a theoretical and experimental analysis of radiofrequency

A Theoretical and Experimental Analysis ofRadiofrequency Ablation with a Multielectrode,Phased, Duty-Cycled SystemMICHAEL LAU, M.ENG.,* BETTY HU, M.S.,* RANDY WERNETH, M.S.,*MARSHALL SHERMAN, B.S.E.E.,* HAKAN ORAL, M.D.,† FRED MORADY, M.D.,†and PETR KRYSL, PH.D.‡From the *Medtronic Ablation Frontiers, Carlsbad, California; †University of Michigan Health System, Ann Arbor,Michigan; and ‡University of California, San Diego, California

Background: The development of a unique radiofrequency (RF) cardiac ablation system, for the treat-ment of cardiac arrhythmias, is driven by the clinical need to safely create large uniform lesions whilecontrolling lesion depth. Computational analysis of a finite element model of a three-dimensional, mul-tielectrode, cardiac ablation catheter, powered by a temperature-controlled, multiphase, duty-cycled RFgenerator, is presented.

Methods: The computational model for each of the five operating modes offered by the generator iscompared to independent tissue temperature measurements taken during in vitro ablation experimentsperformed on bovine myocardium.

Results: The results of the model agree with experimental temperature measurements very closely—theaverage values for mean error, root mean square difference, and correlation coefficient were 1.9◦C, 13.3%,and 0.97, respectively. Lesions are shown to be contiguous and no significant edge effects are observed.

Conclusions: Both the in vitro and computational model results demonstrate that lesion depth de-creases consistently as the bipolar-to-unipolar ratio increases—suggesting a clinical application to po-tentially control lesion depth with higher fidelity than is currently available. The effect of variable designparameters and clinical conditions on RF ablation can now be expeditiously studied with this validatedmodel. (PACE 2010; 33:1089–1100)

ablation, multielectrode, radiofrequency, phasing, duty-cycle, finite element

IntroductionRadiofrequency (RF) catheter ablation is an

accepted therapeutic approach for treating varioustypes of cardiac arrhythmias such as supraven-ticular tachycardia, the Wolff–Parkinson–WhiteSyndrome, atrial flutter, atrial fibrillation, andventricular tachycardia.1–3 Recently, a cardiacablation system, consisting of a multielectrodeablation catheter driven by a phased, temperature-controlled, duty-cycled RF generator, has beendeveloped. Initial reports using this system forpulmonary vein isolation during treatment ofparoxysmal AF suggest significant reduction inboth procedure and fluoroscopy times.4

A number of pioneering publications on thecomputational modeling of RF energy applicationhave become available in the past 15 years andan excellent comprehensive review has recentlyappeared.5 Computational modeling enables the

Address for reprints: Michael Lau, M.Eng., 2210 Faraday Ave.Suite 100, Carlsbad, CA 92008. Fax: 760-827-0131; e-mail:[email protected]

Received October 21, 2009; revised March 10, 2010; acceptedMarch 29, 2010.

doi: 10.1111/j.1540-8159.2010.02801.x

study and optimization of design variables, such aselectrode material/size/spacing/shape, and abla-tion parameters (energy delivery mode, target tem-perature, ablation duration, power control, powerlimit, etc.). In vivo and in vitro experimentationrequire physical prototypes to be built, and canbe costly and time-consuming, sometimes result-ing in irreproducible or inconclusive findings. Inthis article, we improve on established simula-tion methods to model-phased RF ablation witha unique cardiac ablation system, and validate themodel using data collected from controlled in vitroablation. The resulting model can be used in futurework for design optimization and can be modifiedto model a variety of clinical conditions for fur-ther assessment of the performance of the ablationsystem.

Materials and MethodsRF Generator and Multi Array Ablation Catheter

The GENiusTM Multi-Channel RF Abla-tion Generator (Medtronic Ablation Frontiers,Carlsbad, CA, USA) is a temperature-controlled,power-limited, multiphase system to deliverRF energy to multielectrode ablation catheters.Power output to each electrode is regulated toachieve and maintain an operator-defined target

C©2010, The Authors. Journal compilation C©2010 Wiley Periodicals, Inc.

PACE, Vol. 33 September 2010 1089

LAU, ET AL.

temperature at the electrode–tissue interface (maxpower ranging from 6 to 10 W per electrode de-pending on energy mode). Through a combinationof phasing and duty-cycling, the GENius RF Gen-erator offers a selection of five operational modes,which control the ratio of bipolar-to-unipolar en-ergy to be delivered: unipolar only, 1:1, 2:1, 4:1, orbipolar only. For example, the 4:1 energy mode in-dicates that 80% of the energy delivered is bipolarand the remaining 20% is unipolar. Clinically, 1:1and 4:1 energy modes are the most widely used.

The Multi Array Ablation Catheter (MAACTM,Medtronic Ablation Frontiers) is composed ofeight finned platinum electrodes capable of map-ping and ablating in conjunction with the GE-Nius RF Generator. Each 2-mm-long electrode iscylindrical at the tissue interface and with finsto increase convective cooling from blood flow,placating the need for active irrigation. The elec-

Figure 1. (A) The Multi Array Ablation Catheter (MAAC) device. Each electrode contains athermocouple and is driven by a separate PI controller. Electrode fins increase cooling, enablingmore efficient energy delivery. Shaded areas show approximate location of thermocouple (not toscale). (B) A diagram of thermocouple placement at six locations within the tissue specimen formeasuring experimental tissue temperature.

trodes are affixed to an anatomically designed, X-shaped, collapsible nitinol frame (see Fig. 1A),intended to provide optimal contact across allelectrodes, allowing for large area mapping and ab-lation of complex fractionated atrial electrograms.Each arm of the X-frame supports a pair of elec-trodes; with four pairs in total, each ablation is ca-pable of creating up to four lesions. Each electrodehas a thermocouple located directly at electrode–tissue interface for accurate independent temper-ature control. In clinical usage, recommended set-tings are 60◦C target temperature and 60-secondduration.

Experimental Methods

An in vitro ablation experimental setup, pre-viously described,6 was modified for this studyto provide data for development and validationof the computational model. Briefly, a circulation

1090 September 2010 PACE, Vol. 33

MULTIELECTRODE RF ABLATION COMPUTATIONAL ANALYSIS

system was set up to carry out in vitro ablation onbovine myocardium. A 16-L saline bath is attachedto a precision inline heater (Infinity, Norwich, CT,USA), which maintained 0.5% saline at 37 ± 1◦C.The 0.5% saline was delivered via a tube withan inner diameter (ID) of 12.7 mm attached to aswivel nozzle with 20 circular orifices with an IDof 1.85 mm to simulate local blood flow. The flowrate was adjusted to 1.8 L/min or 4.0 L/min us-ing a flow meter (Cole Parmer, Vernon Hills, IL,USA). A force gauge (Imada, Northbrook, IL, USA)was mounted onto the x-y-z metric axis movement(Edmund Optics, Barrington, NJ, USA) to allowprecise positioning of the catheter and consistentelectrode–tissue contact.

Tissue specimens were obtained from freshbovine hearts (Tip Top Meats, Carlsbad, CA, USA).A block of myocardial tissue (approximately 32 ×45 × 15 mm) was placed in an acrylic chamberwith a ground plate. Tissue temperatures wererecorded by T-type thermocouples (0.064-mm di-ameter with Teflon; time constant of 0.1 sec-ond; measurement accuracy of ±0.1◦C; Physitemp,Clifton, NJ, USA). The thermocouples were placedat depths of 2 mm and 4 mm, in the followinglocations: underneath electrode 2, between elec-trodes 1 and 2, and under the mid array (seeFig. 1B). Ablations were conducted with a tar-get temperature of 60◦C for a 60-second dura-tion at each energy mode (unipolar, 1:1, 2:1, 4:1,bipolar). At the conclusion of ablation, the blockswere dissected. Lesions were visually delineatedas areas of marked tissue discoloration and mea-sured from the surface of the tissue to the deepestpoint of the lesion using a metric scale under 10×magnification.

Bioheat Equation

As the experiments are performed in vitro, thebioheat equation may be simplified by neglectingmetabolic heat generation and the heat exchangebetween tissue and blood (the perfusion effect). Itis solved together with the Laplace equation for therate of heat generation due to the resistive current

cpV T = ∇ · (k∇T) + σ (T) ‖E‖2, and

∇ · (σ (T)∇φ) = 0 (1)

where T is the temperature, T = ∂T∂t is the rate of

change in temperature, k is the thermal conduc-tivity, cpV is the specific heat per unit volume,E = −∇φ is the electric field intensity expressedthrough the electric potential φ, and σ (T) is theelectrical conductivity as a function of tempera-ture. In the present model, the material param-eters k and cpV are independent of the tempera-ture, but if and when the temperature dependencebecomes available for the materials at hand, the

model will accommodate it. The two balance equa-tions are coupled by the resistive heating termand the dependence of the electrical conductivityon the temperature, σ (T). The quasi-stationaryelectrical equation is adequate for the RF of500 kHz as the electrical impedance of tissue ismostly resistive at these frequencies.7,8

Geometry

The computational domain geometry wasadopted in the form of a cylindrical subset of16-mm radius of the rectangular tissue sample toreduce the computational effort. Two symmetryplanes separating electrodes 1 and 2 from the resthave been adopted to further reduce the compu-tational domain size. Thus the computational do-main is the top quadrant in Figure 2A, shown asthe computational mesh in Figure 2B. Note thatthe electrodes are pressed into the tissue by asmall amount of force (corresponding to weighton the catheter of about 30 g), which means that asa reasonable first approximation we can considerthe electrodes to be in the contact with the tis-sue through the bottom half of their entire circum-ference. Deformation of the tissue due to catheterplacement is neglected. The electrical contact be-tween the electrode and the tissue is assumed to beperfect, with no resistance to current flow passingfrom the ablation electrode to the tissue.

Thermal Boundary and Initial Conditions

The sample is immersed in a saline bath main-tained at 37◦C, which is taken as the initial tem-perature condition. The zero heat flux boundarycondition was applied on the symmetry planes.On the bottom surface and on the side surfaces ofthe tissue block an artificial Newton’s surface heattransfer term was applied as

qn = ha(T − Tb) (2)

where qn is the normal heat flux, T is the surfacetemperature, Tb is the temperature of the bath,and ha is the artificial heat transfer coefficientwhose value is chosen to approximate the heatflux from the sample into the surrounding envi-ronment, presumed to be at a constant temper-ature Tb. The numerical value was adopted, fornumerical stability but otherwise arbitrarily, asha = 5500 W/(m2 · K)—varying this parameter byan order of magnitude affects the temperature atthe sensors no more than 0.01◦C.

On the top surface of the tissue block and theelectrode surface (including the fin), exposed tothe saline bath, a convective surface heat transferterm was applied to comprehensively account forthe complex heat exchange between the sampleand the flowing saline bath. This coefficient was


LAU, ET AL.

Figure 2. (A) A schematic of the MAAC electrode orientation. During bipolar energy delivery,electrodes 1, 4, 6, and 7 are out of phase with electrodes 2, 3, 5, and 8. Plane 1 is a planeof symmetry and plane 2 is a plane of antisymmetry. (B) The computational mesh. Each cellrepresents either a quadratic 27-node element or a cubic 64-node element. Units of length, width,and depth as shown are millimeters.

estimated from an ad hoc experiment describedin the Appendix as hb = 2713 W/(m2 · K) and thenumerical value agrees with analogous parametervalues reported in the literature.9–11

Temperature Control and Electrical BoundaryConditions

Electrode temperature is measured by a ther-mocouple welded to the center of the electrode atthe electrode–tissue interface. Power delivery toeach electrode is controlled separately to achieveand maintain 60◦C at each electrode during theablation event. The control algorithm used in thegenerator hardware applies a fixed voltage wave-form at near 500 kHz (phased depending on theselected energy mode) in duty cycles of only a fewmilliseconds, modulating the length of the “on”portion of the duty cycle to control power out-put. Replicating the hardware control exactly inthe simulation would lead to significant associatedcomputational cost and for this reason only an ap-proximation to this control was implemented. Inthe simulation, unipolar and bipolar are assumedto each produce its own independent quasi-staticpotential field, with power output modulated byvarying the voltage amplitude. The electrical prob-lem is consequently solved twice in each timestep, and the specific absorption rates are thenmixed together in appropriate ratios for each ofthe five modes.

RF Generation of Heat

In unipolar energy delivery, for simplicity,the voltage of the dispersive electrode is fixedat a zero voltage, and the electrodes each havetheir own proportional-integral (PI) controller toapply the necessary voltage. The boundary condi-tion prescribes the electric potential on the sur-face of the electrodes and on the bottom of thesample (the dispersive electrode). All other sur-faces are associated with zero electric flux bound-ary condition. The parameters of the PI controllersof the two electrodes were taken as K p = 2.5 V/K,Ki = 0.0766 V/(K · s), calibrated to approximatetemperatures recorded at the electrodes for unipo-lar operation.

In bipolar energy delivery, the two electrodesof an electrode pair share a single PI controller toapply a voltage to electrode 1 and an opposite volt-age to electrode 2. The hardware controller drivesthe electrodes so that the electrodes 1, 4, 6, and7 are out of phase with electrodes 2, 3, 5, and8. Consequently, plane 2 is a plane of asymme-try for the electrical problem (see Fig. 2A). Theboundary condition prescribes the electric poten-tial on the surface of the electrodes, zero electricflux through plane 1, and zero potential on plane 2.All other surfaces are associated with zero electricflux boundary condition. The parameters of thePI controller of the pair of active electrodes weretaken as K p = 0.663 V/K, Ki = 0.021 V/(K · s),



calibrated to approximate temperatures recordedat the electrodes for bipolar operation.

For the mixed-modes 1:1, 2:1, and 4:1(bipolar-to-unipolar) energy modes, the electricalproblem is solved twice in each time step, oncefor unipolar mode and once for bipolar mode. Theelectric field for each mode of heat generation isused to calculate the thermal load due to resistiveheating, and the thermal loads are then mixed to-gether in appropriate ratios.

Space Discretization

Figure 2B shows the isometric view of the3,152 hexahedral cells that make up the compu-tational domain. The mesh size is strongly gradedfrom the largest elements (∼5 mm) to the ac-tive electrodes (∼0.3 mm) in order to capture thesharp gradients in both the electric and temper-ature fields. The same mesh is used for both thethermal and the electrical problem. The materialproperties used are given in Table I.

Each cell may be converted to eithera quadratic (27-node) or a cubic (64-node)Lagrangean finite element. The difference betweenthe results computed once with the quadratic dis-cretization and once with the cubic discretiza-tion allows us to estimate the discretization er-ror. The quadratic approximation leads to a totalof approximately 55,000 coupled equations in thethermal-electrical computation; the cubic approxi-mation results in a total of almost 180,000 coupledequations. The results obtained with the quadraticand the cubic discretization was a fraction of a

Table I.

List of Material Properties Used in the Computational Model

Symbol Quantity Value and Units

kt Thermal conductivity of bovine heart tissue 0.55 × 10−3 W/(mm · K)ρt Mass density of bovine heart tissue 1.2 × 10−6 kg · mm−3

cpVt Specific heat per unit volume of bovine heart tissue 3200 ρt J/(mm3 · K)σt Electric conductivity of bovine heart tissue 2.22 × 10−4 (1 + 0.02(T − 37)) S/mmke Thermal conductivity of platinum electrode 73 × 10−3 W/(mm · K)ρe Mass density of electrode 21.44 × 10−6 kg · mm−3

cpVe Specific heat per unit volume of electrode 132.51 ρe J/(mm3 · K)σw Electric conductivity of nitinol wire* 1.0 × 10−6 S/mmkw Thermal conductivity of nitinol wire 18 × 10−3 W/(mm · K)ρw Mass density of nitinol wire 6.5 × 10−6 kg · mm−3

cpVw Specific heat per unit volume of nitinol wire 322 ρw J/(mm3 · K)

*In reality, the wires are electrically insulated, but in our study we achieve the same effect by artificially reducing the electricalconductivity of the nitinol wire to a very low value to avoid short-circuiting the wire to the electrodes.

degree Celsius; from this we conclude that thequadratic discretization was adequately accuratein space.

Time Discretization

The resulting ordinary differential equationsthat result from spatial discretization are

CT + KT = L(f (T)), and A(T)f = b(t) (3)

where T and T are vectors of nodal tempera-tures and rates of temperatures, C and K are thethermal capacity and conductivity matrix, L(f (T))is the thermal load, which incorporates the ef-fect of the boundary conditions and the resistiveheating as indicated by the vector of temperature-dependent nodal electric voltages f (T). A(T) isthe temperature-dependent electrical conductiv-ity matrix, and b(t) is the vector of time-dependentelectrical loads. The coupled system is integratedin time using an adaptive implicit Euler method.The update formula from time t0 to time t1 resultsin a system of nonlinear algebraic equations forT1, f1((�t1)−1C + K

)T1 = −(�t1)−1CT0 + L(f1(T1)), and

A(T1)f1 = b(t1) (4)

which is solved with fixed-point iteration to toler-ance of 0.002◦C as the maximum change in temper-ature between successive iterations. At differencewith prior treatments, the time step is adjustedadaptively without user intervention using theformula


LAU, ET AL.

�t1 = �t0

√tolep

, where

ep =∥∥∥∥T1 − T0 − �t0

�t−1(T0 − T−1)

∥∥∥∥∞

(5)

Here �t1 and �t0 are the desired and the currenttime step, tol is a user-defined temperature toler-ance (taken as 0.5◦C here). Further, ep is the pre-dicted temperature error, which is an approxima-tion of the second-order term of the Taylor seriesfor the temperature. T1, T0, T−1 are the vectors ofnodal temperatures at the end and at the beginningof the current and previous time steps.

Implementation

All computations have been implementedand performed using MATLAB (MathWorks, Nat-ick, MA, USA) with the finite element toolkitSOFEA.12 This allowed us to incorporate all com-putations in an integrated framework that executeswithout user intervention.

Model Accuracy Evaluation

To quantify the accuracy of the model, thepredicted temperature from six locations in theheart tissue were compared to experiment resultsusing the three indicators presented by Jain andWolf: (a) the mean temperature error

T =∫ τ

0 (Tm − Te)dτ

t(6)

where t is ablation duration (60s), Te is exper-imental temperature measurement (◦C), and Tmis model temperature prediction (◦C); (b) the rmsdifference

Diffrms =

√√√√ n∑i=1

(Tei − Tmi)2

n

Te60 − 37× 100% (7)

where Tei is experimental temperature measure-ment at time i (◦C), Tmi is model temperatureat time i (◦C), n is the number of time steps,and Te60 is experimental temperature at 60 sec-onds (◦C); and (c) the correlation coefficientr.10

ResultsSimulation and in vitro results were obtained

at each location for each of the five energy deliv-ery modes. For brevity, we only report tissue tem-perature results for the bipolar-to-unipolar modesused most widely in the clinical setting, 1:1 and4:1. Figure 3 compares the measured in vitro tissuetemperature to the computed temperatures over

the duration of the 60 second ablation and the fol-lowing 60 seconds after ablation for the (a) 1:1energy mode and (b) 4:1 energy mode. Table IIshows the model accuracy indicators, calculatedfor each location and each energy mode. Over-all the model predicted tissue temperature veryclosely—the average values for mean error, rootmean square difference, and correlation coefficientwere 1.9◦C, 13.3%, and 0.97, respectively.

Figure 4 depicts representative lesions for the(a) 1:1 and (b) 4:1 energy modes. Figure 5 comparesthe in vitro lesion measurements with the maxi-mum depth attained by computational results ac-cording to: (a) the TMax ≥ 60◦C boundary surface(tissue temperature reaching at least 60◦C),13 (b)the TMax ≥ 50◦C boundary surface (tissue temper-ature reaching at least 50◦C),14 (c) the “cumulativeequivalent minutes at 43◦C” criterion (we assumeCEM43 = 128 minutes to be representative of val-ues considered for cardiac tissue15), and (d) the Ar-rhenius chemical reaction rate relationship (� = 1represents irreversible damage),16 where the pa-rameters are those reported in the open literaturefor swine and human skin.8 The predicted TMax ≥60◦C boundary closely agrees with the in vitro le-sion measurement of tissue discoloration (as seenin Fig. 5A), while the TMax ≥ 50◦C agrees withthe other methods of predicting tissue viability (asseen in Fig. 5B–D). All computational predictionsas well as the in vitro data show that as the per-centage of unipolar power decreases, lesion depthdecreases. The temperature distribution is illus-trated in Figure 6, which shows isothermal sur-faces for selected time intervals of RF heating forthe (a) 1:1 energy mode and (b) 4:1 energy mode.Note that only half of the computational domainis shown to expose the interior of the domain. Theshape and symmetry of the temperature profiles at60 seconds qualitatively agree with the resultingin vitro lesions.

DiscussionThe improvements made over previous sim-

ulation methods are incremental but nonethelessimportant. The most notable contributions are theintegration of the device controller into simula-tion time steps, the control of simulation accu-racy by varying high-order finite elements in spaceand adaptively in time, and the model for mixedpower delivery for the several operating modes ofthe catheter. The results illustrate that the finiteelement model accurately reproduces the temper-ature distribution in the tissues as measured fromin vitro experiments. In all cases, the computa-tional model predicted tissue temperature well,though it was slightly more accurate at predictingtemperatures for the mixed modes (1:1, 2:1, and



Figure 3. (A) Tissue temperature results for 1:1 (bipolar-to-unipolar) energy mode. (B) Tissue tem-perature results for 4:1 (bipolar-to-unipolar) energy mode. In vitro temperatures in six locations:“und”: under electrodes; “btw”: between electrodes; “mid”: mid-array; “d2”: 2-mm depth; “d4”:4-mm depth. Error bars denote standard deviations from five RF applications. Computationalmodel results are shown by the solid lines.

4:1 energy modes), which include the two mostwidely used energy modes clinically, 1:1 and 4:1.

In Figure 3, the predicted temperature atthe mid-array location (mid-d2) slightly under-estimates the in vitro temperature results. Weconjecture that this is due to error in the in vitromeasurement, caused by conduction of heat fromadjacent electrode pairs along the thermocouplewire leads toward the thermocouple gauge tip.There is also slight over-prediction of the tissuetemperatures toward the end of the heating phase.Both the unipolar and the bipolar PI controller dis-

play slight temperature overshoot, which is notobserved with the hardware controller. The dif-ference is likely due to the continuous functionof the controllers in the computational model, asopposed to the duty cycle of the hardware con-troller. The mismatch may also be partially dueto the material properties being assumed indepen-dent of the temperature. Another limitation of themodel is in the implementation of the power de-livery. The model assumes independent unipolarand bipolar fields, which combine to create thethermal effect of the mixed modes. However, in


LAU, ET AL.

Table II.

Comparison of Experimental and Computational Results at Six Locations for Five Energy Modes Usingthe Three Indicators

Unipolar 1:1 2:1 4:1 Bipolar

T Diffrms r T Diffrms r T Diffrms r T Diffrms r T Diffrms r

mid-2mm 3.7 9.8% 0.99 2.4 10.4% 0.97 1.1 6.9% 0.98 1.7 13.1% 0.93 3.6 19.0% 0.95btw-2mm 7.5 17.9% 0.95 3.3 10.7% 0.98 1.8 11.5% 0.96 0.9 8.7% 0.98 1.6 16.7% 0.91und-2mm 5.2 14.3% 0.93 3.5 11.1% 0.97 1.1 11.7% 0.95 1.0 10.3% 0.96 3.7 16.6% 0.97mid-4mm −4.1 19.2% 0.93 −2.9 16.2% 0.99 −2.5 16.8% 0.99 −1.9 17.2% 0.96 1.1 10.9% 0.99btw-4mm 4.3 14.1% 0.97 2.7 10.6% 0.99 1.0 7.5% 0.98 1.1 7.2% 0.99 2.9 26.9% 0.97und-4mm 5.8 14.5% 0.99 3.1 11.0% 0.99 0.5 6.5% 0.98 0.1 4.8% 0.99 3.6 27.4% 0.98Average 3.7 15.0% 0.96 2.0 11.7% 0.98 0.5 10.1% 0.97 0.5 10.2% 0.97 2.8 19.6% 0.96

T = the mean temperature error (◦C); Diffrms = the rms difference; and r = the correlation coefficient.

Figure 4. Representative photographs of lesions createdin vitro with the MAAC device (taken under 10× magni-fication). Ablations performed with a target temperatureof 60◦C for 60 seconds in the (A) 1:1 and (B) 4:1 (bipolar-to-unipolar) energy modes. Ruler increments at 0.5 mm.

reality, the hardware delivers power through acombination of phasing and mixing duty-cyclesto achieve the mixed modes. Despite these minordiscrepancies and limitations, the computationalmodel accurately predicts the temperature profilein the tissue as a function of time during ablationsfor the various energy modes.

Experimental data from in vivo ablations werenot suitable for model comparison due to the widevariation in data as a result of limited sample sizeand the uncontrolled conditions of the in vivo en-vironment. In addition, previous work has shownthat the perfusion effect is negligible17 and estab-lished in vitro experiments as a suitable proxy.6The large standard deviation in the measured invitro tissue temperature is likely due to limitationsof the experimental setup and variations betweentissue samples. Tissue temperature data are mea-sured from T-type thermocouples inserted intothe tissue at specified locations; however, plac-ing the thermocouples with high spatial accuracyis difficult. In addition, inconsistencies betweentissue samples (fascia, fat content, surface tex-ture, freshness) can cause differences in thermalconductivity and lesion discoloration, which mayaffect measurements. More importantly, firmnessand elasticity of the tissue vary, resulting in in-consistent electrode contact surface area, affectingcurrent density and electrode cooling. The diffi-culty in achieving reliable and reproducible datafrom in vitro and in vivo experiments substantiatesthe need for computational modeling.

Computational model results for lesion depth(see Fig. 5) are consistent with previous workby Panescu et al., which has shown that le-sion discoloration (as measured in vitro) is wellmatched by tissue temperature of 60◦C whereaslesion depth according to tissue viability is wellmatched by tissue temperature of 50◦C.13 Zheng



Figure 5. Comparison of the in vitro lesion measurements with computational results: (A) maxi-mum tissue temperature ≥60◦C, (B) maximum tissue temperature ≥50◦C, (C) cumulative equiv-alent minutes at 43◦C (CEM43), and (D) the Arrhenius chemical reaction rate relationship(� = 1 represents irreversible damage). Results are consistent with the hypothesis that lesiondiscoloration (as measured in vitro) is well matched by tissue temperature of 60◦C whereas lesiondepth according to tissue viability is well matched by tissue temperature of 50◦C.

et al. demonstrated that the creation of contiguouslesions is challenging for multielectrode cathetersdelivering unipolar RF current, but by phasing theRF current (delivering both unipolar and bipolarcurrent simultaneously), long lesions of consistentdepth can be created.18 The lowest temperatureisosurface in Figure 6 is at 50◦C, which is clearlyseen to extend to the symmetry planes, confirm-ing the contiguity of the lesion. This observationcan be made for all modes of power delivery. Ourresults show that lesions of significant depth weregenerated without approaching electrode–tissueinterface temperatures of 100◦C, which may leadto coagulum formation, steam pops, char, and/oran impedance rise, preventing efficient energydelivery.19

It has been suggested that specific compli-cations associated with RF ablation, includingesophageal fistula and PV stenosis, may be a resultof energy titration and the extension of thermaldamage.20,21 Therefore, there is a need to control

energy delivery to create transmural contiguous le-sions without excessive power and depth, therebylimiting peripheral thermal damage to nontargetedtissues. Zheng et al. showed that phasing allowslesion depth and thermal injury to be varied sig-nificantly by changing the phase angle (effectivelychanging the ratio of bipolar/unipolar energy).18

Our results show that as the proportion of unipolarenergy increases, lesion depth increases, a trendpredicted by the computational model and ob-served in vitro. These findings are consistent within vivo data reported for this system by Wijffelset al.22 Thus, with this system, the desired lesiondepth might be selected by energy mode (unipolar,1:1, 2:1, 4:1, or bipolar) according to anatomical lo-cation, potentially reducing peripheral damage inareas of sensitive anatomy.

In addition to being phased, the energydelivered by the ablation system we studyis temperature-controlled and duty-cycled. Intemperature-controlled ablation systems, power


LAU, ET AL.

Figure 6. Isosurfaces of temperature for the (A) 1:1 and (B) 4:1 (bipolar-to-unipolar) energy modeat 50, 60, 70, 80, 90◦C at 15, 30, 60 seconds of heating. The higher ratio of bipolar to unipolarresults in shallower lesions. Units of length, width, and depth as shown are millimeters.

output is regulated to maintain the electrode–tissue interface temperature at a specified targettemperature, typically between 60◦C and 75◦C.23,24

Erdogan et al. demonstrated that to maximize thepower output without overheating, RF energy canbe duty-cycled, thereby allowing better electrodecooling and enabling more RF energy to be deliv-ered, resulting in larger lesions than continuousRF energy.25 Electrode design also has an effecton electrode cooling. To increase and optimizeconvective cooling, the electrodes of the MAACcatheter are designed with fins that protrude intothe blood flow.

Our results show that MAAC device andGENius RF Generator are capable of creating con-

tiguous lesions with a lesion depth that can be con-trolled by adjusting the ratio of bipolar to unipolarenergy. Is it notable that the temperature distri-bution is relatively uniform and shows no signsof a significant edge effect, which has been ob-served with longer electrodes.26 We hypothesizethat the small electrode size allows the centrallylocated thermocouple to more effectively monitorthe temperature across the entire electrode–tissueinterface, suggesting an advantage of multiablationelectrode catheters over single large ablation elec-trode catheters.

This validated model will allow for explo-ration of changing design parameters and clinicalconditions expeditiously. Parameters of interest



for optimization include the duration of abla-tion, target temperature, electrode spacing, elec-trode size/shape/material, and catheter properties.Additional levels of sophistication to the modelmay further improve the correlation of results be-tween the FEA simulation and in vitro experi-ments. Some areas of interest for future develop-ment may be modeling the temperature-dependentthermal material properties, a more sophisticatedsoftware controller incorporating the duty cycle,more accurate RF delivery for mixed modes (1:1,2:1, 4:1), and the possibility of using a coupledfluid flow-thermal-electrical formulation.

ConclusionsA computational model for a unique mul-

tielectrode RF cardiac ablation system has beenpresented. The finite element model implementsa novel solution for simultaneous bipolar andunipolar RF energy delivery, as well as incre-mental improvements (integrated software con-troller, and accuracy control in space and time) to

previous modeling work. The model is validatedwith tissue temperature and lesion depth measure-ments from controlled in vitro ablations, and isfound to be in close agreement with the experi-mental data. Both the in vitro and finite elementmodel results demonstrate that lesion depth de-creases as the bipolar-to-unipolar ratio increases,suggesting a potential clinical application to con-trol lesion depth with higher fidelity than is cur-rently available. The computational model cannow allow the effect of various clinical condi-tions, which may be impractical to recreate on thebench-top, to be studied. In addition, the modelcan serve to provide support for proposed de-sign improvements to the catheter and/or energydelivery.

Acknowledgments: The authors would like to acknowl-edge Sadaf Soleymani and Christine Pan for their work in es-tablishing the foundation for the in vitro experimentation. Theauthors would also like to acknowledge Kathy Gao for her workin data collection and processing.

References1. Zeppenfeld K, Stevenson W. Ablation of ventricular tachycardia in

patients with structural heart disease. Pacing Clin Electrophysiol2008; 31:358–374.

2. Nakagawa H, Jackman W. Catheter ablation of paroxysmalsupraventricular tachycardia. Circulation 2007; 116:2465–2478.

3. Morady F. Radio-frequency ablation as treatment for cardiac ar-rhythmias. N Engl J Med 1999; 340:534–544.

4. Boersma L, Wijffels M, Oral H, Wever E, Morady F. Pulmonaryvein isolation by duty-cycled bipolar and unipolar radiofrequencyenergy with a multielectrode ablation catheter. Heart Rhythm 2008;5:1635–1642.

5. Berjano E. Theoretical modeling for radiofrequency ablation: Stateof the art and challenges for the future. Biomed Eng Online 2006;5:24.

6. Cao H, Vorperian V, Tsai J, Tungjitkusolmun S, Woo E, WebsterJ. Temperature measurement within myocardium during in vitroRF catheter ablation. IEEE Trans Biomed Eng 2000; 47:1518–1524.

7. Plonsey R, Heppner D. Considerations of quasi-stationarity in elec-trophysiological systems. Bull Math Biophys 1967; 29:657–664.

8. Doss J. Calculation of electric-fields in conductive media. Med Phys1982; 9:566–573.

9. Labonte S. A computer simulation of radio-frequency ablationof the endocardium. IEEE Trans Biomed Eng 1994; 41:883–890.

10. Jain M, Wolf P. A three-dimensional finite element model of ra-diofrequency ablation with blood flow and its experimental valida-tion. Ann Biomed Eng 2000; 28:1075–1084.

11. Tangwongsan C, Will J, Webster J, Meredith K, Mahvi D. In vivomeasurement of swine endocardial convective heat transfer coeffi-cient. IEEE Trans Biomed Eng 2004; 51:1478–1486.

12. Krysl P. A Pragmatic Introduction to the Finite Element Method forThermal and Stress Analysis: With the MATLAB Toolkit SOFEA.Hackensack, NJ, World Scientific Publishing Company, 2006.

13. Panescu D, Whayne J, Fleischman S, Mirotznik M, Swanson D,Webster J. Three-dimensional finite element analysis of current den-sity and temperature distributions giving radio-frequency ablation.IEEE Trans Biomed Eng 1995; 42:879–890.

14. Nath S, Lynch III C, Whayne J, Haines D. Cellular electrophysiolog-ical effects of hyperthermia on isolated guinea pig papillary mus-cle: Implications for catheter ablation. Circulation 1993; 88:1826–1831.

15. Haemmerich D, Webster J, Mahvi D. Thermal dose versus isothermas lesion boundary estimator for cardiac and hepatic radio-

frequency ablation. Proceedings of the 25th Annual InternationalConference of the IEEE EMBS, Cancun, 2003, pp. 134–137.

16. Dewey W. Arrhenius relationships from the molecule and cell tothe clinic. Int J Hyperthermia 1994; 10:457–483.

17. Labonte S. Numerical model for radio-frequency ablation of theendocardium and its experimental validation. IEEE Trans BiomedEng 1994; 41:108–115.

18. Zheng X, Walcott G, Rollins D, Hall J, Smith W, Kay G, IdekerR. Comparison of the temperature profile and pathological effectat unipolar, bipolar and phased radiofrequency current configura-tions. J Interv Card Electrophysiol 2001; 5:401–410.

19. Haines D, Verow A. Observations on electrode-tissue interface tem-perature and effect on electrical impedance during radiofrequencyablation of ventricular myocardium. Circulation 1990; 82:1034–1038.

20. Martinek M, Bencsik G, Aichinger J, Hassanein S, Schefl R,Kuchinka P, Nesser H, et al. Esophageal damage during radiofre-quency ablation of atrial fibrillation: Impact of energy settings, le-sion sets, and esophageal visualization. J Cardiovasc Electrophysiol2009; 20:726–733.

21. Ravenel J, McAdams H. Pulmonary venous infarction after ra-diofrequency ablation for atrial fibrillation. Am J Roentgenol 2002;178:664–666.

22. Wijffels M, Oosterhout M, Boersma L, Werneth R, Kunis C, HuB, Beekman J, et al. Characterization of in vitro and in vivo le-sions made by a novel multichannel ablation generator and a cir-cumlinear decapolar ablation catheter. J Cardiovasc Electrophysiol2009.

23. Langberg J, Calkins H, el-Atassi R, Borganelli M, Leon A, KalbfleischS, Morady F. Temperature monitoring during radiofrequencycatheter ablation of accessory pathways. Circulation 1992; 86:1469–1474.

24. Calkins H, Prystowsky E, Carlson M, Klein L, Saul J, Gillette P.Temperature monitoring during radiofrequency catheter ablationprocedures using closed loop control: Atakr multicenter investiga-tors group. Circulation 1994; 90:1279–1286.

25. Erdogan A, Carlsson J, Roederich H, Schulte B, Sperzel J, Berkow-itsch A, Neuzner J, et al. Comparison of pulsed versus continu-ous radiofrequency energy delivery: Diameter of lesions inducedwith multipolar ablation catheter. Pacing Clin Electrophysiol 2000;23:1852–1855.

26. McRury I, Panescu D, Mitchell M, Haines D. Nonuniform heatingduring radiofrequency catheter ablation with long electrodes. Cir-culation 1997; 96:4057–4064.


LAU, ET AL.

AppendixThe estimation of the convection heat trans-

fer coefficient on the top surface of the spec-imen exposed to the saline bath is describedhere. An aluminum alloy block (44 × 31.5 ×15.5 mm; McMaster-Carr, Santa Fe Spring, CA,USA) was insulated with 12.5-mm-thick high-density polystyrene foam (McMaster-Carr, SantaFe Spring, CA, USA) from five sides, leaving onlythe top surface opened to convective cooling. TheT-thermocouples (Omega Engineering, Stamford,CT, USA) were used to measure the temperature ofthe aluminum block at three locations: the centerof the aluminum block at depth of 3 mm, 7.5 mm,and 12 mm. The aluminum block was heated upto 120◦C using a heat gun (Master Appliance Cop.,Racine, WI, USA). The aluminum block was im-mediately placed in the polystyrene foam insula-tion box. The insulated aluminum alloy block was

placed in a 37◦C saline water bath and the flowrate was set to 1.8 L/min. The top foam insula-tion of the aluminum block was then removed toexpose the top surface of the aluminum block tosaline flow. The temperatures of the cooling alu-minum block were recorded. (The flow system andthe temperature recording system were describedin detail in the Method section.) The experimen-tal rig (the aluminum block plus the insulation)was modeled with a three-dimensional mesh, withprescribed temperature of 37◦C on the outer sur-faces of the insulation, and convection heat trans-fer from the aluminum block into the saline flow.The coefficient of the convection heat transfer wasconsidered a free parameter, which was iterativelyadjusted to yield an optimal fit of the computedtemperatures to the experimental data (in the rootmean square sense).


a theoretical and experimental analysis of radiofrequency

Documents