{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T04:36:06Z","timestamp":1768278966964,"version":"3.49.0"},"reference-count":44,"publisher":"Wiley","issue":"6Part1","license":[{"start":{"date-parts":[[2010,5,13]],"date-time":"2010-05-13T00:00:00Z","timestamp":1273708800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2015,9,1]],"date-time":"2015-09-01T00:00:00Z","timestamp":1441065600000},"content-version":"tdm","delay-in-days":1937,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["aip.org"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:sec><jats:title>Purpose<\/jats:title><jats:p>The present report addresses the question of what could be the appropriate dose and dose rate for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0003.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0003\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0004.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0004\"\/> permanent seed implants for breast cancer as monotherapy for early stage breast cancer. This is addressed by employing a radiobiological methodology, which is based on the linear quadratic model, to identify a biologically effective dose (BED) to the prescription point of the brachytherapy implant, which would produce equivalent cell killing (or same cell survival) when compared to a specified external radiotherapy scheme.<\/jats:p><\/jats:sec><jats:sec><jats:title>Methods<\/jats:title><jats:p>In the present analysis, the tumor and normal tissue BED ratios of brachytherapy and external radiotherapy are examined for different combinations of tumor proliferation constant <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0005.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0005\"\/>, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0006.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0006\"\/> ratios, initial dose rate <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0007.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0007\"\/>, and reference external radiotherapy scheme (50 or 60 Gy in 2 Gy per fraction). The results of the radiobiological analysis are compared against other reports and clinical protocols in order to examine possible opportunities of improvement.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>The analysis indicates that physical doses of approximately 100\u2013110 Gy delivered with an initial dose rate of around <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0008.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0008\"\/> and 78\u201380 Gy delivered at <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0009.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0009\"\/> for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0010.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0010\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0011.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0011\"\/> permanent implants, respectively, are equivalent to 50 Gy external beam radiotherapy (EBRT) in 2 Gy per fraction. Similarly, for physical doses of approximately 115\u2013127 Gy delivered with an initial dose rate of around <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0012.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0012\"\/> and 92 Gy delivered at <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0013.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0013\"\/> for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0014.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0014\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0015.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0015\"\/>, respectively, are equivalent to 60 Gy EBRT in 2 Gy per fraction. It is shown that the initial dose rate required to produce isoeffective tumor response with 50 or 60 Gy EBRT in 2 Gy per fraction increases as the repopulation factor <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0016.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0016\"\/> increases, even though repopulation is also considered in EBRT. Also, the initial dose rate increases as the value of the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0017.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0017\"\/> ratio decreases. The impact of the different <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0018.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0018\"\/> ratios on the ratio of the tumor BEDs is significantly large for both the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0019.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0019\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0020.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0020\"\/> implants with the deviation between the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0021.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0021\"\/> ratios and those using the 4.0 and 3.5 Gy values ranging between 18% and 22% in most of the cases.<\/jats:p><\/jats:sec><jats:sec><jats:title>Conclusions<\/jats:title><jats:p>For the cases of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0022.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0022\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0023.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0023\"\/>, the equivalent physical doses to 50 Gy EBRT in 2 Gy per fraction are associated with an overdosage of the involved normal tissue in the range of 4%\u201316% and an underdosage by 10%\u201315% for a BED for normal tissue, using an <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0024.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0024\"\/> value of 3.0 Gy <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0025.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0025\"\/> of 100 Gy. These values are lower by 10%\u201320% than the published value of 124 Gy for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0026.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0026\"\/> and by about 13% when compared to the published isoeffective dose of 90 Gy for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0027.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0027\"\/>. Similarly, the equivalent physical doses to 60 Gy EBRT in 2 Gy per fraction are associated with an overdosage of the involved normal tissue by 10%\u201320% and an underdosage by 4%\u201310% for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/mp6027-math-0028.png\" xlink:title=\"urn:x-wiley:00942405:media:mp6027:mp6027-math-0028\"\/> of 110 Gy.<\/jats:p><\/jats:sec>","DOI":"10.1118\/1.3426027","type":"journal-article","created":{"date-parts":[[2010,6,4]],"date-time":"2010-06-04T14:07:54Z","timestamp":1275660474000},"page":"2572-2586","update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":16,"title":["A radiobiological investigation on dose and dose rate for permanent implant brachytherapy of breast using  or  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