Laser scanning fluorescence confocal microscope (LSFCM) imaging is an extensively used modality in biological research. However, these images present low signal to noise ratio and a time intensity decay effect due to the so called photoblinking/photobleaching (PBPB) phenomenon that corresponds to an intensity fading of a fluorescent probe along the time, as shown in Figure 1. This effect is caused by quantum phenomena associated with the electronic excitation and photochemical reactions among the fluorescent and the surrounding molecules induced by the incident radiation that temporarily or irreversibly destroy their ability to fluoresce. Since illumination is needed to excite and observe the tagging fluorescent proteins in the specimen and all the fluorophores will eventually photobleach upon extended excitation, the acquisition of this type of images becomes a hard task for long exposures.

There are in the literature several proposals to model this fading effects and among them the single and double exponential are the most used. However, simple and tractable theoretical models based on the physics of the observation process to support these empirical laws are not available. In this work, that theoretical model, supported on the underlying physics of the process, is derived to describe the PBPB effect (see Figure 2).

From a fluorescence point of view, tagging molecules can be in three main states (see Figure 3), i) ON-state, where they are able to fluoresce and be observed, ii) OFF-state, where they are temporarily not able to fluoresce and therefore are not visible and finally at the iii) BLEACHED-state where they become permanently OFF. Here, a continuous time differential equation dynamic model is proposed to describe the number of molecules at the ON-state, nON, along the time. The model is based on the underlying quantum mechanic physics theory of the observation process associated with this type of images and the common empirical weighted sum of two decaying exponentials (DExp), usually used in the literature, is derived from the model. The parameters βON and βOff are the transitions rate from and to the ON-state respectively and ξis the decay rate associated with the transitions for the permanent BLEACHED state.

Experiments with synthetic and real data are presented to validate the PBPB model and estimate the physical variables associated with the process. Intensity decay from real data and the corresponding theoretical curve are compared and displayed in Figure 4.

This work was supported by the FCT project [PEst-OE/EEI/LA0009/2011]. The authors thank Dr. José Rino and Profa Carmo Fonseca, from the Molecular Medicine Institute (IMM) of Lisbon, for providing biological technical support and the real data used in this paper.