ANALYSIS OF PHOSPHORESCENCE IN HETEROGENEOUS SYSTEMS USING DISTRIBUTIONS OF QUENCHER CONCENTRATION

A continuous distribution approach, instead of the traditional mono- a nd multiexponential analysis, for determining quencher concentration i n a heterogeneous system has been developed, A mathematical model of p hosphorescence decay inside a volume with homogeneous concentration of phosphor and heterogeneous concentration of quencher was formulated t o obtain pulse-response fitting functions for four different distribut ions of quencher concentration: rectangular, normal (Gaussian), gamma, and multimodal. The analysis was applied to parameter estimates of a heterogeneous distribution of oxygen tension (PO2) within a volume. Si mulated phosphorescence decay data were randomly generated for differe nt distributions and heterogeneity of PO2 inside the excitation/emissi on volume, consisting of 200 domains, and then fit with equations deve loped for the lour models. Analysis using a monoexponential fit yielde d a systematic error (underestimate) in mean PO2 that increased with t he degree oi heterogeneity, The fitting procedures based on the contin uous distribution approach returned more accurate values for parameter s of the generated PO2 distribution than did the monoexponential fit. The parameters oi the fit (M = mean; sigma = standard deviation) were investigated as a function of signal-to-noise ratio (SNR = maximum sig nal amplitude/peak-to-peak noise). The best-nt parameter values were s table when SNR greater than or equal to 20. All four fitting models re turned accurate values of M and sigma for different PO2 distributions, The ability of our procedures to resolve two different heterogeneous compartments was also demonstrated using a bimodal fitting model, An a pproximate scheme was formulated to allow calculation of the first mom ents of a spatial distribution of quencher without specifying the dist ribution. In addition, a procedure for the recovery of a histogram, re presenting the quencher concentration distribution, was developed and successfully tested.