2011 Laboratory E: Inverse Problem Solving

GOAL: Solve inverse problems using Standard Diffusion and Monte Carlo Models.

I. Impact of Optical Properties on Spatially-Resolved Reflectance

  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 start and stop locations to 0.5 and 9.5 mm, respectively with 10 points (every 1 mm).
  5. Set Optimization Parameters to: μa and μ's.
  6. Simulate measured data: set "Forward Simulation Optical Properties:" to: μa = 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: μa = 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.
  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?

II. Change Inverse Model Engine

  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 produced the more accurate converged values?

III. Change number of detectors

  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 analysis plots of ∂R/∂μa and ∂R/∂μ's to help guide their placement.