Parameter Synthesis for Cardiac Cell Hybrid Models Using δ-Decisions

  • Bing Liu
  • Soonho Kong
  • Sicun Gao
  • Paolo Zuliani
  • Edmund M. Clarke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8859)

Abstract

A central problem in systems biology is to identify parameter values such that a biological model satisfies some behavioral constraints (e.g., time series). In this paper we focus on parameter synthesis for hybrid (continuous/discrete) models, as many biological systems can possess multiple operational modes with specific continuous dynamics in each mode. These biological systems are naturally modeled as hybrid automata, most often with nonlinear continuous dynamics. However, hybrid automata are notoriously hard to analyze — even simple reachability for hybrid systems with linear differential dynamics is an undecidable problem. In this paper we present a parameter synthesis framework based on δ-complete decision procedures that sidesteps undecidability. We demonstrate our method on two highly nonlinear hybrid models of the cardiac cell action potential. The results show that our parameter synthesis framework is convenient and efficient, and it enabled us to select a suitable model to study and identify crucial parameter ranges related to cardiac disorders.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Bing Liu
    • 1
  • Soonho Kong
    • 1
  • Sicun Gao
    • 1
  • Paolo Zuliani
    • 2
  • Edmund M. Clarke
    • 1
  1. 1.Computer Science DepartmentCarnegie Mellon UniversityUSA
  2. 2.School of Computing ScienceNewcastle UniversityUK

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