1
Carnegie Mellon
Immune Cells Detection of the In Vivo Rejecting Heart in
USPIO-Enhanced MRI
Hsun-Hsien Chang1, José M. F. Moura1, Yijen L. Wu2, and Chien Ho2
1Department of Electrical and Computer Engineering2Pittsburgh NMR Center for Biomedical ResearchCarnegie Mellon University, Pittsburgh, PA, USA
Work supported by NIH grants (R01EB/AI-00318 and P4EB001977)
2
Carnegie Mellon
• Gold standard diagnosis method (i.e., biopsy) of heart rejection– is invasive.
– is prone to sampling errors.
Research Motivation
• The extreme treatment of the heart failure is transplantation.
• Alternative diagnosis method: contrast-enhanced cardiac MRI– is non-invasive.
– monitors the whole in vivo heart.
3
Carnegie Mellon
Mechanism of Contrast-Enhanced MRI
: immune cells (e.g. macrophages).
rejecting tissue
: contrast agents (USPIO, ultra-small super-paramagnetic iron oxide) label the immune cells
High relaxivity causes low image intensities under T2* weighted MRI.
LVRV
4
Carnegie Mellon
POD 5.
Post Operation Day (POD) 3.
Immune Cells Classification: Challenges
Need an automatic algorithm to classify pixels as USPIO-labeled or unlabeled.
Identify immune cells (i.e., dark pixels):• Large number of myocardial pixels
– Manual classification is labor-intensive and time consuming.
• Dispersion of immune cells– Immune cells accumulate in multiple regions
without known patterns.
• Heart motion blurs images– It is hard to distinguish the boundaries between
the USPIO-labeled and unlabeled pixels
5
Carnegie Mellon
Immune Cells Classification: Overview
• Main idea: – Partition the image into
USPIO-labeled and unlabeled parts.
• Graph theory approach:– Describe the image as a
graph.– Find the optimal edge cut.
6
Carnegie Mellon
Outline
• Introduction
• Methodology: Graph Partitioning – Graph Representation of the USPIO Image – Optimal Edge Cut and the Cheeger Constant– Optimal Classifier via Optimization
• Results and Conclusions
7
Carnegie Mellon
Red dots are the automatically selected USPIO-labeled pixels.
Immune Cells Classification: Algorithm
Graph Representation of the USPIO Image
Classification through an Edge Cut
Optimal Cut from the Cheeger Constant
Optimal Classifier via Energy Minimization
8
Carnegie Mellon
(a) 0.61
(b) 0.89
(c) 0.76
(d) 0.61
(e) 0.46
(f) 1.00
(g) 0.62
(h) 0.51
(i) 0.23
(j) 0.79
(k) 0.38
(l) 0.43
(m) 0.00
(n) 0.17
(o) 0.09
(p) 0.28
Graph Representation of the USPIO Image
Classification through an Edge Cut
Optimal Cut from the Cheeger Constant
Optimal Classifier via Energy Minimization
• Graph: G(V, E). – a set V of vertices representing pixels.– a set E of edges linking the vertices
according to a prescribed way.
• Edge assignment strategies:– Geographical neighborhood– Feature similarities
9
Carnegie Mellon
Graph Representation of the USPIO Image
Classification through an Edge Cut
Optimal Cut from the Cheeger Constant
Optimal Classifier via Energy Minimization
'SSV • Partition:• Edge cut: )',(Edge SS
• Classification of the pixels into USPIO-labeled or unlabeled is equivalent to partitioning the graph into two disjoint subgraphs.
• Graph partitioning: – Divide the vertex set V into disjoint subsets S and
S’.– Remove a set of edges, denoted as Edge(S, S’), to
make S and S’ disconnected.
10
Carnegie Mellon
'S
S52
10
8
3
(a)
(b)
(c)
(d)
(8+5+10)(8+5+2)a+(2+10)c
X(S) =
= 0.85
52
10
8
3
(a)
(b)
(c)
(d)
S'S
(2+5+8+3+10)(2+10)c+(8+3)b
X(S) =
= 1.21
52
10
8
3
(a)
(b)
(c)
(d)S
'S
(8+3+10+2)(8+3)b+(2+10)c
X(S) =
= 1.00
)(Vol
|)',(Edge|min)(
S
SSSX
S
– Assuming that Vol(S) < Vol(S’).– |Edge(S, S’)| = sum of the edges in the cut.– Vol(S) = sum of edges emanating from all the vertices in S.Graph Representation
of the USPIO Image
Classification through an Edge Cut
Optimal Cut from the Cheeger Constant
Optimal Classifier via Energy Minimization
52
10
8
3
(a)
(b)
(c)
(d)
• Consider this example:
• Cheeger constant:
'S
S5
2
10
8
3
(a)
(b)
(c)
(d)
(2+5+3)(2+10)c+(10+5+3)d
X(S) =
= 0.33
11
Carnegie Mellon
1'
1 :
S
Sc• Classifier
Graph Representation of the USPIO Image
Classification through an Edge Cut
Optimal Cut from the Cheeger Constant
Optimal Classifier via Energy Minimization
'S
S5
2
10
8
3
(a)
(b)
(c)
(d)
• Classifier
(a) (b)
(c) (d)+1
0
-1
• Derive an objective functional from the Cheeger constant:
)(Vol )',(Edge)(:Obj SSSSQ
)(Vol )(Edge)(:Obj cccQ
• Optimal classifier: )(minargˆ cQc
)(Vol
)',(Edgemin)(:constCheeger
S
SSSX
S
12
Carnegie Mellon
Outline
• Introduction
• Methodology: Graph Partitioning – Graph Representation of the USPIO Image – Optimal Edge Cut and the Cheeger Constant– Optimal Classifier via Optimization
• Results and Conclusions
13
Carnegie Mellon
Heart Rejection at Different Rejection Stages
Post Operation Day (POD) 3 POD 4
POD 5 POD 6
LVRV LV
RV
LVRV LVRV
(Data were presented in Wu et al, PNAS 2006)
14
Carnegie Mellon
Fig2: manual classification (presented in Wu et al, PNAS 2006)
Fig3: automatic classification
Fig1: USPIO-enhanced images
Classification Results POD3 POD4 POD5 POD6 POD7
15
Carnegie Mellon
Immune Cell Accumulation vs. POD
Immune cell accumulation percentageImmune cell accumulation area
16
Carnegie Mellon
Conclusions
• Develop a graph theoretical approach to classifying immune cells in the USPIO-enhanced images– Represent an image by a
graph.– Consider the Cheeger
constant for the optimal cut.– Adopt the optimization to
find the classifier.
17
Carnegie Mellon
Questions and Answers
18
Carnegie Mellon
(a) 0.61
(b) 0.89
(c) 0.76
(d) 0.61
(e) 0.46
(f) 1.00
(g) 0.62
(h) 0.51
(i) 0.23
(j) 0.79
(k) 0.38
(l) 0.43
(m) 0.00
(n) 0.17
(o) 0.09
(p) 0.28
28.089.061.0ab d
1. Assign edges to the neighboring pixels.
42.0)exp(
)exp(
2
2
2
2
ab
3.028.0
ab
dw
15.046.061.0ae d
85.0)exp( 2
2
ae
ae dw
3. Repeat the procedure to all other pixels.
00.0ad d00.1)exp( 2
2ad
ad dw
01.0ag d99.0)exp( 2
2ag
ag
dw
2. Assign edges to similar pixels ( d < 0.1).
10.0ah d89.0)exp( 2
2ah
ah dw
Weighted Graph Representation of Image