Does volume catheter parallel vary during a cardiac cycle?

conductance

EDWARD B. LANKFORD, DAVID A. KASS, W. LOWELL MAUGHAN, AND ARTIN A. SHOUKAS Department of Biomedical Engineering and Division of Cardiology, The Johns Hopkins Medical Institutions, Baltimore, Maryland 21205

B., DAVID A. KASS, W. LOWELL A. SHOUKAS. Does volume catheter parallel conductance vary during a cardiac cycle? Am. J. Physiol. 258 (Heart Circ. Physiol. 27): H1933-H1942, 1990.-Absolute left ventricular volume measurement by the conductance (volume) catheter requires subtraction of the conductance contribution from structures extrinsic to the cavity blood pool. Previously, this parallel conductance volume (V,) has been assumed constant throughout the cardiac cycle, and the technique described for its estimation in situ yields a single value. We present a new method for parallel conductance determination that yields multiple estimates during systole, enabling an assessment of V, variability [V,(t)]. For isolated blood-perfused ejecting canine left ventricles with empty (vented) right ventricles, V,(t) displayed virtually no variation throughout systole. For in situ hearts, despite the presence of other cardiac chambers, V,(t) also displayed little variation, with no statistically significant deviation from its mean value throughout systole. Volume signal simulations found the new technique to be less sensitive to signal noise and thus more robust than the one previously published. The isolated and in situ heart data indicate that for the left ventricle, the parallel conductance is relatively constant throughout normal ejection. LANKFORD, MAUGHAN,

AND

EDWARD ARTIN

conductance catheter; impedance catheter; in situ heart; saline washout; volume calibration; volume offset

of techniques have been used to measure left ventricular chamber volume of in situ hearts. Most of these approaches require assumptions for geometric modeling (e.g., sonomicrometry) and labor-intensive offline image contouring (e.g., echocardiography, tine and nuclear ventriculography). A recently developed device that avoids these problems is the multielectrode conductance catheter, which provides a continuous on-line volume signal (23). A small alternating current is passed between a proximal and distal electrode pair (located at the ventricular base and apex, respectively), and electrical potentials are measured at the multiple intervening electrodes in the blood chamber. Changes in ventricular conductance are proportional to blood volume changes (2, 7). This approach has the unique advantage of providing an on-line signal and requires only arterial accesswithout alteration of normal closed-chest physiology. It has therefore proven to be well suited for human studies (3, 10, 13). A drawback of the device is that structures such as the myocardium and surrounding tissues that are extrinsic to the ventricular chamber blood pool also A WIDE VARIETY

0363-6135/90

$1.50 Copyright

conduct current. Therefore the conductance measured by the catheter overestimates the conductance due to blood by the “parallel conductance,” G,. This parallel conductance can be easily converted to a volume offset, VP' Several investigators have chosen not to quantify the parallel conductance (2, 7, 13, 16) and have instead presented either relative volumes or impedances. While still useful for some applications, calibration to absolute volume markedly strengthens the catheter’s utility. A technique for determining the parallel conductance has been reported (3, 6, 10, 11) that involves processing the conductance signal over several cardiac cycles after infusion of a small bolus of concentrated saline into the pulmonary artery. Since conductance measured by the catheter is dependent on the electrical conductivity of blood in the ventricular chamber, the hypertonic solution causes a transient increase in the conductance, or volume, signal. The selective change in the left ventricular chamber blood conductivity without altering left ventricular chamber blood volume or the conductance of surrounding structures (myocardium, lungs, etc.) permits estimation of the conductance due to the parallel structures. This method has been validated in situ against dilution methods (3), as well as in isolated ejecting canine left ventricles (6) in which accurate ventricular volumes were obtained simultaneously. The hypertonic saline calibration technique yields a single value for parallel conductance volume (VP) and assumesno significant time variation during the cardiac cycle. Yet simultaneous ejection of blood from the right ventricle, filling of the atria, and changes in left ventricular myocardial shape and blood content could potentially vary VP within the cardiac cycle. In this study, we present a new estimation method that utilizes much more of the available data than that previously described and also provides information about the variation of VP during cardiac contraction. With this approach we tested whether VP could reasonably be considered constant during systolic contraction. Experimental and simulation data were used to compare the two techniques. METHODS

Experimental Preparations Surgical preparation. To evaluate the parallel conductance in ejecting hearts without any contribution of con-

0 1990 the American

Physiological

Society

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ductance variation from extrinsic structures other than the myocardium, isolated canine hearts were prepared as previously described (6). Three pairs of mongrel dogs were anesthetized with pentobarbital sodium (30 mg/kg iv). The femoral arteries and veins of one (support) dog of each pair were cannulated and connected to a perfusion system used to supply oxygenated blood to the heart isolated from the second (donor) dog. The chest of the donor dog was opened, cross perfusion was obtained, and the heart was excised. The left atrium was opened, all chordae tendineae were freed from the mitral valve leaflets, and an adapter ring was sewn to the mitral annulus. This adaptor was connected to a servo-pump system and a saline-filled pericardial balloon placed within the left ventricular chamber. The saline conductivity was adjusted to that of blood [=0.0071 (Q. cm)-I], or resistivity = 140 Q cm. A conductance catheter was inserted into the balloon along the ventricular long axis with the most proximal electrode just above the mitral adaptor ring. The right ventricle was vented to air. Coronary perfusion pressure was maintained constant at 80-90 mmHg by a servo-controlled finger pump (model 1215, Harvard Apparatus). Left ventricular volume was maintained by a piston within a double rolling diaphragm cylinder and positioned by a linear motor (Ling Dynamic Systems model 411/S). The piston position was servo controlled by a computer-generated command signal simulating a threeelement modified windkessel model of aortic input impedance. This system allowed the ventricle to eject physiologically. The ejecting heart was allowed to stabilize for 15 min before any measurements were taken. Left ventricular pressure and volume signals were sampled at 200 Hz and stored on removable cartridge disks (Bernoulli, Iomega) using a 16-bit microcomputer (IBM XT). Custom software for data acquisition and analysis were written in our laboratory. Protocol. Left ventricular volume was simultaneously determined by both balloon and volume catheter under ejecting conditions. The volume catheter offset was estimated by two independent techniques. As volumes varied over a wide physiological range, a continuous plot of catheter (ordinate) versus simultaneous balloon volume (abscissa) was obtained. The y-intercept (apparent catheter volume at zero balloon volume) was V,. The second method for V, estimation required replacement of 10 ml of saline within the volume pump-balloon system with 10 ml of hypertonic saline. The hearts continued to beat at steady-state conditions (end-diastolic volume and stroke volume constant), yet the catheter volume signal increased because of the rising conductance of the solution within the pericardial balloon. These data were used to derive V, and V,(t) estimates (described below).

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The cyclic influence of ventilation on cardiac pressures and volumes was minimized by recording data with ventilation briefly held at end expiration. Seventeen animals were studied closed chest, and five animals underwent median sternotomy. A micromanometer-tipped catheter (Millar SPC-350, 5-F) was inserted into the mid-left ventricular chamber. Animals were instrumented with intravascular balloon occluders in the inferior vena cava and pulmonary artery (cuff occluders for the open-chest animals). A conductance catheter was inserted-into the left common carotid artery and placed along the ventricular longitudinal axis. Catheter position was adjusted under fluoroscopy so it lay straight throughout the cardiac cycle and free of the papillary muscles. Each individual pressure-segmental volume loop was displayed, and the correct number of sensing catheter segments was determined. Viewing each segment from ventricular apex toward the base allowed use of all segments up to but not including the one whose volume remained constant or increased during systole. That segment was considered to be in the aorta. Conductance catheter methods. The conductance catheter is an 8-F, eight electrode catheter (Webster Labs, CA) that is inserted into the left ventricle along its long axis. This catheter is connected to a stimulator-signal processor unit (model Sigma 5, Leycom, The Netherlands) that applies current (0.07 mA root mean square at 20 kHz) at electrodes 1 and 8 (positioned at the apex and aortic root, respectively), and measures the potentials at multiple intervening electrodes. Because the current is constant, these potentials can be converted to conductances of blood-tissue segments between adjacent pairs of electrodes. The conductances in turn are related to the segmental volumes by the relation Vi(t)

= (l/c~)(LF/ab)*

[Gi(t)

To assess V,(t) with an intact circulation, 22 adult male mongrel dogs were acutely anesthetized (pentobarbital sodium 30 mg/kg iv) and ventilated by a volume ventilator. Hexamethonium bromide (20 mg/kg iv) was administered to inhibit reflexes and minimize ectopv.

(1)

where Vi(t) is true left ventricular chamber volume of the ith segment (ml); Li is interelectrode spacing of the ith segment (cm); ob is electrical conductivity of blood cm)-I; Gi( t) is total measured conductance of the ith cm)-‘; segment (Q-l); Gp,i( t) is effective conductance of structures contributing toward G;(t) but outside the blood pool of the ith segment; and cy CYis a slope correction factor. Li is constant for the catheters used in the present study, so total chamber volume V,,(t) can be written as (St

l

h(t) v,,(t)

= =

(l/dL2/~b) (

*G,,,(t)

l/&)(L2/ab)

l

G,,,(t)

-

v,(t) vc(

t)

(2) (2)

where V,(t) V,(t)

== [L”/(a@‘.)] [L”/(aba)]

’’ ii

Gp,i(t) == (1/CY)*Vp(t) Gp,i(t) (1/CY)*Vp(t)

(3) (3)

i=l

and Gtot( ii Gtot(t) t ) = =

In Situ Preparation

- Gp,i(t)]

G;(t) G;(t)

(4) (4)

i=l

where n is the total number of volume segments (n (n == 5 for an &electrode catheter). The slope correction term a could potentially have its own volume dependence [i.e., a(V) rather than a], rendering a true volume vs. catheter signal relation nonlinear. Previous examinations of these

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relations have found them to be quite linear (3), with cy varying between 0.75 and 1.07 under different conditions (3). Based on this data, we assume CYto be constant throughout the cardiac cycle. VP estimation. Estimation of a single (constant) parallel conductance (or volume offset) was performed using a technique previously reported by Baan et al. (3). The principle assumption inherent in this method is that infusion of a small bolus of hypertonic saline increases the blood conductivity but not the volume of blood in the left ventricular cavity, while the conductivity of surrounding (parallel) structures remains constant (Fig. IA). Rewriting Eq. 2 we get Got(t)

= (CY/L2hWt)

+ Gp

(5)

If only cb but not V,,(t), CY,or Gp is varied duri.ng the hypertonic saline infusion, the Gtot can be used to calculate Gp’ From the conductance signal, the two most easily

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FIG. 1. Technique of Baan et al. (3) to determine a single value for V,. A: raw data tracings during hypertonic saline infusion. Catheter volume and simultaneous left ventricular pressure are shown. Maximum and minimum volumes are determined for each cardiac cycle within cursors. B: orthogonal regression using paired minimal vs. maximal volumes generates a linear relation between observed volumes as a function of changing blood conductivity. Extrapolation of relation to line of identity (which corresponds to 0 = 0) gives V, = 28.2 ml.

H1935

identified points from each successive cycle (as 0b increases) are the points of maximum and minimum conductance (end diastolic and end systolic, respectively). Because actual stroke volume is constant, changes in these conductance values are due to altered blood conductivity, not volume. One value is regressed against the other, and the relation is extrapolated to the line of identity (G,,, = G,i,, Fig. IB). At this point the catheter signal stroke volume would appear to be zero (real stroke volume would be unchanged), as if gb had been reduced to zero. By Eq. 5, at 0b = 0, Gtot = G,, thus providing a measure of the parallel conductance. Gmax is paired with subsequent Gminfor this regression, since these two values more likely reflect data obtained at the same cb (i.e., after mitral valve ciosure). The steady-state stroke volume assumption during hypertonic saline inflow is confirmed by near constancy of peak developed left ventricular pressure despite the volume signal change (Fig. 1B). Saline washout is often accompanied by a slight fall in left ventricular pressure, presumably because of a myocardial depressant effect of the concentrated saline. Therefore, only the washin phase data are used for analysis. Since neither Gmaxnor Gmin is a true independent or dependent variable, equal weighting is given both by using orthogonal (as opposed to linear) regression, which minimizes the perpendicular distance between each point and the regression line (4, 12, 15). VP(t) estimation. The method described above for V, estimation yields a single V, value based on conductance measurements taken only at end diastole and end systole. Thus the procedure uses a very small fraction of the available volume data (only 2 points with no smoothing). This could make the technique quite sensitive to signal noise in the volume channel. Another potential shortcoming of this method is that time dependence cannot be determined. That is, the value obtained is a mean value of unknown weighting for the volume offset at the onset of systole and end of systole. If we denote the V, at the start of systole V,, and the V, at the end of systole Vpe, then it can be shown that if V,, and V,, are not equal, the single V, estimate will depend both on V,, and V,, as well as end-diastolic volume and stroke volume. Furthermore, V, will not be a simple average of V,, and V,, and will not even be between V,, and V,, (See APPENDIX

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A).

To overcome these limitations, we developed a new method that is more robust and estimates V, at 20 equally spaced time intervals throughout systole (Fig. 2). Figure 2A shows four consecutive cardiac cycles during hypertonic saline calibration. The first derivative of left ventricular pressure (dP/dt) provided timing end points and systolic volumes be(dP/dtmax and @/dtmin) (1, 8), tween these times were used for analysis. Our technique required assessingthe relative conductivity of each cardiac cycle, which was calculated using proportional increases in ventricular conductance during the hypertonic saline infusion. If the true stroke volume was constant, then the apparent catheter stroke volume (or conductance) would be proportional to blood conductivity, cb. To calculate the proportional increase, each cycle was divided into an identical number of time intervals. The

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ures were summed to yield an estimate of the blood conductivity for each cardiac cycle (Fig. 2B) 42 cb

B

:! A Vi

=

c i=l

[(Gi

Gp,;)

-

(Gn+,-i

=

bL2/d*Gl,(t)

+

=

(~~b/d’Vlv(t)

+

(6)

v,(t)

(7)

v,(t)

= K&,(t)

number of intervals chosen was the largest even integer less than or equal to half the number of raw data samples for the shortest ejection. Conductances were calculated from the raw data using linear interpolation when required. Multiple paired differences of conductance meas-

Gp,n+l---;)I

Because G1, = VI,* ab/L2, then v,,,,(t)

FIG. 2. Technique for determining 20 values of V,(t). A: catheter volumes and time derivative of left ventricular pressure (dP/dt) for same data shown in Fig. 1A. Points of maximal and minimal dP/dt were identified in each cycle and were used as timing markers for onset and end of systole. B: computation of or (relative conductivity) for each cardiac cycle. For each beat, differences between volumes at either end of respective timing window were averaged. Thus difference between first and last volume, second and next to last, etc., were added and result was divided by total number of volume differences. Result was proportional to CT~and less subject to noise than if a simple “maximum minus minimum” stroke volume determination had been used. C: each systolic period was divided into 20 equal time intervals and volume interpolated for each. These values were plotted against respective computed or for each cycle generating 20 isochrones. Extrapolation of each isochrone (solid lines) to point of CT~= 0 yielded 20 independent V,(t) estimates at successive time intervals during systole.

-

where n is the number of time intervals during systole, Gi is the total conductance signal at time point i, and G, i the parallel conductance at the same time point (i.e:, each measured conductance was the sum of blood pool and parallel structures). Initially, values of G, i were unknown, and were therefore set equal to zero. Subsequent iterations yielded estimates for G,; that could be inserted into Eq. 6 as described further below. Each ejection period delimited by dP/dt,,, and dP/dLin was then divided into 20 equal time intervals. Ventricular conductance at each point was obtained by linear interpolation between the appropriate raw data samples. This provided a constant number of V,(t) values regardless of the exact heart rate or sampling rate, as well as allowed correct registration of the isochrones during ejection. The data were then plotted as conductance vs. relative conductivity (C&c = or, where cc is the starting value that is entered as a constant into the calculations) for each cardiac cycle (Fig. 2G). The rewritten Eq. 2 gives v,,,,(t)

C

-

+ V,(t)

(‘)

where K is a constant. Thus each respective V&h(t) time point can be regressed against cr yielding 20 isochrones, each of which intersects the line of c’r = 0 at V,(t). This provides 20 estimates of V, throughout systole. Unlike the first method of determining V,, which required that V,(t) remain constant, this technique requires only that V,(t) remain constant at any given respective time in the cardiac cycle, from cycle to cycle. As noted in Eq. 6, initial estimation of cb required assumptions about the time variation of the parallel conductance. From this equation we see that each value of cb is affected by the sum of n/2 parallel conductance differences, i.e., C( Gp,n+l-i - G, i). If we denote this sum as 6, then Eq. 8 can be rewritten as v,,,,(t)

= K[(ab

+ #(CT, + #h(t)

+ v,(t)

(9)

We first assume E = 0 (Eq. 9 then equals Eq. 8) and calculate 20 values of V,(t) as described above. These are then used to recalculate c leading to a new set of isochrones (by Eq. 9) and thus V,(t) estimates. This process is continued until convergence is achieved. The difference between the initial and final iteration rarely exceeded 0.2 ml. An outline of the V,(t) algorithm with pertinent computer code (FORTRAN) is provided in APPENDIX B. V,(t) estimation technique validation. Since our estimation of V,(t) initially assumed it to be time invariant and relied on an iterative technique to adjust for temporal variation, it was possible that the approach could underestimate V,(t) time variation, or suggest change when

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O/0 0 4A

2--

0 3 Z

-4 I

-2 ~

k

I

0.0

RELATIVE

0.5 CONDUCTIVI-IY

1

1 .o

3. Estimates of V,(t) temporal variation from simulated data. A: result with 0% V,(t) variation; B: result with 10% (+Z ml) variation. When V,(t) is time invariant, regression lines converge to a single point, whereas presence of temporal variation produces variability in y-axis intercept. FIG.

none was actually present. To assess these issues, we simulated pressure-volume data during a hypertonic saline infusion. A volume signal with sequentially increasing amplitude was combined with either a constant or time-varying V,, and the data were then analyzed to yield estimates of V, and V,(t). As shown in Fig. 3A, when there was no V, time variation (and no noise), all 20 regressions converged at the identical point equal to V,. However, when V, was allowed to vary (again with no noise), the regressions no longer converged to a single point (Fig. 3B), but displayed variations whose magnitude was similar to that of the simulated data. Thus despite the iterative approach and assumptions, the new technique was capable of demonstrating V, time variation if it was present, and no change if V, was indeed constant.

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V, and V,(t) were subsequently determined by the hypertonic saline technique. Figure 5A displays an example of recordings obtained after replacing 10 ml of the solution filling the balloon-pump system with an equal volume of concentrated saline. This hypertonic saline mixed with the fluid in the balloon, producing a gradual increase in the catheter volume signal while true balloon pressures and volumes (bottom two traces) remained unchanged. Twenty-eight consecutive beats from this run were used to estimate V,. Figure 5B shows a plot of minimum vs. maximum catheter volume signals from each beat. Regressing the results back to the line of identity yie lded an intersec tion poi nt of 64.4 ml as a V, esti mate. This was very close to the result of the volume vs. volume plot (63.8 ml), consistent with previously published data regarding this estimation technique in isolated hearts (6). V,(t) determination is shown in Fig. 5C. The 20 isoch.rones had nearly a common inte rsection point at CT~ = 0 7 indicating very little variation during ejectio n. The mean of the 20 V,(t) values was 66.3 ml, which also agreed with the estimates obtained by the two other methods (Figs. 4 and 5B). The minimal V,(t) variation shown in this example was typical of the group data (Fig. 6). Data are displayed as the difference from the overall group mean (derived from all 20 time points) -t SD (calculated independently for each time interval). After a very small early reduction in V, (0.5 ml), V,(t) was essentially constant. V,(t) variability was also determined directly by regressing balloon vs. catheter volume signals. Multiple beats at varying preload volumes were obtained, and a mean regression (volume vs. volume) slope and intercept determined (as shown in Fig. 4). Each cardiac cycle was then divided into 40 isochrones (20 in systole and 20 in diastole), and individual regressions at each time point were compared to the average regression to determine the variation from the mean. These results (Fig. 6, dashed line) were similar to those from the hypertonic saline infusion data, revealing little change in V,(t). Diastolic variation (not shown) was somewhat larger, especially in early diastole (maximal mean change of -0.9 ml), possibly because of a rapid isovolumic relaxation ventricular shape change.

RESULTS

Isolated Heart Studies Two independent assessments of V,(t) were obtained in each of the three isolated hearts. Figure 4 shows an example of pericardial balloon volume vs. uncalibrated catheter volume over a wide ejecting volume range. The relation between the two volumes was linear and well described by the equation: Vcath = 1.1 Jballonn + 63.8 (n = 1,315, r2 = 0.98, P < 0.0001). The y-intercept (Vballoon at V&h = 0) provided a measure of the parallel conductance in volume units (V,). The linearity of the volume vs. volume relation indicated little variation in V, or the slope coefficient cy during systole despite changes in ventricular volume. 1

l

1

1

FIG. 4. Direct comparison of Vcath (t) heart. Linear regression and extrapolation 63.8 ml. Relationshin was hirrhlv linear.

with V,,(t) from an isolated to Vcath axis yielded V, =

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s

A

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1500

. .. . .

..

. .. . .

Y .. 3

200 5

. .. . ./

>00

160

-h

z

.

fWE

. .. .. VP m 9

G

.. .. .

**,,/

****

loo--

. +::

. -

~..~'//....

-**-**-

**

120 3

80 0

8

9

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5n

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5.

*

1

.I

50

100

150

457

END DIASTOLIC

TIME

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i

200

(ml)

(set) 65

0

25 RELATIVE

CONDUCTIVITY

FIG. 5. Determination of V,(t) from isolated hearts. A: data tracings during hypertonic saline mixing. At beginning of period, hypertonic saline replaced original saline and slowly mixed during next 28 cardiac cycles with intrapericardial balloon fluid. As Vcath( t) rose, left ventricular pressure and Vballoon(t) remained unchanged. B: regression to a single value of V,. When the technique of Baan et al. (3) is used, regression of 28 pairs of volume points from A yielded V, = 64.4 ml. C: regressions of 20 isochrones, with extrapolation to obtain V,(t). Using new technique, the same 28 cardiac cycles were used to determine V,(t) for 20 time points. Averaging gave mean V,(t) = 66.4 ml.

END SYSTOLE

-2!

I 1

0

5 NORMALIZED

I I

10 TIME DURING

I I

15

I

20

EJECTION

6. Deviation of V,(t) from mean V,(t) [AV,(t)] for all isolated heart experiments. Variation of V,(t) from its mean was very small, with a slight increase over mean V,(t) during early systole. There were no statistically significant differences between any of the time values. Error bars denote SD. FIG.

Unlike the many beats obtainable in the isolated heart preparation, there were typically 5-7 cycles available for in situ V, and V,(t) estimation. Figure 7A shows an example of the isochrones and V,(t) estimates in situ, and Fig. 7B provides group data for A&(t) variability (96 runs from 22 hearts) plotted in an identical fashion to Fig. 6. In situ V,(t) displayed slightly greater variability than in isolated hearts, with a similar initial reduction in early systole. Temporal changes in VP(t) were quite small, on the order of 4% of end-diastolic volume (mean maximal variation = 3.0 ml). The difference between V,(t) at the first and last time interval was 0.61 t 1.0 ml. None of the small variations in mean V,(t) were statistically significant, thus V,(t) could be reasonably represented by a single mean constant, v,(t). Cornparison of VP and VP(t)

In Situ Hearts

The isolated heart data demonstrated little time dependence of V, in a blood-perfused ejecting preparation despite changes in left ventricular volume and shape during systole. However, surrounding structures in situ such as the right ventricle, atria, and lungs could all contribute to greater V, variability. Therefore, we further examined V,(t) in closed- and open-chest dogs.

Theoretical analysis (APPENDIX A) predicted that in the presence of underlying V,(t) variation, the single VP estimation by the Baan approach would not equal the average value. Furthermore, we showed that the greater the intrinsic V,(t) variation, the more that VP vs. v,(t> estimates would differ. Using model simulation data (see METHODS), we combined a volume signal with low amplitude noise and V,(t) variation during systole. Mean

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(Fig. 8) revealed excellent agreement, with a strong linear correlation (y = 1.03.X - 0.17, r2 = 0.98, P C 0.0001) between them that did not significantly differ from the line of identity.

807

DISCUSSION

0

3

6

9

RELATIVE CONDUCTIVITY 4

T END

I

DIASTOLE

=;‘ U

>”

-2

a 0

5 NORMALIZED

10 TIME DURING

15 EJECTION

20

FIG. 7. Determination of V,(t) in in situ hearts. A: determination of V,(t) for an in situ heart showing 20 V,(t) isochrones. Individual regressions converge to a similar V, estimate. B: cumulative results of deviation of V,(t) from its mean value for 96 determinations from in situ hearts. There was a small decrease of V, early in systole (corresponding to isovolumic contraction) followed by little further change. Variations in V,(t) were not statistically significant. Mean difference between first and last value for V,(t) was 0.61 ml. Error bars denote SD.

V,(t) was kept constant (40 ml) while V,(t) was linearly varied by 0, 4, 8, and 12 ml (0, 10, 20, and 30% of the mean, respectively) during ejection. From analysis using the two techniques, the difference between the two estimates became increasingly large (Table 1). Thus the more the intrinsic V,(t) variability, the less likely V, and V,(t) estimates would agree. Yet a comparison of both estimates obtained from the in situ experimental data 1. Difference between V,(t) and VP estimates as V,(t) time variation is increased TABLE

V, Variation, 5%

Difference Between Estimates, ml

Since most biological tissues are conductive, the volume-conductance catheter signal combines components from chamber blood and surrounding tissue. Previous methods to determine the parallel conductance have assumed that it could be treated as a constant offset. In this study we have tested this assumption using a new V, estimation technique that makes use of most of the systolic data obtained from consecutive beats following hypertonic saline infusion. The results in both isolated and in situ hearts showed minimal variability of V,(t) throughout systole. There are several potential sources of V, variability in situ, including right heart ejection, atria1 filling, and myocardial blood volume changes. The isolated heart data effectively eliminated all but muscle wall and geometry factors and demonstrated virtually no variation in V,(t). The minimal influence of altering muscle wall blood content on the catheter signal could be further shown by comparing Vcathvs. Vballoonplots (same isolated heart preparation) at global coronary perfusion pressures of 96 vs. 47 mmHg. As shown in Fig. 9, this marked fall in muscle perfusion led to only a LO-ml parallel shift in the two relations, indicating that the catheter volume signal is only minimally sensitive to changes in muscle wall blood content. This result is consistent with previous in vitro studies (2). The finding of minimal V,(t) variation in situ (as well as in isolated hearts) suggests that despite simultaneous right ventricular ejection, left and right atria1 filling, and varying chamber geometry during ejection, V,(t) remains reasonably constant. This does not imply that V, will be constant under all conditions. Interventions such as extreme right ventricular loading or unloading, pericardial effusion, or orientation changes will likely alter V,. In the in situ hearts, elevations of right ventricular pressure from 12 to 50 mmHg increased V,(t) by 3.5 ml, whereas inferior vena caval occlusion lowered it by 1.1 ml. The estimated time course, but not the mean value of V,(t),

E

>a 5

100

50 t

0 10 20 30

0.0 4.9 11.3 18.5 Data are from model simulation; estimates of V, made according to technique of Baan et al. (3). Simulated pressure-volume data have an added parallel conductance that is either constant (0% variation) or varies by a linear ramp during systole. Note that as V,(t> variation increases, the 2 V, estimates differ more.

FIG. 8. Comparison of mean value of V,(t) [VP(t)] for each calibration run to single V, estimate for same run determined by technique of Baan et al. (3). There was a strong linear correlation between 2 estimates, with a regression slope of 1.03 and an intercept of -0.17 ml. This was statistically indistinguishable from line of identity.

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W 5

6 45-> 5 : : *..:. *** *..:.* .* .*:

I, 20 BALLOON

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of the V, estimates. The average coefficient of variation for repeated estimates is on the order of 4%. Finally, the V, regressions are theoretically (not only empirically) linear, as demonstrated when data is collected over a sufficiently broad range (as in Fig. 2C). Thus despite statistical uncertainty, empirical comparisons (6) have shown close agreement.

-jg 55--

t 35-F 4 25 ! 10

OF

VOLUME

1 30 (ml)

FIG. 9. Effects of changing coronary perfusion pressure on volume catheter signal. In an isolated heart, a direct comparison of V,,,,(t) vs. V balloon(t) was made at two different steady-state coronary perfusion pressures (CPP). Decrease of CPP (from 97 to 46 mmHg) shifted volume vs. volume relationship downward in parallel, so that Vcath was 1 ml smaller at each balloon volume.

seemed to be independent of these different loading conditions. Boltwood et al. (5) recently reported a correlation between cuV, (i.e., V,) and end-systolic catheter volume, suggesting that V, may not be treatable as a constant. In their study, left ven.tricular volume was altered by inferior vena caval, pulmonary, and aortic constrictions, with multiple V, estimates obtained under each condition. However, such interventions could themselves link changes in end-systolic volume and V, by altering filling of all other chambers, (i.e., inferior vena caval occlusion lowrers filling, whereas aortic occlusi.on increases it). In the present study, V,( t ) did not vary with volume during ejection, despite stroke volumes of 25 ml. The linearity of the catheter vs. balloon volume plots from the isolated heart data does not suggest significant V, dependence on absolute left ventricular volumes. Whether broader alterations in left ventricular volume without changes in other chamber volumes would still vary V, remains unknown. The conductance catheter has been used to determine end-systolic pressure-volume relationships in both animals and humans (3, 10, 11, 13, 14). In a typical dog study (end-systolic elastance of 8 mmHg/ml), the endsystolic volume may vary by only 5 ml in combination with a 40-mmHg change in end-systolic pressure. This volume alteration is considerably less than the stroke volume range obtained in the present studies for both isolated and intact hearts. This suggests that V, could reasonably be considered constant over the more limited range of end-systolic volumes obtained during an endsystolic pressure-volume relation determination. The statistical confidence of V, estimations deserves some comment. Clearly, with the limited range of obtainable data and the need for extrapolation to yield V, or V,(t ), statistical uncertainty is present. For example, the average 95% confidence limits about a V, estimate with the technique of Baan et al. (3) are +X2, -9.3 (the lower limit is more distant because of curvature of the hyper-bolic relations). A similar confidence limit would apply to each of the 20 estimates of V,(t); however, by averaging the results from all 20, we obtain an estimate that is less sensitive to signal noise, and thus more robust. Furthermore, we routinely record three or four calibration runs (hypertonic saline infusions) and take the mean

Methodological Limitations Although the new calibration approach presented in this study was able to reveal time variation of V,(t), it could not determine the precise time course of this change. This was a result of the fact that the iterative approach for estimating the relative conductances (a,) did not have a unique solution and depended on the initial values of GPi, and hence E (see Eq. 9). From the simulation data, it’ could be shown that a linear ramp change in GP,i from end diastole to end systole would result in a linear V,(t) variation if such a pattern was assumed initially. Starting with no variation (i.e., setting GP,i values first to zero) as we did still yielded V,(t) variation with an amplitude similar to the model input; however, the time course no longer mirrored the original ramp function. The inability of our technique to determine the precise time course of V,(t) does not prevent it from being useful for examining V,(t) variation during systole. The only way our technique would substantially underestimate V,(t) change would be if the parallel conductance varied with exactly the same time course as left ventricular volume. There is no a priori reason to expect that V,(t) would vary precisely with left ventricular chamber volume. Synchronous changes in right ventricular volume, changes in left ventricular wall thickness, and filling of the atrium may all counterbalance one another, as suggested by data showing near constancy of total heart volume (9). More strikingly, the model simulations demonstrated that as intrinsic variations in V,(t) increased, the larger the differences between V, and V,(t) estimates became. Yet, as shown in Fig. 8, the plot of one estimate vs. the other fell nearly along the line of identity, suggesting little significant underlying variation. Summary We described a new technique for estimating the parallel conductance of the volume (conductance) catheter that enabled estimation of the magnitude of its time variation during ejection. Isolated and in situ heart data revealed no significant variation. Furthermore, results from modeled data revealed the new technique to be less sensitive to signal noise and less dependent on any possible time variation in true parallel conductance. On the basis of these results, it appears that V,(t) can be approximated by a single value for the purposes of most data analysis. APPENDIX

A

To assess the effects of alterations of the parallel conductance from the onset of systole to end systole, call V, at the start of systole V,, and the V, at end systole V,,. Consider what occurs during three ejections during a saline-infusion period.

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PARALLEL

CONDUCTANCE

Let the normal electrical conductivity of blood be CT,and for each of the next two cardiac cycles let the condtdvity of blood increase by &J. Assume that the true stroke volume remains constant at SV. Also assume that this determination will proceed without noise or bias. The pairs of values used will be Minimum Volume

Maximum Volume (ved

+

v,s)

W

[(1+&ved+vps]

ed -

SV

Electrical Conductivity

[(1+26)*(ved-sv)+vpe]

APPENDIX

sv

-

+

vp,

=

thus the y-intercept

(b) is

b = Vpe The point

H1941

CATHETERS

-

Vps

+

(Vps

l

sv/ved)

(fw

at which x = y is where

x = VP, - v,, + (v~~~d~~)-x

+ (vps;dsv)

WV

of VP is

(1 +T3) (1+26;Po

VP

with V,d being end-diastolic volume. The slope of this perfect line is (V,d - SV)/(V,d), so at the initial point the following must be true for the regressed line Ved

VOLUME

so the estimate

+ Vpe>

[(l+ab(Ved--SV)+Vpe]

[(1+26)*ved+vps]

OF

l (veal

+

v,,)

-t-

b

(A0

= vps + wpe - vps)’ ved/sv

(fw

This shows that if VP, and Vpe are not equal, the resulting single estimate of VP will be a function of not only V,, and Vpe, but also the ratio of Ved and SV. Additionally, at the near-normal ejection fraction (SV/Ved) of 0.50, the value for VP is not (VP, + VpJ/2, as expected, but (2V,, - V,,).

B

provides ; a flow description with some FORTRAN code for V,(t) estimation. Pressure Pressure signal array Volume Volume signal array Local Arrays: vsm Smoothed volume signal loc(40) Array of position of maxima and minima of dP/dt array. loc( i),

The following Input Arrays:

i= odd: maxima i= even: minima

in(20) vol(i, j)

Set of 20 parallel conductance values (V,(t)) Volume array used for V,(t) estimation. i ranges from 1 to the number of beats, and j the isochrone index (1 + 20). 1) Input pressure --j Output dP/dt. 2) Input dP/dt + Output location of maxima and minima (i.e., array index values) = lot(i) and number of beats = numbeat 3) Find beat with minimum number of data points between dP/dt,,, and dP/dtmi,. Set number of points for this beat equal to nummin. 4) Obtain number of points to use in computation of relative conductivity (a,) = numless = (2*INT((nummin)/4) - 1). 5) Set initial V,(t) variation = in(i) = 0, for i = 1,20. 6) Smooth volume array and store in array: usm. 7) Compute relative conductivity (a,) for each beat and compute volume array (uol) for each isochrone (20 equally spaced time Store fir values in points during ejection). On subsequent passes, make correction for V,(t) variation on gr calculation. array: conduct(i). DO 500 i = 1, numbeat sum = 0.0 time1 = loc(2*i - I) dif = (loc(2*i)) - time1 DO 300 j = 0, numless timereal = FLOAT(time1) + (FLOAT(dif*j))/FLOAT( numless) timeint = INT(timerea1) frac = FLOAT(timeint + 1) - timereal temvol = frac*dat(timeint) + (1.0 - frac)*dat(timeint + 1) timereal = 1.0 + lS.O*FLOAT( j)/FLOAT( numless) timeint = INT(timerea1) frac = FLOAT(timeint + I) - timereal + 1)) temvol = temvol - (frac*in(timeint) + (1.0 - frac)*in(timeint sum = sum + temvolSIGN(l.0, (numless - (2*j))) CONTINUE 300 conduct(i) = sum C Compute volume array vol(i, j) for the 20 isochrones for current beat i DO400j=1,20 timereal = FLOAT(time1) + (FLOAT( (j - I)*dif))/l9.0 timeint = INT(timerea1) frac = FLOAT(timeint + 1) - timereal vol(i, j) = frac*dat(timeint) + (1.0 - frac)*dat(timeint + 1) CONTINUE 400 500 CONTINUE C Normalize conductivities to conductivity of first ejection = 10.0. 8) Use linear regression to determine V,(t) from each isochrone. X-coordinate array = conduct(i), i = 1 to numbeat. Y-coordinate array = vol(i, j), j = 1 to 20. Output array of y-axis intercepts in array in(j) = V,(t). Mean value of V,(t) = C V,(t)/20; (t = 1,20). 9) Repeat iteration using new in(j) array, go back to 7. Finish iteration when minimal difference between successive in(j) estimates. Downloaded from www.physiology.org/journal/ajpheart by ${individualUser.givenNames} ${individualUser.surname} (137.154.019.149) on January 12, 2019.

H1942

PARALLEL

CONDUCTANCE

We thank Jeff Parks of Physio Control for his suggestion of using perpendicular regression in the determination of V,. We also thank Dr. Kiichi Sagawa for thoughtful comments and suggestions concerning this study. This work was supported by National Heart, Lung, and Blood Institute Grants HL-19039 and HL-33243. D. A. Kass is the recipient of Physician Scientist Award HL-01820. Address for correspondence: E. Lankford, 12 Granada, Briarcrest Gardens, Hershey, PA 17033. Address for reprint requests: A. A. Shoukas, Dept. of Biomedical Engineering, Johns Hopkins School of Medicine, 720 Rutland Ave., Baltimore, MD 21205. Received

23 September

1988; accepted

in final

form

7 February

1990.

REFERENCES 1. ABEL, F. L. Maximal negative dP/dt as an indicator of end of systole. Am. J. Physiol. 240 (Heart Circ. Physiol. 9): H676-H679, 1981. 2. BAAN, J., T. T. A. JONG, P. L. M. KERKHOF, R. J. MOENE, A. D. VAN DIJK, E. T. VAN DER VELDE, AND J. KOOPS. Continuous stroke volume and cardiac output from intra-ventricular dimensions obtained with impedance catheter. Cardiouasc. Res. 15: 328334, 1981. 3. BAAN, J., E. T. VAN DER VELDE, H. G. DEBRUIN, G. J. SMEENK, J. KOOPS, A. D. VAN DIJK, D. TEMMERMAN, J. SENDEN, AND B. BUIS. Continuous measurement of left ventricular volume in animals and humans by conductance catheter. Circulation 70: 812823,1984. 4. BOGGS, P. T., AND C. H. SPIEGELMAN. A computational examination of orthogonal distance regression. J. Econometrics 38: 169201,1988. 5. BOLTWOOD, C. M., R. F. APPLEYARD, AND S. A. GLANTZ. Left ventricular volume measurement by conductance catheter in intact dogs. Circulation 80: 1360-1377, 1989. 6. BURKHOFF, D., E. T. VAN DER VELDE, D. KASS, J. BAAN, W. L. MAUGHAN, AND K. SAGAWA. Accuracy of volume measurement by conductance catheter in isolated ejecting canine hearts. CircuZation 72: 440-447,1985.

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7 CLAVIN, 0. E., J. C. SPINELLI, H. ALONSO, P. SOLARZ, M. E. VALENTINUZZI, AND R. H. PICHEL. Left intraventricular pressureimpedance diagrams (DPZ) to assess cardiac function. Part 1: morphology and potential sources of artifacts. Med. Prog. TechnoZ. 11: 17-24, 1986. 8. GLEASON, W. L., AND E. BRAUNWALD. Studies on the first derivative of the ventricular pressure pulse in man. J. Clin. Inuest. 41: 80-91, 1962. 9. HOFFMAN, E. A., AND E. L. RITMAN. Invariant total heart volume in the intact thorax. Am. J. Physiol. 249 (Heart Circ. Physiol. 18): H883-H890, 1985. 10. KASS, D. A., M. MIDEI, W. GRAVES, J. A. BRINKER, AND W. L. MAUGHAN. Use of a conductance (volume) catheter and transient inferior vena caval occlusion for rapid determination of pressurevolume relationships in man. Catheterization Cardiouasc. Diagn. 15: 192-202, 1988. 11 KASS, D. A., T. YAMAZAKI, D. BURKHOFF, W. L. MAUGHAN, AND K. SAGAWA. Determination of left ventricular end-systolic pres? sure-volume relationships by the conductance (volume) catheter technique. Circulation 73: 586-595, 1986. 12. MALINVAUD, E. In: Statistical Methods of Econometrics. Amsterdam: North-Holland, 1966, 3-11. 13. MCKAY, R. G., J. R. SPEARS, J. M. AROESTY, D. S. BAIM, H. D. ROYAL, G. V. HELLER, W. LINCOLN, R. W. SALO, E. BRAUNWALD, AND W. GROSSMAN. Instantaneous measurement of left and right ventricular stroke volume and pressure-volume relationships with an impedance catheter. CircuZation 69: 703-710, 1984. 14. NOZAWA, T., Y. YASUMURA, S. FUTAKI, N. TANAKA, M. UENISHI, AND H. SUGA. Efficiency of energy transfer from pressure-volume area to external mechanical work increases with contractile state and decreases with afterload in the left ventricle of the anesthetized closed-chest dog. Circulation 77: 1116-l 124, 1988. 15. RIGGS, D. S., J. A. GUARNIERI, AND S. ADDELMAN. Fitting straight lines when both variables are subject to error. Life Sci. 22: 13051360,1978. 16. SPINELLI, J. C., 0. E. CLAVIN, E. I. CABRERA, M. C. CHATRUC, R. H. PICHEL, AND M. E. VALENTINUZZI. Left intraventricular pressure-impedance diagrams (DPZ) to assess cardiac function. Part 2: determination of end-systolic loci. Med. Prog. Technol. 11: 25-32, 1986.

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Does volume catheter parallel conductance vary during a cardiac cycle?

Absolute left ventricular volume measurement by the conductance (volume) catheter requires subtraction of the conductance contribution from structures...
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