# 2010 GUI Interaction E - Inverse Problem Solving

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

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

- Select the
**"Inverse Solver Panel"**. - For
**Fwd Model Engine:**select "Scaled Monte Carlo - NURBS (g=0.8, n=1.4)", for**Inv Model Engine:**select "Standard Diffusion (Analytic - Point Source)". - In
**Solution Domain:**select "Steady State(*R*(ρ))". - Set 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}= 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?

**II. Change Inverse Model Engine**

- Perform the same analysis changing the
**"Inv Model Engine"**to Scaled Monte Carlo - NURBS(g=0.8, n=1.4). - 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.