Modeling of Induced Electric Fields as a Function of Cardiac Anatomy

and Venous Pacing Lead Location

SARA E. ANDERSON, JULIANNE H. EGGUM, and PAUL A. IAIZZO

Departments of Surgery and Biomedical Engineering, University of Minnesota, B172 Mayo, MMC 195,420 Delaware Street SE, Minneapolis, MN 55455, USA

(Received 17 March 2011; accepted 20 July 2011; published online 2 August 2011)

Associate Editor Ajit P. Yoganathan oversaw the review of this article.

Abstract—The combined effects of cardiac anatomy andpacing lead electrode location within left ventricular cardiacveins on resultant pacing thresholds are not well understood.The specific aims of this study were to: (1) develop acomparative electrostatic model based on previouslyobtained histological measurements, and (2) compare result-ing electric fields and voltage gradients with in vitro experi-mental results. In vitro pacing thresholdsmeasured from swinehearts were utilized to model electric fields generated fromdifferent cardiac venous pacing locations within veins ofvarying diameter and fat thickness. The simulated activationfieldswere defined as 100 V/mand allmaterials were defined asisotropic. The obtained results predicted larger activationfields when an electrode was oriented away from the myocar-dium or in free-floating positions, hence requiring moremyocardial tissue to have 100 V/m than when it was orientedtoward the myocardium. Thus, the resultant modeled electricfields followed the same qualitative trends as in vitro experi-ments performed in the swine hearts. In general, whileelectrode position primarily affected pacing thresholds, bothvein diameter and relative epicardial fat thickness also influ-enced pacing thresholds. The electric fields were larger forbasal regions modeled using larger vein diameters and epicar-dial fat thicknesses. These electrostatic field simulationsprovide unique insights as to how varied cardiac anatomiesand relative electrode locations affect thresholds by enablingvisualization of the electric fields propagating through cardiactissues during pacing from the venous system.

Keywords—Pacing, Left ventricle, Microanatomy, Implant

site.

INTRODUCTION

Although transvenous pacing leads were first im-planted in the cardiac venous system in 1968,25 initial

concerns over potential complications including sta-bility, efficacy, stenosis formation, and/or ease ofextractability suggested that other implant sites be used;thus alternate site pacing was the commonly employedclinical protocol until the late 1990s.11,12 However,today the use of transvenous leads is an integral part ofcardiac resynchronization therapy. This therapy isroutinely applied to correct electromechanical dys-synchronies within the heart by pacing the left ventricle(LV) transvenously; it typically involves coordinatingright ventricular and right atrial pacing as well. Cardiacresynchronization therapy has been shown to improvethe heart function of patients with LV remodeling, wideQRS complexes (>120 ms), and low left ejectionfractions (<35%), and/or those classified in the NewYork Heart Association (NYHA) classes III andIV.4,7,9,15,24,30,31 While implanting the pacing leadthrough the coronary sinus to the cardiac venous systemhas proven increasingly successful in treating heartfailure patients, therapeutic response rates are onlyabout 70%.10,21,31,32 Therefore, a better understandingof the effects of varied cardiac anatomies and pacinglead electrode positions could ultimately help explainthese sub-optimal clinical response rates.

In a recent study, we employed passive fixationtransvenous pacing leads in the anterior interventric-ular veins of isolated swine hearts.2 Briefly, electricalpacing thresholds were measured in three differentimplant positions: touching the myocardial side of thevenous wall (M), not touching any part of the venouswall (F), and touching the epicardial side of the venouswall (E; see Fig. 1). The pacing threshold was definedas the minimum voltage required to capture the heart.Pacing thresholds were measured in each implant po-sition in at least five implant sites along the vein’slength. After fixing each heart, the veins were sectionedin 5 mm intervals perpendicular to the vein’s length

Address correspondence to Paul A. Iaizzo, Departments of Sur-

gery and Biomedical Engineering, University of Minnesota, B172

Mayo, MMC 195, 420 Delaware Street SE, Minneapolis, MN 55455,

USA. Electronic mail: iaizz001@umn.edu

Cardiovascular Engineering and Technology, Vol. 2, No. 4, December 2011 (� 2011) pp. 399–407

DOI: 10.1007/s13239-011-0057-3

1869-408X/11/1200-0399/0 � 2011 Biomedical Engineering Society

399

from base to apex. Standard histological methods wereused to prepare slides using Masson’s trichrome stains;slides were then digitized (Super Coolscan�, Nikon,Inc., Melville, NY) and analyzed (Image-Pro� Plus4.1.0, Media Cybernetics�, Bethesda, MD). Measure-ments were made of each vein’s wall thickness andcircumference as well as distances between the veinwalls and the myocardium.2 Average vein diameterswere calculated from measured vein circumferences.These histological measurements were then used todevelop the electrostatic fields model presented here.Thus, simulations of varying vein diameters, distancebetween the vein and myocardial tissue (epicardial fatthickness), and the three electrode positions were per-formed. The resulting electric fields, current densities,and voltage gradients were examined to elucidate theireffects on pacing thresholds in left ventricular veins.

We hypothesized that because pacing thresholdswere lower when pacing electrodes were oriented in theM position, the required electric field would be greaterin a larger amount of myocardial tissue when com-pared to the same pacing threshold voltage in the Eposition. As a result, the capture threshold would belower in the M position compared to the E position,i.e., with the same vein diameter and epicardial fatthickness. For the same pacing voltage, when thepacing lead was in the E position, it was consideredthat the electric field dissipated over the distancebetween the electrode and myocardial tissue beforeenough myocardial tissue could be adequately depo-larized. Voltage losses across the blood, vein wall, and/or epicardial fat when the pacing lead electrode was inthe E position in turn result in lower voltages reachingmyocardial tissue. Thus, a higher pacing thresholdwould be required to elicit myocardial capture fortherapeutic pacing in the E position. Additionally, it isconsidered that the relative effects of vein diameterand/or epicardial fat thickness will also affect bothpacing thresholds and electric fields. We believe that abetter knowledge of how electric fields propagatethrough these biologic tissues will provide a more in-depth understanding of the effects of vein diameters,

epicardial fat thicknesses, and/or pacing lead electrodepositions on resultant pacing thresholds and, impor-tantly, could aid in the design of future transvenouspacing leads. The specific aims of this study were to: (1)develop a comparative electrostatic model based onpreviously obtained histological measurements,2 and(2) compare resulting electric fields and voltage gradi-ents with in vitro experimental results.2

MATERIALS AND METHODS

We used commercially available finite elementmodeling software Maxwell 3D (Ansoft, Pittsburgh,PA) to generate an electrostatic model of the coronaryveins. The model was designed based on histologicresults from the swine hearts measured in previousin vitro experiments2 and material properties found inthe literature.23 The conductivities for all componentsof the model are displayed in Table 1.

The pacemaker electrode and lead insulation (4 Frprototype bipolar passive-fixation left heart lead with21-mm inter-electrode spacing) were modeled usingsizes and conductivities consistent with publishedMedtronic data (Medtronic, Inc., Minneapolis, MN).

FIGURE 1. Fiberscopic view of the pacing lead within the anterior interventricular vein. The camera view was oriented such thatthe myocardium is toward the bottom of the view.2

TABLE 1. Material conductivities.

Material

Conductivity

(S/m) Source

Blood 0.63 Laske et al.23

Electrode 8.30E+06 Generalized Medtronic data

Insulation 0.07 Generalized Medtronic data

Vein wall 0.81a Janjic et al.19

Epicardial fat 0.05 Foster and Schwan;13

Geneser et al.;14

Johnson et al.;20

Panescu et al.;27

Rushet al.; 29

Myocardium 0.43 Panescu et al.;27

Rush et al.; 29

aVein wall conductivity is an average of conductivity in the trans-

verse (0.58 S/m) and longitudinal (1.04 S/m) directions.

ANDERSON et al.400

The electrode and lead insulation were modeled as asphere and cylinder respectively with a radius of0.89 mm.

The blood volume, coronary vein wall, and sur-rounding epicardial fat were designed as cylindersusing histological measurements determined in a pre-vious experiment.1 The venous blood cylinder radiuswas 1.32 mm, 1.10 mm, or 1.02 mm to model basal,mid, and apical regions respectively. The vein wall was0.17 mm thick. The previous experiment showed thatvein wall thickness did not significantly vary along thevein length. The epicardial fat thickness was modeledto be 1.16, 1.81, or 0.46 mm for the basal, mid, andapical regions respectively, which was previouslyaccessed by measuring the distance from the vein to themyocardium.1 The myocardium was modeled to be8.00 mm from the epicardial fat.

Pacing thresholds were measured for hearts thatwere isolated from the body and are presented inTable 2. Nearby anatomical components such as thepericardial fluid and pericardium were not a factor in

the threshold measurements and therefore were notused in this model. Air was also not added as a com-ponent due to its low conductive properties.

Figure 2 shows the cross-sectional and three-dimensional representations of the model. The cylin-ders representing the coronary vein and surroundingtissues were 20.00 mm in height in the model. Themodel represents a portion of the vessel. In the previ-ous experiments, the coronary vein length ranged from90 to 135 mm.1 The components were modeled asstationary. The three different locations of the pacingelectrode, myocardial (M), free-floating (F), and epi-cardial (E), were modeled by varying the electrode andlead insulation position.

Maxwell 3D software was used to calculate theelectric potentials in the components of the model froma cathodic input pacing voltages at the electrode and0 V anodic input at the outer myocardial wall. Thepreviously obtained pacing thresholds displayed inTable 21 were utilized as input pacing voltages. Theinput pacing thresholds varied depending on the po-sition within the vein. The pacing voltage charge wasmodeled as uniformly distributed across the electrodesurface. The software then utilized a DC current flowsolver to derive relative electric potentials and electricfield magnitudes as displayed in Eqs. (1) and (2),respectively:

r � rrUh i ¼ 0 ð1Þ

E ¼ �rU ð2Þ

where r = electric conductivity, F = electric potential,and E = electric field magnitude.

TABLE 2. Pacing thresholds.

Region Pacing position Pacing threshold (V)

Basal E 8.51

Basal F 7.41

Basal M 5.66

Mid E 6.95

Mid F 5.65

Mid M 4.28

Apical E 4.63

Apical F 4.00

Apical M 2.28

FIGURE 2. (a) Cross-section of the FEM model and its labeled components. The cross-section was taken on the xy-plane whenz 5 0. (b) Three-dimensional view of the model and its reference x, y, and z axes.

Electric Field Modeling of Pacing in the Cardiac Veins 401

This approach used adaptive meshing until conver-gence was obtained; all simulations reached a conver-gence of <1% error. The average number of elementsused in all simulations was 100k. The myocardial acti-vation electric field was defined as 100 V/m. In theory,this is the minimum electric field required to activate themyocardium.18 The volume of activated myocardiumwith an electric field of 100 V/m or above was calcu-lated using MATLAB (The MathWorks, Natick, MA).

RESULTS

The primary purpose of our model was to compareobtained electric field results with in vitro experimentaldata. These simulations were then interpreted in anattempt to better understand why pacing thresholdsare lower for M-positioned pacing electrodes com-pared to those in either the F or E positions. Fur-thermore, we used these simulations to understand therelative contributions that variations in fat thicknessand/or vein diameter have on required therapeuticpacing thresholds.

Figure 3 shows the induced electric fields on across-section of the model as a function of pacing leadposition. The model indicates that the amount ofmyocardium activated increases from apical to basalvenous positions and from lead positioning toward themyocardium (M) to away from the myocardium (E).Figure 4a provides a more quantitative view of theamount of activatedmyocardiumbetween thenine cases.A larger volume of tissue is activated in the E and basalpacing lead positions vs. the M and apical positionsrespectively. Figure 4b shows the results for the ninecases generated from a constant voltage input of 2.28 V,which was the pacing threshold that resulted in thesmallest volume of activatedmyocardium. In contrast tothe actual pacing threshold results shown in Fig. 4a, theconstant voltage input resulted in larger myocardialactivation volumes for apical vs. basal positions. The Mpositions result in slightly larger volumes of activatedmyocardium compared to the E positions.

Figures 5a–5c show the electric field as a function oflocation along the y-axis for the apical, mid, and basalmodels respectively. The largest electric field drops oc-curred in both the blood and epicardial fat. This figureshows that relative to the electric field magnitudes in therest of the components, the electric field in the myocar-dium was similar among the pacing positions.

DISCUSSION

This computational study provides two principalfindings as a result of comparing electric fields and

voltage gradients by utilizing in vitro obtained experi-mental input parameters: (1) smaller electric fields werepresent when the pacing lead electrode was orientedtoward the myocardium (M position) compared towhen the electrode was free-floating or oriented awayfrom the myocardium (F or E positions), and (2) withincreasing vein diameters and fat thicknesses, higherpacing thresholds (therefore, larger electric fields) willbe required to consistently pace the underlying myo-cardium.

Pacing Lead Positions

Throughout a given vein, derived electric fields forpacing were smaller when lead electrodes were in the Mposition relative to those in F and E positions. Incontrast, the results from a constant pacing input showthe opposite response as seen in Fig. 4b. This suggeststhat the differences in activated myocardium volumeare dependent on the pacing thresholds that weremeasured previously.2 As indicated by the electric fieldequaling 0 within the conductor and charge presentonly on its surface, the electrode is a conductor. It wasalso determined that blood was less conductive thanthe electrode and therefore a decrease in electric fieldoccurs between the electrode and the vein wall. Thevein wall is typically slightly more conductive thanblood, thus the charge will be present on the outersurface of the vein wall. Thus, increases in pacingthreshold for the free-floating (F) and away from themyocardium (E) positioning vs. toward the myocar-dium positioning (M) are most likely caused by thevoltage and electric field drops that occur in the bloodas seen in Fig. 5. For example, when the pacing lead isin the M position, the pacing pulse does not need totravel through blood before reaching the vein wall, theepicardial fat, and finally the myocardium. However,in both F and E electrode positions, the pacing pulsemust first travel through blood and through vein walland epicardial fat before reaching myocardial tissue.On the other hand, the electric field magnitudes arerelatively similar along the myocardium if compared tothose of the other model components. Note thatthe electric fields in the myocardium did not exceed350 V/m (which is consistent with the order of thetheorized 100 V/m activation field) in any of the cases.

Effects of Fat Thickness and Vein Size

Leads positioned in the basal regions of the heart,which have larger fat thicknesses and vein diameters,produced larger activating electric fields than thosepositioned in apical regions with smaller fat thick-nesses and vein diameters, as seen in Fig. 4a. Againwhen a constant pacing stimulus was applied to all

ANDERSON et al.402

models, the opposite result occurred. This again sug-gests that the volume of activated myocardium isdependent on the pacing threshold.2 One explanationfor the difference in pacing thresholds is the variationin the alignment of the cardiac myocytes. Studies haveshown that the conductivity of the myocardium isgreatest in the direction of the myocardial fibers.8,17,28

The myocytes in the apical areas of the heart may be

aligned in a manner that increases the conductionof the applied pacing signal relative to that of basalareas.

Optimal Lead Placement

According to our model, optimal lead placementwill likely occur in apical regions of the heart with the

FIGURE 3. Visual representations and one-dimensional plots of electric field magnitudes on the xy-plane where z 5 0. The left,middle, and right columns show visual representation of the electric field magnitudes when the lead is positioned toward themyocardium (M), free-floating (F), and away from the myocardium (E), respectively, for pacing threshold measured in vitro. The top,middle, and bottom rows show the modeled electric fields when the lead is placed in basal, mid, and apical regions of the heart.Red indicates activated myocardium (tissue with an induced electric field of 100 V/m or greater). Greater activation fields aregenerated when the lead is positioned toward the myocardium and in more apical regions. Each electric field threshold is denotedat the bottom of the respective graph. Pericardial fluid and pericardium are to the right; myocardium is to the left.

Electric Field Modeling of Pacing in the Cardiac Veins 403

lead electrode placed toward the myocardium. Smallerinduced electric fields indicate more efficient captureand longer battery life. Yet, it should be noted thatclinically it is believed that optimal LV ventricular leadplacement occurs on the site of latest activation, whichmay not be in the apical regions.3,5,6,10,21,26,32 However,the optimal pacing site will vary significantly from pa-tient to patient.22,26 Nevertheless, we consider that thefirst iteration of this model presented here providesnovel insights regarding the electric fields resultingfrom different pacing positions along the entire lengthof a given LV vein. Thus, this model could serve as thebasis for future cardiovascular research includingmodeling how pacing leads move within the coronary

veins with each contraction, how stenosis may affectpacing thresholds, evaluation of different electrode andlead designs, and what pacing positions can be used toavoid phrenic nerve stimulation.

Limitations

The anterior interventricular vein was used to ob-tain swine pacing thresholds because of its accessibilitywith the Visible Heart� apparatus design. Addition-ally, the computational model employed here wascomparative, employing simple half cylindrical shapesand isotropic tissue conductivities. In reality, biologictissues are not isotropic and vary considerably within agiven vessel and/or between individuals.1,17 Cardiactissue conductivity has been shown to be higher in thedirection of fiber orientation.8,17,28 It should also benoted that due to the use of the half cylindrical shapes,fringe effects were observed at the junctions betweendifferent materials (Fig. 3).

In addition, all tissue conductivities used here wereobtained from literature sources in which healthysample populations were studied (Table 1), thuspathological or aging effects need future consideration.Furthermore, the relative in vitro pacing parametersand associated anatomical histologic measurementsentered into this computational model were those fromhealthy swine hearts; to date, no similar human dataare available. However, the purpose of this model wasto compare measured in vitro pacing parameters fromthese healthy swine hearts with model results. It shouldbe noted that we recently reported on human heartmicroanatomical measurements1; these measurementswere taken from diseased hearts, and it is not known ifsuch patients would have required cardiac resynchro-nization therapy. Nevertheless, in future computationsone could easily modify input geometries of the modeland/or analyze other varying criteria, including dis-eased myocardial tissue or fatty and/or fibroticdeposits within the myocardium.

Finally, this computational model was considered inthe steady state, and we know that relative anatomicalfeatureswill change throughout the cardiac cycle and arenot identical to the input parameters obtained from ourin vitro experiments. Nevertheless, due to the transientnature of myocardial cells (peak depolarization occursat approximately 2 ms),16 one can consider that thisinitial model is a good approximation of the electricfields immediately after a pacing stimulus is delivered.

Conclusions

The resultant modeled electric fields followed thesame qualitative trends as those obtained from in vitroexperiments performed in our laboratory—smaller

FIGURE 4. Volume of activated myocardium as a function oflead position using (a) previously measured physiologicalpacing thresholds, and (b) a constant voltage input of 2.28 V.In (a), the volume is greater for basal regions than in apicalregions. The volume of activated myocardial tissue increasesfrom pacing leads oriented toward the myocardium (M), topacing leads oriented away from the myocardium (E). Free-floating (F) pacing lead positions activate less tissue volumethan E positions, but greater volumes than M positions. In (b),the activation volumes increase from the basal regions to theapical regions and slightly decrease from the M position to theE position.

ANDERSON et al.404

FIGURE 5. (a) Electric field magnitude along the y-axis for the apical models. The x-axis indicates the associated model com-ponent. (b) Electric field magnitude along the y-axis for the mid models. The x-axis indicates the associated model component. (c)Electric field magnitude along the y-axis for the basal models. The x-axis indicates the associated model component.

Electric Field Modeling of Pacing in the Cardiac Veins 405

electric fields were present when the pacing lead elec-trode was oriented toward the myocardium, relative tobeing positioned centrally in a vein or away from themyocardium. Lead position, vein diameter, and/orepicardial fat thickness influenced therapeutic pacingthresholds. With increasing vein diameters and fatthicknesses, higher pacing thresholds (and thereforelarger electric fields) will be required to consistentlycapture myocardial tissue. In this model, the amountof activated myocardial tissue was dependent on pac-ing position due to the distance to the myocardium andconduction pathways, voltage losses in the blood,and/or electrode contact with the vein wall. In con-clusion, the described electrostatic field simulationsmay provide novel insights as to how cardiac anatomyand lead electrode location will ultimately affect clini-cal pacing thresholds by providing relative visualiza-tion of the electric fields propagating through cardiactissues during an applied pacing pulse.

ACKNOWLEDGMENTS

The authors would like to thank David Bourn forhis help in developing and analyzing the model, Pro-fessors David Benditt and William Durfee for theirencouragement to perform such analyses, Gary Wil-liams for his assistance with the figures, Emily Fitchfor her assistance with literature searches, and MonicaMahre for her assistance with the preparation of thismanuscript. We would also like to acknowledge theUniversity of Minnesota Supercomputing Institute forproviding computing resources. This research wassupported by a GAANN grant (Graduate Assistancein Areas of National Need) from the U.S. Departmentof Education, as well as the Institute for Engineering inMedicine at the University of Minnesota. We have noconflicts of interest to report.

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