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Evaluation of a mathematical model for blood gases and acid–base status during extracorporeal circulation


Blood gases and acid–base status are important parameters during extracorporeal circulation. They are controlled by the perfusionist, by varying arterial pump flow, gas flow over the oxigenator, inspiratory oxygen fraction, and carbon dioxide content in the inspiratory gas mix. To support the perfusionist with suggestions based on a control algorithm, a reliable system description is needed. Reliability of a complex model of human acid–base and blood gas status under extracorporeal circulation was evaluated using clinical documentation data.


A mathematical model for blood gas and acid–base status under extracorporeal circulation was developed. This model consists of a multiple compartment model for the oxygenator, and models for arterial and venous PCO2, PO2, (including temperature- and pH-dependent shift in oxygen-binding capacity of haemoglobin), SO2, bicarbonate, base excess and pH. It was implemented in a Matlab/Simulink environment. Input parameters were oxygenator type, gas flow, FiO2, arterial pump flow, temperature, haemoglobin concentration and haematocrit. As output parameters, venous and arterial SO2, PO2, PCO2 and pH were analyzed. The model was tested by using clinical monitoring data during extracorporeal circulation of patients undergoing aorto-coronary bypass grafting as input data, and comparing the model output with the results of conventional blood gas analyses (Rapidlab 288®) retrospectively.


Estimations of arterial PO2, PCO2 and SO2 were adequate. They followed the time course appropriately and remained within a narrow error band (Max. dev.: PO2 < 17 mmHg, PCO2 < 7 mmHg, SO2 < 0.01%). Venous PO2 followed appropriately (Max. dev.: <4 mmHg), whereas PCO2 (Max. dev.: <8 mmHg) did not reproduce the time course. Simulations for arterial and venous pH overestimated continuously and were not acceptable (Max. dev.: arterial pH +0.14, venous pH +0.07). The best results were achieved for estimation of SO2.


Modelling the patients' acid–base status and blood gases will be important for further development of control algorithms used in extracorporeal circulation. The presented model shows good concordance with clinical data for blood gas estimation, but needs to be reviewed concerning acid–base status. Further validation and in controlled experimental setups will be required.

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Correspondence to TM Schmidt.

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Schmidt, T., Naujokat, E., Barrho, J. et al. Evaluation of a mathematical model for blood gases and acid–base status during extracorporeal circulation. Crit Care 7 (Suppl 1), 7 (2003).

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