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Robert E. DoddeDepartment of Biomedical Engineering,

University of Michigan,Ann Arbor, MI 48109

Scott F. MillerDepartment of Mechanical Engineering,


James D. GeigerDepartment of Surgery, Medical School,


Albert J. ShihDepartment of Mechanical Engineering,Department of Biomedical Engineering,


Thermal-Electric Finite ElementAnalysis and ExperimentalValidation of BipolarElectrosurgical CauteryCautery is a process to coagulate tissues and seal blood vessels using heat. In this study,finite element modeling (FEM) was performed to analyze temperature distribution inbiological tissue subject to a bipolar electrosurgical technique. FEM can provide detailedinsight into the tissue heat transfer to reduce the collateral thermal damage and improvethe safety of cautery surgical procedures. A coupled thermal-electric FEM module wasapplied with temperature-dependent electrical and thermal properties for the tissue. Tis-sue temperature was measured using microthermistors at different locations during theelectrosurgical experiments and compared to FEM results with good agreement. Thetemperature- and compression-dependent electrical conductivity has a significant effecton temperature profiles. In comparison, the temperature-dependent thermal conductivitydoes not impact heat transfer as much as the temperature-dependent electrical conduc-tivity. Detailed results of temperature distribution were obtained from the model. TheFEM results show that the temperature distribution can be changed with different elec-trode geometries. A flat electrode was modeled that focuses the current density at themidline of the instrument profile resulting in higher peak temperature than that of thegrooved electrode (105 versus 96°C). �DOI: 10.1115/1.2902858�

IntroductionCautery, or the coagulation of tissue, is a surgical technique that

as long been used to denature proteins and minimize bleedinguring surgical procedures �1�. One method to perform cautery islectrosurgery, which uses radio frequency �rf� electrical currentso actively heat biological tissues with high power density �1�.ecause human nerve and muscle stimulation cease at frequenciesver 100 kHz, the electrical energy in rf alternating current can beelivered safely to generate the heat necessary for coagulation.ithout coagulation, the internal bleeding from the cut area is a

anger to the patient and affects the surgeons’ field of view. Elec-rosurgery provides a major advance in surgery by minimizinglood loss and reducing operation time. Miniaturization of thelectrosurgical instrument has enabled the use of minimally inva-ive or laparoscopic surgical procedures, thereby reducing patientecovery time. The success of laparoscopic surgery from both theurgeon and the patient perspective has provided the inertia forsing these instruments in increasingly complex procedures. How-ver, their success in procedures, such as prostatectomy and hys-erectomy, has been hampered by collateral damage to local neuraltructures impacting patient postoperative quality of life �2–4�.

Electrosurgery can be categorized as monopolar and bipolar.onopolar electrosurgery uses current in the gap between the tool

nd tissue to generate heat and ablate tissue. It functions under theame principle as electrical discharge machining �EDM�. Bipolarlectrosurgery employs dispersive electrodes, called forceps, ashown in Fig. 1. The rf electrical current supplied by an electricalenerator flows through only the tissue between the two elec-rodes to complete the circuit. As electrical current passes throughissue, its resistance generates heat for cautery. Bipolar electrosur-ery is investigated in this study.

Contributed by the Manufacturing Engineering Division of ASME for publicationn the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript receivedugust 24, 2007; final manuscript received January 13, 2008; published online April
, 2008. Review conducted by Dong-Woo Cho.
ournal of Manufacturing Science and EngineeringCopyright © 20

ded 22 Apr 2008 to 141.212.132.84. Redistribution subject to ASM

Heat generated from electrosurgery has a harmful side effect ofspreading and damaging the surrounding tissue and, more impor-tantly, the nerves in the neurovascular bundle �NVB� in surgery.This phenomenon is referred to as thermal spread in surgery �5�.Collateral tissue damage has been highlighted as a major concernfor postoperative side effects, especially for procedures occurringnear critical nervous regions, such as prostatectomy and hysterec-tomy �2�. These side effects include impotence and incontinencewith varying lengths of duration from temporary to permanent.Recent advances have been made in generator and control tech-nologies that pulse the input voltage and turn off the power oncethe tissue has been determined to be coagulated. Nevertheless,these advances still report thermal spreads of 3–5 mm in idealsituations, which can cause irreversible side effects during proce-dures as it is difficult for the surgeon to control thermal spreadfrom the electrosurgical instrument. The purpose of this researchis to better understand heat transfer in biological tissues in cauteryprocedures to further improve the design of surgical bipolar de-vices.

Thermal spread in biological tissue is difficult to measure andpredict. Modeling is a necessary tool to understand temperaturedistribution and tissue damage from thermal spread. However, re-search is lacking in this area. Research in the modeling of rfablation has been reviewed by Berjano �6�. Past research has fo-cused on FEM of tissue rf ablation and shortening the design timefor new rf instrumentation. Several researchers have modeled rfablation using a finite element approach �7–9�. However, the lit-erature has been limited primarily to the area of tumor ablation inthe liver and heart, which is characterized by low voltage inputsand procedural times on the order of 480–720 s and 60–120 s,respectively. Cautery is a technique characterized by high voltageinputs and procedural times on the order of 3–10 s, almost twoorders of magnitude shorter than liver rf ablation and one ordershorter than cardiac rf ablation. To date, detailed FEM on thecautery procedures is still new and not well studied. Pearce et al.�10� published the finite difference determinations for the poten-
tial gradient from a smooth rectangular electrode. The modeling
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f such procedures can be important to further the understandingf how tissue responds to rf energy, resulting in improvements tonstrumentation design. In this study, FEM of cautery in bipolarlectrosurgery is performed to investigate the thermal spread andemperature distribution in biological tissue. In vivo surgical ex-eriments are conducted in a porcine model for temperature mea-urement in the spleen. The measured temperatures during bipolarlectrosurgery are compared to simulation results to validate theEM model.In this study, COMSOL was used to model the heat transfer

hrough in vivo tissue during bipolar cautery using the GyrusCMI 5 mm Cutting Forceps, as shown in Fig. 1. The results for

emperature-dependent and temperature-independent models areompared to experimentally measured tissue temperature for vali-ation. In addition, theoretical compression-dependent effects onlectrical conductivity are modeled. The FEM is lastly used tonalyze the thermal profiles of different electrode designs to seeow geometry can be used to reduce thermal spread.

Experimental Setup for In Vivo Electrosurgicalemperature MeasurementExperiments were conducted, as shown in Fig. 2, to measure

emperature in the porcine spleen tissue during an electrosurgicalrocedure with a Gyrus ACMI 5 mm Cutting Forceps along withhe SuperPulse generator. As seen from Fig. 1, the instrumentonsists of two electrodes, each 13 mm long and 1.15 mm wide.he distal 20 mm of this probe is made of 301 stainless steel and

he proximal 4.0 cm of the probe is covered with an electricallynsulating PTFE coating.

A porcine �50% duroc, 25% yorkshire, and 25% landrace�odel weighing about 45 kg was anesthetized and ventilated for

se in the in vivo tissue coagulation experiments. An AgilentSanta Clara, CA� 54833A 1 GHz oscilloscope in peak detectode �PDM� with an Agilent 10076A 100:1 high voltage probeas used to measure the electrical voltage input to the tissue.DM was used due to the limited memory of the oscilloscope as

his only collects the peak readings from each wave form. Dataas acquired via the LABVIEW software. The tissue temperatureas measured with Alpha Technics �Irvine, CA� microthermistorsith a 0.48 mm outside diameter and 0.25 s thermal response

ime. Thermistors were selected over thermocouples and otheremperature sensors due to the high sensitivity and stability in theargeted temperature range �30–100°C� and their relative immu-

ig. 1 The Gyrus ACMI 5 mm bipolar cutting forceps. Note thend of the device is magnified to show electrode detail.

ig. 2 Experimental setup showing positioning of tissue, elec-
rode, and thermistors
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nity to electromagnetic interference. The thermistor relies on thechange in resistance for temperature measurement and is rela-tively immune to the significant electromagnetic field generatedduring electrosurgery.

To maintain the same distance from the cutting edge, a fixturemade of polycarbonate, as shown in Fig. 2, was custom made thatfits the shape of the forceps. The overall dimension of the fixtureis 20�38.2�5.4 mm3. The fixture can stand firmly on the tissueand has a 2.8 mm tall cavity to allow space for vapor to escape, agroove in the shape of the surgical tool tip, and several 0.5 mmdiameter holes at specific distances, 1.0 mm, 1.5 mm, 3.0 mm,and 3.5 mm, from the edge of the forceps. The microthermistorswere inserted through these holes to measure the temperature in-side the tissue at a set distance and depth in relation to the forcepsfor comparison to the temperatures obtained from the FEM.

The electrical input was provided by the Gyrus ACMI Super-Pulse generator, commonly used in surgery. The measured ac volt-age versus time between the two electrodes in the experiment isshown in Fig. 3�a�. The voltage signal has two modes. The “on”mode is a �100 V, 350 kHz frequency sine wave input for about0.22 s duration. A close-up view of this mode, as illustrated inFig. 3�a�, shows the shape and period of the sine wave form. This

(a)

(b)

Fig. 3 Voltage input for FEM „a… measured ac voltage signaland close-up view of the 350 kHz wave form and „b… resultantdc approximation of the wave form equivalent to rms value ofthe rf signal

on mode is repeated five times. The second mode is an “off”

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ode. The voltage signal detected during this time is a factor ofhe amplification of noise from the voltage probe, which uses a00:1 scaling of the signal in order to protect the oscilloscoperom the high voltage signal.

Finite Element Modeling

3.1 Thermal-Electric FEM Formulation. The analyticalodeling of heat transfer in tissue, or bioheat transfer, was pio-

eered by the work of Pennes �11� to represent heat sources frometabolism and blood perfusion. The model has been refined and

tudied extensively in the 1970s, 1980s, and 1990s �12–15�. Thedvancement of finite element and finite difference methods in the990s has enabled the numerical solution of the bioheat transferquation for several specific tissue problems. The bioheat transferodel of tissue includes coupled thermal and fluid �blood� trans-

ort phenomena. Through the advances in the modeling of bioheatransfer, it is assumed that the solid elements can be used to modelhe tissue, a multiphase material consisting of both solid and liq-id, with sufficient accuracy.

The linear bioheat transfer equation for tissue is the generaleat equation for conduction with added terms for heat sourcesnd can be expressed as �11�

�c�T

�t= k�2T + wbcb�T − Ta� + qm + qg �1�

here �, c, and k are the tissue density, the heat capacity, and thehermal conductivity, respectively, wb is the effective blood perfu-ion parameter, cb is the blood heat capacity, T is the local tissueemperature, Ta is the blood inlet temperature or steady-state tem-erature of the tissue, qm is the metabolic heat generation rate ofhe tissue, qg is the external induced heat generation rate due tohe electrosurgical heating of the tissue, and t is the time. For allases, it was assumed that the metabolic heat source and blooderfusion were insignificant �qm=0 and wb=0� as the energy inputnto the system is much greater than that produced during metabo-ism �16� and the compression of the tissue from the electrodesnhibits local blood flow. Since the main interest is to simulate theemperatures achieved throughout a cautery procedure, a time-ependent solution is considered.

A quasistatic electrical conduction model was applied to solvehe electric field in the tissue using Laplace’s equation �17�.

��T� � V� = 0 �2�

here ��T� is the temperature-dependent electrical conductivity,nd V is the electric potential. rf coagulation devices operate be-ween 300 kHz and 550 kHz. At these frequencies, the wave-ength is several orders of magnitude larger than the size of thelectrode. Thus, the majority of the energy generated by the elec-rosurgical device is dissipated through electrical conductionather than capacitive coupling �9�.

The difference in the methodology used to solve these govern-ng equations for the cases of constant and temperature-dependentonductivity stems from the method in which Laplace’s equationEq. �2�� is solved. In the case where the electrical conductivity isonstant, Laplace’s equation can be solved independently from theioheat transfer equation �Eq. �1��. The electric potential �V� cane solved quickly over the entire volume and the solution can bemplemented into the source term of the heat conduction equation.ince temperature varies spatially, temperature-dependent electri-al conductivity is a function of both temperature and position.his dependence requires that Eqs. �1� and �2� be solved simulta-eously, which requires iterative computation of both the electri-al conductivity and temperature.

3.2 Properties of Biological Tissue. The electrical and ther-al properties of the tissue were available in Refs. �8,18–20�. The

roperties for the in vivo spleen and electrodes are shown in Table
. For cases using a temperature-dependent electrical conductivity,
ournal of Manufacturing Science and Engineering


��T�, a standard increase of 2%/°C was used in accordance withScwhan et al. �21�. Thereby the equations used to determine ��T�were:

��T� = �Tref�1 + 0.02�T − Tref�� 3�

where Tref is the base line temperature for the conductivity.There has been work performed on the temperature-dependent

thermal conductivity, k�T�, of porcine spleen by Valvano �20�where the relation can be expressed linearly as

k�T� = kTref+ 0.0013�T − Tref� �4�

3.3 FEM Techniques. In the multiphysics software COMSOL

ver. 3.3, a variation of the heat transfer equation in the bioheattransfer module enables Eq. �1� to be solved. This equation iscoupled simultaneously in the software with the conductive mediadc module to solve Eq. �2�. The coupling term is the externallyinduced heat generation term �qg� from Eq. �1�. This is the resis-tive heating of the tissue from the rf energy and is defined as qg=J ·E, where J is the current density in the unit of A /m2 and E isthe electric field in the unit of V/m.

A schematic of the 3D FEM for this study is shown in Fig. 4.The grooved electrode �to be discussed in Sec. 3.4� embedded inthe tissue is illustrated in Fig. 4�a�. The original mesh of the tissuewas generated using COMSOL’s automatic meshing generator andcontained 35,269 of the 3D four-node linear tetrahedral elements.The mesh refinement feature was used to create a denser mesh inregions near the electrode where temperature information is criti-cal. The mesh was progressively refined until the peak tempera-ture solution at 0.5 mm from the side of electrode did not vary bymore than 2%. This resulted in a mesh of 79,476 elements, asshown in Fig. 4�b�, and all other cases except for the flat electrode�discussed in Sec. 3.4� were performed with this mesh. For eachsimulation, the electric field �E� and temperature �T� werecalculated.

The COMSOL PARDISO �22� direct solver using matrix row elimi-nation to solve for the temperature and electrical field was chosenfor all analyses. Four input combinations for electrical conductiv-ity and thermal conductivity material properties were compared inthe model:

1. Constant electrical conductivity and thermal conductivity��=�Tref

and k=kTref�

2. Temperature-dependent electrical conductivity and constantthermal conductivity ��=��T� and k=kTref

�3. Constant electrical conductivity and temperature-dependent

thermal conductivity ��=�Trefand k=k�T��

4. Temperature-dependent electrical conductivity and thermalconductivity ��=��T� and k=k�T��

All variable material properties were determined according toTable 1 and Sec. 3.2.

In a separate study, the electrical conductivity of the porcinespleen tissue between the bipolar electrodes was decreased tosimulate the impact of tissue compression. Preliminary experi-ments demonstrate that compression influences the tissue electri-cal conductivity. This is an area that has limited research but iscritical to accurately predict thermal profiles �23,24�. Preliminary

Table 1 Properties used in the FEM

ParameterIn vivo spleen

�8,18–20� Electrode �8�

Thermal conductivity �kTref� �W/�m K�� 0.533 70

Density *Specific heat ��*c� �J / �K·m3�� 3.9�106 2.8�104

Electrical conductivity ��Tref� �S/m� 0.33 4.0�106

ex vivo tests by the authors demonstrate a tissue electrical resis-

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ivity increase of four times under 55% compression. In this study,simulation was executed with electrical conductivity 1

2 – 14 times

hat of �Trefwhile still allowing temperature dependence of the

lectrical conductivity but not the thermal conductivity. The tissuen the model was divided into three discrete sections, marked as I,I, and III in the cross-sectional view of the FEM in Figs. 4�c� and�d�. Tissue between the symmetry plane and the electrodes �I�,issue directly between the electrodes �II�, and tissue outside thelectrode profile �III� were modeled with electrical conductivitiesf 1

2��T�, 14��T�, and ��T�, respectively.

3.4 Electrode Design. The effect of the design of electrodeurface in contact with the tissue was studied. The Gyrus ACMI

(a)

(c)

Fig. 4 Schematic of the 3D FEM moand symmetry plane defined by pocase; „c… top view of tissue regdependent regions „I, II, and III… andtemperature measurements; „d… crodependent regions. Letters A–H mascribed in Table 2.

(a) (b)

Fig. 5 Two electrodes: „a… FE; „b… GE in Gyrus ACMI bipo
cross-section for GE
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bipolar grooved electrode �GE� design was compared to a flatelectrode �FE� design, as shown in Fig. 5. For both the FE andGE, the model can be defined using a symmetry plane runningthrough the middle of the electrode, as seen in Fig. 4�a�. Theupper and lower electrode geometries were created by first extrud-ing a 1.25�1.15 mm2 rectangle 12.25 mm in length. This rect-angle was then revolved 180 deg in a circular arc with a0.725 mm inner radius. For the GE, material was removed fromthe base rectangular electrode to create the groove profile shownin Fig. 5�c�.

The seeding of the FE electrodes was identical to that of the GEelectrodes for meshing in order to approximate the mesh densityof the GE model near the electrodes. This resulted in a mesh of

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d)

l showing „a… the tissue, electrodes,EACG; „b… a representative mesh

s identified for the compression-rmistors distance from electrode for-section view of the compression-planes for boundary conditions de-

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4,932 3D four-node tetrahedral elements. In the model, the tem-erature was estimated at the midline, Tmid, of the electrodes andt different distances from the electrode edge in positions corre-ponding to the thermistors in the in vivo tissue temperature ex-eriments, as shown in Fig. 4�c�. Electrical conductivity was mod-led as temperature dependent �+2% / °C� while the thermalonductivity was maintained constant for computational effi-iency. A separate modeling study was conducted by the authorso investigate the impact of varying temperature-dependent elec-rical and thermal conductivities.

3.5 Boundary Conditions. As shown in Fig. 4�a�, the activeortions of the forceps are embedded into a 25 mm �length AE�15 mm �width AB��4.5 mm �depth AC� region that simulates

issue the forceps act on. The boundary conditions were the sameor all simulations. Table 2 specifies the boundary condition forlanes marked by Letters A–H in Fig. 4�a�.

The thermal boundary conditions for the surfaces of the tissueot contacting an electrode �Planes BDHF and EFHG� are set at aonstant temperature T0, which is 31°C in this study. ConvectionPlanes ABFE, ABDC, and CDHG in Fig. 4�a�� was assumed forll surfaces contacting the electrode except the symmetry plane. Inhis study, a convection coefficient of 25 W /m2 K is utilized. Theymmetry plane �Plane ACGE in Fig. 4�a�� was modeled withero heat flux such that n · �k�T�=0. Initial condition for tempera-ure was T0=31°C �measured porcine body temperature� for allimulations with the ambient temperature set to Tamb=25°Croom temperature�.

3.6 FEM Electrical Input. Modeling the ac voltage in the50 kHz frequency range is typically performed by converting theignal to a dc voltage by calculating its root mean square �rms�6�. For each on mode, the ac signal was divided into ten sections0.022 s in each section�, and rms averaged resulting in the signalnput shown in Fig. 3�b�. Five rf energy pulses with pulse on

ode of 0.22 s and off mode of 0.53 s can be identified.

Experimental and FEM Results

4.1 Experimental Validation and Effect of Compression.igure 6�a� shows the comparison of measured tissue temperatureith FEM predictions during electrocautery in porcine spleen. The

emperatures at four points, 1.0 mm, 1.5 mm, 3.0 mm, and.5 mm distance, from the tool electrode are presented. The FEMccurately predicts general trends for thermal profiles during ac-ive electrosurgical heating compared to the experimental valuesbtained but is not able to model the postsurgical cooling as ac-urately. Tissue temperatures reach maxima as late as 7.2 s at.0 mm adjacent to the electrode whereas experimental tissueemperatures drop more quickly after cessation of rf energy.

The tissue temperature was observed to rise in a stepped man-er near the tool electrode �1.0 mm and 1.5 mm� from the pulsedlectrical input described in Sec. 2. At 3.22 s, the temperatureeasured at 1.0 mm adjacent to the instrument edge was 60.1°C

n the experiment and 58.4°C in the model. These temperaturesre above the 50°C threshold identified in Berjano �6� at which

Table 2 FEM boundary conditions as marked in Fig. 4

Plane Electrical boundary condition Thermal boundary condition

ABDC Insulated, n · ��V�=0 Free convection, h=25 W /m2 KACGE Symmetry plane, n · ��V�=0 Symmetry plane, n · �k�T�=0ABFE Insulated, n · ��V�=0 Free convection h=25 W /m2 KBDHF Insulated, n · ��V�=0 T0=31°C

DHG Insulated, n · ��V�=0 Free convection h=25 W /m2 KEFHG Insulated, n · ��V�=0 T0=31°C

roteins denature causing tissue coagulation and permanent ther-



mal damage.Temperature increased slower in the model than the experi-

ments. This is because of lack of knowledge about how materialproperties vary according to temperature and compression. Futurework identified from this research includes more accurate mea-surement of the coupled temperature- and compression-dependentproperties of biological tissue. Other less significant sources oferror could be the generalized electrical potential input used tosimplify the FEM process, the thermistor sensitivity, and variabil-ity of thermistor placement.

Figure 6�b� shows the FEM temperature versus time resultsincluding the compression effect on tissue electrical conductivity.The temperature in this model drops more quickly than the onewithout compression dependency �Fig. 6�a��, more closely reflect-ing the cooling time scale noticed in the experiment. The maxi-mum FEM predicted temperature in Fig. 6�b� at 1 mm and 3.22 s�54.1°C� is much lower than the experimental temperature�60.1°C� and implicates the need for more accurate compression-dependent tissue electrical conductivity data. Further insight intothe compression effect will be given by the temporal and spatialtemperature distributions discussed in Sec. 5.1.

4.2 Effect of Temperature-Dependent Electrical and Ther-mal Conductivities. Figure 7 shows the effect of temperature-

(a)

(b)

Fig. 6 Comparison of thermal profiles for in vivo experimentsand FEM using a GE under a constant thermal conductivity,temperature-dependent electrical conductivity, and „a…compression-independent and „b… compression-dependentsimulation

dependent thermal and electrical conductivity on temperature pro-

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les at 1.0 mm and 3.0 mm from the electrode. The simulationesults reveal significant differences for different temperature-ependent conditions. The model with temperature-dependenthermal conductivity �k�T�� estimated temperatures 0.88°C and.02°C higher than the model without k�T� at 1.0 mm and.0 mm adjacent to the tool edge, respectively, at 3.22 s, resultingn only a maximum of 1% temperature change.

The model with temperature-dependent electrical conductivity��T�� estimated temperatures 14.7°C and 0.85°C lower than theodel without ��T� at 1.0 mm and 3.0 mm from the tool edge,

espectively, at 3.22 s, resulting in a maximum of 20% tempera-ure change. The ��T� has a significant impact and is vital ineveloping an accurate FEM for bipolar electrosurgery. Therefore,he results in the following sections are for simulations withemperature-dependent ��T� and constant k�T�.

Discussion of FEM ResultsAn advantage of FEM is the temperature estimation for differ-

nt conditions, which would be costly to measure experimentally.he following sections present effects of variations in materialroperties and electrode design on tissue temperature. The changen internal energy, �Q, in the unit of joule, was determined by

�Q =��V*

�T0

T1

�cpdTdV* �5�

here V* is the tissue volume, T0 is the tissue temperature at t0 s, and T1 is the tissue temperature at t=3.22 s. �Q is calcu-

ated in this study for comparison of the energy input betweenodels incorporating compression-dependent and compression-

ndependent electrical conductivity values.

5.1 Temporal and Spatial Temperature Distributions. Fig-re 8 shows the temporal cross sections of a plane offset fromlane ABDC �as shown in Fig. 4�a�� by 6 mm at the end of eachf the rf pulses in the simulation. The temperature distributionith a hot spot in the tissue between the electrodes is shown with

he symmetry plane on the left side. The temperature is shown tohange progressively from the resistive heating until it reaches aaximum temperature of 102.7°C at the end of the last pulse,

.22 s into the simulation �Fig. 8�e��.During each of the pulses, the resistive heating happened be-

ween the electrodes and near the symmetry plane. The net in-

ig. 7 FEM of the effect of temperature-dependent � and k onissue temperature. kTref

and k„T… are constant andemperature-dependent thermal conductivity, respectively. �Trefnd �„T… are constant and temperature-dependent electricalonductivity, respectively.

rease of internal energy in the tissue was �Q=37.3 J from the

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resistive heating at the end of the last rf pulse at 3.22 s. Figure 8�f�shows the tissue after sufficient cooling and the temperature ismore evenly distributed.

Figure 9 shows a top view of different planes offset from PlaneABFE �as shown in Fig. 4�a�� at 3.22 s in the simulation. A largespatial temperature gradient can be seen from the top to the bot-tom of the electrode. Figure 9�d� shows the maximum temperaturefor the tissue of 102.2°C at the midplane.

5.2 Effect of Compression on Temporal and Spatial Tem-perature Distributions. Altering the electrical conductivity of thetissue due to the compression applied by the electrodes �discussedin Sec. 3.3� has a significant role in shaping the resultant tempera-ture distribution, especially in the modeled postoperative cooldown. This dramatic impact is shown in Fig. 10. Simulations withcompression-dependent electrical conductivity result in “hotspots” in the tissue. The temperature is shown to grow progres-sively until it reaches a maximum temperature of 91.1°C at theend of the last pulse, 3.22 s into the simulation �Fig. 10�e��. Thecalculated �Q=6.1 J is much lower than the 37.3 J of energyadded in the compression-independent simulation. The tempera-tures are much lower in the simulation with compression-dependent electrical conductivity, as seen in Figs. 8–11. The rea-son the temperature rises and falls more accurately in Fig. 6�b� isthat the position of the temperature measurement is closer to thehot spots, as shown in Figs. 10 and 11. The current density be-comes focused at the outer edges of the electrode due to the in-creased electrical resistivity in the tissue directly between theelectrodes, thereby preferentially heating tissue outside of the pro-file of the instrument.

(c)(a)

(d)

(b)

(f)(e)

Fig. 8 Cross-sectional view of temperature profiles on a planeoffset from Plane ABDC by 6 mm at different times for a con-stant thermal conductivity, temperature-dependent electricalconductivity, and compression-independent simulation using aGE. Times „a…–„e… correlate to the end of each pulse and „f…correlates to the end of the simulation after sufficient cooling.

Fig. 9 Cross-sectional view of temperature profiles at 3.22 son different planes offset from Plane ABFE for a constant ther-mal conductivity, temperature-dependent electrical conductiv-ity, and compression-independent simulation using a GE „dis-tances indicating the offset from Plane ABFE… „same
temperature scale as in Fig. 8….


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5.3 Effect of Electrode Shape on Tissue Temperature. Ashown in Fig. 12, electrode design plays a significant role in shap-ng the resultant thermal profiles for bipolar electrocautery instru-

entation. The temperature at 1.0 mm distance from the tool elec-rode, similar to the simulations of Figs. 6 and 7, is presented. Theimulation shows the smooth electrode producing a higher Tmid of06.3°C with the difference in temperature between the midline

(c)(a)

(d)

(b)

(f)(e)

ig. 10 Cross-sectional view of temperature profiles for a con-tant thermal conductivity, temperature- and compression-ependent electrical conductivity simulation using a GE on alane offset from Plane ABDC by 6 mm at various times. Timesa…–„e… correlate to the end of each pulse and „f… correlates tohe end of the simulation after sufficient cooling „same tem-erature scale as in Fig. 8….

ig. 11 Cross-sectional view of temperature profiles at 3.22 sor a constant thermal conductivity, temperature- andompression-dependent electrical simulation using a GE onifferent planes offset from Plane ABFE „distances indicating

he offset from Plane ABFE… „same temperature scale as in Fig.….

Fig. 12 Effect of GE and FE on temperature profiles



and 1.0 mm from the electrode edge �T=40.4°C. The GE pro-duced a lower Tmid at 96.6°C with a �T=34.6°C. These resultssuggest that the electrode geometry can be redesigned for controlof temperature distributions, Tmid, and �T to minimize collateraltissue damage.

In general, including grooves in the electrode minimizes heatgeneration through a reduction in current density. The collateraltissue damage can be reduced by decreasing the current density,although surgical efficiency drops and surgical time is increased toachieve a similar internal temperature. It was observed by Richteret al. �25� that smooth electrodes tended to not stick as much totissue as GEs but also were less effective in vessel sealing. TheFEM results presented here raise questions about the role the tem-perature plays in tissue sticking and the creation of an effectiveseal.

6 ConclusionsThis study demonstrated the capability of using a FEM to study

bipolar electrosurgical procedures and demonstrated the impor-tance of incorporating appropriate temperature-dependent tissueproperties, electrode geometry, and compression-dependent prop-erties in the FEM model. Incorporating the temperature-dependentthermal conductivity values from the literature into the FEM re-sulted in only a 1% increase in tissue temperature at 1.0 mm ad-jacent to the electrode at 3.22 s. However, incorporating thetemperature-dependent electrical conductivity in the FEM modelresulted in a significant 20% decrease in temperature at 1.0 mmadjacent to the electrode at 3.22 s. FEM results showed that theGyrus ACMI 5 mm Cutting Forceps generated a peak temperatureat 1.0 mm adjacent to the electrode of 58.4°C while an identicalmodel imposing compression-dependent tissue electrical conduc-tivity estimated a peak temperature at 1.0 mm adjacent to theelectrode of 54.1°C at 3.22 s. This is compared to an experimen-tally measured peak temperature of 60.1°C at 1.0 mm adjacent tothe electrode at 3.22 s. The 83.6% difference in �Q from thecompression-dependent to the compression-dependent simulationsconfirmed that significantly less heating took place in thecompression-dependent model. While the model withoutcompression-dependent electrical conductivity more closelymatched the temperature values of the experiment, the model withcompression-dependent electrical conductivity matched the over-all temperature profile, providing a better comparison of the heattransfer time scale. FEs were shown to generate temperatures9.7°C hotter at the symmetry plane and 3.9°C hotter at 1.0 mmadjacent to the electrode as compared to the GE design.

Limitations of this model include its assumption of a continualelectrode-tissue contact, which may not be realistic in all situa-tions. While the voltage signal was seen to be nearly constant forthis case, a more versatile model would include a capability toreproduce a constant power setting. It is known that at tempera-tures near 100°C the temperature-dependent material propertiesexperienced nonlinear phenomenon due to the interstitial fluidphase changes. Therefore, at these high temperatures, the modelwill need refinements to accommodate analyses in these ranges.Also, the impact of the load transmitted to the tissue by the for-ceps and consequent compression exerted on the tissue duringsuch a procedure is unknown and currently being investigated.This compression effect can greatly impact tissue material prop-erties, particularly the thermal and electrical conductivities, andtherefore temperature distributions and thermal energy flowthroughout the tissue. In this model, discrete conductivity changeswere imposed on the tissue, but future models will incorporatecompression-dependent material properties on a continuum.

The impact that electrode geometry design has on thermal pen-etration into tissue lateral to the electrode could play a major rolein the future design of bipolar instrumentation. It is shown in this
study that electrode geometry changes can lead to increased tem-
APRIL 2008, Vol. 130 / 021015-7


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eratures and thermal gradients. Advanced design considerationsan play an important role in minimizing collateral tissue damagend should be implemented whenever feasible.

cknowledgmentSupport from University of Michigan Medical School Transla-

ion Research Innovation Program �TRIP� as well as NSF Granto. 0620756 is greatly appreciated.

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