Chapter 26 TRANSFER OF PRESSURE
Description
Peripheral pressures can be measured noninvasively by different techniques.
For example‚ finger pressure can be reliably measured by photoplethysmo- graphy‚ and radial artery and carotid artery pressure waveforms can be obtained with applanation tonometry. Both techniques are commercially available. Most clinicians use peripheral pressures and typically brachial pressure obtained with the classical sphygmomanometer. Brachial pressure is then used as a substitute for aortic pressure‚ or‚ even more so‚ as a global arterial pressure indicator. However‚ peripheral and central aortic pressures are not the same. The pressure waveform and the systolic and diastolic pressures can be substantially different between locations (see figure in the
box). In general, systolic pressure increases as we move from central to peripheral pressures, a phenomenon called ‘systolic peaking’, which is attributed to wave reflections at the peripheral vascular beds. Diastolic pressure tends to be slightly lower in peripheral vessels than in central arteries.
Definition of Transfer function
One way to obtain aortic pressure from a noninvasively measured peripheral pressure wave is to apply the so-called pressure transfer function. In essence, we define a transfer function, T, which is the ratio of the peripheral pressure wave, to the aortic pressure wave, The two pressures can only be related to each other in the frequency domain (see Appendix 1). So for each harmonic, we define the amplitude of the transfer function as the ratio of amplitudes of the peripheral and aortic pressure wave and the phase of the transfer function as the difference in the phase between the peripheral and aortic pressure (See Appendix 1). This is mathematically expressed very simply as [2,3,4]:
The amplitude and the phase of the transfer function between the radial artery and the aorta is shown schematically in the figure in the box. The zero- frequency value of the transfer function is the ratio of mean peripheral arterial pressure to mean aortic pressure. Because of the small drop in mean pressure between the aorta and the peripheral artery, this ratio is slightly lower than 1. The amplitude of the transfer function is, in general, higher than one for medium range frequencies, reflecting the increase in pulse pressure at the peripheral site. For high frequencies the transfer function decreases to negligible values because high frequencies are damped while traveling. The phase is negative, as a result of the phase lag between the two waves, a direct consequence of the time it takes for the aortic wave to travel towards the periphery.
Several techniques are commercially available to obtain central from peripheral pressures, see [1 and 2]. These methods therefore should be used with utmost care.
Calibration of noninvasively determined pressure wave shapes
Applanation tonometry and echotracking of wall motion are ways to obtain peripheral pressure wave shapes noninvasively, but calibration is not available. Sphygmomanometrically obtained, and thus calibrated values of systolic, and diastolic, pressure in the brachial artery, can help in the calibration [7]. A good estimate of calibrated carotid systolic pressure is to assume that mean pressure and diastolic pressure are not different between brachial to carotid artery: and
Systolic pressure can than be derived assuming that mean pressure in the
carotid artery, equals and in the
brachial artery Rearrangement leads to:
Physical basis and simple mathematical model for Transfer Function
A simple approach, which helps to understand the physical basis of the transfer function, is to consider the entire arterial pathway from the aorta to the peripheral site as a single tube. The aortic pressure wave, consists of its forward running component, and its backward running component or
reflected wave, At the peripheral site the forward and backward running wave components are and, respectively.
As a first approximation, we may assume that the forward wave at the peripheral site is identical to the forward wave at the aorta with the exception of a time delay between the two waves. This time delay is equal to the time it takes for the forward wave to travel from the aorta to the peripheral site, i.e., l being the distance and c the wave speed.
In the frequency domain the time delay is expressed as a phase lag, which is equal to and we may write
THE FORWARD AND BACKWARD WAVES travel from heart to periphery and back.
Following a similar reasoning, the reflected wave at the peripheral site is equal to the reflected wave in the aorta. However, because the reflected wave travels in the opposite direction, the aortic wave now lags the peripheral wave by the same time delay The transfer function, T, can thus be written as:
and thus:
AORTA PRESSURE CAN BE DERIVED FROM BRACHIAL PRESSURE AND VELOCITY OR FLOW WAVES and the travel time of the waves between these two sites. The brachial pressure and flow (or velocity) can be used to calculate forward and reflected pressures. When the backward pressure is advanced and the forward pressure is delayed in time, subsequent addition results in aortic pressure. The theoretical transfer function is close to the measured data. Adapted from [6], used by permission.
Dividing by and taking into account that is equal to the reflection coefficient, we obtain the following final expression for the transfer function T:
This single tube model suggests that the transfer function depends primarily on the reflection coefficient at the distal site and on the time of travel of the waves between the two sites. The model, of course, it is an oversimplification of reality, because it does not take into account the effects of wave damping, and nonlinear elasticity. The model applies to a single uniform vessel and thus cannot be applied when significant reflection sites exist between the aorta and the peripheral site, e.g., major bifurcations. The model gives, however, reasonable predictions of the transfer function between the aorta and the brachial artery, as shown in the figure on the previous page [6].
Physiological and clinical relevance
This figure shows aortic pressure and brachial pressure measured in an individual under control conditions as well as after administration of nitroglycerin [5]. This figure shows that the transfer of pressure depends on the state of the vascular tree.
Under control conditions, systolic brachial pressure is approximately 150 mmHg, overestimating aortic pressure by 10 mmHg. Under nitroglycerin, systolic pressure in aorta drops significantly. Notice the disappearance of the late systolic reflected wave, apparently due to reduced reflections resulting from vasodilatory effects of nitroglycerin. Brachial systolic pressure, however, remains practically unchanged, now overestimating aortic pressure by
more than 30 mmHg. This example demonstrates that peripheral pressure waves are not a reliable substitute for aortic pressure and their relation may vary depending on different physiological parameters, such as arterial vasomotor tone. Therefore, peripheral waves cannot give an accurate estimation of the load on the heart.
A major drawback of the transfer function technique is that a generalized function does not exist. Parameters like body size, arterial elasticity and peripheral resistance, which vary from patient to patient, are important determinants of pressure transfer. One may try to adjust the transfer function based on gender, body size, age, etc., but such an adjustment, which is based on statistical analysis of large population studies may not be precise [3]. One approach would be to use the simple model of pressure transfer presented above and try to derive a transfer function on a ‘per patient’ basis.
SIMULTANEOUS recordings of aortic and brachial pres-sure waves under control conditions and after admini-stration of nitroglycerin. During vasodilation systolic blood pressure in the brachial artery is not affected while systolic aortic pressure is lowered.
Adapted from [5], used by permission.
From a clinical standpoint it is the aortic pressure and not peripheral pressure that is of primary importance in a number of aspects. Aortic pressure is the main determinant of cardiac afterload, and it drives coronary perfusion.
The aortic pressure waveform can be used to derive reliably arterial compliance based on a variety of methods (Chapter 24). During ejection, aortic pressure can be taken as a surrogate of left ventricular pressure and, together with noninvasive measurements of left ventricular volume, can be used to estimate cardiac parameters such as End-Systolic elastance (Chapters
13 and 18).
References
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Estimation of central aortic pressure waveform by mathematical transformation of radial tonometry pressure. Validation of a generalized transfer function.
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Kelly RP, Gibbs HH, O’Rourke MF, Daley JE, Mang K, Morgan JJ, Avolio AP.
Nitroglycerin has more favourable effects on left ventricular afterload than apparent from measurement of pressure in a peripheral artery. Europ Heart J 1990;11:138-144.
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