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Modeling simple epidemics
Title
Modeling simple epidemics.
Creator
Segovia, Linda., Harriet L. Wilkes Honors College
Abstract/Description
Epidemic models help us predict the outcome of an epidemic. I will discuss and compare two simple epidemic models: a deterministic model implemented by a simple differential equation, and a stochastic model, which is more realistic, but harder to analyze. In both models we assume, for simplicity, that each individual goes through only two stages: healthy (susceptible) and sick (infective). Such models, called SI epidemic models, describe infections with no immunity. We will show that, when...
Show moreEpidemic models help us predict the outcome of an epidemic. I will discuss and compare two simple epidemic models: a deterministic model implemented by a simple differential equation, and a stochastic model, which is more realistic, but harder to analyze. In both models we assume, for simplicity, that each individual goes through only two stages: healthy (susceptible) and sick (infective). Such models, called SI epidemic models, describe infections with no immunity. We will show that, when the population gets large, the more realistic stochastic model approaches the simple deterministic model on the average, which will allow us to see that the deterministic model is used for a good reason.
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Date Issued
2007
PURL
http://purl.flvc.org/FAU/40972
Subject Headings
Biomathematics, Medicine, Mathematics, Population biology, Mathematics, Epidemiology, Mathematical models
Format
Document (PDF)
Migration induced epidemics: dynamics of flux-based multipatch models
Title
Migration induced epidemics: dynamics of flux-based multipatch models.
Creator
Liebovitch, Larry S., Schwartz, Ira B.
Date Issued
2004
PURL
http://purl.flvc.org/FAU/165227
Subject Headings
Communicable diseases--Epidemiology--Mathematical models, Emerging infectious diseases, Epidemiologic Methods, Epidemiology, Biomathematics, Medicine-Mathematics, Dynamics-Mathematical models
Format
Document (PDF)
Nonlinear properties of cardiac rhythm abnormalities
Title
Nonlinear properties of cardiac rhythm abnormalities.
Creator
Liebovitch, Larry S., Todorov, Angelo T., Zochowski, Michal, Scheurle, Daniela, Colgin, Laura, Wood, Mark A., Ellenbogen, Kenneth A., Herre, John M., Bernstein, Robert C.
Date Issued
1999-03
PURL
http://purl.flvc.org/fau/165473
Subject Headings
Biophysics--Research, Medicine-Mathematics, Arrythmia--therapy, Fractals, Nonlinear systems, Probabilities-Mathematical Models
Format
Document (PDF)
Empirical beam angle optimization for lung cancer intensity modulated radiation therapy
Title
Empirical beam angle optimization for lung cancer intensity modulated radiation therapy.
Creator
Doozan, Brian, Pella, Silvia, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
Empirical methods of beam angle optimization (BAO) are tested against the BAO that is currently employed in Eclipse treatment planning software. Creating an improved BAO can decrease the amount of time a dosimetrist spends on making a treatment plan, improve the treatment quality and enhance the tools an inexperienced dosimetrist can use to develop planning techniques. Using empirical data created by experienced dosimetrists from 69 patients treated for lung cancer, the most frequently used...
Show moreEmpirical methods of beam angle optimization (BAO) are tested against the BAO that is currently employed in Eclipse treatment planning software. Creating an improved BAO can decrease the amount of time a dosimetrist spends on making a treatment plan, improve the treatment quality and enhance the tools an inexperienced dosimetrist can use to develop planning techniques. Using empirical data created by experienced dosimetrists from 69 patients treated for lung cancer, the most frequently used gantry angles were applied to four different regions in each lung to gather an optimal set of fields that could be used to treat future lung cancer patients. This method, given the moniker FAU BAO, is compared in 7 plans created with the Eclipse BAO choosing 5 fields and 9 fields. The results show that the conformality index improved by 30% or 3% when using the 5 and 9 fields. The conformation number was better by 12% from the 5 fields and 9% from the 9 fields. The organs at risk (OAR) were overall more protected to produce fewer nonstochastic effects from the radiation treatment with the FAU BAO.
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Date Issued
2014
PURL
http://purl.flvc.org/fau/fd/FA00004280, http://purl.flvc.org/fau/fd/FA00004280
Subject Headings
Cancer -- Radiotherapy, Image guided radiation therapy, Lung cancer -- Treatment, Medical physics, Medical radiology -- Data processing, Medicine -- Mathematical models
Format
Document (PDF)
Sparse Modeling Applied to Patient Identification for Safety in Medical Physics Applications
Title
Sparse Modeling Applied to Patient Identification for Safety in Medical Physics Applications.
Creator
Lewkowitz, Stephanie, Kalantzis, Georgios, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
Every scheduled treatment at a radiation therapy clinic involves a series of safety protocol to ensure the utmost patient care. Despite safety protocol, on a rare occasion an entirely preventable medical event, an accident, may occur. Delivering a treatment plan to the wrong patient is preventable, yet still is a clinically documented error. This research describes a computational method to identify patients with a novel machine learning technique to combat misadministration.The patient...
Show moreEvery scheduled treatment at a radiation therapy clinic involves a series of safety protocol to ensure the utmost patient care. Despite safety protocol, on a rare occasion an entirely preventable medical event, an accident, may occur. Delivering a treatment plan to the wrong patient is preventable, yet still is a clinically documented error. This research describes a computational method to identify patients with a novel machine learning technique to combat misadministration.The patient identification program stores face and fingerprint data for each patient. New, unlabeled data from those patients are categorized according to the library. The categorization of data by this face-fingerprint detector is accomplished with new machine learning algorithms based on Sparse Modeling that have already begun transforming the foundation of Computer Vision. Previous patient recognition software required special subroutines for faces and di↵erent tailored subroutines for fingerprints. In this research, the same exact model is used for both fingerprints and faces, without any additional subroutines and even without adjusting the two hyperparameters. Sparse modeling is a powerful tool, already shown utility in the areas of super-resolution, denoising, inpainting, demosaicing, and sub-nyquist sampling, i.e. compressed sensing. Sparse Modeling is possible because natural images are inherrently sparse in some bases, due to their inherrant structure. This research chooses datasets of face and fingerprint images to test the patient identification model. The model stores the images of each dataset as a basis (library). One image at a time is removed from the library, and is classified by a sparse code in terms of the remaining library. The Locally Competetive Algorithm, a truly neural inspired Artificial Neural Network, solves the computationally difficult task of finding the sparse code for the test image. The components of the sparse representation vector are summed by `1 pooling, and correct patient identification is consistently achieved 100% over 1000 trials, when either the face data or fingerprint data are implemented as a classification basis. The algorithm gets 100% classification when faces and fingerprints are concatenated into multimodal datasets. This suggests that 100% patient identification will be achievable in the clinal setting.
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004721, http://purl.flvc.org/fau/fd/FA00004721
Subject Headings
Computer vision in medicine, Diagnostic imaging -- Data processing, Mathematical models, Medical errors -- Prevention, Medical physics, Sampling (Statistics)
Format
Document (PDF)
The Advantages of Collimator Optimization for Intensity Modulated Radiation Therapy
Title
The Advantages of Collimator Optimization for Intensity Modulated Radiation Therapy.
Creator
Doozan, Brian, Leventouri, Theodora, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The goal of this study was to improve dosimetry for pelvic, lung, head and neck, and other cancers sites with aspherical planning target volumes (PTV) using a new algorithm for collimator optimization for intensity modulated radiation therapy (IMRT) that minimizes the x-jaw gap (CAX) and the area of the jaws (CAA) for each treatment field. A retroactive study on the effects of collimator optimization of 20 patients was performed by comparing metric results for new collimator optimization...
Show moreThe goal of this study was to improve dosimetry for pelvic, lung, head and neck, and other cancers sites with aspherical planning target volumes (PTV) using a new algorithm for collimator optimization for intensity modulated radiation therapy (IMRT) that minimizes the x-jaw gap (CAX) and the area of the jaws (CAA) for each treatment field. A retroactive study on the effects of collimator optimization of 20 patients was performed by comparing metric results for new collimator optimization techniques in Eclipse version 11.0. Keeping all other parameters equal, multiple plans are created using four collimator techniques: CA0, all fields have collimators set to 0°, CAE, using the Eclipse collimator optimization, CAA, minimizing the area of the jaws around the PTV, and CAX, minimizing the x-jaw gap. The minimum area and the minimum x-jaw angles are found by evaluating each field beam’s eye view of the PTV with ImageJ and finding the desired parameters with a custom script. The evaluation of the plans included the monitor units (MU), the maximum dose of the plan, the maximum dose to organs at risk (OAR), the conformity index (CI) and the number of fields that are calculated to split. Compared to the CA0 plans, the monitor units decreased on average by 6% for the CAX method with a p-value of 0.01 from an ANOVA test. The average maximum dose remained within 1.1% difference between all four methods with the lowest given by CAX. The maximum dose to the most at risk organ was best spared by the CAA method, which decreased by 0.62% compared to the CA0. Minimizing the x-jaws significantly reduced the number of split fields from 61 to 37. In every metric tested the CAX optimization produced comparable or superior results compared to the other three techniques. For aspherical PTVs, CAX on average reduced the number of split fields, lowered the maximum dose, minimized the dose to the surrounding OAR, and decreased the monitor units. This is achieved while maintaining the same control of the PTV.
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Date Issued
2017
PURL
http://purl.flvc.org/fau/fd/FA00004804, http://purl.flvc.org/fau/fd/FA00004804
Subject Headings
Radiation--Dosage., Optical engineering., Medical physics., Image-guided radiation therapy., Cancer--Radiotherapy., Medical radiology--Data processing., Medicine--Mathematical models.
Format
Document (PDF)