Estimation of blood pressure-related parameters by electrical impedance measurement JAAP
H. J. MUNTINGA
Department
of Medical
AND Physiology,
KLAAS
R. VISSER
University
MUNTINGA, JAAP H. J., ANDKLAAS R. VISSER. Estimationof blood pressure-related parameters by electrical impedance meusurement. J. Appl. Physiol. 73(5): 19464957, 1992.~In 13 healthy volunteers a computerized experimental set-up was usedto measurethe electrical impedanceof the upper arm at changing cuff pressure,together with the finger arterial blood pressurein the contralateral arm. On the basisof a model for the admittance response,the arterial blood volume per centimeter length (1.4 t 0.3 ml/cm), the venous blood volume as a percentageof the total blood compartment (49.2 t 12.6%),and the total arterial compliance as a function of mean arterial transmural pressurewere estimated. The effective physiological arterial compliance amounted to 2.0 t 1.3 ,ul. mmHg-‘. cm-l and the maximum compliance to 33.4 t 12.0 pb mmHg-l cm- ‘. Additionally, the extravascular fluid volume expelledby the occludingcuff (0.3 t 0.3 ml/cm) wasestimated. These quantities are closely related to patient-dependent sourcesof an unreliable blood pressuremeasurementand vary with changesin cardiovascular function, suchasthose found in hypertension. Traditionally, a combination of several methods is neededto estimate them. Such methods, however, usually neglect the contribution of extravascular factors. l
arterial compliance; hypertension; venous pressure
of Groningen,
NL-9712
KZ Groningen,
The Netherlands
quantities. As early as 1910, Janeway and Park (14) tried to determine whether the resistance to compression of the arterial wall introduces an error in blood pressure measurement. In patients with sclerotic or calcified vessels, the vessel wall resists compression by the inflated cuff. Thus a higher pressure is needed to occlude the artery, resulting in spuriously high systolic blood pressure readings (pseudohypertension). In patients with a diagnosis of essential hypertension, Osler’s maneuver may be used for the identifica .tion of pseudohypertension (21). D luring this maneuver, the blood pressure cuff is inflated to above systol .ic pressure and the radial or brachial art ‘cry is palpated di stal to the poi .nt of occlu sion. A patient is described as being Osler positive when either of these pulseless arteries remains clearly palpable. Of course, this is a quite subjective method, and the presence of pseudohypertension does not rule out true hypertension, because both phenomena may coexist. Whole-day ambulatory blood pressure monitoring revealed that ~20% of patients previously found to be hypertensive by standard methods had normal daily blood pressure patterns (26). It has been suggested that the apparent hypertension is caused by an increased level of sympathetic arousal due to anxiety and a conditioned response to the clinical setting (19, 26). Whole-day ambulatory blo od pressure me asuremen t, however, requires cooperation of ’ the patient under all circumstances and therefore encroaches on normal daily activities. Changes in the elasticity or state of contraction of the arteries in the upper arm are reflected in the blood volume and compliance of the total arterial compartment (effective arterial compliance). Arterial compliance is lower in Osler-positive subjects and correlates with the difference between cuff and intra-arterial pressures (21), whereas smooth muscle contraction result% in a horizontal shift of the compli ante-pressure curve toward higher pressure levels (9). so instead of measuring only the arterial pressure, it seems appropriate also to estimate the arterial blood volume and compliance as a function of mean arterial transmural pressure. To achieve this, the electrical impedance was measured. By measuring the electrical impedance of upper arm tissues under an occluding cuff, we attempted to assess the fluid shifts during varying cuff pressure. A model was used to predict the change in electrical admittance as a function of time and cuff pressure. To ascertain the efficacy of th .e method, the parameters of the model were estimated and the clo seness of the predicted admittances to the observed values was analyzed in experiments with
TEZEINDIRECTMEASUREMENT ofarterialbloodpressure by means of the occluding cuff auscultatory technique according to Riva-Rocci and Korotkoff is one of the most frequently applied methods in clinical medicine, Use of this method is commonplace because of its simplicity, on the one hand, an .d the importance of bl .ood pressure as an index of present and future cardiovasc ular health, on the other. Measurements using noninv ,asive ambulatory blood pressure monitoring, however, have shown that single blood pressure readings do not provide an accurate assessment of an individual’s blood pressure (5). The same conclusion has been drawn from treatment trials of hypertension in which average blood pressure fell during the first few weeks in all treatment groups, including those taking placebo tablets and those on observation only (20). At least three measurements on three separate days should be obtained to assess a patient’s blood pressure (30). Despite this and other recommendations (6) for obtaining a representative blood pressure reading, many patients are misclassified as hypertensive (24). This is, at least partly, the result of a lack of information about the elasticity of the arterial wall and the state of contraction of the blood vessels, because not only blood pressure, but also blood pressure measurement, is influenced by these 1946 0161~‘7567/92 $2.00 Copyright 0 1992 the American Physiological Society
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BLOOD
PRESSURE-RELATED
PARAMETERS
1947
FIG. 1. A cuff pressure registration with corresponding admittance response. When cuff inflation starts (at 0) blood and extravascular fluid are squeezed out from tissue under cuff, resulting in a decrease in admittance. This continues beyond end of cuff inflation at time t,. When cuff deflation starts at time tde interstitial space starts to refill, as do blood vessels later on, resulting in increase in admittance up to end of cuff deflation (at F). Cuff pressure equals mean intra-arterial pressure at time tPm.Ydifff difference between admittance measured at end of cuff deflation and that measured before cuff inflation.
13 geriatric subjects. When the analysis showed a significant fit, the parameters were accepted. From the accepted parameters, we calculated several quantities, including the effective arterial compliance at physiological pressure (effective physiological compliance), the maximum compliance, and the arterial and venous blood volumes for the tissue under the cuff. MATERIALS
AND METHODS
TheoreticaL foundations. During a measurement, the cuff is rapidly inflated, held constant at suprasystolic cuff pressure, and then slowly deflated. The blood and extravascular fluid volumes under the cuff vary with changing cuff pressure. This is reflected in changes in the electrical impedance of the upper arm under the cuff and opposite changes in electrical admittance (Fig. l), admittance being the reciprocal of impedance. The tissue under the cuff is considered as a parallel electrical circuit of movable extravascular fluid, blood, and residual tissue, the latter consisting of cells and extracellular fluid remaining permanently in situ. The contributions of these components to the total admittance can be estimated from the admittance changes at varying cuff pressure. The extravascular volume response to changes in cuff pressure is biphasic, because of the presence of rapidly and slowly movable extravascular fluid (l&22). The rapidly movable part of the extravascular fluid is assumed to be squeezed out with the blood. Because of the rapid emptying of the blood vessels as a result of the rapid increase in cuff pressure, the slow admittance decrease at constant cuff pressure after inflation can be due only to slowly movable extravascular fluid. The minimum admittance reached just before cuff deflation (Yti,) is the sum of the admittance of the extravascular fluid that is left behind but would have been squeezed out at continued constant cuff pressure (Y,) and the admittance of the residual tissue (Yti). The exponential nature of the
slow extravascular volume response to changes in cuff pressure is characterized by a time constant 71sthat does not seem to be pressure dependent at suprasystolic pressures (8). Similarly, a monophasic exponential refill of the extravascular space was assumed during the slow decrease in cuff pressure throughout deflation. The time constant of this refill was assumed to be equal to that of the expulsion of the slowly movable extravascular fluid. At cuff pressures below the systolic arterial level during inflation, the expulsion of blood will be delayed by arterial refill during the time when arterial pressure is above cuff pressure. Therefore a time delay (td) in the expulsion of blood has to be assumed. The admittance response, starting at the beginning of inflation and ending at the point where the cuff pressure reaches the level of intra-arterial systolic pressure during deflation, can thus be considered to be the result of the expulsion of blood and rapidly moving extravascular fluid, accompanied and followed by the expulsion of a part of the slowly movable extravascular fluid and then by the return of extravascular fluid (Fig. 2). On the basis of the different admittance responses in time, it is possible to separate the extravascular fluid contributions to the total electrical admittance from the contributions of blood and residual tissue. The parameters estimated for calculating these contributions have been called time-related parameters. During cuff deflation, blood admittance can be estimated by subtracting the contributions of extravascular refill and residual tissue from the total admittance. By using the resistivity of blood, the admittance of blood can be transformed to a volume. As soon as cuff pressure falls below systolic arterial pressure, the arteries will temporarily open and pass some blood to the veins distal from the cuff. Because of the large venous compliance, the resulting change in venous volume will only slightly increase venous pressure. As soon as cuff pressure falls below venous pressure, the veins under the cuff start to refill. At cuff pressures below this threshold pressure
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1948
BLOOD
PRESSURE-RELATED
PARAMETERS
stress relaxation (1, 27).
(delayed compliance)
of the arm veins
Mathematical formulation. The total electrical
tance [Y&t)]
admit-
is written as
ut,ttt) = uiCt) + Ybtt) + yti
(1)
where t is the time after the start of cuff inflation and Y;(t) and Yb(t) designate the admittances of movable interstitial fluid and blood, respectively. With cuff deflation starting at time tti, the biphasic nature of the extravascular admittance response for 0 s t < tdf is described
Yi( t) = yis(t, + Yi,(t)
(2)
where Yi,(t) and Yi,(t) are the admittances of the slowly and rapidly movable parts, respectively. At t = 0, the start of inflation, Eq. 1 reduces to
Y tot0
=
yi*
+
ybO
+
yti
=
yisO
(3)
. 0
\
1. t0
-
fyi,
yis
0)
+
y,
0 +
yti
Yi 0 is the total interstitial admittance, Yiso is the admittance of the slowly movable part of the interstitial fluid, (Y - Y, J is the admittance of the rapidly movable part of ?he interstitial fluid, and Y, 0 is the admittance of the blood at t = 0. Because a linear first-order response was assumed, the change in admittance of the slowly movable part of interstitial fluid before deflation and the change in admittance of the total interstitial fluid during deflation can both be described by
V,,(t) + y,(t) I I
y,(t)---
+
7.
l
18
ttme
FIG. 2. time-related part of predicted admittance as a function of time during varying cuff pressure (top). For t 2 tdft extravascular admittance response is given by Eq. IO. Area within dashed rectangle is enlarged in B. B: constituent parts of admittance response during inflation and constant suprasystolic cuff pressure. Combined contribution of rapidly movable extravascular fluid [Yi,(t)] and blood [Y&Q] to admittance response is given by Eq. 8. Slowly movable part of extravascular fluid contribution [Y,,(t)] is given by 23q. 6 for 0 I t < t, and by IQ. 7 for te5 t < tdf. A:
(Pthr), a linear venous pressure-volume relation was used, At cuff pressures above Pthr, the arterial refill forms the only contribution to the blood admittance. For the arterial pressure-volume relation, the model of Langewouters et al. (17) was used. The time dependency of the quasi-static arterial pressure-volume relationship was neglected, because volume and pressure change slowly and the arterial wall exhibits little viscous behavior (35) during the prolonged arterial refill. It is therefore possible to separate the arterial from the venous contributions by considering them as a function of cuff pressure only. The parameters estimated for calculating these contributions have been called pressure-related parameters. The difference between the admittances measured at the end of cuff deflation and those measured before cuff inflation (Y& was assumed to be the result of reverse
-
d[yi(t)] + Yi(t) = Y,, - y,D’p p,(t) dt
e
(4)
where 7is is the corresponding interstitial time constant, YCO is the interstitial admittance at zero cuff pressure, P,(t) is the cuff pressure at time t, and P, is the cuff pressure at the end of inflation. The pressure in the cuff during inflation is
t P,(t) = -. P
(5) te e where te is the time needed to inflate the cuff to P,. From Ep. 4 and 5 with Yi(t) replaced by Yisft) in Eq. 4 and with initial conditions Y,(O) = Yiso = Y, o and dYi,( t)ldt = 0 at t = 0, we obtain (Fig. 2) for 0 5 t < te Y +
y
l
(1
-
e+s)
(6)
e From Eq. 4 with P,(t) = P,, Yi(t) replaced by Yi,(t), and initial conditions Y,(t) = Yi,( te) and dY,,( t)/dt = -Yi,( te)l rig at t = te [Yi,(t,) calculated from Eq. 61, we obtain (Fig. 2) for te 5 t < taf Y is 0 yi,( t) = -.+5
. (&?/%3- 1) e-t/Tit3 l
(7)
e
The combined
contribution
of rapidly movable
extra-
vascular fluid [Y,,(t)] and blood [Yb(t)] to the admittance response during inflation is written function (Fig. 2) with a td
as an exponential
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BLOOD
PRESSURE-RELATED
PARAMETERS
1949
P,, is the threshold pressure at which the veins start to refill (8). for t, 5 t < ta, where Tbir is the time constant of the Computations. The impedance of the tissue under the expulsion of both blood (rb) and rapidly movable extracuff was transformed to admittance. The cuff pressure at vascular fluid. the start of deflation (P,) and the time constant of the The exponential cuff deflation is described by cuff deflation (Q) were estimated from the cuff pressure P,(t) = p, ~--(t--tdf)~rp = p, . &/T, (9) measurements by use of a linear least-squares exponenwhere Q is the time constant of the cuff deflation and t’ is tial estimation procedure. A description of the mathematical model to predict the the transformation of time t to t’ = t - tw From Eqs. 4 and total admittance as a function of time [Y,,,(t)] can be 9 with initial conditions vi(O) = Y,, Y, o = Yio, and obtained by combining Eqs. 1, i, 6, 7, 10, and 11. This fWi t’)/dt’ = -Yst/Tis at ti = 0, we obtain (Fig. 2) for t > 0 part of the model describes the admittance response up 1 to the time when cuff pressure falls below systolic presQ. e -tf’7P) + 1 W i ) - Y iO* -. ( 7. 1s . e-t’/“8 sure during deflation. The values used in the model for 7p - 7is (10) Ytoto and Ymin were deduced directly from the measure+ y,, . e-t’& ments. With the model, the time-related parameters Y, o, The extravascular admittance at the start of deflation Yi09 Ybo, 7isy7biry and td were estimated at the time interval corresponding with suprasystolic cuff pressure. Then (Y,,) can be written (Eq. 3) as the closeness of the predicted admittances to the obY st = Y min - Y ti = Y min - ytitO + yiO + ybO (II) served values was analyzed. The admittance of blood during cuff deflation (Yb) was A description of the mathematical model to predict Yb determined by subtracting the admittances of residual as a function of cuff pressure during deflation can be Eqs. 12-17. This part of the tissue (Yti) and extravascular refill Yi (Eqs. 10 and I I) obtained by combining from the total admittance model describes the admittance response for cuff pressures above P, 1 during deflation. Yb was converted to a Y b = Y tot - Y ti - Y i (12) blood volume by using a value of 135 Q 4cm for j+, (28). This admittance was converted to blood volume Vb by The cuff pressure P, 1 was taken to be 10 mmHg in accoruse of Nyboer’s expression dance with the hydro&atic pressure difference of the upper arm relative to the heart. With the model, the pres2 vb = Yj./&./ L (13) sure-related parameters V,,, PO, P,, K, and P,,, were where pb is the resistivity of blood (23) and L is the dis- estimated at cuff pressures above P, 1 and below the diatance between the measuring electrodes. The blood vol- stolic level. Then the closeness of the predicted admittances to the observed values was analyzed. ume consists of an arterial (V,) and a venous (V,) part In all computations, values were used that represent V b = v, + v, (14 the mean over a cardiac cycle. At cuff pressures between According to the model of Langewouters et al. (17), the systolic and diastolic pressure, however, the arteries colarterial pressure-volume relationship during cuff deflalapse during a part of the cardiac cycle. Therefore the tion is described by time-related parameters were estimated at suprasystolic cuff pressures and the pressure-related paramet ers at V.=~i,r~tan[‘ptrtpo’]+5j (15) cuff pressures above P,, and below the diastolic level. The admittances at the remaining cuff pressures were calculated using extrapolation. where V, is the arterial volume at mean arterial transBoth time- and pressure-related parameters were estimural pressure (P,,), V,, is the maximum arterial voldata using the BFGS or comume, PO is P,, at maximum arterial compliance, and P, is mated from experimental plementary DFP algorithm (32), based on nonlinear related to the steepness of the arctangent relationship. least-squares parameter estimation. The pa rameter estiP,, at the left upper arm was determined by subtracting the cuff pressure during a cardiac cycle (P,) from the mates began with the same standard initial guess fo r the fitting parameters in all experiments. Then the iterative mean arterial pressure (P,) algorithm improved the parameter estimates in steps. Ptrn= P a- Pc (16) When the successive parameter modifications became For cuff pressures above Pthr during deflation, the ve- negligible ( = v,, L*r
At P,, = P,, the arterial C Imax
l
P PT+ (PtI-PcJ2
compliance
C’max --
reaches a maximum
v max
LgK*P,
The volume of the extravascular fluid that may be squeezed out by cuff inflation (Vi,) was calculated from the estimated value of Yio by use of Nyboer’s expression, with the extravascular resistivity taken to be 50 Q *cm (7). In a similar way, the initial blood volume V, 0 was calculated from Y, 0. Total tissue volume was calculated from the measured arm circumference and L. In this calculation, we considered the tissue between the measuring electrodes as a cylinder. To determine the residual tissue volume (V,), the blood and extravascular volumes were subtracted from the total tissue volume. The resistivity of residual tissue was calculated using an equation analogous to Eq. 13 for a tissue volume. The blood volume after cuff deflation (V,,) was obtained by subtracting the extravascular and residual tissue admittance from the total admittance measured after cuff deflation (Eq. 12) and applying Eq. 13. The arterial part of this blood volume (V,,) was calculated from the estimated parameters and P,, by use of Eq. 15. Because Eq. 17 is based on an assumed linear venous refill, it should not be used for the calculation of the venous blood volume at the end of cuff deflation. The venous blood volume after cuff deflation (V,,) was estimated using V vF = V bF - V aF (20) To compute the initial venous blood volume was subtracted from V,, 0 V vO- - V bO- V aF
(V,,), Vfi
(21)
E3cperiments. Figure 3 shows a block diagram of the experimental set-up. Arterial blood pressure and heart rate were measured noninvasively by a Finapres device (33,34). This instrument continuously measures arterial pressure in the finger by means of a vascular unloading technique, as described by Pefiaz (25). Its inaccuracy compared with intrabrachial blood pressure measurements is approximately -6 mmHg and its imprecision is t4 mmHg (34). A Minnesota impedance cardiograph (model 304A, Instrumentation for Medicine) with a lOO-kHz 4-mA constant-current source (16) was used for impedance measurements. Two potential-measuring (Pl and P2, Fig. 3) and two current-conducting electrodes (11 and 12, Fig. 3), consisting of self-adhesive disposable electrode tape (3M), were applied around the full circumference of the
PARAMETERS
left arm. The measuring electrodes were placed 10.5 cm above the antecubital space 2 cm apart, while the conducting electrodes were applied around the wrist and proximal end of the arm. A 16-cm-wide cuff was placed around the left upper arm; it completely covered the measuring electrodes. Cuff pressure was measured with a pressure transducer (Statham P23 Db) and controlled by two electric valves (24-V direct current model IP65 /IEC144, Martonair). The Finapres device and pressure transducer were calibrated using a mercury manometer. Valve control and data acquisition, storage, and analysis were realized using an IBM-compatible PC/XT with expanded memory and an AD/DA expansion board (MetraByte, Dash-16F). All signals were sampled at a frequency of 20 Hz. Measurements were performed on two healthy male and 11 healthy female volunteers, ranging in age from 62 to 81 yr. All subjects gave informed consent for the study. Information collected on each individual included sex, date of birth, state of health, medication, alcohol and tobacco consumption, body mass, height, arm circumference, and thickness of skinfolds at the level of the measuring electrodes. During the measurements, the subjects were sitting in an armchair. A modification of the protocol proposed by Gizdulich et al. (8) was used. The experiment began when electrodes and cuff were applied around the left upper arm and the subject was in a comfortable sitting position with both arms on the armrests of the chair. To prevent insufficient cuff inflation as a consequence of extreme leftright differences in arterial blood pressure, the arterial pressure on the second phalanx of the middle finger of the left hand was measured first, for 2.5 min. Then the Finapres cuff was placed on the second phalanx of the middle finger of the right hand, while the maximum of the finger arterial pressure at the left hand was determined automatically from the sampled data. After the subject had been instructed to move as little as possible, the automated process of concurrent data acquisition, data storage, and cuff pressure control was started. First, the cuff around the left upper arm was rapidly inflated to 20 mmHg above the maximum of left finger arterial pressure (Fig. 1). After 120 s at constant cuff pressure, the cuff was slowly deflated in -300 s. To obtain the mean arterial pressure at the left upper arm, the mean arterial pressure as measured with the Finapres cuff in the contralateral arm was corrected for both hydrostatic and left-right differences in arterial pressure between the left upper arm and the middle finger of the right hand. Analogous to oseillometric techniques, the maximum pulse amplitude of the first time derivative of the impedance change (dZ/dt) is assumed to signify mean brachial arterial pressure (13). Accordingly, the (lowest) cuff pressure at maximum dZldt pulse amplitude was determined and subtracted from the mean arterial pressure as measured with the Finapres cuff. By subtracting the resulting pressure correction from a11mea-
sured Finapres pressures, the finger blood pressures were transformed to the level of the measuring electrodes around the left upper arm.
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BLOOD
PRESSURE-RELATED
PARAMETERS
1951
r f f f f f f f f f f f f 1 f
f f f t f f f f f f f f f I
f f I f f f f
DASH 16F ADIDA BOARD
FIG. 3. Block diagram of measuring and controlling system with measuring electrodes P1 and P2 and conducting electrodes I1 and 12. Pressure in cuff around left upper arm is controlled through computer program. Cuff pressure and impedance values of left upper arm and Finapres values of left or right - hand are automatically sampled and stored on disk.
RESULTS
All time- and pressure-related parameter estimates showed a significant fit (P < O.OOl), with the parameters unambiguously estimated, starting from the standard set of initial guesses. Figure 4 shows the results of the timerelated parameter estimation in subject 4. The values of the parameters are listed in Table 1. The extrapolation of the estimated values to cuff pressures below the systolic arterial level during cuff inflation (t < tS) shows a lack of fit caused by the delaying refill of the arteries during cuff inflation characterized by td (Table 1). The difference between the admittance of slowly movable extravascular fluid (Y, OtTable 1) and total movable extravascular fluid (Yio, Table 1) indicates the presence of rapidly movable extravascular fluid in subject 4. Table 2 shows the timerelated parameters averaged over all subjects. Rapidly movable extravascular fluid could be demonstrated in only four subjects. In the other subjects only a slowly movable component was found. Figure 5 shows, in subject 4, the various blood volumes derived from the estimated pressure-related parameters and the total blood volume calculated from the original impedance values by conversion to admittance, correction for extravascular fluid and residual tissue, and conversion to volume, plotted as a function of mean arterial transmural pressure. When cuff pressure decreases to
values below the systolic arterial level (P,, Fig. 5), the arteries start to refill. When cuff pressure decreases to values below the threshold pressure of 19 mmHg, the veins start to refill. The estimated parameters have been used to extrapolate to cuff pressures above the diastolic arterial level (Pd, Fig. 5) and below P, 1 taken as 10 mmHg in all subjects (P,,, Fig. 5). The delayed refill of the arteries, caused by the collapse of the arteries during diastole for cuff pressures above the diastolic arterial level, is illustrated by a progressive lack of fit for cuff pressures above mean arterial pressure (Pt,, Fig. 5). The irregularities in the venous blood volume plot are due to variations in Ptm, the venous blood volume being written as a linear function of cuff pressure. The low threshold pressure at which the veins start to refill ( Pthr, Table 3) makes an increased central venous pressure or a decreased compliance of the veins distal to the cuff unlikely in subject 4. In comparing the values of arterial compliances (Table 3), fluid volumes, and other quantities listed in Table 4 with the corresponding values averaged over all subjects (Tables 5 and 6, respectively), subject 4 has a rather high P,, an elevated mean arterial pressure, a high mean heart rate, and a detectable amount of rapidly movable extravascular fluid. Figure 6 shows the effective arterial compliance of all subjects, sorted according to maximum arterial compliance, as a function of P,,.
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BLOOD
PRESSURE-RELATED
PARAMETERS
124
iO6
w
175
time (81
B 20 -
16 --
0
-
!df
f!ze
blood
and
rapidly
movable
extravascular
fluid
G z
FIG. 4. Results of a time-related parameter estimation (cf. Table 1). A: measured (dots) and estimated (solid line) values for time-related admittance response. B: estimated admittance of tissue fluids is separated into admittance of a slowly (dashed line) and a rapidly movable part (solid line). Estimated values have been extrapolated to cuff pressures below systolic arterial level (t,) during inflation. Cuff inflation starts at 0 and ends at time t,. Cuff pressure increases to values above systolic arterial level at time t,. Before this level is reached, arteries refill every time arterial pressure exceeds cuff pressure. This explains lack of fit between measured and estimated values for t < t,. Cuff deflation starts at time tdf.
slowly
time
movable
extravascular
fluid
Is)
TABLE 2. Average values fur estimated time-related parameters
1. Time-related parameters as estimated in subject 4
TABLE
Parameter
Cuff inflation Rise time, s Cuff deflation Maximum cuff pressure (P,), mmHg Time constant (Q, s Extravascular fluid Total admittance (Yio), mS Slow component (YisO), mS Time constant (Q), s Blood Admittance (Y, 0), mS Time constant (Q), s Delay (td), s (Rise time - td), s Residual tissue Admittance (Yti), mS Volume (Vti), ml/cm
Vafue
13.3 188.1 89.0 5.3 0.7 60.4 11.9 2.5 4.9 8.3 104.4 65.5
Subj 4 was a 65yr-old female. DISCUSSION
Although the model has been based on a biphasic extravascular volume response during the period of increasing and constant cuff pressure, we have assumed a monophasic extravascular volume response during cuff deflation. The assumption that the time constant of this monophasic refill equals the time constant of the slow expulsion of extravascular fluid has been justified by parameter estimates in which riS in Eq. 10 has been replaced by an
Parameter
Cuff inflation Rise time, s Cuff deflation Maximum cuff pressure (P,), mmHg Time constant (Q, s Extravascular fluid Total admittance (Yio), mS Slow component (Yi*,), mS Time constant (Tia)y s Blood Admittance (Yb 0), mS Time constant (q,), s Delay (ta), s (Rise time - td), s Residual tissue Admittance (Yti), mS Volume (Vti), ml/cm
Mean
-t SD
Range
13.1t3.6
8.9-24.5
174.3t22.4* 86.5t2.7*
137.1-215.7 82.4-91.7
2.8?2.9* 1.3t0.5” 79.0+46.0*
0.7-11.2 0.6-2.4 25.3-207.5
9.7k3.7” 2.2t0.7’ 6.Ok2.1” 7.2t2.6
3.9-16.7 1.0-3.4 2.7-10.8 2.9-13.7
89.4t34.8* 58.4k9.2
45.2-148.5 49.3-84.2
n = 13. * P < 0.01.
additional parameter 7i that has been estimated together with the other time-related parameters. In all subjects, this yielded a time constant that did not differ significantly from the time constant of the slow expulsion of extravascular fluid. At decreasing cuff pressure, the extravascular fluid volume will be increased not only by the fluid that returns from the surrounding tissues but also by fluid that filters out of the arterial ends of the capillaries into the interstitial space and does not return to the
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BLOOD
PRESSURE-RELATED
mean arterial
I
)
II
t 1
181
transmural
I1
I
PARAMETERS
pressure t1
t w
1953
(mmHg1 I1
1I
I ,I I ‘I
1
i51
104 66 10 0 cuff pressure (mmHg1 FIG. 5. Relative blood volumes vs. mean arterial transmural pressure (P,,) during cuff deflation starting at D and ending at F in subj 4 (cf. Table 3). Dots, values for total blood volume derived directly from measured impedance. Estimated blood volume is plotted as sum of arterial and venous blood volumes (solid lines). Estimated values have been extrapolated to cuff pressures above diastolic arterial level (PJ and below 10 mmHg (P,,). When cuff pressure falls below systolic arterial pressure (P,), arteries open and refill during period when arterial pressure exceeds cuff pressure. When cuff pressure falls below Pd, arteries are open during entire heart cycle. Note progressive lack of fit for cuff pressures above mean arterial pressure (P,), caused by collapse of arteries during diastole. At PIO,cuff pressure is 10 mmHg.
capillaries as long as the veins and lymphatics are obstructed by the occluding cuff. Therefore, at the moment the rapidly movable part of the extravascular fluid would be expected to refill the interstitial space, this space will virtually be refilled already. This results in a monophasic refill of the extravascular space during cuff deflation. Another consequence of the reabsorption of fluid at the venous ends of the capillaries largely being blocked during cuff deflation is that the difference between the admittances at the end and the beginning of the experiment (Ydiff) does not result from incomplete extravascular refilling, as suggested by others (8). Explaining the admittance loss exclusively through assuming incomplete extravascular refill would also deny the property of reverse stress relaxation of the veins. Furthermore the admittance loss was often higher than the admittance corresponding with the movable extravascular fluid. For 3. Pressure-related parameters as estimated in subject 4 TABLE
these reasons, we assume the admittance loss to be the result of reverse stress relaxation. The physiological venous pressure at the level of the cuff is normally 40 mmHg, depending on the length and position of the upper arm. This rather high value results from the hydrostatic pressure and from the compression of the arm veins by their sharp angulation over the first rib (11). Comparison of this physioiogical ve4. Measured quantities and quantities derived from estimated parameters in subject 4 TABLE
Parameter
Value
Height, cm Body mass, kg Arm circumference, cm Mean heart rate, beats/min Mean arterial pressure at left upper arm, mmHg Pressure correction, mmHg Total admittance loss (Ydiff)9mS Tissue resistivity (pti ), In cm Initial blood volume (V,,), ml/cm Per 100 ml of tissue, % Venous % Final blood volume (V,,), ml/cm Arterial (V,), ml/cm Venous (V,,), ml/cm Movable extravascular fluid, ml/cm Per 100 ml of tissue, % Fast component, ml/cm Slow component, ml/cm
65 160.0 72.7 29.5 92 104 -2 4.0 313.7 3.2 4.9 56.0 2.2 1.4 0.8 0.5 0.8 0.5 0.1
Age,yr
l
Parameter
Value
Arterial Maximum volume (V,,,), ml/cm Arctan position (P,), mmHg Arctan steepness (PI), mmHg Physiological compbance (CL), ~1 mmHg-’ cm-l Maximum compliance (C lax ), ~1 mmHg-’ . cm-’ Venous Volume increase constant (IQ, pl/mmHg Threshold pressure (Pthr), mmHg l
l
l
I.5 34.1 16.1 1.5 30.2 87.9 19.0
All values are rounded to the nearest one decimal value.
Downloaded from www.physiology.org/journal/jappl at Macquarie Univ (137.111.162.020) on February 13, 2019.
1954
BLOOD
PRESSURE-RELATED
TABLE 5. Averuge values for estimated pressure-related parameters Parameter
Mean -t SD
Arterial Maximum volume (V,,,), ml/cm Arctan position (PO), mmHg Arctan steepness (P,), mmHg Physiological compliance (Cg), mmHg-’ . cm-’ Maximum compliance (Cl,,), ~1. mmHg-’ cm-’ Venous Volume increase constant (K), pl/mmHg Threshold pressure (P,,), mmHg pl
l
l
1.6*0.4*
Range
0.9-2.4
23.3+12.1*
1 J-46.0
16&6.3*
9.5-30.6
2.0t1.3
0.7-4.9
33.4t12.0
13.9-58.9
92.6+52.0*
30.9-217.6
23.3&10.6*
8.2-51.1
n = 13. * P < 0.01.
nous pressure with the average threshold pressure Pthr (23.3 mmHg) shows that the venous pressure distal to the cuff was only slightly increased during cuff deflation. The presence of rapidly movable extravascular fluid has been found to be associated with an increased interstitial pressure (12) and is probably due to plasma lost from the blood vessels. An increase in the P,, at which the arterial compliance reaches its maximum (P,) ‘has been found to be associated with vasoconstriction (9). At rest, patients with borderline hypertension often show a hemodynamic pattern similar to that of normal subjects during exercise: a plasma efflux from the blood vessels, increased heart rate, and elevated mean arterial pressure. Therefore the findings in subject 4 argue more for a developing hypertension than for an unreliable blood pressure measurement based on an increased sympathetic arousal. In two of the subjects, we found no reverse stress relaxation (Fig. 7). There was an even higher admittance at the end of cuff deflation than at the start of cuff inflation. This may be explained by a dilation of the arm veins under the cuff at the end of deflation caused by an increased venous pressure distal to the cuff. In two other subjects, we observed a pronounced venoconstriction at the end of cuff deflation (Fig. 8), resulting in little venous refill. The admittance responses of these latter two subjects clearly show that when a blood vessel constricts, reverse stress relaxation (characterized by U,,,) increases (4). Arterial and venous blood volume is generally measured invasively using radioactive isotopes. Changes in the diameter of small arteries and arterioles are often assessed indirectly by estimating the vascular resistance from blood flow measurements in a pulsatile artery by use of pulsed Doppler techniques or venous occlusion plethysmography. The arterial compliance is usually noninvasively investigated by estimating the compliance of a single pulsatile artery by use of pulse wave velocity methods or pulsed Doppler techniques. This compliance varies not only with changes in the intrinsic properties of the vascular wall, but also with changes in blood pressure or blood volume. Consequently, when compliance in hypertensive subjects is compared with that in normal subjects, modifications reflect intrinsic alterations only if
PARAMETERS
the two groups are compared at the same pressure and volume. Therefore, estimating the arterial blood volume and compliance of the total arterial bed of a body segment as a function of transmural pressure will increase the accuracy in comparative studies. The effective arterial compliance is often estimated by means of venous occlusion plethysmography at one of the extremities. With this method, changes in blood volume are estimated from the distension of a body segment distal to the occluding cuff inflated to various cuff pressures (starting, for instance, at 40 mmHg). However, all traditional methods of occlusion plethysmography neglect the influence of the extravascular fluid volume, the venous blood pressure, and the venous blood volume on the arterial compartment. Consequently, none of these methods can be used as the “gold standard” in the validation of the presented method. The effective arterial compliance per unit length has been computed as a function of P,,. Most data published concern the compliance of arteries in vitro (18) or the in vivo compliance of the pulsatile part of the arteries (3, 15) as a function of the instantaneous P,,. When these differences are taken into account, the estimated values at physiological pressure compare fairly well with those mentioned in the literature (3,15,18). For the maximum compliance, on the other hand, we computed much higher values, probably as a result of the cumulative effect of the gradual filling of smaller arteries. In two subjects only, we found a clearly decreased effective arterial compliance at physiological pressure (~1 ~1 mmHg-l 4cm-l), without a clearly decreased maximum compliance. This is probably the result of arterial vasoconstriction. Only -30% of the total arterial blood volume is in the larger arteries (10). Taking this percentage as a measure for the blood volume in the brachial artery, we obtained an average value of 42 mm2 for the lumen area of the brachial artery, which compares well with data in the literature ranging from 31 to 67 mm2 (2). In contrast to others who took the same tissue resistivl
TABLE
quantities
6. Average values for quantities measured and derived from estimated parameters Parameter
Mean + SD
Height, cm Body mass, kg Arm circumference, cm Mean heart rate, beats/min Mean arterial pressure, mmHg Pressure correction, mmHg Total admittance 10~s (YdiM), mS Tissue resistivity (pti), Q cm Initial blood volume (V, o), ml/cm Per 100 ml of tissue, % Venous % Final blood volume (V,,), ml/cm Arterial ( VaF), ml/cm Venous (VVF), ml/cm Movable extravascular volume, ml/cm Per 100 ml of tissue, % Fast component, ml/cm Slow component, ml/cm
66.3t5.4 163.7t8.6 69.2t10.3 27.8t2.0 72.2t8.1 89.3t8.0 2.7t13.4 2.8t2.2 312.1t86.7 3.OkO.9 5.2k1.7 49.2t12.6 2.2t0,8 1.4t0.3 0.7t0.5 0.320.3 0.5t0.5 0.2-cO.3 0.1~0.0
4%
Yr
l
Range
62.0-81.0 140.0-181.5
51.8-95.3 25.5-33.0 60.5-92.0 75.0-104.0
- 17.8-29.5 -0.2-6,4 174.8-462.5 1.6-4.5 2.7-8.6 25.6-68.5 1.0-3.9 0.8-2.2 0.1-1.9 0.1-1.1
0.2-2.1 0.0-0.9 0.1-o-2
All values are rounded to the nearest one decimal value. n = 13.
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BLOOD
-11.5
f -20
fI
II 12
arterial FIG. 6. Compliance-pressure meter of artery.
PRESSURE-RELATED
1I
1955
PARAMETERS
II 44
II
transmural
1I 76
pressure
II
I i
II 100
140
(mmHgl
relations of alf subjects, sorted according to maximum arterial compliance per centi-
ity for different subjects (8), we estimated the tissue resistivity for each subject separately. We supposed these values to depend on fat content. However, no relation was found between the thickness of skinfolds and tissue resistivity. Because bone has an even higher resistivity than fat (7), the wide scatter in tissue resistivity among our subjects may primarily be the result of differences in the relative amount of bone tissue. Although many agree that the impedance technique is valid for relative volume measurements, some also point out its limitations. Blood resistivity varies with effective hematocrit, temperature, and cell orientation. Therefore the blood resistivity varies in pulsatile flow due to changes in the orientation of erythrocytes (31). In this study, the mean impedance during a heart cycle was used. Therefore a mean value for the resistivity of blood had to be used. This mean value is lower than the value
for the resistivity of stationary blood (31). Possible changes in effective hematocrit and cell orientation during varying cuff pressure were taken into account by using a value for the blood resistivity that has been shown to give a good estimate of the volume measurement over a broad range of hematocrit changes in vivo (28). By subtracting the time by which the expulsion of arterial blood is delayed during cuff inflation (Q from the cuff inflation rise time, we obtain the maximum rise time at which f;d may be neglected. The values for td and the cuff inflation rise times, listed in Table 2, clearly illustrate that td may be neglected in all cases in which the cuff is inflated in
H. J. MUNTINGA
Department
of Medical
AND Physiology,
KLAAS
R. VISSER
University
MUNTINGA, JAAP H. J., ANDKLAAS R. VISSER. Estimationof blood pressure-related parameters by electrical impedance meusurement. J. Appl. Physiol. 73(5): 19464957, 1992.~In 13 healthy volunteers a computerized experimental set-up was usedto measurethe electrical impedanceof the upper arm at changing cuff pressure,together with the finger arterial blood pressurein the contralateral arm. On the basisof a model for the admittance response,the arterial blood volume per centimeter length (1.4 t 0.3 ml/cm), the venous blood volume as a percentageof the total blood compartment (49.2 t 12.6%),and the total arterial compliance as a function of mean arterial transmural pressurewere estimated. The effective physiological arterial compliance amounted to 2.0 t 1.3 ,ul. mmHg-‘. cm-l and the maximum compliance to 33.4 t 12.0 pb mmHg-l cm- ‘. Additionally, the extravascular fluid volume expelledby the occludingcuff (0.3 t 0.3 ml/cm) wasestimated. These quantities are closely related to patient-dependent sourcesof an unreliable blood pressuremeasurementand vary with changesin cardiovascular function, suchasthose found in hypertension. Traditionally, a combination of several methods is neededto estimate them. Such methods, however, usually neglect the contribution of extravascular factors. l
arterial compliance; hypertension; venous pressure
of Groningen,
NL-9712
KZ Groningen,
The Netherlands
quantities. As early as 1910, Janeway and Park (14) tried to determine whether the resistance to compression of the arterial wall introduces an error in blood pressure measurement. In patients with sclerotic or calcified vessels, the vessel wall resists compression by the inflated cuff. Thus a higher pressure is needed to occlude the artery, resulting in spuriously high systolic blood pressure readings (pseudohypertension). In patients with a diagnosis of essential hypertension, Osler’s maneuver may be used for the identifica .tion of pseudohypertension (21). D luring this maneuver, the blood pressure cuff is inflated to above systol .ic pressure and the radial or brachial art ‘cry is palpated di stal to the poi .nt of occlu sion. A patient is described as being Osler positive when either of these pulseless arteries remains clearly palpable. Of course, this is a quite subjective method, and the presence of pseudohypertension does not rule out true hypertension, because both phenomena may coexist. Whole-day ambulatory blood pressure monitoring revealed that ~20% of patients previously found to be hypertensive by standard methods had normal daily blood pressure patterns (26). It has been suggested that the apparent hypertension is caused by an increased level of sympathetic arousal due to anxiety and a conditioned response to the clinical setting (19, 26). Whole-day ambulatory blo od pressure me asuremen t, however, requires cooperation of ’ the patient under all circumstances and therefore encroaches on normal daily activities. Changes in the elasticity or state of contraction of the arteries in the upper arm are reflected in the blood volume and compliance of the total arterial compartment (effective arterial compliance). Arterial compliance is lower in Osler-positive subjects and correlates with the difference between cuff and intra-arterial pressures (21), whereas smooth muscle contraction result% in a horizontal shift of the compli ante-pressure curve toward higher pressure levels (9). so instead of measuring only the arterial pressure, it seems appropriate also to estimate the arterial blood volume and compliance as a function of mean arterial transmural pressure. To achieve this, the electrical impedance was measured. By measuring the electrical impedance of upper arm tissues under an occluding cuff, we attempted to assess the fluid shifts during varying cuff pressure. A model was used to predict the change in electrical admittance as a function of time and cuff pressure. To ascertain the efficacy of th .e method, the parameters of the model were estimated and the clo seness of the predicted admittances to the observed values was analyzed in experiments with
TEZEINDIRECTMEASUREMENT ofarterialbloodpressure by means of the occluding cuff auscultatory technique according to Riva-Rocci and Korotkoff is one of the most frequently applied methods in clinical medicine, Use of this method is commonplace because of its simplicity, on the one hand, an .d the importance of bl .ood pressure as an index of present and future cardiovasc ular health, on the other. Measurements using noninv ,asive ambulatory blood pressure monitoring, however, have shown that single blood pressure readings do not provide an accurate assessment of an individual’s blood pressure (5). The same conclusion has been drawn from treatment trials of hypertension in which average blood pressure fell during the first few weeks in all treatment groups, including those taking placebo tablets and those on observation only (20). At least three measurements on three separate days should be obtained to assess a patient’s blood pressure (30). Despite this and other recommendations (6) for obtaining a representative blood pressure reading, many patients are misclassified as hypertensive (24). This is, at least partly, the result of a lack of information about the elasticity of the arterial wall and the state of contraction of the blood vessels, because not only blood pressure, but also blood pressure measurement, is influenced by these 1946 0161~‘7567/92 $2.00 Copyright 0 1992 the American Physiological Society
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BLOOD
PRESSURE-RELATED
PARAMETERS
1947
FIG. 1. A cuff pressure registration with corresponding admittance response. When cuff inflation starts (at 0) blood and extravascular fluid are squeezed out from tissue under cuff, resulting in a decrease in admittance. This continues beyond end of cuff inflation at time t,. When cuff deflation starts at time tde interstitial space starts to refill, as do blood vessels later on, resulting in increase in admittance up to end of cuff deflation (at F). Cuff pressure equals mean intra-arterial pressure at time tPm.Ydifff difference between admittance measured at end of cuff deflation and that measured before cuff inflation.
13 geriatric subjects. When the analysis showed a significant fit, the parameters were accepted. From the accepted parameters, we calculated several quantities, including the effective arterial compliance at physiological pressure (effective physiological compliance), the maximum compliance, and the arterial and venous blood volumes for the tissue under the cuff. MATERIALS
AND METHODS
TheoreticaL foundations. During a measurement, the cuff is rapidly inflated, held constant at suprasystolic cuff pressure, and then slowly deflated. The blood and extravascular fluid volumes under the cuff vary with changing cuff pressure. This is reflected in changes in the electrical impedance of the upper arm under the cuff and opposite changes in electrical admittance (Fig. l), admittance being the reciprocal of impedance. The tissue under the cuff is considered as a parallel electrical circuit of movable extravascular fluid, blood, and residual tissue, the latter consisting of cells and extracellular fluid remaining permanently in situ. The contributions of these components to the total admittance can be estimated from the admittance changes at varying cuff pressure. The extravascular volume response to changes in cuff pressure is biphasic, because of the presence of rapidly and slowly movable extravascular fluid (l&22). The rapidly movable part of the extravascular fluid is assumed to be squeezed out with the blood. Because of the rapid emptying of the blood vessels as a result of the rapid increase in cuff pressure, the slow admittance decrease at constant cuff pressure after inflation can be due only to slowly movable extravascular fluid. The minimum admittance reached just before cuff deflation (Yti,) is the sum of the admittance of the extravascular fluid that is left behind but would have been squeezed out at continued constant cuff pressure (Y,) and the admittance of the residual tissue (Yti). The exponential nature of the
slow extravascular volume response to changes in cuff pressure is characterized by a time constant 71sthat does not seem to be pressure dependent at suprasystolic pressures (8). Similarly, a monophasic exponential refill of the extravascular space was assumed during the slow decrease in cuff pressure throughout deflation. The time constant of this refill was assumed to be equal to that of the expulsion of the slowly movable extravascular fluid. At cuff pressures below the systolic arterial level during inflation, the expulsion of blood will be delayed by arterial refill during the time when arterial pressure is above cuff pressure. Therefore a time delay (td) in the expulsion of blood has to be assumed. The admittance response, starting at the beginning of inflation and ending at the point where the cuff pressure reaches the level of intra-arterial systolic pressure during deflation, can thus be considered to be the result of the expulsion of blood and rapidly moving extravascular fluid, accompanied and followed by the expulsion of a part of the slowly movable extravascular fluid and then by the return of extravascular fluid (Fig. 2). On the basis of the different admittance responses in time, it is possible to separate the extravascular fluid contributions to the total electrical admittance from the contributions of blood and residual tissue. The parameters estimated for calculating these contributions have been called time-related parameters. During cuff deflation, blood admittance can be estimated by subtracting the contributions of extravascular refill and residual tissue from the total admittance. By using the resistivity of blood, the admittance of blood can be transformed to a volume. As soon as cuff pressure falls below systolic arterial pressure, the arteries will temporarily open and pass some blood to the veins distal from the cuff. Because of the large venous compliance, the resulting change in venous volume will only slightly increase venous pressure. As soon as cuff pressure falls below venous pressure, the veins under the cuff start to refill. At cuff pressures below this threshold pressure
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1948
BLOOD
PRESSURE-RELATED
PARAMETERS
stress relaxation (1, 27).
(delayed compliance)
of the arm veins
Mathematical formulation. The total electrical
tance [Y&t)]
admit-
is written as
ut,ttt) = uiCt) + Ybtt) + yti
(1)
where t is the time after the start of cuff inflation and Y;(t) and Yb(t) designate the admittances of movable interstitial fluid and blood, respectively. With cuff deflation starting at time tti, the biphasic nature of the extravascular admittance response for 0 s t < tdf is described
Yi( t) = yis(t, + Yi,(t)
(2)
where Yi,(t) and Yi,(t) are the admittances of the slowly and rapidly movable parts, respectively. At t = 0, the start of inflation, Eq. 1 reduces to
Y tot0
=
yi*
+
ybO
+
yti
=
yisO
(3)
. 0
\
1. t0
-
fyi,
yis
0)
+
y,
0 +
yti
Yi 0 is the total interstitial admittance, Yiso is the admittance of the slowly movable part of the interstitial fluid, (Y - Y, J is the admittance of the rapidly movable part of ?he interstitial fluid, and Y, 0 is the admittance of the blood at t = 0. Because a linear first-order response was assumed, the change in admittance of the slowly movable part of interstitial fluid before deflation and the change in admittance of the total interstitial fluid during deflation can both be described by
V,,(t) + y,(t) I I
y,(t)---
+
7.
l
18
ttme
FIG. 2. time-related part of predicted admittance as a function of time during varying cuff pressure (top). For t 2 tdft extravascular admittance response is given by Eq. IO. Area within dashed rectangle is enlarged in B. B: constituent parts of admittance response during inflation and constant suprasystolic cuff pressure. Combined contribution of rapidly movable extravascular fluid [Yi,(t)] and blood [Y&Q] to admittance response is given by Eq. 8. Slowly movable part of extravascular fluid contribution [Y,,(t)] is given by 23q. 6 for 0 I t < t, and by IQ. 7 for te5 t < tdf. A:
(Pthr), a linear venous pressure-volume relation was used, At cuff pressures above Pthr, the arterial refill forms the only contribution to the blood admittance. For the arterial pressure-volume relation, the model of Langewouters et al. (17) was used. The time dependency of the quasi-static arterial pressure-volume relationship was neglected, because volume and pressure change slowly and the arterial wall exhibits little viscous behavior (35) during the prolonged arterial refill. It is therefore possible to separate the arterial from the venous contributions by considering them as a function of cuff pressure only. The parameters estimated for calculating these contributions have been called pressure-related parameters. The difference between the admittances measured at the end of cuff deflation and those measured before cuff inflation (Y& was assumed to be the result of reverse
-
d[yi(t)] + Yi(t) = Y,, - y,D’p p,(t) dt
e
(4)
where 7is is the corresponding interstitial time constant, YCO is the interstitial admittance at zero cuff pressure, P,(t) is the cuff pressure at time t, and P, is the cuff pressure at the end of inflation. The pressure in the cuff during inflation is
t P,(t) = -. P
(5) te e where te is the time needed to inflate the cuff to P,. From Ep. 4 and 5 with Yi(t) replaced by Yisft) in Eq. 4 and with initial conditions Y,(O) = Yiso = Y, o and dYi,( t)ldt = 0 at t = 0, we obtain (Fig. 2) for 0 5 t < te Y +
y
l
(1
-
e+s)
(6)
e From Eq. 4 with P,(t) = P,, Yi(t) replaced by Yi,(t), and initial conditions Y,(t) = Yi,( te) and dY,,( t)/dt = -Yi,( te)l rig at t = te [Yi,(t,) calculated from Eq. 61, we obtain (Fig. 2) for te 5 t < taf Y is 0 yi,( t) = -.+5
. (&?/%3- 1) e-t/Tit3 l
(7)
e
The combined
contribution
of rapidly movable
extra-
vascular fluid [Y,,(t)] and blood [Yb(t)] to the admittance response during inflation is written function (Fig. 2) with a td
as an exponential
Downloaded from www.physiology.org/journal/jappl at Macquarie Univ (137.111.162.020) on February 13, 2019.
BLOOD
PRESSURE-RELATED
PARAMETERS
1949
P,, is the threshold pressure at which the veins start to refill (8). for t, 5 t < ta, where Tbir is the time constant of the Computations. The impedance of the tissue under the expulsion of both blood (rb) and rapidly movable extracuff was transformed to admittance. The cuff pressure at vascular fluid. the start of deflation (P,) and the time constant of the The exponential cuff deflation is described by cuff deflation (Q) were estimated from the cuff pressure P,(t) = p, ~--(t--tdf)~rp = p, . &/T, (9) measurements by use of a linear least-squares exponenwhere Q is the time constant of the cuff deflation and t’ is tial estimation procedure. A description of the mathematical model to predict the the transformation of time t to t’ = t - tw From Eqs. 4 and total admittance as a function of time [Y,,,(t)] can be 9 with initial conditions vi(O) = Y,, Y, o = Yio, and obtained by combining Eqs. 1, i, 6, 7, 10, and 11. This fWi t’)/dt’ = -Yst/Tis at ti = 0, we obtain (Fig. 2) for t > 0 part of the model describes the admittance response up 1 to the time when cuff pressure falls below systolic presQ. e -tf’7P) + 1 W i ) - Y iO* -. ( 7. 1s . e-t’/“8 sure during deflation. The values used in the model for 7p - 7is (10) Ytoto and Ymin were deduced directly from the measure+ y,, . e-t’& ments. With the model, the time-related parameters Y, o, The extravascular admittance at the start of deflation Yi09 Ybo, 7isy7biry and td were estimated at the time interval corresponding with suprasystolic cuff pressure. Then (Y,,) can be written (Eq. 3) as the closeness of the predicted admittances to the obY st = Y min - Y ti = Y min - ytitO + yiO + ybO (II) served values was analyzed. The admittance of blood during cuff deflation (Yb) was A description of the mathematical model to predict Yb determined by subtracting the admittances of residual as a function of cuff pressure during deflation can be Eqs. 12-17. This part of the tissue (Yti) and extravascular refill Yi (Eqs. 10 and I I) obtained by combining from the total admittance model describes the admittance response for cuff pressures above P, 1 during deflation. Yb was converted to a Y b = Y tot - Y ti - Y i (12) blood volume by using a value of 135 Q 4cm for j+, (28). This admittance was converted to blood volume Vb by The cuff pressure P, 1 was taken to be 10 mmHg in accoruse of Nyboer’s expression dance with the hydro&atic pressure difference of the upper arm relative to the heart. With the model, the pres2 vb = Yj./&./ L (13) sure-related parameters V,,, PO, P,, K, and P,,, were where pb is the resistivity of blood (23) and L is the dis- estimated at cuff pressures above P, 1 and below the diatance between the measuring electrodes. The blood vol- stolic level. Then the closeness of the predicted admittances to the observed values was analyzed. ume consists of an arterial (V,) and a venous (V,) part In all computations, values were used that represent V b = v, + v, (14 the mean over a cardiac cycle. At cuff pressures between According to the model of Langewouters et al. (17), the systolic and diastolic pressure, however, the arteries colarterial pressure-volume relationship during cuff deflalapse during a part of the cardiac cycle. Therefore the tion is described by time-related parameters were estimated at suprasystolic cuff pressures and the pressure-related paramet ers at V.=~i,r~tan[‘ptrtpo’]+5j (15) cuff pressures above P,, and below the diastolic level. The admittances at the remaining cuff pressures were calculated using extrapolation. where V, is the arterial volume at mean arterial transBoth time- and pressure-related parameters were estimural pressure (P,,), V,, is the maximum arterial voldata using the BFGS or comume, PO is P,, at maximum arterial compliance, and P, is mated from experimental plementary DFP algorithm (32), based on nonlinear related to the steepness of the arctangent relationship. least-squares parameter estimation. The pa rameter estiP,, at the left upper arm was determined by subtracting the cuff pressure during a cardiac cycle (P,) from the mates began with the same standard initial guess fo r the fitting parameters in all experiments. Then the iterative mean arterial pressure (P,) algorithm improved the parameter estimates in steps. Ptrn= P a- Pc (16) When the successive parameter modifications became For cuff pressures above Pthr during deflation, the ve- negligible ( = v,, L*r
At P,, = P,, the arterial C Imax
l
P PT+ (PtI-PcJ2
compliance
C’max --
reaches a maximum
v max
LgK*P,
The volume of the extravascular fluid that may be squeezed out by cuff inflation (Vi,) was calculated from the estimated value of Yio by use of Nyboer’s expression, with the extravascular resistivity taken to be 50 Q *cm (7). In a similar way, the initial blood volume V, 0 was calculated from Y, 0. Total tissue volume was calculated from the measured arm circumference and L. In this calculation, we considered the tissue between the measuring electrodes as a cylinder. To determine the residual tissue volume (V,), the blood and extravascular volumes were subtracted from the total tissue volume. The resistivity of residual tissue was calculated using an equation analogous to Eq. 13 for a tissue volume. The blood volume after cuff deflation (V,,) was obtained by subtracting the extravascular and residual tissue admittance from the total admittance measured after cuff deflation (Eq. 12) and applying Eq. 13. The arterial part of this blood volume (V,,) was calculated from the estimated parameters and P,, by use of Eq. 15. Because Eq. 17 is based on an assumed linear venous refill, it should not be used for the calculation of the venous blood volume at the end of cuff deflation. The venous blood volume after cuff deflation (V,,) was estimated using V vF = V bF - V aF (20) To compute the initial venous blood volume was subtracted from V,, 0 V vO- - V bO- V aF
(V,,), Vfi
(21)
E3cperiments. Figure 3 shows a block diagram of the experimental set-up. Arterial blood pressure and heart rate were measured noninvasively by a Finapres device (33,34). This instrument continuously measures arterial pressure in the finger by means of a vascular unloading technique, as described by Pefiaz (25). Its inaccuracy compared with intrabrachial blood pressure measurements is approximately -6 mmHg and its imprecision is t4 mmHg (34). A Minnesota impedance cardiograph (model 304A, Instrumentation for Medicine) with a lOO-kHz 4-mA constant-current source (16) was used for impedance measurements. Two potential-measuring (Pl and P2, Fig. 3) and two current-conducting electrodes (11 and 12, Fig. 3), consisting of self-adhesive disposable electrode tape (3M), were applied around the full circumference of the
PARAMETERS
left arm. The measuring electrodes were placed 10.5 cm above the antecubital space 2 cm apart, while the conducting electrodes were applied around the wrist and proximal end of the arm. A 16-cm-wide cuff was placed around the left upper arm; it completely covered the measuring electrodes. Cuff pressure was measured with a pressure transducer (Statham P23 Db) and controlled by two electric valves (24-V direct current model IP65 /IEC144, Martonair). The Finapres device and pressure transducer were calibrated using a mercury manometer. Valve control and data acquisition, storage, and analysis were realized using an IBM-compatible PC/XT with expanded memory and an AD/DA expansion board (MetraByte, Dash-16F). All signals were sampled at a frequency of 20 Hz. Measurements were performed on two healthy male and 11 healthy female volunteers, ranging in age from 62 to 81 yr. All subjects gave informed consent for the study. Information collected on each individual included sex, date of birth, state of health, medication, alcohol and tobacco consumption, body mass, height, arm circumference, and thickness of skinfolds at the level of the measuring electrodes. During the measurements, the subjects were sitting in an armchair. A modification of the protocol proposed by Gizdulich et al. (8) was used. The experiment began when electrodes and cuff were applied around the left upper arm and the subject was in a comfortable sitting position with both arms on the armrests of the chair. To prevent insufficient cuff inflation as a consequence of extreme leftright differences in arterial blood pressure, the arterial pressure on the second phalanx of the middle finger of the left hand was measured first, for 2.5 min. Then the Finapres cuff was placed on the second phalanx of the middle finger of the right hand, while the maximum of the finger arterial pressure at the left hand was determined automatically from the sampled data. After the subject had been instructed to move as little as possible, the automated process of concurrent data acquisition, data storage, and cuff pressure control was started. First, the cuff around the left upper arm was rapidly inflated to 20 mmHg above the maximum of left finger arterial pressure (Fig. 1). After 120 s at constant cuff pressure, the cuff was slowly deflated in -300 s. To obtain the mean arterial pressure at the left upper arm, the mean arterial pressure as measured with the Finapres cuff in the contralateral arm was corrected for both hydrostatic and left-right differences in arterial pressure between the left upper arm and the middle finger of the right hand. Analogous to oseillometric techniques, the maximum pulse amplitude of the first time derivative of the impedance change (dZ/dt) is assumed to signify mean brachial arterial pressure (13). Accordingly, the (lowest) cuff pressure at maximum dZldt pulse amplitude was determined and subtracted from the mean arterial pressure as measured with the Finapres cuff. By subtracting the resulting pressure correction from a11mea-
sured Finapres pressures, the finger blood pressures were transformed to the level of the measuring electrodes around the left upper arm.
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BLOOD
PRESSURE-RELATED
PARAMETERS
1951
r f f f f f f f f f f f f 1 f
f f f t f f f f f f f f f I
f f I f f f f
DASH 16F ADIDA BOARD
FIG. 3. Block diagram of measuring and controlling system with measuring electrodes P1 and P2 and conducting electrodes I1 and 12. Pressure in cuff around left upper arm is controlled through computer program. Cuff pressure and impedance values of left upper arm and Finapres values of left or right - hand are automatically sampled and stored on disk.
RESULTS
All time- and pressure-related parameter estimates showed a significant fit (P < O.OOl), with the parameters unambiguously estimated, starting from the standard set of initial guesses. Figure 4 shows the results of the timerelated parameter estimation in subject 4. The values of the parameters are listed in Table 1. The extrapolation of the estimated values to cuff pressures below the systolic arterial level during cuff inflation (t < tS) shows a lack of fit caused by the delaying refill of the arteries during cuff inflation characterized by td (Table 1). The difference between the admittance of slowly movable extravascular fluid (Y, OtTable 1) and total movable extravascular fluid (Yio, Table 1) indicates the presence of rapidly movable extravascular fluid in subject 4. Table 2 shows the timerelated parameters averaged over all subjects. Rapidly movable extravascular fluid could be demonstrated in only four subjects. In the other subjects only a slowly movable component was found. Figure 5 shows, in subject 4, the various blood volumes derived from the estimated pressure-related parameters and the total blood volume calculated from the original impedance values by conversion to admittance, correction for extravascular fluid and residual tissue, and conversion to volume, plotted as a function of mean arterial transmural pressure. When cuff pressure decreases to
values below the systolic arterial level (P,, Fig. 5), the arteries start to refill. When cuff pressure decreases to values below the threshold pressure of 19 mmHg, the veins start to refill. The estimated parameters have been used to extrapolate to cuff pressures above the diastolic arterial level (Pd, Fig. 5) and below P, 1 taken as 10 mmHg in all subjects (P,,, Fig. 5). The delayed refill of the arteries, caused by the collapse of the arteries during diastole for cuff pressures above the diastolic arterial level, is illustrated by a progressive lack of fit for cuff pressures above mean arterial pressure (Pt,, Fig. 5). The irregularities in the venous blood volume plot are due to variations in Ptm, the venous blood volume being written as a linear function of cuff pressure. The low threshold pressure at which the veins start to refill ( Pthr, Table 3) makes an increased central venous pressure or a decreased compliance of the veins distal to the cuff unlikely in subject 4. In comparing the values of arterial compliances (Table 3), fluid volumes, and other quantities listed in Table 4 with the corresponding values averaged over all subjects (Tables 5 and 6, respectively), subject 4 has a rather high P,, an elevated mean arterial pressure, a high mean heart rate, and a detectable amount of rapidly movable extravascular fluid. Figure 6 shows the effective arterial compliance of all subjects, sorted according to maximum arterial compliance, as a function of P,,.
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BLOOD
PRESSURE-RELATED
PARAMETERS
124
iO6
w
175
time (81
B 20 -
16 --
0
-
!df
f!ze
blood
and
rapidly
movable
extravascular
fluid
G z
FIG. 4. Results of a time-related parameter estimation (cf. Table 1). A: measured (dots) and estimated (solid line) values for time-related admittance response. B: estimated admittance of tissue fluids is separated into admittance of a slowly (dashed line) and a rapidly movable part (solid line). Estimated values have been extrapolated to cuff pressures below systolic arterial level (t,) during inflation. Cuff inflation starts at 0 and ends at time t,. Cuff pressure increases to values above systolic arterial level at time t,. Before this level is reached, arteries refill every time arterial pressure exceeds cuff pressure. This explains lack of fit between measured and estimated values for t < t,. Cuff deflation starts at time tdf.
slowly
time
movable
extravascular
fluid
Is)
TABLE 2. Average values fur estimated time-related parameters
1. Time-related parameters as estimated in subject 4
TABLE
Parameter
Cuff inflation Rise time, s Cuff deflation Maximum cuff pressure (P,), mmHg Time constant (Q, s Extravascular fluid Total admittance (Yio), mS Slow component (YisO), mS Time constant (Q), s Blood Admittance (Y, 0), mS Time constant (Q), s Delay (td), s (Rise time - td), s Residual tissue Admittance (Yti), mS Volume (Vti), ml/cm
Vafue
13.3 188.1 89.0 5.3 0.7 60.4 11.9 2.5 4.9 8.3 104.4 65.5
Subj 4 was a 65yr-old female. DISCUSSION
Although the model has been based on a biphasic extravascular volume response during the period of increasing and constant cuff pressure, we have assumed a monophasic extravascular volume response during cuff deflation. The assumption that the time constant of this monophasic refill equals the time constant of the slow expulsion of extravascular fluid has been justified by parameter estimates in which riS in Eq. 10 has been replaced by an
Parameter
Cuff inflation Rise time, s Cuff deflation Maximum cuff pressure (P,), mmHg Time constant (Q, s Extravascular fluid Total admittance (Yio), mS Slow component (Yi*,), mS Time constant (Tia)y s Blood Admittance (Yb 0), mS Time constant (q,), s Delay (ta), s (Rise time - td), s Residual tissue Admittance (Yti), mS Volume (Vti), ml/cm
Mean
-t SD
Range
13.1t3.6
8.9-24.5
174.3t22.4* 86.5t2.7*
137.1-215.7 82.4-91.7
2.8?2.9* 1.3t0.5” 79.0+46.0*
0.7-11.2 0.6-2.4 25.3-207.5
9.7k3.7” 2.2t0.7’ 6.Ok2.1” 7.2t2.6
3.9-16.7 1.0-3.4 2.7-10.8 2.9-13.7
89.4t34.8* 58.4k9.2
45.2-148.5 49.3-84.2
n = 13. * P < 0.01.
additional parameter 7i that has been estimated together with the other time-related parameters. In all subjects, this yielded a time constant that did not differ significantly from the time constant of the slow expulsion of extravascular fluid. At decreasing cuff pressure, the extravascular fluid volume will be increased not only by the fluid that returns from the surrounding tissues but also by fluid that filters out of the arterial ends of the capillaries into the interstitial space and does not return to the
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BLOOD
PRESSURE-RELATED
mean arterial
I
)
II
t 1
181
transmural
I1
I
PARAMETERS
pressure t1
t w
1953
(mmHg1 I1
1I
I ,I I ‘I
1
i51
104 66 10 0 cuff pressure (mmHg1 FIG. 5. Relative blood volumes vs. mean arterial transmural pressure (P,,) during cuff deflation starting at D and ending at F in subj 4 (cf. Table 3). Dots, values for total blood volume derived directly from measured impedance. Estimated blood volume is plotted as sum of arterial and venous blood volumes (solid lines). Estimated values have been extrapolated to cuff pressures above diastolic arterial level (PJ and below 10 mmHg (P,,). When cuff pressure falls below systolic arterial pressure (P,), arteries open and refill during period when arterial pressure exceeds cuff pressure. When cuff pressure falls below Pd, arteries are open during entire heart cycle. Note progressive lack of fit for cuff pressures above mean arterial pressure (P,), caused by collapse of arteries during diastole. At PIO,cuff pressure is 10 mmHg.
capillaries as long as the veins and lymphatics are obstructed by the occluding cuff. Therefore, at the moment the rapidly movable part of the extravascular fluid would be expected to refill the interstitial space, this space will virtually be refilled already. This results in a monophasic refill of the extravascular space during cuff deflation. Another consequence of the reabsorption of fluid at the venous ends of the capillaries largely being blocked during cuff deflation is that the difference between the admittances at the end and the beginning of the experiment (Ydiff) does not result from incomplete extravascular refilling, as suggested by others (8). Explaining the admittance loss exclusively through assuming incomplete extravascular refill would also deny the property of reverse stress relaxation of the veins. Furthermore the admittance loss was often higher than the admittance corresponding with the movable extravascular fluid. For 3. Pressure-related parameters as estimated in subject 4 TABLE
these reasons, we assume the admittance loss to be the result of reverse stress relaxation. The physiological venous pressure at the level of the cuff is normally 40 mmHg, depending on the length and position of the upper arm. This rather high value results from the hydrostatic pressure and from the compression of the arm veins by their sharp angulation over the first rib (11). Comparison of this physioiogical ve4. Measured quantities and quantities derived from estimated parameters in subject 4 TABLE
Parameter
Value
Height, cm Body mass, kg Arm circumference, cm Mean heart rate, beats/min Mean arterial pressure at left upper arm, mmHg Pressure correction, mmHg Total admittance loss (Ydiff)9mS Tissue resistivity (pti ), In cm Initial blood volume (V,,), ml/cm Per 100 ml of tissue, % Venous % Final blood volume (V,,), ml/cm Arterial (V,), ml/cm Venous (V,,), ml/cm Movable extravascular fluid, ml/cm Per 100 ml of tissue, % Fast component, ml/cm Slow component, ml/cm
65 160.0 72.7 29.5 92 104 -2 4.0 313.7 3.2 4.9 56.0 2.2 1.4 0.8 0.5 0.8 0.5 0.1
Age,yr
l
Parameter
Value
Arterial Maximum volume (V,,,), ml/cm Arctan position (P,), mmHg Arctan steepness (PI), mmHg Physiological compbance (CL), ~1 mmHg-’ cm-l Maximum compliance (C lax ), ~1 mmHg-’ . cm-’ Venous Volume increase constant (IQ, pl/mmHg Threshold pressure (Pthr), mmHg l
l
l
I.5 34.1 16.1 1.5 30.2 87.9 19.0
All values are rounded to the nearest one decimal value.
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1954
BLOOD
PRESSURE-RELATED
TABLE 5. Averuge values for estimated pressure-related parameters Parameter
Mean -t SD
Arterial Maximum volume (V,,,), ml/cm Arctan position (PO), mmHg Arctan steepness (P,), mmHg Physiological compliance (Cg), mmHg-’ . cm-’ Maximum compliance (Cl,,), ~1. mmHg-’ cm-’ Venous Volume increase constant (K), pl/mmHg Threshold pressure (P,,), mmHg pl
l
l
1.6*0.4*
Range
0.9-2.4
23.3+12.1*
1 J-46.0
16&6.3*
9.5-30.6
2.0t1.3
0.7-4.9
33.4t12.0
13.9-58.9
92.6+52.0*
30.9-217.6
23.3&10.6*
8.2-51.1
n = 13. * P < 0.01.
nous pressure with the average threshold pressure Pthr (23.3 mmHg) shows that the venous pressure distal to the cuff was only slightly increased during cuff deflation. The presence of rapidly movable extravascular fluid has been found to be associated with an increased interstitial pressure (12) and is probably due to plasma lost from the blood vessels. An increase in the P,, at which the arterial compliance reaches its maximum (P,) ‘has been found to be associated with vasoconstriction (9). At rest, patients with borderline hypertension often show a hemodynamic pattern similar to that of normal subjects during exercise: a plasma efflux from the blood vessels, increased heart rate, and elevated mean arterial pressure. Therefore the findings in subject 4 argue more for a developing hypertension than for an unreliable blood pressure measurement based on an increased sympathetic arousal. In two of the subjects, we found no reverse stress relaxation (Fig. 7). There was an even higher admittance at the end of cuff deflation than at the start of cuff inflation. This may be explained by a dilation of the arm veins under the cuff at the end of deflation caused by an increased venous pressure distal to the cuff. In two other subjects, we observed a pronounced venoconstriction at the end of cuff deflation (Fig. 8), resulting in little venous refill. The admittance responses of these latter two subjects clearly show that when a blood vessel constricts, reverse stress relaxation (characterized by U,,,) increases (4). Arterial and venous blood volume is generally measured invasively using radioactive isotopes. Changes in the diameter of small arteries and arterioles are often assessed indirectly by estimating the vascular resistance from blood flow measurements in a pulsatile artery by use of pulsed Doppler techniques or venous occlusion plethysmography. The arterial compliance is usually noninvasively investigated by estimating the compliance of a single pulsatile artery by use of pulse wave velocity methods or pulsed Doppler techniques. This compliance varies not only with changes in the intrinsic properties of the vascular wall, but also with changes in blood pressure or blood volume. Consequently, when compliance in hypertensive subjects is compared with that in normal subjects, modifications reflect intrinsic alterations only if
PARAMETERS
the two groups are compared at the same pressure and volume. Therefore, estimating the arterial blood volume and compliance of the total arterial bed of a body segment as a function of transmural pressure will increase the accuracy in comparative studies. The effective arterial compliance is often estimated by means of venous occlusion plethysmography at one of the extremities. With this method, changes in blood volume are estimated from the distension of a body segment distal to the occluding cuff inflated to various cuff pressures (starting, for instance, at 40 mmHg). However, all traditional methods of occlusion plethysmography neglect the influence of the extravascular fluid volume, the venous blood pressure, and the venous blood volume on the arterial compartment. Consequently, none of these methods can be used as the “gold standard” in the validation of the presented method. The effective arterial compliance per unit length has been computed as a function of P,,. Most data published concern the compliance of arteries in vitro (18) or the in vivo compliance of the pulsatile part of the arteries (3, 15) as a function of the instantaneous P,,. When these differences are taken into account, the estimated values at physiological pressure compare fairly well with those mentioned in the literature (3,15,18). For the maximum compliance, on the other hand, we computed much higher values, probably as a result of the cumulative effect of the gradual filling of smaller arteries. In two subjects only, we found a clearly decreased effective arterial compliance at physiological pressure (~1 ~1 mmHg-l 4cm-l), without a clearly decreased maximum compliance. This is probably the result of arterial vasoconstriction. Only -30% of the total arterial blood volume is in the larger arteries (10). Taking this percentage as a measure for the blood volume in the brachial artery, we obtained an average value of 42 mm2 for the lumen area of the brachial artery, which compares well with data in the literature ranging from 31 to 67 mm2 (2). In contrast to others who took the same tissue resistivl
TABLE
quantities
6. Average values for quantities measured and derived from estimated parameters Parameter
Mean + SD
Height, cm Body mass, kg Arm circumference, cm Mean heart rate, beats/min Mean arterial pressure, mmHg Pressure correction, mmHg Total admittance 10~s (YdiM), mS Tissue resistivity (pti), Q cm Initial blood volume (V, o), ml/cm Per 100 ml of tissue, % Venous % Final blood volume (V,,), ml/cm Arterial ( VaF), ml/cm Venous (VVF), ml/cm Movable extravascular volume, ml/cm Per 100 ml of tissue, % Fast component, ml/cm Slow component, ml/cm
66.3t5.4 163.7t8.6 69.2t10.3 27.8t2.0 72.2t8.1 89.3t8.0 2.7t13.4 2.8t2.2 312.1t86.7 3.OkO.9 5.2k1.7 49.2t12.6 2.2t0,8 1.4t0.3 0.7t0.5 0.320.3 0.5t0.5 0.2-cO.3 0.1~0.0
4%
Yr
l
Range
62.0-81.0 140.0-181.5
51.8-95.3 25.5-33.0 60.5-92.0 75.0-104.0
- 17.8-29.5 -0.2-6,4 174.8-462.5 1.6-4.5 2.7-8.6 25.6-68.5 1.0-3.9 0.8-2.2 0.1-1.9 0.1-1.1
0.2-2.1 0.0-0.9 0.1-o-2
All values are rounded to the nearest one decimal value. n = 13.
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BLOOD
-11.5
f -20
fI
II 12
arterial FIG. 6. Compliance-pressure meter of artery.
PRESSURE-RELATED
1I
1955
PARAMETERS
II 44
II
transmural
1I 76
pressure
II
I i
II 100
140
(mmHgl
relations of alf subjects, sorted according to maximum arterial compliance per centi-
ity for different subjects (8), we estimated the tissue resistivity for each subject separately. We supposed these values to depend on fat content. However, no relation was found between the thickness of skinfolds and tissue resistivity. Because bone has an even higher resistivity than fat (7), the wide scatter in tissue resistivity among our subjects may primarily be the result of differences in the relative amount of bone tissue. Although many agree that the impedance technique is valid for relative volume measurements, some also point out its limitations. Blood resistivity varies with effective hematocrit, temperature, and cell orientation. Therefore the blood resistivity varies in pulsatile flow due to changes in the orientation of erythrocytes (31). In this study, the mean impedance during a heart cycle was used. Therefore a mean value for the resistivity of blood had to be used. This mean value is lower than the value
for the resistivity of stationary blood (31). Possible changes in effective hematocrit and cell orientation during varying cuff pressure were taken into account by using a value for the blood resistivity that has been shown to give a good estimate of the volume measurement over a broad range of hematocrit changes in vivo (28). By subtracting the time by which the expulsion of arterial blood is delayed during cuff inflation (Q from the cuff inflation rise time, we obtain the maximum rise time at which f;d may be neglected. The values for td and the cuff inflation rise times, listed in Table 2, clearly illustrate that td may be neglected in all cases in which the cuff is inflated in
