Estimation of Central Aortic Pressure Waveform by Mathematical Transformation of Radial Tonometry Pressure
Validation of Generalized Transfer Function
Background Central aortic pressures and waveform convey important information about cardiovascular status, but direct measurements are invasive. Peripheral pressures can be measured noninvasively, and although they often differ substantially from central pressures, they may be mathematically transformed to approximate the latter. We tested this approach, examining intersubject and intrasubject variability and the validity of using a single averaged transformation, which would enhance its applicability.
Methods and Results Invasive central aortic pressure by micromanometer and radial pressure by automated tonometry were measured in 20 patients at steady state and during hemodynamic transients (Valsalva maneuver, abdominal compression, nitroglycerin, or vena caval obstruction). For each patient, transfer functions (TFs) between aortic and radial pressures were calculated by parametric model and results averaged to yield individual TFs. A generalized TF was the average of individual functions. TFs varied among patients, with coefficients of variation for peak amplitude and frequency at peak amplitude of 24.9% and 16.9%, respectively. Intrapatient TF variance with altered loading (>20% variation in peak amplitude) was observed in 28.5% of patients. Despite this, the generalized TF estimated central arterial pressures to ≤0.2±3.8 mm Hg error, arterial compliance to 6±7% accuracy, and augmentation index to within −7% points (30±45% accuracy). Individual TFs were only marginally superior to the generalized TF for reconstructing central pressures.
Conclusions Central aortic pressures can be accurately estimated from radial tonometry with the use of a generalized TF. The reconstructed waveform can provide arterial compliance estimates but may underestimate the augmentation index because the latter requires greater fidelity reproduction of the wave contour.
Central aortic systolic and diastolic pressures are determinants of cardiac loading and perfusion, and they impact importantly on cardiovascular function. Knowledge of these pressures is often crucial to precise monitoring and titration of interventions in disease states. In addition to the pressures themselves, the arterial pressure waveform conveys useful information regarding systemic vascular stiffness,1 reflected waves,2 compliance, and other features of value in the bedside physical examination.3 Central arterial pressures can also be combined with measured aortic flows or left ventricular volumes to derive indexes of cardiac systolic function4 5 and ventricular-vascular interaction.6 7 8 However, widespread application of such analysis has been hindered by the requirement for invasive pressure measurements. An ability to accurately and noninvasively estimate aortic pressure waves would indeed be a valuable addition to current noninvasive tools such as those provided by echo/Doppler9 10 and magnetic resonance imaging.11
We previously validated a noninvasive technique to estimate central aortic systolic and diastolic pressures and the ascending portion of the pressure waveform.12 Coupled with radionuclide ventricular volumetry, this method was useful for assessing contractile function in heart failure patients13 and evaluating mechanisms of new drug therapies.14 However, this technique did not provide real-time, beat-to-beat pressures. Moreover, the reconstructed waveform was truncated after peak systolic pressure, so that the late systolic and the diastolic portions of the waveform were unavailable. Another noninvasive technique is applanation tonometry, which uses an externally applied micromanometer-tipped probe to continuously record peripheral pulse waveforms.15 16 Accurate recording with this method requires that the vessel wall be flattened by the probe so that transmural forces are perpendicular to the arterial surface.17 We and others have shown that reasonable estimates of central aortic pressure waveforms can be obtained by tonometry from the carotid artery.18 This technique is suboptimal, however, because the artery is surrounded by loose tissue, making it difficult to ascertain and consistently achieve optimal applanation.
In contrast to the carotid artery, the radial artery is very accessible and well supported by bony tissue, making optimal applanation far easier to achieve. The main disadvantage of using the radial pulse is that the pressure contour changes appreciably as it travels from the aorta to more peripheral sites, so that radial pressures cannot be used directly as a surrogate for central aortic pressure.19 However, it may be possible to estimate the central aortic pressure wave from radial tonometry data with the use of a mathematical transformation. Karamanoglu et al20 recently proposed such an approach using a single group-averaged TF to reconstruct aortic pressures. However, that study did not systematically assess interpatient and intrapatient variability of the TF, nor did it critically test potential influences of such variance on estimated parameters from the reconstructed waveforms. Because age and disease can dramatically affect vascular properties, it is unclear if a generalized approach can be used or if individualized transformation tailored to age, sex, and disease state is needed for accurate resynthesis.
Therefore, the principal goals of the present study were to determine the magnitude of interpatient and intrapatient variation of the TF between central and radial pressure waves under baseline conditions and during physiological maneuvers that substantially altered blood pressure. We further tested whether an averaged (generalized) transformation was sufficient to accurately estimate central pressures despite such variability. Radial pressures were measured by an automated tonometry21 device and were compared with micromanometer pressures measured in the central aorta.
Twenty patients referred for diagnostic cardiac catheterization at Johns Hopkins Hospital were enrolled for this study. Informed consent in a form approved by the institutional review board was obtained in all subjects. There were 16 men and 4 women with a mean age of 59 years (range, 36 to 78 years). Table 1⇓ provides a summary of clinical characteristics, cardiovascular diagnosis, ejection fraction, and aortic and radial blood pressures at baseline and after maximal load reduction.
Central Aortic and Radial Artery Pressure Recording
After completion of routine catheterization, a micromanometer (SPC-320, Millar Instruments) was advanced inside the lumen of a pigtail catheter placed in the ascending aorta. In some patients, aortic pressure was recorded by a micromanometer mounted on a multielectrode pressure-volume catheter (SSD-768, Millar Instruments).
Radial pressure waves were recorded with the use of an improved automated tonometry device (Jentow, Colin Medical Inst Corp). Previous studies had used hand-held tonometers.20 Although this was probably adequate for brief steady-state data, manual recording was too unstable for accurate pressure tracking during hemodynamic transients, and it introduced an element of user dependence and thus potential bias to the data. The automated system circumvented these limitations. It used a wristwatchlike sensor with an array of 30 piezoresistive pressure transducers and included a servo-feedback mechanical system to optimize sensor position over the radial artery, determine the subset of microsensors from which to derive the pulse tracing, and adjust applanation hold-down pressure to maximize the recorded pulse pressure.21 The sensor was attached to a splint to keep the wrist hyperextended and immobilized. During the study, the tonometer was calibrated to manually triggered oscillometric arm-cuff pressures.
Pressure recordings were digitized at 200 Hz and stored for off-line analysis. During the study, the automatic cuff-inflation feature of the tonometer device was disabled. This was critical to assess hemodynamic transient responses. Two-minute steady-state data recordings were made in each subject. Data were then recorded during one or more of several hemodynamic transient maneuvers: Valsalva maneuver, manual compression of the upper abdomen, intravenous bolus of 200 μg nitroglycerin, or balloon obstruction of inferior vena caval inflow. Subjects were advised to keep the instrumented wrist and arm still during data acquisition.
Calibration of Radial Tonometry
Although the radial tonometry signal was already calibrated to an oscillometric cuff systolic and diastolic pressure (a component of the Jentow device), there was still some uncertainty regarding the accuracy of this calibration. Because our main goal was to test the reliability of reverse transformation from radial to aortic waveforms, we first minimized such potential calibration errors by matching mean and diastolic pressures of the radial pulse signal to those measured by aortic micromanometer for steady-state data.22 In a separate analysis, we then tested the sensitivity of the resynthesized aortic pressures to calibration errors in the radial signal.
Selection of Data During Hemodynamic Transients
Optimal applanation was occasionally lost during maneuvers such as Valsalva or abdominal compression, generally due to subconscious movement or stiffening of the instrumented wrist. Therefore, several sets of data recorded during these maneuvers were unreliable. Loss of adequate applanation was suspected in 6 of the 20 patients on the basis of a sudden marked loss of correlation between the two pressure recordings during the transient. These data tracings were not used for subsequent analysis.
Estimation of TF
TFs between aortic pressure and radial pressure signals were derived in each patient by the linear ARX model (see “Appendix”). This methodology yields more statistically stable and thus reliable spectral estimates from limited data compared with nonparametric (Fourier transform) approaches.23 Mean individual patient TFs and their variances were evaluated by three to five TFs estimated from separate steady-state data sequences (ITFss). Typical sequences reflected four to eight sequential beats with a total of 1000 to 2000 data points. A TF GTFss was obtained by averaging the ITFss from all 20 patients. For each of the 14 subjects with stable hemodynamic transient data, an ITFtr was determined by averaging functions derived from data reflecting the wide range of hemodynamic conditions measured during the transient. The ITFtr results were also group averaged, yielding a GTFtr.
TFs were calculated in the physiological (forward) direction, ie, transforming aortic pressure to radial pressure as occurs with blood flow from central to peripheral vasculature. To reconstruct the aortic waveform from radial tonometry, the individual and generalized inverse TFs (ITFss−1, ITFtr−1, and GTFss−1) were calculated (see “Appendix”).
Evaluation of Reconstructed Aortic Pressure Waves at Steady State
For each subject, two reconstructed steady-state aortic pressure waves were derived by applying the GTFss−1 and ITFss−1 to steady-state data. Aortic, radial, and the two estimated aortic pressure waves were then signal averaged to generate four pressure waveforms for each cardiac cycle. Systolic, diastolic, and pulse pressures; total arterial compliance; and AI24 were calculated from each ensemble of pressure waves and compared. Waveforms were phase aligned, and point-by-point differences and regressions were used to compare waves. Overall agreement between the radial, reconstructed aortic, and invasive aortic pressures were quantified by the sum of squares of these differences normalized to the number of data points.
An error-sensitivity test was applied to evaluate the impact of the radial pressure calibration inaccuracies on estimated central pressures. Because the most common inaccuracy is in the diastolic pressure measurement, radial pressures were modified so that the input diastolic blood pressures were increased or decreased by 15 mm Hg in steps of 5 mm Hg, with systolic pressure kept constant. The GTFss−1 was then applied to this altered radial data, and the influence of calibration error on estimated aortic systolic pressure was determined.
Evaluation of Reconstructed Aortic Pressure Waves During Hemodynamic Transients
We reconstructed three sets of aortic pressure waves from radial pressure waveforms using (1) the GTFss−1, (2) respective ITFss−1, and (3) respective ITFtr−1. Beat-to-beat systolic, diastolic, and pulse pressures from aortic, radial, and the three aortic pressure estimates were determined for each transient sequence. Comparisons were examined by linear regression analysis, with measured central aortic pressures as the dependent variable. In addition, the maximal absolute pressure differences between estimated and measured aortic data during the transient were determined. Thus, we tested the extent to which the transformed radial pressure data could accurately predict the extent of central aortic pressure change induced by the various interventions.
Data are presented as mean±SD. Comparisons between measured and estimated parameters were performed by ANOVA. Significance was accepted at a value of P≤.05.
Aortic-Radial Pressure Differences and TF Analysis
Fig 1A⇓ shows typical features of central aortic and radial tonometry pressure waveforms. The radial waveform at steady state has a more rapid upstroke and rapid decline from peak, enhanced secondary oscillations at the dicrotic notch, and higher peak systolic and pulse pressures. Resting radial systolic pressures exceeded aortic pressure by 10.3±9.4 mm Hg (P=.001), or 8% on average. At maximal pressure reduction (mean 40-mm Hg decline in systolic pressure) during hemodynamic transients, this disparity rose to 17±10 mm Hg, or 16%.
Fig 1B⇑ displays the two GTFs describing the transformation from aortic to radial pressure waveforms. The GTFss (n=20) and GTFtr (n=14) were very similar. The peak amplitude of the GTFs occurred between 4 to 5 Hz (4.38±0.74 and 4.35±0.66 Hz), reaching an amplitude of ≈2.5× the value at zero frequency (2.66±0.66 and 2.54±0.42). However, as indicated by the 95% CIs, there was considerable interpatient variability. The steady-state interpatient coefficient of variation (SD×100/mean) was 25.3% for peak amplitude and 16.9% for the frequency of peak amplitude. Steady-state intrapatient variability was less, with a mean of 6.0% for the peak amplitude (range, 0.9% to 21.0%) and 2.9% for frequency of peak amplitude (range, 0.0% to 10.4%). However, this variability was greater (14.8% and 9.8%, respectively) during hemodynamic transients, with 28.5% of patients displaying >20% change in the peak TF amplitude.
Because the GTFss and GTFtr were similar, only the GTFss−1 was used for waveform resynthesis analysis. The steady-state TF previously reported by Karamanoglu et al20 is also shown in Fig 1B⇑ and was similar to those derived for the present study but with slightly greater variance and amplitude.
Reconstruction of Aortic Pressure Waveform at Steady State
Fig 2⇓ displays examples of pressure tracings for measured central aortic and radial tonometry pressures and estimated aortic pressures from transformed radial data using the GTFss−1 and ITFss−1. Use of the GTFss−1 yielded a waveform with pulse amplitude and contour similar to the centrally measured wave. Application of the ITFss−1 yielded very similar results, with somewhat better fidelity for reproducing high-frequency fluctuations such as the systolic inflection. Fig 2⇓ also displays regressions of radial or transformed (estimated) aortic pressure waveforms versus measured central aortic pressure. There was slightly greater accuracy in waveform estimation (indexed by minimal area of the plot) with the ITFss−1.
Table 2⇓ lists group hemodynamic data derived from central aortic pressures and compares them to values measured from the raw radial pressure tracings and to values estimated after GTFss−1 or ITFss−1 transformation of the radial pressures. GTFss−1-estimated central arterial pressures differed from measured values by ≤0.2±3.8 mm Hg. ITFss−1 transformation reduced this variance to 0.9 mm Hg. Normalized sum-of-squares differences between aortic and radial pressure waves averaged 209±201 mm Hg2 during the cardiac cycle. Corresponding values for the reconstructed aortic pressure wave derived by the GTFss−1 or ITFss−1 were 7±6 and 2±2 mm Hg2, respectively. Thus, GTFss−1 yielded a 96% improvement in the fit between measured and estimated central aortic pressure waveform (P<.001), and the ITFss−1 improved the fit by an additional 3% (P<.001). Error-sensitivity analysis revealed that a 10-mm Hg error in radial diastolic pressure calibration yielded only a 3-mm Hg mean deviation in aortic systolic pressure. This result was similar with both GTFss−1 and ITFss−1 analysis.
Total vascular compliance based on radial pressures was overestimated by 26.4%; this was markedly improved to only a 6.2% error when the GTFss−1 transformation was used. Application of the ITFss−1 to the same radial pressure data did not improve this mean result.
The central arterial AI calculated from reconstructed waveforms was significantly lower than that calculated directly from the aortic pressure wave (both P<.05). On average, the mean AI by GTFss−1 analysis was 30±45% lower. The variance in this underestimation was reduced when the ITFss−1 was used.
Hemodynamic Transient Analysis
Fig 3⇓ displays examples of pressure data measured before and during transient reductions in arterial pressure induced by inferior vena caval occlusion. Although radial pressure generally tracked aortic pressure during the transient, there was an increasing disparity between the two signals at the nadir of the response with respect to both amplitude and waveform. This is highlighted in the lower tracings in Fig 3⇓. Regression analysis of raw radial versus aortic pressures during such transients (Table 3⇓) revealed that the diastolic pressure had the strongest correlation. The maximal disparity between radial and aortic systolic (and pulse) pressures averaged 25±8 mm Hg and was not always observed at the pressure nadir (cf Table 1⇑). Thus, an intervention that appeared to reduce arterial systolic pressures by 15 mm Hg, as measured at the radial artery, might have actually lowered central aortic pressure by as much as 40 mm Hg.
Fig 4⇓ displays the same patient data with radial pressures transformed by GTFss−1 (Fig 4A⇓) or ITFss−1 (Fig 4B⇓). There was marked improvement in concordance of the amplitude at rest and throughout the entire pressure transient with GTFss−1. Slightly better concordance was achieved with ITFss−1 analysis, particularly with respect to the precise waveform shape.
Examples of regressions of systolic, diastolic, or pulse pressure for radial and transformed radial pressures against measured aortic pressure during hemodynamic transients are shown in Fig 5⇓. Application of the GTFss−1 shifted the regressions toward the line of identity, and a slight further improvement was observed if the ITFss−1 was used. There was no further benefit from ITF−1 derived from beats at varying loads (ITFtr−1). Group data in Table 3⇑ support these examples.
The accuracy of GTFss−1 or ITFss−1 resynthesis of central aortic pressure waveforms during a transient loading change depended on the constancy of TF. Although the TF was constant on average, several patients displayed marked changes in TF with load reduction. Fig 6⇓ shows an example of this response. ITFs were calculated from cycles selected during the fall in arterial load. In the patient whose data are shown in Fig 6A⇓, these ITFs were little altered, whereas in the patient whose data are shown in Fig 6B⇓, there was a marked change in ITF during the transient. No single constant TF could therefore accurately reconstruct pressure waveforms during transients in such a patient. It should be noted that this degree of intrapatient variability of TF (coefficient of variation for peak amplitude >20%) was less common, occurring in 4 of 14 subjects.
This study demonstrates that clinically acceptable predictions of central arterial pressure and the pressure waveform can be obtained by mathematical manipulation of radial pressure waves by use of a GTFss−1. These results extend earlier data20 by showing, rather surprisingly, that this method works despite marked changes in pressure induced by hemodynamic transients and that equally surprisingly, only relatively small additional improvement in the prediction is achieved if an ITF−1 is used for each patient. Application of this approach to radial pressure data should improve titration of vasodilators and other medications, as it is well recognized that radial pressures can underestimate the hemodynamic benefit of such drugs.25
The amplitude and phase configuration of the TF relating aortic to radial pressures were generally similar among patients as well as within patients during hemodynamic transients. This finding provides insight into the likely sources for TF variability. The marked changes in radial and central aortic pressure waveforms when mean pressure was lowered reflect the pressure dependence not only of vascular compliance but also of the timing and magnitude of reflected waves. When pulse wave velocity is low, reflected waves return to the aortic region after end ejection, with minimal effects on aortic systolic pressure. When velocity is high, the reflected waves return sooner, augmenting systolic pressure.2 The dependence of pulse wave velocity, arterial compliance, and reflected waves on mean blood pressure varies with age and vascular disease.26 27 28 All of these considerations might lead one to suspect that a generalized TF approach should not work. Yet the opposite was demonstrated in most patients, suggesting that anatomic factors dominate over physiological conditions in determining the TF.
The finding that the GTFss−1 works nearly as well as an ITF−1 suggests that differences in body morphology, age, and sex are not as strong determinants of the TF as the pressure amplification due to vascular branching in the upper extremity that occurs in everyone.29 Indeed, our TF data are in close agreement with previously reported results (peak at 4 Hz with amplification of 2.8).20 Vascular properties in the upper limb are less affected by aging, arterial pressure, or various maneuvers compared with vessels in the trunk and lower limbs,26 27 28 30 and therefore this observation might not hold true for TFs between femoral and aortic pressures.
The present study also showed that in a small percentage of individuals, the TF deviated from this generalized form and that it could also vary as a function of mean blood pressure or other physiological conditions (eg, Fig 6⇑). In such patients, any constant TF, whether calculated as a generalized or individualized function, would yield less reliable predictions. It is possible that part of this disparity stemmed from subtle inaccuracies in applanation during the hemodynamic transients. However, as correlation coefficients between tonometric radial and central aortic systolic or diastolic pressures remained >0.9, this is less likely. Direct radial pressure recordings will be needed to further explore this question.
Although peak and trough pressures were well predicted by the GTFss−1, the exact shape of the central aortic pressure waveform was less well reproduced. It was improved upon by the ITFss−1, but this requires invasive measurements of aortic pressures. Conceivably, individualization of the TF might be achieved by analysis of simultaneous carotid and radial tonometry signals, but this could introduce additional errors and artifacts. For indexes less dependent on the precise waveform contour, such as total arterial compliance, which was estimated by a method using the area under the diastolic portion of the decay curve,1 the GTFss−1 provided reasonable estimates.
For parameters such as AI, which are more dependent on the high-frequency content (≥8 harmonics; see Fig 7⇓) of the pressure wave, this limitation can be problematic. Calculation of AI was in part compromised by the need to low-pass filter the GTF−1, which was required to reduce noise in the reconstructed waveform. The filter cutoff was set by the structure of the ITF−1 to prevent amplification of higher frequencies (within the range of 9 to 12 Hz; see “Appendix”). AI was very dependent on the exact location of this cutoff, contributing to the underestimation.
The TF can be estimated by several techniques. Commonly used Fourier transform approaches are often limited by high variance in the estimated TF and the need for long data sequences to reduce this variance by spectral-estimate averaging (see “Appendix”).23 Such long data sequences can only be acquired during steady state. To overcome this limitation and enable TF estimation from short hemodynamic transients, a more efficient parametric estimation algorithm23 was used for the present study.
Our TF did not approach the value of 1 at 0 Hz as might be expected because the means of both central aortic and peripheral radial pressures were matched. However, we also matched the diastolic blood pressures of both signals, even though the real radial diastolic blood pressure is slightly lower.19 By forcing the two diastolic pressures to be the same, energy was artificially introduced into the radial pressure input so that the TF showed some deamplification in the low-frequency range. This calibration technique is practical and widely used; therefore, the resulting TF is appropriate. Furthermore, even when a correction was made to offset this low-frequency deamplification, the results were within 1 mm Hg of those presented.
The TF between ascending aortic micromanometer pressure and radial tonometric pressure in reality combines two functions: one between aortic pressure and the true radial pressure and the second between radial pressure and the tonometry signal. Because we did not invasively instrument the radial artery with a second micromanometer, the influence of this latter component in our population is unknown. Factors such as the thickness of the intervening subcutaneous tissue, positioning of the tonometric pressure sensor, change in the hold-down pressure during hemodynamic transients, or movement of the fingers and wrist could theoretically alter this TF and thus the radial pressure waveform. The TF between invasive radial pressure and the tonometry signal has been studied previously,21 however, and revealed a flat gain to 6 to 7 Hz, which covers the major portion of the frequency range of interest. Thus, we feel that this second function is not of major significance. Most importantly, we have shown that the reverse-TF approach enabled estimation of invasive aortic pressures from noninvasive data, which was the primary goal.
Because of well-recognized discrepancies between the central and peripheral arterial pressure waveforms,29 it is inadequate to monitor hemodynamic status or pharmacological responses from radial pressures. When a generalized TF is applied, the radial pressure recorded either invasively or noninvasively by a tonometric device can be used to reconstruct the central aortic pressure waveform with clinically acceptable accuracy for systolic and pulse pressures and to estimate vascular compliance. This approach should substantially reduce the uncertainties resulting from radial pressure monitoring for critical care, chronic hypertension therapy, and pharmacological trials.
Selected Abbreviations and Acronyms
|GTF||=||generalized transfer function|
|GTFss||=||generalized steady-state transfer function|
|GTFss−1||=||inverse generalized steady-state transfer function|
|GTFtr||=||generalized transient transfer function|
|ITF||=||individual transfer function|
|ITFss||=||individual steady-state transfer functions|
|ITFss−1||=||inverse individual steady-state transfer functions|
|ITFtr||=||individual transient transfer function|
|ITFtr−1||=||inverse individual transient transfer function|
ARX Parametric Model
The ARX linear model23 describes the properties of a system on the basis of its immediate past input and output data as where T(t) and T(t-I) [I=1,2…na] are present and previous output (radial tonometer) discrete measurements, respectively, and P(t-I) are previous input (aortic pressure) discrete measurements. The a’s and b’s are the parameters of the model, and na and nb represent the order of the model, ie, the number of previous input-output values used to describe the present output.
Model Order Selection
The model order for this study was set to be [10,10], ie, 10 “a” coefficients and 10 “b” coefficients were determined for each TF estimate. The minimal model order was set to be [5,5] to achieve a similar spectral estimate as given by nonparametric methodology (Fourier transform) during steady state. The maximal model order was set at [20,20] on the basis of calculating the Akaike Information Criterion, which measures the estimation performance against the model order.23 The actual model order for the estimation process was selected by testing whether a higher model order yielded a change in the spectral estimate that was larger than the SD of the estimate. This approach was justified because increasing the model order, although resulting in better fit of the measured data, usually increases the variance of the estimate.23 Determination of the smallest model order with sufficient spectral resolution was essential to enable reliable estimation based on short data sequences during hemodynamic transients.
Comparison With Fourier Transform Estimation
Parametric models can be compared with nonparametric methods, eg, TF estimation with the Fourier transform. When the same data set was used, the parametric and nonparametric estimates produced similar results, although the parametric methodology provided a smaller variance of the estimate (Fig 8⇓). The variance of the Fourier-derived spectrum was similar to that of the ARX-derived spectrum only when the larger data set was used.
Direct and Inverse TFs
Direct TFs that correspond to the physiological system were estimated with the aortic pressure used as input and the radial tonometer signal as output. To enable reconstruction of the aortic pressure from the radial tonometer signal, an inverse TF was directly derived from the direct TF (Equation 1) as follows: A problem arises because as the direct TF approaches low gain levels in the frequency range above 8 to 10 Hz (Figs 1⇑ and 8⇑), the inverse TF will have high gains at these frequencies, which amplify high-frequency noise and distort the reconstructed aortic pressure wave. This problem can be solved by convolving the inverse TF with a low-pass filter having a cutoff frequency set at the frequency at which the magnitude of the direct TF gain function declines below 1, except for those cases that resulted in cutoff frequency <9 Hz, in which an average value of 11 Hz was used.
This study was supported by National Institute of Aging grant AG-12249 (Dr Kass), a fellowship grant from Colin Medical Instruments Corporation (B. Fetics), and a Fogarty Foundation Fellowship Award (Dr Nevo). The authors are grateful to Colin Medical Instruments Corp for loaning the tonometer used in these studies. Dr Chen is a Clinical Research Fellow from the Division of Cardiology, Department of Medicine, Veterans General Hospital–Taipei and National Yang-Ming University, Republic of China.
- Received September 11, 1996.
- Revision received November 12, 1996.
- Accepted November 19, 1996.
- Copyright © 1997 by American Heart Association
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