{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T06:19:22Z","timestamp":1789193962162,"version":"build-2803163510"},"reference-count":20,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2011,3,31]],"date-time":"2011-03-31T00:00:00Z","timestamp":1301529600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2011,4]]},"abstract":"<jats:sec><jats:title><jats:bold>Purpose:<\/jats:bold><\/jats:title><jats:p>The objectives of this study were (i) to develop a dose calculation method for permanent prostate implants that incorporates a clinically motivated model for edema and (ii) to illustrate the use of the method by calculating the preimplant dosimetry error for a reference configuration of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0001.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0001\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0002.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0002\"\/>, and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0003.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0003\"\/> seeds subject to edema\u2010induced motions corresponding to a variety of model parameters.<\/jats:p><\/jats:sec><jats:sec><jats:title><jats:bold>Methods:<\/jats:bold><\/jats:title><jats:p>A model for spatially anisotropic edema that resolves linearly with time was developed based on serial magnetic resonance imaging measurements made previously at our center to characterize the edema for a group of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0004.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0004\"\/> prostate implant patients [R. S. Sloboda <jats:italic>et al.<\/jats:italic>, \u201cTime course of prostatic edema post permanent seed implant determined by magnetic resonance imaging,\u201d Brachytherapy 9, 354\u2013361 (2010)]. Model parameters consisted of edema magnitude, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0005.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0005\"\/>, and period, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0006.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0006\"\/>. The TG\u201043 dose calculation formalism for a point source was extended to incorporate the edema model, thus enabling calculation via numerical integration of the cumulative dose around an individual seed in the presence of edema. Using an even power piecewise\u2010continuous polynomial representation for the radial dose function, the cumulative dose was also expressed in closed analytical form. Application of the method was illustrated by calculating the preimplant dosimetry error, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0007.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0007\"\/>, in a <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0008.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0008\"\/> volume for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0009.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0009\"\/> (Oncura 6711), <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0010.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0010\"\/> (Theragenics 200), and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0011.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0011\"\/> (IsoRay CS\u20101) seeds arranged in the Radiological Physics Center test case 2 configuration for a range of edema relative magnitudes <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0012.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0012\"\/> and periods <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0013.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0013\"\/>. Results were compared to preimplant dosimetry errors calculated using a variation of the isotropic edema model developed by Chen <jats:italic>et al.<\/jats:italic> [\u201cDosimetric effects of edema in permanent prostate seed implants: A rigorous solution,\u201d Int. J. Radiat. Oncol., Biol., Phys. 47, 1405\u20131419 (2000)].<\/jats:p><\/jats:sec><jats:sec><jats:title><jats:bold>Results:<\/jats:bold><\/jats:title><jats:p>As expected,<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0014.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0014\"\/> for our edema model indicated underdosage in the calculation volume with a clear dependence on seed and calculation point positions, and increased with increasing values of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0015.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0015\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0016.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0016\"\/>. Values of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0017.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0017\"\/> were generally larger near the ends of the virtual prostate in the RPC phantom compared with more central locations. For edema characteristics similar to the population average values previously measured at our center, i.e., <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0018.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0018\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0019.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0019\"\/>, mean values of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0020.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0020\"\/> in an axial plane located 1.5 cm from the center of the seed distribution were 8.3% for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0021.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0021\"\/> seeds, 7.5% for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0022.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0022\"\/> seeds, and 2.2% for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0023.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0023\"\/> seeds. Maximum values of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0024.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0024\"\/> in the same plane were about 1.5 times greater. Note that detailed results strictly apply only for loose seed implants where the seeds are fixed in tissue and move in synchrony with that tissue.<\/jats:p><\/jats:sec><jats:sec><jats:title><jats:bold>Conclusions:<\/jats:bold><\/jats:title><jats:p>A dose calculation method for permanent prostate implants incorporating spatially anisotropic linearly time\u2010resolving edema was developed for which cumulative dose can be written in closed form. The method yields values for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp8926-math-0025.png\" xlink:title=\"urn:x-wiley:00942405:media:mp8926:mp8926-math-0025\"\/> that differ from those for spatially isotropic edema. The method is suitable for calculating pre\u2010 and postimplant dosimetry correction factors for clinical seed configurations when edema characteristics can be measured or estimated.<\/jats:p><\/jats:sec>","DOI":"10.1118\/1.3568926","type":"journal-article","created":{"date-parts":[[2011,4,1]],"date-time":"2011-04-01T14:43:57Z","timestamp":1301669037000},"page":"2289-2298","source":"Crossref","is-referenced-by-count":4,"title":["Dose calculation for permanent prostate implants incorporating spatially anisotropic linearly time\u2010resolving edema"],"prefix":"10.1002","volume":"38","author":[{"given":"T. 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