Abstract Although systolic pressure in the ascending aorta (AA) can be determined accurately from the radial arterial waveform using a single generalized transfer function (TF) of the upper limb, a better on-line methods is needed for accurate noninvasive synthesis of the AA pressure contour to characterize left ventricular contractile function and ventricular-vascular coupling. AA, tonometric carotid (CA), and photoplethysmographic finger (FA) arterial pressure waveforms were recorded in 12 subjects (10 male, aged 59.1±10.3 years, mean±SD) during cardiac catheterization. The AA-FA TF was estimated using (1) a single generalized TF (GAA), (2) individualized TFs directly determined from CA-FA recordings in each patient (DAA), and (3) individualized TFs computed from CA-FA recordings in each patient with a mathematical model of the human upper limb (MAA). AA pressure waveforms were synthesized from FA recordings in real time using convolution windows derived from these TFs. Under steady state conditions, the root mean square error (RMSE) between measured and synthesized AA was lower by DAA (3.3±1.3 mm Hg) and MAA (3.9±1.2 mmHg) than by GAA (4.8±2.0 mm Hg, P<.05). During dynamic load alteration induced by the Valsalva maneuver, however, the MAA method performed better (5.4±2.8 mm Hg) than both the GAA (5.8±3.3 mm Hg, P<.05) and DAA (6.5±2.7 mm Hg, P<.01) methods. The beat-to-beat AA contour can be accurately and noninvasively synthesized on-line using individualized TFs. During dynamic load alteration, individualized TFs derived with an upper limb arterial model provide greater accuracy.
The ascending aortic pressure wave contour closely matches that of the left ventricle during ejection, which is a requisite for assessing left ventricular contractile function and left ventricular-vascular coupling.1 Conventional noninvasive blood pressure techniques record blood pressure in the upper limb, but the upper limb pressure waveform differs from the ascending aortic waveform under normal conditions,2 during exercise2,3 and respiratory maneuvers,4 and after vasodilation.5–7 To resolve these differences, several attempts have been made to synthesize the ascending aortic pressure pulse from various peripheral pulses. These attempts have included synthesis of the pulse from the upstroke of the brachial waveform by ECG-gated sphygmomanometers,8–10 application of standing wave concepts,11 and use of carotid12,13 and subclavian arterial waveforms14,15 as surrogates for the central aortic pressure waveform. These methods require steady state hemodynamic conditions for several cardiac cycles, precluding examination of dynamic load alterations. They also ignore the effects of wave propagation and wave reflection. These factors can be important determinants of the pressure waveform depending on the measurement site, the age, the vasoactive state, and the heart rate.
Recently, the ascending aortic and peripheral upper limb pressure waveforms in human subjects were related in the frequency domain by transfer function analysis.16 It was found that this relationship is similar over a wide range of different subjects, and is relatively stable during vasodilation by nitroglycerin. Consequently, it proved possible to use a single, generalized upper limb transfer function to estimate the central aortic systolic pressure in different individuals with considerable accuracy.16 Subsequent analyses of these findings with a mathematical model of the upper limb have indicated that the proximal arterial properties of the upper limb, which are strongly affected by aging and vasoactive drugs, have little influence on the transfer function.17 Nevertheless, this generalized transfer function technique had several limitations. First, the technique assumed that the proximal and distal arterial properties of the upper limb were virtually constant between individuals and interventions. Obviously, this assumption constrained the accuracy of the determination of the ascending aortic pressure waveform. Second, the frequency domain approach involved acquisition of the entire peripheral pressure waveform for each beat before it could be transformed into the central waveform, precluding on-line waveform synthesis in real time. Third, the technique provided an interpolated transfer function estimate, thereby constraining its accuracy at intermediate frequencies. Fourth, no information about the arterial properties of the upper limb was provided, precluding analysis of wave propagation/reflection effects in the upper limb.
In this study, we addressed these deficiencies by (1) making on-line pressure waveform synthesis possible, (2) individualizing the transfer functions for each subject, (3) usinga mathematical model to obtain a continuous transfer function, and, thereby, (4) estimating various arterial properties of the upper limb.
Subjects and Study Protocol
Sixteen subjects (2 women) aged 56.7±9.8 (mean±SD) years (range, 44 to 73 years) were recruited from patients undergoing routine diagnostic cardiac catheterization for suspected coronary artery disease. All but one with dilated cardiomyopathy had normal left ventricular function (calculated left ventricular ejection fraction on contrast ventriculography >55%). One patient had evidence of aortic valve insufficiency and one had a transplanted heart. All gave informed consent to participate in the study, and the procedures followed were in accordance with institutional guidelines. Left heart catheterization was performed via an 8F sheath in the femoral artery. Ascending aortic and peripheral arterial pressures were recorded before the routine measurements. Ascending aortic pressure waveforms were recorded with a 6F micromanometer-tipped catheter (model SPC-360, Millar Instruments). Finger arterial pressure was recorded using a photoplethysmographic device (Finapres 2300, Ohmeda). The finger cuff of this device was attached to the middle phalanx of the second or third digit of the left hand. Care was taken in the selection of proper cuff size and proper registration of the finger pulse. Steady state finger pressures were recorded for at least 10 minutes to ensure a consistent pressure waveform before data acquisition. The central aortic and finger pressure waveforms then were recorded simultaneously under steady state conditions and during forced expiration into a partially occluded mouthpiece sufficient to maintain a constant mouth pressure of approximately 20 mm Hg for 20 seconds (Valsalva maneuver). The expiratory pressure was measured using a pressure transducer (model SPT 301, Millar Instruments). After return to steady state conditions, the central aortic and finger pressure waveforms were recorded simultaneously with the carotid arterial waveform, which was recorded with arterial tonometry (model SPT 301, Millar Instruments). Data were digitized on-line using a 12 bit analog/digital converter at 100 Hz, and stored onto a computer hard disk using custom-made software.
On-line Synthesis Technique
The ascending aortic pressure waveform can be related to the finger arterial pressure waveform in the frequency domain by a transfer function, H(ω)AA-FA, that represents the wave propagation/reflection phenomena present in the upper limb arterial system (Fig 1⇓). Once transfer functions are determined successfully, it is possible to synthesize the aortic waveform from peripheral waveforms by using frequency domain techniques.16,18,19 In this study, we used a time-domain technique. Because the multiplication operation performed in the frequency domain is equivalent to a convolution operation in the time domain and vice versa,20 the h(t)FA-AA, the time-domain representation of 1/H(ω)AA-FA, can be obtained by inverse Fourier transform (Fig 1⇓, bottom). The aortic waveform, AA(t), then can be synthesized on-line by convolving the measured finger waveform, FA(t), by the h(t)FA-AA. Because the convolution operation is a multiplication operation with memory, the synthesized aortic waveform will be delayed by an amount corresponding to the depth of this memory. Although this delay alters the actual temporal relationship between the two waves, temporal alignment is possible by subtracting this known time delay from the synthesized aortic waveform signal.
Customized Transfer Functions
In studies where precise determination of the time delay and the wave shape is crucial, individual customization of the upper limb transfer is required to account for differences between individuals (ie, the age, sex, medication, arm length, vessel diameter, and physical properties of the arteries) and in measurement conditions. In this study, we used two approaches to customize the transfer function.
Customization of the upper limb transfer function, H(ω)AA-FA, against actual aortic pressure requires invasive aortic catheterization. To overcome this limitation, we first synthesized the aortic pressure waveform from noninvasive carotid arterial waveform recordings using a previously validated generalized transfer function between the ascending aorta and carotid artery, H(ω)AA-CA.21 This transfer function, derived from a reduced model of the carotid arterial system as a single viscoelastic tube terminated by a modified windkessel, permits accurate derivation of the aortic pressure contour.21 Second, we determined for each individual the upper limb transfer function, H(ω)AA-FA, using the synthesized aortic pressure waveform and its paired finger waveform. Third, we calculated the intermediate frequencies of this transfer function that are not the integer multiples of the fundamental frequency (ie, the heart rate) by interpolation. Fourth, a convolution window, h(t)FA-AA, was calculated from this interpolated transfer function for each patient.
One limitation of the direct method described above is the spectral interpolation required to estimate the intermediate components of the transfer function because the transfer function can have various features depending on the proximal and distal arterial properties.17 Spectral interpolation might not accurately reflect these features, and might estimate an unrealistic transfer function, especially when the fundamental frequency is high. This limitation can be overcome by calculating a continuous transfer function that takes the possible physical properties of the upper limb into account from the outset. For this purpose, we constructed a mathematical model of the human upper limb arterial system, and linked this with the carotid arterial model described above. The resultant combined model consisted of three viscoelastic tubes connected in series and terminated with a modified windkessel (Fig 2⇓, Table 1⇓). A detailed mathematical description of the model and its implications has been reported previously.17 The first viscoelastic tube of this model (equivalent element) represents the combined effect of carotid and subclavian-axillary arteries. The second and third elements represent the path between the axillary and radial arteries and between the radial and finger arteries, respectively.
Using the calibrated carotid pressure waveform and finger pressure waveform and the model, we estimated five model parameters describing this reduced model by iteration. These were the characteristic impedances of the equivalent element (ZEQ), axilla-radial (ZAR), and radial-finger (ZRF) arterial segments, windkessel time constant (τ=R×C) and the reflection coefficient, Γo=R/(R+2ZRF) (Fig 2⇑). There is a unique relationship between these last three model parameters and the actual parameters peripheral resistance (R), peripheral compliance (C), and wall elastance (E) of the radial-finger segment.17
For each measured carotid and measured finger pressure waveform, we traversed the five-dimensional parameter space (ie, ZEQ, ZAR, ZRF, Γo, and τ) to obtain a transfer function, H(ω)CA-FA that yielded the minimum discrepancy (quantified as the root-mean-square-error, RMSE) between measured and synthesized finger pressure waveforms. An initial set of values for the model parameters was selected to represent the minimum values observed in vivo (ZEQ=278, ZAR=532, and ZRF=697 dyne · s/cm3, τ=0.0 seconds, and Γo=0.4). These values correspond to an arm pulse wave velocity of 2.40 m/s, a zero peripheral compliance, and a peripheral resistance of 1626 dyne · s/cm3. The iteration continued with increased values for the model parameters until a maximum set of model parameters (ZEQ=566, ZAR=1086, and ZRF=1422 dyne · s/cm3, τ=0.5 seconds, and Γo=0.99) was reached. In the resulting RMSE space, a global minimum was found. The model corresponding to this global minimum was considered to represent the combined carotid–upper limb arterial system. Consequently, the final model was not dependent on the initial set of model parameters selected.
The individualized carotid–upper limb transfer function, H(ω)CA-FA, and the transfer function between the ascending aorta and carotid arterial system, H(ω)AA-CA, described above then were used to determine the individualized transfer function between the ascending aorta and finger artery, H(ω)AA-FA, from the relation shown below. For each patient, a convolution window, h(t)FA-AA, was calculated from H(ω)AA-FA, as described above in “Direct Method.”
Generalized Transfer Function
Generalized transfer functions using carotid, radial, and brachial pressure waveforms have been described previously.16,21 In this study, we extended these methods to estimate a generalized transfer function between the ascending aorta and finger artery for comparison with the customized methods described above. This generalized transfer function differs from previous generalized transfer function in that it was derived from combined carotid–upper limb model described above. The model parameters determined for each of the individuals were averaged to obtain an average model for all subjects represented by a generalized transfer function, H(ω)CA-FA. This generalized H(ω)CA-FA was then used in Equation 1 to determine a generalized H(ω)AA-FA from which a generalized convolution window, h(t)FA-AA, was calculated.
Series (16 to 20 beats) of ascending aortic, carotid, and finger pressure waveforms were averaged. This number of beats reflects the best compromise between the duration of the Valsalva maneuver and the limited time allowed to use carotid tonometry during cardiac catheterization. The onset of each beat was determined using the first derivative of the aortic pressure signal, dP/dt. A threshold based on the maximum dP/dt signal is used to identify the beginning of each beat. The averaged carotid waveforms for each subject were then calibrated using the mean and diastolic pressures of the finger waveforms. This method assumes that the mean pressure drop along the upper limb is negligible and that amplification due to wave reflection predominantly alters the systolic portion of the wave.17 These averaged arterial waveforms were then used to determine the convolution windows described above.
The discrepancies between all the synthesized and measured aortic waveforms were calculated to document the benefit of application of each synthesis method. This was done under steady state conditions and during the Valsalva maneuver to assess the static and dynamic behaviors of each method. Finger waveforms were convolved with the convolution windows to obtain the synthesized aortic pressures. For each beat, the peak pressures (diastolic and systolic), mean pressure during systole, mean pressure during diastole, and pressures during various time intervals of the cardiac cycle were calculated. The time-domain features extracted for this purpose were the time of occurrence of the foot of the pulse (Tf), the early systolic shoulder (T1), the late systolic shoulder (T2), and the incisura (Ti). The RMSEs along the intervals between these time points were then used to express differences between the measured ascending aortic and measured finger artery pressures (RMSE AA-FA) and between the measured and predicted ascending aortic pressures for each beat using the direct method (RMSE AA-DAA), the modeling method (RMSE AA-MAA), and the generalized transfer function method (RMSE AA-GAA). These feature points were not always clearly identifiable during the Valsalva maneuver. Therefore, only the RMSE for the whole arterial waveform was calculated during the Valsalva maneuver.
The discrepancies between measured and predicted aortic pressure contours were also analyzed using the previously defined shoulder index (SI).7 This index is similar to, but more consistent than, the widely accepted augmentation index (AI) that has been used to quantify the effects of wave reflection.22 As the peak pressure occurs early in systole in peripheral waveforms, the AIs derived from peripheral waveforms are often negative.22 In contrast, the SI is the ratio of the second shoulder’s amplitude to the first shoulder’s amplitude and is never negative. SI is defined as where PTf, PT1, and PT2 are the pressures measured at the wave foot, at the early systolic shoulder, and at the late systolic shoulder, respectively. The algorithm used to extract these feature points automatically has been described previously.7
Data were expressed as mean±SD and analyzed using a commercially available statistical package (Instat, Graphpad Software). Differences between measured and predicted ascending aortic waveforms were compared using repeated measures ANOVA followed by Student-Newman-Keuls multiple comparisons tests. A value of P<.05 was considered significant.
We were unable to obtain technically adequate finger waveforms from one individual and carotid waveforms from three individuals. Table 2⇓ describes the characteristics of the remaining 12 subjects.
There were significant differences between finger, central aortic, and carotid waveforms (Fig 3⇓). Higher systolic pressures were measured in the finger than in the aorta (Table 2⇑). The systolic pressure in the finger waveform was characterized by an early peak, while it was characterized by a late peak in the ascending aortic and carotid waveforms. Consequently, the SI was higher in the ascending aorta than the finger (1.57±0.20 versus 0.64±0.10, P<.001) and became smaller as the waveform traveled distally (Fig 3⇓, top). The initial upstroke of the carotid and finger waveforms also was delayed with respect to the ascending aortic waveform, the delay being greater in the finger waveform. These observations were confirmed by the transfer function between the ascending aortic pressure waveform and the finger waveform (Fig 4⇓). In all patients, the moduli of the transfer function were higher than one between 0 and 8 Hz, indicating amplification of these components. The phase difference was also considerable, approximating to a value of 2π at 8 Hz. The transfer functions exhibited considerable interindividual variability, reflected by scatter in modulus and phase.
Under control conditions, application of all three synthesis methods transformed finger waveforms closer to aortic pressure waveforms by decreasing the early systolic peak and augmenting the second peak (Fig 3⇑, bottom). The resulting differences between peak and mean systolic and diastolic pressures of the synthesized and measured aortic waveforms achieved statistical significance but were negligible in physiological terms (Table 3⇓). During synthesis of the central aortic pulse, the high-frequency components of the peripheral pulse were lost due to filtering and windowing effects. Yet, the point of the incisura and the shoulders and the upstroke all were still identifiable as inflection points in the derived pressure wave.
The modeling (AA-MAA) approach yielded an overall RMSE value of 3.9±1.2 mm Hg at characteristic impedances of 486.3±50.13, 932.2±96.1, and 1221.2±125.9 dyne · s/cm3 for the ZEQ, ZAR, and ZRF, respectively (Table 4⇑). The predicted time constant, τ, was 216.7±185.5 ms, and the predicted reflection coefficient, Γo, was 0.64±17. As judged from the overall RMSE values, the direct customization method yielded the best approximation of the ascending aortic pressure waveform (AA-DAA: 3.3±1.3 mm Hg), followed by the modeling method (AA-MAA: 3.9±1.2 mm Hg), and the generalized transfer function method (AA-GAA: 4.8±2.0 mm Hg). The discrepancy between AA and FA was maximal during the early part of systole, and became progressively smaller later in the cardiac cycle, the diastolic period of the FA being the closest to the AA (Fig 5⇓). The RMSE for the direct method remained unchanged during systole (T1-T2: 3.6± 1.7 mm Hg, T2-Ti: 5.08±2.9, P=NS). The RMSE for the modeling method increased during late systole (T1-T2: 4.5±1.7 mm Hg, T2-Ti: 7.8±3.1 mm Hg, P<.001), as did the RMSE for the generalized method (T1-T2: 5.3±3.41 mm Hg, T2-Ti: 7.4±2.9 mm Hg, P<.05). The SIs derived from the synthesized aortic waveform using the direct method (1.50±0.2) and that derived from the measured aortic waveform (1.57±0.2) were not significantly different. In contrast, both the modeling (MAA: 1.28±0.2, P<.001) and generalized transfer function methods (GAA: 1.25±0.1, P<.001) underestimated the SI.
Fig 6⇓ displays an example of on-line calculation of the aortic pressure wave from the finger pressure wave using convolution windows during preload reduction with the Valsalva maneuver. The synthesized waveforms were close to their ascending aortic counterparts before and during the dynamic alteration of the ascending aortic waveform. As opposed to control conditions, during the Valsalva maneuver, the MAA method performed better (RMSE 5.4±2.8 mm Hg) than both the GAA (5.8± 3.3 mm Hg, P<.05) and DAA methods (6.5±2.7 mm Hg, P<.01).
When combined with existing noninvasive techniques to determine the volumetric ejection contour of the left ventricle, the ability to accurately and noninvasively measure the left ventricular ejection pressure contour could provide a powerful tool for the assessment of ventricular contractile function and ventricular-vascular coupling. The ability to make these noninvasive measurements on-line during beat-to-beat alterations in loading conditions would further enhance the value of the technique. It has been demonstrated previously that transfer functions could be used to estimate the central aortic pressure waveform from the peripheral upper limb pulse.16,18 In these studies, however, transfer functions were determined between the ascending aorta and brachial/radial sites using invasive techniques and were generalized for a population. Furthermore, these transfer functions were applied only in the frequency domain, necessitating waveform averaging that limits their use to off-line analysis of steady state data.
In this study, we extended these earlier techniques by making the pressure measurements noninvasive so that they could be used repeatedly in an outpatient setting. The transfer functions were also tailored for each individual using two different techniques. It is important to note that we derived time-domain representations of these transfer functions as convolution windows. This technique enabled us to synthesize the aortic pressure waveform in real time. We demonstrated the utility of this real-time technique during beat-to-beat alteration of the arterial pressure contour induced by the Valsalva maneuver.
Upper limb transfer functions were determined in this study using noninvasive carotid and finger pressure waveform recordings. Finger and aortic pressure waveforms are considerably different (Figs 3⇑, 5⇑, and 6⇑). These differences are seen mostly during systole, and are caused by reflected waves originating from the periphery. As a consequence of this phenomenon, the early systolic upstroke of the finger waveform is amplified, resulting in higher systolic pressures. This finding is confirmed by the transfer function between the ascending aorta and the finger artery (Fig 4⇑) and RMSEs calculated between the finger and aortic pressure waveforms (Fig 5⇑). The transfer function indicates that the amplification of the aortic pressure waveform is frequency-dependent, and that it can be as high as fourfold at 4 Hz (240 beats per minute [bpm]). Under normal circumstances, the heart does not beat at this frequency, but the pressure waveform contains significant harmonics at higher frequencies, especially during sharp pressure rises such as occur during early systole. This explains the observation that the RMSEs between the finger and aortic pressure waveforms are more pronounced during early systole and become progressively smaller as ejection progresses (Fig 5⇑). This also suggests that these differences should become more pronounced at higher heart rates. Fig 6⇑, which demonstrates an increased discrepancy between aortic and finger waveforms during phase 2 of the Valsalva maneuver, confirms this prediction.
Previously used frequency domain techniques can only be implemented off-line because it not only requires the recording of each peripheral pulse but also involves time-consuming steps of time-to-frequency domain and frequency-to-time domain transformations. As a result, to calculate a synthesized data point from an input sample point, the frequency domain approach using fast Fourier transform routines requires 2W log2 W complex multiplications, where W is the window length. In contrast, the convolution operation requires only W real multiplications, and is thus faster than the frequency domain approach (>4 log2 W times). Additionally, the actual hardware and software implementation will influence relative speed. For example, in our implementation based on a Pentium processor, we found that computation of a single data point using the convolution operation was 142 times faster than the fast Fourier transform approach (400 versus 57 000 μs, respectively).
The generalized transfer function used in this study differs from earlier work16 on several grounds. First, it is defined for the finger arterial site, permitting transduction of the pressure signal that is free of operator errors induced with the human-held transducer used at other arterial sites. Second, it was derived using a mathematical description of the upper limb arterial system. Third, because it is implemented using convolution windows, it provides real-time estimation of the aortic pressure waveform. This generalized transfer function is simpler to implement than the two customization methods. By definition, however, the generalized transfer function method ignores intersubject and interobservation variability. Despite this limitation, the generalized transfer function reproduced the features of the ascending aortic pressure waveform quite well, but to a lesser accuracy than the customized transfer functions. The mean RMSE between measured and synthesized waveforms with the generalized transfer function was 4.8± 1.2 mm Hg. This reasonably good agreement is not surprising given that the finger pressure waveform is band-limited at lower harmonics, where transfer functions are relatively consistent.16
The customization methods have the advantage of “calibrating” the transfer function to allow for anatomic differences, aging, vasodilation, effects of exercise, and certain physical maneuvers. Importantly, customization could be performed as the need arises. This could be achieved by computing the transfer function directly from actual recordings or via mathematical modeling of the upper limb.
The direct method used in this study to determine the transfer functions is computationally more efficient than the modeling method. Yet, it is more accurate than the generalized method, yielding an RMSE of 3.3± 1.1 mm Hg. Unfortunately, it attains this performance without providing any insights into the underlying arterial function.
The modeling method provides physiological variables that might be useful to understand the sources of variability in arterial function between individuals or with various interventions. It has been shown previously that the proximal arterial properties have little impact on upper limb transfer functions.17 Thus, the effects of aging, simulated by increased elastic modulus and increased proximal wall viscosity, had minor impact. In contrast, in the same study,17 the terminal properties (ie, the reflection coefficient and the time constant) were important determinants of pressure-wave amplification. Consequently, in this study, we paid special attention to determination of terminal properties. The reduced model of the upper limb used in this study predicted realistic proximal and distal arterial properties in human subjects (Table 4⇑). A pulse-wave velocity of 6.2±1.7 m/s has been reported for the brachial artery.23 This corresponds to a ZAR value of 651±14.4 dyne · s/cm3. A value of 0.8 for Γo was reported for the femoral artery.24 The modeling method also provides a continuos transfer function eliminating the need for interpolation required with the direct method. It is computationally costly, however, requiring around 600 complex multiplications per step.
Generalized Aortic-Carotid Transfer Function
In deriving the transfer functions between the ascending aorta and finger pressures in this study, we assumed a generalized transfer function between the ascending aorta and carotid artery while allowing for differences in the upper limb properties between subjects. We have shown previously that the former assumption leads to an RMSE of 3.4±1.3 mm Hg during synthesis.21 Based on this small error, one might argue that use of this generaliszed transfer function to synthesize the aortic waveform from the carotid waveform would be preferable to the finger pressure technique because it does not require other measurements and complex customization methods. Unfortunately, there are problems in registering and calibrating tonometrically recorded carotid pressure waveforms.12,14,15 It is difficult to attempt to maintain a constant applanation pressure for carotid tonometry during interventions that change the hemodynamics beat to beat. For example, this is a major impediment to the use of tonometry during the Valsalva maneuver. Use of sphygmomanometrically determined upper limb blood pressures to calibrate the carotid waveform is also difficult because the pressure contours are different. In this study we tried to eliminate these potential problems. The carotid waveforms that were used to determine upper limb transfer functions (generalized or custom-made) were recorded only under steady state conditions, and our method also used contour information in the carotid pressure recordings.
Application of this Technique to Other Arterial Sites
There are various peripheral sites in the body where pressures can be measured noninvasively. These sites include the carotid arteries, upper limb arterial sites (such as finger, radial, brachial, and subclavian arteries), and the arteries of the lower extremities, particularly the femoral and dorsalis pedis arteries. With the exception of finger arteries, however, these sites are not suitable for the determination of the ascending aortic pressure waveform on a continuous basis during physiological and pharmacological interventions that cause beat-to-beat changes in the arterial waveform. Hand-held pressure measurement techniques used at these sites provide only intermittent or uncalibrated waveforms. A newly introduced technique uses a multisensor array to overcome this difficulty.25 Measurement sites in the lower limbs are separated from the ascending aorta by major branches of the aorta. Using a mathematical model of the entire arterial tree, it has been shown, for example, that the vasoactive state of the visceral aortic branches determines the intensity of wave reflections.26 Consequently, the transfer function between the ascending aorta and the lower limb arterial sites may be unstable under varying physiological and pharmacological conditions.
The resynthesis of the aortic pressure is inevitably an operation of low-pass filtering of the peripheral pulse (the inverse operation of amplification is attenuation). Unfortunately, this operation reduces the amount of intermediate frequency components in the peripheral pulse, so that the synthesized pressure waveforms become rounder than the actual waveforms (Fig 4⇑). The combined carotid–upper limb arterial model used single values for the lengths, diameters, wall thicknesses, and wall viscosities of the tube elements. This may have restricted the recursion and introduced errors into the parameter estimation process (Fig 4⇑). Although this problem could easily be overcome by the use of state-of-the-art ultrasound systems to measure arterial diameters and wall thicknesses in individual subjects,23 we focused on determination of a transfer function suitable for synthesis in this study. The use of a single generalized aortic-carotid transfer function might not be appropriate if there is wide variation in carotid arterial properties. Our earlier work demonstrated that this variation was small,16 and the low RMSEs suggested that individualizing carotid arterial parameters is not necessary for the most likely applications of this technique. The use of tonometers to register carotid pressure waveforms has intrinsic limitations due to tonometer orientation and applanation pressure, as discussed above.12 Although we took extreme care to minimize these problems, they might also have affected our results. Also, all three methods relied on steady state carotid and finger recordings to determine the convolution windows. This might influence our results. Consistently higher RMSEs observed during Valsalva maneuver for all methods, than the RMSE at baseline, might be caused by altered properties of the upper limb arterial system.
This study demonstrates considerable interindividual variability in the upper limb transfer functions (Fig 4⇑). A closer analysis, however, reveals that most of this scatter is confined to higher frequency components of the spectrum (ie, above 3 Hz or 180 bpm). Several explanations for this behavior could be suggested, including measurement noise affecting the determination of spectral components at higher frequencies and the effect of viscous forces caused by wall and blood viscosities. It is known that these forces are important at higher frequencies and could be subject to physiological and anatomic variation. We did not investigate these effects. Nevertheless, it is clear from this study that the significance of these differences is relatively minor due to the limited bandwidth of the arterial waveform. When an average transfer function was derived from all patients, we were very successful in predicting the ascending aortic pressure contour and SI in individual patients. There is also the possibility that the finger pressure waveforms recorded noninvasively with the Finapres device might be different from their invasive counterparts, thereby contributing some error. Previous studies have indicated that this error is small if proper precautions are taken, particularly individual selection of proper cuff size and proper placement of the cuff.27 Also, our study population was necessarily small due to the invasive nature of the ascending aortic pressure measurement. It is possible that the methods described in the study might be sensitive to age, sex, clinical status of the subjects, and environmental conditions. Further studies are needed to ascertain the influence of these factors.
The time-domain representation of the transfer function as a convolution window can be used in human adults to synthesize the ascending aortic pressure waveform from finger recordings in real time. This procedure could be used where aortic pressure waveform features are needed in real time on a beat-by-beat basis, such as tilt-table testing, Valsalva maneuver, and aortic counterpulsation. It is important to note that this technique could enhance noninvasive determination of cardiac mechanical properties and ventricular-vascular coupling when combined with other noninvasive techniques that provide the left ventricular volumetric ejection contour.
This study was supported by grants from the Australian Research Council (F49540089) and the National Heart Foundation of Australia (G94S4042). We also gratefully acknowledge the assistance provided by the Cardiac Catheterization Laboratory Staff at St Vincent’s Hospital.
- Received December 30, 1996.
- Revision received February 12, 1997.
- Accepted May 8, 1997.
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