1. McDaniels – Oct 24, 2008

2. Outline MRI Image uncertainty Point uncertainty ADC uncertainty

3. MRI Image Uncertainty Firbank et al – SNR = 0.655 S/σ air – S is Image Signal (Average Intensity) – σ air is the standard deviation of intensity in air area – 0.655 is due to noise centered about zero in raw data, then skewed positive after made into a magnitude image

4. MRI Image Uncertainty Image J returns raw data histogram centered about zero with positive and negative values. Omit 0.655 factor Analyzed “air” noise for about 13K voxels per image

5. MRI Image Uncertainty

6. Typical values of σ (relative) – b=0, σ ≈ 5-8% – b=520, σ ≈ 6-9% – b=850, σ ≈ 8-12%

7. MRI Image Uncertainty

8. Point Uncertainty Points used for Linear Fit Each Point: – Determined from I n = -ln(I b /I b=o ) – Uncertainty in each point σ n 2 = σ b 2 + σ b=0 2 I n +/- σ n

9. Uncertainty in ADC Values Uncertainty in linear fit from Bevington σ 2 = 1/Δ*Σ1/σ i 2 Δ = Σ 1/σ i 2 * Σx i 2 / σ i 2 -(Σ x i / σ i 2 ) 2 e.g. for σ 2 =σ 3 =.2, x 2 =520, x 3 =850 Δ = (1/.04 +1/.04)*(520 2 /.04+850 2 /.04)- (520/.04+850/.04) 2 = 6.8e7 σ = √(1/6.8e7*(1/.04+1/.04)) = 0.00086 ADC ≈ 0.0015 +/- 0.00086 (57%)

10. ADC uncertainty Patient 5 Minimum +/- 18.4% Maximum +/-56.4% Average +/-33.7%

11. ADC Uncertainty