{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T10:17:36Z","timestamp":1776853056993,"version":"3.51.2"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100006120","name":"Ministry of the Environment, Government of Japan","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006120","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Bull Math Biol"],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>The two-hit model proposed by Knudson for retinoblastoma has been widely recognized as a standard model for cancer incidence. It successfully predicted the existence of the tumor suppressor gene known as \"Rb1\" by effectively demonstrating the overall patterns observed in clinical data covering both bilateral and unilateral retinoblastoma cases. However, it is important to note that the model\u2019s prediction currently deviates significantly from clinical data, both qualitatively and quantitatively. Regrettably, this disparity has remained unresolved. In light of this, we conducted a thorough re-evaluation of Knudson\u2019s two-hit model and arrived at a plausible solution that an additional somatic mutation mechanism is required to accurately replicate the magnitude and age dependence observed in both bilateral and unilateral retinoblastoma cases. This revelation offers a fresh and valuable perspective on the development of cancer, highlighting the significance of mutations not only during the cell growth period but also after the retina organ has reached maturity. We refer to this phase as the \"mature period,\" during which the mutation rate has been observed to surpass that of the growth period. With this enhanced understanding of retinoblastoma (Rb), we believe we have shed light on the intricate relationship between somatic and germline mutations. Moreover, this insight provides a promising clue for further exploration into the broader context of cancer incidence resulting from genetic mutations.<\/jats:p>","DOI":"10.1007\/s11538-025-01483-5","type":"journal-article","created":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T02:58:20Z","timestamp":1750906700000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Theoretical Study of Retinoblastoma in the Hereditary and Non-hereditary Processes Including the Cancer Growth"],"prefix":"10.1007","volume":"87","author":[{"given":"Hiroshi","family":"Toki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yoshiharu","family":"Yonekura","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6098-2702","authenticated-orcid":false,"given":"Yuichi","family":"Tsunoyama","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Masako","family":"Bando","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"1483_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/bjc.1954.1","volume":"8","author":"P Armitage","year":"1954","unstructured":"Armitage P, Doll R (1954) The age distribution of cancer and a multi-stage theory of carcinogenesis. 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