GOAL: This GUI Interaction aims to examine (a) the impact of optical absorption and scattering on spatially-resolved and spatial frequency-domain reflectance signals; and (b) the impact of optical properties and measurement selection on the tissue region probed by the detected photons.

I. Compare SDA and scaled Monte Carlo^* predictions for Spatially-Resolved Reflectance

1. Select the Forward/Analysis Panel.
2. In the Fwd Solver: dropdown menu 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.

^* Scaled Monte Carlo results are generated using the method described in Optics Express, Vol. 19, Issue 20, pp. 19627-19642 (2011)

II. Sensitivity of Spatially-Resolved Reflectance to Optical Properties

1. Select the Forward/Analysis Panel.
2. In the Fwd Solver: dropdown menu select Standard Diffusion (Analytic - Isotropic Point Source).
3. In the Solution Domain: select Steady State R(ρ).
4. Select Begin and End locations to 0.5 and 9.5 mm, respectively with 46 points (every 0.2 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 46 points (every 0.2 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 using 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.

III. Optical Property Recovery using Spatially-Resolved Reflectance Measurements: Impact of Noise and Initial Guess

1. Select the Inverse Solver Panel.
2. For Fwd Solver: select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for Inv Solver: select "Standard Diffusion (Analytic - Isotropic Point Source)".
3. In Solution Domain: select "Steady State(R(ρ))".
4. Set begin and end locations to 0.5 and 9.5 mm, respectively with 10 points (every 1 mm).
5. Set Optimization Parameters to: μ_a and μ'_s.
6. Simulate measured data: set "Forward Simulation Optical Properties:" to: μ_a = 0.01 mm^-1, μ'_s = 1 mm^-1, g = 0.8 and n = 1.4 and 2% noise.
7. Confirm the Hold On checkbox is checked.
8. Click the Plot Measured Data button.
9. Set Initial Guess Optical Properties: to: μ_a = 0.05 mm^-1, μ'_s = 1.5 mm^-1, g = 0.8 and n = 1.4.
10. Click the Plot Initial Guess button.
11. Click the Run Inverse Solver button.

Questions:

1. To what optical property values did the inverse solver converge? (Scroll to the bottom of the page to see the output).
2. Why are the converged values not exactly the forward simulation optical properties?
3. Perform the same analysis with 0% noise added to the simulated measured data. How accurate are the converged properties now?
4. Perform the same analysis with initial guess μ_a = 0.001 mm^-1, μ'_s = 0.5 mm^-1, g = 0.8 and n=1.4. How accurate are the converged properties now?

IV. Impact of Inverse Solver Model on Optical Property Recovery

1. Perform the same analysis changing the Inv Solver to "Scaled Monte Carlo - NURBS(g=0.8, n=1.4)".
2. Which Model Engine provided the more accurate converged values?

V. Impact of Number of Measurements on Optical Property Recovery

1. Repeat Section III using only 2 detectors. Can you strategically place the two detectors to obtain the same accuracy in the converged values as you obtained with 10 detectors?
2. Use the plots generated in Section II that showed the sensitivity of spatially-resolved diffuse reflectance to optical properties to help guide their placement.

VI. Sensitivity of Spatial Frequency Domain Reflectance to Optical Properties

First let us examine the sensitivity of Spatial Frequency Domain Reflectance to optical absorption

1. Go to the Forward Solver/Analysis Panel
2. For Fwd Solver: select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)"
3. In Solution Domain: select "Steady State(R(fx))".
4. Set Begin and End spatial frequencies to 0 and 0.5 /mm, respectively with 51 points (every 0.01/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 what spatial frequency regime shows the most sensitivity to μ_a changes?

Now let us examine the sensitivity of Spatial Frequency Domain Reflectance to optical scattering

1. Click the Clear All button and toggle back to Linear y-axis spacing.
2. Set Begin and End spatial frequencies to 0 and 0.5 /mm, respectively with 51 points (every 0.01/mm).
3. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s=1mm^-1, n=1.4.
4. Click the Plot Reflectance button.
5. Confirm the Hold On checkbox is checked.
6. Fix μ_a=0.01mm^-1. Repeat the above steps for μ'_s = 0.5 and 1.5 mm^-1.
7. Now toggle the plots using a logarithmic y-axis spacing.
8. Note what spatial frequency regime shows the most sensitivity to μ'_s.

VII. Optical Property Recovery using Spatial Frequency Domain Reflectance: Impact of Noise and Initial Guess

1. Click Clear All and set Normalization to None.
2. Select the Inverse Solver Panel.
3. For Fwd Solver: select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for Inv Solver: select "Standard Diffusion (Analytic - Isotropic Point Source)".
4. In Solution Domain: select "Steady State(R(fx))".
5. Set begin and end locations to 0 and 0.5 /mm, respectively with 11 points (every 0.05/mm).
6. Set Optimization Parameters to: μ_a and μ'_s.
7. Simulate measured data: set "Forward Simulation Optical Properties:" to: μ_a = 0.01 mm^-1, μ'_s = 1 mm^-1, g = 0.8 and n = 1.4 and 2% noise.
8. Confirm the Hold On checkbox is checked.
9. Click the Plot Measured Data button.
10. Set "Initial Guess Optical Properties:" to: μ_a = 0.05 mm^-1, μ'_s = 1.5 mm^-1, g = 0.8 and n = 1.4.
11. Click the Plot Initial Guess button.
12. Click the Run Inverse Solver button.

Questions:

1. To what optical property values did the inverse solver converge? (Scroll to the bottom of the page to see the output).
2. Perform the same analysis with 0% noise added to the simulated measured data. How accurate are the converged properties now?
3. Perform the same analysis with initial guess μ_a = 0.001 mm^-1, μ'_s = 0.5 mm^-1, g = 0.8 and n=1.4. How accurate are the converged properties now?

VIII. Effect of Measurement Range on Sensitivity to Optical Absorption and Scattering in Spatial Frequency Domain Reflectance

1. Go to the Inverse Solver Panel.
2. Follow the instructions provided in Section VII except modify the Spatial Frequency begin and end values to those obtained in Section VI. "Sensitivity of Spatial Frequency Domain Reflectance to Optical Properties".
3. Rerun the inverse solver.

Questions:

1. Were you able to improve the μ_a and μ'_s converged properties?
2. In what spatial frequency domain is reflectance most sensitive to μ_a? Why is this?
3. In what spatial frequency domain is reflectance most sensitive to μ'_s? Why is this?

IX. Spatially-Resolved Reflectance in a 2-Layer Medium Using a Standard Diffusion Solver

1. Select the Forward Solver/Analysis Panel.
2. Click the "Clear All" button.
3. In the Fwd Solver: dropdown menu select TwoLayer SDA
4. In the Solution Domain: select Steady State R(ρ).
5. Select Begin and End locations to 0.5 and 19.5 mm, respectively with Count equal to 39 (every 0.5 mm).
6. In the Tissue Input Box, for Layer 0 select Start/Stop Layer Heights of 0mm and 2mm to specify a 2mm thick superficial layer
7. Also for Layer Optical Properties: enter μ_a = 0.1mm^-1, μ'_s=1mm^-1, n=1.4.
8. Scroll down in the Tissue Input Box, for Layer 1 select Start/Stop Layer Heights of 2mm and Inf mm to specify the underlying semi-infinite medium
9. For the Layer Optical Properties: enter μ_a = 0.01mm^-1, μ'_s=1mm^-1, n=1.4.
10. Click the Plot Reflectance button.
11. Confirm the Hold On checkbox is checked.
12. Repeat this process so that you also generate R(ρ) for 4mm and 6mm layer thicknesses.
13. Confirm the Hold On checkbox is checked.

    Now, let us see how these curves compare to the spatially-resolved reflectance for a semi-infinite medium with properties corresponding to either the top layer or the underlying semi-infinite medium

14. In the Fwd Solver: dropdown menu select Standard Diffusion (Analytic-Distributed Point Source). Note that this solution is for a semi-infinite medium.
15. Select the R(ρ) radio button and Detector Positions: Begin=0.5 mm, End=19.5 mm, Number=93.
16. Plot this solution using optical properties equal to the top layer.
17. Plot this solution using optical properties equal to the bottom layer.

Questions:

1. Where do the two-layer solutions lie with respect to the one-layer solutions? Why is this?
2. Where do the two-layer solutions agree most with the one-layer tissue with bottom layer optical properties? Can you explain why?
3. Where do the two-layer solutions agree most with the one-layer tissue with top layer optical properties and why?
4. Can you explain the effect of layer thickness? What does this tell you about the depth to which the detected photons penetrate within the tissue?

Time permitting, repeat this entire exercise but with a highly-scattering top layer with properties of μ_a = 0.05mm^-1, μ'_s=1.5mm^-1 and bottom layer optical properties of μ_a = 0.05mm^-1, μ'_s=0.8 mm^-1.

X. Observe SFD Reflectance as a function of wavelength and chromophore concentration

1. Select the Spectral Panel and click Clear All.
2. Select Skin as the Tissue Type and set the blood volume fraction to 2% with 80% saturation.
3. Plot both the μ_a and μ'_s spectra from 500 nm to 1000nm with 50 wavelengths.
4. Select the Forward Solver/Analysis Panel and click the use spectral panel inputs check-box.
5. Select Solution Domain to be R(fx).
6. In the Independent Axis select allow multi-axis selection.
7. Select both the f_x and λ check boxes.
8. Set the Spatial Frequencies from 0 to 0.3 / mm with 4 frequencies, and confirm the Wavelength Range is set from 500 nm to 1000 nm with 50 wavelengths.
9. Select Scaled Monte Carlo: NURBS as the Fwd Solver.
10. Clear the plot view and Plot Reflectance.
11. Repeat the above steps for a blood saturation of 40%.

Questions

1. What wavelengths and spatial frequencies are sensitive to the change in blood oxygen saturation?
2. What chromophore in noticeably present in the 900 to 1000 nm range?
3. How does scattering effect the wavelength and spatial frequency spectrum? For example, change the power b = 2.0.