# 2009 GUI Interaction E - Inverse Problem Solving

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

**I. Impact of Optical Properties on Spatially-Resolved Reflectance**

- On the "Inverse" Panel select: (a)
**Forward Model Engine:**Scaled Monte Carlo (g=0.8),**Inverse Model Engine:**Standard Diffusion (Analytic - Point Source) and (c)**Solution Domain:**Steady State(*R*(ρ)). - Select start and stop locations to 0.5 and 9.5 mm, respectively with 10 points (every 1 mm).
- Set
**Optimization Parameters**to: μ_{a}and μ'_{s}. - Simulate measured data: set Forward Simulation Optical Properties to: μ
_{a}= 1 mm^{-1}, μ'_{s}= 1 mm^{-1}, g = 0.8 and n = 1.4 and 2% noise. - Plot Measured Data and make sure "Hold On" is checked.
- 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. - Plot Initial Guess.
- Press "Run Inverse Solver".

##### 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?

**II. Change Inverse Model Engine**

- Perform the same analysis changing the Inverse Model Engine to Monte Carlo.
- Which Model Engine produced the more accurate converged values?

**III. Change number of detectors**

- 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?
- Use the analysis plots of ∂R/∂μ
_{a}and ∂R/∂μ'_{s}to help guide their placement.