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. 2022 Jan 31;12:1642. doi: 10.1038/s41598-021-03114-0

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Principle of FLIM bi-exponential, Phasor and Pseudo-FLIM analyses. (a) Simulated mono-exponential (fluorophores A and B) and bi-exponential (mixed species of fluorophores A and B with respectively 90% and 10% relative contribution) two-photon excited fluorescence intensity decays (12.5 ns time range; 80 MHz); this shape of A&B bi-exponential decay can be measured in melanin containing samples. In FLIM bi-exponential analysis, the 2PEF intensity decay is adjusted with the function in (a) to compute the values of short- $τ_{1}$ and long- $τ_{2}$ fluorescence lifetimes and their relative contributions $a_{1} [%]$ and $a_{2} [%]$ . Images of FLIM bi-exponential fit and combination parameters such as amplitude- and intensity-weighted lifetimes are used for data analyses. (b) FLIM phasor analysis transforms a decay into a phasor with polar coordinates g, s, corresponding to the real and complex components of the Fourier transform, that can also be expressed as a function of m modulation and φ phase angle. Mono-exponential decays such as A and B will have their phasors on the semi-circle, whereas mixed species will have a phasor along a line connecting the two distinct lifetime phasors of A and B. The relative fractions $f_{A}$ and $f_{B}$ can be computed from the distances of A&B mixed species phasor to B and respectively A phasors. Images of g and s as well as combination parameters such as the apparent phase and modulation lifetimes and their relative fractions are used for data analyses. (c) Pseudo-FLIM analysis firstly involves a temporal binning of the 2PEF decay into a reduced number of time channels with 2 ns integration time per channel (see c1, gray bars indicate the photon intensity of the mixed A&B species within the first 3-time channels with 2 ns binning). The 2PEF intensity of the binned first 3-time channels for simulated A, B and mixed A&B species is given in (c2). After a natural logarithm transformation (c3), a linear regression of the first 3-time channels is performed to calculate the slope of the decay which is multiplied by a − 100 factor to create the Pseudo-FLIM slope parameter. The faster the decay, the higher the slope. Pseudo-FLIM image of the slope parameter is further processed for melanin detection by applying a threshold to keep the pixels with high slope values.