Neusoft Group Ltd. Medical Systems Centerline detection of (cardiac) vessels in CT images Martin Korevaar Supervisors: Shengjun Wang Han van Triest Yan Kang Bart ter Haar Romenij

Neusoft Group Ltd. Medical Systems Overview Introduction Method –Feature space –Minimal Cost Path (MCP) search Results Conclusion Discussion

Neusoft Group Ltd. Medical Systems Introduction Coronary artery and heart diseases are one of the main causes of death in Western world Therefore improvement of diagnosis, prevention and treatment is needed Diagnosis is improved by techniques like CTA and MRA CAD is needed to analyze huge amount of data

Neusoft Group Ltd. Medical Systems Introduction Centerline of vessel is interesting feature for CAD Needed e.g. for CPR and lumen size measurements Should be –Independent of vessel segmentation –Robust with respect to image degradations.

Neusoft Group Ltd. Medical Systems CPR Visualization method Images from: Armin Kanitsar in IEEE Viz Okt

Neusoft Group Ltd. Medical Systems CPR Visualization method Maps 3D path on 2D image Images adapted from: Armin Kanitsar in IEEE Viz Okt

Neusoft Group Ltd. Medical Systems CPR Visualization method Maps 3D path on 2D image Artery can be investigated from just 1 image

Neusoft Group Ltd. Medical Systems CPR Visualization method Maps 3D path on 2D image Artery can be investigated from just 1 image Centerline needs to be correct Images from: Armin Kanitsar in IEEE Viz Okt

Neusoft Group Ltd. Medical Systems Algorithm Create feature space Find Minimum Cost Path with Dijkstra’s algorithm Feature space with: Center of vessel lower value then periphery of vessel Vessel lower value then background

Neusoft Group Ltd. Medical Systems Feature space Filter based on eigenvalues of Hessian

Neusoft Group Ltd. Medical Systems Hessian (1) Matrix with all second order derivatives 2D Hessian: Derivative of image: Convolve derivative of Gaussian with image Gaussian: G(x,y,  ) D xx *G(x,y,  ) D yy *G(x,y,  )D xy *G(x,y,  )

Neusoft Group Ltd. Medical Systems Hessian (2) Eigenvectors / -values 1 < 2 (< 3 ) measure of curvature i relates to v i v 2 points to max. curvature v 1 points to min. curvature, perpendicular to v 1 Rate of change of intensity is curvature of an image 1 v 1 2 v 2

Neusoft Group Ltd. Medical Systems 2 v 2 3 v 3 1 v 1 Eigenvalue of Hessian of a pixel gives information about the local structure (e.g. tube) Hessian (2) Eigenvectors / -values

Neusoft Group Ltd. Medical Systems Tubular structure filter Frangi Distinguishes blob-like structures, cannot distinguish between plate and line-like structures Distinguishes between line and plate-like structures Filters noise.

Neusoft Group Ltd. Medical Systems Tubular structure filters Frangi Wink et al. α = β = 0.5 and c = 0.25 Max[Greyvalue] Olabarriaga et al. α = 1, β = 0.1 and c > 100 => better discrimination center / periphery vessel Chapman et al.α = 0.5, β = ∞ and c > 0.25 Max[Greyvalue] => drops R B -term => better discrimination vessel / background

Neusoft Group Ltd. Medical Systems Tubular structure filters HessDiff Better discrimination background / vessel

Neusoft Group Ltd. Medical Systems Tubular structure filters Hessian is calculated at multiscale (2.6    18.6) Scale with highest response is scale of a voxel Highest response is in center vessel Hessian is scaled with  2

Neusoft Group Ltd. Medical Systems Algorithm Create feature space Find Minimum Cost Path with Dijkstra’s algorithm Feature space with: Center of vessel lower value then periphery of vessel Vessel lower value then background

Neusoft Group Ltd. Medical Systems Invert pixel values (1/pixelvalue) Response highest at center of the vessel. Minimal cost path needs lowest Pixel values are inverted 1 / I

Neusoft Group Ltd. Medical Systems Minimal cost path Select start and end point Find minimal cost path in between Dijkstra’s algorithm to find that minimal cost path

Neusoft Group Ltd. Medical Systems Dijkstra 2a Begin End

Neusoft Group Ltd. Medical Systems Dijkstra 2b Find min neighbours (green) Add it to investigated nodes (red). Remember predecessor 2 (1) [6] (1) [8] 5 (1) [7]

Neusoft Group Ltd. Medical Systems Dijkstra 2c (1)2 (1) [6] 3 (1) [8] 5 (1) [7] 4 (2) [11] Add neighbours (green) Remember predecessor

Neusoft Group Ltd. Medical Systems Dijkstra 2d (1) 1 5 (1) [7] (1) [6] 3 (1) [8] 4 (2) [11] Find min neighbours (green) Add it to investigated nodes (red). Remember predecessor

Neusoft Group Ltd. Medical Systems Dijkstra 2e (1) [8] (1) 2 (1) (1) [6] 5 (1) [7] 7 (5) [13] 4 (5) [10] Add neighbours (green) Remember predecessor Update predecessor and cost if node already in neighbours

Neusoft Group Ltd. Medical Systems Dijkstra 2f (1) [8] (1) 2 (1) 4 (5) [10] (1) [6] 5 (1) [7] 7 (5) [13] Find min neighbours (green) Add it to investigated nodes (red). Remember predecessor

Neusoft Group Ltd. Medical Systems Dijkstra 2g (1) [8] (3) [28] (1) 2 (1) (1) [6] 5 (1) [7] 7 (5) [13] 4 (5) [10] Add neighbours (green) Remember predecessor

Neusoft Group Ltd. Medical Systems Dijkstra 2h (3) [28] (1) 2 (1) 4 (5) [10] (1) [6] 5 (1) [7] 3 (1) [8] 7 (5) [13] Find min neighbours (green) Add it to investigated nodes (red). Remember predecessor

Neusoft Group Ltd. Medical Systems Dijkstra 2i Goal! (5) 6 (4) [17] (1) 2 (1) (1) [6] 5 (1) [7] 3 (1) [8] 4 (5) [10] 7 (5) [13]

Neusoft Group Ltd. Medical Systems Dijkstra 2i Backtrack: 7 => 5 => (5) 6 (4) [17] (1) 2 (1) (1) [6] 5 (1) [7] 3 (1) [8] 4 (5) [10] 7 (5) [13]..

Neusoft Group Ltd. Medical Systems Minimal cost path Defined cost: V(i) is the voxel value a is weight factor i is i th voxel of the path

Neusoft Group Ltd. Medical Systems Minimal cost path Defined cost: V(i) is the voxel value a is weight factor i is i th voxel of the path Higher values of a => Relative difference between center and surrounding increases => Will follow minimum better instead of shortest path

Neusoft Group Ltd. Medical Systems Algorithm Get Eigenvalues of the Hessian Matrix Calculate response to (Frangi’s) filter Invert pixel values (1/pixelvalue) Find minimum cost path with dijkstra’s algorithm

Neusoft Group Ltd. Medical Systems Experiments Original method on different datasets On worst performing dataset a = 1 a = 5 –Different filters Frangi with different parameters –Wink –Olabarriaga –Chapman HessDiff

Neusoft Group Ltd. Medical Systems Result (CPR) 3 Datasets (1) LAD(2) RCx(3) LAD

Neusoft Group Ltd. Medical Systems Different filters and cost functions (CPR) Proximal part Wink a=1Chapman a=1Wink a=5Chapman a=5

Neusoft Group Ltd. Medical Systems Olabarriaga a=5 Different filters and cost functions (CPR) Proximal part Olabarriaga a=1

Neusoft Group Ltd. Medical Systems Sagittal slice at the stenosis Frangi’s filter with Wink’s constants Frangi’s filter with Olabarriaga‘s constants Olabarriaga (a=5) Wink (a=5) Different filters: Wink and Olabarriaga

Neusoft Group Ltd. Medical Systems Sagittal slice heart wall Different filters: Wink and Olabarriaga

Neusoft Group Ltd. Medical Systems Different filters and cost functions (CPR) Proximal part HessDiff a=1

Neusoft Group Ltd. Medical Systems Different filters: HessDiff Low response at stenosis Lot of false positives Strong false positives at the heart wall CT Response

Neusoft Group Ltd. Medical Systems Different filters and cost functions Distal part Wink Chapman OlabarriagaHessDiff a=1 a= 5

Neusoft Group Ltd. Medical Systems Different filters Doesn’t follow vessel at heart wall HessDiff Olabarriaga Wink Chapman Grey

Neusoft Group Ltd. Medical Systems Multiscale Wink Vessel response at low scale Heart wall response at high scale Heart wall response is stronger σ= 2.6σ= 6 σ= 10 σ= 16 σ= AllGrey value

Neusoft Group Ltd. Medical Systems Different cost function α = 5 vs. α =1 Investigates nodes in smaller area –Less computations –More able to follow local minima –Less able to pass local maxima (stenosis) a=1 and a=5 a=1

Neusoft Group Ltd. Medical Systems Discussion Used scales were high (2.6    18.6)  High responses of the heart wall => bad centerline extraction HessDiff and Olabarriaga track the centerline badly: –Low response at stenosis. –HessDiff lot of false positive response Wink and Chapman track the centerline excellent.

Neusoft Group Ltd. Medical Systems Conclusion The centerline is tracked in most cases (more or less) accurate Wink and Chapman are best filters. They can even coop with a stenosis. It returns to the center even if it gets outside the vessel (robust) Different cost functions yield different results: –High power more precise in details and faster. –Low power more robust and slower.

Neusoft Group Ltd. Medical Systems Further research Smaller scales might improve results Use Wink’s constants

Neusoft Group Ltd. Medical Systems Questions?