A Mathematical Model of Whole-Body Potassium Regulation: Global Parameter Sensitivity Analysis
Open accessPublished version of a preprint
Abstract
Abstract Potassium (K + ) is an essential electrolyte that is tightly regulated by various complex physiological mechanisms. In this study, we analyze a mathematical model of whole-body K + regulation to investigate the sensitivity of different model outcomes to parameter values. We used the Morris method, a global sensitivity analysis technique, to evaluate the impact of the parameters on both steady state results and transient simulations during a single-meal. Our results shows that the most influential parameters and processes depend on what you are measuring. Specifically, steady state results relied primarily on parameters that were involved in kidney function, while transient results relied on hormonal feedback mechanisms. This study shows that our mathematical model of whole-body potassium regulation captures known physiological function of potassium regulation despite a large number of uncertain parameters. MSC codes 68Q25, 68R10, 68U05
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Morris screening identified seven parameters with the highest Morris index with respect to maximum cortisol (Bmax), associated with elimination or production of epinephrine, norepinephrine, and cortisol.
“This set of parameters represents the elimination rate of epinephrine, production rate of epinephrine from norepinephrine, elimination rate of norepinephrine, elimination rate of cortisol, stimulation rate of cortisol by epinephrine, half-saturation constant for the stimulation of norepinephrine by stress, and stimulation rate of norepinephrine by stress, respectively.”
From Subject-specific modeling of response to physical stress via hypothalamic-pituitary-adrenal and sympathoadrenal axes (2026) · cites this paper as [16]
Section 3.2 ranks Morris indices for plasma and intracellular potassium, identifying parameters related to aldosterone, insulin, and potassium handling—not seven parameters for maximum cortisol. Section 2.3 likewise identifies the leading steady-state parameters as renal potassium-handling parameters and baseline aldosterone. The cited paper’s reported analysis concerns potassium regulation, not the claimed cortisol, epinephrine, and norepinephrine outcomes. (LLM, conf=0.85)
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Global Sensitivity Analysis. The Primer
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2007) · doi:10.1002/9780470725184 · Cited by 6,430 · see citing works
Global sensitivity indices for nonlinear mathematical models and their monte carlo estimates
Sobol′, I. M. (2001) · Mathematics and Computers in Simulation · doi:10.1016/s0378-4754(00)00270-6 · Cited by 6,389 · see citing works
Factorial Sampling Plans for Preliminary Computational Experiments
Morris, M. D. (1991) · Technometrics · doi:10.1080/00401706.1991.10484804 · Cited by 4,943 · see citing works
Factorial Sampling Plans for Preliminary Computational Experiments
Morris, M. D. (1991) · Technometrics · doi:10.2307/1269043 · Cited by 2,648 · see citing works
An effective screening design for sensitivity analysis of large models
Campolongo, F., Cariboni, J., & Saltelli, A. (2007) · Environmental Modelling & Software · doi:10.1016/j.envsoft.2006.10.004 · Cited by 2,028 · see citing works
Clase, C. M., Carrero, J.-J., Ellison, D. H., Grams, M. E., Hemmelgarn, B. R., Jardine, M. J., Kovesdy, C. P., Kline, G. A., Lindner, G., Obrador, G. T., et al. (2020) · Kidney International · doi:10.1016/j.kint.2019.09.018 · Cited by 498 · see citing works
Electrophysiology of Hypokalemia and Hyperkalemia
Weiss, J. N., Qu, Z., & Shivkumar, K. (2017) · Circulation Arrhythmia and Electrophysiology · doi:10.1161/circep.116.004667 · Cited by 408 · see citing works
Sensitivity analysis of infectious disease models: methods, advances and their application
Wu, J., Dhingra, R., Gambhir, M., & Remais, J. V. (2013) · Journal of The Royal Society Interface · doi:10.1098/rsif.2012.1018 · Cited by 328 · see citing works
Sensitivity analysis methods in the biomedical sciences
Qian, G., & Mahdi, A. (2020) · Mathematical Biosciences · doi:10.1016/j.mbs.2020.108306 · Cited by 169 · see citing works
Studies of the control of plasma aldosterone concentration in normal man
Dluhy, R. G., Axelrod, L., Underwood, R. H., & Williams, G. H. (1972) · Journal of Clinical Investigation · doi:10.1172/jci107001 · Cited by 164 · see citing works
Regulation of the Renal NaCl Cotransporter and Its Role in Potassium Homeostasis
Hoorn, E. J., Gritter, M., Cuevas, C. A., & Fenton, R. A. (2020) · Physiological Reviews · doi:10.1152/physrev.00044.2018 · Cited by 163 · see citing works
To Sobol or not to Sobol? The effects of sampling schemes in systems biology applications
Renardy, M., Joslyn, L. R., Millar, J. A., & Kirschner, D. E. (2021) · Mathematical Biosciences · doi:10.1016/j.mbs.2021.108593 · Cited by 154 · see citing works
Lindinger, M. I. (1995) · Journal of Molecular and Cellular Cardiology · doi:10.1016/0022-2828(95)90070-5 · Cited by 125 · see citing works
Narrative Review: Evolving Concepts in Potassium Homeostasis and Hypokalemia
Greenlee, M., Wingo, C. S., McDonough, A. A., Youn, J.-H., & Kone, B. C. (2009) · Annals of Internal Medicine · doi:10.7326/0003-4819-150-9-200905050-00008 · Cited by 104 · see citing works
Link, K. G., Stobb, M. T., Paola, J. D., Neeves, K. B., Fogelson, A. L., Sindi, S., & Leiderman, K. (2018) · PLoS ONE · doi:10.1371/journal.pone.0200917 · Cited by 83 · see citing works
ACE inhibitors and ARBs: Managing potassium and renal function
Momoniat, T., Ilyas, D., & Bhandari, S. (2019) · Cleveland Clinic Journal of Medicine · doi:10.3949/ccjm.86a.18024 · Cited by 82 · see citing works
Global sensitivity analysis of biological multiscale models
Renardy, M., Hult, C., Evans, S., Linderman, J. J., & Kirschner, D. E. (2019) · Current Opinion in Biomedical Engineering · doi:10.1016/j.cobme.2019.09.012 · Cited by 63 · see citing works
Role of Circadian Rhythms in Potassium Homeostasis
Gumz, M. L., & Rabinowitz, L. (2013) · Seminars in Nephrology · doi:10.1016/j.semnephrol.2013.04.003 · Cited by 61 · see citing works
Potassium homeostasis: sensors, mediators, and targets
McDonough, A. A., & Fenton, R. A. (2022) · Pflügers Archiv - European Journal of Physiology · doi:10.1007/s00424-022-02718-3 · Cited by 61 · see citing works
Global sensitivity analysis in epidemiological modeling
Lu, X., & Borgonovo, E. (2021) · European Journal of Operational Research · doi:10.1016/j.ejor.2021.11.018 · Cited by 60 · see citing works
Evidence for a gastrointestinal-renal kaliuretic signaling axis in humans
Preston, R. A., Afshartous, D., Rodco, R., Alonso, A. B., & Garg, D. (2015) · Kidney International · doi:10.1038/ki.2015.243 · Cited by 57 · see citing works
Potassium homeostasis – Physiology and pharmacology in a clinical context
Kettritz, R., & Loffing, J. (2023) · Pharmacology & Therapeutics · doi:10.1016/j.pharmthera.2023.108489 · Cited by 52 · see citing works
Multi-method global sensitivity analysis of mathematical models
Dela, A., Shtylla, B., & de Pillis, L. G. (2022) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2022.111159 · Cited by 47 · see citing works
What Can We Learn from Global Sensitivity Analysis of Biochemical Systems?
Kent, E., Neumann, S., Kummer, U., & Mendes, P. (2013) · PLoS ONE · doi:10.1371/journal.pone.0079244 · Cited by 44 · see citing works
Extrarenal Effects of Aldosterone on Potassium Homeostasis
Palmer, B. F., & Clegg, D. J. (2022) · Kidney360 · doi:10.34067/kid.0006762021 · Cited by 40 · see citing works
Modelling female physiology from head to Toe: impact of sex hormones, menstrual cycle, and pregnancy
Abo, S., Smith, D., Stadt, M., & Layton, A. (2022) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2022.111074 · Cited by 35 · see citing works
Self-citationA mathematical model of potassium homeostasis: Effect of feedforward and feedback controls
Stadt, M. M., Leete, J., Devinyak, S., & Layton, A. T. (2022) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1010607 · Cited by 19 · see citing works
Self-citationMcFarlin, B. E., Chen, Y., Priver, T. S., Ralph, D. L., Mercado, A., Gamba, G., Madhur, M. S., & McDonough, A. A. (2020) · American Journal of Physiology-Cell Physiology · doi:10.1152/ajpcell.00362.2020 · Cited by 18 · see citing works
His and her mathematical models of physiological systems
Layton, A. T. (2021) · Mathematical Biosciences · doi:10.1016/j.mbs.2021.108642 · Cited by 16 · see citing works
Self-citationStadt, M. M., West, C. A., & Layton, A. T. (2023) · PLoS ONE · doi:10.1371/journal.pone.0279785 · Cited by 14 · see citing works
Self-citationCircadian Regulation of Electrolyte and Water Transport in the Rat Kidney
Stadt, M. M., Abo, S. M. C., & Layton, A. T. (2022) · SIAM Journal on Applied Mathematics · doi:10.1137/22m1480732 · Cited by 13 · see citing works
Self-citationDutta, P., Sadria, M., & Layton, A. T. (2023) · American Journal of Physiology-Renal Physiology · doi:10.1152/ajprenal.00296.2022 · Cited by 12 · see citing works
Self-citationConen, K. L., Scanni, R., Gombert, M.-T., Hulter, H. N., & Krapf, R. (2016) · Journal of Diabetes and its Complications · doi:10.1016/j.jdiacomp.2016.03.017 · Cited by 11 · see citing works
Lasaad, S., & Crambert, G. (2023) · Frontiers in Physiology · doi:10.3389/fphys.2023.1264296 · Cited by 10 · see citing works
High dietary K + intake inhibits proximal tubule transport
Wang, T., Liu, T., Xu, S., Frindt, G., Weinstein, A. M., & Palmer, L. G. (2023) · American Journal of Physiology-Renal Physiology · doi:10.1152/ajprenal.00013.2023 · Cited by 9 · see citing works
Maddah, E., & Hallow, K. M. (2022) · Journal of Pharmacokinetics and Pharmacodynamics · doi:10.1007/s10928-022-09815-x · Cited by 8 · see citing works
ODEsensitivity: Sensitivity Analysis of Ordinary Differential Equations
Weber, F., & Theers, S. (2018) · doi:10.32614/cran.package.odesensitivity · Cited by 8 · see citing works
Stadt, M. M., & Layton, A. T. (2024) · American Journal of Physiology-Regulatory, Integrative and Comparative Physiology · doi:10.1152/ajpregu.00283.2023 · Cited by 4 · see citing works
Self-citationClegg, L. E., Chu, L., Någård, M. B., Boulton, D. W., & Penland, R. C. (2023) · CPT Pharmacometrics & Systems Pharmacology · doi:10.1002/psp4.13084 · Cited by 2 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Harris, H. A., Chan, D. M., Fix, L. E., Nicholson, B. D., & Acevedo, E. O. (2026) · PLOS One · doi:10.1371/journal.pone.0344981 · Cited by 2 · see citing works
Modulation of blood pressure by estrogen: A modeling analysis
Layton, A. T. (2026) · Mathematical Biosciences · doi:10.1016/j.mbs.2025.109610 · Cited by 1 · see citing works
Self-citation
- Authors
- Stadt, M. M., & Layton, A. T.
- Affiliations
- University of Waterloo (CA)
- Corresponding author
- Stadt, Melissa M.
- Venue
- SIAM Journal on Applied Dynamical Systems
- Published
- 2024-10-09
- Volume
- 23
- Issue
- 4
- Pages
- 2623-2642
- ISSN
- 1536-0040 (ISSN-L)
- OpenAlex
- W4403255591
- Cited by
- 3
- References
- 39
- Citations by year
- 2026: 3
- FWCI
- 0.87
- Type
- journal article
- Language
- en
- Open access
- green
- doi.org
- Licence
- cc-by-nc-nd
- Locations
- SIAM Journal on Applied Dynamical Systems (publishedVersion)
- bioRxiv (Cold Spring Harbor Laboratory) (acceptedVersion, cc-by-nc-nd)
- Funders
- Natural Sciences and Engineering Research Council of Canada (RGPIN-2019-03916)
- Topics
- Health Sciences › Medicine › Pulmonary and Respiratory Medicine › Potassium and Related Disorders
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Ion Transport and Channel Regulation
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical Biology Tumor Growth
- Keywords
- potassium homeostasis, parameter sensitivity analysis, Morris method, global sensitivity analysis, renal function, steady state
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
