The Korotkoff Sound

G. M. Drzewiecki

Department of Biomedical Engineering College of Engineering Rutgers University

J. Melbin and A. Noordergraaf

Cardiovascular Studies Unit Departments of Bioengineering and Animal Biology University of Pennsylvania

(Received 2/17/88; Revised 11/2/88)

As the auscultatory method of blood pressure measurement relies fundamentally on the generation of the Korotkoff sound, identification of the responsible mechanisms has been of interest ever since the introduction of the method, around the turn of the century. In this article, a theory is proposed that identifies the cause of sound generation with the nonlinear properties of the pressure-flow relationship in, and of the volume compliance of the collapsible segment of brachial artery under the cuff. The rising portion of a normal incoming brachial pressure pulse is distorted due to these characteristics, and energy contained in the normal pulse is shifted to the audible range. The pressure transient produced is transmitted to the skin surface and stethoscope through deflection of the arterial wall. A mathematical model is formulated to represent the structures involved and to compute the Korotkoff sound. The model is able to predict quantitatively a range of features of the Korotkoff sound reported in the literature. Several earlier theories are summarized and evaluated.

Keywords- Korotkoff sound, Blood pressure measuremen t, A uscultatory method.

INTRODUCTION Rudiments of the auscultatory method of blood pressure measurement can be traced to Vierordt (63) and Marey (44). In 1855 Vierordt offered what was probably the first method of noninvasive measurements of blood pressure capable of pro- viding some quantitative information, by means of known weight applied to the arterial pulse. Pulse obliteration remains an essential element of the current method. Application of weights could not be related to blood pressure easily. To eliminate this problem Marey (44) enclosed the arm in a sealed chamber, thereby applying a known level of uniform fluid pressure. Later, Riva-Rocci (56) replaced Marey's arm chamber with the more convenient arm cuff.

Address correspondenceto G. M. Drzewiecki, Department of Biom.edical Engineering, College of Engi- neering, Rutgers University, Piscataway, NJ 08855-0909. 325 326 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

In 1905, Korotkoff (37), a Russian army physician, reported on the use of a stethoscope in conjunction with an occlusive cuff. In experiments on the collateral circulation in a limb of a dog, Korotkoff noticed that sound could be detected just distal to a pressurized cuff, but only if the collapsed artery is forced open by an incoming pulse. Korotkoff argued that lumen opening must occur when peak arterial pressure just exceeds cuff pressure, thereby introducing a new means of blood pressure determination. This procedure became established as the auscultatory method of blood pressure measurement. Currently, the American Heart Association recom- mended procedures for its use (36). In brief, the technique is applied as follows: A cuff is wrapped around the upper arm, and the cuff pressure is quickly raised to about 30 mmHg above the level of pulse obliteration. Then, cuff pressure is released at the rate of 2-3 mmHg/sec. The first Korotkoff sound heard in the stethoscope is similar to a faint tapping. It is referred to as the phase I sound. As the cuff pressure continues to fall, the sound first becomes louder, goes through a maximum (Phase III), then gradually diminishes and changes character. When the sound becomes muf- fled it is referred to as the phase IV sound. Further decreases in cuff pressure cause the sound to disappear entirely. The last heard is referred to as phase V. The occurrence of phase I is interpreted as cuff pressure being equal to systolic arterial pressure and either phase IV or phase V as equal to diastolic arterial pressure. Comparison with direct blood pressure measurements, carried out by London and London (41), revealed that the accuracy of the auscultatory method is rather limited. Typical mean errors of -5 to -20 mmHg in systolic pressure and of +12 to +20 mmHg in diastolic pressure were found. Automated sphygmomanometers that are based on the auscultatory method offer no improvement in accuracy over the human observer (66). The accuracy of the auscultatory method can be compromised by several factors, which may be categorized as: (a) Cuff size (60), (b) Observer precision and auditory acuity, (c) Choice of phase IV or V for diastolic pressure, (d) Manometer accuracy, (e) Cuff deflation rate, (f) Arm elevation and posture (hydrostatic pressure effect), and (g) Vascular tone in the arm distal to the cuff (23,50,53,70). In the auscultatory method of blood pressure, three functional components may be identified. These are: (a) Cuff pressure transmission to the artery, (b) Korotkoff sound genesis, and (c) Sound transmission to the ear. Of these three, cuff pressure transmission to the artery was analyzed by Alexander et aL (1), and transmission of sound to the ear by Drzewiecki et al. (18,22) and Rabbany et al. (52). The least under- stood component remains the origin of the Korotkoff sound. As a consequence, most of the effects that influence the accuracy of blood pressure readings remain to be clarified. This report offers a quantitative interpretation of the phenomena held responsible for the origin of the Korotkoff sound.

THEORIES ON THE ORIGIN OF THE KOROTKOFF SOUND

It has long been appreciated that the key to a better understanding of the opera- tion of the auscultatory method lies in the identification of the mechanism responsible for the origin of the Korotkoff sound. Accordingly, attempts have been made to identify this mechanism and several theories have resulted. These will be reviewed and evaluated in this section. For the purpose of discussion, theories for the origin of the Korotkoff sound have The Korotkoff Sound 327 been divided into two categories; flow origin and pressure origin (16,43). They place their emphasis almost exclusively on either flow or pressure phenomena. Any theory in the flow origin category requires substantial fluid flow to generate sound. Any theory in the pressure origin category requires a transient pressure change to generate sound.

Flow Origin The Waterhammer theory is probably the oldest of the flow origin theories; it was introduced by Erlanger (29) and again, by Kositskii (38). These researchers proposed that a high velocity stream of blood is released upon the opening of the lumen of the artery. This stream then impacts upon the downstream stationary pool of blood. The resulting sudden deceleration of blood, known as the Waterhammer, is assumed to produce the Korotkoff sound. Other researchers have proposed that disturbed flow may produce the Korotkoff sound. For example, Lange et al. (39) offered the pistol-shot mechanism. In this theory, rapid motion of the arterial wall is supposed to cause a disturbance in the downstream blood flow. This transient change in flow is thought to produce the sound; it should precede the rising portion of the distal pulse. Chungcharoen (13) proposed that a partially constricted vessel will lead to the formation of a downstream fluid jet. The jet causes turbulence and turbulence is a known source of sound (40). Chungcharoen demonstrated the feasibility of flow turbulence in vivo. Earlier, Bruns (12) had introduced this concept with the inclusion of the possibility of turbulence-induced periodic vortices. Rodbard (57) observed that flow in elastic tubes can spontaneously develop periodic oscillations, even with constant inlet and outlet pressures. Conditions for such oscillation to occur, such as external and internal pressures and downstream flow resistance, were examined experimentally by Conrad (15). Although most experiments were performed on elastic tubing, Ur and Gordon (62) demonstrated that such relaxation oscillations may occur in an isolated canine limb. Recently, Bertram (5) dis- covered characteristic patterns in their appearance.

Evaluation of Flow Origin Theories The Waterhammer theory requires flow deceleration to produce sound. McCutch- eon and Rushmer (42) examined the flow patterns in the brachial artery at the time of the occurrence of the Korotkoff sound. This was accomplished by simultaneously recording flow in the brachial artery by means of a Doppler ultrasound flow probe, and the Korotkoff sound by external microphone. Flow was found to be either negligible or just beginning to accelerate when the sound is emitted, in contradiction with the Waterhammer theory. The time of occurrence of the Korotkoff sound is not in agreement with the pistol- shot theory. In direct measurements of the brachial pulse under the occlusive cuff, Tavel et aL (61) found that the Korotkoff sound coincides with the rising portion of the pulse. The disturbed flow/turbulence theories are not in accord with the observed Korot- koff sound in several respects. In particular, the quality of the sound produced by disturbed flow is quite different from the Korotkoff sound. Turbulent flow tends to generate a soft blowing sound or rumbling sound (murmur) that is more random in 328 G.M. DrzewieckL J. Melbin, and A. Noordergraaf

nature than the Korotkoff sound. Moreover, the recognizable waveform of a turbulent sound should persist irrespective of the value of cuff pressure, while the Korot- koff sound depends strongly on the level of cuff pressure. Other considerations make disturbed flow an unlikely candidate for the Korotkoff sound. For example, it has been uncertain whether a disturbed flow phenomenon can provide an audible sound level. Yellin (69) tested this experimentally and found that turbulent flow generated the strongest sound output among a group of disturbed flow patterns and would therefore be the most likely cause of Korotkoff sound. But, since turbulence requires a relatively high velocity jet of fluid, a high peripheral resistance might cause the sound to disappear. However, the Korotkoff sound has been shown to persist even with the application of a tourniquet that occluded blood flow in the forearm (57). Hence, turbulence seems an unlikely cause of the Korotkoff sound, even though it is a popular explanation in current medical textbooks. Although little support has been marshalled in support of the disturbed flow theories, this mechanism may contribute during the phase III Korotkoff sound. The high flow necessary to produce turbulence may then be available, though it appears not to be responsible for the sound utilized for blood pressure determination. Several problems are encountered if relaxation oscillations are applied to explain the Korotkoff sound, the principal one of which is that the Korotkoff sound has been observed to contain a wealth of high frequencies extending into the audible range, while relaxation oscillations have generally been observed to occur in the range of 4 to 8 Hz in arteries (62), well below the range of human hearing.

Pressure Origin The principal theories dealing with the pressure origin of the Korotkoff sound are a preanacrotic wave theory, a shock-wave theory, and a dynamic instability theory of the arterial wall. Erlanger (3) observed wave phenomena that precede the anacrotic or rising portion of the pulse in vessels subjected to external pressure. Steepening of the anacrotic portion of the pulse was often observed to accompany the appearance of preanacrotic waves. Since Erlanger concluded that the occurrence of sound coincides with the preanacrotic waves, he suggested that the formation of the preanacrotic wave is closely related to the generation of the Korotkoff sound. As had Erlanger (30), Bramwell and Hickson (7) noted steepening of the rising portion of the arterial pressure pulse. Proponents of the shock-wave theory explain this phenomenon of pulse steepening in terms of a hydraulic shock-wave. In its support, Beam (4) developed a fluid dynamic theory on the propagation of finite amplitude waves in externally loaded vessels, which indicates development of a shock-wave provided that the wave propagates over a certain 'critical length.' He did not indicate whether the length of an occlusive arm cuff is sufficient for such shock-wave formation. Other shock-wave theories make reference to the classical wave speed limitation. Brower and Scholten (11), on the basis of their measurements in partially collapsed elastic tubes, suggested that flow velocity of blood might exceed the wave speed during collapse of the brachial artery. If these two quantities should become equal, a shock-wave will occur. When an artery transforms from the cylindrical shape into the collapsed shape it The Korotkoff Sound 329

must buckle, while it unbuckles when it returns to its original form. At the point of buckling or unbuckling the arterial wall behaves as a highly compliant structure. Anliker and Raman (2) analyzed the buckling phenomenon for cuff pressure near the diastolic value, while Raman (55) performed an analysis near the systolic level. Using thin-shell membrane theory these authors found that buckling (unbuckling) is dynam- ically unstable such that small pressure fluctuations can be amplified to an audible level. Cohen and Dinnar (14) expanded on this concept by including resonance effects.

Critique of Pressure Origin Theories

The preanacrotic wave theory of the Korotkoff sound can be ruled out on the basis of experimental evidence. From noninvasive measurements Noordergraaf (47) concluded that the Korotkoff sound occurs during the anacrotic phase. Later, Tavel et aL (61) specified further, from invasive pressure measurements, that the Korotkoff sound occurs during the steepened part of the anacrotic wave. Although finite pulse steepening was observed by several investigators, a shock- wave, manifesting itself as a step change in pressure, has not been reported in arteries. Formation of a shock-wave appears unlikely, since, with a time-invariant system like a stethoscope, it would tend to produce Korotkoff sound of consistent frequency content. Thus, the quality of the Korotkoff sound would be expected to be constant and not sensitive to the level of cuff pressure, which contradicts experimental observations. The interpretation based on dynamic instability contains several puzzling features. First, it would be expected that both buckling and unbuckling generates a Korotkoff sound, while only one is heard per heart beat. Second, the Korotkoff sound has been found to be loudest at the distal edge of the cuff (61), where buckling and unbuckling should be minimal or absent. Third, Drzewiecki et al. (24) examined the cross- sectional area of vessels undergoing both distension and collapse due to altered transmural pressure. The measurements obtained for latex tubing and canine femoral artery revealed that buckling is much less pronounced in an artery than in a latex tube. These researchers concluded that nonlinear elasticity of the arterial wall material is responsible for the reduction of the buckling pressure. Thus, buckling in arteries may not be accurately described by the linear mechanics employed in wall instability theories. In summary, this review of the theories on the genesis of the Korotkoff sound does not permit identification of a most likely theory, though it does identify a number of unlikely candidates. None of the available theories has a demonstrated ability to predict the variation in Korotkoff sound intensity versus time or in character with cuff pressure. Only one investigator (69) considered the predicted sound energy level, on which the measurements of blood pressure critically depends. In spite of the avail- ability of a wealth of experimental data, most researchers did not attempt to verify the predictions of their theory against experimental information. In this article a new theory will be proposed. A quantitative model will be developed that is capable of predicting many of the observed Korotkoff sound phenomena, including variation in the quality of sound with the level of cuff pressure and the developed sound levels. 330 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

stethoscope, Pear /\ s,n Pcuff Po P,

proximal artery I I ] ] ]" distal artery

collapsible segment

FIGURE 1. The structures involved in the generation of the Korotkoff sound. Relative to the occlusive cuff, the proximal brachial artery receives pulsatile blood pressure Po, and flow Q. The segment of vessel surrounded by the cuff is assumed to be under uniform radial load, Pcuff, and may collapse. The distal artery connects the collapsible vessel with the peripheral vasculature of the arm. Just distal to the stethoscope detects the Korotkoff sound.

KOROTKOFF SOUND MODEL The fluid and structural dynamic elements associated with the generation of the Korotkoff sound are sketched in Fig. 1. An occlusive cuff loads a segment of the brachial artery with a uniform pressure Pcuff. Depending on the transmural pressure (internal pressure - external pressure), the artery is either open, or partially or completely collapsed. This segment of vessel will be referred to as the collapsible segment. The proximal segment of brachial artery connects the vasculature of the arm with the main part of the systemic circulation. This segment serves to supply the arm with pulsatile blood pressure and flow. It will be assumed that this source is independent of any downstream changes in load. The relationship between pressure and flow in collapsible vessels has been examined theoretically by Griffiths (33), Shapiro (59), Brower and Noordergraaf (10), and Pedley (49). Although these models have been derived from basic fluid mechanics, Brower and Noordergraaf (9) earlier introduced an empirical modeling approach, which permits the distributed properties of the collapsible vessel to be represented in lumped form. Adopting this approach in the model developed here, a detailed analysis of the complex pressure-flow relations in the collapsible vessel can thus be bypassed, allowing a more detailed study of the Korotkoff sound. Following the approach of Brower and Noordergraaf, the vessel is described in terms of its mea- surable external variables consisting of an input pressure, P0, output pressure, P1, external pressure, /)cuff, and flow, Q. In their description of steady flow conditions, input and output flow are equal. It is assumed that the inlet and outlet sections of blood vessel are short and that only the collapsible segment is described by the model. In terms of three-port parameters, the following expressions were developed for the pressure drop across a collapsible vessel:

Q /)cuff -- P1 Ap = Po - P1 Qc (1 + (Q/Qc)n) l/n for AP > Rr.Q (1) The Korotkoff Sound 331 where

Qc = a + be - (Pcuff - PI)/c (2) otherwise,

Ap = g r. a. (3)

Five empirical constants are introduced in Eqs. 1-3; they are: a, b, c, n, and e r. These constants are determined once from measured pressure-flow data during collapse for the particular vessel of interest. In this case, the human brachial artery is most relevant. Qc in Eq. 1 is an empirical variable, introduced by Brower and Noor- dergraaf (9), that is determined from Eq. 2. Rr is a constant equal to the Poiseuille resistance when the vessel is fully open. A set of empirical constants only represents the vessel for which the data were obtained. It is assumed that the arterial constants will apply fundamentally to other arteries of similar size and wall properties and will be an approximation in the analysis that follows. Since actual pressures are pulsatile, the above description of steady pressure-flow relations in a collapsible vessel must be modified. In the analysis here, inertance will not be considered, but a lumped nonlinear compliance will be taken into account. The shape of the collapsible vessel alters due to the distortion of the normally cir- cular cross-sectional of the brachial artery to a buckled binodal form, and then to a completely collapsed artery. In general, the shape will not be uniform along the vessel axis. For the Korotkoff model, the relationship between cross-sectional area and transmural pressure is integrated over the length of the collapsible segment, which relates its total volume to transmural pressure. Compliance is determined from the derivative of volume with respect to transmural pressure. The distal segment of the brachial artery connects the collapsible segment with the downstream vascular bed of the arm. This segment manifests the input impedance to the distal vasculature. The distal segment serves as the site of stethoscope application. It is shown in Fig. 1, placed over the distal artery with a layer of intervening tissue indicated. Since the Korotkoff sound is normally heard in this region, one goal of the model will be to compute arterial pressure and flow in this segment of artery. For computation of acoustic pressure in the auditory canal, these quantities are then applied as inputs to an additional model that incorporates the stethoscope. The analysis does not deal with pressure or flow exclusively, but with their relationship; hence, it fits into neither the pressure nor flow origin categorization.

Equations Describing the Model An electrical analogy is employed for convenience of formulation of the govern- ing equations. This permits mechanical and fluid dynamic quantities to be easily related by applying the following transformation of variables and parameters: pressure- voltage, flow- current, volume- charge, compliance- capacitance, inertance -- inductance, and flow resistance-electrical resistance. The equivalent electrical circuit representing the fluid dynamic model in Fig. 1 is shown in Fig. 2. The proximal artery is the voltagesource Vo(t) that supplies the incoming brachial pressure pulse. 332 G.M. Drgewiecki, J. Melbin, and ,4. Noordergraaf

Vcuff cryt)

c R o

'f ' I T- Vl ' vs-+ C s

1 -

FIGURE 2. Electrical analog of the fluid dynamic components involved in the generation of the Korot- koff sound. The voltage source Vo represents proximal pulsatile pressure, V1 is the pressure just distal to the cuff, and Vs is the peripheral pressure, The pentagonal symbol represents the collapsible artery. R s, C s, and R o make up the modified Windkessel for the distal vasculature. C(Vt) is the nonlinear volume compliance of the collapsible vessel, where Vt represents the downstream transmural pressure,

The vascular system distal to the cuff is represented by a modified Windkessel model, developed by Westerhof et a/. (67) and Noordergraaf (48). Referring to Fig. 2, the modified Windkessel consists of the three elements R0, Rs, and Cs. Ro is equivalent to the characteristic impedance of the brachial artery, Rs to the flow resistance of the arm, and Cs to the total vascular compliance of the arm distal to the cuff. A constant voltage source V~ is also included to account for venous pressure. The collapsible segment of artery is represented by the three-terminal symbol in Fig. 2. Two terminals are required for input and output and a third is added to supply an input for the cuff pressure ~cuff- The latter input serves as a control variable that affects the relationship between pressure and flow. The element C(Vt) represents the nonlinear lumped compliance of the collapsible segment of artery. Compliance is a function of the transmural pressure, Vt = I/1 - Vcuff , where I/1 denotes the pressure just distal to the collapsible segment. This compliance is placed between the downstream and external pressure terminals of the collapsible segment since collapse is more prominent in the distal half than in the proximal half. The model equations are derived from Fig. 2. State space analysis was employed to determine all voltages and currents. The voltage across each capacitor is then defined as a state variable; they are V~ and Vt. Kirchhoff's current law is applied to obtain the current in each capacitor as follows The Korotkoff Sound 333

Ic = Ie -/f = FI(Vo - Vt - Vcuff), Vt} -- (1/R0)(Vcuff + Vt -- Vs) (4)

I s =If-- /r = (1/Ro)(Vcuff-[- Vt- Vs) - (1/Rs)(Vs- Vv). (5)

The state equations are then,

dVt/dt = (1/C(Vt))F{(Vo - Vt - Vcuff), Vii -- (1/goC(Vt))(Vcuff + lit- Vs) (6)

dV~/dt = (1/Rofs)(Vcuff-t- V t - Vs) - (1/RsC~)(V~- Vv). (7)

In the above equations, the function F[ ] is used to express the current Ie- In Eqs. 1-3 flow in the collapsible vessel is the independent variable, hence, an inverse solution is employed. It should be apparent that all other voltage and currents in the model can be determined once Vt(t) and VAt) have been obtained. The distal pressure 1/1 (t) is of particular interest since it is the site of the stethoscope. It can be evaluated as follows

Vl(t) = V~uff + Vt(t). (8)

Another quantity of special interest is the downstream flow If. It is determined from the equation,

If = (1/Ro)(Vcuff + V t - Vs). (9)

COMPUTATIONS

A normal brachial pulse was recorded using a linear noninvasive pulse sensor developed in our laboratories to obtain a representative example of the pulse shape (17,20). The recording was digitized for use on a computer. The digitized version of the pulse was linearly scaled such that standard blood pressures of 120/80 mmHg were obtained. This alters the pulse magnitude to desired levels, but does not change its shape and frequency distribution. The modified pulse was then introduced to the model as V0(t), the proximal brachial pressure. The parameters Ro, Cs, and Rs for the modified Windkessel were computed from a more general model of the human arterial system (67). The major arteries of the arm that were incorporated in the model are the distal portion of the brachial artery and the ulnaris, radialis, and interossea volaris. Smaller arteries, arterioles, and cap- illary beds that terminate each of the major arteries are incorporated as lumped flow resistances. The collapsible segment of the Korotkoff model was represented by means of the empirical expressions, Eqs. 1-3. Before using these equations it is necessary to obtain the parameters a, b, c, n, and Rr from experimental data. Since pressure-flow data for the collapsed human brachial artery were not available, data from the canine femoral artery were substituted. The collapse behaviour of the canine femoral artery was measured by Conrad et al. (16). The human brachial and canine femoral arteries were assumed to be similar in size and mechanical properties. Since Eqs. 1 and 2 are nonlinear, the method of nonlinear least-squares estimation was applied to determine the values of the model parameters. The value of chi- 334 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

TABLE 1. Control values of model parameters and variables.

Quantity Value Units Role

Rs 1.20 x 105 g-cm 4-sec-1 Cs 10.1 x 10 -6 g-l-cm4-sec2 Downstream vascular system R o 3.40 X 103 g-cm-4-sec ~

Po systolic 120.0 mmHg Source pressure Po diastolic 80.0 mmHg Pv 0,0 mmHg Venous pressure Vs(0) 75.0 mmHg Initial condition a --1.25 X 10 3 cm3_sec-1 b 8.18 cm 3-sec-1 c 10.6 mmHg Collapsible vessel parameters n 0.904 -- Rr 1.32 x 103 g-cm-4-sec -1

squared was used as a measure of accuracy of the fit to the data. The parameters were each adjusted until chi-squared was minimized. This procedure was implemented on a computer using the gradient search method. The parameter values that resulted are shown in Table 1. The pressure-flow relation generated by the collapsible vessel model and that of the canine artery data are shown in Fig. 3 for comparison, The value of volume compliance for the collapsible vessel was obtained from data collected by Drzewiecki et al. (24) and Rabbany et al. (51) on canine femoral artery. The measurement was restricted to the physiological range. The compliance data were stored as a look-up table for each value of transmural pressure in increments of 5 mmHg, where each value was obtained from an empirical fit to the data. Interme- diate values of the compliance are obtained by linear interpolation. The data are reproduced in Fig. 4. To solve the model, the state Eqs. 6 and 7 are evaluated. The equations are in a form appropriate for the use of the Runge-Kutta method. The algorithm was implemented on a digital computer. A complete solution results in the transmural pressure Vt(t), and the peripheral vascular pressure in the forearm V~(t). Once these quantities are obtained, Eqs. 8 and 9 render the distal pressure and flow, respectively. Equation 6 requires the inverted form of Eqs. 1-3. Due to their nonlinearity, inversion was accomplished by means of the Muller method. Hence, at every instant of time, the current value of transmural pressure and the pressure drop across the collapsible segment of vessel are used to find the flow by means of root solving. The solution of the state equations requires initial conditions for Vt and V~ at t=0. Physically, V~(0) represents the value of the distal arterial pressure before the lumen opens for the first time. While the brachial artery is occluded by the cuff, blood in the distal arteries will continue to flow into the veins until equilibrium is achieved. The actual value will depend on the subject, the vascular state of the arm, and the duration of occlusion. Hence, V~(0) is highly variable. Tavel et al. (61) measured arterial pressure during the application of an occlusive cuff and found that The Korotkoff Sound 335

H H 14 B

8.~ 0.~ 9.5~ e.76 I .ee I .25 I .$8 I .75 FLOM~ I'IL/$

FIGURE 3. The pressure difference, Po - P1, across the collapsible artery as a function of flow. The solid curve was obtained using the empirical relations, Eqs. 1-3, with parameters derived from in vivo canine arterial data obtained by Conrad et al. (16). The circled points are the experimental data for comparison.

V~(0) typically lies between 30 to 80 mmHg. A value of 75 mmHg was chosen for this study. The initial transmural pressure, Ft (0), was evaluated from Vt = V~ - Fcuff at t=0.

ORIGIN OF THE KOROTKOFF SOUND The arterial pulse just distal to the cuff, P~ (t), corresponds to the voltage, V~ (t), in the model. It was computed for two values of cuff pressure equal to 90 and 115 mmHg. (Distal pulsation is present only for cuff pressure less than 120 mmHg.) Two cycles (fourth and fifth cycles steady-state) of the distal pulse are shown in Figs. 5a and 6a. In each case the normal brachial pulse, Po(t), is provided for comparison. Referring to Figs. 5a and 6a, the difference in pulse form proximal and distal to the cuff as a result of the presence of an external pressure are evident. For cuff pressure between systolic and diastolic pressure, the distal pulse was found to be distorted on both the rising and falling portions. The degree of distortion was greatest for high levels of cuff pressure. As cuff pressure falls, the distal pulse gradually returns to the proximal shape. Specifically, an increased slope was always found on at least a portion of the ascending part of the pulse. 336 G.M. Drzewiecki, .I. Melbin, and A. Noordergraaf

AREA e.2e~

8.15-

+ S;+ +/ +

8.18--

8~ I I I I I I I I I I I i 8e -58 8 58 188 158 TRANSHURAL PRESSURE; mFlg

FIGURE 4. Volume compliance as a function of transmural pressure. Data were obtained from the excised canine femoral artery with a wall thickness of 0.066 cm and an unpressurized radius of 0.138 cm. The solid curve is an empirical fit to the data (24).

To examine the pulses for sound content a digital single-pole high-pass filter with a cutoff frequency of 10 Hz was implemented. The result of the distal pulses is shown in Figs. 5b and 6b. The filter output indicates the presence of sound, coinciding with the steep parts in the distal pressure pulses. Figure 5d displays the sound content present in the normal proximal pulse and can be compared with the computed distal pulse while cuff pressure is applied (Fig. 5b). An apparent increase in sound content is observed due to the presence of the cuff. Based on these findings, it can be concluded that the steep part of the distal pulse contains the Korotkoff sound. The presence of a nonlinear pressure-flow relation causes some of the low frequency energy in the proximal pulse to be transformed into high frequency energy. The steepening of the distal arterial pressure will cause the arterial wall to rapidly distend and displace the overlying skin. This rapid motion of the skin is detected by the stethoscope, conducted to the ear, and heard as Korotkoff sound. Since distal arterial pressure and flow are related, the flow pulse also suffers from distortion. The flow pulse reaches its maximum following the occurrence of the max- The Korotkoff Sound 337 imum in the Korotkoff sound (Figs. 5c and 6c). This is seen as a phase shift in the computed results. Earlier observations by Erlanger (30) associated pulse steepening with the occurrence of the Korotkoff sound. Later, Bramwell and Hickson (7) could not decide whether the Korotkoff sound was associated with pulse steepening for the occurrence of the preanacrotic waves. Noordergraaf (47) who compensated for the propagation delay time inherent in the early instruments, and Tavel et al. (61), who employed invasive arterial recordings of the Korotkoff sound and distal pulse, concluded that the Korotkoff sound and pulse steepening were coincident events. Hence, the proposed theory is supported by the observations of earlier investigations.

COMPARISON WITH PREVIOUS OBSERVATIONS The literature reports on the following categories of experimental data related to the Korotkoff sound:

1. Distal arterial pulse, 2. Frequency content, 3. Microphone record, 4. Time of occurrence relative to pressure, 5. Time of occurrence relative to flow, 6. Spatial intensity of sound, 7. Variation with cuff pressure.

Predictions by the model will be compared with such data. Comparisons for categories 1 and 4 were presented in the preceding sections and in Figs. 5 and 6. Additional data, obtained by Tavel et al. (61), are shown in Fig. 7. These researchers find, from invasive measurements, that pulse steepening occurs and that the external recording of the Korotkoff sound coincides in time with the steepened part. These observations concur with the event and timing predictions of the model.

Frequency Content The frequency content of the Korotkoff sound was computed from the discrete Fourier transform of V~ (t) (Fig. 8). The transform of the normal (upstream) brachial pulse is included on these graphs to serve as a reference sound level. The reference level is normally not detected by the human ear. When the Korotkoff sound is present, the sound intensity increases, in the audible frequency range, by more than 20 dB. Frequency content has been investigated experimentally by Ware and Anderson (64), Golden et al. (32), and Maurer and Noordergraaf (45). Figure 9 shows a specific example obtained by Ware and Anderson, for the different phases of Korotkoff sound. The general feature of these data is that the Korotkoff sound frequency content decreases with increasing frequency. The computed Korotkoff sound also dem- onstrates this characteristic (Fig. 8). For example, the data exhibit a fall in sound energy of 25 dB over the frequency range of 20 to 200 Hz. Over the same range for phase I, the model predicts a 60 dB drop in sound content. 338 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

PROXIMAL AND DISTAL ARTERIAL PRESSURE

120.0

100.0

^ 80.0 i

'" 60.0 Cu?? Pressure : 115 mmH8

co bJ r~ o. 40.0

20 .O

0.0 , l J I , I 18 .O 19.0 20.0 21.0

TIME (see) (al

12.0 COMPUTED KOROTKOFF SOUND

I0 .0 Cu?? Pressure = 115 mmH9

8.0

6.0

v 4.0 c~

w. -~ 2.0 O co O.O

-2.0 -4,0 l -6 .o .... ' I , I , I 18.0 19.0 20.0 21.0

TIME (sec) (b)

FIGURE 5. (a) The proximal pressure input to the model (curve Po) and computed arterial pressure just distal to the collapsible segment of artery (curve P1)- The cuff pressure was held constant at 115 mmHg. (b) Korotkoff sound derived from the distal pressure The Korotkoff Sound 339

DISTAL ARTERIAL FLOU 5,0

Cu#~ Pressure = 115 mmH S

E 3.0 v

1.0

L L

-i .0 I , I I 18.0 19 .O 20.0 21.0

TIME (sec) (c)

I0.0 NORMAL BRACHIAL PULSE SOUND

8.0

6.0 O3 "r

E v 4.0

z D 2.0

0 03 0,0 f -2.0

-4.0 r I , I , I 18.0 19.0 20.0 21.0

TIME (sec) (d)

FIGURE 5. (c| Distal flow computed for the same conditions. (d) Sound derived from the filtered proximal and distal pressures. 340 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

130.0 PROXIMAL AND DISTAL ARTERIAL PRESSURE

Cu?? Pressure = 90 mmH9

110.0

co -I- E e v

Ld QC O~ 9o.o - n~ o.

70 .o ~ I ~ I , I 18.0 19.0 20.0 21.0

TIME (sec)

Ca)

10.0 - COMPUTED KOROTKOFF SOUND

8.0 CuF? Pressure = 90 mmH 9

o~ T 6.0

Q 4.0 Z

0 R.Q CO

o.o

-2.0

-4.o , I , 1 , 18.0 19.0 20.0 21.0

TIME (see) (b)

FIGURE 6. Ca) The proximal pressure input to the model Ccurve Po) and computed arterial pressure just distal to the collapsible segment of artery Ccurve P~). The cuff pressure was held constant at 90 mmHg. (b) Korotkoff sound derived from the distal pressure. The Korotkoff Sound 341

5.0 DISTAL ARTERIAL FLOW

CuFF Pressure = 90 mmH$

3.0

0 .J 1,0 b. -J /.

-i .0 i I i I , I 18.0 19.0 20.0 21.0

TIME (see) (c)

FIGURE 6. (c) Distal flow computed for the same conditions.

It can also be seen from Fig. 9 that the relative frequency content of the Korot- koff sound depends upon the level of cuff pressure. At values near systolic, more high frequency content (>90 Hz) was predicted than at the lower pressure. This may be what is referred to as muffling during phase IV Korotkoff sound. The muffling characteristic is also shown by the model in Fig. 8.

Microphone Records The evaluation of microphone recordings of the Korotkoff sound is complicated by the variety of microphone systems that have been employed (Figs. 10 and 11). Recently, the piezoelectric contact microphone has been used most frequently and was applied here. Since the piezoelectric microphone responds proportionately to the stress acting on its surface, for frequencies between approximately 5 Hz and 500 Hz, it was assumed that the piezoelectric microphone responds directly to the distal brachial pulse provided that firm contact is maintained with the skin (17,20,22). Microphone recordings of the Korotkoff sound were computed for two different values of cuff pressure (Figs. 5b and 6b). The sound shows a dominant initial signal spike, followed by smaller and slower oscillations. Experimental measurements of the Korotkoff sound by means of a piezoelectric microphone have been performed by Whitcher (68), Gupta et al. (34), and Maurer and Noordergraaf (45) (Fig. 10). The characteristic spike is present in these observations. 342 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

Exter~l ~und j i llll I ~,~ 1111 h.

~ach.ilI]IlllItll ~essure ~ N !

2~ Sound Exterrual I LI

[~JI rrFl I I / " i00~Brach, Pressure olltlll1~Jl'I 47 I~!!.!,!o!e' I11 I !

ILIII 1 I I

100

' I il Ji

FIGURE 7. Direct recording of the arterial pressure distal to the cuff by means of a high frequency catheter-manometer system. The rapidly ascending portion of the pulse is indicated by the derivative tracing relative to the derivative of zero cuff pressure data (bottom right). From Tavel, M.E. et al. Korotkoff sounds: observations on pressure pulse changes underlying their formation. Circulation 39:465-474; 1969.

In our laboratory, sounds similar to those predicted by the model were recorded by paying careful attention to microphone placement, filtering, and response characteristics (Fig. 11). This microphone record was obtained from the same subject as the normal brachial pulse curve (input to the model).

Time of Occurrence

The computed time of occurrence of the Korotkoff sound relative to proximal and distal arterial pressure may be read from Figs. 5 and 6. The time of occurrence was The Korotkoff Sound 343

KOROTKOFF SOUND FREQUENCY CONTENT

80.0

Pressure = 115 mmN9 60.0 ~ 40.0

"o v Po ~~~, bJ o 20.0

z co r(z 0.0

-20.0

0 I s 3 :tO iO 10 "iO

FREQUENCY (Hz) (a)

KOROTKOFF SOUND FREQUENCY CONTENT 80.0

" ~~ CuFF Pressure = 90 mmH9 60.0

40.0

20.0 PO

0.0 I f

-20.0

-40.0

-60.0

0 I 2 3 :tO :I.0 10 10 FREQUENCY (Hz) (b)

FIGURE 8. Frequency content of the Korotkoff sound, obtained from the brachial arterial pressure proximal (solid curve) and just distal to the occlusive cuff (dotted curve) for the computed pulses in Figs. 5 and 6. Cuff pressure was (a) 115 and (b) 90 mmHg. Midfrequency audible energy is greater than normally present in the brachial pulse. 344 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

1.0

0.!

.Oi

V',

.001 \

PHASE I PHASE 2 .0001 PHASE 3 PHASE 4 t .000(11 I iO 20 30 SO I00 |00 SQQ 400 q~O

FREQUENCY, H~

FIGURE 9. Measured energy content versus frequency for the Korotkoff sound. From Ware, R.W.; Anderson, W.L. Spectral analysis of the Korotkoff sounds. IEEE Trans. Riomed. Eng. RME-13; 170-174; 1966.

also computed for the whole range of cuff pressures of interest. The result is plot- ted in Fig. 12. The computed Korotkoff sound appears later with increasing cuff pressure. Rodbard (58) found from his observations that the Korotkoff sound is delayed as cuff pressure increases. He proposed that the delay time versus cuff pressure curve should match the shape of the rising portion of the brachial pressure waveform and proposed that this might be a means of noninvasively synthesizing the arterial pulse contour. Other researchers have found similar delay times (3,65). The data of Arzbaecher and Novotney are reproduced in Fig. 13 for comparison. Referring to Figs. 5c and 6c, the computations indicate that the onset of sound occurs at the time when distal arterial flow just begins to accelerate. This result is consistent with the Doppler ultrasound experiments of McCutcheon and Rushmer (42) and McQueen (43), who found that there is either negligible or initial flow build up at the time of the onset of the Korotkoff sound. The Doppler records obtained by McCutcheon and Rushmer are reproduced in Fig. 14 for comparison. The Korotkoff Sound 345

u~ p-

>, rr

rt~ r~

<1 bJ>_

..J bJ O:

0 .04 .08 .12 .16 .20

FIGURE 10. Recording of Korotkoff sound using an external contact microphone. From Gupta, R., et al. Spectral analysis of arterial sounds. A noninvasive method of studying arterial disease. Med. Biol. Eng. 13: 700-705; 1975.

0.8-,

8 0 0.4- U N D Ir 0.8- A O N I Z _JblldUK~.m... ,.aai..Aaa T 0.0- %..,.1. U ~IVu'wU~ IrW~1~ ~ '"" "w~F IWqW~ D E

.4.2- F

.4.4- O.O O.t 0.4 O.O O.O 1.0 I.Z

FIGURE 11. Recording of Korotkoff sound by means of an external microphone; authors" data. 346 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

12C

o~ E E 100

b,. e,l

80 | .30 .40 time; sec.

FIGURE 12. The ascending part of the upstream brachial pressure pulse (curve p), together with the computed time of onset of the Korotkoff sound as a function of cuff pressure (curve k). Zero time reference in both cases is the onset of the brachial pressure pulse. The Korotkoff sound occurs later with increasing cuff pressure and slightly before the moment that the upstream pulse reaches the level of cuff pressure.

150.0 ~-

100.0

i / ~- 50.0 ,, -

r=], , ,,i J,,, ,,r,,,rrl=,,i , ~' ''& A A A A 0 0 0 0 0 0 0 0 0 0 0 C5 o u~ o to o

Time, ms~

FIGURE 13. Measured delay in the appearance of the Korotkoff sound as a function of cuff pressure. The time reference is the R-wave of the electrocardiogram. The solid curve represents a best polynomial fit to the data. From Arzbaecber, R.C.; Novotney, R.L. Noninvasive measurement of the arterial pressure contour in man. Bibl. Cardiol. 31: 63-69; 1973. The Korotkoff Sound 347

FIGURE 14. Doppler flow velocity and microphone records obtained distal to the cuff; modified from McCutcheon and Rushmer (42). Cuff pressure is fixed. Traces from top to bottom: proximal flow velocity, flow velocity under the cuff, proximal signal amplitude (relative arterial wall motion}, signal amplitude under the cuff, Korotkoff sounds. Note that the Korotkoff sound (bottom trace) occurs earlier than the flow pulse (second tracing from top}.

Spatial Sound Intensity It has been observed that the magnitude of the Korotkoff sound varies as it propagates under the cuff and to the periphery. Since the current model is lumped, it is difficult to provide detailed spatial sound information. The locations represented by the model are: proximal to the cuff (Vo(t)), immediately distal to the cuff (V~ (t)), and the peripheral vasculature (V~(t)). The Korotkoff sound at each location was obtained by processing the pulse with the same 10 Hz filter employed earlier and with the cuff pressure at 115 mmHg. The model indicates that sound is present in the proximal artery (Fig. 5d). This sound is normally too low in amplitude and frequency to be audible. Korotkoff sound was found to be maximal in magnitude immediately distal to the cuff. At this position, all of the previously discussed Korotkoff sound phenomena were observed. The pressure at the periphery of the arm (Fig. 15) is identified with the pressure in the total distal compliance. At this site, it can be seen that the sound is much reduced in magnitude. Since the Korotkoff sound cannot be measured easily on the forearm due to the muscle tissue that covers the vessel in this region, little information is available on the variation of sound with position. It is reasonable to assume that the high frequency energy of the sound will be dissipated as it propagates towards the wrist, with- out any discontinuous jumps in intensity. Measurements taken in the region of the cuff by means of a needle manometer, confirm this analysis (61).

Cuff Pressure Variation The variation in the Korotkoff sound with cuff pressure, originally recognized by Korotkoff himself, is the basis for the auscultatory method of blood pressure mea- 348 G.M, Drzewiecki, J. Melbin, and A. Noordergraaf

4 u 120

m =p Z S- AI 18 P N 1" =l E N 8 2- Z T | Y J I" ",,.o" 0- r m m m Q -,% 7O m m !

m -.41I 1 | M 8.8 O.2 8.4 0.0 0.o 1.0 1.2 TJI:NEj U~~

FIGURE 15, The peripheral pulse and its associated sound for a cuff pressure of 110 mmHg.

surement. Clearly, it is one of the most fundamental characteristics of the Korotkoff sound. The computed variation in the Korotkoff sound with cuff pressure is shown in Fig. 16. The results indicate appearance of sound near the level of systolic blood pressure. The sound intensity increases to a maximum thereafter. Then a gradual diminution occurs until diastolic pressure is reached. Residual sound is seen to persist even after cuff pressure falls below the diastolic level. The relationship between Korotkoff sound and cuff pressure has been recorded noninvasively by Whitcher (68), Golden et al. (32), and Maurer and Noordergraaf (45). Tavel et aL (61) has found that an identical pattern can be observed from direct intra-arterial measurements of the pressure within the artery distal to the cuff. An example of Korotkoff sound versus cuff pressure is reproduced here for comparison (Fig. 17), the variation in the shape of the Korotkoff sound is similar to the model predictions. It should be noted that the recorded sound is rather dependent on the characteristics of the applied filter.

Effect of Nonlinear Vessel Compliance

The pattern of Korotkoff sound variation with cuff pressure is sensitive to the proximal pulse and the various model parameters. This becomes evident from comparison with an earlier version of this Korotkoff sound model (19,21,22,25-28). In the earlier version, the effect of volume compliance of the collapsible segment was not included. Korotkoff sound intensity versus cuff pressure from the earlier model is shown in Fig. 18 for comparison. This is equivalent to comparing a stiff (no corn- The Korotkoff Sound 349

140.0 PROXIMAL PRESSURE AND CUFF PRESSURE

120,0

100 ,o v

bJ C~

r O~ bJ 0r Q. 80.0 Po

60.0 I , I , I , I , I 0.0 4.0 8.0 :1.2.0 :1.6.0 20.0

TIME (see) (a)

140.0 COMPUTED DISTAL PRESSURE AND CUFF PRESSURE

120.0

100.0

80.0 E v

bJ rv 60.0 ~o PI lo bJ ~y 0. 40.0

20.0

0.0 I , I , I A , I 0.0 4.0 8 .O 12.0 16.0 20.0 TIME (sec) (b)

FIGURE 16. Computed brachial artery pressure distal to the cuff with continuous variation in cuff pressure. The cuff pressure falls at a linear rate of 2,5 mmHg/sec., beginning at 130 mmHg. In (a) the proximal pulse, the input to the model, and the cuff pressure are shown for time reference. (b) Cuff pressure and unfiltered distal pressure computed from the model. (Continued on overleaf.) 350 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

100.0 COMPUTED KOROTKOFF SOUND FOR FALLING CUFF PRESSURE

90.0 Cut 0~ Frequency = 0.I Hz

60.0 v

>- p- 40.0 z bJ

Z 20,0

Z 0 co 0.0

-20.0

-40.0 I , I I lA ~ I 0.0 4.0 8.0 12.0 16.0 20.0

TIME (sec) (c)

30.0 COMPUTED KOROTKOFF SOUND FOR FALLING CUFF PRESSURE

Cut OFF Frequency = 10 Hz A = 20.0 E E I p-

03 Z bJ ~- 10.0 z

Q z

o co

0.0

A I ~ I , I l IA , I 0,0 4,0 8,0 12,0 16.0 20,0

TIME (sec) (d)

FIGURE 16 continued. The distal pressure was filtered for sound using a high-pass filter with cutoff frequencies of: (c) 0.1 Hz, (d) 10 Hz, and (e) 40 Hz. Arrows signify systolic and diastolic pressure. (Continued on facing page.) The Korotkoff Sound 351

20.0

COMPUTED KOROTKOFF SOUND FOR FALLING CUFF PRESSURE

Cut OPF Frequency = 40 Hz -r- E 10.0 v

b- h-

z j-- Z

z Q.G Q

-10.0 ' I AI , I I I I ,.1^ I I 0,0 4.0 8.0 12.0 16.0 20.0

TIME (see) (e)

FIGURE 16 continued. pliance) brachial artery to one with a larger compliance. The basic difference one finds is that the presence of a compliance reduces the overall amplitude of the sound. In particular, the high frequency content is diminished. Another difference is that the Korotkoff sounds develop in amplitude gradually, instead of abruptly, when cuff pressure begins to fall. Furthermore, the compliance contributes sound in addition to the nonlinear pressure-flow relationship of the collapsible segment. This contri- bution is particularly evident at the time of 14 seconds in Figs. 16d and 18d. In Fig. 18d the sound has diminished to residual levels by this time, while in Fig. 16d sound is still being produced. Since the compliance is the only difference between the two models, it must be the source of sound. Thus, while the volume compliance produces sound during all phases of the Korotkoff sound, it is dominant in phases IV and V. Hence, a model that includes nonlinear volume compliance provides more realistic predictions.

Accuracy of Blood Pressure Measurement It is interesting to note the amount of error in blood pressure measurement that would result from the predicted Korotkoff sound intensity curve. Referring to Fig. 16, phase I occurs at 119 mmHg Cuff pressure and phase V at 85 mmHg. Since the actual blood pressure was prescribed in the model to be 120/80 mmHg, the auscultatory measurement error is -1 mmHg for systolic pressure and +5 mmHg for diastolic pressure (Fig. 18b). Researchers have found that the mean error for systolic pressure ranges from +7 to -25 mmHg and for diastolic pressure ranges from +20 to -5 mmHg, where the auscultatory method was compared with intra-arterial mea- 352 G.M. Drzewiecki, J. Melbin, and A. Noordergraaf

Korotkov No filter I >0.111z

~o,otko, I ! i I | I : ~ i x I0,>40Hz | | | I "

Cuff HM)

t (b)

FIGURE 17. Microphone recording of Korotkoff sound versus continuously decreasing cuff pressure. The sounds were high-pass filtered at the three different cutoff frequencies indicated. From Whitcher, C. Blood pressure measurement. In: Techniques in Clinical Physiology. Bellville, W.J.; Weaver, C.S., eds. New York: MacMillan; 1969.

surements (8,35,41,46,54). Thus, the model prediction is in line with that of accuracy studies.

Korotkoff Sound Transmission and Stethoscope To examine how the stethoscope transmits the Korotkoff sound to the ear, additional modeling was performed. This part of the total model will be summarized here since a complete treatment may be found elsewhere (18,22,26,52). The results are presented here to provide an additional source of experimental measurements with which to compare the new theory. The brachial artery pressure, just distal to the cuff, was related to the pressure transmitted to the ear by the stethoscope. This was accomplished by treating the artery, local tissue, and stethoscope as a linear system. The effects of inertance, resistance, and compliance were taken into account by treating the arterial wall, adjacent tissue, stethoscope bell, and bell volume as lumped mechano-acoustic elements and the stethoscope tubing as a distributed acoustic transmission line. This analysis ulti- mately results in a linear transfer function, assuming small deformations. The input to this subsystem was the distal arterial pressure as generated by the Korotkoff sound model. The sound pressure level in the auditory canal was computed using the acoustic model at 20 Hz, the lowest audible frequency for man, for various cuff pressures. The result is shown in Table 2. According to the measurements of Fletcher and Munsen (31) the threshold of human hearing at 20 Hz is approximately 10 -8 watt/m E. Note that this level of sound corresponds well with the values calculated in Table 2. Therefore, it was found The Korotkoff Sound 353

140.0 PROXIMAL PRESSURE RND CUFF PRESSURE

120.0

~ ~oo.o

SO.O Po

6o.o I , I , I , I , I 0.0 4.0 8.0 12.0 16.0 20.0

TIME (see) (a)

140.0 COMPUTED DISTAL PRESSURE AND CUFF PRESSURE

120.0

100.0

~80.0 i= J v

LLJ ,',, 60.0 (n (n ,i t,J P1 o. 40.0

20.0

I , I , I , I~ , I * 0.0 i A 0.0 4.0 B.O ~.2.0 16.0 2Q.O TIME (sec) (b)

FIGURE 18. Computed Korotkoff sound intensity with continuous variation in cuff pressure. The nonlinear volume compliance of the artery is absent from the model in this case. In (a) the proximal pulse and the cuff pressure for time reference. (b) Cuff pressure and unfiltered distal pressure computed from the model. (Continued on overleaf.) 354 G.M. Drzewiecki, J. Me/bin, and A. Noordergraaf

100.0 COMPUTED KOROTKDFF SOUND FOR FALLING CUFF PRESSURE

Cut 0~ Frequency = O.i Hz 80 .O

-I- 60.0 v }-

z 40.0 W h~ Z

C~ z 20,0 0 uI,

-20,0 "- I ! I ~ t l I ' A A 0.0 4.0 8.0 12.0 16.0 20.0

TIME (see) (c)

100.0 COHPUTED KOROTKOFF SOUUD FOR FALLING CUFF PRESSURE

Cut OFF Frequency = 10 Hz 80.0 3,

ve 60.0

h- o3 7- 40.0 bJ

c~Z 20.0 o (/)

-20.0

-40.0 i Ai i I ~ I ' .,[A ' I 0.0 4.0 S .0 12.0 16.0 20.0

TIHE (see)

{d]

FIGIRE 18 continued. The distal pressure was filtered for Korotkoff sound using a high-pass filter with cutoff frequencies of: (c) 0.1 Hz, (d) 10 Hz, and (e) 40 Hz. Arrows signify systolic and diastolic pressure. (Continued on facing page.) The Korotkoff Sound 355

90 .O

COMPUTED KOROTKOFF SOUND FOR FRLLING CUFF PRESSURE

70.0 Cut 0@? Frequency = 40 Hz O3 "I- E E v 50.0

-j. w Z 30.0 ,"-m ,.j. ,--, O 01'

10.0

-10.0 i A I , I , I , ,,Ix , I 0.0 4.0 8.0 " 12.0 16.0 20.0

TIME (sec) (e)

FIGURE 18 continued.

that sound levels produced by the Korotkoff sound model are commensurate with human hearing. No other theory of the Korotkoff sound has verified this experimental finding.

CONCLUSIONS A new theory for the origin of the Korotkoff sound is proposed. The brachial pulse just distal to the cuff is distorted compared to the proximal pulse by the effect of cuff pressure and arterial collapse. This distortion arises from the nonlinear pressure-flow relationships between the input and output of a collapsed vessel. Pulse distortion was found to be manifested primarily during a portion of the ascending part

TABLE 2. Korotkoff sound intensity at the ear.

Sound pressure level Intensity Cuff Pressure dB [20 Hz] watt/m 2 [20 Hz]

0 -80.0 1.7 x 10 -9 Systolic -58.0 2.7 x 10 7 Mean -68.0 2.7 x 10 -8 Diastolic -78.0 2.7 x 10 -9

0 dB = 1.7 x 10 -5 watt/m 2. 356 G.M. Drzewiecki, J. Meibin, and A. Noordergraaf of the distal pressure pulse and appears as a transient increase in the slope of the pulse. This steep pulse slope was found to contain high frequency harmonics of the basic pulse rate that are either not present or subaudible in the natural brachial pulse. It is concluded that the transient pulse steepening is sensed by the ear via arterial distension, motion of the skin under the stethoscope bell, and transmission through the stethoscope. Compared to earlier theories of the Korotkoff sound, the theory proposed here for the origin of the Korotkoff sound does not fit the conventional pressure or flow origin categories. This is due to the fact that fluid mechanics is based on pressure- flow relations. The proposed theory was tested by developing a lumped fluid dynamic model. This model permitted computation of the pulse distortion downstream of a collapsible segment of artery. The model of the Korotkoff sound generation mechanism is able to predict a wide variety of observed characteristics of the sound. These include the shape of the distal pressure and flow pulses, and frequency content, microphone recordings, time of occurrence, spatial intensity variation, and intensity variation of the sound with cuff pressure. In addition to these comparisons, it was found that the sound energy predicted by the model conforms with the level of human hearing. On the basis of these findings, the proposed theory offers a mechanism for the origin of the Korotkoff sound.

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NOMENCLATURE t ~-- time Po(t) = Pressure upstream of collapsible vessel Pt (t) = Pressure downstream of collapsible vessel Ap = pressure drop across collapsible vessel Pcuff = External pressure due to cuff Vo(t) = Voltage analog of Po(t) V~(t) = Voltage analog of PI (t) V,(t) = Voltage analog of transmural pressure K(t) = Voltage across capacitance Cs Vcuff ~- Voltage analog of cuff pressure Vv = Voltage analog of venous pressure Q(t) = Flow in collapsible vessel I~(t) = Current analog of volume induced flow due to C(Vt) Is(t) = Current in capacitance Cs Ie(t ) = Current analog of flow in collapsible element If(t) = Current analog of total downstream flow L(t) = Current in resistance Rs R o = Characteristic impedance of brachial artery e s = Flow resistance of forearm R r = Flow resistance of fully open collapsible vessel c(v,) = Capacitive analog of nonlinear compliance c+ = Capacitive analog of total arterial compliance of forearm a,b,c,n = Empirical constants for pressure-flow relations of collapse Qc = Intermediate variable of Eqs. 1-3 F{ } = Inverse of Eqs. 1-3