1. Photoblinking Model (βON>βOFF)
Photobleaching and Photoblinking model describing intensity fading in LSFCM images
1,2Isabel Rodrigues and 1,3João Sanches 1Institute for Systems and Robotics 2Instituto Superior de Engenharia de Lisboa 3Instituto Superior Técnico Lisbon, Portugal
Experimental Results
Abstract
Laser Scanning Fluorescence Confocal Microscopy (LSFCM) is a powerful technique used today in biological research to observe in-vivo dynamic processes occurring inside the cells. These images, however, are usually corrupted by a type of multiplicative noise with Poisson distribution and are affected by a fading effect along time, as a consequence of two quantum processes, called photobleaching and photoblinking. The former consists in a permanent ability loss of the fluorophore to fluoresce along the time and the second the consequence of an increasing time of the fluorophore in the OFF-state where it is not visible, which lead to an intensity decreasing of the images, preventing long time experiments. This effect depends mainly on the amount of energy radiated over the specimen. An accurate model for this intensity decay is important in the definition of the observation model in order to obtain effective denoising algorithms for this type of images. In this work a differential based continuous dynamic model describing the photobleaching effect is presented and simulation results with synthetic data are displayed. The main goal is to derive the theoretic model that explains the observed intensity decay in real images and that is usually assumed in the literature to be described by a sum of two decaying exponentials. Results of fitting the model to real data are also presented.
Results of a 10 seconds simulation.
The initial active molecules, n(0) =n0 = 1, are all at the ON-state, nON(0) = n0 and nOFF (0) = 0.
The parameter values chosen respecting the expected relative magnitude between them in real situations:
βON = 0.5 > βOFF = 0.25 > I = 0.1 > = 0.05.
The initial active molecules, all of them at the ON-state, migrate to the OFF-state.
The image intensity, proportional to the number of molecules at the ON-state, decreases continuously.
The number of molecules at the OFF-state starts to increase, due to the migration from the ON-state.
After t=3s nOFF also starts to decrease: the number of molecules that migrate from the ON-state to the OFF-state is not enough to compensate for the number of molecules that become inactive due to the Photobleaching effect.
In the end all the image will be turned off.
Simulations
Fitting de model to Real Data
and 1= , 2=a - 
Problem Formulation
Three main states of the fluorescence molecules:
ON-state - able to fluoresce and be observed
OFF-state - not able to fluoresce and not visible
Permanently-OFF-state - permanently OFF.
Fits of the model to real data of HeLa cells nucleus (data provided by the Instituto de Medicina Molecular, Lisboa).
Hypotheses
The probability of transitions:
decreases with time
is always larger from the ON-state to the OFF-state –> leads to a constant image fading along the time: photoblinking.
Photobleaching: a non-reversible process where the fluorescent molecule looses its ability to fluoresce.
Photobleaching from the ON-state is discarded.
No photobleaching occurs from the excited singlet state, S1 but only from the OFF-states, composed by the triplet, T1−n, and anion, D1−n, states.
When using a one exponential model the RMSE is much bigger then in the case of the proposed two exponentials model.
Denoising with Photobleaching Compensation
n - total number of active molecules.
nON - number of active molecules at the ON-state.
nOFF - number of active molecules at the OFF-state.
I - decay rate associated with the illumination (proportional to the amount of incident radiation).
: decay rate associated with other factors not related with illumination.
Energy Function to be minimized O 1
Photoblinking Model (βON>βOFF)
Photobleaching Model
Total number of active molecules ; 2 3
Model for each point of the noiseless sequence, X:
Initial conditions: ;
Differential equation describing the dynamics of the number of molecules at the ON-state, (directly related with the intensity of the image), from (1-3):
Sequence G26: Images 1, 10 and 17 from the sequence of 26 images.a), d), g) noisy original data; b), e), h) estimated cell nucleus morphology; c), f), i) mesh representations of the respective estimated morphologies ;
Conclusions
In this work a continuous second order differential equation dynamic model for the fluorescence confocal image intensity decay is presented. This model is based on the quantic mechanisms involved in the photobleaching process that are summarized in a Jablonski diagram. The solution to the model for a given set of initial conditions leads to the same intensity decay law that several authors have adopted, based only on experimental data. Denoising results using the proposed model show its adequacy to describe the global photobleaching effect.
Solution:
RECPAD - 14ª Conferência Portuguesa de Reconhecimento de Padrões, Aveiro, 23 de Outubro de 2009