Parameter Identification Using δ-Decisions for Biological Hybrid Systems

Biological systems can possess multiple operational modes with specific nonlinear dynamics in each mode. Hybrid automata and its variants are often used to model and analyze the dynamics of such systems. Highly nonlinear hybrid automata are difficult to analysis and usually have many parameters. An important problem is to identify parameter values using which the system can reach certain states of interests. We present a parameter identification framework for biological hybrid systems using δ-complete decision procedures, which can solve satisfiability modulo theories (SMT) problems over the reals with a wide range of nonlinear functions, including ordinary differential equations (ODEs). We demonstrate our method using two hybrid systems: the prostate cancer progression model and the cardiac cellular action potential model. The results show that the parameter identification framework is convenient and efficient for performing tasks such as model falsification, personalized therapy optimization as well as disease-related parameter range identification.