A physiology-based mathematical model of the renin-angiotensin system, bone remodeling, and calcium homeostasis: Effects of estrogen and renin-angiotensin system inhibitors
- 1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- 2Cheriton School of Computer Science, Department of Biology, School of Pharmacology, University of Waterloo, Waterloo, Ontario, Canada
Abstract
During menopause, estrogen levels decline significantly, leading to substantial physiological changes due to estrogen’s regulatory role in various systems. In particular, estrogen helps prevent excessive bone resorption by its impact on bone remodeling. When estrogen levels decrease, bone resorption increases, often resulting in weakened bones and osteoporosis in post-menopausal women. Experimental studies have also shown that estrogen regulates the renin-angiotensin system (RAS), a hormone system involved in many physiological processes, including blood pressure regulation. Additionally, the RAS has an interconnected relationship with calcium regulatory and bone remodeling systems. Given these dynamic interplays, we developed a physiology-based mathematical model that simulates the interactions of estrogen, key RAS components, calcium regulation, and bone remodeling to investigate how perturbations in one system affect the others. This represents the first known model to include the direct impacts of estrogen on the RAS and to couple the RAS with calcium homeostasis and bone remodelling systems in humans. Through model simulations and sensitivity analysis, we investigated how declining estrogen levels affect the RAS and bone mineral density. Furthermore, we quantified how RAS inhibitors, specifically angiotensin-converting enzyme inhibitors (ACEi) and angiotensin receptor blockers (ARB), may increase bone density during post-menopausal estrogen decline. Our simulation results suggest that ARB treatment may be more effective at improving bone mineral density during postmenopausal estrogen decline, and that this trend remains consistent regardless of the age of RAS inhibitor initiation. Author summary: Post-menopausal estrogen decline is associated with reduced bone mineral density and increased risk of osteoporosis. In addition to its established role in bone metabolism, estrogen also regulates the renin-angiotensin system (RAS), a hormonal system primarily involved in blood pressure regulation. Experimental studies suggest that interactions between these physiological systems contribute to changes in bone remodeling during menopause. To investigate these dynamic interactions, we developed a physiology-based mathematical model that integrates the RAS with calcium homeostasis and bone remodeling in humans. We examined how reductions in estrogen affect bone remodeling pathways and influence bone mineral density. We also evaluated the potential effects of commonly prescribed RAS inhibitors on bone health. Our simulations predict that estrogen decline increases signaling pathways associated with bone resorption and accelerates bone loss. However, RAS inhibitors can reduce these effects and mitigate menopause related bone mineral density loss. The results further suggests that angiotensin receptor blockers may provide greater protection against bone mineral density loss than angiotensin-converting enzyme inhibitors. These findings support emerging clinical evidence linking the RAS to skeletal health and could inform the prescription of RAS inhibitors for postmenopausal women.
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BibTeX
@article{stadt2026physiologybased,
title = {{A physiology-based mathematical model of the renin-angiotensin system, bone remodeling, and calcium homeostasis: Effects of estrogen and renin-angiotensin system inhibitors}},
author = {Melissa M. Stadt and Victoria A. Ralph and Anita T. Layton},
journal = {PLOS Computational Biology},
year = {2026},
month = sep,
doi = {10.1371/journal.pcbi.1013101},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013101},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A physiology-based mathematical model of the renin-angiotensin system, bone remodeling, and calcium homeostasis: Effects of estrogen and renin-angiotensin system inhibitors
AU - Melissa M. Stadt
AU - Victoria A. Ralph
AU - Anita T. Layton
PY - 2026
DA - 2026/09/22
JO - PLOS Computational Biology
DO - 10.1371/journal.pcbi.1013101
UR - https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1013101
AB - During menopause, estrogen levels decline significantly, leading to substantial physiological changes due to estrogen’s regulatory role in various systems. In particular, estrogen helps prevent excessive bone resorption by its impact on bone remodeling. When estrogen levels decrease, bone resorption increases, often resulting in weakened bones and osteoporosis in post-menopausal women. Experimental studies have also shown that estrogen regulates the renin-angiotensin system (RAS), a hormone system involved in many physiological processes, including blood pressure regulation. Additionally, the RAS has an interconnected relationship with calcium regulatory and bone remodeling systems. Given these dynamic interplays, we developed a physiology-based mathematical model that simulates the interactions of estrogen, key RAS components, calcium regulation, and bone remodeling to investigate how perturbations in one system affect the others. This represents the first known model to include the direct impacts of estrogen on the RAS and to couple the RAS with calcium homeostasis and bone remodelling systems in humans. Through model simulations and sensitivity analysis, we investigated how declining estrogen levels affect the RAS and bone mineral density. Furthermore, we quantified how RAS inhibitors, specifically angiotensin-converting enzyme inhibitors (ACEi) and angiotensin receptor blockers (ARB), may increase bone density during post-menopausal estrogen decline. Our simulation results suggest that ARB treatment may be more effective at improving bone mineral density during postmenopausal estrogen decline, and that this trend remains consistent regardless of the age of RAS inhibitor initiation. Author summary: Post-menopausal estrogen decline is associated with reduced bone mineral density and increased risk of osteoporosis. In addition to its established role in bone metabolism, estrogen also regulates the renin-angiotensin system (RAS), a hormonal system primarily involved in blood pressure regulation. Experimental studies suggest that interactions between these physiological systems contribute to changes in bone remodeling during menopause. To investigate these dynamic interactions, we developed a physiology-based mathematical model that integrates the RAS with calcium homeostasis and bone remodeling in humans. We examined how reductions in estrogen affect bone remodeling pathways and influence bone mineral density. We also evaluated the potential effects of commonly prescribed RAS inhibitors on bone health. Our simulations predict that estrogen decline increases signaling pathways associated with bone resorption and accelerates bone loss. However, RAS inhibitors can reduce these effects and mitigate menopause related bone mineral density loss. The results further suggests that angiotensin receptor blockers may provide greater protection against bone mineral density loss than angiotensin-converting enzyme inhibitors. These findings support emerging clinical evidence linking the RAS to skeletal health and could inform the prescription of RAS inhibitors for postmenopausal women.
SN - 1553-7358
ER -