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Matthias Klemm, Dietrich Schweitzer; Multi-exponential Approximation Adapted To Autofluorescence Lifetime Imaging (FLIM) Of The Human Eye. Invest. Ophthalmol. Vis. Sci. 2011;52(14):4051.
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© ARVO (1962-2015); The Authors (2016-present)
To improve detection of metabolic changes before morphologic alterations are visible. Modifications aim to account for the layered structure of the human eye and for the much more complex nature of autofluorescence signals of the human eye compared to signals from fluorescent dyes.
An approach to model the fluorescence lifetime of layered structures was introduced (Patent DE 10 2008 045 886). It enhances the classic sum of exponentials approach (am1) by a time-shift (tc) which enables each exponential to be moved on the time axis independently. This allows for modeling of distances between fluorophores along the excitation laser beam as these distances translate into time lags between the fluorescence emissions of the fluorophores. The layer based approach (am2) was compared to the sum of exponentials approach. For both approaches the parameters have to be determined by an optimization algorithm. Three different optimization approaches (oa) were compared. oa1: all parameters determined by nonlinear optimizer; oa2: amplitudes determined by linear and all others by nonlinear optimizer; oa3: amplitudes and offset determined by linear and all others by nonlinear optimizer. Further on two different optimization strategies (os) were compared. os1: one-stage strategy using a (nonlinear) simplex optimizer; os2: two-stage strategy employing a differential evolution algorithm followed by a simplex optimizer. Altogether 12 simulations were performed (2 am * 3 ao * 2 os). Synthetic data was created by a Monte-Carlo-Method based on data from the fovea centralis of a healthy subject (a1: 89%, a2: 7%, a3: 4%, τ1: 40ps, τ2: 500ps, τ3: 3500ps, tc2: 100ps, tc3: 200ps, offset: 0.1%). A 3-exponential approximation was applied in all cases. The results were evaluated using mean values and standard deviations (std) of 900 synthetic fluorescence decays per simulation.
The best average goodness of fit value (chi²) of 1.26 achieved the combination of am2, oa3 and os2 (a1: 89.0%, a2: 7.0%, a3: 4.0%, τ1: 40ps, τ2: 516ps, τ3: 3476ps, tc2: 126ps, tc3: 224ps, offset: 0.11%). The combination of am2, oa2 and os2 yielded similar results at a slightly higher chi² (1.36) but had a much smaller std of τ3 (68ps vs. 235ps). Worst results were shown by the combination of am1, oa1 and os1. The computation of os2 took on average ca. 10x more time than os1 (6h vs. 40 min per simulation).
Although the combination of layer based approach, oa2 and two-stage optimization strategy achieved only the second-best chi² it delivered the best overall results because of the lower variations in τ3.
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