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



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

Outline



Introduction

Heart valve disease

Heart valve replacement

Position of the heart valves

Heart valve prostheses Mol et al.



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



The native aortic heart valve

Physiological background

Collagen architecture of the native aortic heart valve



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



Input: image stack of TPLSM

Algorithm for 3D orientation analysis

20 micron 5 micron



Coherence- enhancing diffusion


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.



Coherence enhancing diffusion




Principal Curvature Directions in 3D


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



Principal Curvature Directions in 3D


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



Why Scale Selection?


Objects are only meaningfull at a certain scale




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



Scale Selection


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



Scale Selection


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



Scale Selection Implementation


Artificial image

Response of measures over scale



Tensor Voting (TV) in 3D


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



Tensor Voting (TV) in 3D


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



Tensor Voting mechanism


Stick voting communication (E. Franken)

Random walk



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



Coherence Enhancing Diffusion

Validation

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

2 1

var1 var 2

m mSNR



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.



Scale Selection

Validation

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



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.



Tensor Voting

Validation



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



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



TPLSM images:

Results

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

unattached sample

4% strain sample



TPLSM images:

Results

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

unattached sample

8% strained sample



Orientation analysis results from algorithm

Results

Unattached

Attached (0% strain)

4% strain



Results

Unattached

Attached (0% strain)

4% strain

8% strain



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



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.



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.



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



Thank you for your attention!

Questions/Remarks?

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

Documents

d orientation analysis

d orientation analysis

introduction slide

d engineered tissue

micron slide

d engineered tissue

preferred orientation

strained heart valve