{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T03:46:33Z","timestamp":1768016793848,"version":"3.49.0"},"reference-count":19,"publisher":"Wiley","license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2016]]},"abstract":"<jats:p>Researchers have observed that response of tumor cells to treatment varies depending on whether the cells are grown in monolayer, as<jats:italic>in vitro<\/jats:italic>spheroids or<jats:italic>in vivo<\/jats:italic>. This study uses data from the literature on monolayer treatment of SK-N-SH neuroblastoma cells with 15-deoxy-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>P<\/mml:mi><mml:mi>G<\/mml:mi><mml:msub><mml:mrow><mml:mi>J<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>and couples it with data on growth rates for untreated SK-N-SH neuroblastoma cells grown as multicellular spheroids. A linear model is constructed for untreated and treated monolayer data sets, which is tuned to growth, death, and cell cycle data for the monolayer case for both control and treatment with 15-deoxy-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>P<\/mml:mi><mml:mi>G<\/mml:mi><mml:msub><mml:mrow><mml:mi>J<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>. The monolayer model is extended to a five-dimensional nonlinear model of<jats:italic>in vitro<\/jats:italic>tumor spheroid growth and treatment that includes compartments of the cell cycle (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>,<\/mml:mo><mml:mi>S<\/mml:mi><mml:mo>,<\/mml:mo><mml:msub><mml:mrow><mml:mi>G<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>\/<\/mml:mo><mml:mi>M<\/mml:mi><\/mml:math>) as well as quiescent (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>Q<\/mml:mi><\/mml:mrow><\/mml:math>) and necrotic (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:mi>N<\/mml:mi><\/mml:mrow><\/mml:math>) cells. Monolayer treatment data for 15-deoxy-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mi>P<\/mml:mi><mml:mi>G<\/mml:mi><mml:msub><mml:mrow><mml:mi>J<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>is used to derive a prediction of spheroid response under similar treatments. For short periods of treatment, spheroid response is less pronounced than monolayer response. The simulations suggest that the difference in response to treatment of monolayer versus spheroid cultures observed in laboratory studies is a natural consequence of tumor spheroid physiology rather than any special resistance to treatment.<\/jats:p>","DOI":"10.1155\/2016\/3628124","type":"journal-article","created":{"date-parts":[[2016,12,1]],"date-time":"2016-12-01T16:08:22Z","timestamp":1480608502000},"page":"1-11","source":"Crossref","is-referenced-by-count":11,"title":["A Model for Spheroid versus Monolayer Response of SK-N-SH Neuroblastoma Cells to Treatment with 15-Deoxy-<i>PGJ<\/i><sub>2<\/sub>"],"prefix":"10.1155","volume":"2016","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9356-8353","authenticated-orcid":true,"given":"Dorothy I.","family":"Wallace","sequence":"first","affiliation":[{"name":"Department of Mathematics, HB 6188, Dartmouth College, Hanover, NH 03768, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ann","family":"Dunham","sequence":"additional","affiliation":[{"name":"Department of Mathematics, HB 6188, Dartmouth College, Hanover, NH 03768, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paula X.","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, HB 6188, Dartmouth College, Hanover, NH 03768, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michelle","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, HB 6188, Dartmouth College, Hanover, NH 03768, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Milan","family":"Huynh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Evan","family":"Rheingold","sequence":"additional","affiliation":[{"name":"Department of Mathematics, HB 6188, Dartmouth College, Hanover, NH 03768, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Olivia","family":"Prosper","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kentucky, Lexington, KY 40506, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/ijc.2910310502"},{"issue":"1","key":"2","first-page":"221","volume":"8","year":"2002","journal-title":"Clinical Cancer 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