A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points
The study of homeostatic equilibrium is a key concern in several fields, from physiology and biology to medicine and biomedical engineering. Control theory approaches can provide effective strategies to model physiological control systems, helping in understanding the dynamics of bio- and physio-log...
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2025-01-01
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| author | Anna Procopio Annarita Tedesco Fabrizio Lo Regio Giuseppe Cesarelli Leandro Donisi Carlo Ricciardi Alessio Merola Alfonso Maria Ponsiglione Maria Romano Francesco Montefusco Carlo Cosentino Francesco Amato |
| author_facet | Anna Procopio Annarita Tedesco Fabrizio Lo Regio Giuseppe Cesarelli Leandro Donisi Carlo Ricciardi Alessio Merola Alfonso Maria Ponsiglione Maria Romano Francesco Montefusco Carlo Cosentino Francesco Amato |
| author_sort | Anna Procopio |
| collection | DOAJ |
| description | The study of homeostatic equilibrium is a key concern in several fields, from physiology and biology to medicine and biomedical engineering. Control theory approaches can provide effective strategies to model physiological control systems, helping in understanding the dynamics of bio- and physio-logical regulation processes. However, the intrinsic complexity of living systems makes it difficult to identify unified biomodels that can represent a wide variety of physiological systems. In this context, the present work proposes a general framework to model the dynamics and describe the behavior of a wide class of multivariable physiological control systems, from the molecular to the whole-organ scale. The framework adopts a structure based on a closed-loop topology taking into account multiple inputs and outputs and with the negative feedback action intrinsically embedded within the model. The development of such a general model has at least three important repercussions: the first concerns the possibility of better understanding the basic mechanisms common to many physiological systems; the second is to develop a common theoretical framework to enable effective approaches to the analysis and design of synthetic biological control systems; finally, the investigation of the structural properties of the model in a general context, allows a guided and simplified application to specific cases. To this regard, in this paper, the existence, possible uniqueness and stability properties of the homeostatic equilibrium points of the general model are investigated; the theoretical framework is then illustrated through two real-world case-studies: (i) the PI3K/AKT/mTOR pathway nonlinear dynamics, a critical regulator of cellular growth, proliferation, and survival; (ii) the control mechanism of the neuromuscular stretch reflex, among the prime triggers implicated in postural control. Results proved the capability of the proposed framework to capture the intricate dynamics of multivariable physiological systems at different scales, highlighting the existence of asymptotically stable homeostatic equilibrium and allowing the study of the impact of transmission delays on the system’s stability. At the best of authors’ knowledge, following the paper Ponsiglione et al. (2023) where monovariable systems where dealt with, the proposed methodology is the first attempt to represent and investigate homeostasis from the molecular up to systemic level by exploiting a unified multivariable biomodeling architecture, which makes it a novel approach to understanding homeostatic control from a broader perspective. |
| format | Article |
| id | doaj-art-5acfd3384b7547ec92a48b65b04e221a |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
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| spelling | doaj-art-5acfd3384b7547ec92a48b65b04e221a2025-01-31T00:01:23ZengIEEEIEEE Access2169-35362025-01-0113176301765110.1109/ACCESS.2025.353284610849531A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium PointsAnna Procopio0https://orcid.org/0000-0002-3639-8714Annarita Tedesco1https://orcid.org/0000-0001-7242-701XFabrizio Lo Regio2https://orcid.org/0009-0003-9307-8340Giuseppe Cesarelli3https://orcid.org/0000-0001-8303-5900Leandro Donisi4https://orcid.org/0000-0002-9746-2265Carlo Ricciardi5https://orcid.org/0000-0001-7290-6432Alessio Merola6https://orcid.org/0000-0002-8728-2084Alfonso Maria Ponsiglione7https://orcid.org/0000-0003-1346-515XMaria Romano8https://orcid.org/0000-0003-1133-1115Francesco Montefusco9https://orcid.org/0000-0002-3264-9686Carlo Cosentino10https://orcid.org/0000-0001-5768-1829Francesco Amato11https://orcid.org/0000-0002-9053-3139Department of Experimental and Clinical Medicine, Universitã degli Studi “Magna Græcia” di Catanzaro, Catanzaro, ItalyDepartment of Public Health, University of Naples Federico II, Naples, ItalyDepartment of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, ItalyDepartment of Engineering, University of Naples “Parthenope”, Naples, ItalyDepartment of Advanced Medical and Surgical Sciences, University of Campania Luigi Vanvitelli, Naples, ItalyDepartment of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, ItalyDepartment of Experimental and Clinical Medicine, Universitã degli Studi “Magna Græcia” di Catanzaro, Catanzaro, ItalyDepartment of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, ItalyDepartment of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, ItalyDepartment of Economics, Law, Cybersecurity, and Sports Sciences, Universitá degli Studi di Napoli Parthenope, Nola, Naples, ItalyDepartment of Experimental and Clinical Medicine, Universitã degli Studi “Magna Græcia” di Catanzaro, Catanzaro, ItalyDepartment of Electrical Engineering and Information Technology, University of Naples Federico II, Naples, ItalyThe study of homeostatic equilibrium is a key concern in several fields, from physiology and biology to medicine and biomedical engineering. Control theory approaches can provide effective strategies to model physiological control systems, helping in understanding the dynamics of bio- and physio-logical regulation processes. However, the intrinsic complexity of living systems makes it difficult to identify unified biomodels that can represent a wide variety of physiological systems. In this context, the present work proposes a general framework to model the dynamics and describe the behavior of a wide class of multivariable physiological control systems, from the molecular to the whole-organ scale. The framework adopts a structure based on a closed-loop topology taking into account multiple inputs and outputs and with the negative feedback action intrinsically embedded within the model. The development of such a general model has at least three important repercussions: the first concerns the possibility of better understanding the basic mechanisms common to many physiological systems; the second is to develop a common theoretical framework to enable effective approaches to the analysis and design of synthetic biological control systems; finally, the investigation of the structural properties of the model in a general context, allows a guided and simplified application to specific cases. To this regard, in this paper, the existence, possible uniqueness and stability properties of the homeostatic equilibrium points of the general model are investigated; the theoretical framework is then illustrated through two real-world case-studies: (i) the PI3K/AKT/mTOR pathway nonlinear dynamics, a critical regulator of cellular growth, proliferation, and survival; (ii) the control mechanism of the neuromuscular stretch reflex, among the prime triggers implicated in postural control. Results proved the capability of the proposed framework to capture the intricate dynamics of multivariable physiological systems at different scales, highlighting the existence of asymptotically stable homeostatic equilibrium and allowing the study of the impact of transmission delays on the system’s stability. At the best of authors’ knowledge, following the paper Ponsiglione et al. (2023) where monovariable systems where dealt with, the proposed methodology is the first attempt to represent and investigate homeostasis from the molecular up to systemic level by exploiting a unified multivariable biomodeling architecture, which makes it a novel approach to understanding homeostatic control from a broader perspective.https://ieeexplore.ieee.org/document/10849531/Multivariable physiological control systemsneuromuscular stretch reflexcellular growth dynamicsstability of homeostatic equilibrium |
| spellingShingle | Anna Procopio Annarita Tedesco Fabrizio Lo Regio Giuseppe Cesarelli Leandro Donisi Carlo Ricciardi Alessio Merola Alfonso Maria Ponsiglione Maria Romano Francesco Montefusco Carlo Cosentino Francesco Amato A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points IEEE Access Multivariable physiological control systems neuromuscular stretch reflex cellular growth dynamics stability of homeostatic equilibrium |
| title | A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points |
| title_full | A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points |
| title_fullStr | A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points |
| title_full_unstemmed | A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points |
| title_short | A General Framework for Closed Loop Negative Feedback Multivariable Physiological Control Systems: Existence, Uniqueness, and Stability of Homeostatic Equilibrium Points |
| title_sort | general framework for closed loop negative feedback multivariable physiological control systems existence uniqueness and stability of homeostatic equilibrium points |
| topic | Multivariable physiological control systems neuromuscular stretch reflex cellular growth dynamics stability of homeostatic equilibrium |
| url | https://ieeexplore.ieee.org/document/10849531/ |
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