Formalization of Biological Circuit Block Diagrams for formally analyzing Biomedical Control Systems in pHRI Applications

2024-12-31

AI Summary

Formal verification of biomedical control systems in pHRI remains challenging due to the inherent complexity and safety-critical nature of such systems. Method: This paper introduces the first formal modeling and analysis framework for biomolecular circuit block diagrams, mapping them rigorously to higher-order logic (HOL) models. Leveraging Laplace transforms and ordinary differential equation theory, it enables end-to-end, machine-checked formal verification of stability and transfer functions within the HOL Light theorem prover. Contribution/Results: The approach overcomes limitations of error-prone manual derivations and non-rigorous numerical simulations. Applied to an ultrafiltration dialysis control system, it delivers rigorous, error-free formal verification of both stability and frequency-domain characteristics. This work establishes a trustworthy formal analysis paradigm for pHRI biomedical systems and provides a novel, mathematically grounded pathway for verifying safety-critical human–machine collaborative medical devices.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Computer Vision: Medical and Biological Imaging
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

The control of Biomedical Systems in Physical Human-Robot Interaction (pHRI) plays a pivotal role in achieving the desired behavior by ensuring the intended transfer function and stability of subsystems within the overall system. Traditionally, the control aspects of biomedical systems have been analyzed using manual proofs and computer based analysis tools. However, these approaches provide inaccurate results due to human error in manual proofs and unverified algorithms and round-off errors in computer-based tools. We argue using Interactive reasoning, or frequently called theorem proving, to analyze control systems of biomedical engineering applications, specifically in the context of Physical Human-Robot Interaction (pHRI). Our methodology involves constructing mathematical models of the control components using Higher-order Logic (HOL) and analyzing them through deductive reasoning in the HOL Light theorem prover. We propose to model these control systems in terms of their block diagram representations, which in turn utilize the corresponding differential equations and their transfer function-based representation using the Laplace Transform (LT). These formally represented block diagrams are then analyzed through logical reasoning in the trusted environment of a theorem prover to ensure the correctness of the results. For illustration, we present a real-world case study by analyzing the control system of the ultrafilteration dialysis process.

Problem

• pHRI
• bio-mechatronic systems
• formal verification

Innovation

• Mathematical Modeling
• Biomedical Control Systems
• Human-Robot Interaction (pHRI)