# 2017 Laboratory F: Recovery of Tissue Properties from Spatially-Resolved and Spatial Frequency Domain Reflectance Measurements

### From VirtualPhotonics

**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.

Bring up the Silverlight GUI

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

- Select the
**Forward/Analysis Panel**. - In the
**Fwd Solver:**dropdown menu select Standard Diffusion (Analytic - Isotropic Point Source). - In
select Steady State**Solution Domain***R*(ρ). - Select
**Begin**and**End**locations to 0.5 and 9.5 mm, respectively with 19 points (every 0.5 mm). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}= 1 mm^{-1}. - Click the
**Plot Reflectance**button. - Confirm the
**Hold On**checkbox in the Plot View window is checked. - Now select
**Fwd Solver:**Scaled Monte Carlo - NURBS (g=0.8, n=1.4). - Click the
**Plot Reflectance**button. - Repeat the steps for μ
_{a}= 1 mm^{-1}.

**Questions:**

- How do the SDA and MC models compare close to ρ = 0?
- 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**

- Select the
**Forward/Analysis Panel**. - In the
**Fwd Solver:**dropdown menu select Standard Diffusion (Analytic - Isotropic Point Source). - In the
select Steady State**Solution Domain***R*(ρ). - Select
**Begin**and**End**locations to 0.5 and 9.5 mm, respectively with 46 points (every 0.2 mm). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}=1mm^{-1}, n=1.4. - Click the
**Plot Reflectance**button. - Confirm the
**Hold On**checkbox is checked. - Fix μ'
_{s}=1.0mm^{-1}. Repeat the above steps for μ_{a}= 0.1 and 1.0 mm^{-1}. - Note the trend of decreasing reflectance with increasing absorption.
- 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?

- Click the
**Clear All**button and toggle back to**Linear**y-axis spacing. - Select
**Begin**and**End**locations to 0.5 mm and 9.5 mm, respectively with 46 points (every 0.2 mm). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}= 0.5 mm^{-1}, n=1.4. - Click the
**Plot Reflectance**button. - Confirm the
**Hold On**checkbox is checked. - Fix μ
_{a}=0.01mm^{-1}. Repeat the above steps for μ'_{s}= 1 and 1.5 mm^{-1}. - Now toggle the plots using a logarithmic y-axis spacing.
**Question:**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**

- Select the
**Inverse Solver Panel**. - For
**Fwd Solver:**select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for**Inv Solver:**select "Standard Diffusion (Analytic - Isotropic Point Source)". - In
select "Steady State(**Solution Domain***R*(ρ))". - Set
**Begin**and**End**locations to 0.5 and 9.5 mm, respectively with 10 points (every 1 mm). - Set
to: μ**Optimization Parameters**_{a}and μ'_{s}. - 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. - Confirm the
**Hold On**checkbox is checked. - Click the
**Plot Measured Data**button. - 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. - Click the
**Plot Initial Guess**button. - Click the
**Run Inverse Solver**button.

**Questions: **

- To what optical property values did the inverse solver converge? (Scroll to the bottom of the page to see the output).
- Why are the converged values not exactly the forward simulation optical properties?
- Perform the same analysis with 0% noise added to the simulated measured data. How accurate are the converged properties now?

**IV. Impact of Inverse Solver Model on Optical Property Recovery**

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

**V. Impact of Number of Measurements on Optical Property Recovery**

- 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?
- 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

- Go to the
**Forward Solver/Analysis Panel** - For
**Fwd Solver:**select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)" - In
select "Steady State(**Solution Domain***R*(*f**x*))". - Set
**Begin**and**End**spatial frequencies to 0 and 0.5 /mm, respectively with 51 points (every 0.01/mm). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}=1mm^{-1}, n=1.4. - Click the
**Plot Reflectance**button. - Confirm the
**Hold On**checkbox is checked. - Fix μ'
_{s}=1mm^{-1}. Repeat the above steps for μ_{a}= 0.1 and 1.0 mm^{-1}. - 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

- Click the
**Clear All**button and toggle back to**Linear**y-axis spacing. - Set
**Begin**and**End**spatial frequencies to 0 and 0.5 /mm, respectively with 51 points (every 0.01/mm). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}=1mm^{-1}, n=1.4. - Click the
**Plot Reflectance**button. - Confirm the
**Hold On**checkbox is checked. - Fix μ
_{a}=0.01mm^{-1}. Repeat the above steps for μ'_{s}= 0.5 and 1.5 mm^{-1}. - Now toggle the plots using a logarithmic y-axis spacing.
- 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**

- Click
**Clear All**and set**Normalization**to**None**. - Select the
**Inverse Solver Panel**. - For
**Fwd Solver:**select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for**Inv Solver:**select "Standard Diffusion (Analytic - Isotropic Point Source)". - In
select "Steady State(**Solution Domain***R*(*f**x*))". - Set
**Begin**and**End**locations to 0 and 0.5 /mm, respectively with 11 points (every 0.05/mm). - Set
to: μ**Optimization Parameters**_{a}and μ'_{s}. - 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. - Confirm the
**Hold On**checkbox is checked. - Click the
**Plot Measured Data**button. - 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. - Click the
**Plot Initial Guess**button. - Click the
**Run Inverse Solver**button.

**Questions: **

- To what optical property values did the inverse solver converge? (Scroll to the bottom of the page to see the output).
- Perform the same analysis with 0% noise added to the simulated measured data. How accurate are the converged properties now?
- 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**

- Go to the
**Inverse Solver Panel**. - Follow the instructions provided in Section VII
**except**choose**Scaled Monte Carlo NURBS**for both the Fwd and Inv Solver selections. - Limit your number of spatial frequencies to 2.
- Modify the
**Spatial Frequency**begin and end values using the information that you gained in Section VI. "Sensitivity of Spatial Frequency Domain Reflectance to Optical Properties" to obtain measurements that are sensitive to both absorption and scattering. - Rerun the inverse solver.

**Questions:**

- Were you able to improve the μ
_{a}and μ'_{s}converged properties? - In what spatial frequency domain is reflectance most sensitive to μ
_{a}? Why is this? - 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**

- Select the
**Forward Solver/Analysis Panel**. - Click the
**Clear All**button. - In the
**Fwd Solver:**dropdown menu select TwoLayer SDA - In the
select Steady State**Solution Domain***R*(ρ). - Select
**Begin**and**End**locations to 0.5 and 19.5 mm, respectively with**Number**equal to 39 (every 0.5 mm). - In the
**Tissue Input**Box, for Layer 0 select Start/Stop Layer Heights of 0mm and 2mm to specify a 2mm thick superficial layer - Also for
enter μ**Layer Optical Properties:**_{a}= 0.1mm^{-1}, μ'_{s}=1mm^{-1}, n=1.4. - 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 - For the
enter μ**Layer Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}=1mm^{-1}, n=1.4. - Click the
**Plot Reflectance**button. - Confirm the
**Hold On**checkbox is checked. - Repeat this process so that you also generate
*R*(ρ) for 4mm and 6mm layer thicknesses. - 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

- In the
**Fwd Solver:**dropdown menu select Standard Diffusion (Analytic-Distributed Point Source). Note that this solution is for a semi-infinite medium. - Select the
*R*(ρ) radio button and**Detector Positions:**Begin=0.5 mm, End=19.5 mm, Number=39. - Plot this solution using optical properties equal to the top layer.
- Plot this solution using optical properties equal to the bottom layer.

**Questions:**

- Where do the two-layer solutions lie with respect to the one-layer solutions? Why is this?
- Where do the two-layer solutions agree most with the one-layer tissue with bottom layer optical properties? Can you explain why?
- Where do the two-layer solutions agree most with the one-layer tissue with top layer optical properties and why?
- 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}=0.5 mm^{-1}.

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

- Select the
**Spectral Panel**and click**Clear All**. - Select
**Skin**as the**Tissue Type**and set the blood volume fraction to 2% (0.02) with 80% (0.8) saturation. - Plot both the μ
_{a}and μ'_{s}spectra from 500 nm to 1000nm with 50 wavelengths. - Select
**Plot μ**or Plot μ'_{a}Spectrum_{s}Spectrum if you wish to visualize the absorption and/or reduced scattering spectrum in this wavelength interval - Select the
**Forward Solver/Analysis Panel**and click the*use spectral panel inputs check-box*. - Select
**Solution Domain**to be R(fx). - In the
**Independent Axis**select**allow multi-axis selection**. - Select both the f
_{x}and λ check boxes. - 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. - Select
*Scaled Monte Carlo: NURBS*as the**Fwd Solver**. - Clear the plot view and
*Plot Reflectance*. - Repeat the above steps for a blood saturation of 40% (0.4).

**Questions:**

- What can you infer about the wavelength dependence of the optical properties based on the magnitude and spacing of the reflectance spectra at different spatial frequencies?
- Explore how scattering affects the reflectance spectrum by adjusting the scattering parameters? For example, change the scattering power b = 2.0.
- Explore how absorption affects the reflectance spectrum by adjusting the absorption parameters? For example, change the blood volume fraction to 4% (0.04).
- What wavelengths and spatial frequencies are sensitive to the change in blood oxygen saturation?
- What chromophore in noticeably present in the 900 to 1000 nm range?