(Hypertension. 1997;30:1416-1424.)
© 1997 American Heart Association, Inc.
Articles |
On-line Synthesis of the Human Ascending Aortic Pressure Pulse From the Finger Pulse
From the Cardiology Department and Victor Chang Cardiac Research Institute, St Vincent's Hospital, Sydney, Australia 2010.
Correspondence to Mustafa Karamanoglu, PhD, Cardiology Department, St Vincent's Hospital, Victoria Street, Sydney, Australia. E-mail M.Karamanoglu{at}unsw.edu.au
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Abstract |
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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.
Key Words: blood pressure • arterial model • transfer function, simulation
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Introduction |
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TopAbstractIntroductionMethodsResultsDiscussionReferences |
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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.
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Methods |
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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(
)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()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.
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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.
Direct Method
Customization of the upper limb transfer function,
H()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()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()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.
Model-Derived Method
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.
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o. The
modified windkessel of the terminal element has a characteristic
impedance (ZRF), peripheral resistance (R), and
peripheral compliance (C). Inset, Frequency-dependent
behavior of the modulus of the reflection coefficient,
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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 (
=RxC) and
the reflection coefficient, 
o=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, o,
and ) to obtain a transfer function, H()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, =0.0 seconds,
and o=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, =0.5 seconds,
and o=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()CA-FA, and the transfer function between the
ascending aorta and carotid arterial system,
H()AA-CA, described above then were used to determine
the individualized transfer function between the ascending aorta and
finger artery, H()AA-FA, from the relation shown
below.
 | (1) |
)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()CA-FA. This generalized H()CA-FA was
then used in Equation 1 to determine a generalized
H()AA-FA from which a generalized convolution window,
h(t)FA-AA, was calculated.
Data Analysis
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
 | (2) |
Statistical Analysis
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.
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Results |
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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.
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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 2
at 8 Hz. The
transfer functions exhibited considerable interindividual variability,
reflected by scatter in modulus and phase.
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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.
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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,
, was 216.7±185.5 ms, and the predicted reflection coefficient,
o, 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.
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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).
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Discussion |
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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
o 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.
Limitations
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.
Conclusion
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.
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Acknowledgments |
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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; first decision February 12, 1997; accepted May 8, 1997.
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