Modelling

Optimisation of transcutaneous cardiac pacing by three-dimensional finite

element modelling of the human thorax

D. Panescu 1 J . G . Webster 2 W . J . Tompk ins 2 R . A . Stratbucker 3

EP Technologies Inc., 350 Potrero Avenue, Sunni/ate CA 94086, USA 2 Department of Electrical and Computer Engineering, University of Wisconsin, 1415 Johnson Drive,

Madison WI 53706, USA a 7125 Country Club Road, Omaha NE 68152, USA

Abs t rac t - -The goal of the study is to determine by finite element analysis (FE) the optimal electrode placement, size and electrolyte resistivity that minimise the pain experienced by patients during successful transcutsneous cardiac pacing (TCP). The three-dimensional FE model generated for this purpose has 55 388 nodes, 50 913 hexahedral elements and simulated 16 different organs and tissues, as well as the properties of the electrolyte. The model uses a non-uniform mesh with an average spatial resolution of 0.8 cm in all three dimensions. To validate this model, the voltage across 3 cm 2 Ag-AgCI electrodes is measured when currents of 5 mA at 50 kHz are injected into a subject's thorax through the same electrodes. For the same electrode placements and sizes and the same injected current, the FE analysis produced results in good agreement with the experimental data. The optimisation analysis tested seven different electrode placements, five different electrode sizes and six different electrolyte resistivities. The analysis indicates that the anterior- posterior electrode placement, electrode sizes of about 90 c m 2 and electrolytes with resistivity of about 800 ~ �9 cm yield the most uniform current distribution through the skin, thus having the best chances to minimise the pain delivered to the patient during successful TCP. The anterior-anterior electrode placement is the second most efficient.

Keywords--Electrodes, Finite element models, Pacing, Resistivity, Thorax

Med. & Biol. Eng. & Comput., 1995, 33, 769-775

.... j

1 Introduction

IN EMERGENCY situations, transcutaneous cardiac pacing (TCP) is finding increasing use (ZOLL, 1952; BC~<J~, 1989; ZOLL MEDICAL CORPOP.ATtON, 1993). Recently, the American Heart Association (AHA) detenv, ined TCP to be the initial pacing method of choice in emergency cardiac care because of the speed with which it can be instituted and because it is the least invasive pacing technique available (ZOLL MEDICM. r 1993). The AMA treatment algorithms recommend TCP particularly for asystote and symptomatic bradycardia (ZOLL MEDICAL CORPORATION, 1993). The major problem in design- ing and using TCP is to capture the heart with minimal stimulation of other tissues in the chest wail, such as the skin and the intercostal muscles. The current density is usually greater in the skin than in the heart walt. In addition, the ehronaxies of the skin receptors and intercostal muscles are shorter than that of the cache muscle. Thus, the pain threshold is reached before the cardiac pacing threshold (GEDDES et aL, I985; GEDD~S and BAKER, 1989). Corse-

Correspondence should be addressed to d. G. Webster First received 11 July 1994 and in final form 22 March 1995,

�9 IFMBE~ 1995

quently, TCP is usually associated with an uncomfortable sensation of pain. The optimisation objective is to minimise the pain and still be able to successfully capture the heart.

There are several possible ways to improve the efficacy of TCP:

(i) find the optimal stimulus waveshapes. (fi) optimally design the electrodes. (hi) find the optimal electrode placement, size and the optimal electrolyte conductivity that minimise the ratio between the maximal current densities in the skin and in the heart wall, thereby permitting pacing currents which are tess paiaful but still able to capture the heart.

The first traaseutaneous cardiac pacemakers used rectangular waveshapes with pulse duration of less than 10 ms (ZOLL, 1952). More recent studies, that optimised TCP by method (i) showed that it was more comfortable to use durations of 20- .40 ms and different waveshapes (BoCY, A, 1989; GF_.DDES and BAKER, 1989).

Using method (ii), Reddy and Webster described the design of uniform current density electrodes which yielded tess pain during TCP (REDDu and WEBSTER, 1984). For such eIectrodes, the electrolyte resistivity increases from the electrode centre to its edge.

Medical & Biological Engineering & Computing November 1995 769

Our current work optimises TCP by method (iii). It uses finite element (FE) analysis to assess the effects of electrode placement, size and electrolyte resistivity on pacing efficacy,

Previous studies used FE models (FEM) of the human thorax to study cardiac pacing or defibrillation (PANESCU et al., 1994a; FAHY et al., 1987; BLILIE et aL, 1992). Fahy et aL, studied the optimal electrode configurations for external cardiac pacing and defibrillation. They reported that the optimal pacing position places the cathode directly over the heart and the anode on the left lateral chest wall. They were mostly concerned with the sensitivity of surface current densities to the accuracy of internal organ modelling. The importance of the FEM validation was discussed by Ahmed et al. (AHMED et aL, 1991). Their group also reported the construction of a large FEM of the human thorax (BLILIE et al., 1992). However, final results were not available for the optimisation of the defibrillation nor the validation of the FEM. Schmidt presented techniques for the automatic genera- tion of non-uniform FE meshes for electrophysiological modelling (SCHMmT, 1993; PmrdNGTON et al., 1993).

Some of these studies had the limitation of using two- dimensional FE analysis which could not model the currents flowing out of the mesh plane. In addition, only a few FE studies accounted for the mosaic electrical structure of the skin (PANESCU et aL, 1994b).

We have developed a 3-D FEM with a non-uniform mesh that simulates 16 different organs and tissues as well as the properties of the electrolyte. In the presence of higher stimulating voltages the skin breaks down and the current is funnelled through one or more randomly distributed locations under the electrodes (PANESCU et al., t993). Therefore, to estimate more accurately the current density in the skin, our FEM simulates its mosaic electrical structure.

2 Methods and model

This finite element study was performed on a super- computer,* using INGRID (CHgtSTAN and DOVEY, 1992) to generate the 3-]3 mesh, TOPAZ3D as a FE solver and TAURUS as a post-processor of the results (BROWN, 1984). TOPAZ3D is a FE code written for heat transfer applications. In order to use it for electric field problems, voltage was substituted for temperature, current density for heat flux and electric conductivity for thermal conductivity. To select the most appropriate method of solving the linear systems required by the FE analysis, a comparison was performed between two iterative methods CYotr~G, 1971; TONG and ROSSETTOS, 1977) and a direct method (SHAI'mO, 1985; DUFF et al., 1990). The two FEMs used for this comparison simulated the human thorax. Model 1 comprised 54 108 nodes, 49 809 hexahedral elements and 17 regions of different eonduetivities. Model 2 had 16 875 nodes, 14 784 hexahedral elements and 15 regions of different conductivities. Table 1 summarizes the results. The numerical accuracy of all these methods, compared with analytical solutions for inhomogeneous linear models with 19 758 nodes, is 0.1%. The diagonal scaled conjugate gradient method was chosen because it required the smallest computa- tion time and the smallest memory space.

To create the 3-D model, 11 cross-seetiorls of the human thorax were used and ear.ordinates of about 100 points/cross- section were measured from figures published elsewhere (EYCLESHYMER and SCHOEMAKER, 1970; LEDLEY et al., 1977). The mesh was generated by interpolating these data with second-order polynomials. The final model had 55 388 nodes, 50 913 hexahedml elements and contained 16 organs

*Cray Y-MP C-90, National Energy Research Supercomputing Center

Table 1 Computation time and the memory request for different methods of solving linear systems

method m o b i l mo~12

CPU memory, CPU memory, time, s Mbyte time, s Mbyte

diagonal scaled 114 12 31 3.6 conjugate gradient

incomplete Cholesky 922 19.6 112 6 conjugate gradient

direct method 1200 > 250 142 54

and tissues, in addition to the region which modelled the electrolyte. The regions of this FEM are

(i) electrolyte. (ii) skin. (iii) chest wall. (iv) intercostal muscles, modelled as an anistropic region. (v) ribs and backbone. (vi) lungs. (vii) heart muscle, modelled as an anisotropic region. (viii) blood. (ix) oesophagus. (x) diaphragm. (xi) kidneys. (xii) liver. (xfii) stomach and intestines. (xiv) fat. (xv) aorta. (xvi) vena cava. (xvii) pulmonary veins and arteries.

The model includes the thorax starting approximately 1 cm inferior to the clavicles and the upper third of the abdomen. The mesh was non-uniform and had an average spatial resolution of 0.8 cm in all three dimensions. Owing to the resolution of the mesh and because the model employed hexahedral elements, this analysis was limited to rectangular electrodes, as other shapes would have been inaccurately approximated. The model is about 23 em in height, 33 cm in width and 21 cm in depth. Fig. 1 shows different regions ofthe finite element model. Table 2 shows the resistivities of the organs and tissues which we compiled from several sources (GEDDES and BAKER, t967; ZHENG and WEBSTEg, 1984; RABBAT, 1990; PA~X~,~CU et aL, 1993, 1994c).

The pain associated with any transcutaneous stimulation is experienced when the skin breaks down at spots of low breakdown voltage (PaNESCU et aL, 1993, 1994b, c). Thus, it is necessary to reduce the chances of breakdown in order to increase the comfort during TCP. This can be achieved by increasing the uniformity of current density underneath the electrodes. These regions of low breakdown voltage are usually situated around the sweat ducts (GPdMh~S, 1984; PANESCU et aL 1993). To simulate this mosaic electrical structure of the skin, we randomly distributed regions of low breakdown voltage into the skin under the electrodes. As the oarrent flows less along the stratum eornetma (GRIMI~S, t984), we considered the skin to have the transversal conductivity higher than the longitudinal conductivity. For the broken-down regions of the skin the Wansversal conductivity was set to that corresponding to the dermis (PANESCU et at., 1994c). Based on the model presented previously (PAh'ESCU et al., 1994c), we chose 100-fold lower conductivity for the rest of the skin under the electrode. The longitudinal conductivity was set to that of unbroken skin (PANESCU et al., 1994c). The skin outside the outline of the electrode was an isotropic region with the conductivity equal to that of unbroken skin. The intercostal

770 Medical & Biological Engineering & Computing November 1995

Table 2 Conduetivities of the regions in the FEM

region conductivity resistivity, Sm -1 t2. era

electrolyte 10 10 skin outside electrodes 10 -5 107 skin broken down 10 -5, 0-5 107, 200

(~o~g, ~ ) skin under electrode, 10 -5 , 0.005 107 , 20000

not broken down

chest wall 0-05 2000 intercostal muscles 0-667, 0-05 150, 2000

ribs and backbone 0.00602 16600 lungs 0-083 1200 heart wall 0.5, 0.25 200, 400

blood 0.667 150 esophagus 0-25 400 diaphragm 0.25 400 kidneys O. 167 600 liver O- 167 600 stomach 0.167 600 fat 0.05 2000 aorta 0.68 147 eava 0.68 147 pulmonary vessels 0.667 150

muscles and the heart wall were also defined as anisotropic regions. Using local systems of co-ordinates, we specified their corresponding transversal and longitudinal conductivifies.

The model was tested against experiments performed on a human subject. Ideally, the simulated voltage distribution inside the thorax should match that measured during experi-

ments. Based on the uniqueness of the solution to V(trV~ = 0, for checking the accuracy of the simulation, it is enough to compare the voltage diswibution on the boundary of the domain (i.e. on the outer surface of the thorax). For this comparison, we used the locations of the praecordial leads because we were mostly interested in accurately modelling the region around the heart. Two 3 cm 2 Ag-AgC1 electrodes were placed at different locations chosen from the standard ECG praecordial lead placements, VI to V6 (PLONSEY, 1990). A sinusoidal current with an amplitude of 5 mA and a frequency of 50 kHz was applied to the subject's thorax, yielding a measured voltage across the same electrodes. Using the same placements and excitation, simulations were performed on the 3-D model, yielding the voltage across the electrode regions. On the region corresponding to the electrodes the normal current density was specified so that the total current applied into the FEM was 5 mA. The conductivity of the skin was that of the broken-down skin above because at 50 kHz the wansversal impedance of the skin is very low, due to its high capacitance, and the longitudinal current flow is almost non- existent, due to the constitution of the stratum comeum (GPdMN~S, 1984). Table 3 shows the results of the experiments compared with the results of the FE simulations. Although there are differences between the two groups of data, we concluded that the model performs satisfactorily and can be used to study the optimisation of TCE

A search was made of the electrode placement, size and the electrolyte conductivity that minimised the ratio between the average of the maximal current densities in skin at the regions of low breakdowa voltage and the maximal current density in the heart wall RI. Thus, minimising RI implies less excitation to the skin and therefore less pain delivered to the patient. The duration of the pacing pulses was considered to be 40 ms, permitting a steady-state linear FE analysis. At this duration,

Fig. I Some regions of the FEM used for TCP optimisation: (a) stdn and chest wall; (b) rib cage; (c) intercostal muscles; (d) heart; (e) lungs; (I9 aorta and vena cava; (g) diaphragm; (h) liver

Medical & Biological Engineering & Computing November 1995 771

Table 3 Comparison between ~xperirnental data and results of the Table 4 Ratio R j for each of the sm,en FE simulations related to the validation discussed in Section 2 tested electrode placements

electrode experiment, FE simulation, relative error, combination V V %

V1V2 8.72 9.47 + 8.6 V~V3 6-12 6-25 +2.12 VIV,~ 5.36 4.96 - 7.46 VzVs 5-38 4.34 - 19.33 VIV~ 5.40 5-12 -5.19

placement R t

I 1.25 2 1.5 3 1-98 4 2.33 5 2.38 6 22.66 7 8.75

the dependence on frequency of the electrical properties of the organs has negligible effects on the current density distribu- tion. Therefore, the data in Table 2 were considered frequency- independent. To capture the heart, the maXimal current density in the heart wall was always equal to the myocyte stimulation threshold, 20 m_A em -2 (SEPULVEDA et aL, 1990; KARLON et al., 1993). For the determination of the optimal placement, we considered a pair of 83 cm 2 square electrodes and simulated the following seven placements: the cathode at the cardiac apex, right above the diaphragm, and the anode at

(1) the right subscapular region; (2) the right frontal side of the chest, 3 cm below the clavicle; (3) the mid-axillary line 3 em below the right armpit; (4) the mid-axillary line 3 crn below the left armpit;

then the anode at the right subscapular region, and the cathode at

(5) the right frontal side of the chest, 3 cm below the clavicle; (6) the mid-axillary line 3 crn below the left armpit.

Placement (7) has the anode at the mid-axillary line 3 crn below the right armpit and the cathode at the mid-axillary line 3 cm below the left armpit. Fig. 2 shows all these placements. The italicised numbers and dashed lines mark the electrode locations on the posterior of the thorax.

To determine the optimal electrode size, five areas ranging from 20 to 190 crn'- were tested. The number of regions of skin with low breakdown voltage varied as a function of electrode size. All these simulations used the anterior-posterior electrode placement 1, found to be the most efficient, and rectangular electrodes.

To determine the effects of the electrolyte resistivity, six values were tested, ranging from 10 to 25 000 f~.cm, for 83 cm 2 rectangular electrodes placed at location 1.

3 Resul ts

3.1 Effects o f electrode placement

Accounting for the sweat duct density (REILLY, t992) and the average resolution of the model, 10 regions of skin with low breakdown voltage were randomly distributed under the 83 em 2 electrode size. For all simulations, the electrode voltage boundary conditions were set such that the max ima l current density in the heart was equal to the myocyte stimulation threshold. Consequently, the heart was always captured. The normal current density was set to zero on the outex surface of the model, outside the outline of the electrode. The resistivity of the electrolyte was equal to 100 f~-era. Table 4 shows the ratio Rt for each of the seven placements. The anterior- posterior placement 1 minimised RI, and therefore was selected as the most efficient placement. The anterior-anterior placement 2 yielded the second best ratio R1.

Fig. 3 shows contours of current isodensities for placement 1. The current through the skin under the electrode was funnelled

through the regions of low breakdown voltage. Higher levels of current density were present at the edge of the electrodes mostly due to their rectangular shapes.

3.2 Effects o f electrode area

For placement 1, which yielded the best ratio Rt, and a 100 t2-cm electrolyte, the efficacy of TCP was tested for five electrode areas: 21, 39, 83, 120 and 190 cm 2. 3, 7, 10, 15 and 23 regions of skin with low breakdown voltage were randomly distributed under the electrodes, respectively. Fig. 4 shows the

(3),

) ( (I)

1 - - - - 3

(2). 151

(1)

I (4). (S). (7)

1 2 3 -

4 - 5 6

7

Fig. 2 (a) Electrode locations searched for the optimal electrode placement; dashed lines and intalicised numbers indicate locations on the back o f the thorax; (b) approximate cross- sectional views of these placements; inner circlets represent the heart

772 Medical & Biological Engineering & Comput ing November 1995

2"5-

si~.3 Contours of currant isodensities in A cm-e through the sldn under the electrode; current density has high values at the regions of tow-voltage breakdown and at the edge of the electrode; simulation was peu:ormed for placement 1; FEM of human thorax; time=l.0; contours of total flux magnitude; rain=6.139 x 10 -9 at node 14960; max=2.407 at node 32992; contour values: A=0.202; B=0.453; C=0.703; D=0.953; E----I.20; F=1.45; G=1.70; H=1.95; 1=2.21

d

2"0-

1"5 1 10

0"5 t

0

3"0

RI

| " i " ! ' q

50 100 150 200 area. cm ~

Fig. 4 Ratio R1 versus different electrode areas; as the size of the electrode increases, R1 decreases; hence, it is likely that larger electrode sizes reduce the pain delivered to the patient

ration R~ versus the electrode area. As the area increases, Rl decreases. Increasing the electrode size above 90 cm 2 does not reduce Rt significantly.

3.3 Effects o f electrolyte conductivity

After placing a pair of 83 cm 2 electrodes at site 1, which yields the lowest ratio RI, the efficacy of TCP was tested for five electrolyte conductivities: 1, 0.2, 0.125, 0.05 and 0-004 S m - l , corresponding to 100, 500, 800, 2000 and 25 000 f~.cra respectively. To assess how uniformly the current density was distributed through the skin, we computed an uniformity factor R2 as the ratio of the absolute maximal current density in the skin and the average of the ma~dmat current densities in the skin at the regions of low breakdown voltage. A value of Re closer to 1 indicates a more uniform distribution of the current density through the skin. Fig. 5 shows the ratio R1 versus the resistivity of the electrolyte. It also shows the uniformity factor Rz versus the resistivity of the electrolyte. As the electrolyte resistivity increases, both ratios R1 and Ra decrease. However, above 800 f~ .era there is no substantial decrease in these two ratios.

4 Conclusions Our model represents an improvement over previous models

by considering the effects of the electrolyte, the anisotropies of the skin and its mosaic electrical structure, more organs in the thoracic and abdominal cavities and more electrode plazements and sizes. We have tested our model against experimental data obtained from a human subject. The results of the simulations were in good agreement with the tests. For a homogeneous model we would expect to find the lowest voltage developed across the combination V1-V2. This is not the case for the human thorax, because for this combination of electrodes the current must flow through the sternum, which has a high resistance, through the intercostal muscles, the lungs and part of the heart wall. Therefore, this path actually presents a high resistance to current flow. Although this study has the limitation of analysing only one thoracic geome~/, its results were consistent with previously reported information. For

different thoracic morphologies, it is probable that placement 1 is still the optimal placement. However, it is likely that the values of Rl and R2 are dependent on the thoracic geometry.

Of the seven electrode placements simulated, placements 1 and 2 minimised the ratio R1, which indicated these to be the most efficient. Electrodes with an area of 90 cm 2 were found to offer the optimal trade-off between efficacy and consm.tction requirements, Increasing the area above this value did not improve the pacing efficacy significantly but could demand large driving capabilities from the pacing devices. The decrease of R~ with increasing electrolyte resistivity implies that it is tess painful to stimulate transcutaneously using high- resistivity electrolytes. There was no significant improvement of Rl for resistivities larger than 800 fl . cm. Fig. 3 shows that the current through the skin during transcutaneous cardiac pacing is furmelled through the regions of low breakdown voltage. Therefore, the patient would experience most of the pain in these regions. Using larger electrolyte resistivity decreased the ratio R2 towards 1, thus yielding a more uniformly distributed current density. Hence, the chances of skin breakdown are reduced and the comfort of stimulation increased. For electrolyte resistivities larger than 800 f~. era, the ratio R1 did not change significantly. Based on these observations, we chose 800 f~. cm to be the optimal value of the electrolyte resistivity.

Other results reported in the literature support these conclusions. Zotl reported that the sharp pain from stimulation of cutaneous sensory nerves was reduced by the use of large surface pacing electrodes and high-resistivity electrolytes (ZOLL et aL, 1981). Webster noted that high-impedance gel can minimise the stinging sensation which normally appears during TCP (WEBSTER, 1987).

The intense pain which accompanied early closed-chest pacemakers was also reduced by increasing the size of the electrodes to about 50 em z (BOCKA, 1989). Boeka reviewed the history of closed-chest pacemaker development, and reported that most of the currently used electrodes have areas between 80 and 100 cm 2. He also stated that discomfort with intercostal muscle contraction can be minimised by placing the electrodes over the areas of least intercostal muscle (i.e. midline chest and just below the left scapula, which is close to our optimal placement).

Medical & Biological Engineering & Computing November 1995 773

3-13.

2"5

B 2"0

~ 1"5.

~ 2 0'5! , ~ = ,

O,G . . . . . . . . . . . . . . . . . . . . . . . . IO 1oo 1ooo ioooo

r~lsthr ~ c~n

Fig. 5

100000

Dependence o f ratios Rj and Re versus electrolyte resistivity; pain delivered to the patient decreases and the current through the skin becomes more uniformly distributed as the resistivity of the electrolyte increases

Falk and Ngai found experimentally no significant differ- ences in the pacing threshold when electrodes were positioned as follows:

(1) negative electrode at cardiac apex, positive electrode at right subseapular region (our placement 1). (2) negative electrode at cardiac apex, positive electrode at

right parastemal region (our placcmem 2). (3) negative electrode at leR parastemal region, positive electrode at left subscapular region (not simulated) (FALK and NGAI, 1986).

They also reported that pacing attempts were ineffective when electrode polarity was reversed. Our linear FEM could not supply information about the effects of polarity reversal because they deal with the Na + and K + ion flow through the cell membranes, which is a highly non-linear process. Falk and Ngai concluded that the efficacy of TCP was very sensitive to the movement of the cathode from the cardiac apex region (FALK and NGAI, 1986), which is consistent with the results in Table 4.

Oeddes and Baker mapped the pacing thresholds on a canine chest using single I0 ms rectangular pulses, and plotted threshold isocurrent contours (GEDDES and BAKER, 1989). They found that the lowest pacing current was obtained when the negative electrode was placed at the point on the chest where the apex o f the ventricles was closest to the left chest surface, which is consistent with the results in Table 4.

dcknowledgraent~The authors would like to thank Murty Susarla, National Eaergy Research Supercompufing Center (NERSC); John Hallqui~ Livermore Technology Corporation and Arthur Shapiro, Livermore National Laboratory, for their assistance relating to the use of the finite element software on the CRAY Y-MP C-90 supereomputer at NERSC.

The supeav~mputing time was granted by the United States Department of Energy. �9 This work was supported by Robert A. Swatbucker.

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Author's biography

Dorin Panescu received his Diploma Engineer in Electronics from the Polytechnic Institute of Timisoam, Romania in 1985, and his MS and PhD in Electrical Engineering from the University of Wisconsin-Madison in 1991 and 1993, respec- tively. From 1985 to 1987 he was with the Enterprise of Apparatus for Electrical Measure- meats, Timisoara, Romania. From 1987 to 1990 he developed high-performance data acquisition

systems at the Institute for Automation, Cluj-Napoca, Romania. In 1991 he joined the Department of Electrical Engineering of the University of Wisconsin-Madison as a research assistant. His PhD research used finite element modelling of electric fields to improve cardiac electrodes, pacemakers and defibrillators. Since September 1993 he has been a Development Engineer with EP Technologies, Inc., Sunnyvale, California. His research interests are electronic instrumen- tation, VLSI design, signal processing and computer modelling.

Medical & Biological Engineering & Computing November 1995 775