Primary and secondary damage to biological tissue inducedby laser radiation
Gabriel Laufer
A simple analytic model describing the evolution of the thermal injury during and after exposure of biologi-cal tissue to pulses of intense laser radiation is presented. Estimates for the upper and lower bounds of theextent of the thermal injury associated with protein and enzyme denaturization (secondary damage) relativeto the extent of burned tissue (primary damage) are presented. The energy necessary for burn thresholdand the energy required to induce both types of thermal injury increase with laser pulse duration. An opti-mal duration of laser pulse exists at which the extent of the secondary damage relative to the primary dam-age is the smallest.
I. Introduction
High power CO2 lasers are becoming increasinglyimportant surgical tools.1 Their major role, as an al-ternative or an adjunct to the mechanical scalpel, is toexcise or remove excessive tissue.
The advantages associated with the technique arenumerous.1 The operating time may be reduced, thewound is sterilized in the course of the operation,bleeding is limited, the sealing off of vessels eliminatespossible spread of malignant cells and more.
However, the exact physical mechanism responsiblefor the tissue removal is not understood yet. It isclaimed2-4 that the laser beam is absorbed by the watercontained in the tissue. The absorbed energy is rapidlythermalized, thereby vaporizing the water and leavingbehind only tissue debris.
There is no doubt that absorption by water plays animportant role in the tissue excision process. The largecoefficient of absorption exhibited by water at thewavelength of the CO2 laser5 assures the deposition ofmost of the energy in a rather small volume, therebyinducing a rapid temperature increase. However, thepresence of a surface temperature in excess of 1000C aswell as the observation of several degrees of charring atvarious levels of exposure6 7 suggests the simultaneousinfluence of other mechanisms. Furthermore, ablationcan be frequently seen,8 indicating that water continuesto accumulate energy even after evaporation.
The high surface temperature and thereby the hightemperature gradient pointing from the surface into theunderlying tissue layers promote the conduction of heatfrom the illuminated tissue layers to unexposed layers.The rate of heat transfer due to the conduction whensurface temperature exceeds 1000C is higher than the
The author is with Technion, Israel Institute of Technology, Fac-ulty of Mechanical Engineering, Haifa 32000, Israel.
rate which would be anticipated if only water vapor-ization was present. The conducted heat has an ad-verse effect on the surgical process: not only does itdeprive thermal energy from the tissue to be removed,it also transmits the energy to healthy living cells,raising their temperature and causing an irreversibledamage by enzyme and protein denaturization andcoagulation.
This irreversible damage has been found to occur atmoderate temperatures. Moritz and Henriques9
studied extensively the damage induced to human andporcine skin when subjected to heat sources at varioustemperatures and durations. In many experiments,necrosis could be detected after skin temperature hadbeen raised to only 440C. Except for cases of severeburns, microscopic tests did not reveal any noticeablechange, while delayed reaction such as exfoliation andblistering occurred within a few days after exposure.Furthermore,. an unrecognizable reversible damage,which became irreversible only after an additional ap-plication of heat, has been observed. This damagepattern has been named, by Moritz and Henriques, la-tent heat injury. Work by Stoll and Chianta10 yieldedsimilar results. An unrecognizable injury, identifiedonly by a delayed reaction of blistering, was de-scribed.
In most surgical applications, the primary tissuedamage, i.e., the damage caused by the tissue burning,is the desired consequence of the laser exposure.However, the secondary damage, i.e., the damage ofenzyme and protein denaturization does not result intissue removal. Instead, it is likely to injure healthyorgans and therefore should be regarded as undesir-able.
Several investigators studied the pattern of laser-induced injury. Stern et al.1 studied qualitatively andmorphometrically the vocal cord lesions produced bya CO2 laser. They considered exposure times exceeding0.1 sec. The damage to the tissue consisted of a cratersurrounded by a layer of debris of vaporized tissue.Under this layer an additional 600-,um thick layer of
vacuoles surrounding the margins of the crater wasdetected microscopically. The overall damage wasfound to increase with exposure time although the totalapplication (i.e., energy) was maintained the same.Stern et al. suggested that the increase in the overalldamage might result from the increased time to absorbheat and dissipate thermal energy to adjacent tissue.Imakiire et al.7 observed a similar stratified damagepattern: At the bottom of the crater they found a25-Am thick charred layer covering a 400-600-Am thicklayer of honeycomb necrotic tissue generated by thesudden vaporization of cell matter followed by coagu-lation. This layer of dehydrated cells, noticed both byStern et al. and by Imakiire et al., may be consideredas part of the secondary damage. However, an addi-tional damaged layer, unidentified as such under mi-croscopic examination, is likely to be present under thedehydrated layer. This is the damage of enzyme andprotein denaturization which was observed by Moritzand Henriques9 and Stoll and Chiantal0 only by thedelayed reaction. Still deeper, a layer which underwentonly latent heat injury is expected to be present. Inlaser surgery, where multiple pulse application is com-mon, this layer may also become irreversibly dam-aged.
A parameter which has a paramount effect on theextent of the secondary damage relative to the extentof the burned tissue is the laser pulse duration. It af-fects explicitly the amount of the conducted heat and,in addition, has a direct effect on the secondarydamage.
Only a few investigators attempted to study therelation between laser pulse duration and the tissuedamage or tissue temperature response. Pioneeringwork has been done by Mainster et al. 12 and White etal. 13 They developed a numerical algorithm (using thealternate direction implicit method) for the solution ofthe equation of heat conduction with Beer's law typeheat source. The problem they solved describes thechorioretinal thermal behavior. The light is absorbedby the thin pigment epithelium and a choroid layer in-terfaced with the sclera and the vitreous humor. Thewhole ocular medium was assumed to be thermallyhomogeneous and the temperature far from the ab-sorbing layers was assumed to be invariant. Althoughtheir solution yielded spatial temperature distributions,no attention was devoted to the evaluation of the in-duced damage. Similar work was done by Wissler,' 4
again without any description of the thermally inducednecrosis. This work-done analytically-also describesthe ocular thermal response to light.
An early mathematical model of thermal injury in-duced by laser beams has been given by Priebe andWelch.15 They analyzed the effect of beam radius onthe induced thermal damage profile at the ocular retinausing an asymptotic calculation of the temperatureprofile for a steady state (to - c) and impulse (to - 0)applications. The thermal injury considered by Priebeand Welch was protein denaturization which is similarto the secondary damage described above. They didnot address at all the problem of tissue burning. Their
results show that, for impulse type exposure, the centralportion of the illuminated region experiences higherpeak temperatures and for the same total energy ap-plication the axial peak temperature decreases withpulse duration for pulses longer than 10-3 sec. Finally,it can be inferred from their results that the total energyrequired to induce thermal injury due to protein de-naturization increases with exposure duration. Heatconduction accounts for all these observations. In arecent work, a numerical algorithm has been used16 tofurther elaborate the previous solution.'5 This 2-Dcalculation was presented in a dimensionless form andthe thermally induced necrosis was not evaluated.
The only theoretical work known to the author whichconsiders the formation of two types of thermal injury,i.e., complete tissue removal by burning and tissue de-naturization, has been done by Incropera et al.17 Theypresented the analytical solution of the thermal re-sponse of 1-D living tissue exposed to a uniformly dis-tributed heat source. The induced thermal necrosis,similar to the secondary damage described above, hasbeen estimated at the periphery of the exposed regionand was shown to increase with exposure time for thesame applied heat flux. However, the description giventhere is not representative of the case of laser excision:The pulse duration (30 sec) is far longer than the typicalpulse duration of the surgical laser, and the heat sourceis a surface heat source instead of the exponentiallydecaying distributed heat source as required by Beer'slight absorption law.
At present there is no available estimate of the rela-tive magnitudes of the primary and secondary damageinduced to biological tissue in single- or multipulse laserexposures nor is there any functional dependence re-lating them to the laser pulse duration. Therefore, thispaper will present a simple analytic model which de-scribes the evolution of the thermal injury during andafter exposure to pulses of intense laser radiation. Theprimary and secondary damage will be identified andtheir relative magnitudes will be evaluated for laserpulses of various durations.II. Mathematical Model
The process which results in tissue destruction beginswith the absorption of the laser beam. It is usuallyassumed18"19 that direct absorption with an absorptioncoefficient fi and scattering due to optical inhomo-geneities in the tissue are responsible for the attenuationof the propagating beam. However, for an extremelyhigh absorption coefficient, as is the case with the CO2laser, and for long wavelengths, the scattering causesonly a minimal loss. Therefore, the volumetric rate ofenergy deposition in the tissue, S(r,z,t) for a laser beampropagating in the z direction, may be modeled byBeer's law:
(1)
where Io(r,t) is the incident laser beam intensity (W/cm2). The absorbed laser energy is instantaneouslyconverted into heat. Thus, the heat equation for thetemperature distribution T produced by the volumetricheat source S(r,z,t) can be written2 0
where K is the heat conductivity, p is the density, andc is the specific heat of the substance. Implicit in Eq.(2) is the assumption that conduction is the majormechanism for heat transfer. Alternative or competingheat transfer mechanisms such as blood perfusion ormetabolic heat generation21 were assumed to be rela-tively small at most laser surgical applications andtherefore were omitted.
The boundary conditions for the solution of theproblem assume undisturbed temperature distributionfar from the exposed area and no heat loss at the tis-sue-air interface. The last boundary condition can bejustified by recalling that the coefficient for convectiveheat transfer for humans is of the order of 10-5 W/(cm 2
oC). 2 2 Thus, at most laser surgical applications wherethe applied intensity is of the order of 10 W/cm2 orhigher, the overall loss due to convection is expected tobe negligible. Heat reradiation from the tissue is alsonegligible.2 3
This problem, as presented by Eq. (2) and theboundary conditions, has been previously solved for the1-D case.1920 Assuming that the beam is attenuateddue to absorption only and with T(z,o) = 0, we get
T(z,t) = 21 (kt)1/2ierfc [ /2 exp(-z)
+ I( exp(32kt + z) erfc l(kt)1/2 + z
+ Io: exp(fl 2kt - z) erfc fl(kt)1 - Z_ (3)
where k = K/(pc) is the thermal diffusivity. Althoughthe 1-D solution lacks generality it presents a good ap-proximation along the axis of a TEMOO laser beam withthe beam radius (at le of the center line intensity) >>,. This last condition is met in many surgical appli-cations.
The mathematical modeling of tissue damage ofvarious degrees is a most complex task and, therefore,a far reaching assumption will have to be made at thispoint. The onset of the damage is thermochemical innature and has been studied by Henriques24 for cuta-neous thermal injury at temperatures <50°C. Hesuggested that, although tissue damage is likely to beassociated with many different reactions, each with itsown rate coefficient, it can be characterized by a singleprocess. This process relates to protein denaturization,it has an activation energy of 150,000 cal/mole, and ischaracterized by a single rate constant of the Arrheniusform. Thus, if Q denotes a measure of the damage in-duced to the tissue, it can be computed by integratingthe Arrhenius rate equation through time:
Q(z,t) 3.1 X 1098 f expl-150,000/R[T(z,t) + 273]1dt, (4)
where R = 1.986 cal/mole is the universal gas constantand T(z,t) < 50°C. The numerical constant in frontof the integral has been derived by Henriques to yieldQ 1 when a complete and irreversible tissue necrosis
due to enzyme and protein thermochemical denaturi-zation has been observed histologically.
The damage function Q, which was used here to de-scribe the secondary tissue damage, has a strong timeand temperature dependence. The time for irreversibledamage at elevated temperatures is much shorter thanthe time for damage at moderate temperatures. Thetemperature of 58°C which causes an irreversibledamage after an exposure of 1 sec is considered1 8 as thecritical temperature. Although the damage associatedwith this mechanism results with the necrosis of the cellit leaves it physically intact. In many cases the damageis undetectable by microscopic examination. Since thissecondary damage occurs at moderate temperatures itis likely to cause a large extent of tissue necrosis when-ever tissue removal by thermal effects is attempted.
At temperatures approaching 100°C vaporization ofthe cell water occurs. From here on, as temperaturerises, further decomposition of the organic moleculesoccurs, resulting in carbonization and burning of thetissue. This is the process which leads to tissue removaland therefore it is of major interest in the analysis of thelaser scalpel.
There is no clear mathematical model describing thisprocess. Langerholc19 looked only at the phase tran-sition associated with the water vaporization, therebylimiting the maximum surface temperature to 1000C.On the other hand, Imakiire7 suggested that the surfacetemperature may get as high as 10000C. Fukumoto etal.
6 demonstrated experimentally that the surfacetemperature can reach 4500C, well above the temper-ature at which phase transition should occur. Fur-thermore, their numerical analysis which allowed con-tinuous increase in surface temperature without ac-counting for phase transition did match their experi-mental results.
An ordinary vaporization process occurs in two stages.First the medium is heated to the boiling point, then asadditional energy is added vaporization takes place.Analytical description of this process is highly nonlinearand thus must be done numerically.
Supported by Fukumoto's observation, a simplifiedlinear model was introduced. This model allowed acontinuous temperature increase well beyond theboiling point. The temperature rose linearly as energywas absorbed while the specific heat was equal to thatof water through the analysis. The phase transition wasassumed to occur instantaneously as a burn thresholdtemperature was reached.
To account for the vaporization latent heat, the burnthreshold was set at a temperature which for this modelis iso-energetic with saturated water vapor at 1000C.
The present model yielded a faster temperature in-crease than experienced by a tissue during laser surgery.Although the final surface temperature is similar to thatobserved by others it was believed that the overallthermal damage in this model is likely to be too high, i.e.,it presents an upper bound.
For estimating the lower bound of the thermally in-duced damage, a new burn threshold-at 1000C-wasassumed. This is certainly lower than the surface
temperature during laser excision. However, tomaintain the linearity of the model, a new specific heathad to be introduced such that the overall energy re-quired to reach the lower bound burn threshold wasequal to the energy acquired when getting to the burnthreshold in the upper bound model.
Although the overall deposited energies are the samein both models, the temperatures and gradients in thelower bound model are below the values experiencedduring laser excision, therefore, yielding a lower boundestimate for the thermally induced damage.
The damage due to thermochemical processes, i.e.,the secondary damage, was evaluated in both approxi-mations by Eq. (4), while the depth of burned tissue, i.e.,the primary damage, was evaluated as the depth atwhich the temperature exceeded the preset thresholdvalue.
As an example of the simplicity offered by the presentanalytical solution, consider the laser intensity, IT, re-quired to reach the burn threshold at the tissue-air in-terface after an exposure time t. Using Eq. (3) andassuming a burn threshold temperature Tb (o,t) onegets
- _ ,BKTb (0,t)
- (kt)/2 + exp(32kt) erfc[U(kt)1/2] - 1
The total energy deposited by the laser beam in reach-ing the burn threshold is IT X t.
I11. Results
Equation (5) has been used to evaluate the energyrequired to produce burn threshold at the tissue surfacefor various exposure durations.
The absorption coefficient of water at a wavelengthof 10 ,um, 3 = 767 cm-, 5 has been selected as a repre-sentative absorption coefficient of the tissue. From acomprehensive list of parameters describing tissuethermal behavior2 5 the following values were selected:K = 4.2 X 10-3 W/cm K, c = 3.77 X 103 J/kg K, and p =1050 kg/M3 . The temperature representing thethreshold for tissue burning for the upper bound esti-mate was assumed to be 6390C. This is what the tem-perature that saturated water vapor would reach hadit not gone through phase transition. Although theselection of this temperature is somewhat arbitrary itcan be justified by the high surface temperature presentin laser surgery. The burn threshold temperature forthe lower bound approximation was set to 1000C whilec = 3.602 X 104 J/kg K.
The upper curve in Fig. 1 presents the energy for burnthreshold at single-pulse exposure vs laser pulse dura-tion. It is seen that, for pulses shorter than 1 msec, thisenergy is independent of laser pulse duration. How-ever, for longer pulses the energy for damage thresholdrises rapidly. This increase is due to heat conduction,which, as time evolves, transfers energy from the ex-posed area into underlying layers.
The lower curve in Fig. 1 is the lower bound. Again,the energy is rising for pulses longer than 1 msec, al-though at a slower rate, and the increase is associatedwith the onset of heat conduction.
Results of experiments performed on feline tonguesare also presented in Fig. 1. The experimental valuesfor burn threshold energy are enclosed between the twocurves. The trend exhibited by these experimentsclosely matches the trend predicted by the 1-D analyt-ical solution, indicating that the model assumed by Eq.(5) and the upper and lower bound analyses are rea-sonable approximations of the model.
Since conduction is the major mechanism responsiblefor the transfer of heat from the exposed area to theunderlying tissue and since the heat is a major cause forthe secondary damage, it is desirable to operate at pulsesshorter than 1 msec where, as was shown, the conduc-tion is minimized. Unfortunately, the only selectionmost commercial lasers offer is of pulses longer than10-2 sec, where heat conduction is already effective.Therefore, the secondary damage is likely to be exten-sive and its magnitude relative to the primary damageshould be estimated.
The burn threshold calculation just described wasmeant to predict the onset of the burning only and couldnot be used to estimate the depth of burned tissue.However, Fukumoto et al.
6 demonstrated that, after theonset of burning, the tissue temperature continues risingfollowed by increasing carbonization. Thus, it couldbe assumed in the analytic model that surface temper-ature may exceed the burn threshold temperature.Lacking any better estimate, a surface temperature of7000C was selected as the maximum obtainable tem-perature in the upper bound model. The maximumtemperature for the lower bound model was set ac-cordingly to 106.40C. Being relatively close to thethreshold temperatures, these temperatures could yieldan approximation for the near threshold primarydamage by an evaluation of the depth at which thetemperature exceeded the burn threshold tempera-ture.
90 I I I I I
,8, 767 cm-'
80 Kz42.IUO Wr K=4 2X10-3cm K|- C-377x10 J K|_
70- ~~~~kg K70 -- C*3-602x104J
kg K
, _ 60c _ + EXPERIMENTAL RESULTSE (FELINE TONGUE)
50-
z
D 40/
w 30-
20 _
X~~~~~~~~~~+ /10
I0-1 IO 10' 1O-4 10-3 10
1o- I 10
LASER PULSE DURATION (SECONDS)
Fig. 1. Energy for burn threshold vs laser pulse duration. The solidline represents an upper bound while the dashed line is a lower
The pulsed nature of the laser exposure was modeledby introducing an identical heat source at the end of thepulse (t = to) and subtracting its effect from the solu-tion. Equation (5) was used to evaluate the laser in-tensity required to produce on the surface, at the endof the pulse, the maximum temperature (i.e., 700'C or106.40 C). The temperature distribution was calculatedfor both models at various times beginning with theapplication of the laser pulse and ending with final re-covery of the temperature transient. Simultaneouslywith these calculations, the denaturization damage [Eq.(4)] was calculated numerically using the instantaneouslocal temperatures.
Figure 2 presents the calculated depth of burnedtissue and the depth of denaturization as a function oflaser pulse duration for the upper bound model, whileFig. 3 represents the same for the lower bound model.The curves describing the denaturization depth followvery closely the pattern of the energy for burn threshold(Fig. 1): For pulses shorter than 1 msec, they dependonly slightly on pulse duration and then rise very rap-idly. The primary damage curves start rising earlierdue to the stronger effect of heat conduction at thesurface, where high temperature gradients are presentand where most of the primary damage is.
The most striking observation from both these figuresis the relatively large depth at which tissue denaturi-zation occurs. This depth can get at times to over 0.5cm, which is substantially larger (even for the lowerbound model) than the depth of 500 gtm observed mi-croscopically by Imakiire et al.
7 The difference be-tween the experimental observation and the analyticalestimate can be justified by recalling that part of thesecondary damage predicted by this calculation is adenaturization damage which is not accessible to mi-croscopic observation.
In practical surgery it is usually assumed that thedamage to tissue is confined mostly to the burned tissue
2
24
N
I-4
0
I-
10- 10- 1 0-4
10 10-2 I0'
LASER PULSE DURATION (SECONDS)
Fig. 2. Dimensionless depth of denaturization vs laser pulse duration(left scale) and dimensionless depth of burned tissue (right scale) for
Fig. 3. Dimensionless depth of denaturization vs laser pulse duration(left scale) and dimensionless depth of burned tissue (right scale) for
the lower bound model.
and any additional damage may be considered secon-dary. The present calculation, however, demonstratesthat the denaturization damage, although not visibleto the naked eye, is substantial and exceeds the burneddepth.
To further elaborate on this observation, the ratiobetween the two types of damage has been calculated.Figures 4 and 5 present the ratio between the denatur-ization depth at the end of the laser pulse and theburned depth (lower curve) and the ratio between thedenaturization depth when a complete temperaturedecay is established and the burned depth (uppercurve).
Equation (4) which was used to determine the de-naturization depth has been shown9 to be valid only forrelatively long hyperthermic episodes (i.e., episodeswhich result with an irreversible injury at tissue tem-peratures <580C). Therefore, using Eq. (4) for thecalculation of injury induced by heat exposures lastingonly a fraction of a second, as is the case for the lowercurve in Figs. 4 and 5, is questionable. Nevertheless,the inclusion of these curves allows the reader to realizethat, although exposure to laser radiation has ended, asubstantial tissue injury still continues to accumulate.The calculation of the depth of denaturization as pre-sented in Figs. 2 and 3 and both curves in Fig. 1 com-plied with the temperature limit of Eq. (4), i.e., thetemperature at the deepest injured layer did not exceed580 C.
Both curves in Figs. 4 and 5 show a pronouncedminimum. At the short pulse end of these figures, theratio decreases with increasing pulse duration due toincrease in the primary damage resulting from the ini-tiation of the heat conduction. At the long pulse end,the secondary damage increases faster than the primarydamage, therefore increasing the value of the ratio asthe laser pulse gets longer.
U, C.3-77'-3' 140C kg KZ0 t'to - --Cr FINAL -M 120
0
100
Z 80_0
Cr 60-
Z
0 40
0
F 20
10-7 10-6 10-5 104 10- 0o- ' I 10
LASER PULSE DURATION (SECONDS)
Fig. 4. Ratio between the depth of denaturization and the depth ofburned tissue vs laser pulse duration for the upper bound model.
10
9
0W aZ S3I, 7Cr
0
a 6
0
1
2!R
E,-
C10-' 10 -1 ' IO IO- 10' 0 -a 10-'
LASER PULSE DURATION (SECONDS)
Fig. 5. Ratio between the depth of denaturization and the depth ofburned tissue vs laser pulse duration for the lower bound model.
As mentioned before, most commercial surgical lasersoperate at pulses longer than 10-2 sec where excessivesecondary damage is induced. Operating at the optimalpulse length, i.e., 10-3 sec, should yield improved sur-gical results.
IV. Conclusions
A linear 1-D analytic model for the calculation of theevolution of the primary and secondary damage hasbeen introduced. The model is able to predict theupper and lower bounds of burn threshold energy forlaser pulses of various durations. This model suggeststhat previous values of the secondary damage, obtainedby microscopic examination, are underestimated, and
additional damage of an extensive size, unobservablemicroscopically, is likely to be present. This analysisalso predicts the existence of an optimal laser pulseduration at which the ratio between the ultimate extentof the secondary damage and the ultimate extent of theprimary damage is minimal.
The author would like to thank I. Eliachar and H. Z.Joachims from the Rambam Medical Center, J. Katz,and S. Haber for valuable discussions on this work. Thehelp of P. Attal in the numerical work is also gratefullyacknowledged.
This work was partially supported by grant 180-443from the Israel Ministry of Health.
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