A new framework for the estimation of diffusion coefficients from data on fluorescence recovery after photobleaching (FRAP) with confocal laser scanning microscopy (CLSM) is presented. It is a pixel-based statistical methodology that efficiently utilizes all information about the diffusion process in the available set of images. The likelihood function for a series of images is maximized which gives both an estimate of the diffusion coefficient and a corresponding error. This framework opens up possibilities (1) to obtain localized diffusion coefficient estimates in both homogeneous and heterogeneous materials, (2) to account for time differences between the registrations at the pixels within each image, and (3) to plan experiments optimized with respect to the number of replications, the number of bleached regions for each replicate, pixel size, the number of pixels, the number of images in each series etc. To demonstrate the use of the new framework, we have applied it to a simple system with polyethylene glycol (PEG) and water where we find good agreement with diffusion coefficient estimates from NMR diffusometry. In this experiment, it is also shown that the effect of the point spread function is negligible, and we find fluorochrome-concentration levels that give a linear response function for the fluorescence intensity.
- error estimate