msc. thesis presentation florie daniels - june 29, 2006 slide 1 of 36 quantification of collagen...

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 1 of 36

Quantification of collagen orientation in 3D engineered tissue

Florie Daniels

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 2 of 36

Quantification of collagen orientation in 3D engineered tissue

Introduction Physiological background Algorithm for 3D orientation analysis Validation Experiments Results Discussion Conclusions Recommendations

Outline

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 3 of 36

Quantification of collagen orientation in 3D engineered tissue

Introduction

Heart valve disease

Heart valve replacement

Position of the heart valves

Heart valve prostheses Mol et al.

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 4 of 36

Quantification of collagen orientation in 3D engineered tissue

Project goals:

To design an image analysis tool for automatic 3D orientation analysis of collagen fibers in two-photon laser-scanning microscopy (TPLSM) images.

To quantify collagen orientation in 3D unattached, attached and strained heart valve tissue engineered equivalents.

Introduction

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 5 of 36

Quantification of collagen orientation in 3D engineered tissue

The native aortic heart valve

Physiological background

Collagen architecture of the native aortic heart valve

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 6 of 36

Quantification of collagen orientation in 3D engineered tissue

Collagen

Physiological background

diameter ranging from 10 to 500 nm, length ~10 to 30 μm.

several hundred micrometers

1.5 nm in diameter, 300 nm in length

Fibrillogenesis

Hierarchy of collagen

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 7 of 36

Quantification of collagen orientation in 3D engineered tissue

Input: image stack of TPLSM

Algorithm for 3D orientation analysis

20 micron 5 micron

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 8 of 36

Quantification of collagen orientation in 3D engineered tissue

Coherence- enhancing diffusion

Algorithm for 3D orientation analysis

CED was introduced by Weickert et al.

Diffusion occurs along the preferred orientation of the structures in the image NOT perpendicular to the structures

Amount of diffusion increases when a structure is more oriented.

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 9 of 36

Quantification of collagen orientation in 3D engineered tissue

Coherence enhancing diffusion

Algorithm for 3D orientation analysis

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 10 of 36

Quantification of collagen orientation in 3D engineered tissue

Principal Curvature Directions in 3D

Algorithm for 3D orientation analysis

2 ( , )xxx xy xz

yx yy yz

zx zy zz

L L L

L L L L

L L L

2

2( ) ( , )x xxxL L G

x

(L = image) 2

22

2

1( , )

2

x

xm

G e

m-dimensional Gaussian:

Second order derivative:

Hessian Matrix:Eigenvalues Principal curvaturesEigenvectors Principal directions

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 11 of 36

Quantification of collagen orientation in 3D engineered tissue

Principal Curvature Directions in 3D

Algorithm for 3D orientation analysis

Principal direction corresponding to minimal principal curvature points in the direction of the structure.

Two angles describe the orientation of a vector in 3D:

θ: the angle in the xy-plane

φ: the angle from the z-axis

Representation of the angles in 3D

1cos ( )z

1tany

x

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 12 of 36

Quantification of collagen orientation in 3D engineered tissue

Why Scale Selection?

Algorithm for 3D orientation analysis

Objects are only meaningfull at a certain scale

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 13 of 36

Quantification of collagen orientation in 3D engineered tissue

Algorithm for 3D orientation analysis

1 2 3

The eigenvalues of the Hessian indicate the type of structure present in a voxel. The eigenvalues are ordered from small to large:

Structure type Polarity Eigenvalues

blob bright λ1<<0, λ2<<0, λ3<<0

blob dark λ1>>0, λ2>>0, λ3>>0

tubular bright λ1≈ 0, λ2<<0, λ3<< 0

tubular dark λ1≈ 0, λ2>>0, λ3>>0

plane bright λ1≈ 0, λ2 ≈ 0, λ3<<0

plane dark λ1≈ 0, λ2 ≈ 0, λ3>> 0

Scale Selection

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 14 of 36

Quantification of collagen orientation in 3D engineered tissue

Scale Selection

Algorithm for 3D orientation analysis

Collagen fibers appear as bright tubular structures in a darker environment. The conditions for a bright tubular structure in 3D are:

We use normalized Gaussian derivatives to compute the Hessian at different scales.

1

1 2

2 3

2 3

0

0 0and

2( , ) ( , )normalizedG G x x

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 15 of 36

Quantification of collagen orientation in 3D engineered tissue

Scale Selection

Algorithm for 3D orientation analysis

Two measures are used for scale selection.

The confidence measure (Niessen):

with

The vesselness measure (Frangi et al.):

with

2

2

0

( , )1 exp

2

C

c

if λ2>0 or λ3>0,

otherwise

2 2 221 2 2 3 3 1

2 2 2

2 2 2

0

( , )1 exp exp 1 exp

2 2 2A B

V v R R S

c

1

2 3

BR

2

3AR

2jF

j m

S H

if λ2>0 or λ3>0

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 16 of 36

Quantification of collagen orientation in 3D engineered tissue

Scale Selection Implementation

Algorithm for 3D orientation analysis

Artificial image

Response of measures over scale

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 17 of 36

Quantification of collagen orientation in 3D engineered tissue

Tensor Voting (TV) in 3D

Algorithm for 3D orientation analysis

TV takes into account the measurements in the neighborhood. The name “tensor voting” comes from the fact that information is encoded in tensors and these tensors communicate by means of a voting process. (Medioni et al.)

Each tensor has the following form:

11 12 13 1 1

12 22 23 1 2 3 3 2

13 23 33 3 3

0 0

( ) 0 0

0 0

T

T

T

t t t e

t t t e e e e

t t t e

T

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 18 of 36

Quantification of collagen orientation in 3D engineered tissue

Tensor Voting (TV) in 3D

Algorithm for 3D orientation analysis

An second order symmetric tensor can be expressed as a linear combination of three cases; stickness, plateness and ballness.

Stickness: orientation e1, saliency is λ1-λ2

Plateness: orientation is e3, saliency is λ2-λ3

Ballness: no orientation, saliency is λ3

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Quantification of collagen orientation in 3D engineered tissue

Tensor Voting mechanism

Algorithm for 3D orientation analysis

Stick voting communication (E. Franken)

Random walk

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Quantification of collagen orientation in 3D engineered tissue

Artificial image formation

Validation

Steps: Fibers of 1 voxel in diameter are created by stepping into a predefined direction Fibers are blurred with a Gaussian An intensity threshold is set including voxels with intensity higher then ¼ of the maximum intensity Subsampling to reduce the partial volume effect Ground truth with orientations at every voxel belonging to a fiber

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 21 of 36

Quantification of collagen orientation in 3D engineered tissue

Coherence Enhancing Diffusion

Validation

The signal-to-noise ratio is determined before and after CED.

2 1

var1 var 2

m mSNR

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Quantification of collagen orientation in 3D engineered tissue

Scale Selection

Validation

Artificial images with their fibers in the z-direction are used.The diameter in pixels is determined by hand and compared to the scales found by the confidence and vesselness measure.

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Quantification of collagen orientation in 3D engineered tissue

Scale Selection

Validation

The scales were plotted in color over the fiber diameter for both measures:

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 24 of 36

Quantification of collagen orientation in 3D engineered tissue

Minimal principal curvature directions

Validation

Mean orientations for 13 artificial images are determined and compared to the mean of their ground truth in SPSS 14.0.

No significant difference was found.

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Quantification of collagen orientation in 3D engineered tissue

Tensor Voting

Validation

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Quantification of collagen orientation in 3D engineered tissue

Setup

Experiments

Two experiments:

Experiment 1: - E1: unattached- A1: attached (0% strain)- B1: 4% strain

Experiment 2: - E2: unattached- A2: attached- B2: 4% strain- C2: 8% strain Flexercell FX-4000T straining system

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 27 of 36

Quantification of collagen orientation in 3D engineered tissue

Setup

Experiments

Two photon laser scanning microscopy:- 60x magnification - 1.0 NA water-dipping objective - 1.2x optical zoom- 512 x 512 x ± 30 (≈ 180 x 180 x 45 μm)

Fluorescent probe:CNA35: High affinity for collagen type-I (Krahn, 2005)

Preprocessing of TPLSM images:- Memmory reduction- Intensity correction

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Quantification of collagen orientation in 3D engineered tissue

TPLSM images:

Results

Selected images of TPLSM data of experiment 1 (200 x 200 micron)

unattached sample

4% strain sample

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 29 of 36

Quantification of collagen orientation in 3D engineered tissue

TPLSM images:

Results

Selected images of TPLSM data of experiment 2 (170x 170 micron)

unattached sample

8% strained sample

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Quantification of collagen orientation in 3D engineered tissue

Orientation analysis results from algorithm

Results

Unattached

Attached (0% strain)

4% strain

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 31 of 36

Quantification of collagen orientation in 3D engineered tissue

Results

Unattached

Attached (0% strain)

4% strain

8% strain

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 32 of 36

Quantification of collagen orientation in 3D engineered tissue

Results

TPLSM-data Meanorientation of θ(in degrees)

Meanorientation of φ(in degrees)

Variance in θ(in degrees2)

Variance in φ(in degrees2)

Experiment 1

E1 (unattached) 46,8 90,0 31,9 5,4

A1 (0% strain) 90,0 90,0 22,8 4,3

B1 (4% strain) 90,0 90,1 30,4 11,7

Experiment 2

E2 (unattached) 21,6 90,0 34,7 4,7

A2 (0%strain) 90,1 93,6 34,3 7,0

B2 (4%strain) 176,5 90,0 23,6 13,3

C2 (8% strain) 169,2 90,2 22,6 7,8

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 33 of 36

Quantification of collagen orientation in 3D engineered tissue

DiscussionCoherence enhancing diffusion The parameters involved in CED are chosen based on visual

inspection.

Principal curvature directions: Assumption tubular structures. 2nd order Gaussian derivative match with fibers.

Scale selection Confidence measure was used based on validation but is not appropriate for differentiating between plate-like and tubular structures. Range of scales for analysis.

Tensor Voting Not used in the final algorithm. Needs more investigation.

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 34 of 36

Quantification of collagen orientation in 3D engineered tissue

Conclusions

3D principal curvature directions are an effective way to determine local orientation of tubular structures.

CED can be used to enhance collagen fibers in TPLSM images

TPLSM makes it possible to study 3D collagen orientation in tissue engineered constructs.

This study indicates that there is an increase in collagen alignment with increased strain magnitude based on visual inspection of the orientation histograms.

The variance in orientation does not support the observations made from the orientation histograms.

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 35 of 36

Quantification of collagen orientation in 3D engineered tissue

Recommendations

Faster implementation in e.g. C++. Fourier analysis.

Algorithm

Tissue engineering Increasing the number of experiments. Imaging deeper into tissue and/or with less magnification. Investigate other properties of collagen (fiber thickness). Different straining methods. Follow same sample over time

Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 36 of 36

Quantification of collagen orientation in 3D engineered tissue

Thank you for your attention!

Questions/Remarks?