Reachability Analysis and Hybrid Systems Biology - In Memoriam Oded Maler

Reachability analysis consists in computing the set of states that are reachable by a dynamical system from all initial states and for all admissible inputs and parameters. It is a fundamental problem motivated by many applications in formal verification, controller synthesis, and estimation, to name only a few. This article focuses on a class of methods for computing a guaranteed overapproximation of the reachable set of continuous and hybrid systems, relying predominantly on set propagation; starting from the set of initial states, these techniques iteratively propagate a sequence of sets according to the system dynamics. After a review of set representation and computation, the article presents the state of the art of set propagation techniques for reachability analysis of linear, nonlinear, and hybrid systems. It ends with a discussion of successful applications of reachability analysis to real-world problems. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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A Systems Biology Approach in Therapeutic Response Study for Different Dosing Regimens—a Modeling Study of Drug Effects on Tumor Growth using Hybrid Systems

Cancer Informatics ◽

10.4137/cin.s8185 ◽

2012 ◽

Vol 11 ◽

pp. CIN.S8185 ◽

Cited By ~ 3

Author(s):

Xiangfang Li ◽

Lijun Qian ◽

Michale L. Bittner ◽

Edward R. Dougherty

Keyword(s):

Systems Biology ◽

Drug Development ◽

Tumor Growth ◽

Hybrid Systems ◽

Anticancer Agents ◽

Therapeutic Response ◽

Therapeutic Effects ◽

Systems Model ◽

Optimal Drug ◽

Dosing Regimens

Motivated by the frustration of translation of research advances in the molecular and cellular biology of cancer into treatment, this study calls for cross-disciplinary efforts and proposes a methodology of incorporating drug pharmacology information into drug therapeutic response modeling using a computational systems biology approach. The objectives are two fold. The first one is to involve effective mathematical modeling in the drug development stage to incorporate preclinical and clinical data in order to decrease costs of drug development and increase pipeline productivity, since it is extremely expensive and difficult to get the optimal compromise of dosage and schedule through empirical testing. The second objective is to provide valuable suggestions to adjust individual drug dosing regimens to improve therapeutic effects considering most anticancer agents have wide inter-individual pharmacokinetic variability and a narrow therapeutic index. A dynamic hybrid systems model is proposed to study drug antitumor effect from the perspective of tumor growth dynamics, specifically the dosing and schedule of the periodic drug intake, and a drug's pharmacokinetics and pharmacodynamics information are linked together in the proposed model using a state-space approach. It is proved analytically that there exists an optimal drug dosage and interval administration point, and demonstrated through simulation study.

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