Transcript Quantification of collagen orientation in 3D engineered tissue

Quantification of collagen orientation
in 3D engineered tissue
Florie Daniels
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Outline
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Introduction
Physiological background
Algorithm for 3D orientation analysis
Validation
Experiments
Results
Discussion
Conclusions
Recommendations
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Introduction
Heart valve
disease
Heart valve
replacement
Position of the heart valves
Heart valve prostheses
Msc. Thesis presentation Florie Daniels - June 29, 2006
Mol et al.
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Quantification of collagen orientation in 3D engineered tissue
Introduction
Project goals:
 To design an image analysis tool for automatic 3D
orientation analysis of collagen fibers in two-photon laserscanning microscopy (TPLSM) images.
 To quantify collagen orientation in 3D unattached,
attached and strained heart valve tissue engineered
equivalents.
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Physiological background
The native aortic heart valve
Collagen architecture of the native
aortic heart valve
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Physiological background
Collagen
1.5 nm in diameter,
300 nm in length
diameter ranging from 10 to 500 nm,
length ~10 to 30 μm.
several hundred micrometers
Hierarchy of collagen
Fibrillogenesis
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Input: image stack of TPLSM
20 micron
Msc. Thesis presentation Florie Daniels - June 29, 2006
5 micron
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
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.
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Coherence enhancing diffusion
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Principal Curvature Directions in 3D
Hessian Matrix:
 Lxx

2 L(x, )   Lyx
 Lzx

Lxy
Lyy
Lzy
(L = image)
Lxz  Eigenvalues  Principal curvatures
 Eigenvectors  Principal directions
Lyz 
Lzz 
m-dimensional Gaussian:
G ( x,  ) 

1
Msc. Thesis presentation Florie Daniels - June 29, 2006
2 2
2
2
Lxx  L(x)  2 G (x,  )
x
2
Second order derivative:
m
e
x2
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
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

  tan 

1
y

x
 φ: the angle from the z-axis
  cos1 ( z)
Representation of the angles in 3D
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Why Scale Selection?
Objects are only meaningfull at a certain scale
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Scale Selection
The eigenvalues of the Hessian indicate the type of
structure present in a voxel. The eigenvalues are ordered
from small to large:
1  2  3
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
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Scale Selection
Collagen fibers appear as bright tubular structures in a
darker environment. The conditions for a bright tubular
structure in 3D are:
1  0
1  2
2  3
2  0 and 3  0
We use normalized Gaussian derivatives to compute the
Hessian at different scales.
G(x, )normalized   2G(x, )
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Scale Selection
Two measures are used for scale selection.
 The confidence measure (Niessen):
0
if λ2>0 or λ3>0,

C ( ,  )  
  2  otherwise
1  exp  2c 2 



with                   

2
2
1
2
2
2
2
3
3
1
 The vesselness measure (Frangi et al.):
if λ2>0 or λ3>0
0

V (v, )  
 RA 2  
 RB 2  
 S2 
1  exp   2 2   exp   2 2  1  exp   2c 2  







with
RB 
1
2 3
Msc. Thesis presentation Florie Daniels - June 29, 2006
RA 
2
3
S H
F


jm
2
j
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Scale Selection Implementation
Artificial image
Response of measures over scale
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
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:
 t11 t12

T   t12 t22
t
 13 t23
t13 

t23   (e1 e2
t33 
Msc. Thesis presentation Florie Daniels - June 29, 2006
 1 0

e3 )  0 3
0 0

0   e1T 
 T 
0   e2 
3   e3T 
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
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
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Algorithm for 3D orientation analysis
Tensor Voting mechanism
Random walk
Stick voting communication (E. Franken)
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Validation
Artificial image formation
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
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Quantification of collagen orientation in 3D engineered tissue
Validation
Coherence Enhancing Diffusion
The signal-to-noise ratio is determined before and after CED.
m2  m1
SNR 
var1  var 2
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Validation
Scale Selection
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
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Quantification of collagen orientation in 3D engineered tissue
Validation
Scale Selection
The scales were plotted in color over the fiber diameter for both
measures:
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Validation
Minimal principal curvature directions
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
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Quantification of collagen orientation in 3D engineered tissue
Validation
Tensor Voting
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Experiments
Setup
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
Msc. Thesis presentation Florie Daniels - June 29, 2006
Flexercell FX-4000T straining system
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Quantification of collagen orientation in 3D engineered tissue
Experiments
Setup
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
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Quantification of collagen orientation in 3D engineered tissue
Results
TPLSM images:
unattached sample
Selected images of TPLSM data of experiment 1 (200 x 200 micron)
Msc. Thesis presentation Florie Daniels - June 29, 2006
4% strain sample
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Quantification of collagen orientation in 3D engineered tissue
Results
TPLSM images:
unattached sample
Selected images of TPLSM data of experiment 2 (170x 170 micron)
Msc. Thesis presentation Florie Daniels - June 29, 2006
8% strained sample
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Quantification of collagen orientation in 3D engineered tissue
Results
Orientation analysis results from algorithm
Unattached
Attached (0% strain)
4% strain
Msc. Thesis presentation Florie Daniels - June 29, 2006
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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
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Quantification of collagen orientation in 3D engineered tissue
Results
TPLSM-data
Mean
orientation of θ
(in degrees)
Mean
orientation of φ
(in degrees)
Variance in θ
(in degrees2)
Variance in φ
(in degrees2)
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
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
Experiment 1
Experiment 2
Msc. Thesis presentation Florie Daniels - June 29, 2006
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Quantification of collagen orientation in 3D engineered tissue
Discussion
Coherence 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
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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
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Quantification of collagen orientation in 3D engineered tissue
Recommendations
Algorithm
 Faster implementation in e.g. C++.
 Fourier analysis.
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
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Quantification of collagen orientation in 3D engineered tissue
Thank you for your attention!
Questions/Remarks?
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