What's wrong on Arnold's methodology of cardiac output measuring based on capno-volumetric expirogram.


Objective: To disprove a single breath CO2 analysis [1], [2], [4] published by John H. Arnold as a method of cardiac output measurement. To clarify real causes of shape changes in CO2 expirograms in Arnold's animal experiment. To approve a strict mutual CO 2 -expirogram shape and cardiac output independency.

Design: A detailed computer model study of single breath CO2 analysis as a right causality hypothesis validation.

Setting: Laboratory of Biocybernetics and Computer Aided Teaching ( First Faculty of Medicine - Charles Univerzity in Prague, Czech Republic).

Subjects: A mathematical model of lung ventilation, blood circulation (minimal model is sufficient), blood gases transport and exchange. Model structure and behavior are in a good agreement with known clinical data and wide range of published similar models.

Interventions: For the phenomenon under study the working hypothesis of right causalities has been formulated against the direct CO2 expirogram dependency on the cardiac output inadequately speculated in Arnold's work. This working hypothesis has been validated by simulating of 18 specific situations and by comparing of outputs.

Measurements and Main Results: Eighteen situations covering all combinations of normal ventilation or hyperventilation, normal/low/high cardiac output and normal/low/high metabolic CO2 production have been simulated. If all others parameters of simulation are fixed than the appropriate capno-volumetric expirograms obtained during subject's steady state are practically identical for arbitrary value of the cardiac output as it has been clearly showed by the summary below.

Conclusions: There is no doubt about the importance of the capno-volumetric expirogram methodology for noninvasive measurement of lung parameters [5]. But this methodology is on principle inappropriate for the cardiac output measurement!! The data measured (and originally misinterpreted) in Arnold's animal experiment have been explained by side effects of evoked but originally omitted changes in body metabolic CO2 production rate.

The mathematical model

The three variants of the mathematical model implemented in MATLAB/Simulink (version R14SP1) can be downloaded HERE. This downloadable variants have strongly simplified (only tabulated) relations between the partial presures and concentrations of blood gases. Don't worry about this, the obtained results still holds. :o) The simplification was made for higher computational speed and easy sharing of models.

Short summary

Normal cardiac output was assumed to be equal 5 liters per minute, normal metabolic rates were assumed MRO2 equal to 0.24 liters STPD per minute and MRCO2 equal to 0.34 liters STPD per minute. The normal ventilation is specified by amplitude of intrapleural pressure 2 mmHg, breathing period 6 sec including the final 2 sec resting phase. And the hyperventilation is specified by amplitude of intrapleural pressure 3 mmHg, breathing period 4 sec and the included final resting phase is shorted to 0.5 sec.

Figure. The capno-volumetric expirograms obtained after the steady states achieving as the results of 18 simulated situations. Let's highlight there are six groups denoted by uppercase letters (A_ to F_) each containing three coalescent (practically identical) lines specified by lowercase letters (_a to _c)! So the graph contains 18 lines in real!

Simulated situations Cardiac output Metabolic rates Ventilation status
Aa) Twice Twice Normal
Ab) Normal Twice Normal
Ac) Half Twice Normal
Ba) Twice Normal Normal
Bb) Normal Normal Normal
Bc) Half Normal Normal
Ca) Twice Half Normal
Cb) Normal Half Normal
Cc) Half Half Normal
Da) Twice Twice Hyper
Db) Normal Twice Hyper
Dc) Half Twice Hyper
Ea) Twice Normal Hyper
Eb) Normal Normal Hyper
Ec) Half Normal Hyper
Fa) Twice Half Hyper
Fb) Normal Half Hyper
Fc) Half Half Hyper

Table. Tabulated parameters of 18 simulated situations


Main references:

1. pdf file: Arnold JH, Stenz RI, Grenier B, Thompson JE, Arnold LW. Noninvasive determination of cardiac output in a model of acute lung injury. Critical Care Medicine 1997;864-8.

2. pdf file: Arnold JH, Stenz RI, Thompson JE, Arnold LW. Noninvasive determination of cardiac output using single breath CO2 analysis. Critical Care Medicine 1996;1701-5.

3. Kerekeš R, Kofránek J. [In Czech - The progress of noninvasive cardiac output monitoring] Vývoj a trend neinvazivního monitorování srdečního výdeje. 25-38. 1997. Kolín, MSM. Neinvazivní monitorování a měření srdečních funkcí. Sborník referátů presatelitního sympozia IV. kongresu ČSARIM. Conference Proceeding

4. pdf file: Arnold JH, Thompson JE, Arnold LW. Single breath CO2 analysis: Description and validation of a method. Critical Care Medicine 1996;96-102.

5. Fletcher R, Jonson B, Cumming G, Brew J. The Concept of Deadspace with Special Reference to the Single Breath Test for Carbon-Dioxide. British Journal of Anaesthesia 1981;77-88.

Mathematical model references:

6. Fukui Y. A study of the human cardiovascular-respiratory system using hybrid computer modeling. 1-183. 1972. University of Wisconsin. Thesis/Dissertation

7. Heldt T, Shim EB, Kamm RD, Mark RG. Computational modeling of cardiovascular response to orthostatic stress. Journal of Applied Physiology 2002;1239-54.

8. Kofránek J, Velan T, Kerekeš R. Golem: a Computer Simulator of Physiological Functions as an Efficient Teaching Tool. Theo, Y. M., Wong, W. C., Okeu, T. J., and Rimane, R. 407-411. 1997. Singapore, IEE Singapore Section. Legacy for 21 Century. Proceedings of the World Congress on System Simulation. Conference Proceeding

9. Pedley TJ, Schroter RC, Sudlow MF. The Prediction of the Pressure Drop and Variation of Resistance within a Human Bronchiole Airways. Respiration Physiology 1970;371-86.

10. Despopoulos A, Silbernagl S. Color Atlas of Physiology. New York: Georg Thieme Verlag Stuttgart - New York & Thieme Medical Publishers, Inc., New York, 1991:60-108.

11. Douglas AR, Jones NL, Reed JW. Calculation of whole blood CO2 content. American Physiology Society 1988;473-7.

12. Anstey C. A New Model for the Oxyhaemoglobin Dissociation Curve. Anaesthesia and Intensive Care 2003;376-87.

Please, do not hesitate to write any your questions to us: michal.andrlik , or kofranek .