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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 Chien Ho 2 1 Department of Electrical and Computer Engineering 2 Pittsburgh NMR Center for Biomedical Research Carnegie Mellon University, Pittsburgh, PA, USA Work supported by NIH grants (R01EB/AI-00318 and P4EB001977)

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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.

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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

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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

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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.

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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

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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

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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

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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 Partition: Edge cut: 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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10 Carnegie Mellon 5 2 10 8 3 (a)(a)(b)(b) (c)(c)(d)(d) (8+5+10) (8+5+2) a +(2+10) c X(S) = = 0.85 5 2 10 8 3 (a)(a)(b)(b) (c)(c)(d)(d) (2+5+8+3+10) (2+10) c +(8+3) b X(S) = = 1.21 5 2 10 8 3 (a)(a)(b)(b) (c)(c)(d)(d) (8+3+10+2) (8+3) b +(2+10) c X(S) = = 1.00 –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 5 2 10 8 3 (a)(a)(b)(b) (c)(c)(d)(d) Consider this example: Cheeger constant: 5 2 10 8 3 (a)(a)(b)(b) (c)(c)(d)(d) (2+5+3)(2+5+3) (2+10) c +(10+5+3) d X(S) = = 0.33

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11 Carnegie Mellon Classifier Graph Representation of the USPIO Image Classification through an Edge Cut Optimal Cut from the Cheeger Constant Optimal Classifier via Energy Minimization 5 2 10 8 3 (a)(a)(b)(b) (c)(c)(d)(d) Classifier (a)(b) (c)(d) +1 0 Derive an objective functional from the Cheeger constant: Optimal classifier:

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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

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13 Carnegie Mellon Heart Rejection at Different Rejection Stages Post Operation Day (POD) 3 POD 4 POD 5POD 6 LVRV LV RV LVRVLVRV (Data were presented in Wu et al, PNAS 2006)

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14 Carnegie Mellon Fig2: manual classification (presented in Wu et al, PNAS 2006) Fig3: automatic classification Fig1: USPIO-enhanced images Classification Results POD3POD4POD5POD6POD7

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15 Carnegie Mellon Immune Cell Accumulation vs. POD Immune cell accumulation percentageImmune cell accumulation area

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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.

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17 Carnegie Mellon Questions and Answers

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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 1. Assign edges to the neighboring pixels. 3. Repeat the procedure to all other pixels. 2. Assign edges to similar pixels ( d < 0.1). Weighted Graph Representation of Image

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