Annals of BiomedicalEngineering, Vol. 12, pp. 79-102, 1984 Printed in the U.S.A. All rights reserved.

0090-6964/84/$3.00 + .00 Copyright 9 1984 Pergamon Press Ltd.

IMPEDANCE PLETHYSMOGRAPHY IN THE DIAGNOSIS OF ARTERIAL AND VENOUS DISEASE Frederick A. Anderson, Jr. Department of Surgery University of Massachusetts Medical School Worcester, Massachusetts

The objective of this paper is to review the theoretical basis and clinical application of electrical impedance plethysmography in the noninvasive evaluation of peripheral arterial and venous disease. Theoretical, experimental and clinical studies have now demonstrated a direct relationship between electrical impedance changes and limb volume changes. Potential sources of error have also been identified. This has led to the development of clinical tests based on impedance plethysmography for the detection of peripheral arterial disease, venous insufficiency and venous outflow obstruction. Impedance plethysmography, using the method of venous occlusion, is presently the most commonly employed noninvasive method for the detection of deep venous thrombosis. Keywords -- Impedance plethysmography, Peripheral vascular diagnosis, Theoretical basis.

INTRODUCTION Impedance plethysmography is defined as the measurement of volume changes through the measurement of electrical impedance. Whereas impedance plethysmography has been employed to study pulmonary and cardiac volume changes, the present review is confined to the application of impedance to the detection of peripheral arterial and venous diasease. Objective assessment of blood volume change is important in the diagnosis of peripheral vascular disease. Patient safety and comfort are increased when measurements are obtained by means of a noninvasive technique, and the cost of testing is reduced. PIethysmographs based on air or fluid displacement are cumbersome, which greatly limits their application outside the research laboratory; whereas impedance plethysmography is significantly more convenient to use in routine clinical settings. Application of electrodes to the skin is simple and calibration is easily accomplished. The term "impedance plethysmography" was first suggested by Nyboer (13) who conducted early experiments with this technique beginning in about 1939. Address correspondence to Dr. Frederick A. Anderson, Jr., Department of Surgery, University of Massachusetts Medical School, 55 Lake Avenue North, Worcester, MA 01605

79

80

Frederick A. Anderson, Jr.

Until the 1970s there was no experimentally validated theoretical basis from which to predict the relationship between impedance changes and blood volume changes. Impedance plethysmographs were usually one of a kind and, too often, employed an inadequate two-electrode technique. Thus, there was controversy about the acceptance of impedance as a valid plethysmographic method and, consequently, little clinical interest in the technique. In the last decade several well-designed impedance plethysmographs have become commercially available. Many of these instruments were developed specifically for the diagnosis of peripheral arterial and venous disease. More important, the theoretical basis of impedance plethysmography has now been described and verified experimentally. THEORY

In impedance plethysmography electrodes are applied to the skin over the body region of interest. In the extremities electrodes are usually applied as circumferential bands. The configuration shown in Fig. 1 has become more or less standard. A high-frequency current is passed through the current electrode pair. Frequencies between 10 kHz and 100 kHz are commonly employed with a strength of a few milliamperes or less. Thus, the current strength is too weak to be perceived by the patient, and the frequency is too high to stimulate the muscles or heart. Although some instruments display only the real part of the impedance, this is not particularly important, as the modulus of the impedance of a limb is only a few percentages larger than the real part

A C current source

Blood ~ vessel

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Voltmeter FIGURE 1. Four-electrode impedance plethysmography, A weak, high-frequency current passes between I1 and /2. Voltage changes are recorded between I/1 and I/2, reflecting blood volume changes in the body segment under study (25).

Impedance Plethysmography

81

(12). The phase of the impedance, which is related to the ratio of the imaginary to the real part, is less than 12 degrees for the frequency range in which most instruments operate. Therefore, nonresistive effects in a limb are small, and, from an electrical point of view, a limb can be modeled as a set of purely resistive elements. Much of the controversy concerning the relationship between electrical impedance and blood volume was the result of early studies in which a single pair of electrodes was used. It is now recognized that a four-electrode (tetrapolar) technique is necessary to accurately quantify electrical impedance changes from skin electrodes. In this method, a constant-magnitude highfrequency current is passed between two electrodes, and the resultant voltage is sampled at two separate electrodes. This arrangement effectively eliminates skin impedance and reduces the sensitivity to events close to the electrodes. In simple terms, the validity of impedance plethysmography requires that there be a predictable relationship between a blood volume change (d V) and the corresponding impedance change (dR). Several theoretical models have been developed to predict this relationship. Recently, several authors have published results of well-conceived experiments in which adequate instruments were employed to measure impedance and limb volume changes (4,10,12,19,25,26,28). There are consistent differences in these results, however, which seem too large to be explained by experimental error alone. This suggests a systematic error, which may result from the common assumption that a limb can be adequately modeled as a homogeneous volume conductor.

Volume Conductor Theory Nyboer (13) was the first to apply the formula for the resistance of a homogeneous volume conductor to predict the relationship between impedance changes and blood volume changes. The resistivity of a limb can be expressed in terms of its cross-sectional area, voltage electrode separation and resistance:

(1)

RtA Pt-

L

or, since Vt = LA, resistivity can be expressed in terms of the segmental volume,

R,V, &=

L2

where & = resistivity of tissue (ohm-cm) Rt -- segmental resistance (ohms)

,

(2)

82

Frederick A. Anderson, Jr.

A = cross-sectional a r e a (cm 2) L = separation of voltage electrodes (cm) Vt = segmental tissue volume (ml) Nyboer further assumed that the segmental blood volume change (d V) could be modeled as the resistance change due to blood volume (dR) electrically in parallel with the basal tissue resistance (Rt). This led to the well-known "Nyboer formula," dV -

-pbL2dR Rt 2

(3)

This formula has been at the center of the controversy concerning the validity of impedance plethysmography. Convincing in vivo validation of Eq. 3 has not been presented, and many investigators have resorted to empirical "correction" of Eq. 3 to obtain useful results. In our experiments on the calf, air-cuff or strain-gauge plethysmographs were employed simultaneously with impedance to measure venous volume changes. Estimates of blood volume changes based on Nyboer's formula were 40% too low (4). Thus, multiplication by a factor of 1.6 was necessary to obtain reasonable results. A percentage formula, easily derived from the Nyboer formula, is also commonly employed to predict blood volume changes from impedance. Rearranging Eq. 2, the basal resistance of the limb is Rt -

pt L2

(4)

Substitution for one of the Rt's in Eq. 3 gives dV

-pbdR

Vt

ptRt

(5)

For a limb segment, the percent change in volume is equal to a constant times the percent change in impedance. The ratio of the resistivity of blood (oh) to the resistivity of the limb segment (Pt) is sometimes referred to as the "resistivity constant," K. Two independent methods have been employed to determine K. Some investigators have measured percent volume and percent impedance changes simultaneously (4); others have attempted to measure Pb and & directly (19). Viewed separately, these results have small standard deviations and are highly correlated with hematocrit. Comparison of the results of these two approaches, however, reveals a 40% difference in the average value of K, similar to the error previously found in Nyboer's formula. The source of this error may be discovered by carefully reviewing the assumptions used to derive these formulas.

Impedance Plethysmography

83

The Parallel Resistance Assumption. Based on a concept first described by Fricke (7), Schwan (18) proposed a model of the volume-impedance relationship based on Eq. 5. Schwan did not require that the blood vessels be orientated parallel to the axis of the limb segment. Instead, a "form factor," X, was introduced which corrected for the average orientation of the blood vessels. This model was evaluated by Shimazu et al. (19), who employed a clever "compensation technique" to measure X and thus determine the validity of the parallel resistance model. Results demonstrated that a model that assumes that blood vessels are parallel to the axis of a cylindrical limb segment causes a fundamental error of less than 2%. Thus, the parallel resistance assumption is reasonable in the extremities. Resistivity o f Blood. Hematocrit and temperature are the main factors that determine blood resistivity (27). Variations in other blood components are too small to cause significant resistivity changes. Blood temperature, although potentially important, is not a factor in clinical impedance testing, as body temperature is nearly constant. The value of Pb can be estimated from the hematocrit (Fig. 2). With the exception of easily identified groups, such as patients undergoing hemodialysis, hematocrits outside a range of 30% to 50% are unusual. Assuming a constant Pa = 150 ohm-cm, based on an average hematocrit of 40~ (Fig. 2), a variation in Pa of + 20% would be expected for a normal range of variation in hematocrit. This is comparable to the range of error reported in estimation of venous volume change from impedance

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FIGURE 2. Relationship between hematocrit and conductivity of blood at 37 ~ (25).

84

Frederick A. Anderson, Jr.

(4,19). In addition, this error was reduced when Pb was estimated from hematocrit and used to adjust K (4,19). It is simpler to use a constant value for K, and a 20% range of error is often acceptable for clinical screening purposes.

Homogenous Tissue Assumption. Shimazu et al. (19) measured Pb and Pt and found an average ratio Oh~or = 0.67 on the forearm. Others have determined K from the ratio K -

dV/V, dR/Rt

(6)

According to Eq. 5, these should be equivalent. Yet, the ratio of percent volume to percent impedance changes has usually been reported in the range K = 0.72 to 1.07 (4,10,19). Shimazu and associates conclude that this difference is due to measurement error. This may be partly true; however, there are two unaccounted for variables that might cause systematic errors in estimates of K. The first is the measuring frequency of the plethysmograph employed. The second is the nonhomogenous composition of the limbs. These factors have not previously been considered in the theoretical evaluation of the impedance-blood volume relationship. Whereas the resistivity of blood is independent of frequency, the resistivity of tissue is more complex. As shown in Fig. 3, the resistivity of the calf decreases as frequency increases. Similiar results were reported by Jaffrin and Vanhoutte (12) who found a 30% decrease in the impedance of the calf when

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Frequency k H z FIGURE 3. The resistivity of blood is independent of impedance-measuring frequency, whereas the resistivity of the calf decreases with increasing impedance frequency. The resistivity of the muscle was estimated using Eq. 7 (see text).

85

Impedance Plethysmography

the frequency was increased from 5 kHz to 100 kHz. This suggests that the resistivity constant will depend on the measuring frequency of the plethysmograph employed, as well as on the hematocrit. In the derivation of Eq. 3 the assumption was made that the tissue beneath the impedance electrodes is homogenous. This is not true. It has been estimated that an average human calf consists of 13.6% skin and subcutaneous tissue; 26.8% fat, bone, and tendon; and 59.6% muscle (by volume) (21). The gross difference in the electrical resistivity of these tissues is even more striking and important than their relative volumes, however. The resistivity of muscle is typically 200 to 300 ohm-cm, whereas the resistivity of fat or bone is greater than 2,000 ohm-cm (8). Thus, human limbs can be more accurately modeled as a parallel combination of blood and muscle, ignoring the fat, skin, and bone. Although not exact, this model is a distinct improvement over the homogenous tissue model. If the main conductor in the calf at rest is muscle, then the basal resistance (Rt) is mainly due to muscle, or Rt = Rm. Thus, muscle resistivity (Pm) can be estimated from calf resistance measurements by applying a volume correction to Eq. 2:

Rt V, Vm P" =

L2

(7)

Vt

Using a value of 60% for calf muscle volume (Vm/Vt = 0.6), resistivity versus frequency can be estimated for the muscle component (Ore) (Fig. 3). Taking the ratio of Pb to Om gives K = 0.8 for a frequency of 22 kHz and K = 1.1 at 100 kHz. R e v & e d Theoretical E q u a t i o n s

Review of the assumptions employed to derive the Nyboer and percentage formulas shows that the limbs and blood vessels can be modeled as parallel volume conductors. The assumption that the limbs are homogenous conductors fails, however, owing to the large difference in the resistivity of fat and bone as compared with muscle. There is also a significant effect of impedance measuring frequency on the resistivity of muscle which must be considered in the percentage formula. Fortunately, the Rt 2 t e r m in the Nyboer formula avoids this frequency dependence (12). Since the resistivity of fat and bone is much larger than the resistivity of muscle, and since fat and bone are a significant portion of limb volume, then Eq. 4, relating Vt to Rt, is incorrect. Much like the parallel combination of two resistances, one of which is much larger than the other, the volume of fat and bone is not reflected by Rt. Thus, the Nyboer and percentage formulas must be correct by a factor M, which is the ratio of the muscle volume to the total limb volume,

86

Frederick A. Anderson, Jr.

Vm - P m Vt pt

M-

(8)

Then Nyboer's formula becomes dV

-

pbL2dR

(9)

RtZM

Similarly, the percentage formula can be generalized as dV V,

Pb dR -

pt

Rt

1 M

(10)

"

Equations 9 and 10 incorporate the influence of the nonhomogenous nature of the limb tissue (both in terms of volume and resistivity) into the estimation of blood volume changes from electrical impedance changes. In routine applications, useful results are obtained by assuming M - - 1.6 (i.e., muscle volume = 60% of limb volume). Equation 10 can be rearranged as the ratio of percent volume change to percent impedance change, dV/Vt dR/Rt

Pb Pt m

Pb -K Pm

.

(11)

Equation 11 shows that the resistivity constant K is equal to the ratio of the resistivity of blood to the resistivity of muscle. Viewed in this way, seemingly contradictory estimates of K can be re-evaluated and are found to be in reasonable agreement. It should also be remembered that K will depend on the frequency of the plethysmograph employed. Our data show an average K = 0.8 at 22 kHz and K = 1.0 at 100 kHz. Experimental Validation

This theoretical prediction was tested in humans using venous occlusion plethysmography (VOP). Two impedance plethysmographs (22 kHz and 100 kHz) were used. Recordings were made of calf impedance and calf volume, as determined by strain-gauge plethysmography (SGP) or air-cuff plethysmography. Simultaneous recordings from the calf during two minutes of venous occlusion at the thigh demonstrated a high correlation between the signals from these three plethysmographs (Fig. 4). Test results from 89 VOP recordings on 19 subjects (38 legs) are shown in Fig. 5. Percent volume changes determined by air-cuff compared with impedance changes measured at 22 kHz (using a least-squares approximation) showed that K = 0.8 (1,4). Further experiments were performed in which hematocrit was measured by the finger-stick method (mean = 42, S.D. = 4-6.3). The resistivity of blood was calculated from hematocrit using the data of Fig. 2. The muscle resistivity was estimated from volume conductor theory using the resting impedance,

~ ~

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FIGURE 4. VGP recorded simultaneouslyby three plethysmographictechniques 1251.

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FIGURE 5. Comparisonof simultaneousstrain-gauge and impedance recordingsof calf volume changes during VOP (4).

88

Frederick A. Anderson, Jr.

electrode separation, and calf circumference (Eq. 7). Percent impedance change of the calf was measured simultaneously with SGP, first at 22 kHz and again at 100 kHz. Results were plotted and compared with theory as described by Eq. 10. The agreement between experiment and theory is reasonably good, as seen in Fig. 6. Arterial Pulse Amplitude

Electrical impedance changes are mainly due to blood volume changes during slow changes in blood velocity (i.e., VOP). However, where large blood velocity changes occur (i.e., during maximum venous outflow or arterial pulse recordings), there is a component of the impedance which decreases with the increasing absolute value of blood velocity. This "velocity" effect in impedance plethysmography has been explained theoretically as the result of the shearing action of velocity changes on the disk-shaped red blood cells (RBCs). When the blood accelerates, the high resistivity RBCs orientate parallel to the vessel wall. This effectively lowers the resistivity of the blood along the axis of flow by reducing the percentage of vessel cross-section occupied by cells and increasing the relative area occupied by more conductive serum. In vitro experiments using bovine blood have confirmed this effect by demonstrating that an impedance change due to velocity can be measured in a rigid walled tube (i.e., volume changes were eliminated) (16). This velocity effect has been detected during maximum venous outflow following VOP. As shown in Fig. 7, the difference between simultaneous aircuff plethysmography and impedance plethysmography is nearly constant dur-

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Remstivity of Blood / Resistivity of Muscle FIGURE 6. Comparison of the ratio, resistivity of blood (Fig. 2)/resistivity of muscle (Fig. 3) with the ratio, percent calf volume change/percent impedance change (Fig. 5).

Impedance Plethysmography

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Differential FIGURE 7. VOP recorded simultaneously by air cuff and impedance techniques. Difference analysis shows a slight delay in the venous outflow portion of the impedance tracing corresponding to an increase in blood velocity during venous outflow (25).

ing the filling phase of VOP. However, immediately following the release of venous occlusion there is a decrease in impedance, unrelated to calf volume, which disappears as the velocity decreases. Impedance records of arterial pulse amplitude also show decreased impedance correlated with the absolute value of blood acceleration and unrelated to calf volume changes measured by SGP or air-cuff plethysmography. Simultaneous measurement of blood flow velocity using Doppler shows this relationship clearly (Fig. 8). Differences between the SPG pulse and the impedance pulse are consistent with the impedance changes recorded in a rigid tube with pulsatile flow. This difference caused the impedance pulse to have a faster systolic slope and a slower diastolic slope as compared with the SGP pulse recording. The crest amplitude of the impedance arterial pulse was about 60% larger than the corresponding SGP signal. This value was determined by comparing percent calf volume changes to percent impedance changes (at 22 kHz). The ratio of percent calf volume change to percent impedance change was K = 0.6 for arterial pulse amplitude measurements, as compared with K = 0.8 for slower VOP recordings. The reduction in K determined from arterial pulse recordings can be attributed in part to the effect of blood velocity on resistivity. However, the in vitro studies suggest an increase in impedance owing to blood acceleration of only about 10% (i.e., K = 0.7). There is no absolute yardstick for determining arterial pulse volume of the calf. Data are presented in the following

90

Frederick A. Anderson, Jr.

Mercury strain-gauge

_E~~ Impedance

Differential

Doppler

FIGURE 8. Simultaneous recordings of arterial pulsation of the calf. The impedance signal is greater in amplitude and breadth than the mercury strain-gauge tracing. As seen in the difference tracing, signal differences coincide with blood velocity changes measured by Dopper (22).

section of this paper to show that with proper placement, impedance electrodes sample with a nearly uniform sensitivity over the limb cross-section. This high sensitivity is not based on mechanical transmission of pulse volume changes, as with air-cuff plethysmography or SGP transducers. There are no data concerning the spatial sampling sensitivity of mechanical plethysmographic transducers. There is no reason to assume that transmission of electrical and mechanical signals by the tissue will be the same. Thus, it is possible that small, rapid changes in pulse volume are not efficiently transmitted through the tissues of a limb to the skin surface (where they are detected by a mechanical transducer). Further research may demonstrate that, compared with mechanical transducers, impedance plethysmography is capable of greater sensitivity in the measurement of small, rapid volume changes.

Impedance Sampling Field The parallel resistance model of the impedance-blood volume relationship assumes that the voltage gradient field is uniform. It is also assumed that the region measured is the tissue volume contained between the voltage electrodes. Unfortunately, this model does not consider the effect of placing circumferential electrodes at a finite separation. To evaluate the effects of realistic current and voltage electrode separations on the spatial sampling sensitivity of impedance plethysmography, a more general model is needed.

Impedance Plethysmography

91

In 1971 Geselowitz published an electric field theory derivation that allows prediction of the sampling sensitivity of impedance plethysmography (9). This result allows the prediction of the impedance change caused by a conductivity change throughout a given region, provided one knows the "lead vectors" associated with the current and voltage electrode pairs. A "lead vector" is that voltage gradient field that would be produced if one unit of current were to be passed between the electrodes (usually two) that make up the "lead." This general result has been applied by Penney et al. (15) to the specific case of circumferential electrodes on a cylinder of uniform conductivity (Fig. 9). With the use of a digital computer to numerically evaluate analytic expressions for the pertinent lead fields, the impedance measuring sensitivity can be predicted for any electrode configuration (Fig. 10). A surprising conclusion of this theory is that there can be regions where an increase in conductivity will actually increase the measured impedance. This will occur wherever the two lead fields are antiparallel, primarily in superficial regions between a voltage electrode and current electrode of the same polarity (Figs. 9 and 10). Implementation of the field theory model on a digital computer allows prediction of the impedance sampling field for a wide range of electrode locations. Predictions based on typical electrode locations employed in clinical vascular testing have been confirmed in physical models (I5) and in cadavers (3). Normalized impedance data obtained from 2 cc injections of saline into 10 limbs of 10 cadavers are plotted versus injection location in Fig. 11. The experimental data are compared with the theoretical impedance sampling sensitivity using a least-square criteria. The curves represent the theoretical model result for deep and superficial conductivity changes. Vertical lines represent the electrode locations. These studies show that impedance plethysmographic measurements on the calf represent a well-defined region extending only slightly beyond the voltage electrodes. For the electrode configuration typically employed in venous occlusion impedance plethysmography, this region extends less than 2 cm beyond the voltage electrodes (Fig. 10). The sampling efficiency for deep volume changes is 80% of that for superficial changes. As the current electrodes are further separated, the ratio of deep to superficial sampling sensitivity is improved. There are, however, practical limitations due to anatomy and convenience of electrode application which may make extreme separation of electrode pairs undesirable. Particular attention must be paid to the separation between the individual current and voltage electrode pairs. In the limit, as these pairs are moved closer together, a two-electrode technique will result. It is also important to note that superficial volume changes wilI be emphasized as the current and voltage electrode separation is reduced. There may be some situations in which this is desirable. Preliminary theoretical and experimental work has

92

Frederick A. Anderson, Jr.

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FIGURE 9. Sampling efficiency of four-electrode impedance plethysmography can be predicted from knowledge of two electric fields. Part (a) illustrates the field produced by current passing between the current electrodes. Part (b) indicates the field that would be produced by current flow between the voltage electrodes. Superimposing these fields, part (c) indicates the angles of intersection between them. Depending on these angles, part (d), the sensitivity will be positive, negative, or null (25).

Impedance Plethysmography

93

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been performed on noncircumferential arrays of electrodes (5,17). This leads to the interesting possibility of "focused" impedance measurements over a small anatomic region. Thus, in its ability to reflect deep volume changes with the same sensitivity as superficial changes and its ability to measure over a well-defined region, impedance plethysmography possesses attributes of an ideal plethysmographic technique. It is essential, however, to understand the relationship between electrode geometry and sampling sensitivity to avoid errors and to take full advantage of the capabilities of impedance plethysmography. CLINICAL APPLICATION It was established in the preceding sections that the impedance plethysmographic signal from the extremities is related to blood volume changes in the limb segment located between the voltage electrodes. Closer examination of Eq. 2 reveals that this impedance-volumerelationship consists of a transverse dilation (dA), longitudinal stretching (dL), resistivity changes in blood (dob), and resistivity changes in tissue (dRt). These components of the impedance change have been evaluated theoretically and experimentally by Jaffrin (12), who found that the magnitude of change in voltage electrode separation (dL) and blood resistivity (d0b) are on the order of 10% of the total impedance change. More importantly, these effects are opposite in sign and thus should cancel (assuming they are in phase). Resistivity changes of tissue (dRt) are negligible over time periods of a few minutes or less.

94

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FIGURE 11. Top: Results of deep saline injections in 10 cadaver calves. Impedance changes were normalized to the largest change recorded in an individual limb and compared with the theoretical model prediction by a least-squares criterion. Current and voltage electrode pairs were placed at separations of one-half and one-third of the maximum calf circumference, respectively. Bottom: Results of superficial saline injections.

Impedance recordings from the extremities consist of three easily measured components: a resting baseline impedance (RBI), venous volume changes, and arterial pulsation (Fig. 12). It has become standard procedure to display the inverse of these impedance changes, as impedance decreases with increasing blood volume.

Impedance Plethysmography

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FIGURE 12. Components of electrical impedance measured in the extremities. It has become standard practice to display the inverse of impedance changes.

Basal impedance is a function of the electrode separation, limb circumference, the measuring frequency of the plethysmograph employed, and the resistivity of the tissue. Typical RBI values range from l0 to 50 ohms. Venous volume changes occur naturally with respiration (0.2-0.3 Hz), causing a shift in basal impedance (typical dR = 0.1 ohm or 0.5%). Larger venous volume changes are produced by temporary occlusion of the veins proximal to the electrodes (Fig. 12). This is commonly referred to as VOP, which is widely employed for the detection of deep venous thrombosis (DVT). A change in basal impedance of up to 10% may be measured, depending on the occlusive cuff pressure, arterial inflow, central venous pressure, venous tone, and the capacity of the venous bed. In 300 patients with normal venograms, an average impedance change of 4% was measured in VOP tests (1). This volume change has been termed the "venous capacitance" and can be estimated from Eq. 10. I f K = 0.8 at 22 kHz, then %dV = 0.8 (4%dR) = 3.2% calf volume change. A reassuring, although indirect, confirmation of Eq. 10 is provided by several reports of a similar average venous capacitance obtained from normal patients studied with SGP or air-cuff plethysmography (1).

96

Frederick A. Anderson, Jr.

Arterial pulsations (1-2 Hz) recorded from the calf have an amplitude of about 0.02 ohms (0.1%dR) in young normal subjects. Arterial pulse amplitude should be determined by averaging 3 to 5 pulses or by high-pass filtering (0.1 Hz) to avoid measurement errors due to respiration or other gradual shifts in basal impedance. Arterial pulse amplitude and shape are related to the arterial inflow, electrode geometry, arterial wall compliance, proximal obstruction, and peripheral resistance. For example, pulse amplitude decreases with age as the arterial wall becomes less elastic. The impedance arterial pulse recorded across the knee is normally larger than the pulse recorded from the calf. This is related to differences in the relative volumes of bone, tissue, and blood in the impedance sampling field. Therefore, if standards for detection of peripheral vascular disease are to be developed, care must be taken to position the electrodes using standard anatomic landmarks. Detection o f D V T

The most common use of impedance plethysmography has been in the noninvasive detection of DVT using the VOP technique. The details of this test procedure have been extensively reported elsewhere (6,11,23,24). In brief, impedance electrodes are applied to the calf, and a blood pressure cuff is placed loosely around the mid-thigh (Fig. 13). The patient is tested supine with the legs elevated above heart level (20-30 degrees). The thigh cuff is inflated to a pressure above venous pressure, but lower than arterial diastolic pressure (approximately 50 mm Hg). The impedance of the calf is monitored until the volume increase reaches a plateau (approximately 2 minutes). The thigh cuff is then rapidly deflated. The presence of venous outflow obstruction is detected by measuring the maximum venous capacitance (the highest achieved within five test repetitions) and the corresponding venous outflow rate (measured as the venous volume decrease in the first 3 seconds following cuff release). These variables are then plotted on an interpretation graph (Fig. 14). Regions of normal and obstructed venous outflow have been determined by comparison with more than 2,500 contrast X-rays (venograms) (6,11,23,24). The overall accuracy of this method is greater than 94% in the detection of recent DVT proximal to the knee. These results have been independently confirmed in six medical centers (23,24). This test has also been successfully adapted to the detection of venous thrombosis in the arms (14). Detection o f Chronic Venous Insufficiency

Impedance plethysmography has recently been used to measure the reflux of venous blood flow in the calf for the objective diagnosis of chronic venous insufficiency. Normally, venous return from the extremities is aided by the presence of valves in the veins. There are typically three to six valves in the deep veins between the knee and heart. Thus, when venous blood is propelled

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toward the heart by calf muscle contraction, this blood cannot "reflux" back into the calf. These valves may become damaged, often because of previous DVT. The resulting increase in venous blood pressure, particularly at the ankle during standing, may cause the so-called postphlebetic syndrome of chronic pain, ankle swelling, and ulceration. There is increasing clinical interest in objective methods of documenting and quantifying venous reflux. Some investigators have emptied the calf veins by means of active dorsiflexion of the foot and have measured the time to recover to basal venous volume using a photoelectric plethysmograph at the ankle. Recently, an analogous test has been developed using impedance plethysmography (2). With the patient sitting on the edge of the bed, a blood pressure cuff is placed around the calf between the voltage electrodes (Fig. 15). The cuff is inflated and deflated rapidly five times to a pressure

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of 100 mm Hg. The calf volume change is monitored by impedance as the calf veins empty and then refill. A recovery time greater than 11 seconds indicates normal valve function. A recovery time of less than 11 seconds indicates venous reflux (Fig. 15). Evalution of this impedance reflux test in a group of 41 patients with typical symptoms of venous insufficiency and a positive Doppler reflux exam demonstrated an overall accuracy of 90~ Thus, impedance plethysmography is an objective method for the noninvasive evaluation of chronic deep venous insufficiency.

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Impedance plethysmography can be employed for the noninvasive evaluation of arterial perfusion of the limbs. Measurements including the initial rate of calf filling following VOP and the amplitude or maximum systolic slope of the arterial pulse wave have been employed either at rest or following exercise. It may be argued, however, that the clinical need for this information is marginal in the majority of patients with suspected arterial insufficiency (AI). Physical signs and symptoms of AI are fairly sensitive and specific. In addition, the clinical decision to be made is usually whether or not to go on to X-ray contrast studies (arteriography) prior to a final decision concerning surgical treatment. The majority of clinical vascular laboratories now rely on Doppler systolic blood pressure measurements alone to screen patients with suspected AI. This is due to Doppler's high accuracy, relative simplicity, and low cost. Thus, the value of all types of noninvasive volume or flow studies in routine arterial diagnosis has yet to be clearly established. The only patient group in which plethysmography clearly improves the accuracy of Doppler alone is the relatively small percentage of diabetic patients whose arteries have become so calcified that they cannot be compressed by a blood pressure cuff. Resting arterial inflow determined from VOP measurements is not useful in the diagnosis of AI. The resting flow rate does not decrease significantly until the viability of distal tissues is threatened. Exercise or reactive hyperemia testing is potentially useful; yet these tests are time consuming and too often uncomfortable. Arterial pulse amplitude or maximum systolic slope at rest are the most practical plethysmographic indices of AI. However, the relationship between the arterial pulse waveform and total inflow is nonlinear, particularly at the reduced flows that are of clinical interest. These observations apply equally to both mechanical and impedance plethysmography. Controversy about the validity of impedance plethysmography has frequently been related to arterial pulse "volume" studies. Early investigators applied the Nyboer formula to the pulse amplitude and multiplied by the heart rate to estimate the "arterial inflow rate" to the limb in milliliters per minute. As mentioned previously, such measurements are only indirectly related to total flow, as measured by VOP or electromagnetic flow meters. However, since resting arterial inflow is not a sensitive index of AI, plethysmographic measurements of total flow would probably not be clinically useful, even if they could be determined from pulse amplitude. Jaffrin and Vanhoutte avoided these problems by estimating the arterial distensibility from the impedance pulse (12). Van De Water et al. defined the impedance pulse volume times the heart rate as a "pulsatile flow rate" for the entire limb (22). Of particular interest are their graphic representation of the impedance pulsatile flow versus the Doppler systolic pressure at the ankle. A noninvasive index of the peripheral resistance of the limb is created, which may prove to be more useful clinically than measurement of either pressure or flow alone. Unfortunately, too little has been done to study the correlation of arterial

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impedance measurements with clinically relevant data such as symptoms, arteriograms, and operative results. Using impedance plethysmography on the calf, we evaluated resting arterial pulse waveforms in 33 legs with an arteriographically documented obstruction of greater than 50~ diameter reduction in the aortofemoral vessels (20). These results were compared with 28 normal legs. The maximum systolic slope was 0.22%dR/sec in the patient group and 1.10%dR/sec in volunteers (p < .05). The amplitude of the impedance pulse was also evaluated. The mean pulse amplitude was 0.032%dR + 65% S.D. in 33 abnormal limbs and 0.081%dR + 25% S.D. in 28 normal limbs (p < .05). Borderline values of 0.60 %dR/sec and 0.06%dR for systolic slope and pulse amplitude, respectively, produced a sensitivity and specificity of greater than 90%. Thus, impedance plethysmography can be reliably employed in the noninvasive evaluation of AI. The place of such testing, with respect to equally accurate and simpler Doppler systolic blood pressure measurements, may relate to the ability of impedance to record the arterial pulse continuously and to the ease of processing and displaying these data using modern microprocessor technology.

REFERENCES 1. Anderson, F.A., Jr. Quantification of venous volume changes in the human calf from electrical impedance measurements. M.S. thesis. Worcester Polytechnic Institute, Worcester, Massachusetts, 1975. 2. Anderson, F.A., Jr., J.M. Li, and H.B. Wheeler. Application of impedance plethysmography to the detection of venous insufficiency. Bruit 7(5):41-45, 1983. 3. Anderson, F.A., Jr., B.C. Penney, N.A. Patwardhan, and H.B. Wheeler. Impedance plethysmography: The origin of electrical impedance changes measured in the human calf. Med. Biol. Eng. Comput. 18:243-240, 1980. 4. Anderson, F.A., Jr., B.C. Penney, R.A. Peura, and H.B. Wheeler. Evaluation of electrical impedance plethysmography for venous volume measurements. Annual Conference on Engineering in Medicine and Biology (Proceedings) 18:218, 1976. 5. Anderson, F.A., Jr., B.C. Penney, and H.B. Wheeler. Regional impedance plethysmography: An experimental method for the study of specific blood vessels. 14th AAMI Proceedings. 9,1979. 6. Anderson, F.A., Jr. and H.B. Wheeler. Venous occlusion plethysmography for the detection of venous thrombosis. Med. Instrum. 13:350-354, 1979. 7. Fricke, H. The electric conductivity and capacity of disperse systems. Physics 1:106-115, 1931. 8. Geddes, L.A. and L.E. Baker. The specific resistance of biological material-a compendium of data for the biomedical engineer and physiologist. Med. Biol. Eng. Comput. 5:271-293, 1967. 9. Geselowitz, D.B. An application of electrocardiographic lead theory to impedance plethysmography. IEEE Trans. Biomed. Eng. 18:38, 1971. 10. Hill, D.W. and C.E. Hope. A comparison of electrical impedance and other methods of venous occlusion plethysmography. Digest 10th International Conference Medical Biological Engineering. Dresden, East Germany, 1973, p. 245. 11. Hull, R., W.G. Van Aken, J. Hirsh, A.S. Gallus, G. Hoicka, A.G.G. Turpie, I. Walker, and M. Gent. Impedance plethysmography using the occlusive cuff technique in the diagnosis of venous thrombosis. Circulation 53:696-700, 1976. 12. Jaffrin, M. Y. and C. Vanhoutte. Quantitative interpretation of arterial impedance plethysmographic signals. Med. Biol. Eng. Comput. 17:2-10, 1979. 13. Nyboer, J. Electrical impedance plethysmography: A physical and physiologic approach to peripheral vascular study. Circulation. 2:811-821, 1950.

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14. Patwardhan, N.A., F.A. Anderson, Jr., B.S. Cutler, and H.B. Wheeler. Noninvasive detection of auxilary and subclavian venous thrombosis by impedance plethysmography. J. Cardiovasc. Surg. 24:250-255, 1983. 15. Penney, B.C., L.M. Narducci, R.A. Peura, F.A. Anderson, Jr., and H.B. Wheeler. The impedance plethysmographic sampling field in the human calf. IEEE Trans. Biomed. Eng. 26:193-198, 1979. 16. Peura, R.A., B.C. Penney, J. Arcuri, F.A. Anderson, Jr., and H.B. Wheeler. The influence of erythrocyte velocity on impedance plethysmographic measurements. Meal. Biol. Eng. Comput. 16:147-154, 1978. 17. Peura, R.A., C.W. Sherman, F.A. Anderson, Jr., B.C. Penney, and H.B. Wheeler. Regional impedance plethysmography: Experimental and computer model studies for measuring single blood vessels. Vth Intern. Conf. Electrical Bio-Impedance. Tokyo, Japan 1981, pp. 65-68. 18. Schwan, H.P. Electrical properties of body tissues and impedance plethysmography. IRE Trans. Biomed. Eng. 3:32-46, 1955. 19. Shimazu, H., K.I. Yamakoshi, T. Togawa, M. Fukuoka, and H. Ito. Evaluation of the parallel conductor theory for measuring human limb blood flow by electrical admittance plethysmography. IEEE Trans. Biomed. Eng. 29:1-7, 1982. 20. Smith, J.J., B.G. Haffty, B.C. Penney, R.A. Peura, and H.B. Wheeler. Application of impedance plethysmography for arterial diagnosis. 29th Annual Conference Engineering Medicine & Biology Proceedings 18:391, 1976. 21. Strandness, D.E. and D.S. Sumner. Hemodynamics For Surgeons. New York: Grune & Stratton, 1975, p. 210. 22. Van De Water, J.M., B.E. Mount, W.F. Roettinger, and L.A. Trudell. Noninvasive assessment of the peripheral vascular system, Arch. Surg. 112:679-683, 1977. 23. Wheeler, H.B. and F.A. Anderson, Jr. Impedance phlebography: The diagnosis of venous thrombosis by occlusive impedance plethysmography. In Noninvasive Diagnostic Techniques in Vascular Disease (2nd edition), edited by E.F. Bernstein, St. Louis: C.V. Mosby, 1982, pp. 482-496. 24. Wheeler, H.B. and F.A. Anderson, Jr. Impedance plethysmography. In Practical Noninvasive Vascular Diagnosis, edited by S.J.T. Yao and R.F. Kempcyinski. Chicago: Year Book Medical Publishers, 1982, pp. 277-303. 25. Wheeler, H.B. and B.C. Penney. Impedance plethysmography: Theoretical and experimental basis. In Noninvasive Diagnostic Techniques in Vascular Disease (2nd edition), edited by E.F. Bernstein. St. Louis: C.V. Mosby, 1982, pp. 104-116. 26. Yamakoshi, K., H. Shimazu, T. Togawa, and H. Ito. Admittance plethysmography for accurate measurement of human limb blood flow. Am. J. Physiol. 236:H821-829, 1978. 27. Yamakoshi, K., H. Shimazu, T. Togawa, M. Fukuoka, and H. Ito. Noninvasive measurement of hematocrit by electrical admittance plethysmography technique. IEEE Trans. Biorned. Eng. 27:156-161, 1980. 28. Young, D.G., Jr., R.H. Cox, E.K. Stoner, and W.J. Erdman II. Evaluation of quantitative impedance plethysmography for continuous blood flow measurement: III. Blood flow determination in vivo. Am. J. Phys. Med. 46:1450-1456, 1967.