Modelflow as longstanding method for cardiac output estimation with an arterial pressure waveform
Short title: Noninvasive estimation of cardiac output from brachial blood pressure
Diego Álvarez-Montoyaa, Camilo Madrid-Muñoza, Luis Escobar-Robledoa, Jaime Gallo- Villegasa,b, Dagnovar Aristizábal-Ocampoa,c
aCentro Clínico y de Investigación SICOR (Soluciones Integrales en Riesgo Cardiovascular), bFacultad de Medicina, Universidad de Antioquia, cCellular & Molecular Biology Unit, Corporación para Investigaciones Biológicas, Medellín (Colombia).
Supplementary material 4
The Modelflow model has been the cornerstone of cardiac output (CO) monitoring both in invasive and ambulatory settings for several decades. Modelflow method uses the pulsatile systolic area in the arterial pressure waveform in combination with age-related changes in aortic compliance for calculation of CO. This method is based on the solid experimental work from Langewouters and Wesseling (LGW & Wesseling) on static compliance [1].
The solid performance of Modelflow model in invasive settings, which is comparable to thermodilution differs from the results observed in the case of noninvasive devices based on Modelflow (i.e., Finapress and Nexfin). With these devices several researchers have reported accuracy issues for CO evaluation [2-5]. De Vaal et al. reported that estimation of pressure-dependent compliance could be the factor explaining the errors since empiric estimates of aortic cross sectional area could be off by as much as ±30% [6].
Identification of limitations of static compliance for aortic area and volume estimates In our research for a calibrated method for compliance assessment, we discovered that Wesseling et al. had assigned a fixed value of 80 cm to the aorta length in his static compliance estimation [7]. This fixed aortic length could affect subjects´ compliance estimation and it would amplify errors in cross-section area and aortic volume calculations.
After testing whether that fixed value had an effect on noninvasive CO values, it was found that such a fixed aorta length was the source of incorrect values for compliance estimation in subjects under 30 y/o and over 60 y/o as well as in obese individuals. Those findings led to further testing, in a previous invasive study, Murgo & Westerhof used in vivo data for evaluating aortic input impedance in normal men and they reported aortic area measurements [8]. For subjects in that study, aortic pressure-dependent area A(P) was
calculated using LGW & Wesseling equation (shown below) and then A(P) was compared with areas obtained by Murgo & Westerhof.
A(P) = Amax ⌊0.5 +1
πarctang (P−Po
P1 )⌋ Equation 1SDC4
The table 1SDC4 shows the values derived with both methods. The Bland-Altman plot (Fig. 1SDC4) confirms that if aortic area is small, the LGW & Wesseling equation overestimates the aortic area and when aortic area values are high the LGW & Wesseling equation leads to an underestimated area.
According to this analysis, it was clear that in addition to patient´s characteristics described by Wesseling et al., other reported anthropometric and physiological variables, which affected total arterial compliance and CO values were needed to improve compliance estimates [9, 10]. In mammalian species, CO is related to (body weight)3/4 [11] and human studies have demonstrated the importance of body size in CO and other hemodynamic estimates [12, 13]. Therefore, for a solid total arterial compliance estimate, the static compliance reported by LGW & Wesseling needs to be combined with a dimensional compliance component (captured by body weight and body surface area) and, a functional compliance component (captured by heart rate and diastolic pressure decay time constant [Tau]). These complementary refinements in the understanding of arterial compliance behavior were combined in the new method to obtain a more physiological estimate of total arterial compliance.
Improvements in cardiac output estimation with the new features
In the Fig. 2SDC4 and Fig. 3SDC4, the difference between CO measured with echocardiography vs. CO estimation via LGW & Wesseling equation for static compliance only (Fig. 2SDC4) and the comparison with the new method are shown. The new method uses static compliance by LGW & Wesseling and it also includes compliance´s functional and dimensional components (Fig. 3SDC4).
The Fig. 2SDC4 shows that if CO values are low, the LGW & Wesseling model underestimates the CO, and it also leads to overestimation if CO values are high. Those drawbacks of the static compliance model were corrected. The new method improved the accuracy indicated here by a very low mean difference and the much lower standard deviation (Fig. 3SDC4).
Statistical analysis of errors with static compliance and the new compliance model Residuals comparison for body mass index, heart rate and Tau between LGW & Wesseling model (abbreviated LGW model in the Fig. 4SDC4) and the new model showed that errors for those three parameters were, for the new model, evenly distributed around zero while for the same three parameters the magnitude of errors were much greater, across different values, with the LGW & Wesseling alone. Thus, with this significant improvement in the multiple linear regression model for compliance assessment, errors in CO estimation were expected to be greatly reduced (Fig. 4SDC4).
In summary, the new method aims to solve two limitations of the pulse contour technique for CO assessment in ambulatory settings: i) the pulse wave morphology dependency and,
ii) the assumptions in the calculation of the aortic cross-sectional area. Table 2 in the main paper summarizes the sequential calculations, which in a combined fashion account for improvements in total arterial compliance and CO estimation.
Table 1SDC4 Comparison of aortic pressure-dependent area calculated by the LGW &
Wesseling and Murgo & Westerhof equation.
Calculated area by LGW &
Wesseling (cm2 )
Calculated area by Murgo &
Westerhof (cm2 )
4.72 6.16
4.81 7.07
4.27 3.80
4.06 3.80
4.18 5.31
4.31 3.14
4.41 5.31
4.06 5.31
4.49 6.16
4.17 4.52
4.05 3.80
4.25 3.14
4.60 5.31
4.06 6.16
4.03 3.80
3.88 4.52
4.10 5.31
4.15 5.31
Fig. 1SDC4
Bland-Altman plot of aortic pressure-dependent area calculated by the LGW & Wesseling and Murgo & Westerhof equation. The Bland-Altman plot confirms that if aortic area is small, the LGW & Wesseling equation overestimates the aortic area and when aortic area values are high the LGW & Wesseling equation leads to an underestimated area.
Fig. 2SDC4
Bland-Altman plot of cardiac output calculated by the LGW & Wesseling and echocardiography. The Bland-Altman plot shows that if cardiac output (CO) values are low, the LGW & Wesseling model underestimates the CO, and it also leads to overestimation if CO values are high. Mean of difference 0.069 + 2.73 liter/min.
Fig. 3SDC4
Bland-Altman plot of cardiac output calculated by the new method and echocardiography.
The new method improved the accuracy indicated here by a very low mean difference and the much lower standard deviation. Mean of difference 0.027 + 0.67 liter/min.
Fig. 4SDC4
Residuals comparison for body mass index (BMI), heart rate and diastolic pressure decay time constant (Tau) between LGW & Wesseling model (abbreviated LGW model) and the new model.
-6 -4 -2 0 2 4 6
20 22 24 26 28 30 32 34 36
BMI
CO LGW - CO echo (l/min)
LGW model
-6 -4 -2 0 2 4 6
20 22 24 26 28 30 32 34 36
BMI
CO New - CO echo (l/min)
New model
-6 -4 -2 0 2 4 6
45 50 55 60 65 70 75 80 85 90 95 Heart Rate
CO LGW - CO echo (l/min)
LGW model
-6 -4 -2 0 2 4 6
45 50 55 60 65 70 75 80 85 90 95 Heart Rate
CO New - CO echo (l/min)
New model
-6 -4 -2 0 2 4 6
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4
Tau (s)
CO LGW - CO echo (l/min)
LGW model
-6 -4 -2 0 2 4 6
0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Tau (s)
CO New - CO echo (l/min)
New model
References
1. Langewouters GJ, Wesseling KH, Goedhard WJ. The static elastic properties of 45 human thoracic and 20 abdominal aortas in vitro and the parameters of a new model. J Biomech. 1984;17(6):425-35.
2. Gibbons TD, Zuj KA, Peterson SD, Hughson RL. Comparison of pulse contour, aortic Doppler ultrasound and bioelectrical impedance estimates of stroke volume during rapid changes in blood pressure. Exp Physiol. 2019;104(3):368-78.
3. van der Spoel AG, Voogel AJ, Folkers A, Boer C, Bouwman RA. Comparison of noninvasive continuous arterial waveform analysis (Nexfin) with transthoracic Doppler echocardiography for monitoring of cardiac output. J Clin Anesth. 2012;24(4):304-9.
4. Remmen JJ, Aengevaeren WR, Verheugt FW, van ver Werf T, Luijten HE, Bos A, et al.
Finapres arterial pulse wave analysis with Modelflow is not a reliable non-invasive method for assessment of cardiac output. Clin Sci (Lond). 2002;103(2):143-9.
5. Tam E, Azabji Kenfack M, Cautero M, Lador F, Antonutto G, di Prampero PE, et al.
Correction of cardiac output obtained by Modelflow from finger pulse pressure profiles with a respiratory method in humans. Clin Sci (Lond). 2004;106(4):371-6.
6. de Vaal JB, de Wilde RB, van den Berg PC, Schreuder JJ, Jansen JR. Less invasive determination of cardiac output from the arterial pressure by aortic diameter-calibrated pulse contour. Br J Anaesth. 2005;95(3):326-31.
7. Wesseling KH, Jansen JR, Settels JJ, Schreuder JJ. Computation of aortic flow from pressure in humans using a nonlinear, three-element model. J Appl Physiol (1985).
1993;74(5):2566-73.
8. Murgo JP, Westerhof N, Giolma JP, Altobelli SA. Aortic input impedance in normal man: relationship to pressure wave forms. Circulation. 1980;62(1):105-16.
9. Collis T, Devereux RB, Roman MJ, de Simone G, Yeh J, Howard BV, et al. Relations of stroke volume and cardiac output to body composition: the strong heart study. Circulation.
2001;103(6):820-5.
10. Li JK. Cardiovascular Allometry: Analysis, Methodology, and Clinical Applications. Adv Exp Med Biol. 2018;1065:207-24.
11. Gunther B, Morgado E. Allometric algorithms. Biol Res. 1996;29(4):345-53.
12. Sluysmans T, Colan SD. Theoretical and empirical derivation of cardiovascular allometric relationships in children. J Appl Physiol (1985). 2005;99(2):445-57.
13. Evans JM, Wang S, Greb C, Kostas V, Knapp CF, Zhang Q, et al. Body Size Predicts Cardiac and Vascular Resistance Effects on Men's and Women's Blood Pressure.
Front Physiol. 2017;8:561.