Tools for Shape Analysis of Vascular Response using

Two Photon Laser Scanning Microscopy

ByHan van Triest

Committee:

Prof. Dr. Ir. B.M. ter Haar RomenyDr. M. A. M. J. van ZandvoortDr. Ir. H. C. van AssenA. Vilanova i Bartrolí, PhDR.T.A. Megens, MSc

2/43

Overview

1. Biological Introduction2. Technical Introduction3. Vessel Radius Estimation4. Cell counting5. Conclusion and Recommendations

3/43

Biological Introduction

Vascular diseases are a big problem in the western world.

It is estimated that arteriosclerosis is the underlying cause of 50 % of all deaths in the western world

To unravel the underlying mechanisms more research is required

4/43

Biological Introduction – Vessel Anatomy

5/43

Biological Introduction – Remodelling

6/43

1. Excitation2. Energy loss processes3. Emission

Energy of Photon:

hhE

Technical Introduction – Fluorescence

1

2

3

7/43

Technical Introduction – Confocal Laser Scanning Microscopy

8/43

Technical Introduction – Confocal Laser Scanning Microscopy

Advantages:• Optical sectioning

Disadvantages:• Excitation of out-of-focus regions• High energy of excitation photons• Low penetration depth

9/43

Technical Introduction – Two Photon Laser Scanning Microscopy

10/43

Technical Introduction – Two Photon Laser Scanning Microscopy

11/43

Technical Introduction – Two Photon Laser Scanning Microscopy

Advantages:• No pinhole to block out-of-focus light required• Increased penetration depth• Excitation photons of lower energy• Imaging of viable tissue• Multiple dyes usable for targeting of different structures

Disadvantage:• Higher wavelength limits maximal achievable resolution

12/43

Technical Introduction – Imaging

13/43

Processing – Description of Vessels

Features:• Radius of the vessel• Ratio vessel wall thickness – vessel radius• Cell volume fraction

Needed:• Vessel Radius• Number of Cells

14/43

Radius Estimation

15/43

Radius Estimation – Methods

1. Statistical methods: Least squares estimators2. Robust statistics: Reduction of the influence of outliers3. Hough Transform

16/43

Radius Estimation – Hough Transform

xayb

bxay

ˆˆ

ˆˆ

Line through a point in image space

Set of parameters that describe the point

17/43

Radius Estimation – Hough Transform

18/43

Radius Estimation – Circular Hough Transform

Circle can be described by: 222 )()( ryyxx cc

19/43

Radius Estimation – Hough Transform

Advantages:• Robust against noise• Able to find partly occluded objects

Disadvantages:• Expensive, both computational and memory cost

20/43

Radius Estimation – Proposed method

A circle is defined by three non co-linear points.

• Store only center coordinates• Weight vote by average distance

between p1, p2 and p3

Find r by voting for most likely value of the radius

21/43

Radius Estimation – Finding Edge Points

A global threshold is infeasible due to differences in optical paths for emitted photons

22/43

Radius Estimation – Finding Edge Points

Modified Full Width at Half Maximum:

maxI InsideOutside

23/43

Radius Estimation – Experiments

• 20 images, 10 single slices, 10 taken from three dimensional stacks

• Test images have both sides of the wall vissible• Groundtruth given by the average estimate of 12

volunteers• Results compared with common least squares

estimator• Tests are performed for values of α between 0.2 and

0.8 in steps of 0.05, and using 20 to 250 points in steps of 10

• In total 24960 estimates are made

24/43

Radius Estimation – Influence of α

xz-scan:

z-stack slice:

Blue line: LSE

Red line: MHT

25/43

Radius Estimation – Influence of number of points

xz-scan:

z-stack slice:

Blue line: LSE

Red line: MHT

26/43

Radius Estimation – Conclusion

• Proposed method outperforms least squares fitting method for xz-scans

• Proposed method performs equally compared to least squares fitting method for z-stack slices

• The best value for α used in the proposed method is α = 0.4

• At least 100 points is required for a stable result using the proposed method

27/43

Cell counting

28/43

Cell Counting – Algorithm

Noise Reduction

Potential Center Extraction

Potential Edgepoint Extraction

Edgepoint Selection

Ellipsoid Fitting

Oversegmentation Reduction

29/43

Cell Counting – Noise Reduction

Edge-preserving filtering: Median

Filtering

Each pixel is replaced by the median of its surrounding

Purple line: Original objectBlue line: Degraded objectRed line: Median filter, kernel

width 5 pixelsBlack line: Median filter, kernel

width 25 pixels

30/43

Cell Counting – Potential Center Detection

Assumption: Blob-like structures

Center is maximum of the blob

Local maxima within a region are potential centers.

31/43

Cell Counting – Potential Edgepoint Extraction

• Sample rays from each potential center• Rays intersect points along a generalized spiral

32/43

Cell Counting – Potential Edgepoint Extraction

Constraint:Points on a downward flank

These points can be found at points in which the second order derivative switches from negative to positive.

Blue line: Image intensity along ray

Purple line: First order derivative

Sienna line: Second order derivative

33/43

Cell Counting – Dynamic Programming

B

c

d

a

b

A

2

4

5 2

3

6

2

6

7 4

25

9

Shortest Route: AbcB

34/43

Cell Counting – Edgepoint Selection

Find set of most likely edge points

Cost function: 2

max

2max

111

21

,

I

pw

I

ppwppwppC

Ii

l

Ii

Ii

ici

cisii

35/43

Cell Counting – Ellipsoid Fitting

0222 dzryqxpyxhzxgzyfzcybxaQ

Ellipsoid can be described by a quadric, a general polynomial in three dimensions of order two:

Axes proportions

Orientation Position Size

Fitted on the data using a least squares fitting procedure

36/43

Cell Counting – Oversegmentation Reduction

1. Find overlapping nuclei2. Check wether nuclei are parallel3. Merge the sets of edgepoints of parallel overlapping nuclei4. Perform Ellipsoid fitting on the combined data sets

37/43

Cell Counting – Results Before Merging

38/43

Cell Counting – Results After Merging

39/43

Cell Counting – Discussion

Three types of frequent mistakes:A Incorrect merging of two blunt nucleiB Center of cell not foundC No distinct directions

40/43

Cell Counting – Discussion

A another problem is due to leakage of light from other colors

41/43

Cell Counting – Conclusion

Although the method only has been tested on a single dataset, the results show to be promising.

Most of the cells are found while there is a relatively small amount of false negatives and false positives

42/43

Recommendations

• Test the algorithm on more datasets• Investigate the influence of parameters• For the calculation of the cost during the dynamic programming

step, take into account more points on the surface• Remove outliers in the selected set, as outliers have great effect

on the least squares algorithm• Optimize the imaging parameters to get as litle non cellular

structures as possible • Classify the cells into subclasses

Questions?