Analysis of phosphorescence in heterogeneous systems using distributions of quencher concentration

A continuous distribution approach, instead of the traditional mono- and multiexponential analysis, for determining quencher concentration in a heterogeneous system has been developed, A mathematical model of phosphorescence decay inside a volume with homogeneous concentration of phosphor and heterogeneous concentration of quencher was formulated to obtain pulse-response fitting functions for four different distributions of quencher concentration: rectangular, normal (Gaussian), gamma, and multimodal. The analysis was applied to parameter estimates of a heterogeneous distribution of oxygen tension (PO(2)) within a volume. Simulated phosphorescence decay data were randomly generated for different distributions and heterogeneity of PO(2) inside the excitation/emission volume, consisting of 200 domains, and then fit with equations developed for the lour models. Analysis using a monoexponential fit yielded a systematic error (underestimate) in mean PO(2) that increased with the degree oi heterogeneity, The fitting procedures based on the continuous distribution approach returned more accurate values for parameters of the generated PO(2) 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 signal amplitude/peak-to-peak noise). The best-nt parameter values were stable when SNR greater than or equal to 20. All four fitting models returned accurate values of M and sigma for different PO(2) distributions, The ability of our procedures to resolve two different heterogeneous compartments was also demonstrated using a bimodal fitting model, An approximate scheme was formulated to allow calculation of the first moments of a spatial distribution of quencher without specifying the distribution. In addition, a procedure for the recovery of a histogram, representing the quencher concentration distribution, was developed and successfully tested.