GOAL: Examine the effect of Optical Properties, Solver and Source Configuration on Diffuse Reflectance.

I. Impact of Optical Properties on Spatially-Resolved Reflectance

1. Select the "Forward/Analysis Panel".
2. In the dropdown (Fwd Solver Engine) select Standard Diffusion (Analytic - Isotropic Point Source).
3. In the Solution Domain: select Steady State R(ρ).
4. Select start and stop locations to 0.5 and 9.5 mm, respectively with 19 points (every 0.5 mm).
5. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s=1mm^-1, n=1.4.
6. Click the "Plot Reflectance" button.
7. Confirm the "Hold On" checkbox is checked.
8. Fix μ_s'=1mm^-1. Repeat the above steps for μ_a = 0.1 and 1.0 mm^-1.
9. Note the trend of decreasing reflectance with increasing absorption.
10. Now toggle the plots with a logarithmic y-axis spacing. Note the linear behavior at larger detector locations.

    Question: Can you relate this to the underlying analytic approximation?

11. Click the "Clear All" button and toggle back to "Linear" y-axis spacing.
12. Select start and stop locations to 0.5 mm and 9.5 mm, respectively with 19 points (every 0.5 mm).
13. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1 mm^-1, n=1.4.
14. Click the "Plot Reflectance" button.
15. Confirm the "Hold On" checkbox is checked.
16. Fix μ_a=0.01mm^-1. Repeat the above steps for μ'_s = 0.5 and 1.5 mm^-1.
17. Now toggle the plots with a logarithmic y-axis spacing.

Questions: Note the trend of increasing reflectance with increasing scattering close to the source but the opposite far from the source. Is this expected? Why or why not?

Press "Clear All" and return to linear axis spacing.

II. Compare SDA and MC predictions for Spatially-Resolved Reflectance

1. Select the "Forward/Analysis Panel".
2. In the dropdown (Fwd Solver Engine) select Standard Diffusion (Analytic - Isotropic Point Source).
3. In Solution Domain: select Steady State R(ρ).
4. Select start and stop locations to 0.5 and 9.5 mm, respectively with 19 points (every 0.5 mm).
5. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1 mm^-1.
6. Click the "Plot Reflectance" button.
7. Confirm the "Hold On" checkbox is checked.
8. Now select: Forward Model: Scaled Monte Carlo - NURBS (g=0.8, n=1.4).
9. Click the "Plot Reflectance" button.
10. Repeat the steps for μ_a = 0.1 and 1 mm^-1.

Questions:

1. How do the SDA and MC models compare close to ρ = 0?
2. Now switch to a logarithmic y-axis spacing. How do the models compare far from the source?

Press "Clear All" and return to linear axis spacing.

III. Explore the impact of an absorbing layer on Spatially-Resolved Reflectance

1. Select the "Monte Carlo Solver Panel".
2. Click the "Clear All" button.
3. Click the "Load Input File" button and load an input file that specifies a two layer tissue with a highly absorbing top layer, two_layer_ROfRho.xml. Set the top layer (Layer 1) to be 1.5mm thick and have the optical properties μ_a = 0.1mm^-1, μ'_s = 1.5mm^-1 and g = 0.8. Set the bottom layer (Layer 2) optical properties to μ_a = 0.01mm^-1, μ'_s = 1mm^-1 and g = 0.8.
4. Set "Number of Photons" to 10000.
5. Click the "Run Simulation" button and select "Plot View" tab.
6. Make sure "Hold On" is checked.
7. Click on "Forward Solver/Analysis Panel" and select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)" from the pull-down menu. Note that this solution is for a single tissue layer.
8. Select the R(ρ) radio button and "Detector Positions" Begin=0.05 mm, End=9.95 mm, Number=100.
9. Plot this solution using optical properties equal to the top layer.
10. Plot this solution using optical properties equal to the bottom layer.

Questions:

1. Where does the two-layer solution lie with respect to the one-layer solutions? Why is this?
2. Where does the two-layer solution agree most with the one-layer tissue with bottom layer optical properties? Can you explain why?
3. Where does the two-layer solution agree most with the one-layer tissue with top layer optical properties and why?

IV. Impact of Optical Properties on Temporally-Resolved Reflectance

1. Select the "Forward/Analysis Panel".
2. Click "Clear All" and return the "Y Axis Spacing" back to "Linear".
3. In the dropdown (Fwd Solver Engine) select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)".
4. In the Solution Domain: select Time-Domain, (Collimated Beam Source) R(ρ,t).
5. For the Independent axis choose t and set ρ = 10 mm.
6. Choose "Start" = 0 ns and "Stop" = 0.5 ns with 101 time points (1 point every 5 ps).
7. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
8. Click the "Plot Reflectance" button.
9. Repeat the above for μ_a = 0.1 and 1 mm^-1.

   Question: Note also the difference in the amplitude and shape of these plots. What do you believe is responsible for this? Hint: It may help to use both linear and log y-axis spacing.

10. Click the "Clear All" button.
11. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
12. Click the "Plot Reflectance" button.
13. Repeat the above for μ'_s = 0.5 and 1.5 mm^-1.

Questions:

1. Note that no photons are detected before a finite time in the time-resolved reflectance signal. Can you independently calculate the minimal delay time? Note: It may help to visualize this delay using logarithmic x-axis spacing.
2. Note that the peak reflectance values are different and not located at the same time point. Can you speculate as to the origin of these features? Hint: It may help to use both linear and log y-axis spacing.
3. You are designing a time-resolved optical imaging system to detect early formation of a fibrous tumor. What is an approximate time resolution and source detector separation necessary to differentiate normal breast with μ'_s=0.6 mm^-1 from a fibroid tumor with μ'_s=1.2 mm^-1 with such a system?