesota, 1971-06) Johnson, Jack D.; Straub, Conrad P.A nutrient enrichment accounting mathematical model was devised for the New Prague watershed in Minnesota. The New Prague watershed is 23.3 square miles in area and is predominately a rural watershed. Model input data was collected over a 2 1/2 year period from a stream gauging station and two automatic sampling stations. Over 800 water samples were analyzed. Extensive effort was placed on better understanding the nitrogen and phosphorus cycles. It is evident that the spring runoff process and accumulative winter fertilizer applications constitute the major portion of diffuse sources of nutrients in the watershed. Point sources from feedlots and municipal and industrial effluents contribute only 11 percent of the annual EN (total nitrogen, four components) and 7 percent TP (total phosphorus). Disperse sources accounted for 89 percent of EN and 93 percent of TP, with spring runoff in the two months of March and April accounting for 79 percent of the annual EN and 64 percent of the TP. The nutrient output from the watershed could be decreased by increasing penetration of the large amounts of EN and TP in snowpacks into the soil through land terracing to restart rapid spring runoffs and sub-surface drains to allow rapid drainage during the crop season.Item Mathematical Modeling of Cell Migration: Mechanisms in Dictyostelium discoideum.(2023-03) Felix, BryanThis study aims to understand the biochemical pathways involved in the cytoskeleton of Dictyostelium discoideum, particularly the self-organization process of actin structures. While previous models have explored protein dynamics in various contexts, they tend to oversimplify the underlying biochemical mechanisms. This study presents two extended models that offer updated insights into the chemical interactions and feedback mechanisms of Dictyostelium discoideum. The first model explores how bistability emerges from the topology of the underlying network, while the second model focuses on the mechanisms of filopodia initiation and the role of membrane curvature in their emergence.