Analysis of Coronary Microvessel Structures

Analysis of Coronary Microvessel Structures on the Enhancement and Detection of Microvessels in 3D Cryomicrotome Data Master’s project by Edwin Bennink Supervised by dr. Hans van Assen, prof. dr. ir. Bart ter Haar Romeny, dr. ir. Geert Streekstra (AMC), and prof. dr. Jos Spaan (AMC)

The Cryomicrotome • Coronary arteries of a goat heart are filled with a fluorescent dye; • Cryo: The heart is embedded in a gel and frozen (-20°C); • Microtome: The machine images the sample’s surface, scrapes off a microscopic thin slice (40 μm), images the surface, and so on … a. b.

Cryomicrotome Images + Very high resolution: about 40×40×40 µm; + Continuous volume; • Huge stacks (billions of voxels, millions of vessels); • Strange PSF in direction perpendicular to slices; • Scattering; • Broad range of vessel sizes and intensities. 8 cm = 2000 pixels

Process Overview • Sample preparation and imaging; • Microvascular tree modeling; • Preprocessing: • Limiting dark current noise; • Canceling transparency artifacts. • Enhancement of line-like structures; • Binarization and skeletonization; • Extraction of nodes and edges; • Measuring the diameters along the edges; • Postprocessing. • Analysis and simulations on digitized microvascular trees.

Limiting dark current noise • Dark current noise: • arises from thermal energy in the CCD; • is additive noise; • is measured with a closed shutter; • is CCD-specific and nearly constant over time; • can be removed from images by subtraction.

Original data

Dark current noise

Noise subtracted from data

Canceling transparency artifacts Point-spread function in z-direction (perpendicular to slices)

Canceling transparency artifacts • The effect of transparency is theoretically a convolution with an exponent; • s denotes the tissue’s transparency. f(z) 1 0.8 0.6 0.4 0.2 z - - - 6 4 2 2 4

F (f) 0.4 0.3 0.2 0.1 w 1 2 3 4 5 6 Canceling transparency artifacts • In the Fourier domain; • The solid line is the real part, the dashed line the imaginary part.

F (g) 1 0.75 0.5 0.25 w 1 2 3 4 5 6 -0.25 -0.5 Canceling transparency artifacts • Solution to the problem: embed this property in the (Gaussian) filters by division in the Fourier domain; • Multiplication is convolution, thus division is deconvolution.

Canceling transparency artifacts • The new 0th order Gaussian filter k(z) (in z-direction) becomes: k (z) 0.5 0.4 0.3 0.2 0.1 z - - 4 2 2 4

Canceling transparency artifacts Default Gaussian filters Enhanced Gaussian filters z x

Enhancement of line-like structures • Datasets have dimensions over 20003 (the new cryomicrotome images even 40003 voxels); • The filters are Gaussian, thus separable: • Read an x-y slice and filter in x and y direction; • Read some x-z slices and filter in z direction. 2000 pixels 2000 pixels 2000 tiff-files

Enhancement of line-like structures • Lineness filter is based on: • Eigen values and vectors of Hessian matrix; • First order derivatives; • Transparency deconvolution is embedded in the filter kernels;

Enhancement of line-like structures Intensity independence Edge surpression (gradient magnitude) Roundness (ratio between 2nd order derivatives perpendicular to the linear structure) Optimal 2nd order line filter (hotdog shaped kernel)

Enhancement of line-like structures • Take the maximum of the filter response over a range of small scales (up to 160 μm); • The larger vessel can be extracted using a high threshold value (on a slightly blurred, thus PSF corrected stack).

Enhancement of line-like structures Microvessel Analyzer application: • Capable of filtering large stacks in a relative short time...

Original data MIP of 100 slices

Filtered on 40 μm MIP of 100 slices

Binarization and skeletonization • Extraction of vessel centerlines using skeletonization; • K. Palágyi and A. Kuba defined 3×3×3 templates for parallel 3D skeletonization.

To do: Validation study on filtered and skeletonized vascular trees • Comparison with other ‘popular’ filters: • 2th or higher order line filters; • Frangi’s vessel likeliness function; • Steger’s center line detector.

To do: Validation study on filtered and skeletonized vascular trees Original data (normal and log-scale) (The images are inverted)

2nd order line-filter Frangi’s vessel-likeliness Steger’s center- line detector Lineness measure

250 250 250 200 200 200 150 150 150 100 100 100 50 50 50 0 0 0 0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250 250 250 250 200 200 200 150 150 150 100 100 100 50 50 50 0 0 0 0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250

Multi-scale response Frangi’s Vessel Likeliness Filter 250 0.8 200 0.6 150 0.4 100 0.2 50 50 100 150 200 250 0 0 50 100 150 200 250

250 250 250 200 200 200 150 150 150 100 100 100 50 50 50 0 0 0 0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250 250 250 250 200 200 200 150 150 150 100 100 100 50 50 50 0 0 0 0 50 100 150 200 250 0 50 100 150 200 250 0 50 100 150 200 250

Multi-scale responseLineness filter 250 1.4 1.2 200 1 150 0.8 0.6 100 0.4 0.2 50 50 100 150 200 250 0 0 50 100 150 200 250

Analysis of Coronary Microvessel Structures