Pixel-based analysis of FRAP data with a general initial bleaching profile

In Jonasson et al. (2008), we presented a new pixel-based maximum likelihood framework for the estimation of diffusion coefficients from data on fluorescence recovery after photobleaching (FRAP) with confocal laser scanning microscopy (CLSM). The main method there, called the Gaussian profile method below, is based on the assumption that the initial intensity profile after photobleaching is approximately Gaussian. In the present paper, we introduce a method, called the Monotone profile method, where the maximum likelihood framework is extended to a general initial bleaching profile only assuming that the profile is a non-decreasing function of the distance to the bleaching centre. The statistical distribution of the image noise is further assumed to be Poisson instead of normal, which should be a more realistic description of the noise in the detector. The new Monotone profile method and the Gaussian profile method are applied to FRAP data on swelling of super absorbent polymers (SAP) in water with a Fluorescein probe. The initial bleaching profile is close to a step function at low degrees of swelling and close to a Gaussian profile at high degrees of swelling. The results obtained from the analysis of the FRAP data are corroborated with NMR diffusometry analysis of SAP with a polyethylene glycol probe having size similar to the Fluorescein. The comparison of the Gaussian and Monotone profile methods is also performed by use of simulated data. It is found that the new Monotone profile method is accurate for all types of initial profiles studied, but it suffers from being computationally slow. The fast Gaussian profile method is sufficiently accurate for most of the profiles studied, but underestimates the diffusion coefficient for profiles close to a step function. We also provide a diagnostic plot, which indicates whether the Gaussian profile method is acceptable or not.