Parameter Synthesis for Cardiac Cell Hybrid Models Using δ-Decisions

Liu, Bing; Kong, Soonho; Gao, Sicun; Zuliani, Paolo; Clarke, Edmund M.

doi:10.1007/978-3-319-12982-2_8

Cited by 15 publications

(9 citation statements)

References 38 publications

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“…the spike-and-dome AP morphology disappears when τ s2 = 2), which highlights the importance of s gate to epicardial cells. This is consistent with [25] that the model proposed in [15], which does not includes s gate, is unable to capture the dynamics of epicardial cells.…”

Section: Cardiac Cell Modelsupporting

confidence: 88%

Approximate Probabilistic Verification of Hybrid Systems

Gyori

Liu

Paul

et al. 2015

Hybrid Systems Biology

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Hybrid systems whose mode dynamics are governed by nonlinear ordinary differential equations (ODEs) are often a natural model for biological processes. However such models are difficult to analyze. To address this, we develop a probabilistic analysis method by approximating the mode transitions as stochastic events. We assume that the probability of making a mode transition is proportional to the measure of the set of pairs of time points and value states at which the mode transition is enabled. To ensure a sound mathematical basis, we impose a natural continuity property on the non-linear ODEs. We also assume that the states of the system are observed at discrete time points but that the mode transitions may take place at any time between two successive discrete time points. This leads to a discrete time Markov chain as a probabilistic approximation of the hybrid system. We then show that for BLTL (bounded linear time temporal logic) specifications the hybrid system meets a specification iff its Markov chain approximation meets the same specification with probability 1. Based on this, we formulate a sequential hypothesis testing procedure for verifying -approximatelythat the Markov chain meets a BLTL specification with high probability. Our case studies on cardiac cell dynamics and the circadian rhythm indicate that our scheme can be applied in a number of realistic settings.

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Section: Cardiac Cell Modelsupporting

confidence: 88%

Approximate Probabilistic Verification of Hybrid Systems

Gyori

Liu

Paul

et al. 2015

Hybrid Systems Biology

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“…The property does not hold when τ s2 = 2, suggesting that gate s is crucial to epicardial cells. This is supported by the results reported in [46] that a model without s [23] is unable to reproduce the experimentally observed electrodynamics in epicardial cells.…”

Section: The Cardiac Cell Hybrid Modelsupporting

confidence: 81%

“…Under a disease condition (e.g. τ o2 = 0.1 or τ o1 = 0.004, see [46]) the property does not hold for any ε. This implies that the impulse conduction can be blocked by a region of unexcitable cells, which can cause ventricular disorders.…”

Section: The Cardiac Cell Hybrid Modelmentioning

confidence: 99%

Statistical Model Checking-Based Analysis of Biological Networks

Liu

Gyori

Thiagarajan

2019

Computational Biology

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We introduce a framework for analyzing ordinary differential equation (ODE) models of biological networks using statistical model checking (SMC). A key aspect of our work is the modeling of single-cell variability by assigning a probability distribution to intervals of initial concentration values and kinetic rate constants. We propagate this distribution through the system dynamics to obtain a distribution over the set of trajectories of the ODEs. This in turn opens the door for performing statistical analysis of the ODE system's behavior. To illustrate this we first encode quantitative data and qualitative trends as bounded linear time temporal logic (BLTL) formulas. Based on this we construct a parameter estimation method using an SMC-driven evaluation procedure applied to the stochastic version of the behavior of the ODE system. We then describe how this SMC framework can be generalized to hybrid automata by exploiting the given distribution over the initial states and the-much more sophisticated-system dynamics to associate a Markov chain with the hybrid automaton. We then establish a strong relationship between the behaviors of the hybrid automaton and its associated Markov chain. Consequently, we sample trajectories from the hybrid automaton in a way that mimics the sampling of the trajectories of the Markov chain. This enables us to verify approximately that the Markov chain meets a BLTL specification with high probability. We have applied these methods to ODE based models of Toll-like receptor signaling and the crosstalk between autophagy and apoptosis, as well as to systems exhibiting hybrid dynamics including the circadian clock pathway and cardiac cell physiology. We

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“…Note that they consider only discrete time dynamical systems, whereas we treat time as a continuous entity. The work by Liu et al [16] tackles the parameter synthesis problem using δ-complete decision procedures [12] for first-order logic (FOL) formulae to overcome undecidability issues. In this setting, a FOL formula describes the states reachable with a finite number of steps.…”

Section: Discussionmentioning

confidence: 99%

Abstraction-Based Parameter Synthesis for Multiaffine Systems

Bogomolov

Schilling

Bartocci

et al. 2015

Hardware and Software: Verification and Testing

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Abstract. Multiaffine hybrid automata (MHA) represent a powerful formalism to model complex dynamical systems. This formalism is particularly suited for the representation of biological systems which often exhibit highly non-linear behavior. In this paper, we consider the problem of parameter identification for MHA. We present an abstraction of MHA based on linear hybrid automata, which can be analyzed by the SpaceEx model checker. This abstraction enables a precise handling of time-dependent properties. We demonstrate the potential of our approach on a model of a genetic regulatory network and a myocyte model.

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Parameter Synthesis for Cardiac Cell Hybrid Models Using δ-Decisions

Cited by 15 publications

References 38 publications

Approximate Probabilistic Verification of Hybrid Systems

Approximate Probabilistic Verification of Hybrid Systems

Statistical Model Checking-Based Analysis of Biological Networks

Abstraction-Based Parameter Synthesis for Multiaffine Systems

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