Invariant Verification of Nonlinear Hybrid Automata Networks of Cardiac Cells

Huang, Zhengxu; Fan, Chuchu; Mereacre, Alexandru; Mitra, Sayan; Kwiatkowska, Marta

doi:10.1007/978-3-319-08867-9_25

Cited by 32 publications

(24 citation statements)

References 44 publications

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“…SOS optimization has also played a crucial role in enabling the automated computation of other Lyapunov-like functions, such as Barrier Certificates [25,24] and discrepancy functions [4,12]. In [25,17], the authors employ an SOSP 2-like approach, which is based on the S-Procedure of [33] and entails strengthening the Lyapunov-like inequalities over the region-of-interest in the state and input spaces.…”

Section: Related Workmentioning

confidence: 99%

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Computing bisimulation functions using SOS optimization and δ -decidability over the reals

Murthy

Islam

Smolka

et al. 2015

Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

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We present BFComp, an automated framework based on Sum-Of-Squares (SOS) optimization and δ-decidability over the reals, to compute Bisimulation Functions (BFs) that characterize Input-to-Output Stability (IOS) of dynamical systems. BFs are Lyapunov-like functions that decay along the trajectories of a given pair of systems, and can be used to establish the stability of the outputs with respect to bounded input deviations.In addition to establishing IOS, BFComp is designed to provide tight bounds on the squared output errors between systems whenever possible. For this purpose, two SOS optimization formulations are employed: SOSP 1, which enforces the decay requirements on a discretized grid over the input space, and SOSP 2, which covers the input space exhaustively. SOSP 2 is attempted first, and if the resulting error bounds are not satisfactory, SOSP 1 is used to compute a Candidate BF (CBF). The decay requirement for the BFs is then encoded as a δ-decidable formula and validated over a level set of the CBF using the dReal tool. If dReal produces a counterexample containing the states and inputs where the decay requirement is violated, this pair of vectors is used to refine the input-space grid and SOSP 1 is iterated.By computing BFs that appeal to a small-gain theorem, the BFComp framework can be used to show that a subsystem of a feedback-composed system can be replaced-with bounded error-by an approximately equivalent abstraction, thereby enabling approximate model-order reduction of dynamical systems. We illustrate the utility of BFComp on a canonical cardiac-cell model, showing that the four-variable Markovian model for the slowly activating Potassium current IKs can be safely replaced by a one-variable HodgkinHuxley-type approximation.

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Section: Related Workmentioning

confidence: 99%

“…As shown in [1,21], one can appeal to a small-gain theorem to compute BFs that bound the error that is introduced when substituting S for S within D. BFs can also be used in other system design and verification settings, including controller design [11], reachability analysis [19], and simulation-based verification [12,4].…”

Section: Introductionmentioning

confidence: 99%

Computing bisimulation functions using SOS optimization and δ -decidability over the reals

Murthy

Islam

Smolka

et al. 2015

Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control

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“…Using the techniques from Grosu et al [13], we can abstract the MV model into a network of hybrid automata (see Figure 12) that fits our developed framework for pacemaker verification. For details see [15].…”

Section: The Minimal Ventricular Cardiac Cell Heart Modelmentioning

confidence: 99%

“…In Figure 12 we depict a Simulink/Stateflow implementation of 5 cardiac cells connected in a ring; in Figure 13 we depict the voltage level of a cardiac cell for a set of initial conditions. In [15] we have developed techniques on how to compute the over-approximation of the reach set, i.e., the voltage level of the cardiac cell at a given time moment, for a network of cardiac cells given by the MV model. As a future direction we plan to connect the minimal ventricular cardiac cell heart model to the pacemaker model, and investigate more advanced specifications such as linear duration properties [7].…”

Section: All Of the Four Variables Are Time And Positionmentioning

confidence: 99%

On Quantitative Software Quality Assurance Methodologies for Cardiac Pacemakers

Kwiatkowska

Mereacre

Paoletti

2014

Leveraging Applications of Formal Methods, Verification and Validation. Specialized Techniques and Applications

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Abstract. Embedded software is at the heart of implantable medical devices such as cardiac pacemakers, and rigorous software design methodologies are needed to ensure their safety and reliability. This paper gives an overview of ongoing research aimed at providing software quality assurance methodologies for pacemakers. A model-based framework has been developed based on hybrid automata, which can be configured with a variety of heart and pacemaker models. The framework supports a range of quantitative verification techniques for the analysis of safety, reliability and energy usage of pacemakers. It also provides techniques for parametric analysis of personalised physiological properties that can be performed in silico, which can reduce the cost and discomfort of testing new designs on patients. We describe the framework, summarise the results obtained, and identify future research directions in this area.

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“…To turn this idea into an algorithm, we introduced the notion of discrepancy which (a) upper bounds the distance between two neighboring behaviors and (b) the bound converges to zero as the parameter choices for the two behaviors get closer and closer [6], [8]. It has been shown that, for an expressive class of models, indeed one can find discrepancy functions that meet these criteria [7].…”

Section: Introductionmentioning

confidence: 99%

Simulation-Based Verification of Cardiac Pacemakers With Guaranteed Coverage

et al. 2015

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Design and testing of pacemaker is challenging because of the need to capture the interaction between the physical processes (e.g. voltage signal in cardiac tissue) and the embedded software (e.g. a pacemaker). At the same time, there is a growing need for design and certification methodologies that can provide quality assurance for the embedded software. We describe recent progress in simulation-based techniques that are capable of ensuring guaranteed coverage. Our methods employ discrepancy functions, which impose bounds on system dynamics, and proceed through iteratively constructing over-approximations of the reachable set of states. We are able to prove time bounded safety or produce counterexamples. We illustrate the techniques by analyzing a family of pacemaker designs against time duration requirements and synthesize safe parameter ranges. We conclude by outlining the potential uses of this technology to improve the safety of medical device designs.

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Invariant Verification of Nonlinear Hybrid Automata Networks of Cardiac Cells

Cited by 32 publications

References 44 publications

Computing bisimulation functions using SOS optimization and δ -decidability over the reals

Computing bisimulation functions using SOS optimization and δ -decidability over the reals

On Quantitative Software Quality Assurance Methodologies for Cardiac Pacemakers

Simulation-Based Verification of Cardiac Pacemakers With Guaranteed Coverage

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