Myocardial temperature distributionunder cw Nd:YAG laser irradiation in in vitroand in vivo situations: theory and experiment

Robert Splinter, Serguei Y. Semenov, Glenn A. Nanney, Laszlo Littmann,Jan R. Tuntelder, Robert H. Svenson, Chi Hui Chuang, and George P. Tatsis

Tissue samples ranging from 2 to 16 mm in thickness were irradiated at 1064 nm with energies rangingfrom 40 to 2400 J. Coagulation lesions of in vitro and in vivo experiments were subjected to temperatureprofiling and submitted for histology. Irreversible damage was calculated with the damage integralformalism, following the bioheat equation solved with Monte Carlo computer light-distribution simula-tions. Numerical temperature rise and coagulation depth compared well with the in vitro results. Thein vivo data required a change in the optical properties based on integrating sphere measurements forhigh irradiance to make the experimental and numerical data converge. The computer model hassuccessfully solved several light–tissue interaction situations in which scattering dominates overabsorption.Key words: Bioheat equation, canine myocardium, finite-element method, high and low irradiance,

Monte Carlo light simulations, Nd:YAG laser, optical properties, temperature distribution, thermogra-phy.

1. Introduction

The neodymium:YAG laser is currently being used ina clinical study to heat heart tissue to coagulationtemperatures. The purpose of this radiative heatingis to kill specific heart tissues in the treatment ofventricular tachycardia,1,2 a life-threatening irregu-lar fast heart rate.During continuous-wave 1cw2Nd:YAG laser photoco-

agulation 1at the 1064-nm wavelength2 of myocardialtissues, many optical and thermal processes are in-volved in the biological tissue response.3–5 In addi-tion, during endocardial in vivo laser irradiation ofmyocardial tissue the laser–tissue interaction is alsoaffected by the constant contractile movement of theheart and the positioning of the laser fiber.The light-tissue interaction involves scattering and

R. Splinter, L. Littmann, J. R. Tuntelder, R. H. Svenson, C. H.Chuang, and G. P. Tatsis are with the Carolinas Medical Center,Charlotte, North Carolina 28203. S. Y. Semenov is with theBiophysical Laboratory, Kurchatov Institute of Atomic Energy,142092 Troitsk, Moscow region, Russia. G. A. Nanney is withTransform Systems Design Ltd., Charlotte, North Carolina 28205.Received 14 June 1993; revised manuscript received 25 July

1994.0003-6935@95@030391-09$06.00@0.

r 1995 Optical Society of America.

absorption of photons that is governed by the localoptical properties of the tissue constituents.5,6 Thetissue optical properties are defined as the absorptioncoefficient µa 1mm212, the scattering coefficient µs1mm212, and the scattering anisotropy factor or meancosine of the scattering angle, g 122. The thermody-namic light–tissue interaction parameters depend onboth the optical and the thermal properties of thetissue. Light energy is transformed into thermalenergy by absorption and subsequent nonradiativedeexcitation.The distribution of the light-energy fluence rate

and the resulting heat-source function in relation tothe subsequent heat diffusion and tissue coagulationis important from both the theoretical and the clinicalviewpoints.

2. Materials and Methods

The laser delivery system consisted of a cw 100-WMBB MediLas2 Nd:YAG laser system that emitted atthe 1064-nm wavelength, operated at a 9.9-s maxi-mum default irradiation time, and was focused into a400-µm-diameter optical fiber.A thermographic camera was used to monitor the

evolution of the top-surface temperatures duringNd:YAG laser irradiation of the bottom of the tissue

20 January 1995 @ Vol. 34, No. 3 @ APPLIED OPTICS 391

sample. The thermographic camera unit was a Ther-movision 870 1AGEMAInfrared Systems2.The Thermovision 780 has a spectral response that

ranges from 2 to 5 µm. The thermography systemhad a 5% overall inaccuracy. Image acquisition wasat 25@4 frames@s with 280 lines@frame 1interlaced 4:12and 90 resolution elements per line. Imaging wasperformed with a 7° field-of-view lens with a close-upattachment. The thermographic imaging unit waspositioned at the minimum focusing distance of 35 6

2.5 cm above the tissue field under irradiation in thein vitro experiments, yielding the maximum spatialresolution. The area observed per pixel in the invitro setup had a vertical resolution of 0.6 6 0.1 mmand a horizontal resolution of 0.45 6 0.07 mm. Thethermographic camera continuously monitored thetissue surface temperature, yielding the initial tissuetemperature 1Tb2 and the maximum final temperatureat termination of laser irradiation 1Te2. In the in vivosituation the mean distance of the camera to the fieldof observation was 40 6 3 cm, and the area observedper pixel had a vertical resolution of 0.86 0.2 mm anda horizontal resolution of 0.6 6 0.1 mm. The tissuesurface was kept moist with saline to maintain 96%emissivity. The exposed myocardial tissue dehy-drated rapidly when exposed to air, causing theemissivity to drop.7 In the in vivo experiments thethermographic camerameasurements established themaximum final epicardial temperature Tepi. Thethermographic temperature recordings were also usedto establish the elapsed time from the onset of laserirradiation in which the epicardial temperature ex-ceeded an arbitrary temperature level of 57 °C 1t572.This time interval was chosen as an indication of therate of heat deposition at the epicardial surface.

A. Procedure

The light-propagation information follows from aMonte Carlo simulation that gives us an exact thoughnumerical solution to the equation of radiative trans-fer. The temperature distribution in space and timeis described by the solution of the bioheat equa-tion.8–11A numerical solution of the bioheat equation based

on computer simulations of the light and heat distribu-tion was obtained. A light-tissue interaction modelwas adopted to investigate the light and temperaturedistribution in myocardial tissue under controlledcircumstances with well-defined boundary conditionsin an in vitro situation. Further comparisons wereextended to investigate the feasibility of predicting invivo tissue temperatures based on data obtained fromopen-chest transcatheter laser irradiation of the endo-cardium with simultaneous thermographic epicardialtemperature evaluation.3 Comparison of the experi-mental data with theoretical analysis was used toevaluate the feasibility of predicting irreversible laserphotocoagulation damage. Tissue temperatureswerecalculated with the bioheat equation and comparedwith thermographic data. The experimental depth

392 APPLIED OPTICS @ Vol. 34, No. 3 @ 20 January 1995

of coagulation determined by histological examina-tion was correlated to the depth of necrosis calculatedby the use of the damage integral.12

B. Experiments

1. In VitroA schematic overview of the experimental setup isillustrated in Fig. 1. The 400-µm optical fiber wassubmerged in a saline bath and faced upward. Athin plane-parallel slice of myocardial tissue waspositioned approximately 2.5 mm above the fiber tipin the same basin. The tissue sample was flush withthe saline surface level. The fiber positioning rela-tive to the tissue surface was controlled to maintain a2.5-mm-diameter spot size on the bottom face of thetissue. Tissue samples were cut to 2-, 3-, 4-, and6-mm thickness. The tissue samples were irradi-ated at 20 W for 2, 3, 4, and 10 s, respectively. Thepower density in air in this situation measured 407W@cm2. The system was in thermal equilibrium atinitiation of the experiment.The tissue temperatures at the surface opposite to

that of the irradiated site were recorded throughthermographic imaging, and the maximum tempera-ture that was reached was determined.

2. In VivoMixed-breed canines were intubated, anesthetizedwith 2% isoflurane, and ventilated with a Siemensrespirator. The hearts were exposed through a leftthoracotomy. Laser energy was delivered to the en-docardial wall in the closed heart.3 A schematic ofthe laser light delivery and temperaturemonitoring isshown in Fig. 2. The lesions created with laserirradiation were submitted for histological examina-tion. The maximum coagulation depth and width,which represent the dimensions of irreversible ther-mal tissue damage, were measured. In this studyonly samples with approximately 13-mm wall thick-ness were selected for analysis to maintain a consis-tent sample population.

Fig. 1. Schematic of the experimental setup of Nd:YAG laserirradiation of myocardial tissues in in vitro 400-µm fiber directedupward to the z 5 0 surface of a sample of myocardial tissue, withthermographic monitoring at the distal surface 1z 5 z02.

The laser was used at a power setting of 20W at thetip of the fiber during transcatheter laser irradiation,in two configurations, group I and group II. In groupI the 400-µm-diameter optical fiber extended approxi-mately 1 mm from the catheter, and the fiber deliv-ered laser light energy of 600 J or less. The powerdensity at the fiber tip that was in contact with thetissue was 15915 W@cm2. In group II the laser fiberwas retracted from the catheter tip for approximately1 mm, and the fiber had a spot size of approximately 1mmand delivered 20W at 100, 120, and 140 s. Laserirradiation was accomplished in the continuous modewith consecutive pulses of 9.9-s duration, with a 0.5 60.3 s interval between pulses. The hearts wereharvested after 2 weeks for histological examination.All animals were cared for in accordance with theguidelines of theAmericanAssociation for the Accredi-tation for LaboratoryAnimal Care.

C. Theory

The initial heat-source function under continuouslaser irradiation was calculated based on the lightdistribution in a tissue slab of normal myocardium.The light distribution was defined by a two-dimen-sional Monte Carlo model6,13 by the use of the opticalproperties determined by Splinter and coworkers.5,6,14The idealized myocardial tissue model has a homoge-neous structure and uniform optical properties.The light distribution was computed for a Gaussian

beam profile that was consistent with the experimen-tal irradiation conditions for the in vitro experimentsand the noncontact in vivo experiments 1Table 12.The in vivo contact fiber irradiation mandated a flator top-hat beam profile at the aperture of the opticalfiber15 1Table 12. In this particular theoretical studythe optical properties were assumed to remain un-changed during the tissue-heating process. Underhigh-power-density simulations 1.2000 W@cm22,other optical properties were chosen. As for irradi

Fig. 2. Schematic of the in vivo experimental setup of Nd:YAGlaser irradiation of myocardial tissues with real-time thermo-graphic monitoring of epicardial temperatures during endocardialcontact with 400-µm-fiber laser irradiation.

ance below approximately 2000 W@cm2 the opticalproperties were assumed to be independent of tem-perature. The high-power-density situations are dis-cussed in detail in Subsection 2.D.The heat-source function can be included in the

bioheat equation. In a situation of cylinder symme-try in a homogeneous medium the bioheat equa-tion10,16 is

rc1≠T2

≠t5 k1 ≠2

≠r21

≠

r≠r1

≠2

≠z22T 1 q, 112

where r is tissue density, c is heat capacity, k isthermal conductivity, T is temperature rise, t is time,and q is the heat-source function, which is the productof the light fluence-rate distribution 1C2 and theabsorption coefficient

q 5 Cµa. 122

The numerical value of k 5 0.0005 W@mm °C is fromPartovi et al.16 The specific heat of tissue17 is c 53.7 3 103 J@kg °C, and the tissue density is r 51.04 3 1026 kg@mm23.18,19For the boundary condition at the distal surface we

assume that the heat flux at this surface has to becontinuous, so that 19

ktissue≠T

≠z5 kair

≠T

≠z, 132

where kair 5 0.00045 W@mm °C.20 The boundaryconditions at the lateral sides of the heat sourcerequire a continuous gradient in the temperatureprofile. The heat flux 1q182 out of the coagulatedvolume equals the heat flux into the normal tissue1q282, q8 5 2k1≠T@≠r2,21 with identical heat-diffusioncoefficients for both regions.The bioheat equation was solved numerically

through a finite-element method by the use of a 100squares 3 100 squares grid, implying that the griddimensions depended on the sample thickness. Thesample width was chosen to be equal to the sampledepth. The simulation time intervals can be prese-lected in 4 time frames to incorporate 112 a start-upsurge, 122 standard irradiation time, 132 a shut-downperiod, and 142 a cool-down time. These featureswere assigned to allow for a diversity of energysources and their intrinsic properties and relations to

Table 1. Optical Parameters of Tissues Used in the Illustrations for MonteCarlo Simulations for the Determination of the

Heat-Source Function

SampleThickness

1mm2µa

1mm212µs

1mm212g122

SpotSize1mm2

ExperimentalConditions

Irradiance1W@cm22

2 0.04 17.5 0.975 2.5 In vitro ,2000

6 0.04 17.5 0.975 2.5 In vitro ,200013 0.04 17.5 0.975 0.4 In vivo ,200013 0.04 17.5 0.975 0.9 In vivo ,200013 0.04 14.0 0.999 0.4 In vivo $2000

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tissue thermal interaction in temperature simulations.The tissue-temperature calculationswithMonte Carlolight simulations that were used in the bioheat simu-lation were integrated over 0.1-s steps. Furtherincreases in integration time yielded deviant results.Calculation integration over time yields the tempera-ture distribution after a period of laser irradiation.The temperature distribution has been expressed inisotherms in a two-dimensional representation of thetissue cross section.Irreversible tissue damage can subsequently be

determined by the use of the damage integral asdescribed by Welch,12 Sagi et al.,17 and Henriques andMoritz,22

V1t2 5 A e0

t

exp12E@RT2dt, 142

where R is the universal gas constant 1R 5 8.314 3103 J kmol21 K212, t is the irradiation time, the rateconstant A 5 3.1 3 1098 s21, and E is the activationenergy for burn injury 1E 5 6.28 3 105 J@mol2, all ofwhich were experimentally determined by Henriquesand Moritz.22Following the criteria outlined by Sagi et al.17 and

Henriques and Moritz,22 we can establish the bound-ary of irreversible damage.

D. Optical Anomaly

In previous experiments with high-power-density la-ser irradiation of myocardial tissues, an increase inthe collimated transmissionwas observedwhen powerdensities exceeded approximately 2000 W@cm2.23,24The measured total attenuation coefficient droppedsharply from 1.42 6 0.02 mm21 to 0.73 6 0.05 mm21

around 2000 W@cm2. This drop in attenuation wasinterpreted as a nonlinearity in the optical propertiesof the tissue as a function of the laser irradiationpower density. The irradiance of 2000 W@cm2 wasused to distinguish between low-irradiance 1,2000W@cm22 and high-irradiance 1$2000W@cm22 situations.We used the Monte Carlo model and the bioheatequation to adapt the optical properties of the tissueto match the most likely fit of the experimentaltemperature observations. The optical parametersof the tissues under low-power-density and high-power-density irradiation conditions are summarizedin Table 1.

3. Results

The in vivo experimental conditions and histologicalresults, in combinationwith the temperaturemeasure-ments, are listed in Tables 2 and 3. The data inTable 2 represent the irradiation conditions at 20 W,with total delivered energy of 600 J with a 400-µmfiber in tissue contact. Table 2 also presents thehistological data for lesion dimensions and the tem-perature measurements at the epicardium and theendocardium. All lesions presented in Table 2 weretransmural, and the lesion depth equals the thicknessof the heart muscle at that location. The experimen-

394 APPLIED OPTICS @ Vol. 34, No. 3 @ 20 January 1995

tal conditions with a 400-µm fiber retracted from thetissue surface, which created a 1-mm-diameter spotsize, and the histology and temperature results arelisted in Table 3.Themeanmaximum increase in temperature at the

top surfaces of the sample for the different samplethicknesses and laser exposure times, for both in vitroand in vivo conditions, are listed in Table 4. Thenumerically attainedmaximum temperature increase atthe distal surface is represented in Table 4 as DTcomp.In all the experiments the myocardium was partiallycoagulated on the perimeter of laser impact. Thedepth of coagulation compared with the irreversibledamage boundary from the damage integral 1D2 showeddifferent results for the various tissue samples in thein vitro and in vivo situations 1Table 42. The in vitroexperimental and theoretical data were as follows:for the 2-mm-thick samples the depth was 1.0 6 0.2mm and D 5 1.2 mm; for the 3-mm-thick samples thedepth was 1.1 6 0.3 mm and D 5 1.0 mm; for the4-mm-thick samples the depth was 1.6 6 0.3 mm andD 5 1.6 mm; and for the 6-mm-thick samples thedepth was 2.9 6 0.3 mm and D 5 2.9 mm. Theexperimental and numerical in vivo values for depthof coagulation varied based on the use of either a

Table 2. Lasing Parameters, Endocardial ATprox B and Subendocardial ATdist BTemperatures, Epicardial Maximum Temperatures ATepi B, Lesion

Dimensions, and Epicardial Temperature Rise to an Arbitrary 57 °C At57Bduring Endocardial Lasing with 400- mm Fiber in Contact a

LaserPower1W2

LasingTime1s2

Tdist

1°C2Tprox

1°C2Tepi

1°C2

LesionDepth1mm2

LesionWidth1mm2

t571s2

20 30 105 105 76 10.4 10.1 3.0

20 30 105 100 73 11.5 9.5 10.020 30 85 100 57 13.5 16.0 30.020 30 100 80 77 10.6 8.5 4.520 30 95 108 58 11.2 9.8 10.020 30 105 95 76 10.6 10.1 5.020 30 85 100 70 12.1 11.8 3.020 30 100 80 76 11.3 12.8 5.020 30 105 95 76 10.1 11.1 5.020 30 90 95 75 13.8 11.6 4.020 30 80 100 77 13.2 10.6 5.020 30 85 100 73 11.6 9.7 10.0

Mean 95 97 72 12 11 8SD 10 9 7 1 2 7

aThe table includes data from Splinter et al.3

Table 3. Lasing Parameters, Endocardial ATprox B and Subendocardial ATdist BTemperatures, Epicardial Maximum Temperatures ATepi B, Lesion

Dimensions, and Epicardial Temperature Rise to an Arbitrary 57 °C At57Bduring Endocardial Lasing with 1-mm Spot Size a

LaserPower1W2

LasingTime1s2

Tdist

1°C2Tprox

1°C2Tepi

1°C2

LesionDepth1mm2

LesionWidth1mm2

t571s2

20 100 55 85 60 16.0 15.5 30.0

20 120 95 130 67 12.0 10.5 30.020 140 85 85 60 15.0 22.0 60.0

aData are from Splinter et al.3

Table 4. Myocardial In Vitro Tissue-Temperature Rise Recorded with Thermography as a Result of Laser Irradiation at 20 W with a 2.5-mm Spot Sizein a Saline Environment on the Backside of a Thin Tissue Sample for Short Irradiation Times and In Vivo Tissue-Temperature Recordings

for Irradiation with a 400- mm Bare Fiber in Close Contact Determined from the Maximum Temperature Recorded with Thermography ATeBMinusBaseline Temperature ATbB, ADTexp 5 Te 2 TbBa

Tissue Thickness1mm2

Spot Size1mm2

ExperimentalCondition

Energy1J2 Tb 1°C2 Te 1°C2 DTexp 1°C2 Depth 1mm2

DTcomp

1°C2 D 1mm22 2.5 In vitro 40 40.5 6 0.5b 49.0 6 1.0 8.5 6 1.3 1.0 6 0.2 10.9 1.2

3 2.5 In vitro 60 31.1 6 0.6 40.5 6 1.2 9.4 6 1.2 1.1 6 0.3 9.1 1.04 2.5 In vitro 80 31.7 6 0.6 37.3 6 1.3 5.6 6 0.9 1.6 6 0.3 6.5 1.66 2.5 In vitro 200 35.4 6 0.9 41.0 6 2.9 5.6 6 2.1 2.9 6 0.3 5.7 2.913 0.4 In vivo 600 38.2 6 0.4 72.0 6 7.7 33.8 6 7.6 13.0 6 1.0 1.6, 37.7c 6.4, 13c

13 0.9 In vivo 2400 38.2 6 0.4 67.0 6 9.8 28.8 6 9.6 12.9 6 1.1 7.3 9.2

aIn addition to the theoretical temperature rise 1DTexp2, experimental depth of coagulation were measured with histological examination1Depth2 and depth of irreversible damage was calculated with the bioheat equation and the damage integral 1D2.

bMean 6 standard deviation.cNumerical values for the low- and high-power-density light-distribution models, respectively.

low-irradiance5,6 or a high-irradiance light-distribu-tion model. The 600-J in vivo lesions were mostlytransmural, with a depth of 12.3 6 1.1 mm, and thelow-irradiance light distribution determined the 57 °Cisotherm at a 5.6-mm depth and D 5 6.4 mm.However, the use of a light-distribution model basedon nonlinear optical behavior under high irradianceled to the prediction thatD5 13mm. The experimen-tal and theoretical depth of coagulation is, however,limited by the tissue thickness. The optical param-eters used in the Monte Carlo light-distribution simu-lations shown in Figs. 4–8 for the various in vitro andin vivo experiments are listed in Table 1.A representative experimental case that illustrates

the thermographic image for the 2-mm situation isshown in Fig. 3 for laser irradiation at 20 W for 2 swith a 2.5-mm spot size. The respective numericalresult from the calculated temperature distribution isdisplayed in Fig. 4. The conditions for the 6-mmsample at 20 W, 10 s, are presented in Figs. 5 and 6,respectively.The numerical results for the conditions of 20-W

irradiation for 30 s are presented in Fig. 7 for a

classical light-distribution temperature profile from a400-µm incident beam.6 The contrast with a modelbased on nonlinear tissue optical behavior14,23,24 un-der high irradiance is shown in Fig. 8. The MonteCarlo simulation for the high irradiance used thefollowing optical parameters, which resulted from aniteration process that led to the best fit: µa 5 0.04mm21, µs 5 14.0 mm21, and g 5 0.999. This particu-lar high-irradiance light profile resulted in epicardialtemperatures at time frames that were calculated bythe use of the bioheat simulation that corresponded tothe temperatures measured at the epicardium duringthe in vivo experiments 1Table 22. The maximumdistal temperatures calculated by the use of thebioheat computer simulation at these parameters forthe light-distribution simulation did not exceed 76 °Cafter 30-s simulation time, and the temperaturesconform to the experimental observations listed inTable 2. A representative cylindrical lesion createdby laser irradiation at 20W for 30 s through a 400-µmfiber in contact with the left ventricular free wall isshown in Fig. 9. This lesion shows an accurate

Fig. 3. Thermographic image for a 2-mm sample thickness at 20W for 2 s with a 2.5-mm spot size recorded from the z0 5 2 mmsurface. The temperature scale on the right-hand side is indegrees Celsius. The base tissue temperature is 40.2 °C, and themaximum epicardial temperature is 48.3 °C.

Fig. 4. Calculated cross-sectional temperature distribution in a2-mm sample after lasing at 20 W for 2 s with a 2.5-mm spotsize. The temperature outline on the central z axis is shown to theright of the heat distribution, and the temperature profile on thedistal surface 1z0 5 2 mm2 in the radial direction is below the heatdistribution.

20 January 1995 @ Vol. 34, No. 3 @ APPLIED OPTICS 395

resemblance with the high-irradiance model de-scribed in Fig. 8. The computer-simulated isothermsare presented on a linear scale in Figs. 4–8, andintermediate temperatures can consequently be foundby the use of interpolation.The experimental and numerical results attained

for irreversible tissue damage are summarized in Fig.10. In Fig. 10 the combined data for the depth of thecoagulation lesions established in both the in vitroand in vivo experiments are plotted versus the calcu-lated depth of necrosis that results from the damageintegral as a function of time under 20-W laserirradiation.

4. Discussion

The numerical data for coagulation depth were withinthe standard deviation of the in vitro experimentalresults. The calculated temperature rise at the dis-tal surface was in excellent agreement with all the invitro experimental results, with a deviation in only

Fig. 5. Thermographic image for a 6-mm sample thickness at 20W for 10 s with a 2.5-mm spot size recorded from the z0 5 2 mmsurface. The temperature scale on the right-hand side is indegrees Celsius. The base tissue temperature is 32.8 °C, and themaximum epicardial temperature is 39.4 °C.

Fig. 6. Calculated cross-sectional temperature distribution forthe 6-mm sample at 20 W, 10 s, with a 2.5-mm spot size. Thetemperature outline in the z direction for r5 0 is shown to the rightof the heat distribution, and the radial temperature profile on thedistal surface 1z0 5 6 mm2 is shown below the heat distribution.

396 APPLIED OPTICS @ Vol. 34, No. 3 @ 20 January 1995

the 2-mm-thickness case. The overall correlationcoefficient 1R 5 0.992 between model and experi-ments indicates that the model is reliable for predic-tion of temperature and necrosis. The spread inexperimental data canmost likely be explained by thevariability in composition of the inhomogeneous myo-cardial tissues, which leads to a variability in tissueproperties. Reduction of the absorption coefficientby 10% to µa 5 0.036 mm21 in the computer simula-tions for the 2-mm sample leads to the prediction ofvirtually identical surface temperatures in the tem-perature profile at the z 5 2 mm surface, although thetheoretical coagulation depth 1D2 decreases from 1.2 toonly 0.6 mm.

Fig. 7. Numerical solution for contact 400-µm-fiber laser irradia-tion at 20 W, 30 s of 13-mm thickness myocardium. The simu-lated classical light distribution and the resulting classical tempera-ture profile. The temperature outline on the z axis for r 5 0 isshown to the right of the heat distribution, and the temperatureprofile on the distal surface 1z0 5 13 mm2 in the radial direction isshown below the temperature distribution.

Fig. 8. Temperature distribution calculated with a nonlinearlight-distribution model 1optical properties modified to µa 5 0.04mm21, µs 5 14.0 mm21, and g 5 0.9992. The temperature outlineon the z axis for r 5 0 is shown to the right of the heat distribution,and the temperature profile on the distal surface 1z0 5 13 mm2 inthe radial direction is shown below the heat distribution. Themaximum epicardial temperature exceeded 57 °C in this simula-tion at 5 s elapsed time.

Theoretical criteria regarding the damage integraldemand that we perform integration to infinity todetermine the full extent of irreversible damage.However, calculations with this model did not show astatistically significant difference in lesion dimensions.In addition, no statistically significant difference wasobserved in maximum epicardial and endocardialtemperatures between simulations that were run forthe total laser irradiation time and for simulations inwhich the irradiation time was exceeded until thepoint where the baseline temperature 139 °C2 wasreached 1or exceeded2, and any latent heat effects wereincorporated. The fact that there are no perceivablenumerical differences between infinite and finite simu-lation times appears to be in agreement with ourobservations on the tissue thermal relaxation times1t 5 1.2 6 0.32 that were deduced from the tempera-ture–time relations measured by the use of thermo-couples 1Fig. 112 and thermography.3 Tissue tempera-tures were shown to drop to baseline temperaturewithin 4 to 5 s on both the epicardium and theendocardium.The in vivo experimental data are not correctly

predicted by the use of optical properties obtainedfrom integrating sphere measurements.5,6 However,when a nonlinearity is introduced in tissue opticalproperties at power densities in excess of 2000W@cm2,

Fig. 9. Histology after 2 weeks survival of a representativecylindrical lesion created in the left ventricular free wall by laserirradiation at 20 W for 30 s 1Masson–Trichrome stain2. Theentrance point of the laser beam at the endocardial surface, shownat the top of the image, is concealed by a cutting artifact.

the experimental and numerical data converge. Thehigh-irradiance model compares well with the experi-mental data reported by Splinter et al.23 and listed inTable 2, in the cases in which epicardial coagulationtemperatures were reached within 6 s of laser irradia-

Fig. 10. Calculated depth of necrosis resulting from the damageintegral 1,2 and the experimental depth of coagulation 1s2 for boththe in vitro and in vivo situations as a function of time under 20-Wirradiation. The calculated depth of irreversible tissue damagewith nonlinear tissue optics under high-power-density irradiation1d2 demonstrates relevance.

Fig. 11. Representative recording of the endocardial 1Tprox2 andsubendocardial 1Tdist2 temperature profile from type K thermo-couples around the termination of laser irradiation 1laser off 2. Atemperature ripple that is presumably synchronous with the heartcontraction rate can be observed.

20 January 1995 @ Vol. 34, No. 3 @ APPLIED OPTICS 397

txtion. The numerical and experimental lesionshapes are also in agreement. Comparison with thedata shown by Splinter et al.3, where a temperature of57 °C was reported within 6 s of laser irradiationfollowing the simulation with the optical propertiesderived under the high-irradiance conditions.Comparison of the initial light and heat distribu-

tions with the isotherms computed from the bioheatequation indicates that when the power density re-mains below the assumed threshold of 2000 W@cm2

for optical anomaly, lesion formation can be calcu-lated within 90% accuracy. In all computer simula-tions the temperatures at the impact zone of the laserbeam remained below carbonization or vaporizationtemperatures, coincidingwith our experimental obser-vations.The optical properties of the various myocardial

tissues and the optical properties of some specifictissue constituents displayed a great deal of diver-sity.5,14 In addition there is a wide range in thermo-dynamic variables, especially in an in vivo situation.Heat generation in regions that correspond to thelight propagation in a beating heart will be a functionof the tissue density 1contraction2, perfusion 1bloodflow, various-size blood vessels, intracellular flow2,and the angle of incidence of the light that emergesfrom the fiber aperture at the rough tissue surface,25and surface cooling.26 All these factors put restric-tions on the feasibility of making accurate predictionsof local and global tissue temperatures under cw laserirradiation for clinical use based on the concepts ofconstant and uniform optical properties.2,6,14 Futuremodels would require one to specify local tissueinhomogeneities to allow for an accurate spatial andtemporal solution.

5. Conclusions

The data presented above show that the computermodel gives us an accurate description of actual lesionformation and is flexible in data acceptance to covermany different light–tissue interaction situations.This model may complement other theoretical modelsbased on Beer’s law approximations that describesituations inwhich absorption dominates over scatter-ing, yielding only a one-dimensional exponential light-attenuation function.17 The overall correlation be-tween theory and experiment indicates a reliablemodel for lesion generation and prediction. Themodel can interpret light–tissue interaction situa-tions in which scattering dominates over absorptionand optical anomalies that arise from high-power-density irradiation. In addition the model is capableof dealing with dominating absorption when theproper light distribution is entered. Ultimately thetissue-coagulation process may be predicted providedthat the proper local optical and thermodynamicproperties can be attained. The simulations mayalso help to identify optical anomalies in the tissuethrough fitting of theoretical damagemodels to experi-mental lesions by the use of iteration sequences.

398 APPLIED OPTICS @ Vol. 34, No. 3 @ 20 January 1995

The authors acknowledge the expert help and ad-vice of Kathy R. Dezern, Michelle Thompson, GregoryG. Brucker, Kammey Cousar, Keyna Winkler, and M.YasinA. Raja.

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Chuang, ‘‘Current status of lasers for arrhythmia ablation,’’ J.Cardiac Electrophysiol. 3, 345–353 119922.

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