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Articles 1 - 5 of 5
Full-Text Articles in Medicine and Health Sciences
Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein
Modeling An Infection Outbreak With Quarantine: The Sibkr Model, Mikenna Dew, Amanda Langosch, Theadora Baker-Wallerstein
Rose-Hulman Undergraduate Mathematics Journal
Influenza is a respiratory infection that places a substantial burden in the world population each year. In this project, we study and interpret a data set from a flu outbreak in a British boarding school in 1978 with mathematical modeling. First, we propose a generalization of the SIR model based on the quarantine measure in place and establish the long-time behavior of the model. By analyzing the model mathematically, we determine the analytic formulas of the basic reproduction number, the long-time limit of solutions, and the maximum number of infection population. Moreover, we estimate the parameters of the model based …
Operations Research Methods For Optimization In Radiation Oncology, M Ehrgott, Allen Holder
Operations Research Methods For Optimization In Radiation Oncology, M Ehrgott, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Operations Research has a successful tradition of applying mathematical analysis to a wide range of applications, with one of the burgeoning areas of growth being in medical physics. The original application was in the optimal design of the influence map for a radiotherapy treatment, a problem that has continued to receive attention. However, operations research has been applied to other clinical problems like patient scheduling, vault design, and image alignment. The overriding theme of this article is to present how techniques in operations research apply to clinical problems, which we accomplish in three parts. First, we present the perspective from …
A Clustering Approach For Optimizing Beam Angles In Imrt Planning, Gino J. Lim, Allen Holder, Josh Reese
A Clustering Approach For Optimizing Beam Angles In Imrt Planning, Gino J. Lim, Allen Holder, Josh Reese
Mathematical Sciences Technical Reports (MSTR)
In this paper we introduce a p-median problem based clustering heuristic for selecting efficient beam angles for intensity-modulated radiation therapy. The essence of the method described here is the clustering of beam angles according to probability that an angle will be observed in the final solution and similarities among different angles and the selection of a representative angle from each of the p resulting cluster cells. We conduct experiments using several combinations of modeling parameters to find the conditions where the heuristic best performs. We found a combination of such parameters that outperformed all other parameters on three of the …
Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G Mcquillen, D Nevin, P Uhlig, B Salter
Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G Mcquillen, D Nevin, P Uhlig, B Salter
Mathematical Sciences Technical Reports (MSTR)
Optimally designing radiotherapy and radiosurgery treatments to increase the likelihood of a successful recovery from cancer is an important application of operations research. Researchers have been hindered by the lack of academic software that supports head-to-head comparisons of different techniques, and this article addresses the inherent difficulties of designing and implementing an academic treatment planning system. In particular, this article details the algorithms and the software design of Radiotherapy optimAl Design (RAD).
Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim
Tracking Plasma Lactate Concentration In Vivo With A Catheter-Tip L-Lactate Sensor, Brett T. Weinzapfel, Mark D. Ball, Lee R. Waite, Nacer E. Abrouk, Shun P. Lim
Mathematical Sciences Technical Reports (MSTR)
To circumvent the problems of repeated blood sampling for in vitro analysis, a catheter-tip L-lactate sensor has been developed. The sensor was tested in anesthetized pigs (n=6). The sensor in vivo tracked the lactate concentration non-linearly, seeming to obey Michaelis-Menten kinetics. Calibration time was short, typically 1.5 min per lactate standard. Furthermore, time drift was small, typically -1.3% to -3.3% per hour of in vivo use.