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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
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 19 of 36
Quantification of collagen orientation in 3D engineered tissue
Tensor Voting mechanism
Algorithm for 3D orientation analysis
Stick voting communication (E. Franken)
Random walk
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 20 of 36
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
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 22 of 36
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.
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 23 of 36
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.
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 25 of 36
Quantification of collagen orientation in 3D engineered tissue
Tensor Voting
Validation
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 26 of 36
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
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 28 of 36
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
Msc. Thesis presentation Florie Daniels - June 29, 2006 Slide 30 of 36
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?