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					                                          Photobleaching and Photoblinking model
                                         describing intensity fading in LSFCM images
                                  1,2Isabel          Rodrigues (irodrigues@isr.ist.utl.pt) and 1,3João Sanches (jmrs@isr.ist.utl.pt)
                                                                      1Institute for Systems and Robotics
                                                                 2Instituto Superior de Engenharia de Lisboa
                                                                           3Instituto Superior Técnico

                                                                                 Lisbon, Portugal                                                             ISEL
      Abstract                                                                 Experimental Results                             •Results of a 10 seconds simulation.

      Laser Scanning Fluorescence Confocal Microscopy (LSFCM) is a             Simulations                                      •The initial active molecules, n(0) =n0 = 1, are all at the ON-
      powerful technique used today in biological research to observe in-                                                       state, nON(0) = n0 and nOFF (0) = 0.
      vivo dynamic processes occurring inside the cells. These images,
      however, are usually corrupted by a type of multiplicative noise with                                                     •The parameter values chosen respecting the expected
      Poisson distribution and are affected by a fading effect along time,                                                      relative magnitude between them in real situations:
      as a consequence of two quantum processes, called                                                                                βON = 0.5 > βOFF = 0.25 > I = 0.1 > = 0.05.
      photobleaching and photoblinking. The former consists in a                                                                •The initial active molecules, all of them at the ON-state,
      permanent ability loss of the fluorophore to fluoresce along the time                                                     migrate to the OFF-state.
      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                                                    •The image intensity, proportional to the number of
      intensity decreasing of the images, preventing long time                                                                  molecules at the ON-state, decreases continuously.
      experiments. This effect depends mainly on the amount of energy
      radiated over the specimen. An accurate model for this intensity                                                          •The number of molecules at the OFF-state starts to
      decay is important in the definition of the observation model in                                                          increase, due to the migration from the ON-state.
      order to obtain effective denoising algorithms for this type of
      images. In this work a differential based continuous dynamic model                                                        • After t=3s nOFF also starts to decrease: the number of
      describing the photobleaching effect is presented and simulation                                                          molecules that migrate from the ON-state to the OFF-state
      results with synthetic data are displayed. The main goal is to derive                                                     is not enough to compensate for the number of molecules
      the theoretic model that explains the observed intensity decay in                                                         that become inactive due to the Photobleaching effect.
      real images and that is usually assumed in the literature to be
      described by a sum of two decaying exponentials. Results of fitting                                                       •In the end all the image will be turned off.
      the model to real data are also presented.
                                                                                       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
    Hypotheses                                                                                                                                                  data of HeLa cells nucleus
    • The probability of transitions:                                                                                                                           (data provided by the Instituto
           •decreases with time                                                                                                                                 de Medicina Molecular,
           •is always larger from the ON-state                                                                                                                  Lisboa).
           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.


    n - total number of active molecules.                                                    Denoising with Photobleaching Compensation
    nON - number of active molecules at the ON-state.
                                                                                             Energy Function to be minimized
    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.



O
1                                         Total number of active molecules

O
2                                                          Photoblinking Model (βON>βOFF)

O
3
                                  ;                         Photobleaching Model             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
                                                                                              Sequence G26: Images 1, 10 and 17 from the sequence of 26 images.a), d), g) noisy original
    image), from (1-3):                                                                       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
     Solution:                                                                                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.



       RECPAD - 14ª Conferência Portuguesa de Reconhecimento de Padrões, Aveiro, 23 de Outubro de 2009

				
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