Finite element analysis of defibrillation fields in a human torso model for ventricular defibrillation

Progress in

PERGAMON

Progress in Biophysics & Molecular Biology 69 (1998) 353±386

Biophysics & Molecular Biology

Finite element analysis of de®brillation ®elds in a human torso model for ventricular de®brillation Xiaoyi Min *, Rahul Mehra Medtronic, 7000 Central Avenue N.E., MS T305, Minneapolis, MN 55432, USA

Abstract In order to optimize de®brillation electrode systems for ventricular de®brillation thresholds (DFTs), a Finite Element Torso model was built from fast CT scans of a patient who had large cardiac dimensions (upper bound of normal) but no heart disease. Clinically used de®brillation electrode con®gurations, i.e. Superior Vena Cava (SVC) to Right Ventricle (RV) (SVC-RV), left pectoral Can to RV (Can-RV) and Can+SVC-RV, were analyzed. The DFTs were calculated based on 95% ventricular mass having voltage gradient >5 V/cm and these results were also compared with clinical data. The low voltage gradient regions with voltage gradient <5 V/cm were identi®ed and the e€ect of electrode dimension and location on DFTs were also investigated for each system. A good correlation between the model results and the clinical data supports the use of Finite Element Analysis of a human torso model for optimization of de®brillation electrode systems. This correlation also indicates that the critical mass hypothesis is the primary mechanism of de®brillation. Both the FEA results and the clinical data show that Can+SVC-RV system o€ers the lowest voltage DFTs when compared with SVC-RV and Can-RV systems. Analysis of the e€ect of RV, SVC and Can electrode dimensions and locations can have an important impact on de®brillation lead designs. # 1998 Elsevier Science Ltd. All rights reserved.

1. Introduction More than 300,000 people die annually of sudden cardiac death in the United States (Myerburg and Castellanos, 1992). Sudden cardiac death is usually due to a lethal cardiac arrhythmia, i.e. ventricular ®brillation, which completely ceases cardiac blood-pumping function. Since attempts to deal with ventricular ®brillation were thwarted by the lack of e€ective antiarrhythmic drugs, much of the clinical e€ort to prevent sudden cardiac death has * Corresponding author. Tel.: +1-612-514-3754; Fax: +1-612-514-6260; E-mail: [email protected] 0079-6107/98/$19.00 # 1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 7 9 - 6 1 0 7 ( 9 8 ) 0 0 0 1 5 - 7

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turned to the use of implantable de®brillators. In the last decade, transvenous de®brillation has become routine clinical practice due to ease of implantation of pectoral devices and technology advances which has resulted in a reduction of device size. However, to provide patients an e€ective de®brillation system with the smallest device size, design of transvenous de®brillation systems with low de®brillation energy requirement is still critical and remains a challenge. Optimization of de®brillation electrode con®guration and design can reduce the de®brillation threshold (DFT), and decrease device size. This can potentially minimize morbidity and mortality by increasing the de®brillation safety margin. Even though the mechanism of de®brillation is controversial, most experimental work indicates that de®brillation can be achieved by developing adequate current density or voltage gradient in a critical volume of the myocardium. This has been referred to as the critical mass hypothesis (Zipes et al., 1975; Ideker et al., 1994). In general, de®brillation electrode systems yielding a lower voltage DFT can be achieved with a better ®eld distribution in the heart and with a lower electrode impedance. However, the ®eld distribution and electrode impedance are critically dependent on the location, geometry and dimension of the electrodes. Experimentally, a large number of studies are required to determine the e€ect of electrode parameters on DFT owing to the probabilistic nature of de®brillation and large variance in clinical DFT measurements. Repetitive ventricular ®brillation (VF) induction for DFT testing also puts patients at additional risk. A computer model, using the ®nite element analysis method and a human thorax model, can improve our understanding of various critical de®brillation parameters and therefore help to optimize de®brillation electrode systems. Finite element analysis method (FEA) is a numerical technique that has been widely used to solve a di€erential equation with proper boundary conditions in a complex domain. A human thorax is a complicated structure consisting of various organs and tissues. Many researches have reported on ®nite element analysis of the thorax models for de®brillation. Beside many animal thorax models (Claydon et al., 1988, Schmidt et al., 1992, Karlon et al., 1993, 1994), there are several 3D ®nite element models of human thorax. Camacho et al. (1995) reported on a ®nite element human model to evaluate the e€ect of transthoracic paddle electrode size and position on transthoracic de®brillation ecacy. Jorgenson et al. (1995b) used a uniform brick®nite-element human thorax model to study the sensitivity of tissue resistivity and model variables on DFTs with transthoracic or hybrid (patch-skin to a transvenous lead) electrode systems. Panescu et al. (1995) also reported on a ®nite element thorax model to reduce the myocardium damage for transthoracic de®brillation by optimizing surface electrode position and size. Most of these previous models vary in both tissue resolution and anatomical detail, and were more focused on the modeling of transthoracic de®brillation. The Utah Torso model (Johnson et al., 1992; Klepfer et al., 1995) has been used for the inverse and forward electrocardiographic ®eld problems and also recently being used for transvenous de®brillation. Since transvenous de®brillation systems is being widely used clinically, an investigation of transvenous de®brillation systems by a FEA human thorax model can have signi®cant implications. While these models have evaluated de®brillation thresholds, the validity of these models has not been well tested. However, validation of de®brillation potential at various locations in the models has been reported. Jorgenson et al. (1995a) reported validation of their pig thorax models by measuring de®brillation potentials at 52 sites when a shock was delivered across a

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chest patch and a transvenous coil electrode. Their study showed a good correlation between the model prediction and the experimental measurements. The average relative rms error was bigger at the sites near the electrode and was improved with adjustment of tissue resistivity, electrode-tissue interface and lead-wire impedance. Panescu et al. (1995) compared the transthoracic voltage measured between two surface electrodes with that predicted by the model and a good correlation was found. Even though we don't consider the probabilistic nature of de®brillation, there are some uncertainties in FEA modeling of a human thorax, which can also lead to errors. One source of errors in FEA is inherent in approximation of complex thorax geometry with discrete elements. Finer elements may render smoother surfaces of organs, but require more computational e€orts. Schimpf et al. (1997) reported that less than 5% di€erence in DFTs (calculated at several percentile of critical mass for certain transvenous electrode con®gurations) was detected at a mesh resolution of 2.3  2.3  3.0 mm compared with that of 1.2  1.2  3.0 mm. Another source of computational errors is due to the level of anatomical detail incorporated in the model as well as its material properties. Even though some details vary, all the models cited above are similar mathematically as they are all monodomain models which compute electrostatic ®eld distribution. In a thorax model used for transvenous de®brillation study, sucient cardiac detail should be included. Validation of FEA results with clinical results is necessary so that the model can be used to predict future clinical outcomes. In spite of the work mentioned above, there has been a lack of analysis and optimization of clinically used de®brillation electrode systems and quantitative comparison with clinical measurement. In this paper, we present a 3D FEA human thorax model constructed from fast CT scans with more anatomical structural details and better resolution than published previously (Min et al., 1993). We used the model to optimize electrode con®gurations, location and dimensions in order to achieve the lowest voltage de®brillation thresholds (DFT). We analyzed two and three electrode de®brillation systems which yield low DFTs and are most commonly used in clinical practice. We also validated the FEA model by comparing the computed DFTs and the impedance with those measured clinically. 2. Methods 2.1. Finite element analysis Finite element analysis is well suited to problems involving irregular shape and inhomogeneous volumetric domain, such as a human torso. Since the time constant (ratio of permittivity to conductivity) of heart tissue is in the range of nanoseconds, the electrical charge dissipates very fast compared to the time duration of de®brillation shock which is a few milliseconds in duration. Therefore, the de®brillation ®eld is governed by a quasi-electrostatic equation r…srf† ˆ 0

in T

…1†

where f is the potential ®eld and s the conductivity and T is the solution domain which is human torso in this case. The conductivity s could be a tensor when tissue anisotropy is

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Figs 1 and 2 (captions opposite).

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Table 1 Resistivity values (r) for various organs/tissues used in the model Tissue

r (O cm)

Ventricular myocardium Atrial myocardium Blood Connective tissue Lung Myocardium fat Skeletal muscle Bone

400 400 150 400 1275 2000 400 2000

Tissue Fat Kidney Air Cartilage Liver Spleen Esophagus Stomach

r (O cm) 2000 600 1020 2000 600 600 400 600

considered, but it is merely a scalar in this paper. Since electrodes are very good conductors, equal potential is maintained on the surface of an electrode as speci®ed by f…r†jSi ˆ Vi

…2†

where Si is the ith electrode surface, Vi is the voltage maintained on the ith electrode, and r represents coordinates of a point on the ith electrode surface. Also on the outer surface S0 of a thorax, the normal current component is zero, i.e. @f…r† j ˆ0 @n S0

…3†

Using FEA, the solution to Eqs. (1)±(3) is obtained by applying variational principle to the functional … F…f† ˆ rf
…srf†dV …4† T

where T represents the thorax volumetric space. A potential distribution which minimizes Eq. (4) will satisfy Eq. (1) at the same time. Although the boundary condition of Eq. (2) needs to be enforced in minimization of Eq. (4), boundary condition Eq. (3) is not enforced because it is implicated in Eq. (4), which is also called the natural boundary condition. Nonuniform brick ®nite elements were chosen to discretize a human torso from CT scans due to its simplicity and numerical accuracy. It is also easier to generate brick elements from CT scans since they are represented by pixels. Finer meshes were used within the heart and the regions enclosing the electrodes. The same meshes were repeatedly used for di€erent electrode con®gurations and for electrode parameter studies, in order to limit the numerical error resulting from di€erent meshes. The model was solved by a in-house FEA solver with preconditioned conjugate gradient iterative matrix solver. To speed up the solution for 700,000 Fig. 1. One meshed layer of the torso sections across the heart (66 mm above the apex of heart) at end diastole. Di€erent colors represent various tissues and organs. Fig. 2. Illustration for electrodes generated by referencing anatomical structures represented by the contours obtained from CT images.

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Fig. 3. Anterior view of the human torso model with heart, vessels and lungs.

nodes in the model, an iterative sparse matrix solver was also developed. Contrary to many iterative solution method, the system matrix coecients were not permanently stored in memory, but dynamically generated when needed in every iteration. This approach is well suited for large scale problems with limited memory availability. Calculations were conducted on an HP 9000/755 workstation. 2.2. Human torso model generation An anatomic human thorax model was reconstructed from transverse fast CT scans of a patient in supine position. Since the cardiac anatomy during ventricular ®brillation is similar to that at end-diastole, the CT scans were gated at end-diastole of the cardiac cycle. To allow the heart chambers and vessels to be better de®ned on the images, radiopaque contrast agent was injected during the scan. Forty-nine slices with 6 mm separation were taken from the neck to the navel.

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Two-dimensional contours of each organ on each CT slice were manually generated and were used to construct the 3D human torso model (Fig. 3). This model contains detailed anatomical structures, up to 27 thoracic organs and tissues such as myocardium, blood, connective tissue, major vessels, skeletal muscle, subcutaneous fat, bone, lung, liver, stomach, intestines etc. The ventricular and atrial myocardium are separated in order to facilitate computation of atrial and ventricular DFTs. The bone structure includes sternum, spine, rib cage and the left and right clavicle. The blood vessels in the vicinity of the heart were identi®ed and included in the model, which include the ascending and descending aorta, the pulmonary arteries and veins, the coronary sinus vein, the superior and inferior vena cava, the innominate, azygous, and subclavian veins. The anisotropy of skeletal and myocardium has not been incorporated in this analysis. Figure 1 shows one of the torso sections across the heart at end diastole after meshing. Di€erent colors represent various tissues and organs. The stack of 49 slices were combined to form a 3D ®nite element model with 700,000 brick elements. 2 mm resolution in meshes were achieved within the heart (2  2  2 mm) and surrounding vessels and 4 mm resolution outside. Schimpf et al. (1997) reported that 2.3  2.3  3 mm adaptive mesh resolution is sucient for building transvenous models. The 3D structures were also generated from the 2D contours by using the commercial software IDEAS (SDRC, Milford, OH) for the purpose of generating electrodes. By referencing the anatomical structures of the model, the de®brillation electrodes were generated and placed at desirable positions using the IDEAS software (Fig. 2). The electrodes were then mapped into the brick elements of thorax. Subsequently all brick elements within an electrode surface were identi®ed and assigned with the electrode conductivity and the applied voltages. Due to the limited availability of human data, animal resistivity data at a low frequencies were used (Kinnen et al., 1964; Witsoe and Kinnen, 1967; Wang and Patterson, 1995). Great vessels (SVC, IVC, aorta, pulmonary veins, arteries, etc.) and heart chambers (RA, RV, LV and LA) were assigned a resistivity value of the blood (Table 1). Rib cage, spinal cord, vertebrae, clavicles, sternum etc. were assigned the resistivity value of bone (Table 1). The resistivity r simply equals to 1/s. The resistivity values used in this model are very close to those validated against animal measurement (Jorgenson et al., 1995a). The size of a heart can be an important variable a€ecting DFTs. In this model, the myocardial volume was calculated and compared with measurements in the literature. In 50 formalin ®xed hearts (Kitzman et al., 1988) of 50±59 years old males, the mean heart mass was 330 g (311 cm3 with 1060 kg mÿ3 cardiac mass density). The upper bound of the volume of female hearts (Kirklin and Barratt-Boyes, 1992) was 351 cm3 (heart mass = 372 g). In our model, the volume of the heart was 339 cm3; the ventricle 282 cm3; and the atria 57 cm3, which was on the mean of the males and close to the upper bound of normal female hearts. We also measured the anterior view projection of the distance between the tricuspid valve and the apex of the heart in this model and it was 12.4 cm. This is comparable to the same measurement taken from the X-rays of 16 patients receiving implantable de®brillators (12.5 24.0 cm). 2.3. Calculation of de®brillation thresholds Although the mechanism of de®brillation is controversial, the classical de®brillation theory is based on the critical mass hypothesis (Zipes et al., 1975; Ideker et al., 1994). It states that

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Fig. 4. A plot of percentage of ventricular mass that has current density greater than the indicated value with a 100 V shock across the electrodes for the primary de®brillation electrode systems.

successful de®brillation occurs if a critical mass of myocardium has current density exceeding a certain value. It is assumed that any activation fronts in the myocardium not included in this critical mass are incapable of maintaining ®brillation. In our model, the DFT was the value when 95% of ventricular myocardium had a voltage gradient (or current density) greater than 5 V/cm (or 12.5 mA/cm2: sHf = 2.5 mS/cm*5 V/cm). Once the potential distribution in the thorax was obtained, the de®brillation ®eld or current density distribution, impedance, voltage and current DFTs were calculated. The low current density (or voltage gradient) regions were subsequently viewed with a visualization tool such as the IDEAS software. The impedance of the de®brillation system was calculated based on the total dissipated power (P = fOsHf
Hf dV) in the thorax and the shock voltage V, i.e., Z = V2/P. The DFTs were determined from a relationship (Fig. 4) between current density and percentage of myocardial volume (varying from zero to 100%) that has current density greater than that value for a 100 V shock (Mehra and Cybulski, 1994). In order that the current density be at least equal to the threshold value of 12.5 mA/cm2, this 100 V value is appropriately scaled to determine the DFTs. For example, when a 100 V shock is applied across Can and superior vena cava (SVC) electrodes to RV electrode (Fig. 4), 95% of the ventricular myocardium has current density greater than 4.38 mA/cm2. For 95% of the ventricular myocardium to have a current density greater than 12.5 mA/cm2 so that de®brillation can occur, the voltage required would be 285 V which is calculated as 12.5 (mA/ cm2)/4.38 (mA/cm2)*100 V = 285 V. The current DFT was computed by dividing the voltage DFT by impedance across the electrode system and the stored energy DFT was calculated as 0.5CV2 where C is a de®brillator capacitance storing the voltage and V the voltage DFT.

3. Lead con®gurations for ventricular de®brillation Since the pioneering work conducted by Mirowski et al. in the early 1970s, rapid advancement in implantable cardioverter±de®brillators (ICDs) and de®brillation electrode systems has occurred. The electrode systems have experienced several remarkable changes, i.e.

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from epicardial patches, to transvenous system with or without subcutaneous patches and then to pectoral Can electrodes which are also the enclosure for the de®brillator hardware. Transvenous systems typically use a coil electrode in the SVC and another coil inside the right ventricle (RV) and a shock is delivered between SVC electrode and RV electrode (the SVC-RV system). Since clinical studies had shown that the perioperative mortality and morbidity associated with epicardial electrodes is higher than with endocardial systems, the use of endocardial electrode systems has increased signi®cantly. Initially, some of the transvenous electrode systems required higher de®brillation voltages than epicardial de®brillation systems until the pectoral Can electrode system was developed and tested. With recent advances in technology, the size of ICDs has been further reduced, which has made pectoral implants of ICDs more feasible and the procedure as easy as a pacemaker implant. The unipolar Can electrode system uses the Can of an ICD located in the pectoral region as one de®brillation electrode and the RV electrode as the other electrode. A shock is delivered between the Can and RV electrodes and this system is also called Can-RV system. Even though a tranvenous system such as Can-RV has de®brillation energy requirement in the range of the epicardial systems (Marchlinski et al., 1986; Yee et al., 1990), any additional improvement in de®brillation ecacy o€ers the opportunities to further decrease de®brillator size by lowering maximum device output voltage. In this paper we will present our analysis of SVC-RV, CanRV and Can + SVC-RV electrode systems and also on the e€ect of the electrode parameters and their location on DFTs. In this model, the electrodes were placed in locations similar to their use in clinical practice. Unless electrode location and size are speci®ed di€erently, they are as indicated here. The 80 cm3 Can electrode (Medtronic Model 7219C) was placed subcutaneously in the left pectoral region below the clavicle; the 5 cm long RV electrode with 2.85 mm in diameter (Medtronic Model 6936) was placed inside RV with its distal end 3 cm away from the endocardial RV apex and a 5 cm long SVC electrode with 2.26 mm in diameter (Medtronic Model 6947) was placed inside SVC with its distal end at the junction of RA/SVC (Low SVC or LSVC position) or inside the left innominate vein with its distal end at the bifurcation of SVC and left innominate vein (high SVC or HSVC position).

Table 2 FEA results based on 95% ventricular mass having a voltage gradient greater than 5 V/cm for Can-RV, SVC-RV, and Can + SVC-RV systems

Can-RV LSVC-RV Can + HSVC-RV Can + LSVC-RV

Impedance (O)

Voltage DFT (V)

Stored energy DFT (J)

58 47 44 37

347 438 308 285

7.2 11.5 5.7 4.9

Current DFT (A) 6.0 9.3 7.0 7.7

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Fig. 5. The relationship between voltage DFTs and percentage critical mass used in the calculation for the primary de®brillation systems.

4. Comparison of SVC-RV, Can-RV and Can + SVC-RV de®brillation systems: FEA results and clinical data In this section, FEA results obtained from the model will be discussed and compared with paired clinical data. The ®eld distribution results will also be presented to increase our understanding of factors that a€ect DFTs. Then paired electrode con®gurations of SVC-RV vs. Can-RV (Min et al., 1994b) and Can-RV vs. Can + SVC-RV (Min et al., 1996) will be analyzed for comparing system performance and validation with clinical data. 4.1. The model results The factors that impact voltage DFTs are the impedance of the de®brillation system and the current DFT which is the measure of global ®eld distribution. As stated in Section 2, although the DFTs were calculated based on 95% ventricular mass achieving a voltage gradient greater than 5 V/cm (Table 2), the choice of critical ventricular mass and voltage gradient threshold a€ects the values of the calculated DFTs. With a ®xed threshold of voltage gradient, the

Fig. 6. The relationship between current DFTs and percentage critical mass used in the calculation for the primary de®brillation systems.

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Figs 7 and 8 (captions overleaf ).

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relationship between DFTs and ventricular mass is nonlinear and illustrated in Figs. 5 and 6 for a threshold voltage gradient of 5 V/cm. Experimental work in animals (Ideker et al., 1994) indicates that the critical mass required for de®brillation may be greater than 80%. With a ®xed critical mass, DFTs are linear with voltage gradient threshold so that the DFT ratios between di€erent electrode systems are unchanged. In an ideal case if an uniform ®eld was created in myocardium, the DFTs would be independent of the critical mass and it would be a vertical line as indicated in Fig. 5. It would be a rectangular pulse function as in Fig. 4 where a graph of the percentage of critical mass that has current density greater than the values is plotted as function of current density when a 100 V shock is delivered across electrodes. In order to appreciate the factors responsible for the di€erences in the DFTs, two sets of sectional ®eld plots are presented. One was obtained with a given ®xed voltage (100 V) (Fig. 7) and the other with a given ®xed current (1 A) (Fig. 8) between the shocking electrodes. The plots with input current of 1 A show the ®eld distribution without the e€ect of system impedance and facilitate understanding of the di€erences in current DFTs. There are total 15 horizontal sectional slices with 6 mm separation covering the ventricles. In the both ®gures, three cross sections were examined in each set, one close to the epicardial apex of the heart (12 mm above the apex), one was across the middle section of the heart (48 mm above the apex), and the third one was close to the base of the heart (84 mm above the apex). For the plots with 100 V (Fig. 7), current density has been divided into ten ranges from zero (dark blue) to 25 mA/cm2 (orange) in continuous spectrum and any value greater 25 mA/cm2 is shown in red. For the plots with 1 A (Fig. 8), current density has been also divided into nine ranges from 0.7 mA/cm2 (dark blue) to 7 mA/cm2 (orange) in continuous spectrum and any value greater 7 mA/cm2 is also shown in red. 4.2. Comparison of LSVC-RV and Can-RV systems The FEA results (Table 2) indicate Can-RV system reduced voltage DFT by 20% compared with LSVC-RV system (347 V vs. 438 V), which corresponds to a 40% reduction in stored energy DFT (7.2 J vs. 11.5 J) with a 120 uF capacitor. This reduction in DFT was mainly due to an improvement in ®eld distribution indicated by lower current DFT (6.0 A vs. 9.3 A), since the impedance with Can-RV was higher (58 O vs. 47 O). Fig. 7. Current density plots when 100 volts was applied across the following de®brillation electrode systems. (a) LSVC-RV; (b) Can-RV; and (c) Can + LSVC-RV. The top row is a section close to the base of the heart (84 mm above the apex), the middle row is a section from the mid portion of the heart (48 mm above the apex), and the bottom row a section close to the apex of the heart (12 mm above the epicardial apex). Current density from zero (dark blue) to 25 mA/cm2 (orange) is mapped into ten intervals in a continuous spectrum and red color for tissue at a current density greater than 25 mA/cm2. Fig. 8. Current density plots when 1 A was applied across the following de®brillation electrode systems. (a) LSVCRV; (b) Can-RV and (c) Can + LSVC-RV. The top row is a section close to the base of the heart (84 mm above the apex), the middle row is a section from the mid portion of the heart (48 mm above the apex), and the bottom row is a section close to the apex of the heart (12 mm above the apex). Current density from 0.7 (dark blue) to 7 mA/cm2 (orange) is mapped into nine intervals in a continuous spectrum and red color indicates tissue with current density greater than 7 mA/cm2.

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Table 3 Clinically measured and model results for Can-RV and LSVC-RV electrode systems Impedance (O) clinical Can-RV LSVC-RV Ratios

56 2 8 54 2 7 1.04

FEA 58 47 1.23

Voltage DFT (V)

Current DFT (A)

clinical

clinical

FEA *

3722 73 4342 80* 0.86

347 438 0.80

FEA *

6.9 2 1.7 8.1 2 1.3* 0.85

6.0 9.3 0.65

*

P < 0.05 for Can-RV vs. SVC-RV.

The ®eld distribution plots in Figs. 7 and 8 help explain the di€erence in the voltage and current DFTs. The di€erence in DFTs is more attributable to the mass of tissue with low voltage gradient or current density. The low voltage gradient region, i.e. 5% mass with voltage gradient less than 5 V/cm, was identi®ed as the apex of the heart for LSVC-RV and the apex of the heart and the posterior LV free wall for Can-RV. With 1 A of current into electrode systems, Fig. 8 illustrates that current density with the LSVC-RV system was lower in the posterior LV free wall and the apical regions as compared to the Can to RV system. The LSVC-RV created a greater nonuniformity of ®eld distribution in myocardium. This is also illustrated in Figs. 4 and 5 compared with the uniform ®eld. Additional current was injected into the high current density regions in the septum due to the proximity of the SVC electrode, where the current density was already a few times greater than the threshold. Current shunting through the blood between SVC and RV electrodes was also another major factor contributing to higher current DFTs for LSVC-RV system. Similarly by viewing the plots with 100 V (Fig. 7), ®eld distributions were similar to those in Fig. 8 except for the di€erent scaling factors due to the impedance of the electrode systems and voltage DFT with LSVC-RV would be higher as illustrated in Fig. 7.

Fig. 9. Ratios of voltage DFTs with LSVC-RV and Can-RV de®brillation systems plotted as a function of critical mass.

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Table 4 Clinical data from 15 patients (Bardy et al., 1994) and model results for Can-RV and Can + HSVC-RV electrode systems Impedance (O)

Can-RV Can + HSVC-RV Ratios

clinical

FEA

61 2 6* 49 2 3* 1.24

58 44 1.32

Can + HSVC-RV vs. Can-RV:

**

Voltage DFTs (V)

Current DFT(A)

clinical

clinical

FEA

5.52 2.0$ 6.32 1.8$ 0.87

5.9 7.0 0.84

FEA

3342 116** 347 3062 83** 308 1.09 1.13

P = 0.25; *P < 0.05; $P = 0.062.

The voltage DFTs are lower with the Can to RV system in spite of a higher impedance. Though the size of the Can electrode was much bigger than the SVC electrode, the impedance of the Can-RV system was higher than with the SVC-RV system (58 O vs. 47 O) because the Can electrode is surrounded by a higher resistivity tissue (i.e. subcutaneous fat and skeletal muscle) and the higher resistivity tissue of lung is in the current pathway. As we mentioned before, the values used in the critical mass and voltage gradient threshold would a€ect the values of calculated DFTs. Comparing the two curves of LSVC-RV and CanRV (Fig. 5), the two voltage DFT curves intersect at the point around 70% and the DFT with Can-RV system was lower when the critical mass was greater than 70%. However the current DFTs were lower with Can-RV system for all the values of the critical mass. Comparing the curves with the case of uniform ®eld, we could see that Can-RV system has more uniform ®eld distribution than that with LSVC-RV. Conceptually, one would expect that electrodes far from the cardiac tissue create more uniform ®eld distribution. With Can-RV system, there is one extracardiac electrode whereas with SVC-RV, both the electrodes are proximal to the heart. These FEA results were compared with a clinical study in 15 patients (Zardini et al., 1993). The mean values of voltage DFTs and their ratios are similar to the FEA results (Table 3). When the ratios of DFTs between SVC-RV and Can-RV systems are compared, the clinical ratio in this patient group matches the FEA curve at 95% critical mass and also the ratio of FEA results became less than one around 70% critical mass (Fig. 9).

Table 5 Clinically measured results in 19 patients (Gold et al., 1995) and model results for Can-RV and Can + LSVC-RV electrode systems Impedance (O)

Can-RV Can + LSVC-RV Ratios

clinical

FEA

55 2 10* 36 2 7* 1.53

58 37 1.57

Can + LSVC-RV vs. Can-RV: *P < 0.05.

Voltage DFTs (V)

Current DFT (A)

clinical

clinical

FEA

6.72 1.9* 8.92 2.9* 0.75

5.9 7.7 0.77

3552 93* 3052 71* 1.16

FEA 347 285 1.22

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Fig. 10. Ratios of voltage DFTs, i.e. the voltage DFT with Can-RV (V1) scaled by that with Can + HSVC-RV (V2) or Can + LSVC-RV (V3), plotted at the selected critical mass with voltage gradient threshold at 5 V/cm.

4.3. Comparison of Can-RV and Can + SVC-RV electrode systems FEA results (Tables 4 and 5) show that addition of an electrode at either low (LSVC) or high SVC (HSVC) position reduces voltage DFTs (18% with LSVC and 12% with HSVC) compared with Can-RV system. The LSVC position yielded lower DFTs (7%) than that with HSVC position. The reduction in voltage DFTs was attributed to the signi®cant reduction in the impedance, i.e. 34% with LSVC and 24% with HSVC electrode. This reduction in impedance occurs because there is a parallel path for the current to ¯ow, i.e. it can ¯ow from the Can as well as the SVC electrode. This reduction in impedance dominated the e€ect on voltage DFTs even though the ®eld distributions deteriorated due to shunting of current through the blood from the SVC to RV coil. The current DFT increased by 23% with LSVC and 17% with the HSVC electrodes. Figure 5 shows that the voltage DFTs with Can + SVC-RV were lower for all the values of critical mass and LSVC position had lower voltage DFT than with HSVC position. On the other hand, the current DFTs (Fig. 6) for Can + SVC-RV were higher than with Can-RV system and the HSVC position had lower current DFTs than LSVC position. Comparing the curves with the uniform ®eld (Fig. 5), the uniformity of ®eld distribution with Can + SVC-RV was less than that with Can-RV and it was clearly greater than that with LSVC-RV. When the ratios of voltage DFTs (Fig. 10), i.e. the voltage DFT with Can-RV (V1) scaled by that with Can + HSVC-RV (V2) or Can + LSVC-RV (V3), were plotted, the change of FEA ratios was not as big as the case in Fig. 9 in the range of 50% to 95% critical mass percentile. The clinical ratios did not intersect the curves of FEA ratios but their values were close to them. The plots in Fig. 8 show that when 1 A of current is passed through the electrodes, the region of low current density increases in the basal, mid and apical cardiac sections (greater regions with dark blue) with the Can + SVC to RV system as compared to the Can to RV system. This indicates a deterioration of the ®eld distribution with the 3 electrode system. The low voltage gradient region (5% ventricular mass with voltage gradient <5 V/cm) for Can + SVC-RV system was identi®ed as the apex of the heart, which is similar to that with LSVC-RV. This deterioration occurs in spite of the fact that the area of the high current density region increases in the basal section with the Can + SVC to RV electrode system. Due

0 12 30 40 55

RV electrode spacing (mm)

314 317 347 437 534

5.2 5.3 6.0 7.5 9.4

61 60 58 58 57

303 330 438 625 899

voltage (V)

impedance (O)

voltage (V)

current (A)

LSVC-RV

Can-RV

5.8 6.6 9.3 13.6 20.4

current (A) 52 50 47 46 44

impedance (O)

208 228 285 371 483

voltage (V)

5.1 5.8 7.7 10.3 13.8

current (A)

Can + LSVC-RV

41 40 37 36 35

impedance (O)

Table 6 The e€ect of the spacing between the distal end of RV electrode and endocardial RV apex based on 95% ventricular mass with voltage gradient >5 V/cm

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369

the reduction in impedance, Fig. 7 illustrates higher current density overall in each of the sections with the 3 electrode de®brillation system when 100 V is applied across the electrodes. The SVC electrode provides some improvement in current density in the posterior LV free wall adjacent to the base of the heart and some in the anterior RV free wall. At the same time, the volume of septum with high current density (shown in red) also increases resulting in a greater nonuniformity of ®eld distribution in myocardium. These FEA results were compared with the clinical data in 15 patients (Bardy et al., 1994) with HSVC and in 19 patients (Gold et al., 1995, 1997) with LSVC electrode position. With HSVC (Table 4), both FEA and the clinical data show that the addition of SVC electrode at HSVC position reduced DFTs but the clinical study did not have enough statistical power to show the statistical di€erence with 15 patients (P = 0.25). The ratios of the current and voltage DFTs with the two systems were also similar. The clinical data with the LSVC position (Table 5) also shows a good correlation with the FEA results and indicates that the reduction in voltage DFT occurred primarily due to a reduction in impedance.

4.4. Summary In summary, FEA results indicate that the voltage DFT with Can-RV system was lower than LSVC-RV due to a better ®eld distribution (more uniform and higher current density in the low voltage gradient regions) and the Can + SVC-RV had the lowest voltage DFTs caused by a signi®cant reduction in impedance with the 3 electrode system. The voltage DFT with HSVC position was higher than with LSVC position for Can + SVC-RV system. This ratio of DFTs correlates well with the clinical results. The sectional ®eld plots from the FEA analysis indicate that the low voltage gradient regions (5% mass with voltage gradient <5 V/cm) were the apex of the heart for SVC-RV and Can + SVC-RV systems, and the apex of the heart as well as posterior LV free wall for Can-RV system.

Fig. 11. FEA results of voltage DFTs (based on 95% ventricular mass with voltage gradient >5 V/cm) plotted as a function of spacing between the distal end of RV electrode and endocardial RV apex for three de®brillation systems.

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5. E€ect of RV electrode positions and length on de®brillation ecacy for SVC-RV, Can-RV and Can + SVC-RV systems 5.1. E€ect of distal RV electrode position on DFTs As stated in the previous section, the apex of the heart is the common low voltage gradient region for SVC-RV, Can-RV and Can + SVC-RV systems. Since the edge e€ect of RV electrode results in current peaks near the ends (the distal and the proximal) of the coil, we hypothesized that placing a RV electrode distally towards the apex would inject more current into low voltage gradient region, resulting in lower DFTs. We analyzed the e€ect of changing the location of the RV electrode on DFTs (Min and Mehra, 1996a). All the electrodes except the RV electrode remain unchanged. A 5 cm long RV electrode was placed with the distal end 0, 1.2, 3.0, 4.0 and 5.5 cm away from the endocardial RV apex of the heart. The RV electrodes were generated along the `wireframe' which simulated the lead coming from SVC and RA through the tricuspid valve into the endocardial RV apex. With 4.0 cm spacing, the proximal end of the RV electrode was 3 mm below the tricuspid valve. The results with various RV electrode placement are listed in Table 6 and plotted in Fig. 11. FEA results indicate that voltage DFTs decreased when the RV electrode was placed distally for all three electrode systems. The DFTs for all systems were relatively stable at spacing less than 1.2 cm. The DFTs for LSVC-RV were higher and increased at a higher rate when the spacing increased. For all the systems, the impedance increased slightly as RV electrodes were placed distally due to the bigger inter electrode separation. However, the current DFTs decreased because the current density in the low voltage gradient region (the apex of the heart) was elevated with distal location of the RV electrode. The improvement in the ®eld distribution contributed primarily to the reduction of voltage DFTs. The low current density regions, i.e. 5% ventricular mass with voltage gradient less than 5 V/cm remained similar except for that some of them was shifted from the apex of the heart to the posterior LV free wall as the RV electrode was placed towards the apex. No clinical data as yet directly supports the FEA results on distal RV electrodes. However, animal studies have shown that distal RV electrode position results in lower DFTs for the SVC-RV system.

Table 7 Experimental data in eight swine at 0 (RV0), 1 (RV1) and 2 cm (RV2) spacing between the distal end of the coil and the endocardial apex of RV

Separation (cm) Voltage DFT (V) Current DFT (A) Stored Energy DFT (J) Impedance (O)

RV2

RV1

RV0

2 5652 95* 9.22 2.0* 27.6 2 9.5* 43.8 2 5.1*

1 5002 58 7.52 1.6* 20.92 4.7 48.52 5.7*

0 4582 47 6.3 2 1.0 17.1 2 3.8 52.3 2 5.4

Mean 2 S.D., *P < 0.05, RV2 vs. RV0 or RV1 vs. RV0.

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Table 8 The model results on the e€ect of septal RV electrode positions for LSVC-RV

LSVC-Ant S RV LSVC-Mid S RV LSVC-RV

Impedance (O)

Voltage DFT (V)

Current (A)

48 46 47

382 405 438

8.0 8.8 9.3

Usui et al. (1994) reported on DFTs with the SVC-RV systems in eight swine at three RV electrode positions (Table 7) and observed that the voltage DFT decreased with decreasing distance from the endocardial RV apex. Their results were similar to the model prediction that the mean voltage DFT was reduced by 8% from RV1 to RV0 (P = ns), and by 19% from RV2 to RV0, and this reduction was mainly due to better ®elds distribution indicated by lower mean current DFTs (16±32%). Another animal study (Heil et al., 1994) in twelve swine also reported similar results with the SVC-RV systems. They observed a 10% reduction in voltage DFT when the tip of the RV coil moved from 2 to 1.2 cm towards the endocardial apex. In summary, FEA results predict that distal RV electrode position results in lower DFTs for all the systems discussed here. Even though no clinical study has been conducted to test the e€ect of this variable, the animal results for SVC-RV system are consistent with our FEA data. In the clinical settings, the spacing between the endocardial RV apex and the RV electrode could be highly varied due to the locations of the tip, the designs of RV electrode, and the implant technique etc. We recommend that the tip of the RV electrode needs to be positioned as far into the endocardial apex as possible so that lowest DFTs can be achieved. 5.2. E€ect of septal RV electrode position on DFTs The e€ect of RV position related to intraventricular septum was also investigated in this model. With a spacing of 3.0 cm between the distal end of the coil and the endocardial apex, a 5 cm long RV electrode was positioned at three di€erent locations. In the standard `free wall' position (RV), the RV coil was the same one described in the Section 2, which was generated to simulate the common clinical position following the natural curve from SVC, RA and into the endocardial RV apex. It is proximal to the junction of the posterior RV free wall and the septum. We also generated a RV coil along RV out¯ow called `anterior septum' (Ant S RV) position and another one at intermediate position (lower than Ant S RV but higher than RV

Table 9 The model results on the e€ect of septal RV electrode positions for HSVC-RV

HSVC-Ant S RV HSVC-mid S RV HSVC-RV

Impedance (O)

Voltage DFT (V)

Current DFT (A)

59 58 62

418 446 446

7.1 7.7 7.2

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Table 10 The model results on the e€ect of septal RV electrode positions for Can-RV

Can-Ant S RV Can-Mid S RV Can-RV

Impedance (O)

Voltage DFT (V)

Current DFT (A)

58 57 58

389 396 347

6.7 6.9 6.0

positions) called `mid septum' (Mid S RV). A SVC electrode was placed in either high (with 8 cm long coil) or low SVC position (with 5 cm long coil) in the model. The e€ect of septal RV positions was studied for SVC-RV, Can-RV and Can + SVC-RV systems. For LSVC-RV (Table 8), mid or anterior septal positions result in lower voltage DFTs (8± 13%) compared with the free wall position. The impedance did not change much but current DFTs decreased with the septal RV positions indicating a improvement of ®eld distribution. With all the electrode positions, the low current density region remained around the apex of the heart. With septal RV electrode positions, more current was injected into low current density region, i.e. the region of septal insertion to ventricular free walls, and the apex of the heart. For Can-RV system, the e€ect of septal RV positions was di€erent (Table 10). Mid and anterior septal positions result in higher voltage DFTs (12±14%) instead. The impedance was almost the same and therefore the increase in voltage DFTs was due to an increase in current DFTs. Since Can electrode was in the anterior upper region over left margin of the heart, the septal RV position made more current ¯owing out¯ow tract resulting worse ®eld distribution. The low voltage gradient region (5% ventricular mass with voltage gradient <5 V/cm) was still the apex of the heart but more starving. The ®eld distribution became less uniform with septal RV positions. Since the change in voltage DFTs respect to septal positions with Can-RV system had the opposite trend to that with LSVC-RV, the change for HSVC-RV would be expected to be inbetween. For HSVC-RV (Table 9), anterior septal RV position resulted in slightly lower voltage DFTs (6%) compared with the free wall position. At mid septal position, the impedance was slightly lower but current DFTs were slightly higher so that no change in DFTs observed compared with free wall position. The e€ect of septal RV position on DFTs was smaller compared with LSVC-RV system. Similar to the case of HSVC-RV, e€ect of septal RV positions for Can + LSVC-RV (Table 11) would be somewhere in-between Can-RV and LSVC-RV. Mid or anterior septal positions result in almost the same voltage DFTs (1±3%) compared with the free wall position. Table 11 The model results on the e€ect of septal RV electrode positions for Can + SVC-RV

Can + LSVC-Ant S RV Can + LSVC-Mid S RV Can + LSVC-RV

Impedance (O)

Voltage DFT (V)

Current DFT (A)

38 36 37

271 278 285

7.1 7.7 7.7

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Table 12 The e€ect of RV electrode length for Can-RV de®brillation system as computed in the model RV electrode length (cm)

Stored Energy (J) Current DFT (A) Voltage DFT (V) Impedance (O)

7.4

6.5

5

9.5 7.36 397 54

8.7 6.95 382 55

7.2 5.98 347 58

3.5

2.5

7.48 5.69 353 62

8.35 5.52 373 67.6

In summary, e€ect of septal RV positions on voltage DFTs was di€erent for di€erent systems. For LSVC-RV system, anterior or mid septal RV electrode locations reduced voltage DFTs compared with the free wall position. The reduction of voltage DFTs was due to improvement of ®eld distribution. For Can-RV system, the voltage DFTs increased with septal positions caused by poorer ®eld distribution and the change in DFTs was negligible for HSVCRV and Can + LSVC-RV systems. There are several animal and clinical studies that investigate the e€ect of septal RV lead positions on de®brillation ecacy. A prospective animal study in twelve swine (Winter et al., 1995) showed that mid or anterior septal locations of the RV electrode yielded signi®cantly lower energy DFTs (30%) (21.9 21.1 vs. 31.821.2 J, with P < 0.05) than that with free wall position for LSVC-RV system. Recently Winter et al. (1997) showed in a paired clinical study in eight patients that the septal RV position also yielded lower DFTs (6.62 1.4 vs. 10.521.9 J, with P < 0.05) for LSVC-RV system. No clinical work has been reported yet for Can-RV and Can + SVC-RV systems. 5.3. E€ect of RV electrode length on DFTs The RV coil length is another parameter that can a€ect de®brillation ecacy. The optimal RV coil length, however, may depend on multiple factors, including dimensions of heart, location of RV electrode etc. To determine the e€ect of RV coil length on DFTs, we studied several RV lengths for Can-RV and SVC-RV systems in this model (Min and Mehra, 1996b). A RV electrode was placed with its distal end 3.0 cm away from the endocardial apex of RV and a 5 cm long SVC electrode was placed at LSVC position. DFTs were computed at RV electrode lengths of 2.5, 3.5, 5, 6.5 and 7.4 cm. Table 13 FEA results on the e€ect of RV electrode length for LSVC-RV RV coil length (cm)

Current DFT (A) Voltage DFT (V) Z (O)

7.4

5

3.5

2.5

12.6 517 41

9.3 438 47

7.9 413 52

7.8 446 57

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Table 14 FEA results on the e€ect of RV electrode length for Can + LSVC-RV RV electrode length (cm)

Current DFT (A) Voltage DFT (V) Z (O)

7.4

5

3.5

2.5

9.8 304 31

7.7 285 37

6.9 284 41

6.2 293 47

For Can-RV (Table 12), the voltage DFT was the minimum around 5 cm RV electrode length, but the di€erence in voltage DFTs was very small (only 2%) between 3.5 and 5.0 cm RV electrode length. With 6.5 cm RV electrode length, the proximal end of RV electrode was about 3 mm above the tricuspid valve. Increasing RV electrode length from 5 to 6.5 cm increased voltage DFTs (10%) due to an increase in current DFTs (21%). The increase in current DFTs may be caused by greater current being wasted in the RA when the proximal end of the electrode crosses the tricuspid valve. Decreasing RV electrode length from 5.0 to 2.5 cm increased the voltage DFT slightly (5%) due to an increase in impedance caused by a shorter coil length and larger inter-electrode spacing. The lower current DFTs with a shorter RV coil was due to better ®eld distribution resulting from the proximal end of the electrode getting closer to the endocardial RV apex or low voltage gradient regions. For LSVC-RV (Table 13), the lowest voltage DFTs were obtained with the 3.5 cm RV electrode length. The voltage DFT with 3.5 cm RV electrode length was 6 or 7% lower than that for 5 or 2.5 cm respectively. The impedance increased as the RV electrode length decreased, and the current DFTs decreased as RV electrode length decreased. Clearly at 3.5 cm, the reduction in current DFT was the more dominant e€ect, resulting in the lowest voltage DFT. As one would expect, the e€ect of RV electrode length for Can + LSVC-RV system would be similar to the two systems discussed above. As shown in Table 14, voltage DFTs were the same with either 3.5 or 5 cm RV electrode length and higher with 7.4 cm. In summary, the optimal RV electrode length was approximately between 3.5 to 5.0 cm for LSVC-RV, Can-RV and Can + LSVC-RV systems in this model. As expected, longer electrode had lower impedance but higher current DFTs indicating less ecient ®eld distribution. And the change in voltage DFTs with RV electrode length depended upon the dominance of one variable over the other. 5.4. Summary For e€ect of distal RV electrode position, FEA results predict that distal RV electrode position results in lower DFTs for SVC-RV, Can-RV and Can + SVC-RV system. Even though no clinical study has been conducted to validate this, the animal results for SVC-RV system are consistent with our FEA data. In the clinical setting, we recommend that the tip of the RV electrode to be positioned as far into the endocardial apex as possible so that lower DFTs could be achieved.

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Table 15 Modeling and clinical data (Stajduhar et al., 1996) comparing LSVC and HSVC positions for SVC-RV system FEA

Clinical (n = 16)

LSVC Voltage DFT (V) Current DFT (A) Impedance (O)

438 9.3 47

LSVC vs. HSVC: *P = 0.06 and

**

HSVC 496 8.4 59

LSVC

HSVC *

525 2 103 ± 55 2 5.7**

4762 102* ± 68 2 8.4**

P = 0.0001.

The e€ect of septal RV positions on voltage DFTs was di€erent for di€erent systems. For LSVC-RV system, anterior or mid septal RV electrode locations reduced voltage DFTs compared with the free wall position. For Can-RV system, the voltage DFTs increased with septal positions caused by poorer ®eld distribution. The reduction of DFTs became insigni®cant for HSVC-RV and Can + LSVC-RV systems. The animal and clinical studies with LSVC-RV systems had consistent results with FEA data. For e€ect of RV electrode length, the optimal RV electrode length was approximately between 3.5 to 5.0 cm for LSVC-RV, Can-RV and Can + LSVC-RV systems in this model. As we expected, longer electrode would have lower impedance but has higher current DFTs indicating less ecient ®eld distribution. The di€erence in DFTs, however, was not very signi®cant with di€erent coil length. 6. E€ect of SVC electrode position and length on DFTs for SVC-RV and Can + SVC-RV electrode systems 6.1. E€ect of SVC electrode position As stated in Section 4, lower de®brillation threshold (DFT) can be obtained by connecting the SVC electrode to the Can and shocking to RV, i.e. Can + SVC to RV. Since the SVC electrode can be located in the LSVC or HSVC position, we analyzed the e€ect of the SVC coil position on DFTs for SVC-RV and Can + SVC-RV systems. Table 16 Modeling and clinical data (Gold, personal correspondence) comparing LSVC and HSVC positions for Can + SVC-RV system FEA

Clinical (n = 20)

LSVC Voltage DFT (V) Current DFT (A) Impedance (O) LSVC vs. HSVC: *P = 0.73;

285 7.5 38 **

HSVC 308 7.0 44

P < 0.05; $P = 0.78.

LSVC

HSVC

362.3 2 100.3* 6.7 2 2.5$ 38 2 4**

382.4 2 86.4* 6.5 2 2.2$ 42 2 6**

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Table 17 The model results on e€ect of SVC coil length for LSVC-RV, HSVC-RV and Can + HSVC-RV SVC coil length (cm) LSVC-RV

Voltage DFT (V) Impedance (O) Current DFT (A)

HSVC-RV

Can + HSVC-RV

5.0

8.0

5.0

8.0

5.0

8.0

438 47 9.3

403 44 9.2

628 62 10.1

551 56 9.8

308 47 6.6

313 46 6.8

As in the previous cases, the Can electrode was positioned in the left pectoral region subcutaneously and a 5 cm RV coil was placed with its distal end 3.0 cm from the endocardial apex of RV (the control position, i.e. free wall position). The 5 cm long SVC coil was placed at either the HSVC or the LSVC position. For SVC-RV (Table 15), the LSVC position resulted in a 12% lower voltage DFT compared with the HSVC position mainly due to a lower impedance. The current DFT was lower with HSVC position. These results do not correlate well with the clinical results which show lower voltage DFTs with the HSVC position than with LSVC position (P = 0.06) (Stajduhar et al., 1996) in sixteen patients. The discrepancy between the FEA and the clinical data might be due to the variations in cardiac anatomy in this patient population. For Can + SVC-RV system (Table 16), FEA results show that the voltage DFT was slightly lower with LSVC position (7%) compared with the HSVC position. This was primarily due to a lower impedance (14%) with LSVC position while the current DFT was higher by 7%. The current DFT was higher because the ®eld distribution was worse with low SVC position due to greater current being shunted through the blood. However, the reduction of de®brillation impedance compensated for the degradation in ®eld distribution resulting in slightly lower voltage de®brillation threshold. This trend in DFTs was consistent with the clinical results in twenty patients (Gold, personal correspondence). The paired clinical data shows the same trend although the di€erences are not statistically signi®cant (P = 0.73).

Table 18 The model results on e€ect of SVC electrode length for Can + LSVC-RV SVC electrode length (cm)

3.5 5.0 8.0 12.0

Can + LSVC-RV voltage (V)

impedance (O)

293 285 283 278

38 37 36 35

current (A) 7.7 7.7 7.9 7.9

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6.2. E€ect of SVC electrode length The SVC electrode length is another parameter which could be optimized for de®brillation with the SVC electrode at either the LSVC or HSVC position. Several SVC electrode lengths were tested, 5 and 8 cm for LSVC-RV, HSVC-RV and Can + HSVC-RV systems, and 3.5, 5, 8 and 12 cm for Can + LSVC-RV. For LSVC-RV (Table 18:), increasing SVC coil length from 5 to 8 cm decreased voltage DFT (8%). The reduction in voltage DFT was mainly due to a reduction of impedance as the current DFTs were unchanged. This was not unexpected since theoretically, one would expect longer coil electrodes to have lower impedance. Also for HSVC-RV system (Table 18), voltage DFT was lower by 12% with the 8 cm coil due to a reduction in impedance as the current DFTs were almost the same. With HSVC-RV system, the data was obtained with 4.0 cm spacing between the distal end of RV electrode and the endocardial RV apex. These reductions in voltage DFTs with the longer SVC coil lengths are not observed with the Can + HSVC-RV system because there is almost no change in system impedance as the SVC coil length increased from 5 to 8 cm (Table 17). Also for Can + LSVC-RV (Table 18), increasing the SVC electrode length greater than 5 cm also did not signi®cantly improve the DFTs (02%). Again, due to the parallel connection of the SVC coil with the Can electrode, the e€ect of a change in the SVC coil impedance is minimized and the system impedance does not decrease much with increasing length (3±5%) while there is a small increase in current DFTs (3%).

6.3. Summary Lower DFTs can be obtained with LSVC position due to lower impedance for SVC-RV and Can + SVC-RV systems in the model. This trend in FEA results correlates with the clinical data for Can + SVC-RV system but not for SVC-RV system. Increasing SVC length greater than 5 cm does not improve voltage DFTs for Can + SVCRV. However, longer SVC coil length decreased voltage DFTs for SVC-RV system due to a reduction in impedance.

Table 19 The model results on e€ect of Can size for Can-RV system Can size (cm3)

Impedance (O)

80 60 40 20

46 47 52 59

Voltage DFT (V) 338 346 383 427

Stored energy (J) 6.9 7.2 8.8 10.9

Current DFTs (A) 7.4 7.4 7.4 7.2

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Table 20 Comparison of FEA and clinical results on e€ect of Can sizes in seventeen patients for Can-RV de®brillation Can sizes (cm3) Impedance (O) FEA 80 60 40 *

P = 0.67;

clinical **

46 47 52 **

Voltage DFT (V)

55 2 7 58 2 7** 62 2 9**

ratios

FEA

1.2 1.23 1.19

clinical

ratios *

338 346 383

3432 82 3642 115* 3722 90*

1.01 1.05 0.97

P = 0.05.

7. E€ect of Can electrode size and position on DFTs for Can-RV and Can + SVC-RV systems 7.1. E€ect of Can electrode size As stated before, clinical studies showed that low DFTs can be obtained by utilizing active Can systems. Reducing de®brillation threshold would minimize the maximum stored energy in ICDs and reduce their size. With more ecient electrode systems and higher energy density capacitors and batteries, the Can size is also expected to get smaller. On the other hand, a smaller Can electrode would result in higher impedance and therefore potentially increase the voltage DFTs. In this section, the e€ect of downsizing Can electrode from 80 to 60, 40 and 20 cm3 on DFTs will be analyzed for Can-RV (Min et al., 1994a) and Can + LSVC-RV systems. A 80 cm3 Can electrode (Model 7219C, Medtronic Inc.) was positioned in the left pectoral region subcutaneously and scaled down proportionally from 80 to 60, 40 and 20 cm3. The 80 cm3 Can used in this analysis was positioned slightly di€erently from in the previous sections as it was slightly more inferior. The e€ect of Can position in the left pectoral region will be discussed later in this section. A 8 cm SVC electrode was placed at LSVC position and a 5 cm RV coil was placed 3 cm away from the endocardial RV apex in the free wall position. For Can-RV system (Table 19), reducing the Can size from 80 to 60 cm3 increased the impedance and the corresponding voltage DFT very slightly (2%) since the current DFT was unchanged. Reducing Can sizes further (from 80 to 40 cm3) caused a greater increase in voltage DFT and impedance (12%). And the increase in voltage DFTs and impedance became very signi®cant (21% in voltage and 22% in impedance) when the Can size was reduced from 80 to 20 cm3. The current DFT remained almost the same for the various Can sizes which Table 21 The model results on e€ect of Can sizes for Can + LSVC-RV. I1 is the current in the Can to RV pathway and I2 in the SVC to RV pathway Can sizes (cm3)

Impedance (O)

80 60 40 20

33 33.6 34.4 36

Voltage DFT (V) 268 272 280 291

Stored Energy (J) Current DFTs (A) I1/I2 4.3 4.4 4.7 5.1

8.1 8.1 8.2 8.1

0.95 0.92 0.74 0.61

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379

Fig. 12. FEA results of voltage DFTs as a function of Can electrode size for Can-RV and Can + LSVC-RV de®brillation systems.

indicates the ®eld distribution in the heart was not altered. One would expect the ®eld in the cardiac structures to remain unaltered since the Can electrode is relatively far. We compared these FEA results with a prospective clinical study (Jones et al., 1994) in 17 patients (Table 20). The ratios of computed and the clinically measured impedance and voltage DFTs are also listed. Clinical as well as the FEA data showed that the impedance increases with a smaller Can and this ratio remained relatively constant across di€erent sizes. The reason why this ratio is not unity is probably a result of the speci®c resistivity values e.g. of the skeletal muscle chosen in the this model. Clinically, there was no statistical di€erence in voltage DFTs (P = 0.67) between the Can sizes but the trend was consistent with the FEA results. For Can + LSVC-RV, one would expect even a smaller change in voltage DFTs by changing Can sizes due to the fact that the electrical connection of SVC and Can electrodes further minimizes the e€ect of changes in the Can electrode impedance. FEA results show (Table 21) that reducing Can sizes from 80 to 60 cm3 did not change voltage DFTs. Reducing the Can size further to 40 and 20 cm3 increased voltage DFTs by 4 and 8% respectively. The current DFTs remained relatively unchanged which indicates that the ®eld distribution did not alter. The small changes in voltage DFTs mainly were due to a change in impedance. With a SVC electrode connected to the Can, the increase in voltage DFTs are much smaller than that with Can-RV system (Fig. 12). It was observed that a dimensional change in either SVC or Can electrode has less e€ect on system impedance and DFTs when the SVC and Can electrodes are electrically connected. This is not unexpected as the impedance of multiple Table 22 Comparison of FEA and clinical data (Neuzner et al., 1996) in eleven patients on e€ect of Can sizes for Can + LSVC-RV Can sizes (cm3) Impedance (O) FEA 60 20 P = ns.

33.6 36

Voltage DFT (V)

Current DFTs (A)

clinical

FEA

clinical

FEA

clinical

39.75 2 1.9 40.75 2 1.9

272 291

323.5 2 17.8 3112 30.0

8.1 8.1

8.412 0.7 7.962 1.1

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Table 23 The model results on e€ect of Can positions in the left pectoral region for Can-RV de®brillation Can position

Control mid (SQ)

Voltage DFT(V) Current DFT(A) Impedance (O)

338 7.3 46

2 cm below mid (SM) 317 7.2 44

lat 315 6.4 49

mid 322 8.1 40

4 cm below lat

312 6.9 45

mid

lat

334 10.9 31

332 8.3 40

electrodes connected in parallel (with the same polarity) is highly dependent on the area bounded by the electrodes instead of the metallic area between them (Min and Mehra, 1993). The ratios of the current from Can-RV (I1) to that from SVC-RV (I2) indicate that more current ¯owed through SVC electrode when the Can impedance increased due to it's size reduction. With 80 or 60 cm3 Can, the current ratios were close to 1, and with 40 cm3 Can, the ratio down to 0.74 (20% change). The change in Can size did not alter the low voltage gradient regions and the ®eld distribution. We compared the FEA results with a clinical study (Neuzner et al., 1996) in which the Can sizes were altered but were slightly di€erent than those used in this model. 65 and 28 cm3 Can sizes were used in the clinical study (but 60 and 20 cm3 in the model) (Table 22) and no statistical di€erence in voltage and current DFTs and impedance was observed. In summary, for Can-RV system, DFTs did not change much by reducing the Can size from 80 to 60 cm3 and DFTs increased marginally from 80 to 40 cm3. The increase in DFTs became more signi®cant when the Can size was reduced from 80 to 20 cm3. The increase in voltage DFTs was due to an increase in the impedance. For Can + LSVC-RV system, e€ect of reducing Can sizes on voltage DFTs was much smaller than with Can-RV. The increase in voltage DFTs was small (about 8%) when the Can sizes was reduced from 80 to 20 cm3. The clinical results are compatible with these observations. 7.2. Sensitivity of DFT to Can position in the left pectoral region The Can electrode position during an ICD implant can vary within the left pectoral region among patients and it can be below the clavicle or at the level of the heart. Since the location of Can electrode in the left pectoral region might impact DFTs, we investigated the e€ect of several Can electrode positions for Can-RV and Can + LSVC-RV de®brillation (Min and Mehra, 1996c). For Can-RV, the Can electrode was in a submuscular pocket and positioned Table 24 The model results on e€ect of Can positions in the left pectoral region for Can + LSVC-RV de®brillation Can position

Voltage DFT (V) Current DFT (A) Impedance (O)

Control

2 cm below

4 cm below

SM

SQ

SM

SM

255 7.5 34

258 7.6 34

249 7.8 32

264 9.8 27

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underneath the clavicle (control position) and then 2 and 4 cm interiorly in the left pectoral region in submuscular (SM) pockets. The control location is used most frequently during a clinical implant and the location 4 cm interiorly was the case where the lower edge of Can was at the level of the upper border of heart. In addition to the positions described above, the Can position was also been shifted to a more lateral SM position (Lat) by 2 cm at all the corresponding locations (Table 23). For both Can-RV and Can + SVC to RV de®brillation, a submuscular Can at the control position was also compared with the corresponding subcutaneous position (SQ) where Can electrode was partially inside skeletal muscle and partially inside fat. For both con®gurations, a 5 cm RV electrode was placed 2.5 cm from the endocardial RV apex and for Can + SVC to RV, a 8 cm long SVC coil was located in the LSVC position. With Can to RV de®brillation, the FEA analysis showed that a lower Can electrode position results in lower impedance but higher current threshold. As a result, moving Can electrode interiorly in the left pectoral region tends to increase voltage DFT (2±6%) and the control position had the lowest voltage DFTs. The reduction in impedance at the inferior locations is probably associated with a smaller distance between the two high voltage electrodes and lower resistive current path ways. Moving the Can electrode laterally resulted in slightly higher impedance but lower current thresholds so that voltage DFTs did not change signi®cantly. DFTs with a submuscular and a subcutaneous Can location were also compared at the control location (Table 23), and the voltage DFT and the impedance were higher (6%) with the subcutaneous position. The lower submuscular impedance is due the lower resistivity of skeletal muscle compared with fat. Note that the voltage DFT and the impedance with this Subcutaneous Can location was di€erent compared with the one used in the previous sections (Table 2) mainly due to the di€erence in Can locations. For Can + LSVC-RV (Table 24), the increase in voltage DFT with inferior Can positions was similar (only 3±6%) and there was almost no di€erence in voltage DFTs comparing submuscular and subcutaneous Can locations. In summary, the FEA results indicate that for Can to RV de®brillation, Can electrode position in left pectoral region had some impact on de®brillation ecacy. Superior positions close to clavicle and submuscular locations tend to reduce voltage DFTs. When an SVC electrode is connected to the Can electrode, the change in voltage DFTs is similar.

Table 25 FEA results comparing the right pectoral (RP) Can and left pectoral (LP) Can positions Can-RV

Voltage DFT (V) Current DFT (A) Stored energy (J) Impedance (O)

RP Can + SVC-RV

LP

RP

313 7.0 5.9 45

481 9.1 13.9 53

LSVC 346 9.1 7.2 38

HSVC 359 9.3 7.7 42

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7.3. Comparison of right and left pectoral Can positions In a few patients, a Can electrode can not be placed in the left pectoral (LP) region due to the presence of a cardiac pacemaker or prior infection from a device implant. An alternative location for the Can electrode is in the right pectoral (RP) region. In this section, we will compare the DFTs with RP and LP Can position for Can-RV (Min and Mehra, 1995) and Can + SVC-RV systems and also compare these results with those for LSVC-RV. For this analysis, a 80 cm3 RP Can was placed in the right pectoral submuscular region with its upper edge at the level of the top of sternum and the LP Can was located symmetrically. A 5 cm RV electrode with its distal end 2.5 cm away from the endocardial apex of RV and a 5 cm SVC electrode located in the either the LSVC or HSVC positions were also utilized. For Can-RV (Table 25), the voltage DFT increased signi®cantly (35%) with a right pectoral Can and it was even higher than that with LSVC-RV (9%). The increase of voltage DFT was due to both impedance rise (15%) and worse ®eld distribution indicated by an increase in current DFT (23%) compared with a LP Can. The higher impedance is probably caused by a greater volume of non cardiac tissue including lung tissue between the RV and the Can electrodes. It is interesting to note that the current DFT with RP Can are similar to those with LSVC-RV and the 9% increase in DFTs is primarily due to a higher RP Can-RV impedance (11%). Also with the RP Can, the low current density region was identi®ed as the apex of the heart which is similar to that with LSVC-RV illustrating a similar ®eld distribution between RP Can-RV and LSVC-RV systems. As discussed in Section 4, with the LP Can, the low current density region was primarily localized over the apex of the heart and posterior LV free wall. Adding an SVC electrode at either LSVC or HSVC position to RP Can-RV reduced the voltage DFTs and brought them closer to those with LP Can-RV. Since the SVC electrode creates a similar ®eld vector as the RP Can, the current DFTs were almost the same with or without the SVC electrode. The reduction in voltage DFTs by adding a SVC electrode to RP Can system was therefore due only to a reduction in impedance. The low voltage gradient regions for all RP Can system were the apex of the heart. In summary, the voltage DFT increased signi®cantly with RP Can. The increase in voltage was due to both impedance rise and degradation of ®eld distribution. RP Can-RV had similar ®eld distribution to LSVC-RV but higher impedance, therefore higher voltage DFTs. However, if a Can electrode cannot be placed in the left pectoral region, the right sided position should be attempted. Addition of a SVC electrode at either LSVC or HSVC position would reduce voltage DFTs with RP Can system. The low voltage gradient regions (5% ventricular mass with voltage gradient <5 V/cm) are the apex of the heart for RP Can-RV and RP Can + SVC-RV systems. 7.4. Summary FEA results on e€ect of Can size predicted by the model support downsizing the size of ICDs up to a limit. For Can-RV system, voltage DFT increases are less than 12% for sizes up to 40 cm3 and may be acceptable. One must ensure that there is adequate safety factor for de®brillation ecacy if the output voltage is maintained at present levels. However, the

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increase in voltage DFTs became more signi®cant when Can size was reduced to 20 cm3 and is primarily due to an increase in impedance. For Can + LSVC-RV system, e€ect of reducing Can sizes on voltage DFTs was much smaller than with Can-RV. The increase in voltage DFTs was about 8% by reducing Can sizes from 80 to 20 cm3 and indicate that this would be the system of choice as device become smaller. The FEA results are also consistent with some of the clinical data available to date. The model results also indicate that Can electrode position in left pectoral region had some impact on de®brillation ecacy for Can-RV system. Superior position close to clavicle and submuscular position in left pectoral region tended to have lower voltage DFTs. With the addition of an SVC electrode, these changes in voltage DFT are similar. Comparing RP Can with LP Can position, the voltage DFT increased signi®cantly with the Can located in the right pectoral region. The increase in voltage DFT was due to impedance rise and degradation of ®eld distribution. RP Can-RV had similar ®eld distribution to LSVCRV but higher impedance and therefore a higher voltage DFT. However, if a Can electrode cannot be placed in the left pectoral region, the right sided position should be attempted. Addition of a SVC electrode at either LSVC or HSVC position would further reduce voltage DFTs with RP Can systems.

8. Limitations of the model and future work One limitation of this model relates to variations in cardiac anatomy. As stated in Section 2, this is a model of a patient who had normal cardiac anatomy but large heart size close to the upper bound of normal hearts. Recently, we have constructed a second model of a patient with a dilated LV and LV hypertrophy. Analyzing DFTs in the second model indicate that cardiac anatomy can alter the DFTs signi®cantly, and FEA results from the model discussed in this paper with normal cardiac anatomy correlates better with the clinical results suggesting that this model is a better representation of an average ICD patient. The results of the second human torso model will be discussed in detail in a future manuscript. Anisotropy of conductivity in skeletal muscle and myocardium was not included in the model. We expect that DFTs with Can electrode systems might be a€ected by anisotropy in skeletal muscle since the Can electrode was adjacent to it, whereas the e€ect on DFTs for SVC-RV system may be much smaller since the electrostatic ®eld attenuates quickly. We studied e€ect of anisotropy in skeletal muscle on DFTs for Can-RV by arranging the skeletal muscle ®ber circumferentially around the upper chest of the torso. The anisotropy was described by the ratio of the circumferential (along the ®ber) and transverse to ®ber conductivity and the ratio of 4:1 (6.7 to 1.7 mS/cm) was simulated. The FEA results were compared with the case with isotropic conductivity (2.5 mS/cm) and very small di€erence in voltage DFTs was found (3%). We also studied the DFT sensitivity to the variation in the isotropic conductivity of tissue or organs such as lung, connective tissue et al. Our experience with model told us that the relative di€erence in DFTs or at least the trend remained unchanged once we kept the conductivity values for all tissue or organs ®xed when we compared the systems. We suspect that the e€ect of anisotropy in myocardium may be canceled out to some degree since the orientation of ®bers change from layer to layer. Recent

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work by Eason et al. (1998) shows that the anisotropy of myocardium by incorporating Auckland Model into their human torso has small e€ect on DFTs (less than 5%) of Can-RV system even though the low voltage gradient regions altered to some degree. Another limitation of our analysis is that all the DFTs were calculated based critical mass hypothesis. Even though that a good agreement between the FEA and the clinical results suggests that the critical mass hypothesis may be the primary mechanism of de®brillation, a better understanding of de®brillation mechanism is needed. A hybrid model which simulates cardiac electrical activation and repolarization as well as interaction with de®brillation shocks would allow one to investigate de®brillation mechanisms in greater detail.

9. Conclusions A good correlation between the model results and the clinical data supports the use of ®nite element analysis of a human torso model for optimization of de®brillation electrode systems. This correlation also supports that the critical mass hypothesis is the primary mechanism of de®brillation. Both the FEA results and the clinical data show that Can + SVC-RV system o€ers the lowest voltage DFTs when compared with SVC-RV and Can-RV systems and it does not increase system complexity because the SVC and RV electrodes can be on a single lead. The model is a useful tool for optimizing the electrode design parameters to lower de®brillation thresholds. We studied the e€ect of RV, SVC and Can electrode dimensions and locations on de®brillation thresholds. We concluded that locating the RV electrode as far into the endocardial apex as possible would improve de®brillation ecacy. The optimal RV electrode length was identi®ed to be between 3.5 to 5 cm and the septal RV electrode position. The Can + SVC-RV DFT was the most robust with respect to electrode parameters, i.e. the least sensitive to SVC electrode and Can electrode dimension and location. Decreasing Can electrode size from 80 to 20 cm3 has a less than 8% impact on voltage DFTs for Can + SVCRV system even though the DFTs with Can-RV may increase signi®cantly. Increasing SVC electrode length would improve DFTs for SVC-RV but not for Can + SVC-RV systems. Can electrode location in the left pectoral region has some impact on DFT for Can-RV and Can + SVC-RV systems. Placing the Can electrode in the right pectoral region increases DFTs signi®cantly and adding a SVC electrode to right pectoral Can would be important to improve de®brillation ecacy. The model also gave insight into the ®eld distributions and impedance so that the factors responsible for di€erences in DFTs with various con®gurations could be appreciated. The 5% of the ventricular mass with the lowest voltage gradient regions were identi®ed as the apex of the heart for SVC-RV and Can + SVC-RV systems, and the apex of the heart as well as posterior LV free wall for Can-RV system. This ®eld distribution can be improved by elevating current density in the low voltage gradient regions of the heart such as by locating the RV electrode distally towards the RV apex. The ®eld distribution was the most uniform with Can electrode systems, which indicates a more ecient use of current. It is evident that lower voltage DFTs can be obtained by either of two strategies, i.e. reducing the impedance of de®brillation electrode systems or improving the ®eld distribution.

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In spite of the reasonable correlation with clinical results, the e€ect of di€erences in cardiac anatomy on DFTs still need to be investigated in order to provide a rationale method for optimizing the de®brillation system for a speci®c patient. Also, a better model needs to be developed that incorporates the mechanism of ®brillation and the electrophysiologic e€ects of de®brillation. Having a hybrid model in the future which simulates cardiac electrical activation, repolarization and the interaction with de®brillation shocks should facilitate our understanding of these processes.

Acknowledgements The authors are grateful to L. Wang, P.J. DeGroot and M.R.S. Hill of Medtronic, for their e€orts in tissue segmentation on the CT images and various discussions on human anatomy and clinical studies. The authors would also wish to thank J.F. Breen at Mayo Foundation for providing CT scan images to construct the human torso model.

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