{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,22]],"date-time":"2026-10-22T07:29:57Z","timestamp":1792654197187,"version":"4.5.0"},"reference-count":26,"publisher":"Wiley","issue":"11","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T00:00:00Z","timestamp":1761955200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2025,11]]},"abstract":"Abstract<\/jats:title>\n \n Background<\/jats:title>\n The Spatially Fractionated Radiotherapy (SFRT) treatment technique is characterized by its highly heterogeneous dose distribution, with an alternating pattern of high\u2010 and low\u2010dose areas inside large tumors. For lattice SFRT, a technique that utilizes high\u2010dose spheres, a common obstacle is maximizing the number of high\u2010dose spheres within the tumor while maintaining spacing rules to preserve the low\u2010dose regions.<\/jats:p>\n <\/jats:sec>\n \n Purpose<\/jats:title>\n We propose a novel algorithm that uses the R\u00f6dl nibble methodology to optimize the number of lattice vertices placement for SFRT planning. By increasing the number of vertices, tumor dose metrics can be enhanced, potentially improving patient outcomes.<\/jats:p>\n <\/jats:sec>\n \n Materials and methods<\/jats:title>\n \n Our new proposed algorithm, which utilizes the R\u00f6dl nibble technique, was benchmarked against the standard lattice deployment method, where the lattice centers are placed onto a rigid grid within the tumor. Both techniques used a 1.5\u00a0cm diameter lattice sphere, with center\u2010to\u2010center spacing of 3\u221a2\u00a0cm. Twenty patients previously treated with MLC\u2010based 3D\u2010conformal SFRT were included in this cohort. All replans utilized four full VMAT arcs, with collimator angles in increments of 15\u00b0, 6 MV\u2010FFF beams, and were to be delivered on a C\u2010arm LINAC. Both sets of replans used the same optimization objectives and priorities and were prescribed a nominal dose of 15\u00a0Gy to the GTV. Several benchmarking metrics were evaluated, including GTV D\n mean<\/jats:sub>\n , D\n 10%<\/jats:sub>\n , D\n 50%<\/jats:sub>\n , D\n 90%<\/jats:sub>\n , V\n 50%<\/jats:sub>\n , peak\u2010to\u2010valley ratio (PVDR\u00a0=\u00a0D\n 10%<\/jats:sub>\n \u00f7 D\n 90%<\/jats:sub>\n ), D\n 2cm<\/jats:sub>\n , as well as the D\n max<\/jats:sub>\n of nearby critical organs were evaluated.\n <\/jats:p>\n <\/jats:sec>\n \n Results<\/jats:title>\n \n The R\u00f6dl nibble algorithm substantially increased the number of spheres (\u0394 mean\u00a0=\u00a09.2 vertices), with an algorithm execution time of 71.26\u00a0\u00b1\u00a074.43\u00a0s (12.89\u2013246.30\u00a0s). This resulted in a statistically significant increase in D\n mean<\/jats:sub>\n (\u0394 mean\u00a0=\u00a02.61\u00a0Gy), D\n 5%<\/jats:sub>\n (\u0394 mean\u00a0=\u00a02.22\u00a0Gy), D\n 10%<\/jats:sub>\n (\u0394 mean\u00a0=\u00a02.19\u00a0Gy), D\n 50%<\/jats:sub>\n (\u0394 mean\u00a0=\u00a02.68\u00a0Gy), D\n 90%<\/jats:sub>\n (\u0394 mean\u00a0=\u00a03.52\u00a0Gy), and V\n 50%<\/jats:sub>\n (\u0394 mean\u00a0=\u00a027.0%); however, this led to decreased PVDR (\u0394 mean\u00a0=\u00a0\u22126.41) and an increase in D\n 2cm<\/jats:sub>\n (\u0394 mean\u00a0=\u00a01.11\u00a0Gy). An increased D\n max<\/jats:sub>\n to nearby critical organs was also observed. Overall, all R\u00f6dl nibble replans were clinically acceptable for SFRT treatments. An end\u2010to\u2010end example clinical case is provided to demonstrate the utility of this method.\n <\/jats:p>\n <\/jats:sec>\n \n Conclusion<\/jats:title>\n Our novel nibble algorithm significantly increased the number of lattice spheres packed within the tumor volume, resulting in enhanced dose metrics while being computationally efficient. The enhanced tumor dose metrics come with the cost of increased dose outside the tumor. As we implement this method in our clinic, further research will be directed toward site\u2010specific optimal beam geometry to minimize dose spillage and increase the dose heterogeneity.<\/jats:p>\n <\/jats:sec>","DOI":"10.1002\/mp.70116","type":"journal-article","created":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T01:18:00Z","timestamp":1762305480000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Nibbling toward optimal sphere packing for lattice spatially fractionated radiotherapy of large and bulky unresectable tumors"],"prefix":"10.1002","volume":"52","author":[{"given":"Joshua","family":"Misa","sequence":"first","affiliation":[{"name":"Medical Physics Graduate Program Department of Radiation Medicine University of Kentucky Lexington Kentucky USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James R.","family":"Castle","sequence":"additional","affiliation":[{"name":"Medical Physics Graduate Program Department of Radiation Medicine University of Kentucky Lexington Kentucky USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas A.","family":"Oldland","sequence":"additional","affiliation":[{"name":"Medical Physics Graduate Program Department of Radiation Medicine University of Kentucky Lexington Kentucky USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Damodar","family":"Pokhrel","sequence":"additional","affiliation":[{"name":"Medical Physics Graduate Program Department of Radiation Medicine University of Kentucky Lexington Kentucky USA"},{"name":"Indiana University Health System Department of Radiation Oncology Indianapolis Indiana 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