Personalized graph reconstruction of coronary artery network Roman Pryamonosov INM RAS, MIPT Work group of circulatory and vascular diseases modeling (INM RAS) RSF 14-31-00024 (mew laboratories)

Outline Definitions and instruments Anatomical background Segmentation Thinning and graph reconstruction Discussion

Definition of segmentation Instruments Anatomy Segmentation Graphs construction Discussion Definition of segmentation 2D (3D) image Segmentation is an assigning of some label for each voxel of the image Segmentation results in mask In case of only two labels(0 and 1) mask is called binary Suppose we have 2D or 3D image. I will refer to 3D images and voxels rather than pixels. Segmentation is a process of marking each voxel with one of labels. When only one interesting object to segment is presented on the image the result of segmentation contains only two labels: 0 или 1. This object is called binary mask. In the case of many interesting objects we call it simply the mask. Illustration of «segmentation» notion

Instruments Anatomy Segmentation Graphs construction Discussion Distance map Distance map of a binary image is a integer mask, that contains distance to forground border in every voxel Distance map may be computed either for foreground or background In background case foreground voxels are marked by 0 and vise versa The example of the 2D binary mask and its background distance map

IDT and Vesselness Filter Instruments Anatomy Segmentation Graphs construction Discussion IDT and Vesselness Filter IDT* inputs a binary mask and one voxel, cuts mask in bottlenecks and outputs connectivity component containing given voxel. Frangi Vesselness Filter** outputs a “vesselness” measure for each voxel Mask can be produced by thresholding vesselness values. Example of IDT with two circles Two main instruments used in segmentation algorithms, presented in this work, are Isoperimetric Distance Trees (IDT algorithm) and Frangi Vesselness Filter. The IDT algorithm inputs connected binary mask and a seed voxel, cuts the input mask in bottlenecks and outputs part of the initial mask containing the seed voxel. This picture shows example with two connected circles in the foreground of a mask. This point is a seed pixel, delineated circle is the output of the IDT algorithm Frangi Vesselness Filter is based on eigenanalysis of Hessian computed in neighbourhood of voxel. In each voxel the filter computes vesselness value, that is the probability of the voxel to be contained in tubular structure. The binary mask of vessels can be found via thresholding of vesselness values. Illustration of vesselness measure * Grady L. Fast, quality, segmentation of large volumes – Isoperimetric distance trees. Computer Vision ECCV 2006 – 2006. – P. 449-462. ** Frangi A. [et al.] Multiscale vessel enhancement filtering. Medical Image Computing and Computer-Assisted Intervention – MICCAI'98 – 1998. – P. 130-137.

Anatomy of coronary arteries Instruments Anatomy Segmentation Graphs construction Discussion Anatomy of coronary arteries Coronary vessels supply the heart and lay on its surface Two branches of coronary arteries are rooted on the aorta surface Aorta is much larger than coronary arteries Start points of coronary arteries is called ostium

Segmentation of coronary arteries Instruments Anatomy Segmentation Graphs construction Discussion Segmentation of coronary arteries Input data is 3D DICOM datasets acquired via contrast enhanced CTA Segment aorta using Hough Circle Transformation, IDT, and morphological operations Calculate vesselness Find ostia points as two distinct local maxima of vesselness near aorta border Segment coronary vessels as connectivity components containing ostia points

Examples of segmentation Instruments Anatomy Segmentation Graphs construction Discussion Examples of segmentation Data set Case 1 Case 2 Dimensions 512x512x 451 501 Spacing 0.76x0.76x 0.80 mm 0.62x0.62x0.80 mm Aorta 5.80s 8.03s Frangi Vesselness 128.92 Vesselness was computed at 3 scales: 1,2 and 3 voxels. Tests were run on Intel Core i7 CPU.

Thinning by DOHT* Thinning procedure provides skeleton Instruments Anatomy Segmentation Graphs construction Discussion Thinning by DOHT* Thinning procedure provides skeleton Skeleton is a voxel set, that is 1-voxel thick, medial and with a same topology as segmentation Distance Ordered Homotopic Thinning (DOHT) orders voxels by its distance map value and deletes voxels layer by layer without changing topology DOHT produces skeleton containing false twigs – short skeletal segments corresponding to no real vessel * Chris Pudney. 1998. Distance-Ordered Homotopic Thinning. Comput. Vis. Image Underst. 72, 3 (December 1998), 404-413. DOI=http://dx.doi.org/10.1006/cviu.1998.0680

False twigs elimination* Instruments Anatomy Segmentation Graphs construction Discussion False twigs elimination* Skeletal voxels separated to inner voxels (2 neighbors) and voxel-nodes Voxel is simple if its deletion does not distort topology of binary mask Voxel-node is an end-node if it has only 1 neighbor All terminal segments considered as false twigs False twigs are deleted simultaneously and procedure repeats Sequential deletion may produce incorrect results Terminal segments shorter than 11 (left) and 5 (right) voxels are considered to be false twigs *Danilov A, Ivanov Y, Pryamonosov R, Vassilevski Y. Methods of graph network reconstruction in personalized medicine. Int J Numer Method Biomed Eng. 2016 Aug;32(8). doi: 10.1002/cnm.2754. Epub 2015 Nov 11.

False twigs elimination* Instruments Anatomy Segmentation Graphs construction Discussion False twigs elimination* Red node is non-terminal end of false twig. Inner voxels and terminal voxel-node of each false twig are deleted always, while deletion of red node depends on situation Red nodes are defined simultaneously and deleted if they are simple If voxel-node is to be deleted its neighboring voxel-nodes are marked as blue nodes Blue node is to be deleted if it’s simple and it is not end-node Red nodes are often end-nodes Different scenarios of red and blue nodes deletion *Danilov A, Ivanov Y, Pryamonosov R, Vassilevski Y. Methods of graph network reconstruction in personalized medicine. Int J Numer Method Biomed Eng. 2016 Aug;32(8). doi: 10.1002/cnm.2754. Epub 2015 Nov 11.

Instruments Anatomy Segmentation Graphs construction Discussion Graph Construction Once a skeleton is cleaned from false twigs, every skeletal segment represents one and only one real vessel trunk Graph edges are associated with skeletal segments Graph nodes are associated with connective components of voxels Lengths and mean radii are computed for every graph edge Two real patient cases. Coronary artery segmentation, skeleton without false twigs and corresponding graphs

Instruments Anatomy Segmentation Graphs construction Discussion Graph Construction Skeletal segments may contain zigzags while actual centerline is smooth Heuristic formula computes length of a broken line with vertices in every S-th voxel:     Step size S was set to minimize difference in length acquired with the heuristic formula and methods of VMTK software (www.vmtk.org) Average radius of vessel trunk is computed using radius at every voxel of segment Radius at voxel is defined as the shortest distance to the border of original binary mask and is computed via distance map steepest descent

Examples of other reconstructed 1D graphs Instruments Anatomy Segmentation Graphs construction Discussion Examples of other reconstructed 1D graphs Lymphatic system Rabbit kidney Bronchial system

Instruments Anatomy Segmentation Graphs construction Discussion Discussion Automatic algorithm for segmentation of coronary arteries is implemented Integration with MultiVox GUI is on developing stage Segmentation can be used for 3D blood flow simulations Automatic algorithm for graph reconstruction of cerebral arteries implemented 1D graph is a computational domain for 1D blood flow models With given 3D voxel representation any network can be reduced to 1D graph by presented algorithm.

Thank you for your attention!