2015 Laboratory F: Analysis of Temporally Resolved and Temporal Frequency Domain Signals
GOAL: This GUI Interaction aims to examine (a) the impact of optical absorption and scattering on temporallyresolved and temporal frequencydomain reflectance signals; and (b) the impact of optical properties and measurement selection on the tissue region probed by the detected photons.
I. Sensitivity of TimeResolved 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 Solution Domain: select TimeDomain, R(ρ,t).
 For the Independent Axis choose t and set ρ = 10 mm.
 In Detection Times choose "Begin" = 0 ns and "End" = 0.5 ns with "Number" = 201 time points (1 point every 5 ps).
 In Optical Properties: enter μ_{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 yaxis spacing.

 Click the Clear All button.
 Start again with Optical Properties: μ_{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 timeresolved 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 yaxis spacing.
 You are designing a timeresolved 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 TemporallyResolved 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 Solution Domain: select "TimeDomain(R(ρ,t))".
 Select t as the Independent Axis and ρ=10mm.
 In Detection Times choose "Begin" = 0 ns and "End" = 1.0 ns with "Number" = 51 time points (1 point every 20 ps).
 Set Optimization Parameters to: μ_{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 Detection Times to improve the inverse solution? Run the inverse solution with this new time window and check your results.
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 Solution Domain: select "Frequency Domain(R(ρ,ft))".
 Select Independent Axis ft and set ρ=10mm.
 In Temporal Frequency choose "Begin" = 0 GHz and "End" = 2.0 GHz with "Number" = 101 frequency points (1 point every 20 MHz).
 In Optical Properties: enter μ_{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 yaxis spacing.
 In Temporal Frequency choose "Begin" = 0 GHz and "End" = 2.0 GHz with "Number" = 101 time points (1 point every 20 GHz).
 In Optical Properties: enter μ_{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 Solution Domain: select "Temporal Frequency(R(ρ,ft))".
 Select Independent Axis ft and set ρ=10mm.
 In Temporal Frequency choose "Begin" = 0 GHz and "End" = 0.5 GHz with "Number" = 51 time points (1 point every 20 GHz).
 Set Optimization Parameters to: μ_{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?