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Growing evidence has revealed that, for a single-focused multileaf collimator, lateral penumbra width is leaf position dependent and largely attributed to the leaf end shape. In our study, an analytical method for leaf end induced lateral penumbra modelling is formulated using Tangent Secant Theory. Compared with Monte Carlo simulation and ray tracing algorithm, our model serves well the purpose of cost-efficient penumbra evaluation. Leaf ends represented in parametric forms of circular arc, elliptical arc, B\u00e9zier curve, and B-spline are implemented. With biobjective function of penumbra mean and variance introduced, genetic algorithm is carried out for approximating the Pareto frontier. Results show that for circular arc leaf end objective function is convex and convergence to optimal solution is guaranteed using gradient based iterative method. It is found that optimal leaf end in the shape of B\u00e9zier curve achieves minimal standard deviation, while using B-spline minimum of penumbra mean is obtained. For treatment modalities in clinical application, optimized leaf ends are in close agreement with actual shapes. Taken together, the method that we propose can provide insight into leaf end shape design of multileaf collimator.<\/jats:p>","DOI":"10.1155\/2016\/9515794","type":"journal-article","created":{"date-parts":[[2016,1,19]],"date-time":"2016-01-19T21:35:10Z","timestamp":1453239310000},"page":"1-13","source":"Crossref","is-referenced-by-count":3,"title":["Lateral Penumbra Modelling Based Leaf End Shape Optimization for Multileaf Collimator in Radiotherapy"],"prefix":"10.1155","volume":"2016","author":[{"given":"Dong","family":"Zhou","sequence":"first","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peiqing","family":"Ye","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/s0167-8140(99)00062-6"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1002\/ijc.1038"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.radmeas.2007.01.010"},{"issue":"3","key":"4","doi-asserted-by":"crossref","first-page":"219","DOI":"10.7785\/tcrt.2012.500197","volume":"10","year":"2011","journal-title":"Technology in Cancer Research and Treatment"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/s13246-011-0070-8"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.4103\/0971-6203.42757"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/461801"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1088\/0031-9155\/53\/11\/017"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s00291-009-0187-2"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/0360-3016(95)00096-H"},{"key":"12","year":"2004"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejmp.2013.07.127"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1118\/1.4866228"},{"issue":"3","key":"15","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1120\/jacmp.v11i3.3101","volume":"11","year":"2010","journal-title":"Journal of Applied Clinical Medical Physics"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/9515794.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/9515794.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2016\/9515794.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T10:04:29Z","timestamp":1589623469000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2016\/9515794\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"references-count":14,"alternative-id":["9515794","9515794"],"URL":"https:\/\/doi.org\/10.1155\/2016\/9515794","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]}}}