Transcript 3D shape variability of the healthy and infarcted mouse heart

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3D shape variability of the
healthy and infarcted mouse
heart
Korbeeck, J.M.
Eindhoven, July 1st 2004
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Contents
•
•
•
•
Goals;
Anatomy heart;
Modes of LV deformation;
Method:
– Tagging MRI;
– Statistical Shape Models.
• Results;
• Future research.
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Introduction
• Infarction  major
cause of death;
• Temporal shape
changes 
mechanical pumping
efficiency  warning
system of heart
failure?
All Other
Causes
41%
Diseases
of the Heart
29%
Cancer
23%
Stroke
7%
[From “Stroke Facts 2004: All Americans”, American
Heart Association, 2004]
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Goals
• Study the left ventricle motion of the heart:
– Design of Statistical Shape Model algorithm;
– Interpretation of shape variability results 
physiological changes described in literature.
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Heart anatomy
• Left ventricle (LV) is
studied:
– Volume corresponds
with stroke volume 
pumping-efficiency;
– Blood through entire
circulation  thickest
wall.
[From Marieb1997, page 661]
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Layers of the heart wall
[From Marieb1997, page 658]
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Modes of LV deformation
• Deformation:
– Radial displacement;
– Axial torsion;
– Circumferential
contraction with long
axis extension.
• Rotation;
• Translation.
[From Arts1992]
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Tagging MRI (C-SPAMM)
• Cine gradient echo
MR image of beating
heart;
• C-SPAMM:
– Tag pattern applied by
applying magnetic field
gradient;
– Deformation of the
myocardium can be
calculated using phase
tracking.
[From Heijman2004]
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Mouse heart
• Left ventricle:
posterior
– Large;
– Thick wall.
• Right ventricle:
myocardium
RV wall
RV
LV
anterior
– Smaller;
– Thinner wall 
tagging MRI not yet
possible.
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Statistical Shape Models
• Modelling shape and shape variation:
– Without shape assumptions.
• Shape represented by set of points in time;
• Model the variation using PCA.
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Principal Component Analysis
1
2
• Parameterised model:
x  f shape (b)  x  x  Φb
• Reduce
dimensionality:
1
2
x
x
b1
 1
– Eigenvectors of
covariance;
– Eigenvectors  main
directions;
– Eigenvalue 
variance along
eigenvector.
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Algorithm
• Represent points of 2D image as vector x:
x  ( x 1,x n , y 1,y n )T
• Compute the mean and covariance:
1
1
x  x
S
( x  x)(x  x)
s
s 1
s
s
T
i 1
i
i 1
i
i
• Compute  and  of S, approximation of x:
x  x  Φb
b  ΦT ( x  x)
• Choose t largest eigenvalues such that
   f V where fv defines the proportion of total variation
t
i 1
i
v T
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Example
[From Cootes2004]
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Cardiac Motion Model
[From Suinesiaputra2002]
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Results
• “Normal” (i.e. healthy)
heart;
• Heart with infarction
(LDA occluded by
ligation):
– Slice through
infarction;
– Slice above infarction.
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Eigenvalues
• Healthy heart  more
eigenvalues  mix of
more different shape
variabilities;
• Slice through infarction 
less deformation modes
(mainly translation)
caused by infarction;
• Great compression
component to
compensate for infarction.
Percentage
of total 
Healthy
Infarction
Above infarction
0.4
0.3
0.2
0.1
0
2
4
6
8
10
Eigenmode 
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Eigenmodes healthy
Radial
compression
or
compression
with long axis
extension
Rotation or
torsion
Translation
Unknown
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Eigenmodes infarction
Translation
Deviated radial
displacement
Unknown
Unknown
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Eigenmodes above infarction
Strong
compression
to compensate
for infarction
Normal
translation
Unknown
Unknown
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Use as filter method
Eigenmodes
1-4
• Good approximation with only four eigenmodes
( 95%).
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Use as filter method
Eigenmode
1
• The end of ventricular systole is almost
completely described by the first eigenmode.
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Use as filter method
Eigenmodes
2-4
• Filtering out of the compression (described by
the first eigenmode) works fine.
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Future research
• Better statistics  increment of mice;
• Use PCA with foreknowledge;
• Analysis of spatial derivatives 
(circumferential) strain;
• 3D tagging MRI/long axis slices;
• Link with DTI (fibre tracking).
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Future
• Better indication of heart failure during a
hospital consult after heart dysfunction.