GOAL: This GUI Interaction aims to examine (a) the impact of optical absorption and scattering on time-domain and temporal frequency-domain reflectance signals; and (b) the impact of optical properties and source-detector separation on the tissue region probed by the detected photons.

I. Impact of Optical Properties on Time-Resolved Reflectance R(t)

1. Select the Forward Solver/Analysis Panel.
2. Click Clear All and return the Y Axis Spacing back to Linear.
3. In the Fwd Solver Engine drop down menu select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)".
4. In the Solution Domain: select Time-Domain, R(ρ,t).
5. For the Independent Axis choose t and set ρ = 10 mm.
6. In Detection Times choose "Begin" = 0 ns and "End" = 1.0 ns with "Number" = 201 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. Confirm that the Hold On checkbox is selected.
10. Repeat the above for μ_a = 0.05, 0.1 and 0.3 mm^-1.

    Question: Note the difference in the magnitude and shape of these plots. What do you believe is responsible for this? Hint: It may helpful to view the results under both linear and log y-axis spacing.

11. Click the Clear All button.
12. Start again with Optical Properties: μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
13. Click the Plot Reflectance button.
14. Confirm that the Hold On checkbox is selected.
15. 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 the 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 using such a system?

II. Sensitivity of Temporally-Resolved Diffuse Reflectance to Optical Properties

1. Select the Forward Solver/Analysis Panel.
2. In the Fwd Solver Engine drop down menu select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)".
3. In Solution Domain: select Time-Domain R(ρ,t).
4. For the Independent axis choose t and set ρ = 10 mm.
5. In Detection Times choose "Begin" = 0 ns and "End" = 1.0 ns with "Number" = 101 time points (1 point every 10 ps).
6. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
7. Click the Plot Reflectance button.
8. Confirm that the Hold On checkbox is selected.
9. Increase the absorption coefficient by 10% to μ_a = 0.011mm^-1.
10. Click the Plot Reflectance button.
11. Now, in the Plot View window, select the Curve Radio Button in the Normalization Controls. This operation divides each of the time-resolved reflectance results in the plot view window by the first R(t) result. Thus each result becomes R_i(t) / R₁(t) where R₁(t) is the first reflectance result and R_i(t) is any successive reflectance result. This results in the first R₁(t) result getting transformed to a series of '1' values.

    Question: Can you explain these results intuitively? Note the magnitude of the relative changes in reflectance.

12. Now Click the Clear All button and select the None Radio Button in the Normalization Controls
13. Repeat this examination of a 10% increase in absorption (i.e., from a μ_a = value of 0.01 to 0.011mm^-1) on the R(t) signal for values of μ'_s = 0.5 and 1.5 mm^-1.

    Question: Does the impact of the changes in the background tissue scattering on the relative changes in the R(t) signal with a 10% increase in absorption make sense? Can you explain? How might these results relate to the partial derivative ∂R/∂μ_a?

    Now let us examine the impact of optical scattering on these time-resolved reflectance signals

14. Begin with clicking the Clear All button and selecting the None Radio Button in the Normalization Controls
15. Use the same selections for Solution Domain, Detection Times, and Optical Properties as in II.2-II.6 above.
16. Click the Plot Reflectance button.
17. Confirm the Hold On checkbox is checked.
18. Now plot R(t) when the reduced scattering is 10% higher i.e., for Optical Properties: of μ_a = 0.01mm^-1, μ'_s=1.1mm^-1
19. Click the Plot Reflectance button.
20. Now, in the Plot View window, select the Curve Radio Button in the Normalization Controls.

    Question: Can you explain these results intuitively? Note the magnitude of the relative changes in R(t) due to the increased scattering.

21. Repeat this examination of a 10% increase in scattering (from a μ'_s = value of 1.0 to 1.1mm^-1) on the R(t) signal for values of μ_a = 0.1 and 0.3 mm^-1.

    Question: Does the impact of the changes in the background tissue absorption on the relative changes in the R(t) signal with a 10% increase in reduced scattering make sense? Can you explain? How might these results relate to the partial derivative ∂R/∂μ'_s?

III. Impact of Optical Properties on Temporal Frequency-Domain Reflectance R(f_t)

First let us examine the impact of optical absorption on the Temporal Frequency-Domain Reflectance

1. Select the Forward/Analysis Panel.
2. Click Clear All and return the "Y Axis Spacing" back to "Linear".
3. In the Fwd Solver Engine drop down menu select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)".
4. In the Solution Domain: select Frequency-Domain, R(ρ,f_t).
5. For the Independent axis choose ft and set ρ = 10 mm.
6. Choose "Begin" = 0 GHz and "End" = 1 GHz with 101 frequency points (1 point every 10 MHz).
7. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
8. Click the Plot Reflectance button. What you see is the modulation frequency dependence of both the Real and Imaginary components of the Frequency-Domain Reflectance
9. To view the amplitude and phase select the Amp and Phase radio button, respectively, in the Plot Toggle menu below the plot.
10. Verify that the Hold On checkbox is selected.
11. Repeat the above for μ_a = 0.05, 0.1 and 0.3 mm^-1.

    Question: Note the variation in magnitude and shape of these amplitude and phase plots. What do you believe is responsible for this?

    Now let us examine the impact of optical scattering on these signals

12. Begin with clicking the Clear All button.
13. Begin with the same selections for Solution Domain, Detection Times, and Optical Properties as in III.3-III.7 above.
14. Click the Plot Reflectance button. What you see is the modulation frequency dependence of both the Real and Imaginary components of the Frequency-Domain Reflectance
15. To view the amplitude and phase select the Amp and Phase radio button, respectively, in the Plot Toggle menu below the plot.
16. Verify that the Hold On checkbox is selected.
17. Repeat the above for μ'_s = 0.5, 1.5 mm^-1.

    Question: Note the variation in magnitude and shape of these Amplitude and Phase plots. What do you believe is responsible for this?

IV. Sensitivity of Temporal Frequency-Domain Reflectance to Optical Properties

1. Select the Forward Solver/Analysis Panel.
2. Click "Clear All" and return the Y Axis Spacing back to Linear.
3. In the Fwd Solver Engine drop down menu select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)".
4. In the Solution Domain: select Frequency-Domain, R(ρ,f_t).
5. For the Independent Axis choose ft and set ρ = 10 mm.
6. Choose "Begin" = 0 GHz and "End" = 1 GHz with 101 frequency points (1 point every 10 MHz).
7. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s = 1mm^-1.
8. Click the "Plot Reflectance" button.
9. To view the amplitude and phase select the Amp and Phase radio buttons, respectively, in the Plot Toggle menu below the plot.
10. Verify that the Hold On checkbox is selected.
11. Now plot the temporal frequency domain amplitude when the tissue absorption is 10% higher i.e., for Optical Properties: μ_a = 0.011mm^-1, μ'_s=1mm^-1
12. Click the Plot Reflectance button.
13. Now, in the Plot View window, click the Curve Radio Button in the Normalization Controls. This operation divides the each of the frequency-dependent amplitude curves Amp_i(f_t) by the first Amp₁(f_t) result. Thus the first Amp₁(f_t) result gets transformed to a series of '1' values while the other results Amp_i(f_t) are normalized relative to this first result: Amp₁(f_t) / Amp_i(f_t).
14. Examine the results for Phase using the Plot Toggle and Normalization controls.

    Question: Can you explain this results intuitively? Note the magnitude of the relative changes in frequency-dependent amplitude and phase.

15. Repeat this examination of a 10% increase in absorption (from a μ_a = value of 0.01 to 0.011mm^-1) on the R(f_t) signal for values of μ'_s = 0.5 and 1.5 mm^-1.

    Question: Does the impact of the changes in the background tissue scattering on the relative changes in Amp(f_t) and Phase(f_t) signals with a 10% increase in absorption make sense? Can you explain? How might these results relate to the partial derivatives ∂Amp/∂μ_a and ∂Phase/∂μ_a?

    Now let us examine the impact of optical scattering

16. First Clear All and set the Normalization Controls to None.
17. Begin with the same selections for Solution Domain, Detection Times, and Optical Properties as in IV.3-IV.7 above.
18. Click the Plot Reflectance button. What you see is the modulation frequency dependence of both the Real and Imaginary components of the Frequency-Domain Reflectance
19. To view the amplitude and phase select the Amp and Phase radio buttons in the Plot Toggle menu below the plot.
20. Verify that the Hold On checkbox is selected.
21. Now plot the temporal frequency domain amplitude and phase when the tissue scattering is 10% higher i.e., for Optical Properties: of μ_a = 0.01mm^-1, μ'_s=1.1mm^-1
22. Click the Plot Reflectance button.
23. Examine the results for both amplitude and phase using the Plot Toggle and Normalization controls.

    Question: Can you explain this results intuitively? Note the magnitude of the relative changes in amplitude and phase.

24. Repeat this examination of a 10% increase in reduced scattering (from a μ_a = value of 1 to 1.1mm^-1) on the R(f_t) signal for values of μ_a = 0.1 and 0.3 mm^-1.

    Question: Does the impact of the changes in the background tissue scattering on the relative changes in Amp(f_t) and Phase(f_t) signals with a 10% increase in scattering make sense? Can you explain? How might these results relate to the partial derivatives ∂Amp/∂μ'_s and ∂Phase/∂μ'_s?

V. Impact of Optical Properties and Source-Detector Separation on Photon Hitting Density

Goal: This portion of the GUI Interaction is to examine how source detector separation and optical properties affect the region of tissue that is sampled in a spatially-resolved diffuse reflectance measurement R(ρ).

1. Select the Fluence/Interrogation Solver Panel.
2. In the Fwd Solver Engine drop down menu select "Standard Diffusion".
3. In Map Type select phd (Photon Hitting Density).
4. In Solution Domain: select phd(ρ,z).
5. Use default values for Rho and Z Ranges.
6. In Optical Properties: enter μ_a = 0.01 mm^-1, μ'_s = 1 mm^-1. Note that μ'_s / μ_a = 100.
7. Set the "Source-Detector Separation" (ρ = ) to 20 mm.
8. Click the Generate Fluence/Interrogation Map button at the bottom of the panel.
9. Examine the shape and magnitude of the photon hitting density. Use of the Auto Scale, Colormap Type:, and Log10 controls may be useful here.
10. Determine the mean sampling depth <z> of all the detected photons.
11. Repeat for source-detector separations of ρ = 10 mm and 5 mm.
12. What is the variation in <z> with ρ?
13. Repeat V.5-V.12 for fixed μ'_s = 1 mm^-1 with μ_a values of 0.03 and 0.1 mm^-1.

Problem Based Learning Exercise:

1. You are designing a dual wavelength fiber optic probe with 3 source-detector pairs to detect the formation of new blood vessels during the integration of a skin graft. The neovascular layer is expected to form 2mm below the surface in a highly scattering tissue with μ'_s = 2mm^-1. The initial blood volume fraction (BVF) in the graft is 0.5% at 60% oxygenation and you wish to detect changes in the BVF up to 3% along with an increase in blood oxygenation up to 85%. Do you think this is possible? If not, why not?If so, what 3 source-detector separation distances and 2 wavelengths would you choose.