{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T13:34:10Z","timestamp":1791207250313,"version":"4.1.0"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2005,3,30]],"date-time":"2005-03-30T00:00:00Z","timestamp":1112140800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0\/"},{"start":{"date-parts":[[2005,3,30]],"date-time":"2005-03-30T00:00:00Z","timestamp":1112140800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/2.0\/"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Theor Biol Med Model"],"abstract":"<jats:title>Abstract<\/jats:title><jats:sec>\n                        <jats:title>Background<\/jats:title>\n                        <jats:p>Mathematical models describing growth kinetics are very important for predicting many biological phenomena such as tumor volume, speed of disease progression, and determination of an optimal radiation and\/or chemotherapy schedule. Growth models such as logistic, Gompertz, Richards, and Weibull have been extensively studied and applied to a wide range of medical and biological studies. We introduce a class of three and four parameter models called \"hyperbolastic models\" for accurately predicting and analyzing self-limited growth behavior that occurs e.g. in tumors. To illustrate the application and utility of these models and to gain a more complete understanding of them, we apply them to two sets of data considered in previously published literature.<\/jats:p>\n                     <\/jats:sec><jats:sec>\n                        <jats:title>Results<\/jats:title>\n                        <jats:p>The results indicate that volumetric tumor growth follows the principle of hyperbolastic growth model type III, and in both applications at least one of the newly proposed models provides a better fit to the data than the classical models used for comparison.<\/jats:p>\n                     <\/jats:sec><jats:sec>\n                        <jats:title>Conclusion<\/jats:title>\n                        <jats:p>We have developed a new family of growth models that predict the volumetric growth behavior of multicellular tumor spheroids with a high degree of accuracy. We strongly believe that the family of hyperbolastic models can be a valuable predictive tool in many areas of biomedical and epidemiological research such as cancer or stem cell growth and infectious disease outbreaks.<\/jats:p>\n                     <\/jats:sec>","DOI":"10.1186\/1742-4682-2-14","type":"journal-article","created":{"date-parts":[[2005,3,31]],"date-time":"2005-03-31T06:16:05Z","timestamp":1112249765000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":62,"title":["Hyperbolastic growth models: theory and application"],"prefix":"10.1186","volume":"2","author":[{"given":"Mohammad","family":"Tabatabai","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"David Keith","family":"Williams","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zoran","family":"Bursac","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2005,3,30]]},"reference":[{"key":"27_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1086\/412574","volume":"57","author":"S Kingland","year":"1982","unstructured":"Kingland S: The refractory model: The logistic curve and history of population ecology. 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