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Bisimulation-Based Abstraction of Sodium-Channel Dynamics in Cardiac-Cell Models. Abhishek Murthy & Md. Ariful Islam Computer Science, Stony Brook University Joint work with: Ezio Bartocci, Flavio Fenton, Scott Smolka and Radu Grosu Spring 2012 CMACS Virtual PI Meeting. Outline. - PowerPoint PPT Presentation
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Bisimulation-Based Abstraction of Sodium-Channel Dynamics in Cardiac-CellModelsAbhishek Murthy & Md. Ariful IslamComputer Science, Stony Brook University
Joint work with: Ezio Bartocci, Flavio Fenton, Scott Smolka and Radu Grosu
Spring 2012 CMACS Virtual PI Meeting
Outline1. MotivationComputational modeling and analysisTowers of abstractionCardiac cell modeling2. ApproachSodium channel abstractionMethodologyParameter Estimation from Finite Traces (PEFT)Rate-Function Identification (RFI)3. ResultsHodgkin-Huxley (HH)-type abstractionSubstitutivity via bisimulation4. Ongoing Work and Summary*
MotivationMathematical ModelingMathematical Model (Possibly Non-linear)Hybridization, over-approximation, abstractionFormal Analysis Exhaustive exploration of state space
Model Checking (MC), Abstract Interpretation (AI), Parameter Estimation.Biological Phenomena (Cardiac excitation: cell & tissue-level behavior)Qualitative/ Quantitative Insights(Abstract parameter and state-space)Computational ModelLinear Hybrid Automata (LHA), Kripke structure, etc. *
*Towers of AbstractionIntermediate model1Intermediate model21st abstraction2nd abstractionseries of abstractions
*Cardiac ElectrophysiologyMacro (tissue) level simulation
Isotropic diffusion of charge from excitable cells to neighbors
*Cell membrane(selective ion permeability)The Iyer Model
*The Minimal ModelScaled membrane potentialAbstract currents fast inward (fi)slow outward (so)Slow inward (si)Amenable to formal analysis, post hybridization
Abstract variables no physiological interpretation
*Hodgkin-Huxley (HH) Formalismfor Sodium Channels
*Sodium Channel Abstraction
*MethodologyParameter Estimation from Finite Traces(PEFT)Rate-Function Identification(RFI)
*Parameter Estimation from Finite Traces (PEFT)Parameter Estimation from Finite Traces(PEFT)
*Parameter Estimation from Finite Traces (PEFT)Time stepTime step
*Rate-Function Identification (RFI)Rate-Function Identification(RFI)
*Rate-Function Identification (RFI)V (mV)V (mV)
*Rate-Function Identification (RFI)V (mV)V (mV)
*Results
*ResultsV(mV)
*Substitutivity via Bisimulation- Labeled Transition Systems (LTS)
*Substitutivity via Bisimulation- Labeled Transition Systems (LTS)mhTimeTime(t)
*
*Substitutivity via Bisimulation- Approximate Bisimulation
*Substitutivity via Bisimulation
*Ongoing Work
*SummaryTowers of abstraction translate analysis results into physiological insights
Sodium channel m-type and h-type gates
Modeled as being independent (HH-type, 8-state) or dependent (Iyer, 13-state)
1st abstraction enforce conditional independence between m-type and h-type
Proof-of-concept of establishing towers of abstraction
PEFT and RFI optimization-based techniques to identify abstraction
Approximate bisimulation notion of approximate system equivalence
Prove abstraction and original model approximately bisimilar
Approx. bisimulation ensures Substitutivity
Weve assembled a world class team to combine and advance two mature, and powerful methods*