Fast algorithms for the analysis of single and double exponential decay curves with a background term. Application to time-resolved imaging microscopy

Theodorus W J Gadella Jr, Thomas M Jovin
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Abstract

Computer programs have been developed to determine decay time constants from a temporal sequence of digitized images with decaying intensities characterized by either single or double exponentials plus a constant background term. The very fast algorithms are evaluated at every pixel position. A non-iterative Prony-like method provides high quality initial estimates that are used for the subsequent non-linear least-squares procedure in which the normal equations are solved directly. Error analysis routines enable a pixel-by-pixel estimation of the quality of the experimental data. The stand-alone programs were fully integrated into a commercial image-processing environment (SCIL-Image) for a convenient and optimal display of the decay analysis. The features of the programs are illustrated by the analysis of simulated image data. With current workstations, the fitting routines (including reading of data, initial estimate and error analysis) require 0.13 ms/pixel using the single exponential algorithm applied to 50 time points, and 1.37 ms/pixel for 100 time points and the double exponential algorithm. The programs are of general applicability and have been used to analyse data from time-resolved fluorescence, phosphorescence, and photobleaching-based microscopy. Two examples of the latter case are shown, illustrating the utility of the programs for the quantitative evaluation of spatially resolved fluorescence resonance energy transfer (FRET) and for generating contrast by allocating specific cellular structures to particular decay components in a fluorescence image.

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具有背景项的单指数和双指数衰减曲线的快速分析算法。应用于时间分辨成像显微镜
计算机程序已经开发,以确定衰减时间常数从数字化图像的时间序列衰减强度的特点是单指数或双指数加上一个恒定的背景项。非常快的算法在每个像素位置进行评估。非迭代类prony方法提供了高质量的初始估计,用于随后的非线性最小二乘程序,其中直接求解正规方程。误差分析程序可以逐像素地估计实验数据的质量。独立的程序完全集成到商业图像处理环境(sci - image)中,以便方便和最佳地显示衰减分析。通过对仿真图像数据的分析,说明了程序的特点。在目前的工作站中,50个时间点单指数算法的拟合程序(包括数据读取、初始估计和误差分析)需要0.13 ms/pixel, 100个时间点双指数算法的拟合程序需要1.37 ms/pixel。该程序具有普遍适用性,并已用于分析时间分辨荧光,磷光和基于光漂白的显微镜的数据。显示了后一种情况的两个例子,说明了空间分辨荧光共振能量转移(FRET)的定量评估程序的效用,并通过在荧光图像中分配特定的细胞结构来产生对比度。
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