{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:01:14Z","timestamp":1792785674368,"version":"4.5.0"},"reference-count":18,"publisher":"IOP Publishing","issue":"19","license":[{"start":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:00:00Z","timestamp":1791504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T00:00:00Z","timestamp":1791504000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"National Institutes of Health","award":["R01-HL-108119"],"award-info":[{"award-number":["R01-HL-108119"]}]},{"name":"National Heart, Lung, and Blood Institute","id":[{"id":"https:\/\/ror.org\/012pb6c26","id-type":"ROR","asserted-by":"crossref"}]},{"name":"Burroughs Wellcome Fund CAMS","id":[{"id":"https:\/\/ror.org\/01d35cw23","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2026,10,14]]},"abstract":"Abstract<\/jats:title>\n \n Dynamic imaging in emission computed tomography allows the determination of physiological parameters that have important clinical implications. In myocardial imaging, three parameters of interest are the uptake and washout rates,\n \n \n \n <\/jats:tex-math>\n \n \n \n K<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n and\n \n \n \n <\/jats:tex-math>\n \n \n \n k<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , respectively, and the blood-volume fraction,\n \n \n \n <\/jats:tex-math>\n \n \n V<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n . These parameters can be determined from time-activity curves (TACs) of the blood (i.e. the input function) and the myocardium. However, the volumes of interest for the dynamic images may show overlap of these regions; this overlap can be expressed as a mixing matrix. Herein, we address the requirements for mathematical uniqueness of the solutions. The relationship of the TACs of the myocardium and blood pool with model parameters is evaluated under the structural identifiability criterion, which requires equal observed TACs to have a one-to-one mapping with the model parameters. This leads to constraints on the model parameters. Those constraints lead to system invariants, specifying the relationship between the true solution of the equations and other candidate solutions consistent with the observations for the TACs. Structural identifiability is achieved for\n \n \n \n <\/jats:tex-math>\n \n \n \n K<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n ,\n \n \n \n <\/jats:tex-math>\n \n \n \n k<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n , and\n \n \n \n <\/jats:tex-math>\n \n \n V<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n if all parameters of the mixing matrix are known. These results provide a complete structural identifiability analysis for a one-tissue compartment model with a mixing matrix that accounts for partial-volume effects and spill-in\/out of volumes of interest. Prior results showed a more relaxed condition when\n \n \n \n <\/jats:tex-math>\n \n \n \n k<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:inline-formula>\n was assumed to be zero.\n <\/jats:p>","DOI":"10.1088\/1361-6560\/ae968a","type":"journal-article","created":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T22:57:05Z","timestamp":1786057025000},"page":"195035","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Simultaneously quantifying\n \n \n \n K<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n ,\n \n \n \n k<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n , and blood volume in myocardial imaging with overlapping volumes of interest: structural identifiability"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9935-0024","authenticated-orcid":true,"given":"Scott D","family":"Metzler","sequence":"first","affiliation":[{"name":"University of Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-4007-2035","authenticated-orcid":true,"given":"Dale J","family":"Stentz","sequence":"additional","affiliation":[{"name":"University of Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0766-1253","authenticated-orcid":false,"given":"Marie A","family":"Guerraty","sequence":"additional","affiliation":[{"name":"University of Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"266","published-online":{"date-parts":[[2026,10,9]]},"reference":[{"key":"pmbae968abib1","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0027755","type":"journal-article","article-title":"Structural identifiability of systems biology models: a critical comparison of methods","volume":"6","author":"Chis","year":"2011","journal-title":"PLoS One"},{"key":"pmbae968abib2","first-page":"945","type":"journal-article","article-title":"The derivation of the gamma-variate relationship for tracer dilution curves","volume":"24","author":"Davenport","year":"1983","journal-title":"J. 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Published on behalf of Institute of Physics and Engineering in Medicine by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2025-12-11","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-08-06","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-10-09","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}