McDaniels – Oct 24, 2008

Outline MRI Image uncertainty Point uncertainty ADC uncertainty

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

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

MRI Image Uncertainty

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

MRI Image Uncertainty

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

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)- (520/ /.04) 2 = 6.8e7 σ = √(1/6.8e7*(1/.04+1/.04)) = ADC ≈ / (57%)

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

ADC Uncertainty