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Learning and Detecting Emergent Behavior in Networks of Cardiac Myocytes

Learning and Detecting Emergent Behavior in Networks of Cardiac Myocytes. Radu Grosu Stony Brook University. Joint Work With. Ezio Bartocci, Flavio Corradini University of Camerino, Italy E. Entcheva, S.A. Smolka and A. Wasilewska Stony Brook University, USA.

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Learning and Detecting Emergent Behavior in Networks of Cardiac Myocytes

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  1. Learning and Detecting Emergent Behavior in Networks of Cardiac Myocytes RaduGrosu Stony Brook University

  2. Joint Work With Ezio Bartocci, Flavio Corradini University of Camerino, Italy E. Entcheva, S.A. Smolka and A. Wasilewska Stony Brook University, USA

  3. Emergent Behavior in Heart Cells ECG Surface Arrhythmia afflicts more than3 million Americansalone

  4. Excitable Cells • Generate action potentials (elec. pulses) in response to electrical stimulation • Examples: neurons, cardiac cells, etc. • Local regeneration allows electric signal propagation without damping • Building block for electrical signaling inbrain, heart, and muscles Neurons of a squirrel University College London Artificial cardiac tissue University of Washington

  5. Action Potential (AP) Membrane’s AP dependson: • Stimulus (voltage or current): • External • Neighboring cells • Cell’s state Schematic Action Potential voltage Threshold Stimulus failed initiation Resting potential time

  6. Stimulated Hybrid Automaton Model

  7. Stimulated Hybrid Automaton Model

  8. Stimulated Hybrid Automaton Model

  9. Fibrillation/Defibrillation(400x400 neonatal-rat cells)

  10. Finite Mode Abstraction • Preserves spatial properties (4160,000 images)

  11. Problems to Solve • Detection problem: • Does a simulated tissue contain a spiral ? • Specification problem: • Encode above property as alogic formula? • Can we learn the formula? How? Use Spatial Abstraction

  12. Superoposition Quadtrees (SQTs) Abstract position and compute PMF p(m) ≡ P[D=m]

  13. modal SSL Superposition Quadgraphs (Fractals): linear / branching SSL Kripke Structure: SQGs and Kripke Structures (KSs)

  14. The Path to the Core of a Spiral Root 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 Click the core to determine the quadtree 1 2 3 4

  15. Linear Spatial-Superposition Logic Syntax Semantics

  16. SQGs, KSs and LSL

  17. Overview of Our Approach

  18. The Wave Front • Measure density of mode stimulated (yellow) • Yellow modes represent the wave front

  19. Learning Formula Input – Sequence of images (mode distribution) Output – Set of records with attributes (a table) 3 4 5 1 2

  20. Class Description Formula

  21. Creating/Checking an LSSL formula Decision tree algorithm: simplifies the CDF if a7≤ 0.875 then {if a2 > 0.049 then celse ¬c} else if a3 ≤ 0.078 then { if a0 > 0.025 thenc else ¬ c} else ¬c LSSL formula φ : gives meaning to attributes ai X7(P(D=s)≤ 0.875) ∧ X2(P(D=s)> 0.049) ∨ X7(P(D=s)> 0.875) ∧ X3(P(D=s)≤ 0.078) ∧ (P(D=s)> 0.025) Spiral detection for SQT T: reduces toBMCofT ⊨ φ

  22. Overview of Our Approach

  23. Using Weka

  24. Emerald: Learning LSSL Formula Emerald: Bounded Model Checking

  25. Results Prediction accuracy for spiral detection inEmerald

  26. Future Directions • Investigate expressivity of various SSL logics • Parameter identification for SSL patterns • Analysis of spatio-temporal patterns

  27. Thank you for the attention !!!

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