{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,28]],"date-time":"2026-10-28T09:38:47Z","timestamp":1793180327880,"version":"4.5.0"},"reference-count":19,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2026,10,28]],"date-time":"2026-10-28T00:00:00Z","timestamp":1793145600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2026,10,28]],"date-time":"2026-10-28T00:00:00Z","timestamp":1793145600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"JST CREST, Japan","award":["JPMJCR2003"],"award-info":[{"award-number":["JPMJCR2003"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Methods Appl. Fluoresc."],"published-print":{"date-parts":[[2026,12,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We formulate and numerically evaluate a direct, non-iterative algebraic estimator for multicomponent fluorescence lifetimes using harmonic phase measurements in a two-photon excitation scheme. The method operates on the complex harmonic responses available at the repetition frequency of a femtosecond pulse train and its harmonics. Rather than performing iterative nonlinear lifetime fitting, we map the measured harmonic responses through a linear coefficient-reconstruction step to the denominator polynomial of a rational representation of the multiexponential decay and obtain the decay constants from its roots. This procedure requires neither initial lifetime estimates nor iterative nonlinear minimization. Numerical simulations were performed for a three-component system, with photon-limited performance evaluated using Poisson counting statistics. For the closely spaced lifetime set of 0.5, 1.5, and 2.5 ns, the mean relative lifetime error decreased from 14.49% at a peak expected count of 100 photons per time bin to 5.94% at 1000 photons and 1.31% at 10\u2009000 photons, with each condition evaluated by averaging 500 statistically independent acquisitions. In a matched 500-trial Monte Carlo comparison at\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mo>\u00d7<\/mml:mo>\n                          <mml:msup>\n                            <mml:mn>10<\/mml:mn>\n                            <mml:mrow>\n                              <mml:mn>7<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    expected photons per pixel, the success probabilities were 0.484 for the unconstrained algebraic estimator, 0.854 for the DC-constrained algebraic estimator, and 0.898 for single-start nonlinear least-squares (NLLS). Thus, imposing the DC constraint substantially improved the photon-noise robustness of the algebraic reconstruction relative to the minimally determined unconstrained formulation, while single-start NLLS remained slightly more robust than the DC-constrained algebraic estimator. In a separate matched 500-sample computational benchmark at\n                    <jats:inline-formula>\n                      <jats:tex-math>\n                        \n                      <\/jats:tex-math>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:mo>\u00d7<\/mml:mo>\n                          <mml:msup>\n                            <mml:mn>10<\/mml:mn>\n                            <mml:mrow>\n                              <mml:mn>8<\/mml:mn>\n                            <\/mml:mrow>\n                          <\/mml:msup>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    expected photons per pixel, the median parameter-estimation times were 0.138, 0.095, and 5.552 ms per pixel for the unconstrained algebraic, DC-constrained algebraic, and single-start NLLS estimators, respectively. Relative to the DC-constrained algebraic median, the unconstrained algebraic and single-start NLLS calculations required approximately 1.45 and 58.35 times longer processing time, respectively. These results identify both a constraint-induced robustness improvement within the algebraic formulation and a robustness\u2013computation trade-off relative to iterative fitting. The present work should therefore be regarded as a theoretical and numerical algebraic implementation within the established multifrequency frequency-domain framework. Experimental validation and harmonic-dependent instrument-response calibration remain necessary for practical two-photon FLIM implementation.\n                  <\/jats:p>","DOI":"10.1088\/2050-6120\/aeb34e","type":"journal-article","created":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T22:53:12Z","timestamp":1791845592000},"page":"045010","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Algebraic multicomponent fluorescence lifetime estimation from harmonic phase measurements under two-photon excitation"],"prefix":"10.1088","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-9256-8830","authenticated-orcid":true,"given":"Kenji","family":"Saijo","sequence":"first","affiliation":[{"name":"Shizuoka University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-7122-9337","authenticated-orcid":true,"given":"Yu","family":"Masuda","sequence":"additional","affiliation":[{"name":"Shizuoka University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3803-5161","authenticated-orcid":false,"given":"Maciej","family":"Kretkowski","sequence":"additional","affiliation":[{"name":"Shizuoka University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7127-5760","authenticated-orcid":true,"given":"Wataru","family":"Inami","sequence":"additional","affiliation":[{"name":"Shizuoka University"},{"name":"Shizuoka University"},{"name":"Shizuoka University"},{"name":"Shizuoka University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0830-8010","authenticated-orcid":false,"given":"Yoshimasa","family":"Kawata","sequence":"additional","affiliation":[{"name":"Shizuoka University"},{"name":"Shizuoka University"},{"name":"Shizuoka University"},{"name":"Shizuoka University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"266","published-online":{"date-parts":[[2026,10,28]]},"reference":[{"key":"mafaeb34ebib1","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/B978-0-12-407761-4.00020-8","type":"journal-article","article-title":"Fluorescence lifetime imaging microscopy for quantitative biological imaging","volume":"114","author":"Chen","year":"2013","journal-title":"Methods Cell Biol."},{"key":"mafaeb34ebib2","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1117\/1.1586704","type":"journal-article","article-title":"Fluorescence lifetime imaging for the two-photon microscope: time-domain and frequency-domain methods","volume":"8","author":"Gratton","year":"2003","journal-title":"J. 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Chem."},{"key":"mafaeb34ebib14","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1080\/05704928408081716","type":"journal-article","article-title":"The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometry","volume":"20","author":"Jameson","year":"1984","journal-title":"Appl. Spectrosc. Rev."},{"key":"mafaeb34ebib15","doi-asserted-by":"publisher","first-page":"L14","DOI":"10.1529\/biophysj.107.120154","type":"journal-article","article-title":"The phasor approach to fluorescence lifetime imaging analysis","volume":"94","author":"Digman","year":"2008","journal-title":"Biophys. J."},{"key":"mafaeb34ebib16","doi-asserted-by":"publisher","DOI":"10.1117\/1.JBO.19.4.046017","type":"journal-article","article-title":"Application of phasor plot and autofluorescence correction for study of heterogeneous cell population","volume":"19","author":"Szmacinski","year":"2014","journal-title":"J. Biomed. Opt."},{"key":"mafaeb34ebib17","doi-asserted-by":"publisher","first-page":"1557","DOI":"10.1364\/OE.17.001557","type":"journal-article","article-title":"mhFLIM: resolution of heterogeneous fluorescence decays in widefield lifetime microscopy","volume":"17","author":"Schlachter","year":"2009","journal-title":"Opt. Express"},{"key":"mafaeb34ebib18","doi-asserted-by":"publisher","first-page":"10126","DOI":"10.1021\/acs.jpcb.0c06946","type":"journal-article","article-title":"Blind resolution of lifetime components in individual pixels of fluorescence lifetime images using the phasor approach","volume":"124","author":"Vallmitjana","year":"2020","journal-title":"J. Phys. Chem. B"},{"key":"mafaeb34ebib19","doi-asserted-by":"publisher","DOI":"10.1088\/2050-6120\/ab8570","type":"journal-article","article-title":"Resolution of 4 components in the same pixel in FLIM images using the phasor approach","volume":"8","author":"Vallmitjana","year":"2020","journal-title":"Methods Appl. Fluoresc."}],"container-title":["Methods and Applications in Fluorescence"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,28]],"date-time":"2026-10-28T09:19:27Z","timestamp":1793179167000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2050-6120\/aeb34e"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10,28]]},"references-count":19,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2026,10,28]]},"published-print":{"date-parts":[[2026,12,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2050-6120\/aeb34e","relation":{},"ISSN":["2050-6120"],"issn-type":[{"value":"2050-6120","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,10,28]]},"assertion":[{"value":"Algebraic multicomponent fluorescence lifetime estimation from harmonic phase measurements under two-photon excitation","name":"article_title","label":"Article Title"},{"value":"Methods and Applications in Fluorescence","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2026 IOP Publishing Ltd. All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2026-05-07","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-10-12","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2026-10-28","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}