A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation

Abstract

Global fitting algorithms have been shown to improve effectively the accuracy and precision of the analysis of fluorescence lifetime imaging microscopy data. Global analysis performs better than unconstrained data fitting when prior information exists, such as the spatial invariance of the lifetimes of individual fluorescent species. The highly coupled nature of global analysis often results in a significantly slower convergence of the data fitting algorithm as compared with unconstrained analysis. Convergence speed can be greatly accelerated by providing appropriate initial guesses. Realizing that the image morphology often correlates with fluorophore distribution, a global fitting algorithm has been developed to assign initial guesses throughout an image based on a segmentation analysis. This algorithm was tested on both simulated data sets and time-domain lifetime measurements. We have successfully measured fluorophore distribution in fibroblasts stained with Hoechst and calcein. This method further allows second harmonic generation from collagen and elastin autofluorescence to be differentiated in fluorescence lifetime imaging microscopy images of ex vivo human skin. On our experimental measurement, this algorithm increased convergence speed by over two orders of magnitude and achieved significantly better fits.

FIGURE 1

Comparison of the ability of lifetime invariant fit, integrated differential equation and iterative convolution global fits to retrieve the two lifetimes and their ratio hidden in the simulated FLIM image. The lower left image shows five typical decay curves extracted from this image.

FIGURE 2

(A) and (B) Comparison of the ratio coefficients c_2i+2 obtained from the iterative convolution fit (○) and from the time invariant fit (Δ) with the true values of these coefficients for an average photon count number of 10³ (A) or 10⁴ (B). (C and D) Histogram of the deviation of the coefficients from the true value for IC fit (solid line) and time invariant fit (dotted line) for an average photon count number of 10³ (C) or 10⁴ (D).

FIGURE 3

Schematic of the segmentation technique. (A) Intensity image of the simulated cell showing the six different intensity regions selected. (B) Summed lifetime information from the six regions selected. (C) Map of the ratio coefficient after the initial fitting procedure. (D) One pixel decay and its fits from the five high intensity regions in the image. (E) Map of the ration coefficients after the global fit. (F) True map of the ratio coefficients.

FIGURE 4

Evolution of the least-square estimate χ² during the global fit (including the prefitting time), using different technique to generate the initial guess: full guess (∇), image average (⋄), division (Δ), segmentation (○), and quadrant average (□). The dashed line is the optimum χ² calculated using the true coefficients used to generate the image.

FIGURE 5

Comparison of the ratio coefficients c_2i+2 obtained from the iterative convolution fit (A) and from the time invariant fit (B). (C) Gaussian fit of the histogram of the difference between the true coefficients and the ones obtained the iterative convolution (solid line) and time invariant (dotted line) optimizations.

FIGURE 6

(A) Map of the ratio of SHG versus autofluorescence obtained from the global fit. (B) Sample of decay pixels and their fits from high (○) and low (□) fluorescence regions. (C) Evolution of the least-square estimate χ² during the optimization using different strategies: full guess (∇), image average (⋄), division (Δ), segmentation (○), and quadrant average (□).

FIGURE 7

(A) Intensity map of the fluorescence emitted by cells stained with calcein AM and Hoechst 33342. (B) Two typical lifetime measured from both the cytoplasmic (□) and nucleic (○) regions of the cells. The solid lines represent the fit of these decays. The inset shows these same fits normalized. (C) Map of the proportion of 2.4 ns decay versus 3.7 ns decay in each pixel of the image. (D) Histogram of the lifetime ratio for the cytoplasmic (solid line) and nucleic (dotted line) regions.

FIGURE 8

Evolution of the least-square estimate χ² during the optimization using different strategies: full guess (∇), image average (·), division (Δ), segmentation (○), and quadrant average (□).