Formalization of Heart Models Based on the Conduction of Electrical Impulses and Cellular Automata

Tools and techniques based on formal methods have been recognized as a promising approach to supporting the process of verification and validation of critical systems in the early stages of their development. In particular, medical devices are very prone to showing unexpected system behaviour in operation because of the stochastic nature of the systems and when traditional methods are used for system testing. Device-related problems have been responsible for a large number of serious injuries. Officials of the US Food and Drug Administration (FDA) have found that many deaths and injuries related to these devices are caused by flaws in product design and engineering. Cardiac pacemakers and implantable cardioverter---defibrillators (ICDs) are the most critical of these medical devices, requiring closed-loop modelling (integrated system and environment modelling) for verification purposes before obtaining a certificate from the certification bodies. No technique is available to provide environment modelling for verifying the developed system models. This paper presents a methodology for modelling a biological system, such as the heart, to enable modelling in a biological environment. The heart model is based mainly on electrocardiography analysis, which models the heart system at the cellular level. The main objective of this methodology is to model the heart system and integrate it with a model of a medical device such as a cardiac pacemaker to specify a closed-loop model. To build an environment model for a closed-loop system is currently an open problem. The industry has long sought such an approach to validating a system model in a virtual biological environment. Our approach involves a pragmatic combination of formal specifications of the system and the biological environment to model a closed-loop system that enables verification of the correctness of the system and helps to improve the quality of the system.