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Critical Reviews™ in Biomedical Engineering

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ISSN Imprimir: 0278-940X

ISSN On-line: 1943-619X

SJR: 0.262 SNIP: 0.372 CiteScore™:: 2.2 H-Index: 56

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Mathematical Models of Oxygen and Carbon Dioxide Storage and Transport: Interstitial Fluid and Tissue Stores and Whole-Body Transport

Volume 33, Edição 3, 2005, pp. 265-298
DOI: 10.1615/CritRevBiomedEng.v33.i3.20
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S. Andreassen
Center for Model Based Medical Decision Support Systems, Aalborg University, Denmark
S. E. Rees
Center for Model Based Medical Decision Support Systems, Aalborg University, Denmark

RESUMO

This article describes a mathematical model of whole-body O2 and CO2 transport. The model includes representation of the acid-base chemistry of the blood, interstitial fluid, and tissues, plus transport of O2 and CO2 between compartments representing tissues, interstitial fluid, arterial and venous blood, and lungs. The model includes equations for calculation of all concentrations in the compartments, including equations describing the physicochemical properties and reaction equations of interstitial fluid and tissues. In addition, the model includes equations that describe the flow of substrate between the compartments and differential equations allowing calculation of the changes in state variables caused by the flow of substrates between the compartments. This model is designed to calculate the effects of metabolic and respiratory perturbations, such as variation in breathing pattern or production of strong acid at the tissues. The model reproduces the results of published experiments when used to simulate (1) normal conditions in the lungs, arterial and venous blood, interstitial fluid, and tissues during normal ventilation; (2) the characteristic two-exponential response to changes in minute ventilation; and (3) the relationship between arterial blood values of PCO2 and HCO3,p during inspiration of different fractions of CO2.

CITADO POR

  1. Lai Nicola, Camesasca Marco, Saidel Gerald M., Dash Ranjan K., Cabrera Marco E., Linking Pulmonary Oxygen Uptake, Muscle Oxygen Utilization and Cellular Metabolism during Exercise, Annals of Biomedical Engineering, 35, 6, 2007. Crossref

  2. Rees S. E., Allerød C., Murley D., Zhao Y., Smith B. W., Kjærgaard S., Thorgaard P., Andreassen S., Using physiological models and decision theory for selecting appropriate ventilator settings, Journal of Clinical Monitoring and Computing, 20, 6, 2006. Crossref

  3. Rees Stephen E., The Intelligent Ventilator (INVENT) project: The role of mathematical models in translating physiological knowledge into clinical practice, Computer Methods and Programs in Biomedicine, 104, 2011. Crossref

  4. Agrafiotis Michalis, Strong ion reserve: a viewpoint on acid base equilibria and buffering, European Journal of Applied Physiology, 111, 8, 2011. Crossref

  5. Karbing Dan S., Allerød Charlotte, Thomsen Lars P., Espersen Kurt, Thorgaard Per, Andreassen Steen, Kjærgaard Søren, Rees Stephen E., Retrospective evaluation of a decision support system for controlled mechanical ventilation, Medical & Biological Engineering & Computing, 50, 1, 2012. Crossref

  6. Lindinger Michael I., Heigenhauser George J.F., Effects of Gas Exchange on Acid‐Base Balance, in Comprehensive Physiology, 2012. Crossref

  7. Wang Ang, Mahfouf Mahdi, Mills Gary H., Panoutsos G., Linkens D.A., Goode K., Kwok Hoi-Fei, Denaï Mouloud, Intelligent model-based advisory system for the management of ventilated intensive care patients. Part II: Advisory system design and evaluation, Computer Methods and Programs in Biomedicine, 99, 2, 2010. Crossref

  8. Allerød Charlotte, Rees Stephen E., Rasmussen Bodil S., Karbing Dan S., Kjærgaard Søren, Thorgaard Per, Andreassen Steen, A decision support system for suggesting ventilator settings: Retrospective evaluation in cardiac surgery patients ventilated in the ICU, Computer Methods and Programs in Biomedicine, 92, 2, 2008. Crossref

  9. Larraza S., Dey N., Karbing D.S., Jensen J.B., Nygaard M., Winding R., Rees S.E., A mathematical model approach quantifying patients’ response to changes in mechanical ventilation: Evaluation in volume support, Medical Engineering & Physics, 37, 4, 2015. Crossref

  10. Larraza S., Dey N., Karbing D.S., Jensen J.B., Nygaard M., Winding R., Rees S.E., A mathematical model approach quantifying patients' response to changes in mechanical ventilation: Evaluation in pressure support, Journal of Critical Care, 30, 5, 2015. Crossref

  11. Larraza Sebastian, Dey Nilanjan, Karbing Dan S., Nygaard Morten, Winding Robert, Rees Stephen E., A mathematical model for simulating respiratory control during support ventilation modes, IFAC Proceedings Volumes, 47, 3, 2014. Crossref

  12. SHEARMAN SAMANTHA, DWYER DAN, SKIBA PHILIP, TOWNSEND NATHAN, Modeling Intermittent Cycling Performance in Hypoxia Using the Critical Power Concept, Medicine & Science in Sports & Exercise, 48, 3, 2016. Crossref

  13. Rousing Mark Lillelund, Hahn-Pedersen Mie Hviid, Andreassen Steen, Pielmeier Ulrike, Preiser Jean-Charles, Energy expenditure in critically ill patients estimated by population-based equations, indirect calorimetry and CO2-based indirect calorimetry, Annals of Intensive Care, 6, 1, 2016. Crossref

  14. Rees Stephen E., Karbing Dan S., Model-based advice for mechanical ventilation: From research (INVENT) to product (Beacon Caresystem), 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015. Crossref

  15. Gøtzsche Mette, Nielsen Stinne Klitgaard, Rees Stephen E., A combined model of respiratory drive and acid-base status, IFAC Proceedings Volumes, 42, 12, 2009. Crossref

  16. Rees Stephen E., Karbing Dan S., Allerød Charlotte, Toftegaard Marianne, Thorgaard Per, Toft Egon, Kjærgaard Søren, Andreassen Steen, The Intelligent Ventilator Project: Application of Physiological Models in Decision Support, in Artificial Intelligence in Medicine, 6747, 2011. Crossref

  17. Deb Sanjoy K., Gough Lewis A., Sparks S. Andy, McNaughton Lars R., Determinants of curvature constant (W’) of the power duration relationship under normoxia and hypoxia: the effect of pre-exercise alkalosis, European Journal of Applied Physiology, 117, 5, 2017. Crossref

  18. Wolf Matthew B., Whole body acid-base and fluid-electrolyte balance: a mathematical model, American Journal of Physiology-Renal Physiology, 305, 8, 2013. Crossref

  19. Rees Stephen E., Karbing Dan S., Determining the appropriate model complexity for patient-specific advice on mechanical ventilation, Biomedical Engineering / Biomedizinische Technik, 62, 2, 2017. Crossref

  20. Ježek Filip, Kofránek Jiří, Modern and traditional approaches combined into an effective gray-box mathematical model of full-blood acid-base, Theoretical Biology and Medical Modelling, 15, 1, 2018. Crossref

  21. Deb Sanjoy K., Gough Lewis A., Sparks S. Andy, McNaughton Lars R., Sodium bicarbonate supplementation improves severe-intensity intermittent exercise under moderate acute hypoxic conditions, European Journal of Applied Physiology, 118, 3, 2018. Crossref

  22. Poulsen Peter, Karbing Dan S., Rees Stephen E., Andreassen Steen, Tidal breathing model describing end-tidal, alveolar, arterial and mixed venous CO2 and O2, Computer Methods and Programs in Biomedicine, 101, 2, 2011. Crossref

  23. Leypoldt John Kenneth, Goldstein Jacques, Pouchoulin Dominique, Harenski Kai, Extracorporeal carbon dioxide removal requirements for ultraprotective mechanical ventilation: Mathematical model predictions, Artificial Organs, 44, 5, 2020. Crossref

  24. Wolf Matthew B., Physicochemical Models of Acid-Base, Seminars in Nephrology, 39, 4, 2019. Crossref

  25. Natasha , Dumat Camille, Shahid Muhammad, Khalid Sana, Murtaza Behzad, Lead Pollution and Human Exposure: Forewarned is Forearmed, and the Question Now Becomes How to Respond to the Threat!, in Lead in Plants and the Environment, 2020. Crossref

  26. Shastri Lisha, Kjærgaard Søren, Thyrrestrup Peter S., Rees Stephen E., Thomsen Lars P., Is venous blood a more reliable description of acid-base state following simulated hypo- and hyperventilation?, Scandinavian Journal of Trauma, Resuscitation and Emergency Medicine, 29, 1, 2021. Crossref

  27. Wolf Matthew B., Mechanisms of Acid-Base Kinetics During Hemodialysis, ASAIO Journal, Publish Ahead of, 2021. Crossref

  28. Wolf Matthew B., Mechanisms of Peritoneal Acid-Base Kinetics During Peritoneal Dialysis, ASAIO Journal, Publish Ahead of, 2020. Crossref

  29. Pstras Leszek, Stachowska-Pietka Joanna, Debowska Malgorzata, Pietribiasi Mauro, Poleszczuk Jan, Waniewski Jacek, Dialysis therapies: Investigation of transport and regulatory processes using mathematical modelling, Biocybernetics and Biomedical Engineering, 42, 1, 2022. Crossref

  30. Leypoldt John K., Kurz Jörg, Echeverri Jorge, Storr Markus, Harenski Kai, Modeling acid‐base balance for in‐series extracorporeal carbon dioxide removal and continuous venovenous hemofiltration devices, Artificial Organs, 45, 9, 2021. Crossref

  31. Leypoldt John K., Kurz Jörg, Echeverri Jorge, Storr Markus, Harenski Kai, Targeting arterial partial pressure of carbon dioxide in acute respiratory distress syndrome patients using extracorporeal carbon dioxide removal, Artificial Organs, 46, 4, 2022. Crossref

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