Pulse




(1)
Professor of Anesthesiology, Albany Medical College, Albany, NY, USA

 



Keywords

Arterial pulseSphygmologyHarmonyMusical lawsPulse diagnosisWaveform analysisWindkessel methodFourier analysisResonant systemTransmission line modelWave intensity analysisActive aortic pulsationsHarmonic analysisPulse wave velocityAugmentation indexCentral arterial pressurePulse wave contour


22.1 The Art of Pulse Diagnosis: Historical Perspective


The pulse is recognized as the most fundamental sign of life, and its palpating at the wrist remains an essential part of clinical assessment. Ars Sphygmica or the art of diagnosis from the pulse has a long and distinguished history with written records going back as far as 2500 years BCE in ancient China and 600 BCE in India. Different qualities of pulse were ascribed not only to individual patients according to sex and age but also to the function and condition of the vital organs. Symptoms, type, and prognosis of an illness could be decided entirely by the pulse which took on a different nuance during the course of the day and with the change of seasons [1]. An elaborate method of pulse diagnosis remains an integral part of contemporary Chinese acupuncture [2] and Ayurvedic medical practice [3].


As suggested (cf. Sect. 15.​3), the foremost concern of Greco-Roman physicians was a living connection between the human being, the microcosm, and her/his environment, the macrocosm.1 Earth, water, air, and fire, the four principal elements in the outer world, were also active in a transformed way within the body as four “humors”: blood, phlegm, black, and yellow bile. These, in turn, corresponded to the four seasons and were related to the temperaments: sanguine, phlegmatic, melancholic, and choleric [5]. Harmonious mixture of humors as the basis of health was based on the Pythagorean law of numbers that imprints its signature on all things. Thus, a harmony between cosmic and inner rhythms was the basis of health and, lack thereof a chaotic state, the cause of illness.


Herophilus (335–280 BC), Alexandrian physician and anatomist, is considered the originator of western sphygmology. He maintained that knowledge of music and geometry was required to master the art and recognized four main qualities of the pulse: size, frequency, force, and rhythm. The later was considered particularly important and was compared to measure in music and cadence of speech. The Greeks distinguished between some 20 different types of rhythms of speech. Herophilus taught that dilation of the arteries draws in pneuma2 from the heart, and their contraction moves it toward the periphery. Herophilus was the first to measure heart rate by timing the pulse against the water clock or clepsydra [7]. Galen (129–199 CE), recognized as the foremost sphygmologist of antiquity, took the art of feeling the pulse to the zenith. He devoted a large part of his writings to the subject (18 books) with topics ranging from different types and causes of pulse, to its diagnosis and prognosis. Based on frequency, speed, and size, Galen described 27 varieties of pulses and their meaning. Like Aristotle, Galen argued that arteries possess an intrinsic “pulsific faculty” and that contraction and dilation of arteries occur simultaneously with the heart [1]. Diastole of the heart was considered an active phase by which pneuma merged with the “innate heat” (cf. Sect. 15.​3). Besides being filled by the heart, Galen maintained that the blood “consumption” at the periphery created vacuum, pulling blood toward the periphery. In addition, the blood was attracted to the periphery by active expansion of the arterial wall [8]. Galen’s sphygmology was an integral part of the comprehensive respiratory doctrine that dominated Western medicine long after Harvey’s discovery of circulation [1].


The Pythagorean notion that world harmony and its musical laws find their expression in rhythms of breath and pulse was common knowledge among the leading savants of the Renaissance period, such as J.B. Van Helmont (1577–1644), J. Kepler (1571–1630), and R. Fludd (1574–1637). Kepler’s discovery that planets follow elliptical, rather than circular orbits around the sun as originally proposed by Nicolaus Copernicus (1473–1543), turned the symmetric, sun-centered solar system into a living universe in which the sun and the planets are mutually supported by laws of musical harmonies [10].3 Fludd, a fellow student of Harvey’s at Padua and a personal friend, arranged for the publication of De Motu Cordis and allayed Harvey’s fears of being ostracized by the contemporaries on account of his revolutionary discovery [11]. Fludd’s treatise on the pulse, a combination of ancient sphygmology and metaphysics, demonstrates the influence of alchemy on medicine of the period (Fig. 22.1).

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Fig. 22.1

Title page of Robert Fludd’s Treatise on the Pulse, 1629 (a). According to Fludd, the pulse, in the state of health, reflects the divine music of the spheres and unites the Alpha and Omega, i.e., the beginning and the end of existence. (b) The celestial monochord from Fludd’s Utriusque Cosmi Historia (1617) depicts planetary orbits corresponding to musical intervals on a string of a monochord. The fact that subdividing a string by a whole number produces a harmonious scale was well-known to instrument makers and to savants of the period. The search for harmonic laws implicit in the Pythagorean tradition of musical intervals led Johannes Kepler to the discovery of the laws of planetary motion published in Harmonices Mundi (1619). Kepler maintained that harmonic laws of planetary motions have a counterpart in the microcosm of the human soul. (Reproduced from ref. [12])


With the dawn of the scientific age in the Renaissance, the art of Galen’s pulse doctrine, based on a qualitative relationship between the higher (soul/spirit) and lower members (physical and vital aspect) of the human constitution, gradually gave way to quantitative methods of pulse assessment. Harvey, the man on the cusp between the natural philosophers of antiquity and the beginning of modern science, was increasingly in conflict with Galen’s doctrine, such as when he maintained that ventricular systole, rather than diastole, is the active phase of heart’s action and the cause of arterial pulse.




There is just the one cause of arterial pulsations throughout the body, and that is contraction of the left ventricle. The pulsation of the artery-like vein (pulmonary artery) is similarly contraction of the right ventricle…In correspondence with the tension of the heart the arterial pulsations become larger, more forcible, frequent, rapid, while preserving the rhythm, volume and order of the heartbeat….For the pulse of the artery is nothing save the impulse of the blood entering the vessels [13].


Harvey moreover observed that the heartbeat originates in the right atrium. He maintained, however, that dilatation of the heart, the primal of the two motions, is activated by “inner warmth” rather than the passive inflow of blood. Automatic action of the heart is thus caused by its sensing the change in temperature of the inflowing blood (cf. Sect. 15.​3). The arteries, on the other hand, are filled passively, “…are distended because they are filled like sacs or bladders.”4 Harvey agreed with Aristotle that the pulse appears in all arteries simultaneously.


The unintended consequence of separating the respiratory and circulatory functions of the blood, by which the blood ceased to be an autonomously moving agent and the heart a propulsion pump, was already discussed (cf. Chap. 15). An extension of this reasoning was the gradual loss of appreciation for the qualities of the pulse and a striving for its validation by objective means. Perceptive faculties of the human being, “the measure of all things”,5 were consequently projected into the physical world and found expression in the construction of mechanical implements. An early prototype of such devices that followed in the wake of Galileo’s (1564–1642) invention of the pendulum was the pulsilogy by S. Sanctorius (1561–1636). (Of interest, Galileo counted the swings of the lamp in the Pisa cathedral against his own pulse.) The device consisted of a vertical, calibrated rod against which the physician would swing the pendulum in synchrony with the subject’s pulse. John Floyer (1649–1734) was the first to measure the pulse with a portable timepiece with a stoppable second hand, the “Physician Pulse Watch.” François-Nicolas Marquet of Nancy (1657–1759) sought inspiration in the work of Herophilus and devised a special musical notation to symbolize 12 principal types of pulse. For Marquet, the best judges of the pulse were musicians, in particular the lute players [1].


A significant step in objectifying the pulse was Jules Herisson’s sphygmometer (1834), a mercury-filled glass tube inserted into a rubber bulb, which, placed over the artery, would make pulsations visible (Fig. 22.2). Herisson demonstrated the differences in qualities of pulse in various heart valve defects and argued, for the first time, that the device is superior to a physician’s touch. The invention of the kymograph by Carl Ludwig (1847) made it possible to produce a permanent record of pulse waveforms allowing for comparison and graphic analysis of pulse in various conditions (Fig. 22.3). E. J. Marey developed a portable sphygmograph with recording capability (1859), a notable improvement on the cumbersome contrivance designed by K. Vierordt. Marey demonstrated differences in arterial pulse between younger and older individuals, confirming the dictum that “man is as old as his arteries.” F. Mahomed further refined Marey’s sphygmograph and compared arterial waveforms in patients with essential hypertension which he distinguished from the recordings obtained in patients with glomerulonephritis [7, 14].

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Fig. 22.2

Herisson’s sphygmometer placed over the radial artery. The instrument consisted of a graduated glass tube filled with mercury, inserted into a hemispherical metal base. The force needed to occlude the pulse was reflected in the height of the mercury column and enabled visual assessment of its amplitude and rhythm


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Fig. 22.3

Ludwig’s kymograph. (a) Smoked drum kymograph invented by Carl Ludwig was originally used for recording of direct measurement of arterial blood pressure but was later adapted for use in sphygmography. Sample recordings of radial artery sphygmograms. ((a) Reproduced from ref. [7]; (b) Reproduced from ref. [15])


Unlike time-consuming and often difficult-to-reproduce sphygmomanometric waveforms, the ease and convenience of pressure recording introduced by Riva Rocci (1896) gained rapid popularity and further eroded the art of pulse diagnosis (cf. Sect. 14.​1). Sir James Mckenzie, one of the fathers of modern cardiology and author of the acclaimed book on sphygmographic analysis of the pulse, “The Study of the Pulse” (1902), vented his frustration with those who uncritically accept the numbers provided by the cuff: “… we get now a definite and precise figure which most people imagine to be more scientific” (quoted in [16]).


22.2 Arterial Waveform Analysis in Time and Frequency Domains


The modern era of pulse waveform analysis began with Otto Frank (1865–1944) who constructed the first accurate invasive blood pressure transducer and formulated the pulsatile behavior of the arterial tree in mathematical form. Frank used a two-element Windkessel model (a concept first proposed by S. Hales in 1733, cf. Sect. 16.​3) consisting of resistance and compliance elements and derived stroke volume (and cardiac output) on the basis of exponential decay of arterial pressure in diastole [17]. Frank moreover employed the wave model, correctly derived the speed of arterial waves and their reflection from the periphery, and analyzed their spectral composition. However, there is an inherent conflict between the Windkessel, where the arterial system is represented by a single compartment, and the wave model which assumes that information travels in the arteries in the form of sinusoidal wave trains. Frank was well aware of the dichotomy, but could not resolve it [18].


22.2.1 The Controversy


The above-mentioned dichotomy in the analysis of arterial pulse faced by Frank turned into a scientific controversy in the 1960s between those who looked at pressure and flow waves in arterial reservoir (Windkessel) as unique events in time and those who considered arterial waves as an elastic system of tubes subject to periodic oscillations powered by the heart. The former, which included seasoned researchers, such as E. Wetterer, J. Remington, R. Alexander, and W. Hamilton, looked at the events in the arteries more phenomenologically, while the latter, headed by D. McDonald, J. Womersly, M. Taylor, and their students, approached arterial wave as a steady-state oscillation amenable to Fourier analysis [19].


These events coincided with the publication of the first edition of “Blood Flow in Arteries” where McDonald proposed that mathematical analysis of pressure waves by way of Fourier’s method is more representative and even “simpler” than the alternative, where pulses are considered as singular events in time [21]. The suggestion was based on the premise that regularity of arterial pulses can be best represented as a condition of steady-state oscillation that is best described by Fourier series whereby a shape of any wave can be represented by the fundamental frequency and its higher harmonic terms (Fig. 22.4). Since any number of higher harmonics can be generated, the method can describe any complex waveform. The reconstituted wave is simply a sum of component terms and a best approximation of the original. The method is analogous to harmonic analysis of signals widely used in electrical and acoustic engineering. Remington objected to this analytical approach because arterial circulation is a nonlinear system where beat-to-beat variation, rather than regularity, is the physiologic norm. The length of the cardiac cycle is affected by hemodynamic, neurogenic, i.e., sinus arrhythmia and chemical influences, to name a few, all of which would affect the velocity of wave travel. Far from being a sine wave generator, the sinus node exhibits a complex nonlinear behavior best described by the chaos theory and fractal mathematics (cf. Chap. 23). It follows, argued Remington, that if the fundamental is reset, a different harmonic series will be required for each change in the cycle length. Since the length of systole rarely equals half of the cardiac cycle length, the sum of two systolic intervals rather than the length of a cardiac cycle should be taken as the fundamental. A concern was moreover voiced over the assumption that harmonics obtained by Fourier fitting exist as separate waves traveling independently with nodes at different points along the aorta [22]. Finally, concluded Remington, “The fact that an analysis of uniform heart rate is easier to make does not mean that the premise is correct” [21].

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Fig. 22.4

Example of Fourier series transformation of a periodic wave. (a) Mean term (or 0 harmonic) with harmonics 1–6 of a pressure wave recorded in the ascending aorta of a dog. (b) The shape of the wave is relatively well reproduced with the sum of first six harmonics (0 + 1… + 6), better with the sum of ten harmonics (0 + 1… + 10), and almost identical to the original wave with the summation of the first 20 harmonics (0 + 1… + 20), bottom trace. A shortcoming of the impedance method is that it assumes linearity and periodicity of waves and fails to account for missed beats. (Reproduced from ref. [20], used with kind permission of Dr. N. Westerhof)


22.2.2 Arterial Circulation as a Resonant System: The Windkessel


By comparing arterial waveforms recorded at different points between the aortic arch and femoral artery in dogs, Hamilton and Dow noted that the beginning (the foot) of the pressure wave was progressively delayed, while the peaks occur virtually simultaneously at all locations along the lumen of the vessel (Fig. 22.5). They concluded that despite great variation of pulse forms, the presence of a “standing wave” suggested “resonance” of the arterial system. Regardless of variations in shape, the surface area under the curves (and hence the mean pressure) was identical within the limits of error. Finally, the upper and the lower aortic waves were 180° out of phase, signifying a nodal point of zero pressure oscillation somewhere between the two [23]. The reciprocal oscillations are remarkably robust, persist during vagal stimulation and readily appear after the first beat following a prolonged cardiac arrest. Prompt achievement of resonance suggests a functional unit that “molds” the heart’s ejection waves “into a pattern consistent with its own resonant properties” [21].

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Fig. 22.5

Simultaneous recording of pressure at intervals between the aortic root and iliac artery in the human aorta. The foot of the wave arrives later at the periphery and the reflected wave returns with some delay to the heart. Note that peaks of the waves coincide (green dashed line). (Adapted from ref. [24], used with permission of Wolters Kluwer Health)


The presence of aortic standing waves was moreover verified in dogs by Alexander who proposed a rhythmic to-and-fro surge of the aortic blood column between the root of the aorta and the femoral bed. The peak of pulsations was identified in the descending thoracic aorta where the pressure wave was minimal and the flow at its maximum [25]. Alexander proposed the analogy of a tubular orchestral chime, which, when struck, vibrates at the frequency of its own form, independent of the impacting force. Similarly, “the impact of cardiac ejection strikes the elastic aortic system, and this is thrown into an oscillation whose frequency is unrelated to heart rate, but rather is determined by the elastic properties of the vascular tree” [26].


Although poorly modeled by an electrical analog of Frank’s two-element Windkessel system,6 wave behavior in animal models seemed to confirm this concept. The resonant frequency of the system was in the range of 2–10 cycles per second (cps) with higher frequencies seen in increased cardiac output and hypertension due to sympathetic vasoconstriction. On the contrary, hypotension and a drop in cardiac output resulted in decrease of resonant frequencies [27].


Finally, a different type of resonance has been confirmed by studies on athletes in whom the synchrony between the heart and the pace of running may favorably affect athletic performance [28]. During aerobic exercise, the amplitude arterial pulse can increase up to twice its basal value in the peripheral arteries and by 50% in central arteries [29]. During peak exercise, the heart rate and the pace of running often approximate so that the heart rate (in the range of 140–160 beats per min) approximates the stride rate [30]. O’Rourke demonstrated in runners that the arterial pulse pressure is affected by upward and downward movements of the body with the generation of an arterial wave with an amplitude comparable to left ventricular ejection. When the runners consciously synchronized the rhythm of leg movement with the heart rate, a significant augmentation of pulse pressure occurred. Such augmentation of pulse pressure, known as entrainment or “beating” was achieved in all subjects (at the rate of 1–10 per min). The possible effect of lowered pulse pressure, when the heart and body wave are out-of-sync, remains to be determined [30].


22.2.3 Transmission Line Model


The existence of standing waves was challenged by McDonald and Taylor on the basis that resonance can occur only with complete wave reflection and in the absence of attenuation [31].


The major weakness of Frank’s two-element Windkessel model was that it described the arterial system in terms of pressure and flow only at its entrance, i.e., at the juncture between the heart and the aorta, but gave no information on wave travel and reflection within the arterial compartment. If resonance was to occur, the length (dimension) of the reservoir would have to be known, in analogy to the length of a vibrating string on a string instrument. Because wave reflection occurs at many different points in the arteries, the length of the reservoir (Windkessel) is unknown. This accounted for poor correlation between predicted and experimentally measured flows and pressures.


Behavioral similarities between arterial wave dynamics and electrical transmission lines originally proposed by Landes (1946) were developed further by Taylor [18]. Accurate measurement of aortic flow and development of algorithms that enabled rapid calculation of power spectra of complex Fourier series7 in the mid-1960s (a task that previously required hours could be accomplished by computer in seconds) was followed by the introduction of aortic capacitance and impedance. Theoretical work by John Womersley on the oscillatory flow in elastic tubes, in association with Donald McDonald and his successors, laid much of the ground work for the study of arterial blood flow dynamics in frequency domain. Their work is summarized in now classic text, currently in its sixth edition [33].


In the following years, attempts to understand arterial circulation from a phenomenological perspective largely gave way to analytical methods that would reconcile linear relationship between pressure, flow, and inertance8 (in place of resistance) using electrical analog for alternating current (Ohm’s law, cf. Sect. 14.​1).6 The gap between wave analysis in time and frequency domains has in the meantime been “successfully bridged” [17, 32] by the method of separation of pressure and flow waves into their respective forward and backward components [34] by employing sophisticated algorithms that “utilize the fundamental language of science—mathematics” [16]. The introduction of transmission line concepts to the two-element Windkessel significantly improved the accuracy of the (now three-element) Windkessel model (cf. Sect. 16.​3) and provided the link9 to the wave model Frank was unable to establish [17].


However, in spite of the predominance of wave methods, the original reservations addressed by Remington remain [22]. The problem has been aptly summarized by Avolio et al. in the editorial to a special issue devoted to arterial wave analysis: “To an engineer a discussion (on the merit of frequency vs. time domain analysis) seems rather theoretical since only the measured pressure and flow signals exist and Fourier decomposition only predicts, based on assumed linearity, what single, separate harmonics would do” [35].


22.2.4 Wave Intensity Analysis


The notion that the arterial system is in a state of steady-state oscillation has been contested by Parker on the grounds that, in similarity with engineered structures, such as pressure transducers, biological systems possess critical damping in the form of friction or viscosity [36]. Since the arterial system is subject to “forced” oscillations impelled by the heart, these oscillations can be either under-damped, and continue to vibrate after forcing has stopped, or over-damped and cease vibrating immediately when forcing has stopped. Ideally, the arterial system is critically damped and will become stationary within a single period. The argument is supported by the observation that the response to a dropped beat is an exponential fall in blood pressure, followed by its prompt restoration with an “overshoot,” within a few beats following the compensatory pause. Thus, each beat should be thought of as an isolated event in time, a solitary wave, much like an ocean tsunami or a tidal river bore, rather than a succession of periodic waves.


It is important to remember that a moving wave involves transmission of energy through a medium, i.e. a vessel filled with blood, without implying a net movement of the medium. A wave can therefore propagate longitudinally along the vessel at speeds that greatly exceed the flow of blood. From the perspective of fluid mechanics, a longitudinal wave can be characterized as net compression or expansion, which in a system of compliant vessels, also implies a change in diameter. The method that describes conceptual and mathematical behavior of such waves in gases and fluids as individual events is wave intensity analysis (WI). The work performed by a wave involves kinetic energy associated with velocity of flow and potential energy manifest as expansion of the arterial wall. By definition, the former is considered blood’s total energy and the latter is “wave intensity,” comprising about 30% of total hydraulic power [37].


By this method, a wave is assumed to be a sequence of small wave fronts which combine to produce the observed wave that can be quantified by simultaneous recording of pressure and velocity signals in the time domain (Fig. 22.6) [36]. There are forward and backward waves with four possible net effects: forward/backward compression, and forward/backward expansion (i.e., suction), each exerting additive of subtractive effects on wave velocity. In contrast to impedance (Fourier) method, wave intensity (WI) can be related temporarily with a beat-to-beat analysis of the arterial pulse [38]. Unlike the pressure and flow signals which represent the momentum of moving blood, WI provides information that can be compared to the “engine noise” [39], or shall we say, the “acoustic energy” of the undulating arteries (Fig. 22.7).

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May 1, 2020 | Posted by in CARDIOLOGY | Comments Off on Pulse

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