Diapositivo 1

1
Photobleaching and Photoblinking model describing
intensity fading in LSFCM images
1,2Isabel Rodrigues (irodrigues_at_isr.ist.utl.pt)
and 1,3João Sanches (jmrs_at_isr.ist.utl.pt)
1Institute for Systems and Robotics 2Instituto
Superior de Engenharia de Lisboa3Instituto
Superior TécnicoLisbon, 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
• ßON 0.5 gt ßOFF 0.25 gt I 0.1 gt ?
  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 t3s 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 ?, ?2a - ?
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 gt 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

Model for each point of the noiseless sequence, X
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)

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