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 (Forward Model) select Standard Diffusion (Analytic - 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 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 (Forward Model) select Standard Diffusion (Analytic - 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. Impact of Optical Properties on Temporally-Resolved Reflectance

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

9. Click the "Clear All" button.
10. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
11. Click the "Plot Reflectance" button.
12. 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?