Improvement in intracardiac impedance volumes by field extrapolation R. W. SALO

Research Department, Cardiac Pacemakers, Inc., 4100 N. Hamline Ave., St. Paul, MN, U.S.A. 55112

KEY WORDS: Intracardiac impedance, conductance catheter,fieldextrapolation. The measurement of volume by electrical impedance is complicated by non-homogeneous current distribution resulting from small current sources, by the irregular shape of the ventricle, and by loss of current to surrounding anatomical structures. A mathematical technique, field extrapolation, was developed to partially correct the current distribution. The technique mathematically transforms measured potentials into the potential distribution which would result from infinitely distant current sources. The linear correlation coefficient between impedance stroke volume or cardiac output using field extrapolation and thermodilution stroke volume or cardiac output was 0-83 (n = 86) in 11 dogs and 0-76 (n = 92) in 12 patients. The average linear correlation coefficient between impedance stroke volume and integrated aorticflowin four dogs was 0-83 ± 0-09 (n = 49) usingfieldextrapolation.

Introduction There is a highly non-linear and complex relationship between the electrical potentials generated by an intracardiac impedance (conductance) catheter and chamber volume. Intracardiac impedance measurements are influenced by at least two factors in addition to chamber volume. These factors, the inherent non-homogeneity of the current density produced by small current sources and the effect of surrounding conductive structures, modify the generated electrical potentials such that the simple Nyboer equation, equation 1, relating the resistance, R, of a volume, V, to the resistivity of the material, p, and the distance between measuring electrodes, L, is no longer an adequate representation: (1) Even with the simplest geometry, a cylindrical volume with a uniform transverse cross-section, the distribution of equipotential surfaces generated by a pair of point current sources along the longitudinal axis, as displayed in Fig. 1, is non-uniform. At least two approaches to delineate the impedance-volume relationship are possible. The first involves generating an alternative to the Nyboer equation by developing an analytical solution to Poisson's equation, equation 2, a partial differential equation which relates electrical potential, 0, conductivity, o, and current density, p, which takes into account geometry, conductivity, and position of current sources: V •

- p=0

(2)

However, even if such an analytical solution were possible, information about chamber geometry, conductivity of surrounding structures (including myocardial tissue) and position of electrodes with respect to the heart are not Correspondence: R. W. Salo, Research Department, Cardiac Pacemakers Inc., 4100 N. Hamfine Avenue, SL Paul, MN, 55112-5798, U.S.A.

O195-668X/92/0EO035 + 05 S08.00/0

available at the time of a study and in most cases the information does not exist at all. The second approach is to develop a stepwise solution in which each of the contributing factors is addressed independently. Field extrapolation addresses the inherent non-homogeneity due to point sources by transforming actual potentials into the equivalent potentials which would be measured with infinitely distant current sources. The Nyboer equation can then be applied to the extrapolated potentials with some confidence, although not with complete accuracy since the cardiac chamber does not have a uniform cross-section. The effect of current lost to surrounding structures is not addressed, but a parallel current path can be shown1'1 to have little effect on the accuracy of stroke volume measurements. Therefore, impedance stroke volume values would be expected to compare more favourably with accepted standards than other ventricular volumes (e.g. end-diastolic or end-systolic volumes). This conclusion, as well as the ready availability of accepted stroke volume standards and the relative dearth of universally accepted standards for other volumes, dictate that we concentrate on stroke volume comparisons at this time. An early innovation by Baan el al. reduced the impact of the most dramatic non-linearities (near the current sources) by sensing potentials with a multipolar catheter, which effectively divided the ventricle into a stack of vertical 'slices', and then applying empirically derived multiplicative constants to each slice12'. These constants were dependent on the geometry of the chamber and the position of the catheter (neither of which was generally available to the investigator during a procedure) and thus the efficacy of the corrections was variable. Field extrapolation is a mathematical construct development to lineararize the generated electricalfield1'-3'.It is a transformation applied to a set of potentials generated and measured by a practical electrode geometry which produces a new set of potentials which correspond to an © 1992 The European Society of Cardiology

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R. W. Salo

Contour plot of model data

X axis

Figure 1 Equipotential lines generated by two current sources in one plane of a three-dimensional, cylindrical, three-compartment,finite-difference,numerical model. Lines are separated by 50 volts. A uniform current distribution would exhibit equally spaced parallel lines perpendicular to the longitudinal axis. Note instead the non-uniform shapes and distribution of equipotential lines. Apparent distortion near the outer boundaries of the model are due to non-uniform spacing of nodes in these regions.

unattainable, idealized electrode geometry. The extrapolated potentials may then be used to compute chamber volume with improved accuracy. Methods In practice, a constant sinusoidal current is driven between a pair of 'outer' current sources positioned on a catheter at the extreme apex and base of the ventricle and a second sinusoidal current (of equal magnitude but at a different frequency) is driven between a pair of inner current sources located on the catheter between the outer sources. In fact, the proximal sources may be located outside of the chamber in the aorta for a left ventricular placement and in the right atrium for a right ventricular placement. Generated potentials are sampled by catheter 'sensing' electrodes arrayed between the inner sources. The potential difference between a pair of sensing electrodes, due to the current from the outer drive electrodes, may be scaled by the applied current from these electrodes to compute the impedance Z,, between the sensing electrode pair. (The impedance phase angle for measurements made in blood in the ventricles is less than seven degrees in the 1-0-10-0 kHz frequency range and, therefore, the impedance may be considered to be a pure resistance). Likewise, an impedance Zj may be computed, corresponding to the inner drive electrodes. Zj must be greater than Z,, since it is derived from closer current sources. If the distance is defined as in equation 3 the relationship between impedance and electrode separation is approximately

linear as it appears in Fig. 2 for the apical segment of a human heart in vivo. 1 "•EQUIVALENT

_

1 sl-dl

1 d2-s2

1 d2-sl

s2-dl

(3)

l/dEQurvALENT IS a funct'on °f t ' l e coordinates of the distal

(dl) and proximal (d2) current sources and the coordinates of the distal (SI) and proximal (S2) sensing electrodes. Therefore, the measured impedance is also a function of the positions of current sources and measuring electrodes. The measured impedance may be extrapolated to any arbitrary electrode separation including an infinite separation. The Z value for infinite separation (where Z corresponds to the 'y' intercept) is particularly desirable because it is more simply related to chamber volume since it corresponds to a uniform current density throughout the volume, and permits the use of the Nyboer equation, equation 2. The actual procedure follows these steps: Step 1: measure the potential difference between a pair of sensing electrodes within the chamber for at least two different pairs of current sources. This can be done by using current sources operating at distinctly different frequencies and selectively filtering out each of the frequencies. For each pair of current sources a different resistance will be measured with the largest resistance measured for the closest pair of current sources. Step 2: plot the measured resistances as a function of l/dEQUIV and determine the relationship between resistance and l/dEQlJiv. Step 3: based on the relationship determined in step 2, extrapolate the resistance,

Improvement in intracardiac impedance

REXT at

l/dEOuiv = 0. Step 4: use REXT in the Nyboer equation to compute a volume for the sensed segment.

Apical Segment 2 0 cm length rings (2,4)

-2 20

£ en

0-8

1-0

1-2

1-4

1

OIV (cm" )

Figure 2 A plot of measured segmental resistance at end-diastolic (V) and end-systolic (•) volume for the apical (2-0 cm) segment of a human heart plotted as a function of l/dEQuiv for several different current source positions. Measurements were made serially by manually switching the current source connections to a 12 pole catheter with 10 cm electrode spacings. Measurements were made in vivo at 10 microamperes RMS and 2-5 kHz.

z

37

Figure 3 illustrates a system developed to complete the above procedure in 'real-time' permitting 'on-line' computation and recording of ventricular volume141. Thermodilution measurements, made with 10 ml iced saline solution and hand injection, were accepted if they displayed normal temperature profiles during and after injection. The mean cardiac output was divided by mean heart rate to obtain a mean stroke volume measurement. This value was compared to the mean left ventricular impedance stroke volume at the time of the thermodilution measurements Although the conductivity of blood is a function of temperature and blood composition, a thermodilution injection was assumed to have no effect on left ventricular impedance measurements. The cooled blood was assumed to return to its original temperature during its passage through the lungs and to be thoroughly mixed with undiluted blood. The change in blood conductivity was ignored although conductivity of blood was determined at the beginning and end of each study to determine overall change during a procedure. All patient measurements were made at rest under baseline conditions. Canine thermodilution cardiac output measurements were made similarly. Inferior vena caval (IVC) balloon occlusions and dobutamine infusions were used to decrease and increase stroke volume respectively. Dobutamine infusions were titrated to give significant stroke volume increases without simultaneous increases in heart rate. Cardiac output or stroke volume comparisons were made, as much as possible, under steady-state conditions to improve the accuracy of the thermodilution mea-

28

26

22

18

94

Figure 3 Simplified schematic representation of a three-channel, dual frequency, microprocessor-controlled intracardiac impedance system using field extrapolation.

38

R. W. Salo

surement and to minimize the impact of beat-to-beat variations between left and right ventricle. Canine flow measurements were made with electromagnetic flow probes positioned around the aorta at least one month before the study. The flow and impedance volume signals were simultaneously digitized at 200 Hz and recorded. IVC balloon occlusions were used to decrease cardiac output and 25-100 fig equivalents of dobutamine were infused as a bolus to increase cardiac output. Beat-bybeat comparisons between impedance stroke volume and integrated aortic flow were made either during balloon inflation while stroke volumes were dropping or during dobutamine infusion while stroke volumes were increasing. Since the flow probes were not calibrated, slopes and intercepts could not be determined for the entire population. Only a mean correlation coefficient was computed. Numerical modelling was carried out with a modification of a finite-difference model discussed previously151. The model consisted of a cylinder filled with a substance with the conductivity of blood (i.e.CT= 0-7 S/m), surrounded by a shell of uniform thickness with a different (usually lower) conductivity. The cylinder with its shell was positioned within a rectangular solid with the approximate dimensions of a torso. The conductivities of shell and torso were under operator control.

Results Field extrapolation relies on the relationship between measured resistance and l/dE0Uiv. Due to the nature of the extrapolation, relatively small errors can lead to substantial errors in the computed volume. In order to explore these effects more completely a series of numerical modelling studies was conducted on cylindrical volumes.

200

150 -

100 3

a. E o

80

100

120

140

Actual volume (ml)

Figure 5 A comparison between volumes computed from impedance measurements using either the uncorrected Nyboer equation or field extrapolation in the cylindrical, finite-difference, numerical model of Fig. 4. • = actual volume; T = extrapolated volume; V = Nyboer volume. Since field extrapolation does not explicitly address parallel current paths121, the modelling work concentrated on models without parallel current paths, in this case cylindrical models 7-5 cm in length with a radius varying from 0-5 to 3-0 cm and non-conducting walls. In these cylindrical volumes, the impedance was only approximately a linear function of l/dEOijrv as is evident in Fig. 4. The data also imply that the relationship is influenced by the radius of the cylinder.

o

•o

o

•p o

o

0-5

10

1-5

20

2-5

1

1/dgQuiv (cm" )

Figure 4 A plot of measured resistance as a function of l/dEW;iv for a cylindrical,finite-difference,numerical model with non-conducting walls. The non-linearity of the relationship is readily apparent, especially for the smallest (1-0 cm radius) cylinder. • = 3-0 cm; V = 2-0 cm; T = 10 cm.

Cardioc output by thermodilution (I mm"1)

Figure 6 A comparison between cardiac output computed from left ventricular impedance by field extrapolation and cardiac output measured by thermodilution in 11 dogs. Measurements were made under resting conditions, during IVC balloon occlusion, and during dobutamine infusion.

Improvement in intracardiac impedance

39

stroke volumes in animals and in man. There are also anecdotal indications that computed volumes are less sensitive to catheter position and motion following field extrapolaI 8 tion. The impedance catheters were positioned in patients quite rapidly without monitoring the volume waveform 6 -and with minimal effort to optimize the position. The only criterion for placement was that the tip of the catheter f 4should be near the ventricular apex. Even under these conC0z=l-5l + 0-75'COro ditions, which are probably typical of clinical procedures r = 0-76 2 where little time is available for repositioning, the catheter yS Identity line position was quite adequate. This was true, although the . / I I 1 I patient population included cardiomyopathies and 2 4 6 8 10 myocardial infarcts which would result in both abnormal Cordioc ouput by themwdilutiofi (I mm"') geometries and wall motions. Figure 7 A comparison between cardiac output computed from Although field extrapolation addresses only the inhomoleft ventricular impedance byfieldextrapolation and cardiac outgeneity in current density and neglects both parallel conput measured by thermodilution in 12 patients uder clinical condiductance and ventricular shape considerations, it results in tions. significant improvements experimentally. These findings are somewhat in conflict with the results of the cylindrical numerical model with non-conducting walls which would Since the actual relationship between Z and l/dEouiv predict some improvements in linearity but a nearly 50% was not truly linear, especially for large separations (small over-estimation of stroke volume. There are several potenl/dEQurv). there was an error involved in field extrapola- tial explanations for this apparent contradiction. Field tion. The impact of the error is displayed in Fig. 5. In this extrapolation may be shape dependent and better suited to figure the true volumes of the cylindrical models of Fig. 4 the ellipsoidal shape of the left ventricle than to a cylinder. are compared to volumes computed by the uncorrected Field extrapolation may be influenced by parallel current Nyboer equation and byfieldextrapolation. It is clear that paths which would tend to reduce large potential differthe difference between the volumes is a function of the ences within the ventricle. It is even possible that the 50% radius of the cylinder. At small radii (0-5-1-5 cm) both over-estimation is consistent with experimental measuretechniques compute accurate volumes. For larger cylinders, ments but is counterbalanced by under-estimations due to the Nyboer equation consistently underestimates true vol- inability to sense volume distal to the most distal and proxiumes, while field extrapolation nearly equally overesti- mal to the most proximal sensing electrodes. This is obviously an area requiring further study. mates true volumes. Figure 6 displays the results of a comparison in 11 dogs Based on experimental results it appears that the appliof thermodilution cardiac output and cardiac output mea- cation of this 'first order correction' technique improves sured by impedance using field extrapolation. The overall accuracy and possibly reduces the level of skill necessary relationship appears to be linear with an overall corre- to position an impedance catheter. This will hopefully result lation coefficient of 0-83, n = 86. Figure 7 summarizes a in more widespread application of intracardiac impedance similar comparison of stroke volume measured by in research and clinical cardiology. impedance to stroke volume by thermodilution in 12 patients. Since all measurements were made under baseline conditions, the range is rather small. However, once References [1] Salo RW. The theoretical basis of a computational model for again the relationship appears reasonably linear (with perthe determination of volume by impedance. Automedica haps some overestimation at large volumes) with a linear 1989; 11: 299-310. correlation coefficient of 0-76, = 5 92. In a study comparing [2] Baan J, Van Der Velde ET, De Bruin HG et al Continuous impedance stroke volume to integrated aortic flow in four measurement of left ventricular volume in animals and dogs with chronic flow probes using IVC occlusion to humans by conductance catheter. Circulation 1984; 70: 812-23. reduce stroke volume and dobutamine infusion to increase [3] Spinelli JC, Salo RW. The role of thefieldextrapolation techstroke volume, the mean linear correlation coefficient was nique in obtaining a linear relationship between intraventri0-83 ± 0-09, n = 49. cular admittance and volume. IEEE EMBS Proc 1990; 12:

T»

Discussion Despite some non-linearity in the impedance vs 1/dEouiv relationship, the field technique has been shown to generate reasonably accurate infracardiac impedance

707-8. [4] Salo RW. Method and apparatus for measuring ventricular volume. United States Patent, 4674518,1987. [5] Salo RW, Wallner TG, Pederson BD. Measurement of ventricular volume by intracardiac impedance: theoretical and empirical approaches. IEEE Trans Biomed Eng 1986; BME33:189-95.