Towards Personalized Prostate Cancer Therapy Using Delta-Reachability Analysis

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ $\delta$-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for personalized cancer therapy.Comment: HSCC 201

Approximated Symbolic Computations over Hybrid Automata

Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the real systems and infinite precision measurements. Such assumptions are not only unrealistic, but often lead to the construction of misleading models. For these reasons we believe that it is necessary to introduce more flexible semantics able to manage with noise, partial information, and finite precision instruments. In particular, in this paper we integrate in a single framework based on approximated semantics different over and under-approximation techniques for hybrid automata. Our framework allows to both compare, mix, and generalize such techniques obtaining different approximated reachability algorithms.Comment: In Proceedings HAS 2013, arXiv:1308.490

Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Sapo: Reachability Computation and Parameter Synthesis of Polynomial Dynamical Systems

Sapo is a C++ tool for the formal analysis of polynomial dynamical systems. Its main features are: 1) Reachability computation, i.e., the calculation of the set of states reachable from a set of initial conditions, and 2) Parameter synthesis, i.e., the refinement of a set of parameters so that the system satisfies a given specification. Sapo can represent reachable sets as unions of boxes, parallelotopes, or parallelotope bundles (symbolic representation of polytopes). Sets of parameters are represented with polytopes while specifications are formalized as Signal Temporal Logic (STL) formulas

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Towards Cancer Hybrid Automata

This paper introduces Cancer Hybrid Automata (CHAs), a formalism to model the progression of cancers through discrete phenotypes. The classification of cancer progression using discrete states like stages and hallmarks has become common in the biology literature, but primarily as an organizing principle, and not as an executable formalism. The precise computational model developed here aims to exploit this untapped potential, namely, through automatic verification of progression models (e.g., consistency, causal connections, etc.), classification of unreachable or unstable states and computer-generated (individualized or universal) therapy plans. The paper builds on a phenomenological approach, and as such does not need to assume a model for the biochemistry of the underlying natural progression. Rather, it abstractly models transition timings between states as well as the effects of drugs and clinical tests, and thus allows formalization of temporal statements about the progression as well as notions of timed therapies. The model proposed here is ultimately based on hybrid automata, and we show how existing controller synthesis algorithms can be generalized to CHA models, so that therapies can be generated automatically. Throughout this paper we use cancer hallmarks to represent the discrete states through which cancer progresses, but other notions of discretely or continuously varying state formalisms could also be used to derive similar therapies.Comment: In Proceedings HSB 2012, arXiv:1208.315