Technical Report on Formalisation of the Heart using Analysis of Conduction Time and Velocity of the Electrocardiography and Cellular-Automata

Formal methods based tools and techniques have been recognised to be a promising approach to support the process of verification and validation of a critical system in early stage of the development. Specially, medical devices are very prone to show an unexpected behavior of the system in operating due to stochastic nature of the system and when a system uses traditional methods for system testing. Device-related problems are responsible for a large number of serious injuries. FDA officials has found that many deaths and injuries related to the devices are caused by product design and engineering flaws. Cardiac pacemaker and implantable cardioverter-defibrillators (ICDs) are main critical medical devices, which require close-loop modeling (integration of system and environment modeling) for verification purpose to obtain a certificate from certification bodies. No any technique is available to provide an environment modeling to verify the developed system model. This report presents a methodology to model a biological system, like heart, for modeling a biological environment. The heart model is mainly based on electrocardiography analysis, which models the heart system at cellular level. Main objective of this methodology is to model the heart system and integrate with medical device model like cardiac pacemaker to specify a close-loop model. Close-loop model of an environment and a device is an open problem in real world. Industries are striving for such kind of approach from long time to validate a system model under a virtual biological environment. Our approach involves the pragmatic combination of formal specification of a system and a biological environment to model a close-loop system to verify the correctness of a system and helps in quality improvement of the system

The cellular automata formalism and its relationship to DEVS

Cellular automata (CA) were originally conceived by Ulam and von Neumann in the 1940s to provide a formal framework for investigating the behaviour of complex, spatially distributed systems. Cellular Automata constitute a dynamic, discrete space, discrete time formalism where space is usually discretized in a grid of cells. Cellular automata are still used to study, from first principles, the behaviour of a plethora of systems. The Discrete EVent system Specification (DEVS) was first introduced by Zeigler in 1976 as a rigourous basis for discrete-event modelling. At the discrete-event level of abstraction, state variables are considered to change only at event-times. Furthermore, the number of events occurring in a bounded time-interval must be finite. The semantic