Next, proponents of the Windkessel-based AUC approach (such as Warner et al.39) divide SV into 2 components: systolic outflow and diastolic outflow (QS and QD).
QD is proportionate to “the increment in mean pressure over the whole arterial bed at the end of systole” (referred to as end-systolic mean distending pressure, abbreviated Pmd by Warner et al.39, or some variation of Pmd. For graphical representations, see Figure 6) and a constant k that must, by definition, incorporate estimates of vascular resistance, vessel compliance, and in some cases, aortic input impedance (Equation 1).
SV is the sum of systolic flow and diastolic flow (SV=QS + QD). Because peripheral vascular resistance is assumed to be constant over the course of 1 cardiac cycle, it is assumed that QS and QD are proportionate to their respective areas under the pressure curve (AS =AUC for systole, AD =AUC for diastole), i.e., that QS/AS =QD/AD. Therefore:
Because SV=QS + QD, and QS =QD × (AS/AD), and QD =k × Pmd (as noted above) it follows that:
To use Equation 5, or some variation of it, SV had to be measured by invasive means (i.e., the model requires calibration). This would allow the user to solve for k (because Psystole, AS, and AD could be calculated from the blood pressure tracing). Once k was known, SV could be followed on a beat-to-beat basis.
The exact equations used by the original proponents of this method vary slightly, mostly in the means by which they calculate Pmd,30,39,42,43 but also in their use of AS and AD (which, as the definition of Pmd is changed, must be adjusted accordingly). For unclear reasons, some authors chose to use TS and TD, the time spent in systole and diastole, respectively. The technique described above is based on a 2-element Windkessel model, the major components of which are peripheral resistance and Windkessel compliance.
Several investigators have attempted to develop an AUC method based generally on the outline presented above.30,39,44 When tested in an uncontrolled clinical environment, all of these early methods failed,45,46 prompting subsequent investigators to refine the Windkessel-based methodology.40,43
This approach entails several assumptions. First, it assumes no backward flow during any part of the cardiac cycle, thus should not be considered reliable in the setting of aortic insufficiency. Second, it neglects the effects of wave reflections on the pressure waveform (Frank's Windkessel model assumed that the vessel had infinite length, i.e., that reflected pressure waves were negligible). Of note, Mukkamala and Xu47 have attempted to correct for this assumption using “long time interval analysis techniques,” the preliminary data for which look promising. Third, it assumes that vascular resistance is constant over the cardiac cycle. Fourth, it assumes that vascular resistance can be accounted for by the changing shape of the pressure waveform.
Consider the following 2 waveforms (Fig. 7), the mean arterial blood pressures (MAPs) of which are identical. Based on the traditional approach to blood flow (output=driving force/resistance), without knowledge of systemic vascular resistance (SVR), the relative SV of both curves would appear to be identical. Application of the generic Windkessel-based AUC method to these curves suggests that the SV associated with these 2 curves is vastly different, despite the identical MAPs − Pmd × (1 + AS/AD) is equal to 47.5 for the first curve (blue), whereas Psystole × (1 + AS/AD) is equal to 68.2 for the second curve (green).
The generic Windkessel-based AUC method, which assumes that k is constant, must therefore assume that the SV of the green curve is 43% higher than the SV of the blue curve. Because MAP is identical, SVR in the green curve must therefore be 30.4% less than in the blue curve. Intuitively, one might look at the above waveforms and guess that SVR is lower in the green curve, as the upstroke is less steep. However, this may reflect decreased contractility, and not a difference in SVR, which would imply reduced SV.
Whether SVR can be reliably calculated from the shape of an arterial waveform is not known. Awad et al.48 attempted to correlate SVR to the width of plethysmographic waveform and achieved a statistically significant relationship; however, the correlation was too weak (standard deviation was 587.3 dynes/s/cm5) to be useful on a beat-to-beat basis.
One variation of the Windkessel-based approach is the characteristic impedance (cZ) method developed by Wesseling et al.42 The major difference between the cZ method and other 2-element techniques is that the cZ method attempts to use the concept of impedance (which represents resistance to pulsatile flow), rather than the static concept of resistance. The forces that oppose blood flow at any point are dependent on both blood pressure (which affects aortic cross-sectional area as well as compliance) and HR (which affects the influence of peripherally reflected pressure waves).49 It is important to note that cZ is actually an HR- and pressure-corrected variant of resistance and not identical to actual impedance. Wesseling et al.42 thus described cZ as a function of both MAP and HR (in Hz, fH, Equation 7).
In the most basic form of the cZ method, SV is equal to area under the pressure curve during systole [end-diastole∫end-systole P(t)] divided by cZ (Equation 8).50
The Modelflow technique, also developed by Wesseling et al.,51 attempts to incorporate both peripheral resistance (R) and Windkessel compliance (C), as well as characteristic impedance (cZ), into a 3-element Windkessel model. This model assumes that aortic compliance and impedance can be estimated based on patient data, and that resistance can be subsequently determined by fitting blood pressure data to the 3-element model. Empiric estimates of aortic area can be off by as much as 30%, thus the Modelflow technique still requires an initial calibration against known cardiac output.49 A variation of the Modelflow technique, which uses more accurate estimates of the pressure/aortic cross-sectional area relationship, called the Hemac technique, was recently developed.49
As with the cZ method, the PulseCO system (LiDCO Group, London, UK) also incorporates characteristic impedance into its model. However, the PulseCO system modifies Wesseling's original approach by considering the difference between peripheral and central pressures using a transfer function (see Estimates of Central Arterial Pressure).52 Additionally, the LiDCO device, which relies on the PulseCO algorithm to analyze the arterial waveform, also uses a lithium dilution curve to self-calibrate.
The PiCCO system adds an estimate of aortic compliance (derived from analysis of the pressure waveform distal to the dicrotic notch) to the cZ approach, and incorporates both aortic compliance [C(p), a function of pressure] and instantaneous pressure changes (dP/dt) into the calculation, which is integrated over the time period of systole (Equation 9).50
The PiCCO equation is notable for its treatment of compliance as a dynamic variable that changes with time (and is thus appropriately, and uniquely, included in the integral portion of the cardiac output equation). These modifications are intended to account for the fact that a nontrivial fraction of ventricular output is stored in capacitance vessels and subsequently ejected into the peripheral vasculature during diastole. Despite these modifications, the PiCCO requires an initial calibration to determine k.
A major paradigm shift in the AUC method came with the development of the FloTrac (Edwards Life Sciences, Irvine, CA).53 Rather than be burdened by the assumptions inherent in the Windkessel-based AUC approach, the FloTrac assumes only that SV is related to 2 empiric numbers, ςAP, which represents the relationship between pulse pressure and SV, and χ, which represents the effect of vascular tone on waveform morphology (Equation 10). Thus:
In addition to being an empiric (as opposed to theoretical) approach, the FloTrac does not require calibration. ςAP and χ are determined based on correlations developed from a proprietary hemodynamic database. ςAP is related to the standard deviation of the arterial blood pressures recorded over a 20-second epoch (Equation 11):
χ is related to a several variables, including HR, body surface area (BSA), compliance, as well as several numerical descriptors of the waveform, abbreviated μn (μ1, μ2, μ3, and μ4 represent MAP, the standard deviation of a 60-second data sample, the skewness of a 60-second data sample, and the kurtosis over a 60-second data sample, respectively). Additional parameters [μn] are also included, although their exact description is not available (Equation 12).
Compliance is a function of instantaneous pressure and is related to both maximal aortic root cross-sectional area (estimated based on patient demographics) and the shape of the compliance curve (empirically derived).
Thus, unlike prior techniques, which tried to force empirical data into elegant constructs that were thought to accurately depict reality, the FloTrac approach tries to find meaningful correlations regardless of whether the results can be explained by a physiologic theory. Early results in postsurgical patients were promising, with mean biases of 0.20 and 0.55 L/min reported (as compared with intermittent thermodilution).54,55
Studies of the PulseCO,56 PiCCO,57,58 and FloTrac59–61 suggest that the accuracy of AUC methods is degraded in the setting of hemodynamic instability. A recent meta-analysis that included 714 subjects in 24 studies suggested that the mean-weighted bias of AUC methods was 1.22 L/min, which was worse than esophageal Doppler (1.07 L/min), partial CO2 rebreathing (1.12 L/min), and thoracic bioimpedance (1.14 L/min) techniques.62
In a simultaneous comparison of the FloTrac, LiDCO, and PiCCO monitors with intermittent thermodilution in 20 patients after cardiac surgery, the bias and limits of agreement, as compared with the pulmonary artery (PA) catheter, were −0.18, 1.38, −1.74 L/min for the LiDCO, 0.24, 2.3, and −1.98 L/min for the PiCCO, and −0.43, −2.94, and 3.80 L/min for the FloTrac.63 The substantial difference in the limits of agreement between uncalibrated and calibrated devices was also reported by a similar comparison of the LiDCO and FloTrac with intermittent thermodilution.64
Improving the AUC Method: Pulse Wave Velocity
The velocity (V) of a pulse wave through an elastic tube can be described in terms of the elasticity (E, Young modulus of elasticity, defined as stress/strain), wall thickness (h), and diameter of the tube (D), as well as the density of the fluid (ρ), which is known as the Moens-Korteweg equation (Equation 13).65,66
Because the human cardiovascular system behaves as a complex series of elastic tubes, changes in pulse wave velocity (PWV) or pulse wave transit time may imply changes in elasticity, vessel diameter, or fluid (blood) density. The utility of PWV analysis is based on the assumption that changes in vascular impedance (ultimately mediated by changes in vascular tone, which lead to changes in both vessel compliance and cross-sectional diameter67) will result in changes in the speed at which a pressure wave, originating in the LV, travels to the periphery.66
Animal studies have revealed various relationships between PWV and diastolic blood pressure,65 ventricular dP/dtmax,68 and SVR.66 This latter relationship was used by Ishihara et al.69 to improve the accuracy of noninvasive cardiac output monitors; incorporation of pulse wave transit time into a plethysmographic contour-based CCO monitor eliminated the need for recalibration after significant changes in vascular resistance. A similar strategy applied to arterial contour-based CCO techniques might mark a significant advancement in achieving clinical applicability across a wide range of hemodynamic conditions. Indeed, the PulseCO algorithm incorporates an estimate of aortic PWV (based on patient age, gender, and MAP) into its calculation of characteristic impedance,52 a potential source of error (and improvement).
The “gold standard” for the measurement of cardiac output is the Fick method, which is clinically impractical. Thermodilution, which requires placement of a PA catheter, is considered the clinical gold standard, and is generally used to validate new devices. The PA catheter is not as accurate as the Fick method.32–35 To truly assess the utility of CCO monitors, a well-validated standard means of estimating cardiac output on a beat-to-beat basis is required. Currently, there is no such device, although a recently reported PA catheter incorporating orthogonally placed Doppler probes is promising.70
Practitioners are therefore left with the knowledge that AUC-based techniques deviate from thermodilution-based techniques in the setting of hemodynamic instability (it is impossible to know which is more “correct”), for the most part have not been tested against the Fick method, and are much more responsive than their more invasive counterpart, the PA catheter. The empiric approach used by the FloTrac, although convenient, may decrease the accuracy of the device in the setting of rapidly changing hemodynamics.63,64
Assuming that AUC-based techniques are less accurate than the true gold standard(s), they still may be of use, for several reasons. First, they are less invasive. Second, the response time of arterial waveform analysis methods, which can estimate SV on a beat-to-beat basis, is significantly faster than intermittent thermodilution and continuous thermistor-based techniques.31 Lastly, even if arterial waveform analysis cannot predict absolute values of cardiac output, predicting changes in cardiac output may be important. Sacrificing the ability to measure absolute values for an increased ability to track changes71 may actually improve the utility of these devices, depending on the clinician's needs.
ESTIMATES OF CENTRAL ARTERIAL PRESSURE
When arterial pressure is monitored invasively, it is almost always accomplished using a radial artery catheter. Because few clinicians care about blood flow to the hand specifically, the use of the radial artery implies that radial pressures provide other, more meaningful information. Unfortunately, myocardial delivery of oxygen is related to aortic (not radial) systolic pressure,72 and LV afterload is well represented by aortic input impedance.73–75 Central pressures are superior to peripheral pressures for the measurement of LV afterload, for estimation of carotid and coronary artery pressures,76 and for estimating changes in SV.47 The inability of peripheral (e.g., radial, brachial) arteries to represent aortic pressure (particularly systolic pressure)72,77–79 (Fig. 8) may be one of the reasons that most investigations have failed to find a meaningful relationship between peripheral arterial blood pressure and clinical outcomes during anesthesia.
Most techniques used to estimate central pressure are based on the concept of the transfer function; blood pressure tracings are acquired for both central and peripheral arteries, and compared. A mathematical function that relates the central to peripheral pressure tracing is developed for each individual, which is called an individual transfer function (ITF). ITFs are developed for a population, and then combined (usually averaged) to produce a generalized transfer function (GTF) that best fits the population as a whole.
Karamanoglu et al.79 measured ascending aortic, brachial, and radial artery pressures in 14 patients in the cardiac catheterization laboratory. Blood pressures at each site were decomposed into a series of sine waves, each of which had an amplitude and phase shift component. The amplitude and phase shifts of each pressure tracing (aortic, brachial, radial) were then compared and related. ITFs were developed for all 14 patients, then pooled to develop a single GTF. Application of the developed GTF reduced the difference between peripheral and central systolic pressures from 20 to 2.4 mm Hg (Fig. 9).79 This frequency domain approach has been validated by >15,000 readings from >1600 patients (r2 =0.94 between estimated and measured aortic systolic pressure).29
Chen et al.80 examined blood pressure waveforms in the time domain. ITFs were developed for 20 patients using a linear mathematical model in which aortic and radial pressures were related by the previous 10 measurements. A GTF was then produced by averaging the ITFs, and the model was tested in the setting of hemodynamic instability (created by transient occlusion of the inferior vena cava). Pauca et al. showed that in elderly, hypertensive adults, the second systolic peak of the radial artery waveform was highly correlated with aortic systolic pressure.72,81
In an additional attempt to estimate central pressures without the use of a tonometer, Wassertheurer et al.82 modified a conventional blood pressure cuff by adding a high-fidelity pressure sensor (Freescale MPX5050, Tempe, AZ). The increased accuracy of this modified cuff allowed Wassertheurer et al. to transform the brachial artery pressures to aortic pressures, using a frequency-based general transfer function similar to that developed by Karamanoglu et al. Indeed, the mean bias between the ARCSolver method, as it is known, and the technique of Karamanoglu et al. was 0.1 mm Hg (SD 3.1 mm Hg).82
Transfer functions are currently used in at least 3 commercially available devices. The SphygmoCor device estimates aortic blood pressures based on tonometric readings from the radial artery.29 Clinical use of central pressure estimates has been almost exclusively the domain of the cardiologist29,76; however, a modification of the original SphygmoCor device (the SphygmoCor CPM) accepts input from a radial artery catheter and could potentially be used intraoperatively. The LiDCO monitor uses a transfer function to convert radial to aortic pressure (for which the cZ model is used to estimate SV). The NexFin HD (BMEYE, Amsterdam, The Netherlands) estimates SV based on transformed finger pressure readings (and the Modelflow technique, described above).83 Advances in blood pressure cuff technology82 may soon allow for an additional means by which central pressures can be estimated completely noninvasively.
The ability to accurately estimate central pressures in the intraoperative setting will allow anesthesiologists to determine whether monitoring central pressures (which more accurately estimate LV afterload and perfusion pressure to major organs) can improve clinical outcomes. In the meantime, it is worth noting that data from the SphygmoCor validation studies suggest that, for the purposes of assessing central systolic blood pressure, a standard sphygmomanometer cuff seems to be more accurate than a radial artery catheter.29 Thus, the clinician interested in monitoring LV afterload may be well advised to continue taking periodic sphygmomanometric measurements even after placing a more invasive, peripheral monitor such as a radial artery catheter.
Peripheral dP/dtmax seems to be related to LV contractility, although the relationship may be confounded by other hemodynamic variables. SV estimates based on the AUC method have a significantly shorter response time than thermodilution-based techniques, but are burdened by relatively wide limits of agreement compared with thermodilution-based techniques, particularly when loading conditions change. Direct comparisons suggest that calibrated devices may better account for these changes than uncalibrated devices. Central pressures may provide more insight into LV afterload and into the perfusion pressure of vital organs than peripheral blood pressures. Central systolic pressure may be estimated using a sphygmomanometer. The mathematical techniques used to transform peripheral pressures into central pressures (and the accompanying limitations) are an essential component to several commercial devices designed to measure SV.
Arterial waveform analysis has provided the anesthesia community with a relatively noninvasive means of estimating ventricular contractility and SV on a beat-to-beat basis. Knowledge of the mathematical assumptions that are inherent in these approaches allows the anesthesia provider to more fully understand the advantages and limitations of this technology, and thus use it appropriately to improve patient care.
Marcel E. Durieux is Section Editor of Anesthetic Pre-Clinical Pharmacology for the Journal. This manuscript was handled by Dwayne R. Westenskow, Section Editor of Technology, Computing, and Simulation, and Dr. Durieux was not involved in any way with the editorial process or decision.
Name: Robert H. Thiele, MD.
Contribution: Manuscript preparation.
Name: Marcel E. Durieux, MD, PhD.
Contribution: Manuscript preparation.
This manuscript was handled by: Dwayne R. Westenskow, PhD.
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