Skip to main content
SpringerLink
Log in

Mathematical modelling of the acid–base chemistry and oxygenation of blood: a mass balance, mass action approach including plasma and red blood cells

  • Original Article
  • Published:
European Journal of Applied Physiology Aims and scope Submit manuscript

Abstract

Mathematical models of the acid–base chemistry of blood based upon mass action and mass balance equations have become popular as diagnostic tools in intensive care. The reference models using this approach are those based on the strong ion approach, but these models do not currently take into account the effects of oxygen on the buffering characteristics of haemoglobin. As such these models are limited in their ability to simulate physiological situations involving simultaneous changes of O2 and CO2 levels in the blood. This paper describes a model of acid–base chemistry of blood based on mass action and mass balance equations and including the effects of oxygen. The model is used to simulate the mixing of venous blood with the same blood at elevated O2 and reduced CO2 levels, and the results compared with the mixing of blood sampled from 21 healthy subjects. Simulated values of pH, PCO2, PO2 and SO2 in the mixed blood compare well with measured values with small bias (i.e. 0.000 pH, −0.06 kPa PCO2, −0.1% SO2, −0.02 kPa PO2), and values of standard deviations (i.e. 0.006 pH, 0.11 kPa PCO2, 0.8% SO2, 0.13 kPa PO2) comparable to the precision seen in direct measurement of these variables in clinical practice. These results indicate that the model can reliably simulate the mixing of blood and has potential for application in describing physiological situations involving the mixing of blood at different O2 and CO2 levels such as occurs in the mixing of lung capillary and shunted pulmonary blood.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Allerød C, Rees SE, Rasmussen BS, Karbing DS, Kjærgaard S, Thorgaard P, Andreassen SA (2008) Decision support system for suggesting ventilator settings: Retrospective evaluation in cardiac surgery patients ventilated in the ICU. Comput Methods Programs Biomed 92:205–212

    Article  PubMed  Google Scholar 

  • Constable PD (1997) A simplified strong ion model for acid–base equilibria: application to horse plasma. J Appl Physiol 83:297–311

    CAS  PubMed  Google Scholar 

  • Constable PD (2001) Total weak acid concentration and effective dissociation constrant of nonvolatile buffers in human plasma. J Appl Physiol 91:1364–1371

    CAS  PubMed  Google Scholar 

  • Constable PD (2003) Hyperchloremic acidosis: the classic example of strong ion acidosis. Anesth Analg 96:919–922

    Article  CAS  PubMed  Google Scholar 

  • Dubin A, Menises MM, Masevicius FD, Moseinco MC, Kutscherauer DO, Ventrice E, Laffaire E, Estenssoro E (2007) Comparison of three different methods of evaluation of metabolic acid–base disorders. Crit Care Med 35:1264–1270

    Article  CAS  PubMed  Google Scholar 

  • Duffin J (2005) The role of acid–base balance in the chemoreflex control of breathing. J Appl Physiol 99:2255–2265

    Article  CAS  PubMed  Google Scholar 

  • Figge J, Jabor A, Kazda A, Fencl V (1998) Anion gap and hypoalbuminemia. Crit Care Med 26:1807–1810

    CAS  PubMed  Google Scholar 

  • Funder J, Weith JO (1966) Chloride and hydrogen ion distribution between human red cells and plasma. Acta Physiol Scand 68:234–245

    Article  CAS  Google Scholar 

  • Honore PM, Joannes-Boyau O, Boer W (2009) Strong ion gap and outcome after cardiac arrest: another nail in the coffin of traditional acid–base quantification. Intensive Care Med 35:189–191

    Article  PubMed  Google Scholar 

  • Lindinger MI, Kowalchuk JM, Heigenhauser GJF (2005) Applying physiochemical principles to skeletal muscle acid–base status. Am J Physiol Regul Integr Comp Physiol 289:R891–R894

    CAS  PubMed  Google Scholar 

  • McKelvie RS, Lindinger MI, Jones NL, Heigenhauser GJF (1992) Erythrocyte ion regulation across inactive muscle during leg exercise. Can J Physiol Pharmacol 70:1625–1633

    CAS  PubMed  Google Scholar 

  • Morgan TJ (2005) The meaning of acid–base abnormalities in the intensive care unit-effects of fluid administration. Critical Care 9:204–211

    Article  PubMed  Google Scholar 

  • Radiometer Medical A/S (2004) ABL 800 Flex Reference Manual

  • Rees SE, Andreassen S (2005) Mathematical models of oxygen and carbon dioxide storage and transport: the acid–base chemistry of blood. Crit Rev Biomed Eng 33:209–264

    Article  CAS  PubMed  Google Scholar 

  • Rees SE, Allerød C, Murley D, Zhao Y, Smith BW, Kjærgaard S, Thorgaard P, Andreassen S (2006a) Using physiological models and decision theory for selecting appropriate ventilator settings. J Clin Monit Comput 20:421–429

    Article  CAS  PubMed  Google Scholar 

  • Rees SE, Toftegaard M, Andreassen S (2006b) A method for calculation of arterial acid–base status from measurements in the peripheral venous blood. Comput Methods Programs Biomed 81:18–25

    CAS  PubMed  Google Scholar 

  • Rees SE, Hansen A, Toftegaard M, Pedersen J, Kristiensen SR, Harving H (2009) Converting venous acid–base and oxygen status to arterial in patients with lung disease. Eur Respir J 33:1141–1147

    Article  CAS  PubMed  Google Scholar 

  • Schwartz WB, Relman AS (1963) A critique of the parameters used in the evaluation of acid–base disorders “whole-blood buffer base” and “standard bicarbonate” compared with blood pH and plasma bicarbonate concentration. N Engl J Med 268:1382–1388

    Article  CAS  PubMed  Google Scholar 

  • Siggaard-Andersen O (1974) The acid–base status of the blood. Munksgaard, Copenhagen

    Google Scholar 

  • Siggaard-Andersen M, Siggaard-Andersen O (1995) Oxygen status algorithm, version 3, with some applications. Acta Anaesthsiol Scand 39(S107):13–20

    Article  Google Scholar 

  • Siggaard-Andersen O, Wimberly PD, Gøthgen I, Siggaard-Andersen M (1984) A mathematical model of the haemoglobin-oxygen dissociation curve of the human blood and of the oxygen partial pressure as a function of temperature. Clin Chem 30:1646–1651

    CAS  PubMed  Google Scholar 

  • Siggaard-Andersen O, Wimberly PD, Fogh-Andersen N, Gøthgen I (1988) Measured and derived quantities with modern pH and blood gas equipment: calculation algorithms with 54 equations. Scand J Clin Lab Invest 48(S189):7–15

    Article  Google Scholar 

  • Singer RB, Hastings AB (1948) An improved clinical method for the estimation of disturbances of the acid–base balance of human blood. Medicine 27:223–242

    Article  CAS  PubMed  Google Scholar 

  • Stewart PA (1983) Modern quantitative acid–base chemistry. Can J Physiol Pharmacol 61:1444–1461

    CAS  PubMed  Google Scholar 

  • Toftegaard M, Rees SE, Andreassen S (2009) Evaluation of a method for converting venous values of acid–base and oxygenation status to arterial values. Emerg Med J 26:268–272

    Article  CAS  PubMed  Google Scholar 

  • Wooten EW (1999) Analytic calculation of physiological acid–base parameters in plasma. J Appl Physiol 86:326–334

    CAS  PubMed  Google Scholar 

  • Wooten EW (2003) Calculation of physiological acid–base parameters in multicompartment systems with application to human blood. J Appl Physiol 95:2333–2344

    PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Model-based Medical Decision Support, Institute for Health Science and Technology, Aalborg University, Fredrik Bajers vej 7E, 9220, Aalborg, Denmark

    Stephen Edward Rees & Steen Andreassen

  2. Department of Clinical Chemistry, Aalborg Hospital, Aalborg, Denmark

    Elise Klæstrup & Søren Risom Kristensen

  3. Department of Anaesthesia, Intensive Care Medicine and Pain, Chelsea and Westminster Hospital, London, UK

    Jonathan Handy

  4. Critical Care Research Group, Imperial College, London, UK

    Jonathan Handy

Authors
  1. Stephen Edward Rees
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elise Klæstrup
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jonathan Handy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Steen Andreassen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Søren Risom Kristensen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stephen Edward Rees.

Additional information

Communicated by Susan Ward.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rees, S.E., Klæstrup, E., Handy, J. et al. Mathematical modelling of the acid–base chemistry and oxygenation of blood: a mass balance, mass action approach including plasma and red blood cells. Eur J Appl Physiol 108, 483–494 (2010). https://doi.org/10.1007/s00421-009-1244-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00421-009-1244-x

Keywords

Search

Navigation