{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T10:09:49Z","timestamp":1775470189236,"version":"3.50.1"},"reference-count":5,"publisher":"Wiley","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["24654023"],"award-info":[{"award-number":["24654023"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["16H06576"],"award-info":[{"award-number":["16H06576"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"publisher","award":["24654023"],"award-info":[{"award-number":["24654023"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"publisher","award":["16H06576"],"award-info":[{"award-number":["16H06576"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2017]]},"abstract":"<jats:p>We consider ordinary differential equation (ODE) model for a pathway network that arises in extracellular matrix (ECM) degradation. For solving the ODEs, we propose applying the mass conservation law (MCL), together with a stoichiometry called<jats:italic> doubling rule<\/jats:italic>, to them. Then it leads to extracting new units of variables in the ODEs that can be solved explicitly, at least in principle. The simulation results for the ODE solutions show that the numerical solutions are indeed in good accord with theoretical solutions and satisfy the MALs.<\/jats:p>","DOI":"10.1155\/2017\/5924270","type":"journal-article","created":{"date-parts":[[2017,5,30]],"date-time":"2017-05-30T17:05:00Z","timestamp":1496163900000},"page":"1-15","source":"Crossref","is-referenced-by-count":3,"title":["Finding Solvable Units of Variables in Nonlinear ODEs of ECM Degradation Pathway Network"],"prefix":"10.1155","volume":"2017","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6298-1065","authenticated-orcid":true,"given":"Shuji","family":"Kawasaki","sequence":"first","affiliation":[{"name":"Iwate University, Morioka 020-8550, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5767-3546","authenticated-orcid":true,"given":"Dhisa","family":"Minerva","sequence":"additional","affiliation":[{"name":"Osaka University, Toyonaka 560-8531, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Keiko","family":"Itano","sequence":"additional","affiliation":[{"name":"Osaka University, Toyonaka 560-8531, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takashi","family":"Suzuki","sequence":"additional","affiliation":[{"name":"Osaka University, Toyonaka 560-8531, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","year":"2011"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1038\/370061a0"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002479"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1003086"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1074\/jbc.m403627200"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2017\/5924270.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2017\/5924270.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2017\/5924270.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,5,30]],"date-time":"2017-05-30T17:05:11Z","timestamp":1496163911000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/cmmm\/2017\/5924270\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"references-count":5,"alternative-id":["5924270","5924270"],"URL":"https:\/\/doi.org\/10.1155\/2017\/5924270","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"value":"1748-670X","type":"print"},{"value":"1748-6718","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}