A phenomenological mathematical framework to model homeostasis as a robust, adaptive control system. Similarities with continuum nonlinear physics with internal variables

Doblaré, Manuel (Universidad de Zaragoza) ; Pérez-Aliacar, Marina ; Ayensa-Jiménez, Jacobo ; Ashrafi, Mehran

Resumen: Living systems exhibit remarkable resilience to withstand diverse and often extreme environmental conditions. Central to this adaptability are mechanisms like homeostasis and epigenesis. The first refers to the ability of organisms to maintain internal stability amidst external fluctuations, while the second provides organisms with the capacity for adjusting their homeostatic response to persistent environmental stressors. A thorough understanding of these physiological processes is essential for preventing disease, maintaining health, and facilitating recovery.
We present here a conceptual framework in which homeostasis is modeled as a robust, adaptive, spatially-dependent control system, where the adaptation block is regulated by epigenetic changes. This approach offers a powerful and integrated tool to predict the point-wise evolution of macroscopic biological systems due to short and long term environmental perturbations. Conceptual and methodological similarities with well-established predictive tools in Continuum Physics, particularly Continuum Mechanics, with internal variables are also highlighted.
After reviewing the problem and stating the equations in two different examples: thermoregulation to illustrate short term homeostasis, and tumor cell plasticity to clarify epigenetic adaptation, we analyze bone remodeling. This is a classic homeostatic process where bone mass and architecture are locally and dynamically regulated in response to mechanical demands and micro-damage accumulation. In here, we assimilate bone remodeling to a damage–repair problem, employing concepts and tools from time-dependent Continuum Damage Mechanics. The possibility of long term adaptation of this regulatory process by epigenesis-induced changes in the control signal reference is also analyzed. This permits to adjust bone microstructure to permanent changes in the mechanical conditions as happens under long periods of low gravity.
This modeling framework provides a valuable quantitative tool for investigating how organisms cope with environmental challenges, evolve their adaptive response over time, and potentially develop diseases when these regulatory mechanisms fail, offering new avenues for research at the intersection of Biology, Medicine and Engineering.

Idioma: Inglés

DOI: 10.1016/j.mechmat.2025.105546

Año: 2025

Publicado en: MECHANICS OF MATERIALS 213 (2025), 105546 [19 pp.]
ISSN: 0167-6636

Financiación: info:eu-repo/grantAgreement/ES/AEI/PID2021-126051OB-C41
Financiación: info:eu-repo/grantAgreement/ES/DGA/T62-230R
Financiación: info:eu-repo/grantAgreement/ES/ISCIII/FORT23-00028

Tipo y forma: Article (PrePrint)

Área (Departamento): Área Mec.Med.Cont. y Teor.Est. (Dpto. Ingeniería Mecánica)