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Because determining the adequate aperture requires several imaging trials, an appropriate way to optimize the system is through the use of light propagation models generated using the Monte Carlo method. These are computational algorithms that depend on repeated random sampling to obtain results that are probabilistically close to real life situations. Using this method is possible as the radiative transfer equation (that describes the transport equation) can be approximated as ‘diffusion’ of photons in biological tissue. Using an open-source MATLAB program MCmatlab, Team Imagivo was able to verify the dual aperture normalization methodology and determine an adequate aperture combination.
Figure 1: This closed aperture image (left) was obtained using a half-angle of 3.65° and was obtained by simulating raster scanning across the sample using a detector with a single pixel field-of-view. The corresponding plot of signal versus depth is shown on the right. The coefficient of determination was calculated to be 0.873.
Figure 2: This open aperture image (left) was obtained using a half-angle of 30.0° and was obtained by simulating raster scanning across the sample using a detector with a single pixel field-of-view. The corresponding plot of signal versus depth is shown on the right. The coefficient of determination was calculated to be 0.870.
Figure 3: This ratio image (left) was obtained by taking the ratio of the closed aperture image shown in Figure 1 and the open aperture image shown in Figure 2. The corresponding plot of signal versus depth is shown on the right. The coefficient of determination was calculated to be 0.943.
To verify that there is a better correlation between the ratio signal and depth compared to that of the closed or open apertures, plots of signal versus depth were generated for the three images. Using the coefficient of determination (R^2) to assess the correlation, it can be seen that the plot for ratio signal is better correlated with fluorescence depth. Additionally, there is a greater dynamic range when using the ratio metric signal plot at greater depths when compared to the open aperture or closed aperture signal plots. This allows for the distinguishing between depths to be much easier at the range of depths that the team is focused on (0-5 mm).
In these simulations, the concentration, the specific absorbance, or the quantum efficiency of the fluorescence dye can be ignored, as these factors are the same for all apertures tested. In further validation steps, these factors will be taken into account in order to see how these factors affect signal quality, determine an adequate illumination time of the sample, and determine an average imaging time.
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