Publicado 6 números por año
ISSN Imprimir: 0278-940X
ISSN En Línea: 1943-619X
Indexed in
Mathematical Models of Oxygen and Carbon Dioxide Storage and Transport: The Acid-Base Chemistry of Blood
SINOPSIS
This article describes a mathematical model of the acid-base chemistry of blood. The model is formulated from first principles by considering the "components" of blood and the reaction equations in the plasma and erythrocyte fractions. Equations are formulated to describe the total concentration of blood components, the physicochemical properties, and the equilibrium position of reactions. The model includes 28 equations and 12 parameters. All equations can be solved from six variables included in the model. The model uses simple mathematics, without introducing intermediate concepts or linear coefficients necessary for algebraic solution. Model equations are solved simultaneously using numerical methods. Model parameters are estimated and the model verified for plasma, fully oxygenated blood, and deoxygenated blood. Published data are used to estimate model parameters and normal conditions and to verify model simulations. The model reproduces experimental results, including addition or removal of CO2, or strong acid to plasma; CO2, strong acid or haemoglobin to blood; and the effects of deoxygenating blood. The model can also be used as the basis for models of whole body CO2 transport as illustrated in the accompanying article. As such, it is possible to simulate the effects on blood of physiological changes in ventilation or metabolism.
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Rees Stephen Edward, Klæstrup Elise, Handy Jonathan, Andreassen Steen, Kristensen Søren Risom, Mathematical modelling of the acid–base chemistry and oxygenation of blood: a mass balance, mass action approach including plasma and red blood cells, European Journal of Applied Physiology, 108, 3, 2010. Crossref
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Rees Stephen E., Kjærgaard S., Andreassen S., Hedenstierna G., Reproduction of inert gas and oxygenation data: a comparison of the MIGET and a simple model of pulmonary gas exchange, Intensive Care Medicine, 36, 12, 2010. Crossref
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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
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Rees S.E., Toftegaard M., Andreassen S., A method for calculation of arterial acid–base and blood gas status from measurements in the peripheral venous blood, Computer Methods and Programs in Biomedicine, 81, 1, 2006. Crossref
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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
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Karbing Dan S., Allerød Charlotte, Thorgaard Per, Carius Ann-Maj, Frilev Lotte, Andreassen Steen, Kjærgaard Søren, Rees Stephen E., Prospective evaluation of a decision support system for setting inspired oxygen in intensive care patients, Journal of Critical Care, 25, 3, 2010. Crossref
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Wolf Matthew B., DeLand Edward C., A comprehensive, computer-model-based approach for diagnosis and treatment of complex acid–base disorders in critically-ill patients, Journal of Clinical Monitoring and Computing, 25, 6, 2011. Crossref
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Agrafiotis Michalis, Strong ion reserve: a viewpoint on acid base equilibria and buffering, European Journal of Applied Physiology, 111, 8, 2011. Crossref
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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
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Matousek S., Handy J., Rees S. E., Acid–base chemistry of plasma: consolidation of the traditional and modern approaches from a mathematical and clinical perspective, Journal of Clinical Monitoring and Computing, 25, 1, 2011. Crossref
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Lindinger Michael I., Heigenhauser George J.F., Effects of Gas Exchange on Acid‐Base Balance, in Comprehensive Physiology, 2012. Crossref
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Handy J.M., Acid–base disturbances: A need to reunify clinical and scientific medicine, Current Anaesthesia & Critical Care, 20, 5-6, 2009. Crossref
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Rees Stephen E., Diemer Tue, Kristensen Søren Risom, A method for estimation of plasma albumin concentration from the buffering properties of whole blood, Journal of Critical Care, 27, 5, 2012. Crossref
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Karbing Dan S., Kjærgaard Søren, Andreassen Steen, Espersen Kurt, Rees Stephen E., Minimal model quantification of pulmonary gas exchange in intensive care patients, Medical Engineering & Physics, 33, 2, 2011. Crossref
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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
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Karbing Dan S., Kjærgaard Søren, Andreassen Steen, Rees Stephen E., Mathematical Modelling of Pulmonary Gas Exchange, in Modelling Methodology for Physiology and Medicine, 2014. Crossref
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Mateják Marek, Kulhánek Tomáš, Matoušek Stanislav, Adair-based hemoglobin equilibrium with oxygen, carbon dioxide and hydrogen ion activity, Scandinavian Journal of Clinical and Laboratory Investigation, 75, 2, 2015. Crossref
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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
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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
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Dash Ranjan K., Korman Ben, Bassingthwaighte James B., Simple accurate mathematical models of blood HbO2 and HbCO2 dissociation curves at varied physiological conditions: evaluation and comparison with other models, European Journal of Applied Physiology, 116, 1, 2016. Crossref
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Johansen Troels, Winkler Tilo, Kelly Vanessa Jane, Osorio-Valencia Juan Sebastian, Greenblatt Elliot Eliyahu, Harris Robert Scott, Venegas Jose Gabriel, A method for mapping regional oxygen and CO2 transfer in the lung, Respiratory Physiology & Neurobiology, 222, 2016. Crossref
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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
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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
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Mogensen Mads L., Karbing Dan S., Steimle Kristoffer L., Rees Stephen E., Andreassen Steen, A stratified model of pulmonary gas exchange, IFAC Proceedings Volumes, 45, 18, 2012. Crossref
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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
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O’Neill David P., Robbins Peter A., A mechanistic physicochemical model of carbon dioxide transport in blood, Journal of Applied Physiology, 122, 2, 2017. Crossref
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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
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Wolf Matthew B., DeLand Edward C., A mathematical model of blood-interstitial acid-base balance: application to dilution acidosis and acid-base status, Journal of Applied Physiology, 110, 4, 2011. Crossref
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Thomsen Lars Pilegaard, Aliuskeviciene Asta, Sørensen Kasper, Nørgaard Astrid Clausen, Sørensen Peter Lyngø, Mark Esben Bolvig, Riddersholm Signe Juul, Thorgaard Per, Non-invasive estimation of respiratory depression profiles during robot-assisted laparoscopic surgery using a model-based approach, in CMBEBIH 2017, 62, 2017. Crossref
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Rees Stephen E., Kjærgaard S., Andreassen S., Hedenstierna G., Reproduction of inert gas and oxygenation data: a comparison of the MIGET and a simple model of pulmonary gas exchange, in Applied Physiology in Intensive Care Medicine 1, 2012. Crossref
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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
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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
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Karbing Dan S., Rees Stephen E., Oxygen, in Cotes’ Lung Function, 2020. Crossref
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Karbing Dan Stieper, Panigada Mauro, Bottino Nicola, Spinelli Elena, Protti Alessandro, Rees Stephen Edward, Gattinoni Luciano, Changes in shunt, ventilation/perfusion mismatch, and lung aeration with PEEP in patients with ARDS: a prospective single-arm interventional study, Critical Care, 24, 1, 2020. Crossref
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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
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Rees Stephen Edward, Klæstrup Elise, Handy Jonathan, Andreassen Steen, Kristensen Søren Risom, Evaluation of a mathematical model of the acid‐base chemistry of blood, The FASEB Journal, 24, S1, 2010. Crossref
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Magor-Elliott Snapper R. M., Fullerton Christopher J., Richmond Graham, Ritchie Grant A. D., Robbins Peter A., A dynamic model of the body gas stores for carbon dioxide, oxygen, and inert gases that incorporates circulatory transport delays to and from the lung, Journal of Applied Physiology, 130, 5, 2021. Crossref
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Pietribiasi Mauro, Leypoldt John K., Modeling acid-base transport in hemodialyzers, Biocybernetics and Biomedical Engineering, 41, 3, 2021. Crossref
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Shastri Lisha, Kjærgaard Søren, Thyrrestrup Peter Søndergaard, Rees Stephen Edward, Thomsen Lars Pilegaard, Mathematically arterialised venous blood is a stable representation of patient acid–base status at steady state following acute transient changes in ventilation, Journal of Clinical Monitoring and Computing, 2021. Crossref
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Patel Brijesh, Mumby Sharon, Johnson Nicholas, Falaschetti Emanuela, Hansen Jorgen, Adcock Ian, McAuley Danny, Takata Masao, Karbing Dan S., Jabaudon Matthieu, Schellengowski Peter, Rees Stephen E., Decision support system to evaluate ventilation in the acute respiratory distress syndrome (DeVENT study)—trial protocol, Trials, 23, 1, 2022. Crossref
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Leypoldt John K., Pietribiasi Mauro, Echeverri Jorge, Harenski Kai, Modeling acid–base balance during continuous kidney replacement therapy, Journal of Clinical Monitoring and Computing, 36, 1, 2022. Crossref
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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
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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
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Garfield Benjamin, Handslip Rhodri, Patel Brijesh V., Ventilator-Associated Lung Injury, in Encyclopedia of Respiratory Medicine, 2022. Crossref
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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