GOAL: Solve Spatially-Resolved Reflectance inverse problems.

I. Impact of Noise and Initial Guess on Spatially-Resolved Reflectance Measurements

1. Select the Inverse Solver Panel.
2. For Fwd Solver Engine: select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for Inv Solver Engine: 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?

II. Impact of Inverse Solver Model on Optical Property Recovery

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

III. Impact of Number of Measurements on Optical Property Recovery

1. Repeat II 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 Lab C, Section VII that showed the sensitivity of spatially-resolved diffuse reflectance to optical properties to help guide their placement.

GOAL: Solve Spatial Frequency Domain Reflectance inverse problems.

IV. 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 Engine: select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)"
3. In Solution Domain: select "Steady State(R(fx))".
4. Set start and stop locations 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. Now plot the spatial frequency domain reflectance when the tissue absorption is 10% higher i.e., for Optical Properties: of μ_a = 0.011mm^-1, μ'_s=1mm^-1
9. Click the Plot Reflectance button.
10. Now, in the Plot View window, click the Curve Radio Button in the Normalization Controls. This operation divides all spatial frequency domain reflectance results in the plot view window by the first R(fx) result. Thus each result becomes R_i(fx) / R₁(fx) where R₁(fx) is the first reflectance result and R_i(fx) is any successive reflectance result. This results in the first R₁(fx) result getting transformed to a series of '1' values.
11. 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 Clear All and set Normalization to None.
2. In Optical Properties: enter μ_a = 0.01mm^-1, μ'_s=1mm^-1, n=1.4.
3. Click the Plot Reflectance button.
4. Confirm the Hold On checkbox is checked.
5. Now plot the spatial frequency domain reflectance when the tissue scattering is 10% higher i.e., for Optical Properties: of μ_a = 0.01mm^-1, μ'_s=1.1mm^-1
6. Now, in the Plot View window, click the Curve Radio Button in the Normalization Controls. This operation divides all spatial frequency domain reflectance results in the plot view window by the first R(fx) result. Thus each result becomes R_i(fx) / R₁(fx) where R₁(fx) is the first reflectance result and R_i(fx) is any successive reflectance result. This results in the first R₁(fx) result getting transformed to a series of '1' values.
7. Note what spatial frequency regime shows the most sensitivity to μ'_s.

V. Impact of Noise and Initial Guess on Spatial Frequency Domain Reflectance

1. Click Clear All and set Normalization to None.
2. Select the Inverse Solver Panel.
3. For Fwd Solver Engine: select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for Inv Solver Engine: 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?

VI. 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 V except modify the Spatial Frequency begin and end values to those obtained in Section IV. "Impact of Optical Properties on Spatial Frequency Domain Reflectance".
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?