Tutorial for using simulations with N&B
This is a tutorial for use N&B analysis with simulations. The tutorial for the N&B analysis for real data can be found in a separate file.
There are two types of simulations you can perform to test the N&B analysis. In the first type, you can simulate particles of different brightness and numbers. Also you can simulate analog or photon counting detectors. In this mode, the image is uniform and you cannot test the N&B capability to separate regions of different brightness. In the second type of simulation you can set regions of the image called T-zones in which particles have different brightness depending on the position relative to the zones.
To perform the first type of simulation (not spatially resolved) set up the simulation for a certain kind of brightness, box size, detector type and scan parameters. The following example illustrates the first type of non-spatially resolved simulation.
Setting up the simulation

200 particles of 100000 c/s/m moving in a grid of 256 points were selected using the detector in the photon-counting mode (default value).
Run the simulation using diffusion in a volume tab and then go to analysis, RICS and then in tools select N&B analysis.
N and B analysis

For this analysis the smooth button was used twice.
In the RICS screen, you have three maps corresponding to the map of N, B and the average intensity. Note the values of true n and true e in this screen. These values are always calculated. Note also the histograms of the number of particles, which is approximately Gaussian and of the B value, which is slightly biased towards larger B values. Note also the ratio of variance/intensity, which is larger than 1, indicating that the particles are moving. Can you explain the values obtained for n and

on the basis of the parameters used for the simulation?
Spatially resolved N&B
To perform spatially-resolved brightness simulation you must use the T-zone mode of the simulation page.

In this simulation particles are constrained to be in a plane. The plane is divided in zones where the particles are transiently confined. In the zones, the particles can diffuse slower than in the rest of the plane and they can have a different brightness. The zones are periodic. You can set the size of the zone and the distance between the centers of the zones. Then you set the diffusion ratio between the particles in the zones and in the rest of the plane. You can also set a probability of escaping from the zone. The center of the first zone can be placed in every point of the plane.
According to the values chosen, the TZ does not affect the number of particles or the diffusion, since the diffusion ratio is 1 and the probability to jump out is 1. It only affects by a factor of 2 the brightness inside the T-zone. In the simulation the brightness ratio can be any number including 0.
In the start simulation tab use the t-zone diffusion in a membrane entry rather than the normal diffusion in a volume.
For the above values you should get the N&B analysis as shown below. Data are shown for the 3 kind of analysis to illustrate the differences between them.
N and B maps x= 1.95932 y= 0.45714 #pixels= 15414 in= 875
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TChart
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0 1 2 3 0 brightness 0 20 40 60 80 100 120 140 160 180 200 220 240
Note that the N map is not independent on the brightness. As predicted by the theory the apparent number of particles increases with brightness. .
True epsilon and true n maps

x= 0.99851 y= 0.94286 #pixels= 10904 in= 789
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Only the true n map is independent on the brightness as shown above. The simulation shows that the number of particles is the same in the two zones but the brightness differ by a factor of 2.
Variance/intensity vs intensity maps.
Note that the variance/intensity map is different in the zones.

TChart x= 0.87672 y= 1.95714 #pixels= 12101 in= 792
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0 1 2 3 0 intensity 0 20 40 60 80 100 120 140 160 180 200 220 240
The intensity increases in the zone because of the different brightness. The variance/intensity must be subtracted by 1 to get the true brightness. When this is done, the B – 1 value differs by a factor of two between the 2 zones.
Questions:
1.
From the B vs intensity map evaluate the brightness of the particles in count/s/molecule.
2.
Is the number of particle recovered what was expected? Do you need to use the factor gamma to obtain the expected number of particles in the excitation volume?
3.
If you perform the simulation using the Gaussian Lorentzian excitation profile, will you get the same brightness? The same number of particles?
4.
The value of brightness is independent on the number of particles. As you increase the number of particles, is the recovered value of the number of particles always correct? Do you expect the same result for experimental data? Explain.
5.
The N&B analysis gives you the choice of 3 different calculations. Can you reason why we offer 3 different analyses? (Hint: try adding immobile particles to the simulation)