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Articles 1 - 6 of 6
Full-Text Articles in Mathematics
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).
Optimal Treatments For Photodynamic Therapy, Allen G. Holder, D Llagostera
Optimal Treatments For Photodynamic Therapy, Allen G. Holder, D Llagostera
Mathematics Faculty Research
Photodynamic therapy is a complex treatment for neoplastic diseases that uses the light-harvesting properties of a photosensitizer. The treatment depends on the amount of photosensitizer in the tissue and on the amount of light that is focused on the targeted area. We use a pharmacokinetic model to represent a photosensitizer's movement through the anatomy and design treatments with a linear program. This technique allows us to investigate how a treatment's success varies over time.
Treatments Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Ken Kun Zhao
Treatments Of Chlamydia Trachomatis And Neisseria Gonorrhoeae, Ken Kun Zhao
Mathematics Theses
Chlamydia Trachomatis and Neisseria Gonorrhoeae rank as the two most commonly reported sexually transmitted diseases (STDs) in the United States. Under limited budget, publicly funded clinics are not able to screen and treat the two diseases for all patients. They have to make a decision as to which group of population shall go through the procedure for screening and treating the two diseases. Therefore, we propose a cubic integer programming model on maximizing the number of units of cured diseases. At the same time, a two-step algorithm is established to solve the cubic integer program. We further develop a web-server, …
Beam Selection In Radiotherapy Design, M Ehrgott, Allen G. Holder, Josh Reese
Beam Selection In Radiotherapy Design, M Ehrgott, Allen G. Holder, Josh Reese
Mathematics Faculty Research
The optimal design of a radiotherapy treatment depends on the collection of directions from which radiation is focused on the patient. These directions are manually selected by a physician and are typically based on the physician's previous experiences. Once the angles are chosen, there are numerous optimization models that decide a fluency pattern (exposure times) that best treats a patient. So, while optimization techniques are often used to decide the length of time a patient is exposed to a high-energy particle beam, the directions themselves are not optimized. The problem with optimally selecting directions is that the underlying mixed integer …
The Influence Of Dose Grid Resolution On Beam Selection Strategies In Radiotherapy Treatment Design, Ryan Acosta, Matthias Ehrgott, Allen G. Holder, Daniel Nevin, Josh Reese, Bill Salter
The Influence Of Dose Grid Resolution On Beam Selection Strategies In Radiotherapy Treatment Design, Ryan Acosta, Matthias Ehrgott, Allen G. Holder, Daniel Nevin, Josh Reese, Bill Salter
Mathematics Faculty Research
The design of a radiotherapy treatment includes the selection of beam angles (geometry problem), the computation of a fluence pattern for each selected beam angle (intensity problem), and finding a sequence of configurations of a multilef collimator to deliver the treatment (realization problem). While many mathematical optimization models and algorithms have been proposed for the intensity problem and (to a lesser extent) the realization problem, this is not the case for the geometry problem. In clinical practice, beam directions are manually selected by a clinician and are typically based on the clinician’s experience. Solving the beam selection problem optimally is …
An Introduction To Systems Biology For Mathematical Programmers, Evind Almaas, Allen G. Holder, Kevin D. Livingstone
An Introduction To Systems Biology For Mathematical Programmers, Evind Almaas, Allen G. Holder, Kevin D. Livingstone
Mathematics Faculty Research
Many recent advances in biology, medicine and health care are due to computational efforts that rely on new mathematical results. These mathematical tools lie in discrete mathematics, statistics & probability, and optimization, and when combined with savvy computational tools and an understanding of cellular biology they are capable of remarkable results. One of the most significant areas of growth is in the field of systems biology, where we are using detailed biological information to construct models that describe larger entities. This chapter is designed to be an introduction to systems biology for individuals in Operations Research (OR) and mathematical programming …