Lasers in Surgery and Medicine 45:108–115 (2013)

Finite Element Analysis of Thermal and AcousticProcesses During Laser Tattoo Removal

Alexander Humphries, BEng,1,2�Tom S. Lister, BSc,2,3 Philip A. Wright, PhD,2 and Mike P. Hughes, PhD

1

1Centre for Biomedical Engineering, School of Engineering, University of Surrey, Guildford, Surrey GU2 7XH,United Kingdom

2Wessex Specialist Laser Centre, Salisbury District Hospital, Salisbury, Wilts SP2 8BJ, United Kingdom3Department of Electronics and Computer Science, University of Southampton, University Road,Southampton SO17 1BJ, United Kingdom

Background and Objective: Q-switched laser therapyis commonly used for the removal of tattoos. However,despite ever increasing demand for this intervention,a better understanding of the mechanisms that resultin pigment reduction is required in order to optimise out-comes and reduce the number of treatment episodes.Study Design: A finite element analysis computer simu-lation was developed to model the fragmentation responseof ink granules during irradiation of a professional blacktattoo using a Q-switched Nd:YAG laser. Thermal andacoustic mechanisms were considered, allowing the opti-mal laser settings to be predicted throughout the courseof treatment. Changes in the thermal properties of theink during heating were taken into account to improvethe reliability of the results obtained.Results: The simulated results are in close agreementwith clinical observations. Thermal fragmentation wasshown to be the dominant mechanism in pigment reduc-tion when using a 6 nanoseconds pulse at 1,064 nm. Inorder to provide maximum clearance whilst maintainingacceptable levels of tissue thermal damage, later treat-ments were shown to benefit from higher fluence levelsthan initial treatments. Larger spot diameters were alsopreferable throughout the course of treatment.Conclusions: The results from the simulation build uponprevious work carried out in the field, applying inkthermal coefficients which vary with temperature for thefirst time. These results compliment clinical knowledge,suggesting that a proactive increase in fluence during acourse of treatments is likely to improve the response tolaser therapy. Lasers Surg. Med. 45:108–115, 2013.� 2012 Wiley Periodicals, Inc.

Key words: laser therapy; tattoo removal; acousticresponse; thermal response; black ink; computer simula-tion; fragmentation mechanism; Q-switched

INTRODUCTION

Despite an increase in popularity of tattoos in recentyears an estimated one in five people with tattoos expressa desire for tattoo removal [1]. Q-switched lasers are thetreatment of choice for reducing the pigmentation of inkwithin tattoos, although comparatively little is known

about the mechanisms of tattoo ink fragmentation. Conse-quently, there is limited consensus for optimal laser set-tings in initial and subsequent treatment sessions. Arecent study found that eight or more sessions are oftennecessary for a satisfactory result [2]. Total clearance of atattoo is rare, quoted in one study as being only three of238 paying patients [3]. In order to optimise laser para-meter selection, increase the efficacy of each treatmentsession, and minimise the total number of treatment ses-sions required, an improved understanding of the mecha-nisms of pigment reduction is necessary.The majority of tattoos, which present for removal at

our centre are composed primarily of black inks and havebeen created by a professional tattoo artist. Such tattooshave been shown to contain ink granules, which are rela-tively homogeneous in size and depth [4]. This makes theprediction of optimal laser settings a more reliable exer-cise when compared to amateur tattoos, or tattoos com-prising various colours of ink.The purpose of laser treatment is to fragment the ink

granules, which form the tattoo. The resulting fragmentsare smaller in size and are therefore more likely to beabsorbed through macrophagic processes [5]. Successivetreatments result in fewer and smaller ink granules.However, if laser parameters are not altered to accountfor the progressive reduction in the size and number ofthe ink granules that comprise the tattoo, a greater num-ber of treatment sessions may be required to reach a satis-factory clinical end point [6]. Observations at our centredemonstrate reduced changes in pigmentation followinglatter treatment sessions, compared to those seen in theinitial treatments. These observations emphasise the

Conflict of interest Disclosures: All authors have completedand submitted the ICMJE Form for Disclosure of Potential Con-flicts of Interest and none were reported.

Contract grant sponsor: Centre for Biomedical EngineeringUniversity of Surrey Guildford.

*Corresponding to: Alexander Humphries, BEng, Centre forBiomedical Engineering, School of Engineering, University ofSurrey, Guildford, Surrey GU2 7XH, United Kingdom.E-mail: a.humphries@surrey.ac.uk

Accepted 26 November 2012Published online 31 December 2012 in Wiley Online Library(wileyonlinelibrary.com).DOI 10.1002/lsm.22107

� 2012 Wiley Periodicals, Inc.

potential benefit of anticipating changes to laser para-meters required throughout the course of treatment inorder to optimise the clinical response.There is controversy in the literature surrounding the

mechanism of tattoo pigment reduction in tissue. The twomajor mechanisms, which have been proposed for thefragmentation of tattoo ink granules, are termed thermaland acoustic. The majority of studies consider only frag-mentation through thermal mechanisms [7–9], whilstothers suggest that the acoustic mechanism predominatesin short pulsed laser therapy [10][11]. In contrast, Welchet al. [[12], pp. 715–717] suggest that the laser-induceddamage may be caused by a combination of thermal andacoustic effects. Accordingly, a wide range of predicted op-timal parameters for laser treatment is presented in theliterature. Thus, it is apparent that an improved under-standing of the mechanisms responsible for ink granulefragmentation is required in order to predict optimal laserparameters more accurately.Computer simulations of laser therapy of tattoos to date

have applied ink thermal properties that remain constantwith temperature [7,10]. However, this assumption islikely to have a considerable effect on the reliability of theresults obtained due to phase changes in the constituentink compounds [13]. Additionally, simulations for thelaser therapy of tattoos to date have not considered theinteraction between the thermal and acoustic mecha-nisms, affecting the fragmentation response of the ink.In this study the ink fragmentation responses for both

thermal and acoustic mechanisms are predicted for Nd–YAG laser therapy of professional black tattoos using afinite element analysis simulation. The properties of theink are varied as a function of temperature, improvingthe reliability of the results compared to previous studies.Laser settings are predicted for the initial and subsequenttreatment sessions, which provide maximal ink fragmen-tation whilst maintaining acceptable levels of adverseeffects to surrounding tissues.

MATERIALS AND METHODS

A finite element model was created using COMSOLMultiPhysics Version 4.1 (COMSOL, Burlington, MA) tosimulate the thermal and acoustic response to laser radia-tion of tattoos. The project was divided into a number ofstages to enable the simulation to be built and validated.Initially, the transport and absorption of laser lightthrough tissue was simulated. Following this, the thermaland acoustic mechanisms of ink granule fragmentationwere evaluated. Finally, optimal laser parameters werepredicted for initial and subsequent treatment sessionsby varying the modelled tattoo characteristics andQ-switched Nd:YAG laser settings.

Creating the Simulation

A two-dimensional model geometry was used, encom-passing the epidermis, dermis, and tattoo ink granules,as illustrated in Figure 1. The granule’s circular cross-section enabled its thermal and stress profile to be

analysed. A two-dimensional geometry was therefore ap-propriate due to the symmetry of the granule and tattooregion. The depth of the epidermis was assumed to be con-stant and equal to that measured for the forearm at75 mm [14], whilst the interface with the dermis was as-sumed to be parallel to the epidermis surface. The widthand depth of the tissue model were 12 and 10 cm, respec-tively, ensuring that the boundary effects of the modelhad negligible influence on the power penetration. To re-duce the effect of total internal reflection of scattered lightat the model boundaries, simulating the progressionof light to the surrounding tissue, an absorbing layersurrounded the sides of the tissue. The boundary absorp-tion coefficient of 104 m�1 and specific heat value of1 � 106 J/kg K were shown to absorb the vast majority oflight incident upon the boundary with minimal rise intemperature. Furthermore, plane wave boundary condi-tions were applied such that the pressure waves were notreflected from the edges of the geometry when consideringthe acoustic mechanism.

The range of laser parameters used in the simulationwere based upon the nominal values stated on the techni-cal specification for the Cynosure affinity Q-switchedNd:YAG laser. The incident laser beam was modelledusing a ‘top hat’ profile applied to the surface of the epi-dermis at the centre of the model. The pulse duration wasfixed at 6 nanoseconds for the source, while the fluencewas varied between 4 and 18 J/cm2 in 2 J/cm2 intervalsand the spot diameter varied between 2 and 4 mm in0.2 mm intervals.

Fig. 1. 2D Model geometry of the boundary layers, ink and

tissue. Not to scale.

MODELLING RESPONSE TO LASER TATTOO REMOVAL 109

The characteristics of tattoos have been shown to varybetween each treatment session [4]. This variation wasapplied to the model to correspond to the tattoo propertiesin the initial and subsequent treatment sessions, but wasassumed to remain uniform across the tattoo. The diame-ters of tattoo ink granules have been measured by Tayloret al. [4], showing that before irradiation the granuleswithin the dermis can have a maximum diameter of 6 mmand the mean diameter reduces after laser treatment.Since the maximum diameter of granule that can beabsorbed by the lymphatic system is approximately0.4 mm [5], this specified the lower limit for the simulatedgranule diameter, corresponding to the diameter in thelatter treatment sessions. To allow the effect of granulediameter to be assessed in the simulation, values of 6, 1and 0.4 mm were used as the average ink granule diame-ter. The granule depth remained uniform throughout theanalysis at 400 mm, since professional tattoos are general-ly located in the upper to mid-dermis region [4].

During the course of laser therapy the number densityof the ink granules in the tattoo has been shown to de-crease. Hu et al. [15] estimated the proportion of ink with-in an area of tattoo, showing that black ink covered amaximum area of 10.5% before treatment and a minimumof 0.75% following a single treatment. Therefore, granulenumber densities of 10.5%, 5% and 0.75% of the area wereused in the simulation, corresponding to the distributionof granules in the initial and subsequent treatmentsessions.

Light scattering was simulated through diffusion theo-ry, using the Helmholtz equations (Eq. 1) to evaluate theeffects of anisotropic light scattering and to evaluate theabsorbed energy of each ink granule. Light transport wasassumed to be time independent as it occurs in consider-ably less time than thermal conduction [16]

rð�DruÞmau ¼ f (1)

where u is the fluence rate within each element of themodel, D is the diffusion coefficient, ma represents theabsorption coefficient and f is the source term.

The optical coefficients of the tissue [17,18] wereapplied (Table 1) and assumed to remain constant withtemperature, where the epidermal absorption coefficientwas modelled to have a melanosome content comparableto a moderately pigmented adult. Mie scattering isproposed as the dominant scattering mechanism within

the tissue, meaning anisotropic scattering characteristicsare an important consideration in the simulation [[12],pp. 325–328]. An anisotropy factor of 0.85 was used forthe tissue to ensure the majority of the laser source wasundeflected [10]. The optical properties of black tattoo inkare less well documented. Although Bashkatov et al. [19]calculated the absorption coefficients of diluted black tat-too ink, its scattering coefficient is unreported (Table 1).Since the internal light scattering properties of the inkhave negligible effect on the scattering response when thegranule diameter is in the same order of magnitude asthe wavelength of light, the ink scattering coefficient wasassumed to be comparable to the tissue’s.

Thermal Mechanism

As laser light energy is absorbed by the tattoo ink gran-ules, it generates random vibrations of the molecules lead-ing to localised heating and thermal gradients within theink and tissue [11]. This localised absorbed energy wasapplied as the source term in the Bioheat equation(Eq. 2), allowing the changes in temperature across themodel to be simulated. The heat energy from the ink wasassumed to conduct to the surrounding tissue, while theeffects of perfusion were neglected [[12], p. 770]. Thisallowed the thermal mechanism to be analysed, such thatthe ink’s fragmentation response and tissue thermaldamage could be evaluated

rCP@T

@t¼ r krTð Þ þQs þQp þQm (2)

where r is the density of the medium, CP is its specificheat and k is its thermal conductivity. The heat sourcefrom the absorbed light (QS), the metabolic activities (Qm)and the heat loss due to blood perfusion (QP) were alsoconsidered.The tissue thermal coefficients (density, specific heat

and thermal conductivity) used in the simulation areshown in Table 2. These properties are assumed to remainconstant over the relatively small range of tissue temper-atures modelled. Conversely, the temperature of the inkvaries significantly during irradiation, giving rise tochanges in the thermal properties of the ink and its con-stituents. Previous analysis of black tattoo ink by theauthors demonstrated considerable variation in its prop-erties with temperature [13]. Accordingly these tempera-ture dependent ink properties between 08C and 1,0008C

TABLE 1. Absorption (ma) and Scattering Coefficients

(ms) for Epidermal, Dermal and Ink Layers

ma (m�1) Epidermis 500

Dermis 30

Ink 525,300

ms (m�1) Epidermis 11,500

Dermis 11,500

Ink 11,500

TABLE 2. The Thermal Coefficients for the Epidermis,

Dermis and Ink Layers

Density

(r) (kg/m3)

Specific heat

(Cp) (J/kg-K)

Thermal

conductivity

(k) (W/m-K)

Epidermis 1,100 [20] 3,600 [20] 0.209 [21]

Dermis 1,100 [20] 3,600 [20] 0.322 [22]

110 HUMPHRIES ET AL.

were used in the simulation to model more accuratelythe change in properties of the ink as its temperaturechanged during irradiation.The ink fragmentation threshold was modelled as

1,0008C as previously described for tattoo ink lightening[4]. Similarly, the occurrence of thermal damage to thesurrounding tissue was estimated as 608C, since thiscorresponds to the temperature required for protein dena-turation [11].The time-dependent temperature of the granules and

surrounding tissue was simulated for 15 nanoseconds toevaluate its peak temperature and cooling rate. The pre-dicted peak tissue temperature and proportion of gran-ules exceeding the fragmentation threshold were recordedto enable the degree of tissue thermal damage and inkfragmentation to be estimated for a range of laser param-eters and tattoo variables.

Acoustic Mechanism

The effects of optical breakdown and the subsequentcreation of plasma as a mechanism for pressure wave in-duction were not considered in this study as the thresholdfluence for plasma production for a 9 nanoseconds pulseat 1,064 nm is estimated at 2,800 J/cm2 [23], more thantwo orders of magnitude higher than the greatest fluenceconsidered in this simulation.The expansion and inertial properties of the granules

during 1,064 nm irradiation have been postulated toinfluence the magnitude of the acoustic stress waves pro-duced [24]. This mechanism was simulated in the fre-quency domain using acoustic-solid interaction boundarylayers between the ink and tissue to enable the ink stressand tissue pressure waves to interact. The rate of changein the expansion of the granules due to heating definedthe tissue loads; while the tissue pressure defined theload on the granules. Non-linear propagation of acousticwaves was considered in the simulation to predict the be-haviour of the pressure and stress waves in the tissue andink granules. The peak stress was analysed to determineif this exceeded the threshold for fracture. In accordancewith Ho et al. [10], it was assumed that the fracture stressof graphite was comparable to that of the ink, giving anestimation of 300 bar in the simulation [25].The acoustic mechanism was simulated in parallel to

the thermal model, allowing the appropriate ink densityto be determined [13] for the granule’s temperature.Consequently, the granule expansion rates varied withtemperature during irradiation. Changes in density withtemperature allowed the increase in diameter of the gran-ule to be calculated and specified as a displacement at thegranule’s edge. Expansion of the ink granule was simulat-ed to affect its stress and induce a pressure wave withinthe tissue.The acoustic properties of the ink were assumed to be

comparable to those of graphite [10] in the simulation,while the properties of the surrounding tissue were as-sumed to be linearly elastic and remain constant over thesmall range of temperatures experienced. The speed ofsound in the tissue was specified as 1,498 m/second [26]

and the density of the tissue defined as 1,100 kg/m3 [20].The in plane Young’s modulus and Poisson’s ratio for theink were defined as 1.153 TPa and 0.195, respectively[27].

Predicting the Optimal Laser Settings

Initially, the optimal spot diameter was assumed to bethat which maximised the area of fragmentation. The op-timal fluence was then predicted using the data obtainedat this spot diameter. The fluence that led to the greatestarea of fragmented ink granules and caused tissue tem-peratures to remain below the threshold for collateraldamage (608C) was determined for initial and subsequenttreatment sessions.

RESULTS

Thermal Mechanism

The peak granule temperature was simulated at theend of the laser pulse, resulting in a peak tissue tempera-ture within 2 nanoseconds after the pulse. Figure 2 showsthe temperature profile for the granule under the centreof the irradiated region. Granules within the irradiatedregion were shown to achieve greater temperatures as aresult of increased power penetration (Fig. 3), indicatingthat these were most likely to fragment by the thermalmechanism.

Fig. 2. Magnification of the 6 mm granule’s temperature pro-

file (K) under the centre of the irradiated region. Not to scale.

MODELLING RESPONSE TO LASER TATTOO REMOVAL 111

The effect of changing the laser settings showed thatlarger spot diameters heated a larger area of tattoo, caus-ing greater fragmentation, but also had a small influenceon increasing the central granule’s temperature. Con-versely, the peak temperature of the granules increasedconsiderably at higher fluence settings, as illustrated inFigure 4. Increasing fluence was shown to result in anincrease in the fragmentation response and the area overwhich fragmentation occurred. A corresponding increasein the temperature was also predicted, giving a greaterprobability of collateral damage of tissue surrounding thegranules.

The simulation predicted that the thermal mechanismcaused granule fragmentation within the irradiated re-gion during the initial and subsequent treatments. Inktemperatures were higher in the initial session, demon-strating that granules in this session were most likely tofragment by the thermal mechanism. Ink temperatureswere considerably lower for sessions towards the end ofthe treatment course when constant laser settings wereapplied throughout all treatment sessions.

Acoustic Mechanism

The central granules were found in the simulation to besubject to the greatest rate of change in temperature,meaning these expanded rapidly and generated the

greatest pressure waves within the tissue. No granuleswere subject to stresses above the fracture threshold,although constructive interference and nonlinear propa-gation of the pressure waves generated high stress gra-dients within granules outside the irradiated region,which approached the fracture threshold (Fig. 5). As thewaves propagated through the tissue, their magnitudedecreased. Thus the simulation predicted that acousticfragmentation was most likely in the ink immediatelysurrounding the irradiated area.When considering the effects of changing the laser set-

tings on the acoustic mechanism, the simulation sug-gested that larger fluence values induced higher stressesin granules and the region of maximum stress was dis-placed further from the irradiated area, as illustrated inFigure 6. However, the simulation also indicated thatstresses achieved by only the highest fluence values werecomparable to those required to fragment the ink gran-ules. In contrast, simulated changes in the spot diameterof the source led to negligible changes in the maximumvalue of ink stress.When the tattoo was composed of small diameter gran-

ules at low number densities, with parameters compara-ble to those seen towards the end of the course oftreatment, the magnitude of the pressure wave decreased.This induced low amplitude stresses within granules out-side the irradiated region. The maximum stresses wereseen in the initial treatment session. Thus, the simulationpredicted that the initial treatments were most suscepti-ble to granule fragmentation by the acoustic mechanismunder controlled laser settings.

Predicting the Optimal Laser Settings

The simulation data enabled the optimal laser settingsto be predicted for initial and latter sessions. Throughoutthe course of treatment using a 6 nanoseconds pulse, the

Fig. 3. Light scattering contour plot showing the local power

penetration within the tissue (W/cm2), relative to the gran-

ules located 400 mm below the tissue surface. The magnitude

of the penetration depth was validated by hand calculations

and corresponds with those stated in the literature [8]. Not to

scale.

Fig. 4. Maximum ink temperature (K) within each granule

across the tattoo lesion obtained from the simulation for a

range of fluence settings, using a 2 mm spot diameter.

112 HUMPHRIES ET AL.

predominant influence on fragmentation was thermalrather than acoustic. Accordingly, the thermal responsewas used to predict the optimal laser settings. Larger spotdiameters were shown to be beneficial during the initialsession as they fragmented a larger area of the tattoo, al-though they had little benefit in the latter treatments. Asa result, the largest spot diameter of 4 mm was consid-ered to be optimal throughout the course of treatment.

Using this large spot diameter, it was shown that a great-er fluence achieved a larger fragmented area and higherpeak granule temperatures, as illustrated in Figure 7.Subsequently, the higher fluence settings led to greatertissue temperatures (Fig. 8). Using this data, the modelpredicted that the optimal absolute fluence for the initialsession would be lower, in the region of 7 J/cm2, while forthe latter session it would be 11 J/cm2 to achieve maximalink fragmentation whilst maintaining only a small risk ofthermal damage.

DISCUSSION

The simulation allows the changes in the tattoo param-eters to be assessed and laser settings to be predicted toachieve optimal treatment outcomes. The predicted opti-mal settings correspond to absolute values for the skinmodel in question, since the output of a laser often differsfrom the nominal settings selected by the user [28]. Itshould be noted however, that the simulation models theprofessional black tattoo and does not account for varia-tions in the properties of skin and tattoos between indi-viduals, thus limiting the clinical applicability of theseresults.

Fig. 5. Contour plot of the simulated pressure wave within

the tissue (Pa) when using a 2 mm spot diameter. Not to

scale.

Fig. 6. Maximum stresses induced within each granule

across the tattoo lesion obtained from the simulation for a

range of fluence settings, using a 2 mm spot diameter.

Fig. 7. Simulated changes in the fragmented region of the

ink in the initial and latter treatment sessions for a range of

fluence settings when using a 4 mm spot diameter.

Fig. 8. Simulated changes in the maximum tissue tempera-

ture experienced in the tissue surrounding the granules.

Data are plotted for a range of fluence settings in the initial

and latter treatment sessions using a 4 mm spot diameter.

MODELLING RESPONSE TO LASER TATTOO REMOVAL 113

Larger granules, as expected during the initial treat-ment sessions, are shown to reach higher temperaturesand therefore have a greater chance of fragmentationcompared to smaller granules found in later treatmentsessions. As smaller granules absorb less energy, largerspot diameters and higher fluence settings are found to benecessary to reach appropriate granule temperatures.The simulation predicts that these higher fluence valuescould be used without increasing the risk of thermal dam-age to the surrounding tissue. Accordingly, the optimalfluence for later treatments is predicted to be higher thanthat required for the initial treatment session, whilst alarge spot diameter is found to be optimal throughout thecourse of laser therapy.

The simulation predicts that acoustic fragmentation ismost likely to occur at high fluence values in initial treat-ments due to the increased rate of granule heating. Thisgenerates faster granule expansion and therefore largermagnitude pressure waves in the tissue, inducing higherstresses in granules further from the irradiated region.These observations from the simulation are supported byHo et al. [10], who suggests that larger diameter granulesgenerate greater stresses in the ink, leading to an in-creased chance of acoustic fracture. The simulation pre-dicts that the ink fragmentation is dominated by thethermal mechanism, when using a 6 nanoseconds pulsewith the Nd:YAG Q-switched laser. This supports the the-ory that the acoustic mechanism is less dominant fortreatments with longer pulsed lasers [10]. Consequently,qualitative estimates were made regarding the acousticmechanism during the 6 nanoseconds pulse treatment.

Studies suggest that an increased spot diameter andbeam fluence improve the lightening response of tattoos[6], corresponding with the authors’ observations fromthe simulation. Conversely, variations in the pulse widthare shown to have little influence on the fragmentationresponse. Furthermore, the authors’ observations duringclinic demonstrate that initial treatments frequently ex-perience improved reduction in pigmentation compared tolatter treatments, but with an increased occurrence of ad-verse effects. The rapid increase in the tissue temperatureunder the irradiated region is likely to be responsible forthe ‘popcorn’ effect, described by Verdaasdonk et al. [29],as a result of explosive vaporization and rapid productionof steam at the stratum corneum. It is noteworthy thatthe predicted fluence levels from the simulation resultsare broadly consistent with nominal values used routinelyin the authors’ institution. Therefore, the response of themodel to changes in laser parameters can be seen to corre-late with clinical experience as well as observations statedin the literature. However, caution must be taken inapplying these precise fluence levels elsewhere, as theoutput and treatment response can vary considerablybetween individual devices and patients. A proactiveincrease in the laser fluence is therefore suggested for usein subsequent treatment sessions to achieve improvedtreatment response.

The results of the simulation add to the current under-standing in the literature regarding laser therapy of

tattoos. This further improves the knowledge of the mech-anisms involved, showing how changes in the absolutelaser settings can improve the treatment response duringa course of laser therapy. By predicting that the thermalmechanism was dominant for the Nd:YAG laser treat-ment, optimal laser parameters were evaluated. The laserfluence is shown to have the most influence on the treat-ment response and the largest effect on the occurrence ofthermal damage, identifying that this parameter is themost instrumental in the control and optimisation oftreatment response between treatment sessions. The opti-mal fluence is shown to increase for the latter treatmentsto improve pigment reduction, whilst maintaining accept-able levels of tissue thermal damage. These conclusionscan be used to compliment clinical knowledge and used toinform the optimal parameters, suggesting that a proac-tive increase in the fluence improves the response to lasertherapy. The model therefore provides a valuable tool tounderstand the fragmentation mechanisms and predicthow laser parameters can improve the treatment re-sponse for the professional black tattoo.

REFERENCES

1. Laumann AE, Derick AJ. Tattoos and body piercing in theUnited States: A national data set. J Am Acad Dermatol2006;55:413–421.

2. Green JB, Metelitsa AI. Optimising outcomes of laser tattooremoval. Skin Ther Lett 2011;16(10):1–3.

3. Jow T, Brown A, Goldberg DJ. Patient compliance as a majordeterminant of laser tattoo removal success rates: A 10-yearretrospective study. J Cosmet Laser Ther 2010;12(4):166–169.

4. Taylor CR, Anderson RR, Gange RW, Michaud NA, FlotteTJ. Light and electron microscopic analysis of tattoos treatedby Q-switched ruby laser. J Invest Dermatol 1991;97:131–136.

5. Swartz MA. The physiology of the lymphatic system. AdvDrug Deliv Rev 2001;50(1–2):3–20.

6. Pfirrmann G, Karsai S, Roos S, Hammes S, Raulin C. Tattooremoval—State of the art. JDDG 2007;5(10):889–898.

7. Cumnock K, Gerson L, Stroncek J, Yagerman S. Think be-fore you ink: Modeling laser tattoo removal [pdf]. CornellUniversity. 2008; Available at: http://hdl.handle.net/1813/11134 [Accessed: 8 September 2011].

8. Mohammed Y, Verhey JF. A finite element method model tosimulate laser interstitial thermo therapy in anatomicalinhomogeneous regions. BioMed Eng (Online) 2005;4(2),Available at: http://www.biomedical-engineering-online.com/content/4/1/2 [Accessed: 14 September 2011].

9. Welch AJ. The thermal response of laser irradiated tissue. JQuantum Electron 1984;20:1471–1481.

10. Ho DDM, London R, Zimmerman GB, Young DA. Laser-tattoo removal—A study of the mechanism and the opticaltreatment strategy via computer simulations. Lasers SurgMed 2002;30:389–397.

11. Anderson RR, Parrish JA. Selective photothermolysis: Pre-cise microsurgery by selective absorption of pulsed radiation.Science 1983;220(4596):524–527.

12. Welch AJ, van Gemert MJC. Optical–thermal response oflaser-irradiated tissue, 1st edition. New York: Plenum Press;1995.

13. Humphries A, Lister TS, Wright PA, Hughes MP. Determi-nation of the thermal and physical properties of black tattooink using compound analysis. Lasers Med Sci 2012; DOI:10.1007/s10103-012-1198-9.

14. Sandby-Møller J, Poulsen T, Wulf HC. Epidermal thicknessat different body sites: Relationship to age, gender, pigmen-tation, blood content, skin type and smoking habits. ActaDerm Venereol 2003;83:410–413.

114 HUMPHRIES ET AL.

15. Hu XH, Wooden WA, Vore SJ, Cariveau MJ, Fang Q,Kalmus GW. In Vivo study of intradermal focusing for tattooremoval. Lasers Med Sci 2002;17:154–164.

16. Franco W, Childers M, Nelson JS, Aguilar G. Laser surgeryof port wine stains using local vaccum pressure: Changes incalculated energy deposition (Part II). Lasers Surg Med2007;39:118–127.

17. Jacques SL. Origins of tissue optical properties in the UVA,visible and NIR regions. OSA TOPS: Adv Opt ImagingPhoton Migration 1996;2:364–369.

18. Jacques SL, McAuliffe DJ. The melanosome: Threshold tem-perature for explosive vaporization and internal absorptioncoefficient during pulsed laser irradiation. Photochem Photo-biol 1991;53(6):769–775.

19. Bashkatov AN, Genina EA, Tuchin VV, Altshuler GB. Skinoptical clearing for improvement of laser tattoo removal.Laser Phys 2009;19(6):1312–1322.

20. Datta AK, Rakesh V. Introduction to modeling of transportprocesses—Applications to biomedical systems. New York:Cambridge University Press; 2010. pp. 421–428.

21. Lefevre J. Studies of the thermal conductivity of skin in-vivoand the variations induced by changes in the surroundingtemperature. Journal de Physique Theorique et Appliquee1901;10(1):380–388.

22. Lipkin M, Hardy JD. Measurement of some thermalproperties of human tissues. J Appl Physiol 1954;7:212–217.

23. Venugopalan V, Guerra III A, Nahen K, Vogel A. Role of la-ser-induced plasma formation in pulsed cellular microsur-gery and micromanipulation. Phys Rev Lett 2002;88(7):078103.

24. Viator JA, Choi B, Ambrose M, Spanier J, Nelson JS. In vivoport-wine stain depth determination with a photoacousticprobe. Appl Opt 2003;42(16):3215–3224.

25. Waterman NA, Ashby MF. CRC—Elsevier material selector,Vol. 2. Boca Raton: CRC Press; 1991. p. 1446.

26. Dussik KT, Fritch DJ, Kyriazidou MMD, Sear RS. Measure-ments of articular tissues with ultrasound. Am J Phys Med1958;37(3):160–165.

27. Cho J, Luo JJ, Daniel IM. Mechanical characterization ofgraphite/epoxy nanocomposites by multi-scale analysis.Compos Sci Tech 2007;67:2399–2407.

28. Wright PA, Widdowson DC, Ahmed S, Shakespeare PG. Howwell does your ruby laser work? Lasers Med Sci 2005;20:104–106.

29. Verdaasdonk RM, Borst C, Gemert MJC. Explosive onset ofcontinuous wave laser tissue ablation. Phys Med Biol 1990;35(8):1129–1144.

MODELLING RESPONSE TO LASER TATTOO REMOVAL 115