354

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 37, NO. 4. APRIL 1990

Finite Element Analysis of Cardiac Defibrillation Current Distributions NESTOR G . SEPULVEDA, JOHN P. WIKSWO, JR.,

Abstract-We have developed a two-dimensional finite element model of the canine heart and thorax to examine different aspects of the distribution of current through cardiac tissue during defibrillation. This model allows us to compare various electrode configurations for the implantable cardioverterldefibrillator. Since we do not yet know the electrical criteria to apply for predicting defibrillation thresholds, such as the minimum current density required for defibrillation or the critical mass if indeed such quantities are applicable, we measured defibrillation energy in dogs to determine the voltages to apply to the model for calculating current distributions. By analyzing isopotential contours, current lines, power distributions, current density histograms, and cumulative current distributions, we estimated the critical fraction and threshold current density for defibrillation, compared various electrode configurations, and assessed the sensitivity of the defibrillation threshold to electrode position, patch size, and tissue conductivity. We found that blood can shunt defibrillation current away from the myocardium, particularly in configurations using a two-electrode catheter, that myocardial tissue conductivity strongly affects the current distributions, and that epicardial patch size is more important that subcutaneous patch size. O u r results are consistent with successful defibrillation requiring that 80 f 5 % of the heart must be rendered inexcitable by a current density of 35 f 5 mA/cm2 o r greater. This twodimensional, isotropic model has allowed us to analyze some of the determinants of defibrillation, but more detailed interpretation of experimental data may require the extension of the model to three dimensions.

I. INTRODUCTION

A

N IMPROVED understanding of the determinants of ventricular defibrillation will be useful for optimizing the performance of the automatic implantable cardioverteddefibrillator. The design of a system with the minimal energy and implantation requirements will be aided by a detailed investigation of various electrode configurations and the characterization of defibrillation current density distributions. Thus far, optimization of defibrillating electrode placement on either the heart or thorax has been largely empirical [1]-[8] because there are no suitable measurement techniques to determine directly the current density distribution within the thorax or the heart. Although current density measurements within biological tissues are possible and have been demonstrated in the Manuscript received, January 13, 1988; revised June 23, 1989. This work was supported in part by grants from Cardiac Pacemaker, Inc., Office of Naval Research Contract N00014-82-k-0107, an AHA Tennessee Affiliate Grant-in Aid to Dr. Echt, a Whitaker Foundation Grant, and an AHA Tennessee Affiliate Grant to Dr. Sepulveda. N. G. Sepulveda and J. P. Wikswo, Jr. are with the Departments of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235. D. S . Echt is with the Cardiology Division, Department of Medicine, Vanderbilt University School of Medicine, Nashville, TN 37232. IEEE Log Number 8933593.

MEMBER, IEEE, A N D

DEBRA S . ECHT

brain and in the spinal cord [9], [lo], application of these techniques to cardiac tissue may be difficult. Researchers in the field of electrical defibrillation have in general measured peak current or have computed average current [l l]. One study [12] reported an external threshold average current density obtained from an isolated canine heart in an isoresistive and isotonic volume conductor, which excludes the influence of the surrounding structures of the heart and other factors. From measurements of the potential field gradient created by epicardial defibrillation electrodes in dogs, Chen et al. [13] found that the major portion of the applied voltage is dropped at the electrodetissue interface and the tissue immediately adjacent to defibrillation electrodes. Most importantly, they identified a substantial variation in the electric potential gradients on the epicardial surface. Chen et al. [ 131 conclude that the region of the myocardium with the lowest potential gradient is the site where fibrillation will be reinitiated after the shock. Choi and Thakor [14] describe an experimental technique for measurements of electrical fields in an isolated dog heart. They also compare the experimental results with derived numerical results obtained using the finite element method. A computer simulation study used to calculate the cardiac currents induced in transthoracic defibrillation is described by Doian et al. [151. They conclude that the commonly-used electrode positions are not necessarily the best choice. Ben Fahy et al. [16] describe a two-dimensional inhomogeneous model of the human thorax used to study electrode designs for electrosurgery, defibrillation, and external cardiac pacing. According to the critical mass hypothesis defibrillation will be successful whenever a critical mass of myocardium is rendered inexcitable by the defibrillation pulse [18]. The size of the critical mass, if it does exist, is unknown, but has been estimated to be as high as 75 % [ 113. According to Chen et al. [ 131 defibrillation is attained only after the upper limit of vulnerability is exceeded-. This vulnerability hypothesis states that low energy pulses halt fibrillatory activation fronts, but that areas distant from the defibrillating electrodes having weak potential gradients reinitiate fibrillation. Therefore, successful defibrillation requires pulses that are greater than those which can initiate fibrillation at sites distant from the electrodes. If the vulnerability hypothesis is valid, it would be advantageous to have the entire myocardium defibrillated at least to the same level of inexcitability and to avoid complex postshock activation wavefronts. Critical mass and

0018-9294/90/0400-0354$01.OO O 1990 IEEE

SEPULVEDA et al. : ANALYSIS OF CARDIAC DEFIBRILLATION

355

vulnerability hypotheses could coexist, and homogeneity of defibrillation current may be important for both. While local changes in transmembrane potential from the defibrillation current must be the primary determinant of the subsequent electrical behavior of a myocardial cell, the relation between the change in transmembrane potential and the local applied current density is as yet unknown. The literature abounds with references to the current density as being the key factor in defibrillation. Since little is known about myocardial current densities during defibrillation and even less is known about their gradients or about the transmembrane potential, for the present analysis we assume that the net current density in the tissue is the proper measure of stimulus strength. An important physiological justification for the apparent applicability of local current density as a criteria for defibrillation is based upon the observation of the proportionality between the magnitude of the junction-induced local gradients in the transmembrane potential and the local current density reported by Plonsey and Barr [ 171. Since not all the physiological mechanisms responsible for defibrillation are well known, a numerical study of the nature and distribution of electric fields produced within the heart by the defibrillation currents can contribute to the understanding of defibrillation. Because of the geometric complexity and the inhomogeneous, anisotropic impedance of the heart and its surrounding structures, it is difficult to estimate analytically the electrical fields generated within the heart by a particular array of defibrillating electrodes. We present a finite element model to predict the current at locations in the heart and thorax where measurements would be difficult or impossible.

METHODS Mathematical Formulation We assume that biological tissues are continuous materials whose conductivity U represents an average over a volume of tissue containing many cells. Furthermore, we consider cardiac tissue to be an isotropic monodomain whose conductivity represents the combined average contributions of intracellular, extracellular, and junctional conductivities. By doing this, within any particular region of tissue, all the electrical processes that result from the application of a defibrillating pulse are also characterized by average field quantities that are defined at every point in space within the tissue. We also assume that the tissues are linear so that U is independent of the electric field strength, and that phase-shifts between the applied electric field and the resulting current density are negligible within the range of frequencies of physiological interest. Thus, in this quasi-static limit the electrical potential V obeys the following “quasi-harmonic” equation

?

*

(U?V)

=

0.

( 1)

The potential I/ is uniquely determined after specifying all the boundary conditions. For defibrillation, the boundary conditions include the potential at each defibrillating

electrode, and the constraint that no current can leave the body, i.e., the current density in an outward direction normal to the surface of the body is zero. Within our assumptions the potentials generated by a given stimulating electrode configuration depend only on the magnitude of the applied voltage, on the location and size of the electrodes, and on the conductivities and geometrical shapes of the various parts of the medium. To solve (1) with its associated boundary conditions we use the finite element method, which is one of the most suitable numerical techniques for solving partial differential equations [20]-[22]. The major advantage of the finite element method over other numerical techniques is its flexibility to deal with curved boundaries and complicated boundary conditions. For the calculation we created an idealized two-dimensional model representing an oblique section through the canine heart and surrounding structures taken between the IV and V intercostal space, that include both the atria and the ventricles. The dimensions of the section are the average values from direct in vivo measurements, taken in four dogs weighing 20-22 kg, and these values were compared with published values [23]. The model was divided into finite elements, ensuring that the edges of the elements coincide with the interfaces between regions as well the external boundaries. The material within the boundary of each element was assigned average resistivities of 600 Q cm for skeletal muscle; 1700 fl * cm for lung tissue; 500 Cl * cm for cardiac tissue; and 135 Q cm for blood [24]. The finite elements used are the isoparametric eightnode quadrilateral and the isoparametric six-node triangle. In both of them the nodes are placed one at each corner and one at the midpoint of each side. Since the element sides can follow parabolic shapes, the curvilinear geometry of the section can be modeled with fewer elements of these types than with straight-sided elements. Furthermore, it is well known that for the same number of total nodes in the model better accuracy in a finite element solution is obtained by the use of fewer of these elements in place a larger number of three-node triangles or four-node quadrillaterals [20]-[22]. The accuracy of the calculations cannot be easily verified for this two-dimensional, curvilinear, isotropic, nonhomogeneous model. An estimate of the accuracy of a finite element model can be determined by obtaining several solutions with different number of elements and by comparing results in electrical potential at selected points within the myocardial tissue. The mesh of Fig. 1 was considered satisfactory within the imposed limit of discretization errors (less than 5 % ) .

-

Electrode Conjigurations Since we do not yet know the electrical criteria to apply for predicting defibrillation thresholds, such as the minimum current density required for defibrillation, we conducted a series of animal studies to determine what voltages to apply to the finite element model. This allows the

356

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 31, NO. 4, APRIL 1990 ENTER VIA JUGULAR VEIN

CHEST

PROXIMAL CATHETER

DISTAL CATHETER

(a)

T

SO PATCH ELECTRODE

ENTER VIA JUGULAR VEIN

EPICARDIAL PATCH ELECTRODE

DISTAL CATHETER ELECTRODE

(b) Fig. 2. Placement of electrodes using: (a) a subcutaneous patch, (b) an epicardial patch

Fig. 1. Finite element grid of canine heart and surrounding structures. Darker areas represent the defibrillating electrodes. The lung region is white, the myocardial tissue is dotted, and the thoracic muscle is shaded.

calculation to proceed without assumptions regarding the mechanism for defibrillation and enables us to compute and compare threshold defibrillation current distributions. Internal defibrillating electrode systems, as seen in Fig. 2, are used in the following combinations:

SP-C C-C SP-C-C

EP-C-C

The subcutaneous patch (anode) and the proximal catheter (cathode), a system not requiring thoracotomy. The proximal (anode) and distal (cathode) catheter representing the simplest system, requiring only a single transvenous lead. The subcutaneous patch and proximal catheter electrodes connected in parallel (anode) and the distal catheter (cathode) to form an orthogonal system not requiring thoracotomy. The epicardial patch and proximal catheter electrodes connected in parallel (anode) and the distal catheter (cathode) as an orthogonal system.

We performed two series of experiments in dogs to evaluate the four electrode configurations for internal defibrillation, as well as to measure defibrillation energy thresholds (Appendix A). The mean Vth SD were: SP-C 75 V , C-C = 425 +_ 83 V , SP-C-C = 425 = 570

86 V, EP-C-C = 390 f 92 V . These voltages, specific for each electrode configuration, provided us with the thresholds needed to calculate the potential and current density distributions for the two-dimensional model of the canine thorax which incorporated electrodes of similar size and position as in the canine experiments. RESULTS Fig. 3(a)-(d) show the isopotential contours for the four electrode configurations. Fig. 4(a)-(d) show the current -+ lines of the current density vector J(x, y ) = - (T ?V. These current lines are obtained by solving the equation

where ?x and 7, are the components of the current density vector j(x, y), in the x and y directions, respectively. Fig. 5 shows the cumulative current distribution functions for the ventricular myocardium for the four electrode configurations. These functions are obtained_by integrating the magnitude of the current density J(x, y ) within myocardial tissue as a function of the myocardial area A ,

F(A) =

sI

j(x, Y ) (

(3)

Table I gives the threshold voltages and currents, the maximum and minimum epicardial voltage gradients, and the maximum and minimum myocardial voltage gradients and current densities for the four configurations. In configuration SP-C in Fig. 3(a), the voltage drop is marked at the lung region near the subcutaneous patch. Approximately 65 % of the total stimulating voltage drop occurs in this region, so the potential gradients are very

SEPULVEDA et a / .: ANALYSIS OF CARDIAC DEFIBRILLATION

TABLE I SUMMARY OF MEASUREMENTS A N D CALCULATIONS FOR Configuration/Parameter Experiments Energy ED90 (joules) Threshold voltage (volts) Simulation Total current, amps Myocardial voltage gradient minimum V/cm maximum V /cm ratio max/min Myocardial current density minimum mA/cm2 maximum mA/cm2 ratio max/min

SP-c

THE

c-c

FOURELECTRODE CONFIGURATIONS

SP-c-c

EP-C-C

46 f 12 ( n = 4) 38 12 (n = 23) 25 f 10 ( n = 18) 21 f 10 (n = 5 ) 570 75 520 f 83 425 f 86 390 rt 92

+

0.84

2.90

2.62

2.80

8.2 63.2 7.7

13.5 156 11.5

7.8 149 19.1

2.6 328 126.1

16.4 126 7.7

27.1 311 11.5

15.6 298 19.1

5.2 658 126. I

Fig. 3. Isopotential contours for the four configurations. The applied voltages were SP-C,570 V (a); C-C, 520 V (b); SP-C-C, 425 V (c); EP-CC , 390 V (d), corresponding to the average ED 90% for the same four configurations evaluated in dogs. Hence, all four potential distributions as shown can be viewed as having successfully defibrillated the heart.

steep near the subcutaneous patch, with the strength of the field highest near the apical parts of the left ventricle. The regions of weakest potential gradient are in the right ventricular free wall, as well as in the upper portions of the left ventricle. The current flow as seen in Fig. 4(a) is more or less uniform through the myocardial region. In configuration C-C in Fig 3(b), the potential distribution resembles a dipolar field. Potential gradients are

Fig. 4. The current lines (0.1 Ailine) for the isopotential contours in Fig. 3.

relatively constant through the septum and right ventricular wall, with the highest gradients near the lower parts of the septum, while the regions of the weakest gradient are located in the left ventricular free wall, such that there is relatively little current flow through this region, as seen in Fig. 4(b). However, an appreciable current flows through the septum and the right ventricular wall. The blood in the right heart conducts a great portion of the current (almost 50%). In configuration SP-C-C in Fig. 3(c), the voltage drop

358

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 31. NO. 4, APRIL 1990

0

100 200 CURRENT DENSITY, rnA/cmZ

300

Fig. 5 . The cumulative current distribution function for the ventricular myocardium with the four electrode configurations.

TABLE I1 SUMMARY OF CALCULATIONS FOR THE SIXDIFFERENT POSITIONS OF THE DISTAL ELECTRODE FOR CONFIGURATION c-c __________

~

Change in Total Current Position

(%)

1*

-8 - 22

2 3 4 5 6

- 18

-4

+ 10

The Current Density in the Low Current Density Regions

decreases decreases slight increase slight increase decreases

*Position 1 is the reference.

is also marked at the lung region near the subcutaneous patch, as in SP-C. Approximately 30% of the total stimulating voltage drop occurs in this region. The potential gradients are steeper near the subcutaneous patch and the proximal catheter. The highest gradients occur in the lower parts of the septal region, as in C-C, while the weakest gradient regions are in the left ventricular wall. The inclusion of the subcutaneous patch has no marked effect over the field in the left ventricular free wall. As seen in Fig. 4(c), the blood in the right heart conducts approximately 50% of the total current as in configuration C-C. However, in the septum and right ventricular wall there is a higher current flow as compared with C-C. The subcutaneous patch is contributing approximately 1.5 % to the total stimulating current. In configuration EP-C-C in Fig. 3(d), there is a marked voltage drop in the apical region of the left ventricle near the patch. The potential gradients are steepest near the patch, and the distal catheter. The weakest gradient regions correspond to the upper portions of the left ventricular free wall but are not sharply differentiated. In this analysis, EP-C-C is the only configuration with an electrode in direct contact with the myocardium, and as a re-

sult the maximum gradients and currents may be affected adversely by errors in modeling the tissue-electrode interface. It can be seen from Fig. 4(d) that the blood in the right heart also conducts approximately 50% of the total current as in configuration C-C. The epicardial patch contributes almost 36% to the total current. This added current mainly flows through the basilar portions of the left ventricle as well as the septum. It can be seen from the cumulative current distribution functions of Fig. 5 , that for current densities between 50 and 80 mA/cm2, the myocardial area having a particular current density increases from SP-C to EP-C-C while the voltage thresholds decrease. Below 50 mA/cm2, the relationship between the four curves becomes more complex, and all four curves pass near the point given by 35 k 10 mA/cm2 and 80 k 5 % . As we will discuss in more detail later, the fact that each of the configurations produced 90% success in defibrillation may be consistent with the existence of a point of intersection of the cumulative current distributions.

Sensitivity to Electrode Position In the canine experiments, the defibrillation energy for the transvenous two-electrode catheters ( C-C) -varied within the same animal when tested on two occasions a week apart, decreasing in two studies and increasing in the remaining three. Since the direction of the change in defibrillation energy on the second study was not consistently higher for C-C (Table V), we hypothesized that electrode position was an important contributing factor. We used the model to determine the effects of variations in the position of the tip (distal) electrode of the catheter configuration C-C on the current distribution. Five additional positions for the right ventricular electrode were selected, and the cumulative current density distribution functions were calculated (Fig. 6). It can be seen from

SEPULVEDA er al. : ANALYSIS OF CARDIAC DEFIBRILLATION

359

U

0

50 LL

0 Z W

U

25

a P6 .

(b)

7

0

,

,

,

,

1

~

1

1

I1

I

I

,

,

,

,

,

,

,

,

,

50 100 CURRENT DENSITY, r n A / c r n 2

,

,

/

150

Fig. 6. (a) Six different positions of the distal electrode for configuration C-C. The dark square is the reference position in Fig. 3b. (b) The cumulative current distribution functlon for the six positions of the distal electrode.

Fig. 6 that when the distal electrode is in positions 2, 3, and 6 (farther away from the septal region) there is a decrease of the current density in the regions of low current density (below 50 mA/cm2). The calculations (Table 11) suggest that the current density can change by 10-20% in the regions of low current density for I cm displacements of the catheter. These changes may have greater impact in the voltage defibrillation thresholds since experimental evidence [13] indicates that the low current density regions are the ones where fibrillation can be reinitiated. Then, it is possible to conclude that the movement of the right ventricular electrode up and toward the right ventricular free wall causes a decrease in the current density in the regions of low current density, which would require an increase in the defibrillation energy compared to the reference position.

TABLE 111 SUMMARY OF CALCULATIONS FOR DIFFERENT SIZESOF THE SUBCUTANEOUS A N D EPICARDIAL PATCHES I N SP-C-C A N D EP-C-C ELECTRODE CONFIGURATIONS Current Given by the Patch Total Current (amps)

Amps

2.62 2.56 2.64 2.69

0.41 0.34 0.47 0.54

2.80 2.62 2.87 2.90

1.01 36.1 0.74 28.2 1.18 41.1 1.27 43.8

%

Current Density (rnA/cm2) Min

Max

Subcutaneous Patch (SP-C-C)

s s*

0.5 times S S 1.5 times S S 2.0 times S S Epicardial Patch (EP-C-C)

s s*

0.5 times S S 1.5 times S S 2.0 times S S

15.7 15.5 298 13.3 16.0 291 17.8 14.3 303 20.0 13.7 309 5.2 6.5 2.4

1.9

656 512 634 628

*Standard size.

Sensitivity to Subcutaneous and Epicardial Patch Size Since it has been shown that it is easier to defibrillate flowing through the blood in the right heart is essentially the heart using larger epicardial patches, the configuration the same for all three cases (Table 111). Fig. 8 shows the similar calculation for variations in utilizing a two-electrode transvenous catheter together with an subcutaneous patch electrode (SP-C-C) was ana- epicardial patch size in configuration EP-C-C, with lyzed for patches 0.5, 1.5, and 2.0 times the size of the patches of 0.5, 1.5, and 2.0 times the size of the original. original. Fig. 3(d) shows the isopotential contours for the Fig. 3(c) shows the isopotential contours for the standard standard patch. Fig. 7(a) depicts the isopotential contours patch, while Fig. 8(a) is for the largest patch. Fig. 8(b) for a patch twice standard size; Fig. 7(b) shows the cu- shows the cumulative current distribution function for the mulative current distribution functions for all four patch four sizes. It is clear from Table I11 that the size of the sizes. The same voltage (425 V) was applied in all three epicardial patch affects appreciably the current distribucases. Elren though there is a small change in the current tion through the myocardium, most significantly in rethrough the apical left ventricular wall, the current re- gions of the basal septum and the basilar portion of the mains essentially the same in the septum and in the basilar left ventricular wall. Comparison of the cumulative curparts of the left ventricular wall. The amount of current rent distributions in Figs. 7(b) and 8(b) suggests that patch

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 37. NO. 4. APRIL 1990

360

100

200

300

CURRENT DENSITY, r n A / c r n P Fig. 7 . (a) Isopotential contours for a subcutaneous patch twice the size of that in SP-C-C in Fig. 3(c). (b) The cumulative current distribution for the four sizes of the subcutaneous patch.

0

100 200 CURRENT DENSITY, rnA/crn2

300

Fig. 8. (a) Isopotential contours for an epicardial patch 2.0 times the size of the patch for configuration EP-C-C in Fig. 3(d). (b) The cumulative current distribution for the four sizes of the epicardial patch.

electrode size is important when attached to the epicardium, but not when located in a subcutaneous precordial position. Kallok et al. [25] performed a series of animal experiments to evaluate the contribution of patch size for a comparable orthogonal configuration except that a skin electrode and sequential pulses were utilized rather than a subcutaneous electrode and single pulses. These investigators found that the defibrillation energy required with skin electrodes of 48 cm2, 109 cm2, and 172 cm2 were similar. Animal data are not available to substantiate the

prediction that the size of a patch electrode on the epicardium is important, but results of human studies [7] indicate that larger patches on the heart are associated with lower defibrillation energy requirements than are small patches.

Sensitivity to Conductivity Variation The resistivity of living tissues is not a constant, readily-determined quantity, but rather one whose value depends on many factors and is often reported in the litera-

SEPULVEDA

er

al. : ANALYSIS OF CARDIAC DEFIBRILLATION

361 1oc

Nomlnal : 500 ohms-cm Low : 300 ohms-crn Hlgh : 1000 ohms-cm

---- .. . -

1

Nomlnal : 135 ohms-cm Low : 70 ohms-crn High : ZOO ohms-cm

\'\

7:

SP-c

5C

25 ,

-

. . .

.

. .

.

... . . ~

..

.

.

.

.

.

---- ...-

.

100 200 CURRENT DENSIN. mA/cml

300

0

,

,

.

.

,\;,

.-,

. .

,

100

..

,

,

,

,

.

,

,

,

200

300

200

300

(b)

(a)

100 200 CURRENT OENSIPI. mA/em2

0

500

0

too

CURRENT DENSITY. rnA/cmZ

(d)

(C) ioa

S %

\' 76

A

-

; g

:. :

Nomlnal : 500 ohms-cm Low : 300 ohms-crn High : 1000 ohms-crn

---- ...-

: 200 ohms-cm

-

. . . -

\ \.

SP-c-c

sc

b c w

E

25

L

'0 CURRENT DENSITY. rnA/sm2

(e)

100 200 CURRCNT DENSITY, mA/crn2

300

(0

Fig. 9. Cumulative current distribution for configurations SP-C, C-C, and SP-C-C for: cardiac resistivity variation 300-1000 f? . cm [(a), (c), and (e)] and for blood resistivity variation 70-200 f? . cm [(b), (d), and (f)]. respectively.

ture as a range of values. To determine the effects of resistivity on the current distribution, we analyzed the four electrode configurations, using lower and upper bounds for the resistivities of 300-1000 fl cm for cardiac tissue; 70-200 fl cm for blood; 300-1000 fl cm for thoracic muscle; and 1500-2000 fl * cm for lung tissue, The results are summarized in Table IV. Fig. 9(a) shows the cumulative current density distribution functions for configuration SP-C for average and extreme resistivities of cardiac tissue. Similar qualitative results were found for changes in resistivity values for the thoracic muscle and the lung tissues, but cardiac resistivity has the most marked effect. For this particular electrode configuration, the lower the resistivity of a given

-

tissue the higher the current density throughout all the myocardium. Fig. 9(b) displays the. cumulative current distribution functions for average and extreme resistivities of blood. By reducing the resistivity of the blood, the current density decreases in regions of low current density, while it increases in regions of high current density. Fig. 9(c) shows the cumulative current distribution function for configuration C-C for the average and extreme resistivities of cardiac tissue. Increasing the resistivity of cardiac tissue decreases the current through the myocardium. In contrast to this and to SP-C, changes in thoracic muscle resistivity and lung resistivity do not affect the current density flowing through the myocardium. From Fig. 9(d) it is apparent that the changes in blood

362

IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 37. NO. 4. APRIL 1990

TABLE IV OF VARIATIONS I N CARDIAC A N D BLOOD THEPREDICTED EFFECTS ON DEFIBRILLATION THRESHOLD BASEDUPONA N ASSUMPTION RESISTIVITIES THAT 80% OF THE HEART MUSTHAVEA CURRENT DENSITY OF 35 rnA/crn* Threshold Voltage, (volts) Electrode configuration Tissue Cardiac

Blood

Resistivity ( Q . crn)

SP-C

C-C

SP-C-C

EP-C-C

300 500 (nominal) 1000

387 570 746

312 520 1205

278 425 665

273 3 90 606

70 135 (nominal) 200

488 570 651

520 520 600

425 425 463

425 425 425

resistivity have little effect on the low current density regions, but as the resistivity of blood decreases the current density increases in the regions of high current. Fig. 9(e) gives the cumulative current distribution functions for electrode configuration SP-C-C for average and extreme resistivities of cardiac tissue, with lower cardiac resistivity resulting in higher current density through the myocardium. However, variations in thoracic muscle and lung resistivities have essentially no effect on the current density distribution. Changes in blood resistivity, Fig. 9(f), affect only the current density in regions of high current density. Similar qualitative effects to those of configuration SP-C-C were found for configuration EP-C-C.

DISCUSSION To examine myocardial defibrillation current distributions, we have used an approximate solution that allows us to predict how the defibrillation current is distributed through a two-dimensional model of the myocardium and surrounding structure. If we knew the local current density threshold required for inexcitability , we would be able to use this model to determine immediately, for a given electrode size and defibrillation voltage, the fraction of the heart that is rendered inexcitable (or not reexcitable) for that pulse. It has been postulated that if that fraction exceeds a certain critical fraction, the heart will be successfully defibrillated; if the fraction is too small, defibrillation will be unsuccessful. One problem with prediction of defibrillation thresholds is the determination of both the critical fraction and the local current density threshold. Since we know neither of these values, if indeed they exist as physiologically meaningful quantities, we used canine data to provide threshold voltages for our numerical simulation. In turn, the analysis of defibrillation current distributions at these threshold voltages for the several electrode configurations may provide us with new information regarding both values. If the critical mass hypothesis is valid, the cumulative current distribution is then a valuable tool for predicting defibrillation threshold. A horizontal line at the critical mass and a vertical one at the threshold current density would identify a single point in the graph. We hypothesize that if the line describing the cumulative current distribution passes above (and to the right of) this point, defibrillation would be successful since a larger than critical fraction of tissue would have the threshold current density

required for defibrillation. If it passes below (and to the left), defibrillation would be unsuccessful. When the cumulative distributions for the threshold defibrillation pulses for various configuration are computed, the cumulative distribution curves should all cross at the point determined by the threshold current density and the critical fraction. If a particular voltage produces an cumulative current distribution that passes to the left of the critical fraction/threshold point, it is obvious that a higher voltage is required. Since the conductors are assumed to be linear, increasing the voltage results in a proportional scaling of the horizontal axis and a uniform stretching of the distribution to the right. This allows us to predict what voltage is required for any configuration. The isopotentials in Fig. 3, the current lines in Fig. 4 and the power distribution (no shown) showed marked differences in the distributions of voltages, currents and power dissipation in the myocardium. However, they all had one significant factor in common: each one resulted in a 90% probability of defibrillation. Hence, if the critical mass hypothesis is valid, each distribution should have the same fraction of myocardium with a current density greater than some threshold value. Examination of Fig. 5 shows that each of the four cumulative current distributions do have one feature in common: they all pass near the point corresponding to 80% of the heart having a current density equal or above 35 mA/cm2. While our simulation involves a two-dimensional representation of a three-dimensional heart, these results suggest the existence of a critical mass and a threshold current density. Failure of the curves to cross exactly at a single point could be due to our two-dimensional approximation, or might indicate that different regions of the heart have different local thresholds. While 35 mA/cm2 is significantly higher than the minimum current densities observed by Chen et al. [13], this difference simply reflects the fact that the critical fraction is on the order of 80%. Were the critical fraction loo%, the minimum observed current density would in fact be the threshold value. For critical fractions less than 100% the minimum gradients observed may be substantially less than the threshold value. The critical mass and the threshold current density suggested by Fig. 5 support the hypothesis that the success or failure of defibrillation is determined by the size of the regions of low current density. This implies that alteration of system parameters that affect the low current density regions can significantly alter defibrillation threshold. For example, we can now reexamine Figs. 6-9 in terms of the changes in defibrillation threshold voltage. The variation in distal electrode position in Fig. 6 would cause the defibrillation threshold to range from 500 to 597 V. In Fig. 8, the 1.5 and 2.0 times normal subcutaneous patches would have reduced thresholds of 335 and 336 V, respectively, as compared to the original 425 V for SP-C-C, while the epicardial patches in Fig. 9 would have thresholds of 204 and 163 V instead of the 390 V for EP-C-C. While the cumulative current distributions in Fig. 9, for example appear simply to shift to the left and right as the cardiac resistivity is increased or decreased, the relative changes in myocardial current density at the 80% point

SEPULVEDA el al.: ANALYSIS OF CARDIAC DEFIBRILLATION

363

are quite significant. It may be possible to use this type proach we have chosen is that the finite element technique of analysis in experiments that vary in blood or cardiac has the capability of modeling the heart to any desired resistivities and thereby provide another estimate of the level of complexity, The concept of the cumulative current distribution critical fraction and the threshold current density. For the electrode configurations analyzed, cardiac re- function (Fig. 5 ) can be used as a tool for the comparison sistivity is a major factor that can modify substantially the of electrode configurations and it suggests that for all the current distribution through the myocardium. Thoracic electrode configurations studied, defibrillation is associmuscle and lung resistivities affect the myocardial current ated with low current densities over large myocardial distribution only in configuration SP-C. Blood resistivity areas. This result seems to indicate that if the hypothesis changes have little effect over the current distribution in of the “critical mass” for defibrillation is valid and if the the areas of low current density for configuration C-C, cumulative current distributions intersect at the critical SP-C-C, and EP-C-C. However, in configuration SP-C, fraction and the threshold current density, then the critical the lower the blood resistivity, the lower the current den- fraction is large and the threshold current is low. Whether sity through the myocardium in the areas of low current this intersection of the curves indicates the threshold for density. In the high current density areas, the lower the inactivation or that for preventing reexcitation is not yet blood resistivity, the higher the current density through known. the myocardial region in all electrode configurations. Since cardiac resistivity is predicted to be an important APPENDIX factor for ventricular defibrillation, the accuracy of the INTRODUCTION cardiac tissue resistivity measurements from the data of In order to evaluate four electrode configurations for Geddes and Baker [24] and Tacker (personal communi- internal defibrillation two series of experiments were percation) utilized in this model is a possible limiting factor. formed in 18 dogs. In series I, SP-C, C-C, and SP-C-C Since these measurements were obtained from isolated were compared in 13 dogs. In series 11, five dogs were myocardial tissue during sinus rhythm, it is possible that studied twice; C-C and SP-C-C were compared on one these values are inaccurate. Moreover, it is likely that in- day, and C-C and EP-C-C were compared one week later. farcted, ischemic, or fibrillating myocardium has a different tissue resistivity, which could affect the current denSURGICAL PROTOCOL sity distributions greatly. Such studies should be Following intravenous pentobarbital anesthesia (25 performed in the future, and the results applied to the simulation study. Furthermore, the extreme sensitivity of the mg /kg), tracheal intubation for mechanical ventilation, cumulative current distribution to myocardial resistivity and insertion of a femoral arterial catheter for blood pressuggests that the observed anisotropy in myocardial resis- sure monitoring and a venous catheter for intravenous intivity could play a major role. We are presently extending fusion, the internal cardiac defibrillating electrodes were placed. Actual electrode systems used in the experiments the model to include the effects of anisotropy. The two-dimensional model has allowed us to analyze consisted of a transvenous two-electrode catheter having in detail some of the determinants of defibrillation and it a 10 cm’ proximal defibrillating electrode constructed of has provided us with new tools for the analysis and com- coiled titanium and a 5 cm2 distal defibrillating electrode parison of different electrode configurations. However, located 1 cm from the catheter tip and constructed of silother important factors that can contribute to a better un- ver, with a 10 cm interelectrode distance. An additional derstanding of defibrillation have been ignored. For ex- electrode pair was usually located at the catheter tip for ample, the anisotropic characteristics of cardiac tissue endocardial recording or stimulation. The 14 cm2 patch may play a significant role in the distribution of current electrode was constructed of wire mesh woven into dacthrough the myocardium. The current distribution result- ron. The transvenous catheter was inserted via the right ing from the applied stimulus could change due to the jugular vein and advanced to the right ventricular apex nonlinear characteristics of the biological tissues. The bi- under fluoroscopy. The patch electrode was sutured to the syncytial nature of cardiac tissue may greatly influence subcutaneous precordial tissue for SP-C-C. For EP-C-C, the current flowing through myocardial tissue. Further- a left thoracotomy was performed and the patch sutured more, a two-dimensional representation of what is in real- to the anterolateral epicardial surface of the left ventricle. ity a three-dimensional structure is too coarse an approx- Ventricular fibrillation was induced from the catheter tip imation, and thus quantitative interpretation of data will using 60 Hz current. Internal defibrillation was accomrequire the extension of the model to three dimensions. plished using an ECD unit, which delivered 1-40 J with a single truncated exponential waveform of 60% tilt and Each of the limitations will be addressed in the future. variable pulse duration (approximately 6.5 ms when deCONCLUSION livered into a 50 il load). The finite element-based numerical model is a powerful OF DEFIBRILLATION ENERGY MEASUREMENT tool for the analysis of defibrillation currents from differTHRESHOLDS ent electrode configurations. The significance of this parThe method of Davy et al. [26] was utilized. Briefly, ticular analysis is that it demonstrates how finite element calculations can extend our understanding of the electrical this method includes the estimation of the defibrillation determinants of defibrillation; the significance of the ap- threshold, and the selection of five energies ranging from

3 64

IEEE TRANSACTlONS ON BIOMEDICAL ENGINEERING, VOL. 31. NO. 4. APRIL 1990

8 J below and above the estimate for each electrode configuration. Each energy level selected was delivered in a randomized order five times. The defibrillation test energy was delivered after 10 s of fibrillation, and only the first attempt was analyzed. If the test energy was unsuccessful, transthoracic energy of up to 320 J was delivered. Test energy determinations were separated by 3 min.

100

m

i

W

.-

n 50

e-SP-C

c-c

A-

STATISTICAL ANALYSIS OF ENERGY The relationship of energy to the percent of successful defibrillation tests was analyzed using logistic regression to derive curves of best fit, as shown in Fig. 10, and to determine the energy level associated with 90% successful defibrillation (ED90). When energies tested at or below 40 J were not consistently effective, the logistic regression analysis would predict 90 % effective energies of values greater than 40 J and these values were analyzed. However, when the maximal pulse energy of 40 J was consistently ineffective on multiple determinations, the ED90 could not be calculated and therefore, data were not available for the determination of the mean energy. The absence of these data points would tend to minimize energy differences due to electrode configuration. Statistical analysis of the defibrillation energy data was performed by paired and unpaired Student’s t-test and analysis of variance when more than two electrode configurations were compared. The results are shown in Table V .

8 0

Vavg = 1/T

1

,U

( t ) dt.

ACKNOWLEDGMENT We gratefully acknowledge the technical assistance of Dr. E. Gerhardt and R. Rames with the animal studies,

16 24 ENERGY (JOULES)

8

32

40

Fig. 10. Relationship of energy to percent successful defibrillation attempts from one experiment comparing SP-C, C-C, and SP-C-C.

TABLE V MEASURED DEFIBRILLATION ENERGY THRESHOLDS FOR FOUR ELECTRODE CONFIGURATIONS Series I

ED 90 (joules) Dog #

SP-c

c-c

1 2 3 4 5 6 7

36

19 7

+ + + + + + + +

22 35 34 34 40 38

46 f 12

33 f 13

22 f8*

+

+

62 37

9 10 11 12 13 Mean

SD

~~

11 6 30 15 23 36 21 25 24 28 30 16 20

50

Heart Weight (grams)

SP-c-c ~~

8

RESULTS OF DEFIBRILLATION ENERGY TESTING Energy requirements were significantly lowered with the addition of a precordial patch to the catheter system. The ED90 for SP-C-C was lower than SP-C or C-C in the first series of dogs, and SP-C was rarely effective at all with 40 J (Table V). SP-C was effective in the first dogs because the dogs were substantially smaller in size. Larger dogs were subsequently used because the proximal catheter electrode was not all within the thorax in dogs less than 18 kg. In the second series of experiments EP-C-C was better than SP-C-C but this did not reach statistical significance. There was no statistically significant difference in the C-C ED90 on the two different test days. However, intraindividual differences did occur, and this observation was evaluated further with numerical analysis of catheter position. When the ED90 values were normalized for the heart weight of each dog, the differences between electrode configurations were unchanged. The ED90 values for series I and I1 were pooled and the mean voltage values calculated for the truncated exponential waveform of 60% tilt and 6.5 ms of duration, using the formula

SP-C-C

23 31 54

52

125 176 244 141 164 187 131 133 178 149 163 123 181

*p = 0.002 (ANOVA) +No data because energy required to defibrillate was always greater than 40 J . Series I1

ED 90 (joules) Study Phase A

Study Phase B

Dog #

C-C

SP-C-C

C-C

EP-C--C

Heart Weight (grams)

14 15 16 17 18

45 56 45 36 41

31 69 44 17 31

30 54 41 43 56

6 24 31 16 30

141 2 19 192 154 166

45 f 7

38 f 19

43 f 14

21 f IO*

174 f 31

Mean

SD

*p = ,0056 compared to C-C (paired student’s t )

the patience of B. Harlow with the preparation of this manuscript, and the comments of Dr. R. Ideker and L. Wikswo. We are indebted to D. Humphrey, M . A. Wikswo, and L. Li for preparing the illustrations. Computing time was provided by the College of Arts and Science, Vanderbilt University.

SEPULVEDA et al. : ANALYSIS O F CARDIAC DEFIBRILLATION

REFERENCES J. C. Schuder, H . Stoeckle, J . A. West, and P. Y . Keskar, “Relationship between electrode geometry and effectiveness of ventricular defibrillation in the dog with catheter having one electrode in right ventricle and other electrode in superior vena cava, or external jugular vein, or both,” Cardiovasc. Res., vol. 7, pp. 629-637, 1973. M. Mirowski, M. M. Mower, A. Langer, M. S . Heilman, and J. Shreibman, “A chronically implanted system for automatic defibrillation in active conscious dogs,” Circ., vol. 70. no. 11, p. 370, 1978. G. M. Deeb, B. P. Griffith, M. E. Thompson, A. Langer, M. S . Heilman, and R. L. Hardesty, “Lead systems for internal ventricular defibrillation,” Circ., vol. 64, pp. 242-245, 1981. J . C . Schuder, H. Stoeckle, J. H . Gold. J . A. West, and J. A. Holland, “Ventricular defibrillation in the dog using implanted and partially implanted electrode systems,” Amer. J . Cardiol., vol. 33. pp, 243-247, 1974. J. D. Bourland, W . A. Tacker, J. L. Wessale, J . E. Graf, and M. J . Kallok, “Reduction of defibrillation threshold by using sequential pulses applied through multiple electrodes: A preliminary report,” in Proc. AAMI. Annu. Meet., 1984. D. L. Jones, G. J. Klein, and M. J . Kallok, “Improved internal defibrillation with twin pulse sequential energy delivery to different lead orientations in pigs,” Amer. J . Cardiol., vol. 5 5 , pp. 821-825, 1985. P. J. Troup, P. D. Chapman. G. N. Olinger, and L. H. Kleinman, “The implantable defibrillator: Relation of defibrillating lead configurations and clinical variables to defibrillation threshold,” JACC, vol. 6, pp. 1315-1321, 1984. D. S . Echt, K. Armstrong. P. Schmidt, P. Oyer, B. S . Edward. and R. A. Winkle, “Clinical experience, complications, and survival in 70 patients with the automatic implantable cardioverteridefibrillator,” Circ., vol. 2, pp. 289-296, 1985. J . A. Freeman and C . Nicholson, “Experimental optimization of the current source-density technique: Application to the anuran cerebellum,” J . Neuroph., vol. 38, no. 11, pp. 369-382, 1975. T. Swiontek and A. Sances, Jr., “Experimental current density measurements,” in Neural Stimulation, J . Myklebust, J. Cusik, A. Sances, and L. Sanford, Eds. Boca Raton, FL: CRC Press, 1985, vol. I . rnn. 47-68. r W A Tacker and L A Geddes, Electrical Defrhrillatron Boca Raton, FL CRC Press, 1980 L. A. Geddes, M J . Niebauer, C F Babbs, and J D Bourland, “Fundamental criteria underlying the efficacy and safety of defibrillating current waveforms,” Med Biol Eng Comp , vol 23, pp. 122130, 1985 [I31 P S Chen, P D Wolf, F J Claydon, E G Dixon, H J Vidaillet, N D Danieley, T C Pilkington, and R E Ideker, “The potential & gradient field created by epicardial defibrillation electrodes in dogs,” Circ., vol 74, pp 626-636, 1986 [ 141 E T Choi and N V Thakor, “Defibrillation electric fields An experimental and computer modeling study,” in Proc. 9th IEEE Frontiers Eng. Comput. Health Care, 1987, pp. 683-686. A. M. Doian, B. M. Horacek, and P. M. Rautaharju, “Evaluation of cardiac defibrillation using a computer model of the thorax,” Med. Instrument., vol. 12, pp. 53-54, 1978. J . Ben Fahy, Y. Kim, and A. Ananthaswamy, “Optimal electrode configurations for external cardiac pacing and defibrillation: An inhomogeneous study,” IEEE Trans. Biomed. Eng., vol. BME-34, pp. 743-748, 1987. R . Plonsey and R. G . Barr, “Effect of microscopic and macroscopic discontinuities on the response of cardiac tissue to defibrillating (stimulating) currents,” Med. B i d . Eng. Comp., vol. 24, pp. 130-136, 1986. D. P. Zipes, J . J. Heger, W. M. Miles, Y. Mohamed, J. W. Brown, R. Spielman, and E. N. Prystowsky, “Early experience with an implantable cardioverter,” New Eng. J . Med., vol. 3 11, pp. 485-490, 1984. S . Weidmann. “Electrical constants of trabecular muscle from mammalian heart,” J . Physiol., vol. 210, pp. 1041-1054. 1970. 0. C. Zienkiewicz, The Finite Element Method. New York: McGraw-Hill, 1977. K . H . Huebner, Finite Element Method for Engineers. New York: Wiley, 1975. E. Hinton and D. J. R. Owen, An Introduction to Finite Element Compurations. Swansea, U . K.: Pineridge, 1979.

365 [23] J. S . Rankin, P. A. McHale, C. E. Arentzen, D. Ling, J. C. Greenfield, and R. W. Anderson. “The three-dimensional dynamic geometry of the left ventricle in the concious dog,” Circ. Res., vol. 39, pp. 305-313, 1976. [24] L. A. Geddes and L. E. Baker, “The specific resistance of biological materials: A compendium for the biomedical engineer and physiologist,” Med. Biol. Eng. Comp., vol. 5, pp. 271-293, 1967. (251 M. J. Kallock, D . L. Jones, and G. J . Kline, “Sequential pulse defibrillation using a catheter and skin electrodes,” J . Amer. Col/. Curdiol., vol. 7 , p. 14A, 1986. [26] J. M. Davy, E. Fain, P. Dorian, and R. A. Winkle, “Is there a defibrillation ‘threshold’?,” Circularion, vol. 70, no. 11, p. 40, 1984.

Nore Added in Proof: The computer model described in [ 141 has been examined in more detail by K. P. Kothiyal, B. Shanakar, L. J. Fogelson, and N. Y. Thakor, “Three-dimensional computer model of electric fields in internal defibrillation,” Proc. IEEE, vol. 76, pp. 720-730, 1988. Nestor G . Sepulveda was born in Barbosa, Santander, Colombia, in 1946. He received the B.S.E.E. degree in 1970 from the Universidad Distrital, Bogota, and the M.S. and Ph.D. degrees in biomedical engineering from Tulane University, New Orleans, LA, in 1981 and 1984, respectively. He has been an Assistant Professor of Electronics Engineering at the Universidad de Antioquia and Universidad Pontificia in Medellin, Colombia, and an Assistant Professor and then Associate Professor of Electrical Engineering at the Universidad Tecnologica in Pereira, Colombia. Since 1984 he has been a Research Assistant Professor of Physics in the Department of Physics and Astronomy at Vanderbilt University, Nashville, TN. His research interests include the use of finite element and other mathematical modeling techniques to study the electrical properties of biological systems, particularly the response of cardiac tissue to applied electrical currents.

1

John P. Wikswo, Jr. (S’75-M’75) was born in Lynchburg, VA, in 1949 He received the B A degree in physics from the University of Virginia, Charlottesville. in 1970, and the M S and Ph D degrees in physics from Stanford University, Stanford, CA, in 1973 and 1975, respectively He was a Research Fellow in Cardiology at the Stanford University School of Medicine from 1975 to 1977, where he continued his work on determining the relationship of the electric and magnetic fields of the heart and developing instrumentation and analysis techniques for magnetocardiography. He joined the faculty of Vanderbilt University, Nashville, T N , in 1977, where he is now a Professor of Physics. His current research is directed towards using electric and magnetic measurements and electromagnetic theory for studying the propagation of electrical activity in nerve and muscle cells and for nondestructive testing. Debra S. Echt was born in Cleveland, OH, in 1951 She received the B S E degree in biomedical engineering from Purdue University in 1973, and the M.D. degree from Case Western Reserve University, Cleveland, OH, in 1977 After residencies in Internal Medicine at Case Western Reserve and Cardiology at Stanford University, Stanford, CA, she served as a Physician Specialist and Research Associate in Medicine and Cardiology at Stanford Since 1984, she has been an Assistant Professor of Medicine, Cardiology, at the Vanderbilt University School of Medicine, where she is also the Director of both the Cardiac Electrophysiology Laboratory and the Heart Station She is a Diplomat in the American Board of Internal Medicine with a subspecialty of cardiovascular medicine Her research interests are in clinical cardiac electrophysiology, arrhythmias, and defibnllation She has conducted extensive research on the implantable cardioverter/defibrillator.