J Thorac Cardiovasc Surg 1999;117:1231-1233
© 1999 Mosby, Inc.
Aortic function in patients during intra-aortic balloon pumpingdetermined by the pressure-diameter relation
Michael Poullis, MD
Department of Cardiothoracic Surgery
Hammersmith Hospital
DuCane Rd
East Acton
National Heart and Lung Institute
ImperialCollege of Science
London W12 0NN, United Kingdom
To the Editor:
Stefanadis and associates
1 provide an important analysis of aortic function in patients duringintra-aortic balloon pumping, which aids in the understanding of the improvedcirculatory function that results from its use. However, two points need furtherclarification.
First, in Fig. 4 they state that the fourth derivative of the aorticpressure and diameter was used to estimate (1) minimum aortic pressure anddiameter and (2) the point of inflection of the aortic pressure and diameter,thus allowing calculation of the pressure augmentation index. The fourth derivativehas been previously described as the optimum way of deriving these points. 2
The use of the fourth derivative is against the basic principles ofcalculus, in which the first derivative is used to evaluate minima and maxima,with the second derivative used to distinguish between these and points ofinflexion, negative at maxima, positive at minima, and zero at points of inflexion. 3 The third and fourth derivativeshave no use with regard to the aforementioned points. To prove this, we digitizedthe aortic blood pressure of a patient every 10 ms; the first four derivativesare shown in Fig. 1. The first derivative crosses zero threetimes, indicating the maxima and two minima of the blood pressure trace. Thesecond derivative is positive at the first and third zero point of the firstderivative, indicating a minima, and is negative at the second zero point(it should be noted that the sign of the second derivative determines themaxima/minima status, and not the actual value). In addition, the second derivativeis zero during the upstroke of the pressure tracing, indicating that the pointof inflection occurs at this point.
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Fig. 1 Typical blood pressure tracingfrom a patient's aorta, and the first four derivatives (see text for explanation).
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Second, no measurements of systemic vascular resistance/ impedance (SVR/SVI)were made, and yet the SVR and SVI have a major effect on the pressure tracingthat is obtained, thus influencing the augmentation index measured. Fig. 2demonstrates the influence of SVR as measured by a thermodilution catheter(Swan-Ganz; Baxter Healthcare Corp, Edwards Div, Santa Ana, Calif) on theaugment pressure generated by an intra-aortic balloon pump in 11 patientsafter cardiac surgery. It could be argued that the pressureaugmentation index measured on the balloon pump augmentation pulse would bemore accurate than on the heart ejection pulse part of the blood pressuretracing, but this remains to be validated.
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Fig. 2 The effect of systemic vascularresistance on the augmented pressure produced by an intra-aortic balloon pump.
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References
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Stefanadis C, Dernellis J, Tsiamis E, StratosC, Kallikazaros I, Toutouzas P. Aortic function in patients during intra-aorticballoon pumping determined by the pressure-diameter relation. J Thorac CardiovascSurg 1998;116:1052-9.[Abstract/Free Full Text]
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Kelly R, Hayward C, Avolio A, et al. Noninvasivedetermination of age-related changes in the human arterial pulse. Circulation 1989;80:1652-9.[Abstract/Free Full Text]
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Lamb H. Applications of the derived function.In: Infinitesimal calculus. Cambridge University Press; 1944. p. 95-125.
