1 Carnegie Mellon Immune Cells Detection of the In Vivo Rejecting Heart in USPIO-Enhanced MRI Hsun-Hsien Chang 1, José M. F. Moura 1, Yijen L. Wu 2, and.

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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)

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• 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.

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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

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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

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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.

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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

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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

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(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

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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.

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'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

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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

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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

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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)

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Fig2: manual classification (presented in Wu et al, PNAS 2006)

Fig3: automatic classification

Fig1: USPIO-enhanced images

Classification Results POD3 POD4 POD5 POD6 POD7

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Immune Cell Accumulation vs. POD

Immune cell accumulation percentageImmune cell accumulation area

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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.

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Questions and Answers

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(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