McDaniels – Oct 10, 2008

Outline Geometric Uncertainty Uncertainty in average intensity due to lesion placement ADC uncertainty

Geometric Uncertainty Uncertainty in number of voxels – Transcription from contour to DW image, 4 contour voxels for each DW voxel – Algorithm rounds to nearest voxel – Voxels in center of lesion certain – Voxels on perimeter of lesion uncertain – Estimate each DW voxel on average has +/- ¼ – Affects weighted calculation of whole lesion

Geometric uncertainty Lesion geometry, roughly circular section Area => n = πr 2 Perimeter => n p = 2πr +/- ¼*(2πr ) σ n = πr/2 = √(n/ π) For n = 150, σ n ≈ 7 Typical uncertainty about 2-3% Doesn’t include 2-3% scaling from Contour to DW

Geometric uncertainty Slice matching – Contour – 4mm slice, 4mm spacing – DW – 5mm slice, 7mm spacing Not all contour slices have a matching DW slice All DW slices have matching contour slice DW slice overlaps contour slice

Lesion Placement Estimated by placing ROI and analyzing histogram, then shifting and reanalyzing Variation in average intensity for shifts of 1-2 pixels was about 2-3%

Uncertainty in ADC Values Statistical uncertainty in image intensity – Statistical fluctuation – Structure (GM, WM, CSF) Typically 15-30% -ln(I/Io) => σ = √( ) ≈ 0.21 Linear fit from fixed point and two points with uncertainty

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 +/-43% Maximum +/-215% Average +/-104%