I. Distributed Point Source ("Pencil Beam")

Goal: This portion of the GUI Interaction is to examine how the fluence distribution produced by a narrow collimated beam whose strength falls exponentially with depth at a constant decay rate of μ'_t equivalent to 1/l ^* .

1. Select Fluence/Interrogation Solver Panel. Note that this panel lists various types of source configuration and solver options.
2. In the Fwd Solver Engine: dropdown menu select Standard Diffusion (Analytic - Distributed Point Source).
3. In Solution Domain: Select Φ(ρ,z).
4. Use default values for Rho and Z Range.
5. In Optical Properties: enter μ_a = 0.01 mm^-1, μ'_s = 1 mm^-1. Note that μ'_s / μ_a≈100.
6. Click the Generate Fluence/Interrogation Map button at the bottom of the panel.
7. Examine the shape and magnitude with depth of the fluence distribution along the centerline.
8. Replot the fluence distribution for μ_a = 0.1 and 1 mm^-1 and examine the effect of the increased absorption on the magnitude, axial and lateral penetration depths.
9. Now keep absorption constant at μ_a = 0.01 mm^-1 and examine the effect of varying the reduced scattering coefficient μ'_s = 0.5, 1.0, and 1.5 mm^-1 on the magnitude, axial and lateral penetration depths.

II. Distributed Gaussian Beam Source

Goal: This portion of the GUI Interaction is to examine the impact of beam diameter on the amplitude and axial/lateral dispersion of the light in turbid tissues.

1. Select Fluence/Interrogation Solver Panel. Note that this panel lists various types of source configuration and solver options.
2. In the Fwd Solver Engine: dropdown menu select Standard Diffusion (Analytic - Distributed Gaussian Source).
3. In Solution Domain: Select Φ(ρ,z).
4. Use default values for Rho and Z Range.
5. In Optical Properties: enter μ_a = 0.01 mm^-1, μ'_s = 1 mm^-1. Note that μ'_s / μ_a≈100.
6. Select a Gaussian Beam Diameter of 0.2mm.
7. Click the Generate Fluence/Interrogation Map button at the bottom of the panel.
8. Keeping the μ'_s value fixed, plot the fluence distribution for μ_a = 0.03, 0.1, 0.3, and 1 mm^-1 and examine the effect of the increased absorption on the magnitude, axial and lateral penetration depths of the fluence distribution.
9. Now set the absorption coefficient, μ_a = 0.01 mm^-1 and examine the effect of varying the reduced scattering coefficient μ'_s = 0.5, 1.0, and 1.5 mm^-1 on the magnitude, axial and lateral penetration depths.
10. Click the Generate Fluence/Interrogation Map button at the bottom of the panel.
11. Repeat the above for Gaussian beam diameters of 0.5mm and 2mm.

III. Monte Carlo Simulations of Narrow Collimated Beam Irradiation

Goal: This portion of the GUI Interaction is to examine the impact of optical properties on the amplitude and axial/lateral dispersion of the light in turbid tissues.

1. Select the Monte Carlo Solver Panel.
2. In the Input File Specification, click the Load Input File button. Select the file: infile_one_layer_ROfRho_FluenceOfRhoAndZ.xml. This is a Monte Carlo simulation input file that specifies a Discrete Absorption Weighting (DAW) simulation to produce reflectance as a function of source-detector (ρ) separation, R(ρ).
3. Set the optical properties of the tissue layer to be μ_a = 0.01mm^-1, μ'_s = 1mm^-1, g=0.8.
4. Set Number of Photons to 1000.
5. Click the Run Simulation button.
6. Note the Mean Depth magnitude, axial and lateral penetration depths of the fluence distribution.
7. Increase the absorption coefficient to μ_a = 1mm^-1, keeping all other properties constant.
8. Click the Run Monte Carlo Simulation button.
9. Note the magnitude of the Mean Depth, axial and lateral penetration depths of the fluence distribution.
10. Now repeat this exercise keeping μ_a constant at 0.1mm^-1 and μ'_s values of 0 and 1mm^-1, noting the mean depth of penetration.

Questions:

1. How does increasing absorption change the magnitude, axial and lateral penetration depths?
2. How does increasing scattering change the magnitude, axial and lateral penetration depths?
3. How do these results compare with those obtained using the Standard Diffusion Solver in Section I?

IV. Visualizing Radiance versus Fluence distributions using the Monte Carlo CommandLine Application

Goal: This portion of the lab exercise is to examine the directional aspect of radiance in turbid tissues.

1. Go to the Documents folder.
2. Holding down the shift key, right click the MCCL folder and select Open command window here.
3. Execute the Monte Carlo Command Line Application using the command is mc infile=infile_one_layer_FluenceOfRhoAndZ_RadianceOfRhoAndZAndAngle.xml. This infile specifies a perpendicular point source impinging on the tissue at (0,0,0). The tissue is homogeneous with optical properties μ_a = 0.01mm^-1, μ'_s = 1mm^-1, g=0.8 and n = 1.4. Executing this command creates a folder called "one_layer_FluenceOfRhoAndZ_RadianceOfRhoAndZAndAngle" in the MCCL directory with fluence and radiance detector results.
4. Go into the MCCL folder.
5. Click on load_results_script. This will bring up MATLAB and also a window to edit load_results_script.m. Change datanames to be one_layer_FluenceOfRhoAndZ_RadianceOfRhoAndZAndAngle. Enter load_results_script at the MATLAB prompt.
6. Three figures should appear, one plot of Fluence, and two plots of radiance in the lower and upper hemispheres. Note that the lower hemisphere is notated as [0-pi/2] and the upper hemisphere as [pi/2-pi]. These angles are with reference to the positive z-axis which is into the tissue.

Questions:

1. In what way can the angular information shown in the radiance plots be useful?
2. Which plot of radiance looks most like Fluence and why?

Additional Questions: Consider the situation where you using a laser-based therapy to treat an embedded tumor. For this application, it is critical that you maximize the axial penetration of the light field. However during the treatment, the tissue absorption may increase due to increased blood flow and scattering may decrease due to morphological changes in the tissue. In this context comment on the following:

1. How does an increase in absorption impact (a) the axial penetration of the light field and (b) the lateral dispersion of the light field?
2. How does a decrease in scattering impact (a) the axial penetration of the light field and (b) the lateral dispersion of the light field?
3. Would increasing the beam diameter improve (a) the axial penetration of the light field and/or (b) the lateral dispersion of the light field? Is this impact the same regardless of the optical properties?

V. Impact of Optical Properties on Spatially-Resolved Reflectance

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

VI. 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 Engine: dropdown menu select TwoLayer SDA
4. In the Solution Domain: select Steady State R(ρ).
5. Select start and stop locations to 0.5 and 19.5 mm, respectively with 93 points (every 0.2 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 Engine: 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.

VII. Sensitivity of Spatially-Resolved Diffuse Reflectance to Optical Properties

Goal: This portion of the GUI Interaction is to examine the impact of optical absorption and scattering on R(ρ).

1. Select the Forward Solver/Analysis Panel.
2. In the Fwd Solver Engine: dropdown menu select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)".
3. In Solution Domain: select Steady-State R(ρ).
4. Select start and stop 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.
6. Click the Plot Reflectance button.
7. Confirm the Hold On checkbox is checked.
8. Now plot the spatially-resolved 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 spatially-resolved reflectance results in the plot view window by the first result R₁(ρ). Thus the first result gets transformed to a series of '1' values while the second result R₂(ρ) is represented as R₂(ρ) / R₁(ρ) relative to this first result.

    Question: Can you explain this results intuitively? Please note the magnitude of the relative changes in reflectance

11. Repeat this examination of a 10% increase in absorption (from a μ_a = value of 0.01 to 0.011mm^-1) on the R(ρ) 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(ρ) signal with a 10% increase in absorption make sense? Can you explain? How might these results relate to the partial derivative ∂R/∂μ_a?

12. Click the Clear All button.
13. Now begin again with "Optical Properties" μ_a = 0.01mm^-1, μ'_s=1mm^-1.
14. Click the Plot Reflectance button.
15. Confirm the Hold On checkbox is checked.
16. Now plot the spatially-resolved reflectance when the reduced scattering is 10% higher i.e., for Optical Properties: of μ_a = 0.01mm^-1, μ'_s=1.1mm^-1
17. Click the Plot Reflectance button.
18. Now, in the Plot View window, click the "Curve" Radio Button in the Normalization Controls. This operation divides all spatially-resolved reflectance results in the plot view window by the first R(ρ) result.

    Question: Can you explain this results intuitively? Please note the magnitude of the relative changes in R(ρ).

19. Click the Clear All button and, select the None Radio Button in the Normalization Controls.
20. Repeat this examination of a 10% increase in scattering (from a μ'_s = value of 1.0 to 1.1mm^-1) on the R(ρ) 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(ρ) 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?