# 2017 Laboratory G: Recovery of Tissue Properties from Time-Resolved and Temporal Frequency-Domain Reflectance Measurements

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**GOAL:** This GUI Interaction aims to examine (a) the impact of optical absorption and scattering on temporally-resolved and temporal 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. Sensitivity of Time-Resolved Reflectance R(t) to Optical Properties**

- Select the
**Forward Solver/Analysis Panel**. - Click
**Clear All**and return the**Y Axis Spacing**back to**Linear**. - Uncheck
**use spectral panel inputs**. - In the
**Fwd Solver**drop down menu select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)". - In the
select Time-Domain,**Solution Domain***R*(ρ,*t*). - For the
**Independent Axis**choose t and set ρ = 10 mm. - In
choose**Detection Times****Begin**= 0 ns and**End**= 0.5 ns with**Number**= 201 time points (1 point every 5 ps). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}= 1mm^{-1}. - Click the
**Plot Reflectance**button. - Confirm that the
**Hold On**checkbox is selected. - Repeat the above for μ
_{a}= 0.03, 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.

- Click the
**Clear All**button. - Start again with
μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}= 1mm^{-1}. - Click the
**Plot Reflectance**button. - Confirm that the
**Hold On**checkbox is selected. - Repeat the above for μ'
_{s}= 0.5 and 1.5 mm^{-1}.

**Questions:**

- 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 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.
- 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. Optical Property Recovery using Temporally-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 "Time-Domain(**Solution Domain***R*(ρ,*t*))". - Select
*t*as the**Independent Axis**and ρ=10mm. - In
choose**Detection Times****Begin**= 0 ns and**End**= 1.0 ns with**Number**= 51 time points (1 point every 20 ps). - 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}= 0.02 mm^{-1}, μ'_{s}= 1.2 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?
- Perform the same analysis with initial guess μ
_{a}= 0.05 mm^{-1}, μ'_{s}= 0.7 mm^{-1}, g = 0.8 and n=1.4. How accurate are the converged properties now? - How would you modify the
to improve the inverse solution? Run the inverse solution with this new time window and check your results.**Detection Times**

**III. Sensitivity of Temporal Frequency Domain Reflectance to Optical Properties**

First let us examine the sensitivity of Temporal 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 "Frequency Domain(**Solution Domain***R*(ρ,*f**t*))". - Select
**Independent Axis**ft and set ρ=10mm. - In
choose**Temporal Frequencies****Begin**= 0 GHz and**End**= 2.0 GHz with**Number**= 101 frequency points (1 point every 20 MHz). - In
enter μ**Optical Properties:**_{a}= 0.01mm^{-1}, μ'_{s}=1mm^{-1}, n=1.4. - Click the
**Plot Reflectance**button. - The
**Plot Toggle**radio buttons toggle the plot from real/imag results to phase and amplitude results. The phase is shown in units of degrees. - Confirm the
**Hold On**checkbox is checked. - Fix μ'
_{s}=1mm^{-1}. Repeat the above steps for μ_{a}= 0.03 and 0.1 mm^{-1}. - Note the trend of decreasing reflectance with increasing absorption.
- Note what temporal frequency regime shows the most sensitivity to μ
_{a}changes. - Is the temporal frequency that shows the most sensitivity to μ
_{a}the same for real/imag, phase and amplitude?

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

- Click the
**Clear All**button and toggle back to**Linear**y-axis spacing. - In
choose**Temporal Frequencies****Begin**= 0 GHz and**End**= 2.0 GHz with**Number**= 101 time points (1 point every 20 GHz). - 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}= 1.0 and 1.5 mm^{-1}. - Note what temporal frequency regime shows the most sensitivity to μ'
_{s}changes. - Is the temporal frequency domain that shows the most sensitivity to μ'
_{s}the same for real/imag, phase and amplitude?

**IV. Optical Property Recovery using Temporal Frequency Domain Reflectance Measurements: 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 "Temporal Frequency(**Solution Domain***R*(ρ,*f**t*))". - Select
**Independent Axis**ft and set ρ=10mm. - In
choose**Temporal Frequencies****Begin**= 0 GHz and**End**= 0.5 GHz with**Number**= 51 time points (1 point every 20 GHz). - Set
to: μ**Optimization Parameters**_{a}and μ'_{s}. - Simulate measured data: set
**Forward Simulation Optical Properties:**to: μ_{a}= 0.05 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}= 0.01 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?

**V. Effect of Measurement Range on Sensitivity to Optical Absorption and Scattering in Temporal Frequency Domain Reflectance**

- Go to the
**Inverse Solver Panel**. - Follow the instructions provided in Section IV
**except**modify the**Temporal Frequency**begin and end values to those obtained in Section III. "Sensitivity of Temporal Frequency Domain Reflectance to Optical Properties". Note that the inverse solution fits the real/imag measurements. - Rerun the inverse solver.

**Questions**

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