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J Thorac Cardiovasc Surg 2006;131:506-507
© 2006 The American Association for Thoracic Surgery

Letter to the Editor

A new modeling for each population

Experimental Toxicology, Department-Modeling Group, INERIS (National Institute for industrial Environment and RISks), 60550 Verneuil en Halatte, France

To the Editor:

I read with great interest the recently published study by Fakler and associates ¹ in the August 2005 issue of the Journal. They found, in their investigation, a poor agreement between the measured oxygen consumption (VO₂) and the VO₂ estimated using the formulas of Krovetz and Goldbloom ² and LaFarge and Miettinen. ³ According to the Krovetz-Goldbloom formula, the mean difference was –53 mL/min/m² and the limits of agreement were –95.5 and –11.1 mL/min/m² for the lower and upper limits, respectively. Use of the Krovetz-Goldbloom formula led to a systematic and significant overestimation in VO₂ values (P = .0001). However, a significant correlation was shown between measured and assumed VO₂ values with this formula (R = .61; P = .0001). According to the LaFarge-Miettinen formula, the mean difference was –15.6 mL/min/m² and the limits of agreement were –120.0 and 88.8 mL/min/m² for the lower and upper limits, respectively. A systematic and significant overestimation was also reported using the LaFarge-Miettinen formula. A significant correlation was, however, indicated between measured and assumed VO₂ with this model (R = 0.38; P = .0037). I speculated that the reason that the measured VO₂ values were significantly different from the assumed VO₂ using both Krovetz-Goldbloom and Lafarge-Miettinen formulas was because of a methodologic weakness in statistics and modeling.

As discussed by the authors, these differences between measured VO₂ and VO₂ estimated by the formulas might be due to a difference of population. I agree with this statement, but more credible is the argument that these differences are explained by the coefficients of these formulas (Krovetz-Goldbloom formula: VO₂ = a · height + b · weight – c; Lafarge-Miettinen formula: VO₂ = a' – b' · ln(age) + c' · heart rate for male subjects and VO₂ = a' – b'' · ln(age) + c' · heart rate for female subjects). These coefficients (a, b, c and a', b', b'' and c') depend on the characteristics of the population included in the study. That is why the use of published formulas without any coefficient correction cannot be applied in other populations, as shown in another study. ⁴ To overcome this problem, new formulas with new coefficients should be calculated from the population included in the investigation. For example, in the study of Fakler and associates, ¹ new formulas with new coefficients could be calculated using 70 patients included in their investigation and could be validated against the remaining 73 patients for comparing measured and estimated VO₂.

Fakler and associates ¹ reported that the routine use of assumed VO₂ when calculating cardiac output with the direct Fick principle might frequently result in large errors in the estimation of cardiac output and dependent parameters. To obtain reliable cardiac output values by the direct Fick equation, VO₂ should be measured as concluded by Fakler and associates ¹ or estimated with a new formula calculated using the population included in the study.

	References

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1. Fakler U, Pauli C, Henning M, Sebening W, Hess J. Assumed oxygen consumption frequently results in large errors in the determination of cardiac output. J Thorac Cardiovasc Surg 2005;130:272-276.[Abstract/Free Full Text]
   
2. Krovetz LJ, Goldbloom S. Normal standards for cardiovascular data. I. Examination of the validity of cardiac index. Johns Hopkins Med J 1972;130:174-186.[Medline]
   
3. LaFarge CG, Miettinen OS. The estimation of oxygen consumption. Cardiovas. Res 1970;4:23-30.[Abstract/Free Full Text]
   
4. Laitinen PO, Räsänen J. Measured versus predicted oxygen consumption in children with congenital heart disease. Heart 1998;80:601-605.[Abstract/Free Full Text]
   

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