Basic Research in
Cardiology
Basic Res Cardiol 89:411-426 (1994)
Dependence of anisotropic myocardial electrical resistivity on cardiac phase and excitation frequency P. Steendijk, E. T. van der Velde, and J. Baan Leiden University Hospital, Department of Cardiology, Cardiac Physiology Laboratory, Leiden, The Netherlands
Summary.Knowledge of myocardial electrical resistivity is of interest because passive electrical properties govern the electrotonic spread of current through the myocardium and influence the shape and velocity of the excitation wave. In addition, measurements of myocardial resistivity may provide information about tissue structure and components. The aim of the present study was to determine the excitation frequency dependence and the changes during the cardiac cycle of anisotropic myocardial electrical resistivity. Longitudinal and transverse myocardial resistivity were measured using an epicardial sensor in four open-chest dogs with excitation frequencies in the range of 5-60 kHz. Mean longitudinal resistivity gradually decreased from 313-t-49 ~). cm at 5 kHz to 2124-32 f~-cm at 60 kHz, transverse resistivity decreased from 4874-49 to 378~53 f~. cm. To analyze the phasic changes, we compared mean resistivity (averaged over the full cardiac cycle) with resistivity during four cardiac phases: pre-ejection, ejection, early diastole and late diastole. Longitudinal resistivity was significantly higher during the ejection phase (+9.6• ~ . cm) and lower during late diastole (-6.9• f~. cm). Transverse resistivity was significantly higher during late diastole (+4.0• f~- m). The values during the other cardiac phases were not significantly different from mean resistivity. The phasic changes in longitudinal and transverse resistivity during the cardiac cycle were independent of the excitation frequency. We speculate that these changes are related to geometrical changes, especially to changes in myocardial blood volume. Key words: Myocardial electrical anisotropy-cardiac phase-excitation frequency-epicardial sensor-myocardial blood volume
Introduction
Knowledge of the electrical resistivity of cardiac tissue is essential to the study of the electrical properties of the heart. Passive electrical properties govern the electrotonic spread of current through the m y o c a r d i u m and have been shown to directly influence shape and velocity of the activation wave (5, 22, 28). The quantitative interpretation of electrocardiographic findings in general requires knowledge of the resistivities of all m e d i a interposed between the cardiac sources and the registration sites but this applies especially to myocardial resistivity (17, 21, 23). F r o m another viewpoint, electrical impedance measurements have been used extensively to study biological systems (1, 8, 25) and measurements of myocardial resistivity m a y provide information about tissue structure and components. To investigate whether geometric changes of the intra- and extravascular compartments and the muscle cells during contraction result in phasic changes in myocardial resistivity, we measured anisotropic myocardial resistivities on the free wall of the left ventricle (LV) in four open-chest dogs. For this purpose, we developed a small epicardial sensor incorporated in a flexible suction cup, as described previously (33). Due to the 854
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Basic Research in Cardiology, Vol. 89, No. 5 (1994)
electrical properties of the cell membranes, myocardial resistivity is expected to depend on excitation frequency (25, 27, 30, 32). At higher excitation frequencies the membrane impedance is reduced, allowing current to flow more uniformly through the tissue. This will result in a decrease in resistivity. But, since the current distribution over the myocardial components has changed and thus the relative contribution of the different myocardial components to the overall signal may have changed, the phasic changes in resistivity may also be affected. This would open up the theoretical possibility to "image" (changes in) different tissue components or compartments by using different excitation frequencies. To avoid confusion, it should be noted that the changes in membrane impedance during depolarization, which are important for the electrogenesis of the action potential, are unlikely to affect myocardial resistivity as measured in this study. This point will be substantiated in the discussion. We used the four-electrode (FE) resistivity technique with excitation frequencies from 5-60 kHz. The electrode distance was 1 m m to achieve an effective sample volume large enough to overcome inhomogeneities at the microscopic level and small enough to obtain the resistivity longitudinal and transverse to the local fiber direction (33). Methods
The four-electrode technique
The FE technique has been described in detail previously (33). Briefly, this technique employs a linear array of four electrodes, the outer two of which are used to apply a current to the medium under study, while the inner two electrodes sense the resulting potential difference. Measurements were performed using a modified analog signal conditioner-processor (3) (Leycom Sigma-5, CardioDynamics, Rijnsburg, The Netherlands): a 30 lxA (RMS) sinnsoidal current (frequency range 5-60 kHz) is applied to the outer pair of electrodes and the voltages on the inner pair are fed into a high input impedance (> 1 Mf~) differential amplifier. The system uses synchronous detection to select the component in phase with the excitation current and delivers a DC output signal, which is a continuous measure of the real component of the sample impedance. Effective resistivity of the medium was calculated on the basis of a volume conductor model described below. Volume conductor model
The myocardium was modeled as a uniform anisotropic volume conductor with resistivity RL in the fiber direction and resistivities R T in the two transverse directions (24). This volume conductor model is meaningful only if the assumption of parallel fibers is valid in the sample volume of the array, while on the other hand the electrode distance should be large enough to overcome the inhomogeneities at a microscopic cellular level. The estimation of the sample volume of a FE system in case of an anisotropic medium and the validity of the volume conductor model have been treated previously (33) (see The sensor, below). When a FE system is applied to the surface of an anisotropic medium which is assumed to be semi-infinite, the potential difference (qg) depends on the orientation of the electrode array with respect to the fiber direction (19). If the FE an'ay is aligned along the fiber direction we define qb as ~L and: q)L = RT 9 I/(27za),
(1)
413
Steendijk et al., Anisotropic myocardial electrical resistivity
where I is the applied current and a the electrode spacing. With the array positioned perpendicular to fiber direction go is defined as got and: got = (RL 9 RT) I/2 = I/(2r~a).
(2)
Therefore, when goL and gOT are measured, the two resistivities are obtained as: RT = q)c " 2rca/I Rt =
((I)T2/goL)
9
(3) 2na/I.
(4)
The sel~soF
To obtain local myocardial resistivities in two perpendicular directions, we previously developed the epicardial sensor (33) which is shown in Fig. 1. Briefly, two linear arrays of four equidistant platinum electrodes were inserted crosswise in a perspex disk. The diameter of the electrodes is 0.4 m m and the inter-electrode distance is 1 ram. The electrode system is incorporated in a small flexible silicone suction cup with a 16-mm outer diameter. Using a slight vacuum, maintained with a pump via a suction tube, the sensor is affixed to the beating heart in a manner similar to that developed for epicardial Doppler flow velocity measurements by Wangerl et al. (40). The main advantage of this sensor is that it can easily be applied and removed. By using suction a stable contact with the epicardium is obtained without the need for a penetrating electrode system, which would cause cell damage and consequently might affect measurements at such a small scale. The effect of suction on the measurements was minimized by making the sensor very light and flexible and applying the vacuum outside the area of measurements. We have previously FLEXIBLE. SUCTION~ TUBE &
~
:
WIRINGELECTRODE
FLEXIBLE t SUCTION /CUP
8"Pt ELECTRODES (O.D. 0.4mm) Fig. 1. The sensor, an eight electrode transducer consisting of two perpendicular arrays of 4 platinum electrodes (inter-electrode distance 1 mm) inserted in a perspex holder, incorporated in a small flexible suction cup. For resistivity measurements one of the arrays is selected: the outer two electrodes are used to apply a current, I, while the inner pair senses the resulting potential difference, O.
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Basic Research in Cardiology; Vol. 89, No. 5 (1994)
shown that measurements of resistivity with this system are confined to a 2-ram-thick epicardial layer (33), a region within which the myocardial cells of a canine left ventricle have a fairly uniform direction (35). The system was calibrated by submerging the sensor in a large container filled with saline solutions of known resistivities in the range 100-600 f2 - cm. Instrumentation and protocol
Measurements were obtained in four open-chest mongrel dogs with body masses ranging from 20 to 25 kg. After premedication with 5-10 ml of Hypnorm (10 mg fluanison and 0.315 mg of fentanyl per ml) intramuscularly and 1 ml of atropine subcutaneously the dogs were intubated and ventilated with a fixed-volume positive-pressure respirator (Dr~iger-Pulmomat, Ltibeck, Germany) with a mixture of 02 and room air. Anesthesia was maintained with an intravenous infusion of methadone (Symoron, 2.5 mg/hr) and droperidol (Dehydrobenzperidol, 12.5 mg/hr). Pancuronium (Pavulon, 1 mg/hr i.v.) was used as a muscle relaxant. A dual micromanometer catheter (Dr~iger Medical Systems, Best, The Netherlands) was inserted into the LV via the right carotid artery with the proximal pressure transducer above the aortic valve and the distal transducer in the LV. After thoracotomy, the pericardium was opened and the resistivity sensor was placed in the perfusion region of the LAD with one of the electrode arrays along the epicardial muscle fiber direction as estimated by visual inspection. After reading the measured resistance values from both arrays the sensor was rotated slightly as needed to maximize the difference between the two signals. In this position the higher resistance value was taken to represent Rv and the lower value (RT 9 R E ) 1/2 (equations 1 and 2). Visual inspection showed no migration of the sensor on the beating heart. After stable recording were obtained for about 5 rain, longitudinal and transverse resistivities were measured at excitation frequencies of 5, 10, 15, 20, 30, 40, 50 and 60 kHz. For both arrays a frequency scan was made by recording the signal from that array for approximately 5 cardiac cycles at each frequency. The total data acquisition time for each scan was typically 30 s. This protocol was repeated after repositioning the sensor in a slightly different position. Recordings of myocardial resistivity, ECG, LV and arterial blood pressure were made on an eight-channel paper recorder and acquired with a sample frequency of 100 Hz and 12-bit accuracy using an analog-to-digital converter on an LSI-11/23 minicomputer (Digital Equipment Corp., Maynard, MA). Data were stored on floppy disk for later analysis. The study protocol was approved by the institutional committee for animal experiments. Data-analysis
Initial data-analysis was performed using dedicated software on a personal computer, statistical analyses were performed using StatView II (Abacus Concepts Inc, Berkeley, CA) on a Macintosh SE microcomputer. Figure 2 shows a typical example of the data obtained. The top panel shows the resistivity signals: both arrays were subsequently scanned over the 5-60 kHz range. The tracings in the lower panel show the longitudinal resistivity signal at 5 kHz in more detail, together with the ECG, LV and aortic pressure. At each frequency step, one representative cardiac cycle (starting at the peak of a QRS complex) was selected. To allow detailed comparisons independent of heart rate, we normalized the time scales by dividing each R-R interval into 20 equidistant time intervals. The average signal from each interval yielded a time-normalized resistance signal that was used in further analysis. The signal from the array parallel with the fiber direction
415
Steendijk et aL, Anisotropic myocardial electrical resistivity
longitudinal
560
-----
transverse - - - - - 4 , 5
tst ~ 20]~ r'm
3o~ 5kHz myocardial resistivity (~- cm)
40
50N
--v" IAlil~ 15 I'tlv Itll, r 40
\ 38o -
2o \
I
1
I\ I
I
I
1
10 pressure (ram Hg) 10.50 125.55 Aortic pressure (ram Hg) 97.80 ECG 1.83 , 0.30 471.80 Resistivity ( n. era) 446.50 3.0
I
time (s)
I
[
[
I
20
I I 30
__
~
@
@
A
~
~
~ _
~
3.5
time (s)
~
4.0
4.5
Fig. 2. Frequency scan: The top tracing shows the resistance signals from the arrays longitudinal and transverse to the fiber direxxion obtained stepwise at 5-60 kHz. As an example, the other tracings show the longitudinal resistance signal at 5 kHz in more detail together with the simultaneous left ventricular and aortic pressures and the ECG. represents RT (Equ. (3)), whereas RL was obtained by calculating (for each time interval) the square root of the product of the two signals (Equ. (4)). Figure 3 shows a typical example of the phasic RL and RT for each frequency thus obtained. For statistical analysis the phasic signals were subdivided into four periods as indicated by the dashed lines in Fig. 3: pre-ejection (P1), ejection (P2), early diastole (P3), and late diastole (P4). These cardiac phases were defined on the basis of the ECG and the pressure signals (PLv and P~o): P1 starts at the R-top of the ECG, P2 starts when PLv>P~o, P3 starts when PL~<P~o, P4 starts at the P-top of the ECG and ends at the next R-top. To analyze the frequency dependence and the phasic pattern of longitudinal and transverse resistivities, the data were fitted to a multiple linear regression model. Effects coding was used to assess the
416
Basic Research in Cardiology, VoL 89, No. 5 (1994) 1
2
3
4
ECG
LV pressure aortic pressure
350 ~ / i
// /
~ I I
/
/
~
~
i
ill
/
x i
i
f
[
i
1
--.. \
I|
i
i
i
i
i
I 5 kHz
]
300
I
-
longitudinal resistivity (g~-cm) 250
10
15 20 30 40 5O 60
2OO 0.00
0.20
500 ~
0.40
-
0.60
0.80
1.00
d
510kHz
450 transverse resistivity (n. cm)
20 :
~ _
~ '
I
-
-
1
30
'
_
400 ~
,pl, i/
350
0.00
P2
i i 0.20
t
P3
I
i
P4
Ill I I I I t t II I I 0.40 0.60 0.80 relative time (R-R interval)
40 50 60
-
I
IX 1.00
Fig. 3. Typical example of longitudinal (top) and transverse (bottom) resistivity during one cardiac cycle. RL and Rs were obtained at 8 different excitation frequencies. The dashed lines separate four cardiac phases: pre-ejection (P1), ejection (P2), early diastole (P3) and late diastole (P4). effects of interanimal variability, excitation frequency, and cardiac phase (12, 43). We investigated whether interaction between any of the variables was present by adding interaction variables to the regression equation which, consequently, is given by: R x = cz~
+
Ig ~i D -
Di +
Y. (xi F 9
F i + ,Y-,~ip 9 Pi +
~;Y, czijDF 9 Dj 9 F i + ~g~g ~ijD'P. Dj 9 Pi + Y's czijFp" Fj 9 Pi.
(9)
Steendijk et aL, Anisotropic myocardial electrical resistivity
417
In this equation R Xstands for R L o r RT. The dummy variables D i code for the four dogs (dog 1: {Di}=(1,0,0), dog 2: (0,1,0), dog 3: (0,0,1) and dog 4: ( - 1 , - 1 , - 1 ) . Similarly, F i codes for the eight excitation frequencies (5 kHz: {Fi}=(1,0,0,0,0,0,0), etc., 60 kHz: (-1,-1,-1,-1,-1,-1,-1)) and Pi codes for the cardiac phases (Pl:{Pi}=(1,0,0), el cetera). The Dj 9 F i terms describe the interaction between interanimal variability and excitation frequency, the Dj 9 Pi terms describe the interaction between interanimal variability and cardiac phase, and the Fj - Pi terms describe the interaction between excitation frequency variability and cardiac phase. The data from the initial and the repeated protocol were pooled, so each "state" (defined by dog, cardiac phase and excitation frequency) is observed twice. Consequently, the interpretation of coefficients of the multiple regression equation is as follows : cd is the mean resistivity (RL or Re) averaged over all dogs, frequencies, and cardiac phases. The variability of the data-points from the mean value is attributed to interanimal variability, to changes during the cardiac cycle and to variation of the excitation frequency. The variability between animals is given by the coefficients cqD (therefore, e.g. mean resistivity in dog 3 can be estimated as: a~ + %D). Likewise, the changes in resistivity between cardiac phases are given by the c o e f f i c i e n t s Sip and the changes with excitation frequency by the coefficients ai F. The coefficients of the interaction variables indicate significance and magnitude of the corresponding interaction, e.g., the ctijD F indicate whether and how much the frequency dependence varied between different animals. The variability of a set of variables is estimated by calculating the standard deviation of the corresponding coefficients (12). To determine the statistical significance of each set of dummy variables, an F-statistic was calculated by dividing the mean square of that set of variables by the mean square of the residual error. The numerator degrees of freedom (DF) of this F-statistic is the number of independent variables (3 for the dog variables, 7 for the frequency variables, 3 for the cardiac phase variables, and 9 or 21 for the interaction variables) and the denominator DF is the residual DE Statistical significance was considered to be p < 0.05.
Results R E a n d e T were measured over a full cardiac cycle at a range of excitation frequencies (5-60 kHz) in four dogs. The cardiac cycle was divided in four phases and the average resistivity in each phase was determined, Thus, 256 data points for both R L and RT (4 dogs 9 8 frequencies - 4 phases/cycle 9 2 observations) were obtained. We used multiple linear regression analysis to determine the independent effects of interanimal variability, excitation frequency and cardiac phase and the interactions between these effects. The results are given in Table 1. For both R E and RT the regression equation fitted the data very well (r = 0.991, respectively r = 0.983) with SEE's of 8.12 and 13.6 ~ 9 cm. The interanimal variability of RE was 41.26 U2 . cm or 15.9 % of the mean value, for RT the interanimal variability was 49.62 f~ 9 cm (11.5 % of the mean value). The variability between cardiac phases was fairly small: 6,02 f~ - cm (2.3 %) for R E and 3.84 f~ . crn (0.9 %) for RT, but the F-values indicate that for both R E and RT the phasic changes were statistically highly significant. The F-test for the set of excitation frequency variables shows that both R E and RT depended highly significantly on the excitatior~ frequency. The F value for the set of 7ijPFs was 0.077 for R L and 0.013 for RT which indicates that cardiac phase and excitation frequency did not interact. This means that the phasic
Basic Research in Cardiology, Vol. 89, No. 5 (1994)
418
changes w e r e similar (i.e., not significantly different) at each excitation f r e q u e n c y or conversely, that the f r e q u e n c y d e p e n d e n c e did not vary b e t w e e n cardiac phases. T h e r e fore, these two effects can be c o n s i d e r e d as i n d e p e n d e n t p h e n o m e n a and treated separately.
Phasic changes The significance o f the set o f d o g - c a r d i a c phase interaction variables, indicates that the i n t e r a n i m a l variability v a r i e d b e t w e e n cardiac phases. We used the ~Ps and the interaction variables cq3DP to calculate the m e a n phasic changes in e a c h d o g separately. O n e sample t-tests w e r e c o n d u c t e d to test for significant differences f r o m zero and paired t-tests to test for significant differences b e t w e e n the group means. W e used the B o u f e r roni c o r r e c t i o n to adjust for m u l t i p l e c o m p a r i s o n s . The results are g i v e n in Fig.4: During
Table 1. Influence of interanimal variability, excitation frequency, and cardiac phase on longitudinal and transverse myocardial resistivity Longitudinal resistivity Regression equation: R L = ~~ + 52 ~iD.Di Jr- ~ (ZiF.Fi@ Y, ~iP-Pi -] 2 2 ~ijDF'Dj'Fi @ ~ 2 :xijDP'Dj'Pi+ ZZ 0qjFP'Fj'Pi N = 256, R = 0.991, DFtot
255,
DFreg r =
Coefficient Mean
c~~
259.17
Dogs
al D c~2D c~3D
12.09 -62.62 - 1.80
cqF et2F r
53.70 33.52 19.77
Excitation frequency
64, DF~s = 191, F = 173.2, p
0.0001, SEE = 8.12
SD
Fs~t
P
41.26
1756
<0.001
32.66
503.2
<0.001
(~4F
6.52
cc5F ~6F ~vF
- 8.38 -20.93 -37.47
Cardiac phase
~i p ~zp %e
-
1.01 9.64 - 1.68
6.02
41.69
<0.001
Dogs- exc. frequency interaction
~ j D-F .. r DF
range: - 10.56 12.39
6.42
5.271
<0.001
Dogscardiac phase interaction
ctHD.P .. (z33DP
range: - 6.06
3.44
5.188
<0.001
Cardiac phase -exc. freq. interaction
cx~lP.F .. r PF
range: - 1.05 1.34
0.58
0.077
NS
5.25
4 l9
Steendljk et al., Anisot~vpic myocardial electrical resistivity Table 1. Continued Transverse resistivity Regression equation: Rv = ao + Z ~iD-Di @ ~ ~iF.Fi -~ • ~iP.Pi q52~ O:ijDF.Dj.Fi @ Z 2 ~zijDP.Dj.P i @ Y~Y~0qjFP.Fj-P i N = 256, R = 0.983, DFtot = 255, DFregr = 64, DF~rs = 191, F -= 86.26, p = 0.0001, SEE = 13.6 Coefficient
SD
F~et
p
Mean
c~~
430.47
Dogs
cqD ~,D_ %D
78.86 -46.12 --38.34
49.62
1518
<0.001
cq v c~2v %~ :~4F cq F %~ cx7v
57.17 38.73 23.94 9.37 - 10.91 -24.85 -42.17
36.35
225.6
<0.001
Cardiac phase
cq p <x~p ~3P
2.49 - 0.78 - 5.89
3.84
6.42
<0.001
Dogs-exc. frequency interaction
%~ov ~73D.F
range: -- 15.76 12.47
11.54
2.712
<0.00l
Dogs cardiac phase interaction
Cl1iDP .. (Z33Op
range: -16.17 8.26
7.10
9.226
<0.001
Cardiac phase -exc. freq. interaction
~u PF .. ~73PF
range: - 0.79 0.69
0.51
0.013
NS
Excitation frequency
e j e c t i o n (P2) R L w a s s i g n i f i c a n t l y h i g h e r t h a n t h e m e a n v a l u e ( + 9 . 6 • f) 9 c m , p < 0 . 0 5 ) a n d d u r i n g late d i a s t o l e (P4) R L w a s s i g n i f i c a n t l y l o w e r ( - 6 . 9 • f) 9 c m , p < 0 . 0 5 ) . D u r i n g e j e c t i o n R L w a s s i g n i f i c a n t l y h i g h e r t h a n in all o t h e r c a r d i a c p h a s e s . T h e p h a s i c c h a n g e s in RT w e r e less c o n s i s t e n t , o n l y the c h a n g e d u r i n g late d i a s t o l e (P4) w a s s i g n i f i c a n t l y d i f f e r e n t f r o m z e r o ( + 4 . 0 • f~ 9 c m , p < 0 . 0 5 ) . T h e r e w e r e n o s i g n i f i c a n t d i f f e r e n c e s in R v b e t w e e n t h e c a r d i a c p h a s e s .
Frequency dependence In Fig. 5 the m e a n v a l u e s o f RL a n d RT are p l o t t e d as a f u n c t i o n o f e x c i t a t i o n f r e q u e n c y . Since there was no interaction between cardiac phase and excitation frequency, resistivities w e r e a v e r a g e d o v e r full c a r d i a c cycle. M e a n l o n g i t u d i n a l r e s i s t i v i t y g r a d u a l l y decreased from 313• f~ . c m at 5 k H z to 2 1 2 • f~ 9 c m at 6 0 kHz, t r a n s v e r s e r e s i s t i v i t y decreased from 487• to 3 7 8 • f~ - cm. A s s h o w n in T a b l e 1 t h e d e p e n d e n c e o f b o t h
420
Basic Research in Cardiology, Vol. 89, No. 5 (1994) 20
phasic longitudinal resistivity #
.â&#x20AC;˘E10 E o
E
0
E o
g #
~__1 *
[
I
*
-20 P1
20
? 10
E
I -)(--x-
P2 P3 cardiac phase
1 P4
phasic transverse resistivity
E 0 E
g
-20 P1
P2 P3 cardiac phase
P4
Fig. 4. Changes in longitudinal (top) and transverse (bottom) resistivity (mean â&#x20AC;˘ 4 dogs) during four cardiac phases with respect to mean resistivity (averaged over the full cycle). PI: pre-ejection, P2: ejection, P3: early diastole and P4: late diastole. Statistical significanees: #: p<0.05 vs mean, *: p<0,05 between cardiac phases, **: p<0.01 between cardiac phases.
RL and RT on frequency was highly significant. The SD of the coefficients of the dogsexcitation frequency interaction is 6.41 ~) 9 cm for RE and 11.54 ~ 9 cm for RT. This indicates that the interanimal variability of the frequency dependence is much smaller than the interanimal variability of tile mean resistivities (41.26 f~ 9 cm for R L and 49.62 f2 9 cm for RT). Therefore, the overall SDs shown in Fig.5 are mainly due to differences in mean resistivity and much less to a difference in frequency dependence between dogs.
Discussion
It has been known since the work of Rush et al. (24) that myocardial resistivity is anisotropic, with higher values transverse to the fibers than in the longitudinal direc-
421
Steendijk et al., Anisotropic myocardial electrical resistivity Table 2. Longitudinal and transverse myocardial resistivities (f~ - cm) reported in the literature Reference
Transverse
15 26 24 4.1 5 31
Longitudinal 2 t 6(a) 965 (a)
563 :k 84
252 • 76 152 = 39 125 4- 19 296 • 19 265 • 38
391 • 110
42
38 22 16 7 present study
410 (a) 705 • 80 170 • 33 487 • 49 (o
213 • 126 • 151 • 313 •
25 11 25 49 @
Preparation dog dog (b) dog calf trabecula (c) calf trabecula (c) cat papillary muscle (c) cow trabecula (~ dog dog rabbit papillary muscle (e) sheep dog
(a) direction not specified, (b) post mortem, (~ tyrode perfused preparatxon, (d) transmural direction, so (UL - RT)lI2 is measured, (e) perfused by tyrode/erythrocyte mixture, (t) at 5 kHz 9
tion. T h i s anisotropy can be e x p l a i n e d on the basis of the tissue structure. E l e c t r i c currents tend to f o l l o w the relatively l o w - r e s i s t i v e intra- and e x t r a c e l l u l a r pathways. T h e e l o n g a t e d structure and parallel a l i g n m e n t o f cardiac cells and the relatively h i g h i m p e d ance of the cell m e m b r a n e s , result in a l o w e r resistance in the longitudinal c o m p a r e d to the transverse direction. In addition, the v a s c u l a r bed m a y p r o v i d e l o w - r e s i s t i v e p a t h w a y s 'which are m a i n l y in the longitudinal direction (4).
600 transverse 500
400 longitudinal
E :>,
300
~, 200
100
I lO excitation frequency (kHz)
lOO
Fig. 5. Frequency dependence of longitudinal and transverse myocardial resistivity (mean ~c SD, 4 dogs). Note the logarithmic scale on the x-axis.
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Many investigators confirmed Rush's findings, but the reported values vary considerably (Table 2). Values reported in the literature range from 125 to 296 f~ 9 cm for R L and from 170 to 705 ~) 9 cm for Rr (5, 7, 16, 22, 24, 31, 38, 41, 42). A number of factors may explain this wide range. First, it may be related to differences in preparations: measurements in the intact blood-perfused beating heart may not be comparable to, for example, those in Tyrode perfused isolated trabecula. The studies performed in isolated trabecula (5, 31, 41, 42) all used Tyrode perfnsed preparations. A Tyrode's solution typically has a resistivity of 50 f~ 9 cm, whereas whole blood has a resistivity of approximately 150 - cm. In a recent paper (34), we presented a tissue model to assess the effects of various tissue components on R T and RL. One of our findings was that changes in extracellular resistivity, of which blood resistivity is likely to be an important component, greatly affected RT and RL. Therefore, the relatively low values presented in these studies (mean R L was 210 f~ 9 cm) could at least in part be due to the low resistivity of the perfusion solution. Kleber et al. (16) used a papillary muscle perfused with a mixture of Tyrode and bovine erythrocytes, however a fairly low hematocrit (25 %) was used. We estimate that the resistivity of the mixture was approximately 85 f~ 9 cm (6, 37), which is still low compared to the resistivity of blood at a normal hematocrit. In addition, in long and relatively thin muscle preparations, current can be injected relatively far from the voltage sensing electrodes, which allows it to spread more uniformly through the tissue, resulting in a lower resistivity. Among the in vivo studies cited in Table 2 only three give values for both R L and Rs (in other in vivo studies the direction is either not specified or transmural). In the study by Fallert et al. (7) four needle electrodes were inserted 3 mm deep into the myocardium at 3 mm spacing. As recognized by those authors, such a configuration tends to average the effects of fiber orientation, which may explain why the anisotropic ratio (RT/RL) was close to 1. The resistivity values presented by them are substantially smaller than in most other studies, especially when compared with the in vivo studies. Possibly this is related to the traumatic technique, which could lead to cell damage and local formation of edema. Second, the condition of the preparations will have an influence: Van Oosterom et al. (38), Fallert et al. (7), and Tranum-Jensen et al. (36) showed that myocardial resistivity changes dramatically when local ischemia is induced over a period of 30 min to several hours and, more recently, such effects were shown to start within 2 min of coronary occlusion (34). Wojtczak (42) demonstrated changes in the passive electrical properties of cow ventricular muscle with hypoxia. Third, resistivities have been studied at different excitation frequencies. Most reported values were obtained at 1 kHz or less. Model studies and data from skeletal muscle show a decrease in R T above 10 kHz (44). Fourth, another factor may be related to the volume conductor models used. Most investigators considered the myocardium as an infinite or semi-infinite uniform anisotropic volume conductor. The validity of this model, however, is limited, in particular, when the electrode distance is such that the field penetrates deep myocardial layers: namely, fiber direction is not uniform throughout the myocardium (35), Rush et al. (24) and Fallert et al. (7) used four-electrode systems with electrode distances of respectively 5 and 3 mm. As shown in one of our previous papers (33) such measurements reflect properties of a sample volume which extends practically over the entire wall thickness and would in fact require a more complex volmne conductor model. We used a similar semi-infinite volume conductor model, but limited our measurements to a thin epicardial layer to insure sufficient uniformity of fiber direction in our sample volume. Despite these methodological differences values for RT and RL in the present study are in keeping with the
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values from the in vivo studies mentioned above, given the standard deviations. The finding that the value for RL in our study tends to exceed values from literature could be related to the presence of the epicardial membrane. However, theoretically a thin relatively insulting layer would not greatly affect the results. Typically, even a layer with a thickness of 20 % of the electrode distance and a resistivity of 10 times myocardial resistivity would increase the measured values by only 10 % (33). In conclusion, we would like to emphasize that values reported in the literature (including our findings) should be used (e.g., in model studies) with great care, not only because the values may be dependent on species or physiological conditions, but also because the RL and RT reflect a "bulk" property which is dependent on the properties of the measurement technique, such as sample volume, excitation frequency, and the tissue model used to calculate the parameters from measured currents and/or voltages.
Phasic changes and frequency dependence
The myocardium is subject to substantial geometric changes during the cardiac cycle which obviously affect myocardial resistivity. In systole the fibers become shorter and thicker and intramyocardial bloodvolume decreases (13, 18, 39). Considering the relatively high membrane impedance and the low blood resistivity, an increase in macroscopic resistivity during systole would be anticipated. Longitudinal resistivity, RL, indeed showed the expected behaviour: an increase during systole and a decrease during diastole. Transverse resistivity, RT, however tended to behave in an opposite way: during late diastole RT was significantly increased. It could be argued that in diastole the fiber diameters are relatively small and consequently more fibers and thus more cell membranes are present in the sample volume of the sensor. This may, especially in the transverse direction, counteract the effect of increased myocardial bloodvolume. Phasic changes in myocardial resistivity were not noted by Rush et al. (24) or by Van Oosterom et al. (38). However, both of those investigators used a low excitation frequency (_< 1 kHz) and the measured signal was superimposed on the heart's electrical signal. This method probably does not allow to detect small changes a observed by us. In addition, those investigators did not study RL and RT separately in this respect. Van Oosterom et al. (38) measured resistivity using a multi-electrode needle in the transmural direction, thus the signal they obtained reflected (RL - RT)v2. Given the small amplitude and t h e more or less-opposite phasic changes in RL and RT observed in the present study, (RL 9 RT) ~/2 is not expected to vary significantly during the cardiac cycle. Cell membranes can be modeled electrically by a parallel circuit of a capacitance and a resistance. The capacitive component is due to the phospholipid bilayer interposed between two conductive media formed by the intra- and extracellular fluids, and the fluidfilled channels in the bilayer form the resistive pathway (9, 14, 29). Membrane impedance therefore decreases as the excitation frequency is increased and macroscopic resistivity is expected to be dependent on the excitation frequency. TY2Pical values for the membrane capacitance and resistance are respectively 1 laF/cm and 10 kf~. cm (41). This indicates that at 5 kHz the capacitive membrane reactance (= 1/(2~f 9 Cm), with f = excitation frequency and Cm=membrane capacitance) is approximately 30 9 cm 2, which is several orders of magnitude smaller than the membrane resistance. At higher frequencies the capacitive reactance is even smaller. Therefore, even a large reduction in membrane resistance during depolarization would not increase the effective
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transmembrane current appreciably in the frequency range used in this study. Since the capacitive membrane reactance is very small compared to the membrane resistance, no frequency dependence is expected as a consequence of Cm and R m in parallel. However, the membrane impedance (Zm) is in series with the intracellular and extracellular fluids with resistivities typically in the range of 100-200 f~ 9 cm. Using the value of 30 fl 9 cm 2 (Z m at 5 kHz) and a typical cell radius (Ao) of 10 gm, Zm/Ac=3000 ~ 9 cm. A tenfold reduction in this value (by changing the frequency to 50 kHz) brings it in the same range as the fluid resistivities and, consequently, a frequency dependence would be expected. In addition to the frequency dependence, theoretical and experimental studies have shown that for the interpretation of the effective resistivities the electrode distances should also be taken into account. At very small electrode distances current flows mainly through the extracellular spaces and consequently the measurements reflect extracellular properties, whereas with larger distances the injected current is redistributed between intra- and extracellular spaces and the effective resisitivities reflect combined intraand extracellular properties (20). The theoretical analysis by Plonsey and Barr (20) indicates that our 1-mm electrode spacing falls in an intermediate region in this respect. As a further complication Gielen et al. (11) and Albers et al. (2) have shown (in skeletal muscle) that the effect of electrode spacing is modulated by the excitation frequency. Their results indicate that at higher frequencies a complete current redistribution is achieved at relatively smaller electrode distances. Our results show that over the range of 5-60 kHz, both RTand RL decrease by approximately 25 %. Previously, Van Oosterom et al. (38) found no frequency dependence in the low frequency range (10 H z - 5 kHz), Sperelakis and Hoshiko (30), however, reported a decrease of 25 % from 10 Hz to 10 kHz in papillary muscle and Schwan and Kay (27) reported even a 38 % decrease over this range. The frequency dependence of RT was expected because current in this direction encounters many cell membranes. The frequency dependence of RL, however, was very similar. This could be partly due to a capacitive component of the intercalated disk in parallel with the low-resistive pathway formed by the gap junctions (10). In addition, current that passes through the vascular system encounters red cell membranes, especially in the capillaries where the vessel diameter is smaller than the (underformed) red cell diameter. It is possible that the frequency dependence of RL is related to the properties of these membranes. The four-electrode method effectively avoids problems with electrode polarization by using non-current carrying sensing electrodes, however imbalance between the stray capacitance of the connecting wires and the electrode impedances may cause significant phase errors which could be erroneously interpreted as a frequency dependence (1, 38). We carefully checked this by performing measurements in diluted saline solutions, which should be purely resistive in the frequency range used in this study, and did not find significant errors. Theoretically, the effect of geometric changes was expected to be most pronounced at low frequencies when the intracellular medium is more effectively "shielded" by the high-impedance membranes and, consequently, a highly effective "contrast" between intra- and extracellular compartments is present. However, in the frequency range examined, we found no significant interaction between the phasic changes and the frequency dependence, indicating that the phasic changes were similar at each frequency. This may suggest that, despite the decreased resistivity at the higher frequencies, the major current pathways remain extracellular. The interpretation of our data, however, remains somewhat speculative because of insufficient knowledge about, for
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example, precise values of membrane impedances, for muscle cells, capillary vessel walls and erythrocytes. Neither is much known about electrical properties of fluids and structures inside muscle cells and other structures within the wall such as the cytoskeleton. Therefore, more studies of these factors are indicated before electrical measurements can be used effectively to model and analyze myocardial structure and composition, both in normal and pathophysiological conditions. Such further studies appear useful because changes in myocardial electrical properties occuring during ischemia may be recorded rather easily by employing the method described by us (7, 34).
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