{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T10:23:59Z","timestamp":1789467839952,"version":"build-2803163510"},"reference-count":43,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"vor","delay-in-days":14,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["aapm.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Medical Physics"],"published-print":{"date-parts":[[2025,7]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Spatially Fractionated Radiotherapy (SFRT) delivers highly heterogenous dose distribution, characterized by an alternating pattern of high\u2010 and low\u2010dose regions within the large tumor volume. Lattice SFRT (LRT) achieves this dose distribution via high\u2010dose spheres arranged in a hexagonal pattern throughout the tumor. A major obstacle in LRT planning is optimizing the number of spheres within the tumor while maintaining the geometric constraints to allow for steep dose gradients and preserving normal tissue dose levels.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Purpose<\/jats:title>\n                    <jats:p>We present a novel strategy for lattice deployment for LRT using principal component analysis (PCA) to address the sphere packing problem. The aim of this report is improving sphere packing for LRT treatments will increase the volume of the peak dose the tumor receives from a given lattice configuration, potentially enhancing patient outcomes.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>\n                      Three lattice deployment methods were investigated. Our proposed method split\u2010PCA (s\u2010PCA), in which the lattice pattern is oriented split between the first and second principal axes, 1\u2010PCA has the lattice pattern oriented based on the first principal axis, and n\u2010PCA which does not utilize PCA to orientate the lattice pattern within the tumor. Thirty\u2010five previously treated SFRT patients (15\u00a0Gy in 1 fraction) were replanned using each PCA method. All plans utilized four full VMAT arcs, offset collimator angles of\u00a0\u00b1\u00a015\u00b0, 6MV\u2010FFF energy, and a lattice diameter of 1.5\u00a0cm and spacing of 3\u00a0cm. The resulting plans were evaluated based on\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>50%<\/jats:sub>\n                      ,\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>mean<\/jats:sub>\n                      ,\n                      <jats:italic>V<\/jats:italic>\n                      <jats:sub>50%<\/jats:sub>\n                      ,\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>10%<\/jats:sub>\n                      ,\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>90%<\/jats:sub>\n                      , peak\u2010to\u2010valley dose ratio (PVDR\u00a0=\u00a0\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>10%<\/jats:sub>\n                      \u00f7\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>90%<\/jats:sub>\n                      ),\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>2cm<\/jats:sub>\n                      , and\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>max<\/jats:sub>\n                      to nearby critical organs.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      The s\u2010PCA lattice plans had a statistically significant increase in the number of spheres packed within the tumor compared to the 1\u2010PCA (\u0394 mean\u00a0=\u00a00.91,\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0=\u00a00.019) and n\u2010PCA (\u0394 mean\u00a0=\u00a01.43,\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0&lt;\u00a00.001). In addition, the s\u2010PCA method outperformed the n\u2010PCA method in terms of\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>50%<\/jats:sub>\n                      ,\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>mean<\/jats:sub>\n                      ,\n                      <jats:italic>V<\/jats:italic>\n                      <jats:sub>50%<\/jats:sub>\n                      ,\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>10%<\/jats:sub>\n                      , and\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>90%<\/jats:sub>\n                      and statistically outperformed 1\u2010PCA in terms of\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>50%<\/jats:sub>\n                      ,\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>10%<\/jats:sub>\n                      , and\n                      <jats:italic>D<\/jats:italic>\n                      <jats:sub>90%<\/jats:sub>\n                      . However, the s\u2010PCA gave a statistically significant decrease in PVDR in comparison to the 1\u2010PCA (\u0394 mean\u00a0=\u00a0\u22120.94,\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0=\u00a00.036) and the n\u2010PCA (\u0394 mean\u00a0=\u00a0\u22122.21,\n                      <jats:italic>p<\/jats:italic>\n                      \u00a0&lt;\u00a00.001). Within our study cohort, there were no significant differences between the three deployment methods when analyzing D\n                      <jats:sub>2cm<\/jats:sub>\n                      or maximum dose to critical organs.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>This lattice deployment strategy demonstrated enhanced sphere packing, thus improving tumor dose while restricting maximum dose to critical organs. The s\u2010PCA approach may enhance debulking and sensitization of large and unresectable tumors for follow\u2010up treatments. The s\u2010PCA method has been implemented within our clinical practice, with future research focusing on prospective studies to assess clinical outcomes.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.1002\/mp.17982","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T04:19:26Z","timestamp":1752639566000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the use of principal component analysis method to optimize sphere packing algorithm for lattice radiotherapy of large\/bulky unresectable tumor"],"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 KY USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"James R.","family":"Castle","sequence":"additional","affiliation":[{"name":"Medical 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