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International Journal of Thermal Sciences 86 (2014) 175e188

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International Journal of Thermal Sciences

journal homepage: www.elsevier .com/locate/ i j ts

Analysis of skin cooling for quantitative dynamic infrared imagingof near-surface lesions

Tze-Yuan Cheng, Cila Herman*

Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA

a r t i c l e i n f o

Article history:Received 21 October 2013Received in revised form26 June 2014Accepted 26 June 2014Available online

Keywords:Dynamic infrared imagingSkin lesionsMelanomaMedical diagnosticsSkin coolingComputational modelingOptimization

* Corresponding author.E-mail addresses: cherman@jhu.edu, cherman.jhu

http://dx.doi.org/10.1016/j.ijthermalsci.2014.06.0331290-0729/© 2014 Elsevier Masson SAS. All rights res

a b s t r a c t

Dynamic infrared (IR) imaging is a clinical diagnostic method that relies on external cooling to enhancethe thermal contrasts between a lesion and healthy skin during the thermal recovery process after theremoval of the cooling. The subject of this paper is the proper selection of the cooling method, coolingtemperature, time and depth to maximize thermal contrasts while minimizing discomfort to the patient.The systematic computational analysis of the influence of these parameters on the measured signal isreported. Three cooling methods are considered: constant temperature, water-soaked cotton, andconvective cooling. The analysis suggests that 20 �C is a suitable cooling temperature that allows thecooling effect to reach the lesion depth within 2 min. The induced thermal contrast is in the range of0.1�0.3 �C during the thermal recovery. The thermal contrasts enhanced by cooling can be accuratelymeasured by a properly designed IR imaging system. Cooling durations from 5 to 120 s were considered.Two types of thermal responses were identified. Shorter cooling leads to a maximum of thermal contrastwithin the first few seconds of thermal recovery. Longer cooling durations result in a maximum that islower, broader and it appears later in time (20e40 s after the removal of cooling). The computationalmodel was validated using data from in vivo dynamic IR imaging measurements. The analysis in thisstudy provides a quantitative basis for the selection and optimization of cooling conditions in clinicalpractice.

© 2014 Elsevier Masson SAS. All rights reserved.

1. Introduction

Melanoma incidence is increasing at one of the fastest rates forall cancers in the United States, with a current lifetime risk of 1 in55 [1]. According to clinical reports, 1-year survival rates for pa-tients with advanced melanoma range from 40% to 60% [2]. Ifmelanoma is detected at an early stage, i.e. before the tumor haspenetrated the epidermis, the 5-year survival rate is about 99%.However, for patients with advanced disease, the 5-year survivalrate drops dramatically, to 15% [3]. Therefore early detection iscritical to extend the lifespan of patients with more advanceddisease. In order to enable early detection and diagnosis and avoidunnecessary biopsies, it is essential to develop accurate, sensitiveand objective quantitative diagnostic instruments.

The dramatic advances in IR imaging hardware, computers andimage analysis techniques opened new avenues for quantitative IRimaging in a variety of medical and engineering applications. Over

@gmail.com (C. Herman).

erved.

the past decade quantitative IR imaging has become a powerful andaccurate tool in a variety of settings and has overcome many of thechallenges of the past (most past IR imaging and diagnostic appli-cations were qualitative). Active IR imaging involves introducingexternal forcing (also called thermostimulation), heating or cooling,to induce or enhance relevant thermal contrasts between theinvestigated lesion and healthy tissue. The general advantage ofdynamic (active) measurement methods is that they do not requirethe subject to reach a well-defined steady state, which can be verytime consuming and challenging. For example, in the past, whenstatic applications prevailed, the patient was required to spend oneor more hours in a thermally conditioned exam room in order tofully acclimate (reach a steady state) to the environment prior tothe measurement [4]. Reaching a true steady state may not alwaysbe possible and there will still exist individual variations betweentest subjects.

In the dynamic method the thermal response to an excitation,often applied as a step change in the thermal boundary conditions(heating or cooling), is measured. This is a much faster and morerobust approach than the steady method. The dynamic method iswell-established in numerous engineering applications, such as

Nomenclature

C specific heat (J/kg K)Cn specific heat of skin layer n (J/kg K)Cb specific heat of blood (J/kg K)Cw specific heat of water (J/kg K)D(t) cooling penetration depth (mm)d thickness (mm)dn thickness of skin layer n (mm)h convection heat transfer coefficient (W/m2 K)k thermal conductivity(W/m K)kn thermal conductivity of skin layer n (W/m K)kw thermal conductivity of water (W/m K)Q metabolic heat generation (W/m3)Qn metabolic heat generation of skin layer n (W/m3)q0 0

heat flux(W/m2)T temperature (�C)Tn local tissue temperature of skin layer n (�C)Tb temperature of blood (�C)T∞ ambient temperature used for the calculation of

convection (�C)Tc,b core body temperature (�C)Tw temperature of water (�C)Tss temperature profile in skin tissue along y-direction in

steady state (�C)Tcp temperature profile in skin tissue along y-direction in

cooling phase (�C)Tc cooling temperature(�C)Tsur temperature of skin surface used for the calculation of

radiation (�C)Tamb ambient temperature used for the calculation of

radiation (�C)DT thermal contrast between lesion and healthy skin (�C)

DTmax the maximum thermal contrast in thermal recoveryphase (�C)

t time (s)tc cooling time (s)tmax the timing of maximum thermal contrast in thermal

recovery phase (s)x coordinate axis in Cartesian coordinate system (mm)y coordinate axis in Cartesian coordinate system (mm)

Greek lettersε emissivity of skin surfacer density(kg/m3)rb density of blood (kg/m3)rn tissue density of skin layer n (kg/m3)rw density of water (kg/m3)s Stefan-Bolzmann constant, s ¼ 5.670373 � 10�8 (W/

m2 K4)wb blood perfusion rate (1/s)wb,n blood perfusion rate in skin layer n (1/s)

Subscriptsamb ambient condition for radiationb bloodc coolingc,b core bodycp cooling phasemax maximumn skin layer nss steady statesur skin surfacew water∞ ambient condition for convection

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188176

thermophysical property measurements. It also offers advantagesin clinical applications, for which the duration of the measurement,patient comfort and the ease of use are critical. It has beendemonstrated that thermostimulation by cooling can improve thethermal contrast (defined as the temperature difference betweenthe lesion and healthy skin) between healthy and cancerous tissuein the thermography of breast [5]. When the skin surface is imagedduring cooling and thermal recovery following the removal of thecooling stress, the variation in the thermophysical properties of thelesion (when compared to healthy tissue) underneath the surfaceresults in identifiable temperature contours during these tran-sients. These surface temperature contours will differ from thosepresent in steady state observed during passive IR imaging.Therefore themeasurement process consists of three phases: (i) theinitial phase when the skin is exposed to nominal ambient condi-tions, (ii) the cooling phase which is followed by (iii) the thermalrecovery phase. The dynamic thermal response of the structureacquired using active IR imaging provides critical informationwhich allows identifying the malignant lesion, as shown by PirtiniCetingul and Herman [6,7]. Since IR imaging (with proper calibra-tion) yields quantitative data, the method holds the potential ofallowing the staging of the disease.

To optimize diagnostic measurements for medical applications,computational modeling of the tissue response for different cooling(or heating) scenarios is used. It allows better understanding of theinfluence of different system parameters and predicting the re-sponses to various thermal stimuli. The computational model ac-counts for the variations of thermophysical properties, layerthicknesses, metabolic heat generation, and blood perfusion for the

different tissue layers. Several types of computational models ofhuman tissue, based on the Pennes bioheat equation [8], have beenproposed in the literature [9e16]. A tissue layer is generally treatedas a homogenous continuum with vascular network [9]. Thesemodels rely on a variety of assumptions to account for the effects ofblood flow [10e15]. By modeling the tissue as porous matrix,Mahjoob and Vafai [17,18] examined heat transport in biologicalmedia for biomedical applications, such as hyperthermia. In theirmodel, prescribed heat flux is imposed on the cancerous tissue. Inthese studies, several important parameters influencing heattransport through the biological tissue were investigated, includingvolume fraction of vascular network space, depth of organ/tissue,imposed heat flux, metabolic heat generation, and core body tem-perature. For designing thermal management devices and small-scale biomedical applications which utilize porous channels, Mah-joob and Vafai [19,20] analytically investigated the effects ofgeometrical configuration of channels on the heat transfer behavior.

In order to improve the effectiveness and sensitivity of activequantitative IR imaging for diagnostic purposes, in particular for theearly diagnosis of melanoma, a thorough understanding and opti-mization of the cooling process and the subsequent thermal recoveryphase is essential. The challenge is to apply sufficient cooling tomaximize thermal contrast between lesion and healthy tissue thatcanbe accurately quantifiedwith current IR imaginghardware. At thesame time the overcooling of the tissue, which would lead toextended thermal recovery periods, delayed appearance of thermalcontrasts and long measurement times unacceptable in a clinicalsetting, has to be avoided. With competing effects and requirementsthat depend on a wide range of system parameters (thermal and

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188 177

metabolic inputs, geometrical considerations, thermophysical prop-erties) this problem can mathematically be cast as an optimizationproblem in a multidimensional parameter space. In past studies thecooling method, temperature and duration were selected ad hoc,usually by trial and error. The goal of the paper is to systematicallyexamine this parameter space for a range of conditions and developpractical recommendations regarding cooling procedures for clinicalapplications using a computational approach with experimentalvalidation.

In this study a computational model of skin tissue with a near-surface lesion is introduced first, and with the aid of this modelvarious cooling methods and conditions suitable for clinical appli-cation are considered, compared and critically evaluated. Our goalis to find optimal cooling methods and parameters which are easyto apply in a clinical setting and provide strong thermal contrastswhile minimizing patient discomfort and measurement duration.

Since the primary aim of the study is the detection of earlystages of melanoma (before the cancer enters the capillary bed,which is nominally 6mmbelow the surface), the cooling conditionsdiscussed in this paper focus on near-surface lesions. In this studynear-surface lesions are defined as lesions characterized by lessthan 4 mm invasion. As illustrated in Fig. 1(a), (b) and (c), skincancer lesions, port wine stains and some burn lesions would fallinto this category. Deep lesions, such as breast cancer (Fig. 1(d)) ordeep tissue injuries, such as pressure ulcers (Fig. 1(e)), wouldrequire a separate analysis to understand and optimize the coolingconditions. Even though the physical situation considered in thepaper is biomedical, the general considerations and conclusionsdrawn are of interest to other engineering systems described bysimilar sets of equations (for example detection of failure in com-posite materials) and similar geometries.

2. Background

Various skin cooling approaches have become an active researcharea of clinical interest since the introduction of thermally

Fig. 1. (a) Schematic of near-surface skin lesions of various invasion levels: (b) photo of a msurface. Schematics of deep lesions: (d) breast cancer and (e) pressure ulcer.

mediated therapeutic procedures. Cooling burn injuries withpoured or sprayed on water at around 20 �C can improve the initialtreatment of extensive burns [21]. Conductive, convective, andevaporative methods have been used by clinicians to cool down thebody to treat fever or hyperthermia [22]. Wyndham et al. [23]compared the cooling rates of different cooling methods, such asthe spraying of water, the blowing of air or immersion in water, forthe management of hyperpyrexia. In the past, contact skin coolingusing ice or chilled gels was used for local anesthesia in dermato-logic surgery [24] and spray coolants are currently being used forlocal anesthesia and cryosurgery [25]. Chilled water or gas flow forskin cooling are applied in surgical and therapeutic procedures[26e30]. Since the applications and goals of cooling vary broadly,the mathematical models that capture the effects relevant for aparticular application will vary as well.

Di Carlo et al. [31] designed a thermostimulation method forthe detection of melanoma using active IR imaging. Buzug et al.[32] used cold gel packs as the cooling medium to induce thetemperature difference on the skin surface in the imaging of basalcell carcinoma. Santa Cruz et al. [33] cooled the leg of the patientby immersion into a pool of cold water for thermographic imagingto detect the recurrence of melanoma after surgery. PirtiniCetingul and Herman [6,7,34] cooled the area of the skin con-taining the lesion and surrounding tissue with a gel pack or byblowing air from a vortex tube in a patient study conducted by theHeat Transfer Lab of the Johns Hopkins University. This applicationis the immediate motivation for the study reported in the presentpaper.

3. Theory and method

3.1. Physical situation and mathematical model

Melanoma lesions and many of the lesions of interest in clinicaldiagnostics are of irregular shape, therefore a representativeidealized elliptical cross section of the lesion is considered in this

elanoma lesion flush with the skin surface and (c) lesion with elevation above the skin

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188178

study without loss of generality [15]. For a more accurate thermalmodel of a particular lesion, the three dimensional geometry in-formation has to be included into the computational model. In ourstudy, human tissue is modeled as a 2D semi-infinite domainrepresentative of the cross section of the tissue and lesion in theCartesian coordinate system. Five main layers are considered in themodel, the epidermis, papillary dermis, reticular dermis, fat andmuscle (viewed from the surface). As shown in Fig. 2, each layer n ismodeled as a homogeneous medium of finite thickness dn in the ydirection and characterized by its unique thermophysical proper-ties, summarized in Table 1 [15]. The lesion is modeled as anelliptical domain with major axis W and minor axis P, as illustratedin Fig. 2(a) and (b).

Heat transfer processes in the human skin and underlying tissuecan be modeled using the bioheat equation proposed by Pennes(1948) [8], which is the transient heat conduction equation of theform

Fig. 2. (a) Schematic of the tissue layers and the lesion in the computational domain withbutions for the steady state situation and (c) the computational mesh.

rnCnvTnvt

¼ knV2Tn þ rbCbwb;nðTb � TnÞ þ Qn; (1)

where n ¼ 1,2, … 5 denote the tissue layers considered in themodel, epidermis, papillary dermis, reticular dermis, muscle andfat, respectively. rn,Cn,kn,Tn,Qn represent the parameters thatdescribe layer n and denote the tissue density, specific heat of thetissue, thermal conductivity, local tissue temperature and themetabolic heat generation rate, respectively. rb, Cb, wb, Tb denotethe properties of blood: density, specific heat, blood perfusion rateand temperature, respectively. Eq. (1) is solved by imposingappropriate boundary conditions at the skin surface, continuityconditions for the temperature and heat flux at each interface be-tween skin layers, the core body temperature condition at thebottom of the muscle layer and zero heat flux at the lateralboundaries.

For t < 0 we assume that steady state ambient conditions existwithin the tissue. In steady state, the top skin surface at y ¼ 0 is

boundary conditions for the steady state situation, (b) computed temperature distri-

Table 1The properties of tissue layers (based on [15]).

d (mm) C (J/kg K) k (W/m K) r (kg/m3) wb(1/s) Q (W/m3)

Epidermis 0.1 3589 0.235 1200 0 0Papillary

dermis1 3300 0.445 1200 0.00018 368.1

Reticulardermis

1 3300 0.445 1200 0.00126 368.1

Fat 2 2674 0.185 1000 0.00008 368.3Muscle 8 3800 0.51 1085 0.0027 684.2Lesion W ¼ P ¼ 1 3852 0.558 1030 0.0063 3680

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188 179

exposed to ambient natural convective boundary conditions spec-ified as

q00 ¼ hðTðy ¼ 0; t <0Þ � T∞Þ: (2)

The convection heat transfer coefficient h in Eq. (2) is assumedto be h¼ 10W/m2 K (a typical value for natural convection) and theambient temperature T∞ ¼ 21 �C. The same natural convectiveboundary condition is also prescribed at the skin surface during thethermal recovery phase following the removal of the cooling stress.In our simulation, the surface-to-ambient radiation associated withskin emissivity is neglected due to its limited effect. A detaileddiscussion of the influence of radiation is presented in Section 4.4.

The temperature continuity and conservation of heat flux con-ditions at the interface between skin layers can be written as

Tnðy ¼ yn; tÞ ¼ Tnþ1ðy ¼ yn; tÞ;

knvTnvy

����y¼ yn

¼ knþ1vTnþ1

vy

����y¼ yn

; n ¼ 1;…;4:(3)

In Eq. (3) yn denotes the y location of the bottom boundary of thenth tissue layer of thickness dn, yn ¼ yn�1 þ dn. The sixth domain inthis model is the lesion, and the temperature distribution withinthe lesion is also described by the Pennes bioheat equation [8], Eq.(1). Similar interfacial conditions hold at the interface of the lesionand the healthy tissue as those between the skin layers, describedby Eq. (3). The bottomboundary of themuscle layer can be assumedto be at core body temperature Tc,b at all times, which is also theboundary condition commonly prescribed in porous media models[17,18] for heat transfer through biological media. The core bodytemperature in this study is

Tðx; y5; tÞ ¼ Tc;b ¼ 37+C: (4)

In this study we consider small lesions (which are of particularinterest for the early diagnosis of melanoma, for example) and alarger area of healthy tissue surrounding the lesion. We assumezero heat flux from both sides of the computational domain, atx ¼ 0 and x ¼ w, at a sufficient distance from the heat-generatinglesion. This suggests that the temperature at the lateral boundary(as well as the bottom boundary) is unaffected by the presence ofthe lesion in steady state conditions and during thermal recovery.Therefore the lateral boundary condition takes the form

vTnvx

����x¼0;w

¼ 0: (5)

Based on data from the literature [15,35e38], the dimensionsused in our computations and thermophysical properties of eachskin layer are listed in Table 1. In this paper typical nominal valuesintroduced by Ref. [15] were selected for the calculations. Whileindividual and local variations in these properties can exist, a

previous sensitivity analysis carried out by Pirtini Cetingul andHerman (2010) [15] concluded that the impact of these variationson the surface temperature is small. Therefore the general trends ofthe thermal responses relevant for this study remain, with propertyvariations resulting in small variations in absolute values. In gen-eral, the lesion is three dimensional, however the shape has a smallimpact on the surface temperature response. The dominant effectwill be that of the overall volume of the lesion, as shown in Ref. [15].For a more accurate analysis of a particular situation actualmeasured data should be used. Since the lesions of importance forclinical practice are relatively small and confined to the top tissuelayers (near-surface lesions), the impact of small variations of di-mensions and the properties of the deeper tissue layers on thethermal response is relatively small too. We also assume that,because of the relatively short cooling times and small temperaturedifferences used in thermostimulation, the thermophysical prop-erties remain constant during the 1e2 min interval needed for theimaging process.

In addition to the values summarized in Table 1, the propertiesof blood are prescribed as follows: density of blood rb¼ 1060 kg/m3

[39], specific heat specific heat Cb ¼ 3770 J/kg K [38], and bloodtemperature Tb ¼ 37 �C [38]. Regarding the variation range of thethermophysical properties discussed in the literature [35e38],prior studies [15] show that the surface temperatures are mostsensitive to the variations in the blood perfusion rate and skin layerthicknesses. The studies of Song et al. (1984)[40] suggest that acancerous lesion is characterized by increased metabolic activityand blood flow, and a highly vascularized skin tumor may causeincrease of local skin temperature [41]. Thus, in the tissue modelintroduced in this paper, the domain of the lesion is represented asa region of increased metabolic heat generation and blood perfu-sion. As shown in Table 1, based on prior studies [40,42,43], bloodperfusion is considered to be five times larger and the metabolicheat generation is ten times larger in the region of the lesion than innormal surrounding tissue. Since these values were not measuredspecifically for melanoma lesions, in our analysis we consider theselow values as the worst case scenario for IR imaging as well ashigher values which yield good agreement with our experimentalmeasurements.

We used the commercial software COMSOLMultiphysics v.4.0 tofind the numerical solution for our model described by Eqs. (1)e(5)with the dimensions and property values indicated in Table 1. Theheat transfer module of COMSOL 4.0 is used to solve for the steady-state spatial temperature distribution first (Fig. 2(b)), and this so-lution serves as the initial condition for the investigation of thetime-dependent effects of various cooling methods. The softwareuses the finite element method to solve the bioheat transferequation for the five coupled tissue layers and the lesion. Thecomputational domain is 12 mm wide and 12.1 mm deep, with itsdimensions selected to satisfy the conditions described by Eq. (5).Free triangular elements are used in the mesh as shown in Fig. 2(c).Since the temperature of skin surface is of particular interest for IRimaging, we set the maximum element size to be 0.15 mm (finestmesh) in the top layer (epidermis), and to 0.53 mm in other layers.To verify the convergence of the solution with respect to the meshsize, the maximum element size was further refined to 0.02 mm forthe epidermis and to 0.15 mm for other layers. It was found thatthere was less than 1% difference in the solutions before and afterrefining the mesh size.

To validate the numerical model with respect to the existinganalytical model for biological media [18], we divided our tissuemodel into two main layers, lesion and muscle, with thicknesses of4.1 mm and 8 mm, respectively. Based on the thermophysicalproperties of lesion and muscle and the boundary conditionsdescribed in Section 3.1, the steady-state temperature in the skin

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188180

layers was computed and compared with results reported inRef. [18]. For the analytical model [18] we adopted the simplifiedsolution for uniform core temperature of 37 �C and steady-statenatural convection described by Eq. (2) was imposed as the uni-form heat flux at the body surface. According to the analysis pre-sented in Ref. [18], the parameters of the biological tissue matrix K,xb, and xt, were taken to be 0.111, 0.111, and 1, respectively, in thevalidation procedure. The temperature distribution through thetwo layers, predicted by our numerical model, was then comparedwith the analytical solution developed in Ref. [18]. A good agree-ment between the numerical and analytical predictions wasobserved, with the largest temperature differences being less than0.071 �C. The agreement between data obtained using the twomodeling approaches therefore validates our computational model.

3.2. Thermal boundary conditions for the selected cooling methods

A diversity of methods has been applied to achieve skin coolingin clinical applications. The clinical diagnostic application consid-ered in this study requires cooling methods that are easy andinexpensive to apply, easily reproducible and cause little discom-fort to the patient. We selected three cooling methods for ouranalysis, (i) constant temperature cooling (accomplished byapplying melting ice in a pouch that can also be approximated witha gel pack), to be referred to as Case C1, (ii) cooling with a cottonpatch soaked in cold water, Case C2, and (iii) convective cooling byblowing cold air onto the skin or immersion into a liquid, Case C3.During the cooling phase, the thermal boundary condition at skinsurface depends on the cooling method applied. The coolingmethod and temperature will also affect the required or optimalduration of cooling and the thermal contrast between the lesionand healthy tissue.

3.2.1. Constant temperature cooling, Case C1Constant temperature cooling is an idealized case of contact

cooling, for which the temperature of cooling medium applied tothe skin surface remains constant during the entire cooling phase.In practice this condition is challenging to achieve, and can beapproximated by a phase change (melting) process, a very high(infinite) heat capacity cooling patch, or a process with very high(infinite) heat transfer coefficient. This type of cooling is modeledby prescribing a constant cooling temperature Tc at the skin surfaceat y ¼ 0 for the duration of cooling tc as

Tðx; y ¼ 0; tÞ ¼ Tc; 0 � t � tc: (6)

3.2.2. Cooling with a cotton patch soaked in water, Case C2The second cooling method considered in this study involves

applying awater-soaked cottonpatch on the skin surface, which is acommonly used clinical procedure. Since the patch will mainlyconsist of water, we can model the patch as a 2 mm thick waterlayer in direct and ideal contact with the skin surface. In thecomputational model this layer of water will be represented by asixth parallel layer (domain 7) above the tissue layers in Fig. 2, andthe heat transfer in this domain is modeled by the transient heatdiffusion equation of the form

rwCwvTwvt

¼ kwV2Tw; 0 � t � tc; (7)

where the water properties are kw ¼ 0.6 W/m K, rw ¼ 998 kg/m3,Cw ¼ 4186 J/kg K. During the cooling phase, heat flux conservationand temperature continuity are prescribed between the water layerand the skin surface at y ¼ 0 as

Twðy ¼ 0; tÞ ¼ T1ðy ¼ 0; tÞ;

kwvTwvy

����y¼0

¼ k1vT1vy

����y¼0

:(8)

The cooling temperature for Case C2 is defined as the initialtemperature of this water layer at t ¼ 0. In addition, to account forthe heat loss q00 between the soaked cotton and the environment atthe surface of the cotton exposed to ambient air, the convectivethermal boundary condition (with a convective heat transfer co-efficient of h¼ 10W/m K, and T∞¼ 21 �C) is prescribed at the top ofwater layer as

q00 ¼ hðTðy ¼ �2mm;0 � t � tcÞ � T∞Þ: (9)

3.2.3. Convective cooling, Case C3The third cooling method considered in this study is convective

cooling, accomplished by directing a jet of cold air onto the skinsurface or immersion of the area into a stagnant or circulatingliquid. To achieve higher values of the heat transfer coefficient h, aircan be replaced by water as the coolant (cooling by immersion intowater). Mathematically the heat flux q00 due to air convection aty¼ 0 with a heat transfer coefficient h and ambient temperature T∞at the skin surface is prescribed as

q00 ¼ hðTðy ¼ 0;0 � t � tcÞ � T∞Þ: (10)

To analyze the impact of air cooling, the convection heat transfercoefficient h is varied in the range of 50e1000W/m2 K in this study.The ambient temperature T∞ was varied in the range of 4 �Ce20 �C.For Case C3, the ambient air temperature is defined as the coolingtemperature.

3.3. Cooling penetration depth

In order to quantify the extent of tissue cooling during thecooling phase, the concept of the cooling penetration depth D(t) isintroduced, defined as

DðtÞ ¼ y for whichTcpðy; tÞ

Tssðy; t <0Þ ¼ 0:99; (11)

where Tss(y) is the temperature distribution along a vertical lineacross the tissue in steady state (at the central location of the lesion,x¼ 6mm), and Tcp(y,t) the temperature distribution along the sameline at time t during the cooling phase. The duration of cooling tc isvaried in this study to optimize the cooling conditions. The conceptof the cooling penetration depth is illustrated in Fig. 3, bycomparing the steady state temperature profile Tss with two pro-files Tcp(t1) and Tcp(t2), computed at times t1 and t2, t1 < t2 < tc,during the cooling phase, 0 < t < tc. As shown Fig. 3, the longer thecooling is applied, the deeper the tissue will be cooled down,therefore the cooling penetration depth D(t) increases with theduration of the cooling. The location with tissue temperature cor-responding to 99% of the steady state temperature, is defined as thecooling penetration depth D(t). These locations are displayed as fullcircles in Fig. 3 for the temperature profiles D(t1) and D(t2) at timest1 and t2, and they match the points where the steady state profilemerges with the cooling phase profile. We can interpret D(t) as theboundary of tissue region being cooled down, or the depth belowwhich the tissue is still at steady state temperature (unaffected bythe cooling). The cooling penetration depth is a parameter that ishelpful when quantitatively comparing the impact of the coolingmethods investigated in this study.

Fig. 3. Concept of the cooling penetration depth D(t): comparison of the steady statetemperature profile Tss and the temperature profiles at times t1 and t2, Tcp(t1) andTcp(t2).

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188 181

3.4. Thermal contrast during the thermal recovery phase

The goal of the cooling phase in the clinical diagnostic appli-cation that motivated this study is to cool down the skin surfacesufficiently to enhance the temperature differences betweenhealthy and diseased tissue quickly and without causing discomfortto the patient. Therefore, to evaluate the performance of variouscooling methods, the temperature difference between lesion andsurrounding tissue during the recovery phase is analyzed. Thistemperature difference is directly related to the thermal contrastvisualized andmeasured in the thermographic images. As shown inFig. 4, the temperature difference DT(t) at the skin surface, betweena point on the surface above the lesion Tlesion(t) and the healthytissue 4 mm away from the lesion center Tsur(t), is computed in thisstudy during the thermal recovery phase.

4. Results

In this sectionwe discuss the results for cooling cases C1, C2 andC3, by comparing the thermal penetration depth during the coolingphase for three cooling temperatures Tc ¼ 4 �C, 12 �C and 20 �C, andthe thermal contrast as a function of time during thermal recovery.Results are presented in the form of diagrams as well as numericaldata organized into tables. For the convective cooling, fourconvective heat transfer coefficients h, representative of forced andnatural convection using air or liquid, are considered.

Fig. 4. Thermal contrast △T(t) as the difference between the surface temperatureabove the lesion center Tlesion(t) and the surrounding tissue Tsur(t) during the thermalrecovery phase.

4.1. Cooling penetration depth: cooling phase

Fig. 5 shows the cooling penetration depth D(t) during thecooling phase for constant temperature cooling, Case C1, for a timeinterval of 30 s. Only the first 30 s of the cooling phase are displayedin the diagrams in this section, since this time interval is sufficientlylong for the diagnostic applications considered in our study. Theresults indicate that by 30 s the cooling effect has reached the entiredomain (depth) of the lesion. The five tissue layers considered arehighlighted in different colors in Fig. 5 and the subsequent dia-grams. Three representative cooling temperatures relevant forclinical applications, 4 �C, 12 �C, and 20 �C were considered, andtherefore three corresponding curves are plotted in Fig. 5. It can beobserved that, within approximately 20 s from the onset of cooling,the cooling effect penetrates to the depth of 4 mm below skinsurface (depth of the fat layer) for all three cooling temperatures.During the first 5 s of the cooling phase, the cooling penetrationrate and depth are very similar for the three temperatures. Theimpact of the cooling temperature becomes more apparent fortimes 5 s and longer after the onset of cooling. At the same timeinstant, the cooling rate and the cooling penetration depth increasewith decreasing cooling temperature.

The cooling penetration depth curves when applying soakedcotton cooling, Case C2, are displayed in Fig. 6 for the three coolingtemperatures (initial water temperatures). After applying thesoaked cotton to the skin surface, the temperature of the cottonpatch will increase, since it is being warmed up by the skin and theambient (the heat capacity of the patch is finite, contrasted to theinfinite heat capacity of Case C1). Therefore, the rate of coolingpenetration for C2 is less than for C1. For cooling temperatures of4 �C, 12 �C, and 20 �C, it takes around 19 s, 22 s, and 27 s, respec-tively, for the cooling effect to penetrate through the depth of thefat layer (4 mm).

Cooling penetration depth results for convective cooling (air orwater cooling), Case C3, for a range of convection heat transfercoefficients h are shown in Fig. 7. For the heat transfer coefficienth ¼ 50W/m2 K, which is a typical value for forced convection in air,we observe that it takes over 30 s for the cooling effect to reach thedepth of 4 mm for all three cooling temperatures used. As h in-creases to h ¼ 100 W/m2 K (Fig. 7(b)), a value corresponding tohigher air speeds, D(t) approaches the depth of 4 mm within 30 sfor the cooling temperatures Tc ¼ 4 �C and 12 �C. For Tc ¼ 20 �C ittakes longer than 30 s for the cooling effect to reach the depth of4 mm. These results suggest that air cooling will be most suitablefor skin lesions with the depth less than 2mm, if the cooling time isto be kept under 30 s. Since early detection of skin cancer is ofparticular diagnostic interest, this is often going to be the case inclinical applications, whereas advanced cases are easier to diagnoseusing conventional methods. For deeper lesions, cooling times

Fig. 5. Cooling penetration depth D(t) as a function of time for Case C1 for constanttemperature cooling: cooling temperatures Tc ¼ 4 �C, 12 �C and 20 �C.

Fig. 6. Cooling penetration depth D(t) as a function of time for Case C2 for soakedcotton cooling: cooling temperatures Tc ¼ 4 �C, 12 �C and 20 �C.

Fig. 8. Thermal contrast △T(t) as a function of time with cooling time tc as parameter(values of tc are in the range of 5e120 s) for constant temperature cooling (Case C1)with Tc ¼ 20 �C .

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longer than 30 s and lower air temperatures (Tc ¼ 4 �C) may benecessary.

However, as h increases to 500 W/m2 K and 1000 W/m2 K(Fig. 7(c) and (d), Case C3), which are the values characteristic ofliquid (water) cooling, the thermal penetration depths reach themagnitudes similar to the cases with constant temperature cooling(Case C1) and soaked cotton cooling (Case C2). The results inFig. 7(c) and (d) show that for these higher values of h the coolingeffect can penetrate through the depth of fat layer within 30 s.These heat transfer coefficients and cooling temperatures can beachieved by immersing the skin into a pool of stagnant or flowingwater. This cooling method is easy to apply in a clinical setting,when the lesion is located on a limb, for example.

4.2. Thermal contrasts during thermal recovery

In this section we discuss the results for the thermal contrastDT(t) during thermal recovery for the three cooling methodsconsidered in this study, with the cooling temperature beingTc ¼ 20 �C for all three cases.

4.2.1. Thermal contrasts, Case C1The thermal contrast between the lesion and healthy tissue at

the skin surface DT(t), present following the removal of constant

Fig. 7. Cooling penetration depth D(t) as a function of time for Case C3 for convection coolinm2 K, (c) 500 W/m2 K and (d) 1000 W/m2 K and cooling temperatures Tc ¼ 4 �C, 12 �C, an

temperature cooling (Case C1), is plotted in Fig. 8 as a function ofrecovery time t. The duration of cooling tc is the parameter for thefamily of curves shown in Fig. 8, with the values ranging from 5 s to120 s. Two distinctly different responses (behavior types) can beobserved during thermal recovery: one for short cooling times(0e20 s), and another for longer cooling times (>20 s). For shortcooling times, the temperature difference is the largest immedi-ately after the removal of the cooling, and it rapidly decreases withthe recovery time (type one maximum). Therefore the strongestsignal will be available between 0 s and 5 s into the thermal re-covery. For longer cooling times, the thermal contrast initially in-creases after the removal of cooling, and the maximum contrastbetween the lesion and healthy tissue appears at around 40 s intothermal recovery (type two maximum). This region of maximumcontrast is relatively broad compared to the narrow peak devel-oping after the application of short cooling times. After thismaximum, the temperature difference DT(t) gradually and mono-tonically decreases with time.

These results are essential for the design of the measurementsystem for clinical diagnostic applications. They indicate that,depending on the cooling time, the maximum signal can be

g (air or liquid) with convection heat transfer coefficients h¼ (a) 50 W/m2 K, (b) 100 W/d 20 �C.

Fig. 9. Thermal contrast △T(t) as a function of time with cooling time tc as parameter(tc in the range of 5e120 s) for soaked cotton cooling (Case C2) with water temperatureof Tc ¼ 20 �C .

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detected either immediately after the removal of cooling (0e5 s) oraround 40 s into the thermal recovery. The duration of the infraredimage sequence (movie) acquisition during thermal recovery isdetermined by these times. The results suggest that for small le-sions imaging times up to 90 s will be sufficient, which is acceptablein clinical practice. The number of image frames to be analyzed inthe image processing phase is also reasonable and it depends on thesampling rate. The cooling times as well as imaging times can beshorter for smaller and more superficial lesions.

The differences between the two types of responses duringthermal recovery can be attributed to the differences between thethermophysical properties of the lesion and healthy tissue. Becauseof the increased heat generation within the lesion, the surroundinghealthy tissue will cool down more rapidly than the lesion duringthe first 15 s of cooling. During this short time, the temperaturedecrease in the lesion is much smaller, leading to high thermalcontrasts very early during the recovery. After 15 s, the heatingwithin the lesion is overpowered by the external cooling, leading toreduced thermal contrasts. The 40 s recovery time is needed for thelesion heating effects to compensate for the external cooling,leading again to high thermal contrasts. The magnitude of thethermal contrasts for the cooling parameters considered is in therange of 0.3�0.4 �C, and these values can be easily detected bymodern IR cameras. Ideally, in clinical practice, shorter coolingtimes are desired. However, this implies that visual access to thecooled area has to be enabled immediately after the removal of thecooling stress (the source of cooling has to be removed quickly andimaging has to start immediately, leaving no time for focusing andadjustments of the optics).

Table 2 summarizes key results: the cooling penetration depthD(tmax), the time tmax corresponding to DTmax, and the value of themaximum temperature difference DTmax for various cooling timestc. From the data, we can infer that when the cooling time is shorterthan 20 s, the maximum temperature difference will occur within afew seconds after the cooling stress is removed, and the magnitudeof the maximum decreases with increasing cooling time. However,when the cooling time is longer than 25 s, the maximumwill occurapproximately 40 s into the thermal recovery phase, and themagnitude of DTmax increases with increasing cooling time tc. Thethermal penetration depth D(tmax) increases from 2.5 mm for 5 s ofcooling to 7.4 mm for 120 s of cooling. Therefore, cooling andmeasurement times can be adjusted to match the lesion depth: asexpected, shorter cooling time is appropriate for superficial lesionsand longer cooling time for deeper lesions.

4.2.2. Thermal contrasts, Case C2For soaked-cotton cooling similar trends can be observed for the

thermal contrast DT(t) as for Case C1, and they are shown in Fig. 9. Ifthe cooling time is shorter than 40 s, the maximum (type one) will

Table 2Data for constant temperature cooling, Case C1: cooling penetration depth D(tmax),time of maximum thermal contrast tmax and the corresponding △Tmax for variouscooling durations tc.

Coolingtime tc (s)

Coolingpenetrationdepth D(tmax)(mm)

Timing ofmax. DT(t) tmax (s)

Max. DT(t) DTmax(�C)

5 2.5 0.7 0.3810 3.3 0.7 0.3020 4.1 1.4 0.2425 4.5 41 0.23530 5.0 41 0.24660 7.4 41 0.28120 7.4 41 0.298

occur within less than 3 s after the removal of cooling. Once thecooling duration is longer than 60 s, the maximum DTmax (typetwo) will occur around 23 s. The maximum contrast is larger forshorter cooling times, about 0.3 �C, and it decreases to around0.18 �C for longer cooling times.

The decrease of thermal contrast with increasing cooling timecan be explained by the change (increase) of the cotton tempera-ture with time, caused by heating both by the skin and the ambient.Therefore, shorter cooling times are desirable for soaked-cottoncooling, as long as quick optical access (after the removal of thecooling) is feasible. Key results for Case C2 are summarized inTable 3. They suggests that, unlike the constant temperature cool-ing case (Case C1) in which only the second type of maximum in-creases with cooling times, the values DTmax of both types ofmaxima decrease with cooling time. Therefore, to maximize DTmax,the cooling time should be between 40 and 60 s.

4.2.3. Thermal contrasts, Case C3Thermal contrasts as a function of time for convective cooling

with air are shown in Fig. 10(a) and (b). The convection heattransfer coefficients h vary from 50W/m2 K to 100 W/m2 K (typicalvalues for forced convection in gases or free convection in liquids),and cooling times vary from 5 s to 120 s. For all cooling times inFig. 10(a) and (b), the maximum temperature difference DTmaxappears immediately after the cooling stress is removed (0e0.2 sinto the thermal recovery phase). After the initial maximum, thethermal contrast monotonically decreases with time t.

The overall thermal contrast DTmax increases with increasingcooling time tc. Therefore, for air cooling, longer cooling times aredesirable and imaging has to commence immediately after theremoval of cooling, in order to measure the maximal thermalcontrast. Since the thermal contrast is relatively low in magnitudeand decreases rapidly, imaging of the first 20 s of the thermal re-covery with high temporal resolution is crucial. Thermal contrasts

Table 3Data for soaked cotton cooling, Case C2: cooling penetration depth D(tmax), time ofmaximum thermal contrast tmax and the corresponding DTmax for various coolingdurations tc.

Coolingtime tc (s)

Cooling penetrationdepth D(tmax) (mm)

Timing of max.DT(t) tmax (s)

Max. DT(t) DTmax (�C)

5 2.2 0.5 0.33510 2.9 0.6 0.28940 5.1 2.9 0.18743 5.3 11.5 0.18660 6.3 23 0.18480 7.2 23.1 0.179100 8.0 23.1 0.174120 8.6 23.1 0.168

Fig. 10. Thermal contrast △T(t) as a function of time with cooling time tc as parameter (tc is in the range of 5e120 s) for convection cooling (Case C3) with Tc ¼ 20 �C and h ¼(a)50 W/m2 K, (b) 100 W/m2 K, (c) 500 W/m2 K, (d) 1000 W/m2 K.

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188184

are in the range of 0.15e0.22 �C and 0.2e0.28 �C, for h¼ 50W/m2 Kand 100 W/m2 K, respectively. Again, these are temperature dif-ferences that can be measured with modern infrared cameras.

However, as shown in Fig. 10(c) and (d), for higher heat transfercoefficients (h ¼ 500 W/m2 K and 1000 W/m2 K, corresponding tohigh-velocity air or liquid cooling), the trends change and resemblethose for constant temperature (Case C1) and soaked cotton cooling(Case C2). Again, we identify two characteristic behavior types.Using shorter cooling times (below tc ¼ 60 s for h ¼ 500 W/m2 K,and 30 s for h ¼ 1000 W/m2 K) the maximum thermal contrast isobserved within 1 s into the thermal recovery process. The thermalcontrast decreases rapidly during the first 20 s of thermal recovery,therefore rapid imaging immediately after the removal of cooling isessential to capture the maximum. DTmax is relatively large forthese shorter cooling times (0.38e0.29 �C for h¼ 500W/m2 K), andit decreases as the cooling time increases. Therefore, we canconclude that shorter cooling times (<25 s) and short imagingtimes (<15 s) are sufficient for lesions less than 4 mm deep.

As summarized in Table 4, for h ¼ 500 W/m2 K, the second typeof maximum DTmax is detected at 23 s into the thermal recovery forcooling times longer than 110 s. For 110 s of cooling, the coolingpenetration depth D(tmax) reaches 9 mm, therefore longer coolingtimes and imaging times are better suited for imaging of deeperlesions.

For h¼ 1000W/m2 K, the first type of thermal recovery behaviorholds for cooling times up to 30 s, and the maximum contrast isrelatively large (0.41e0.29 �C). For longer cooling times, themaximum is detected around 23 s into the thermal recovery.△Tmax increases with increasing cooling time, as shown inFig. 10(c) and (d).

4.3. Sensitivity analysis for the variation of tissue properties

In order to investigate the influence of the variation of tissueproperties on the thermal contrast, a sensitivity analysis was con-ducted for two model parameters: blood perfusion rate in thepapillary dermis and skin layer thickness. Based on prior results

[15], these two parameters were found to be the key factors leadingto highest surface temperature uncertainties. The sensitivity isaddressed by comparing surface temperature distributions for theranges of the two parameters between the maximum and mini-mum values found in the literature [36e38] and summarized inTable 5.

Four cases were computed for each parameter of interest,respectively, while the remaining parameters (not listed in Table 5)were kept at their nominal values shown inTable 1. CaseM inTable 5represents the set of nominal parameters in the primary modeldescribed in Table 1. When considering the tissue thickness varia-tion range indicated in the literature [36,38], T1 represents the casewith thinnest layer combination (Table 5), and T2 and T3 in Table 5represent the medium and thickest layer combinations. Similar tothis, in the analysis of blood perfusion B1 is the scenario with thelowest perfusion rate in all layers, while B2 and B3 representscenarios of medium and high blood perfusion rates, respectively.

Constant temperature cooling (C1) using 20 �C for 60 s is appliedin all the cases considered, and the results of the sensitivity analysisare displayed in Fig. 11. By comparing case T1 with the nominal caseM in Fig. 11(a), we can observe that the thermal contrast is slightlyhigher due to the reduced thicknesses of the near-surface layers(epidermis and dermis). A similar increase of thermal contrast canalso be observed for the parameter combinations T2 and T3, inwhich both the near-surface and deeper layers are thicker than forT1. Since the thickness increase of the insulating fat layer is largerthan that of the near-surface layer, the increased thermal contrastremains in cases T2 and T3. The thermal conductivity of fat is lessthan half of the thermal conductivity of near surface layers. Thethermal contrast therefore decreases with the increasing thicknessof near-surface layers, however, it also increases with the thicknessof fat layer. This result is significant, since the thickness of the fatlayer can vary in a wide range. This sensitivity analysis demon-strates that the increase of its thickness won't adversely affect thediagnostic ability for near-surface lesions. The results in Fig. 11(a)suggest that the timing of maximum thermal contrast does notchange with the tissue thickness.

Table 4Data for convection cooling, Case C3: cooling penetration depth D(tmax), time ofmaximum thermal contrast tmax and the corresponding DTmax for various coolingtimes tc.

Cooling time tc (s) Coolingpenetrationdepth D(tmax)(mm)

Timing of max.DT(t) tmax (s)

Max. DT(t) DTmax (�C)

h ¼ 50 W/m2 K5 0.8 0 0.15210 1.4 0 0.16630 3.1 0 0.18660 4.0 0 0.203120 6.4 0 0.224h ¼ 100 W/m2 K5 1.2 0 0.20510 2.1 0 0.22830 3.6 0.1 0.24960 5.0 0.2 0.265120 7.9 0.2 0.284h ¼ 500 W/m2 K5 2.0 0.2 0.38110 2.8 0.3 0.37330 4.3 0.5 0.31860 6.7 0.7 0.295120 9.6 23 0.289h ¼ 1000 W/m2 K5 2.2 0.5 0.41810 2.3 0.5 0.37830 4.7 0.7 0.29460 6.8 23.1 0.270120 9.9 23.1 0.294

Fig. 11. Sensitivity of thermal contrast to (a) skin thickness variations and (b) bloodperfusion variations. Properties for T1-T3 and B1eB3 are summarized in Table 5.

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188 185

On the other hand, results in Fig. 11(b) indicate an obviousdecrease of thermal contrast due to increased blood perfusion inskin layers. Since the perfusion rate of the lesion is kept constant inthe analysis, this effect can explained by the enhanced thermalrecovery rate of healthy skin, which reduces the temperature dif-ference between the lesion and healthy skin. In addition, the timingof maximal thermal contrast is shifted to an earlier time, the dif-ference being a few seconds. The data indicate the need to startimaging immediately after the removal of the cooling stress.Several image frames per second should be captured during thefirst 5e10 s. These results confirm the significance of increasedblood perfusion as one of the indicators of cancer, recognizedwidely in the medical literature [9e15,33]. They also suggest thatmeasuring and comparing blood perfusion rates of diseased andhealthy tissue may serve as foundation for quantitative assessmentof cancerous skin lesions. Further clinical studies are needed toinvestigate this hypothesis. The thermal contrast is sensitive to thevariation of blood perfusion, however, even for the highest

Table 5Variation range of tissue thickness and blood perfusion rate for the sensitivityanalysis.

Tissue thickness (mm)

Skin layer T1 M T2 T3

Epidermis 0.08 0.1 0.09 0.1Papillary dermis 1 1 1 1Reticular dermis 0.6 1 0.8 1Fat 2 2 3 4Muscle 8 8 8 8

Blood perfusion rate (1/s)

Skin layer B1 M B2 B3

Epidermis 0 0 0 0Papillary dermis 0.00018 0.00018 0.002 0.0036Reticular dermis 0.00018 0.00126 0.002 0.0036Fat 0 0.00008 0.00009 0.0001Muscle 0.0005 0.0027 0.006 0.01

perfusion case (B3), its maximum value is larger than 0.1 �C, whichis detectable with modern, precision IR cameras.

4.4. Sensitivity analysis for skin surface emissivity

It is a common misconception in the medical and engineeringcommunities that the emissivity of the human skin varies in a widerange, both locally and from individual to individual, and that thisvariation makes thermal models inaccurate and prevents accuratetemperaturemeasurements. However, this is not the case, based onmeasurement data reported in the literature [44e46]. The emis-sivity of intact human skin, in spite of the significant differences incolor and surface structure, is relatively constant, and varies in therange of 0.98 ± 0.01 in the wavelength range of 2 mm e 14 mm[44e46]. In order to evaluate the effects of surface-to-ambient ra-diation on thermal contrast, we incorporated this effect into ourskin heat transfer model as an additional thermal boundary con-dition on the skin surface described by the StefaneBoltzmann lawas

q00 ¼ εs

�T4sur � T4amb

�: (12)

This assumption holds, as the imaged portion of the skin surfaceis small compared to the surroundings (a large exam roomwhich istypically at ambient conditions at 21 �C). In Eq. (12) q

00is the radi-

ation heat flux to the ambient, ε the skin emissivity, s the Ste-faneBoltzmann constant, Tsur the skin surface temperature duringthe thermal recovery phase, and Tamb the ambient temperature,which is 21 �C in the simulation.

For Case C1 (60 s of constant temperature cooling) we evaluatedthe thermal contrast for three representative emissivity values: 0.8(extreme low), 0.98 (typical value), and 1.00 (blackbody, extreme

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188186

high) to assess the role of the emissivity. The computed thermalcontrast during the thermal recovery phase for the three emissivityvalues and for the nominal Case C1 is plotted in Fig. 12. We canobserve only a slight difference in thermal contrast (at later thermalrecovery times which are less important in a diagnostic measure-ment) as a consequence of surface-to-ambient radiation, which isnot going to affect the diagnostic ability of the imaging system. Thechange in the maximum value of the thermal contrast is less than0.13% as a result of surface-to-ambient radiation for the range ofemissivities of 0.8e1.0. Thus, since the normal emissivity variationof human skin is much smaller, 0.98 ± 0.01, we can conclude thatthe sensitivity of thermal contrast measurement to skin emissivityis negligible.

Fig. 13. Comparison between computed results (full line) and experimental data(discrete data points): (a) thermal recovery of the lesion and healthy skin and (b) meanvalue of the measured thermal contrast (nine adjacent pixels) and the computedthermal contrast.

4.5. Model validation and comparison to experimental data

To validate the numerical predictions of skin cooling and ourthermal model reported in this paper, experimental data obtainedby IR imaging of a malignant melanoma lesion and the surroundinghealthy skin, reported in our previous publications [6,7], are usedfor comparison. The malignant melanoma lesion was classified asClark level II (superficial spreading type), with the depth of0.44mm and approximate width 2mm. The lesion is elongated andirregular in shape. In the patient study, the lesion was cooled byapplying a thin gel pack for 60 s, and the temperature of the regionof interest was cooled down to around 14 �C at the end of coolingphase. For more details about the lesion, experimental techniqueand experimental data, the reader is referred to previous publica-tions of our group [6,7]. To simulate the thermal behavior duringcooling and thermal recovery of this lesion, we consider a crosssection of this lesionwhich is assumed to be elliptical in shape, withthe major diameter (W) and minor diameter (P) of 2 mm and0.5 mm, respectively (Fig. 2(a)). To simulate the cooling effect, inthe computational model the cooling with the gel pack wasapproximated by the constant temperature cooling (Case C1) at14 �C.

Measured and computed thermal recovery temperatures for thelesion and healthy skin are plotted in Fig. 13(a); the full line showscomputed results and discrete points correspond to experimentaldata. Experimental results indicate a maximum thermal contrast ofaround 2.5 �C, which is higher than the values computed in theprevious sections. Since the exact parameters and thermophysicalproperties of the melanoma lesion are not available from experi-ment or literature, we increased the blood perfusion rate of thelesion toub¼ 0.045(1/s) in the calculations tomatch themagnitudeof the measured thermal contrast. Our results suggest that generallesion data reported in the literature [42] probably underestimatethe blood perfusion rate of the melanoma lesion. Since property

Fig. 12. Sensitivity of thermal contrast to the variation of skin surface emissivity.

data for lesions, especially very small ones, are rare or nonexistent,the uncertainties in the thermal models and results have to beaddressed through an uncertainty analysis, as discussed previouslyby Cetingul and Herman [15]. Clearly, for accurate thermal models,accurate thermophysical property data are essential, and theirnoninvasive, in vivo measurement poses a continuous challenge.The remaining parameters of the computational model (Table 1)remained the same for the validation analysis.

For the experimental data in Fig. 13, we sampled nine adjacentpixels (arranged in a square pattern) at two selected locations(lesion and healthy tissue), and the template-based motiontracking method [47,48] was applied to record the temperature atthese pixels during thermal recovery. The temperature differencesbetween each pair of lesion/healthy point data sets were computed,and the mean value of the temperature difference between lesionand healthy tissue during the thermal recovery phase is plotted inFig. 13(b). It can be observed that the thermal recovery curves inboth simulation and experiment are very similar. The scatter in theexperimental data can be attributed to imperfect motion tracking(accounting for involuntary movements of the patient) in theinfrared image sequence. In Fig. 13 (b), the trend of the measuredthermal contrasts is very similar to that predicted by the numericalmodel. The maximum value occurs around 40e60 s into the ther-mal recovery phase both in the computed and experimental results.

5. Conclusions

The analysis of cooling penetration indicates that for constanttemperature, soaked cotton and convective cooling with

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sufficiently high heat transfer coefficients (�500 W/m2 K), it takesless than 30 s for the cooling effect to reach the depth of 4 mm. Thisis the desired cooling depth for the detection of near-surface le-sions. Therefore, for the range of cooling temperatures consideredin this study (4 �C e 20 �C), 30 s is an acceptable cooling time for avariety of clinical applications. The analysis of cooling penetrationalso suggests that the cooling temperature of 20 �C is usually suf-ficient for the cooling effect to reach the desired depth within lessthan 1 min.

By analyzing thermal contrast for the three cooling methods,two types of thermal recovery behaviors can be identified, one forshort cooling times and another for longer cooling times. When thecooling time is less than 30 s, i.e. the cooling penetration depth isless than 4 mm, an immediate maximum of thermal contrast ap-pears within the first few seconds after the removal of cooling.Following the maximum, the thermal contrast drops rapidly withinthe next 20 s.

On the other hand, when the cooling time exceeds 40 s, thesecond type of maximum is observed around 20e45 s into thethermal recovery. The magnitude of this maximum increases withincreasing cooling time for constant temperature cooling (Case C1)and convective cooling (Case C3) with high heat transfer co-efficients (�500 W/m2 K). For soaked cotton cooling (Case C2),however, the magnitude decreases with increasing cooling time.

For all cooling methods considered in this study, the magnitudeof the maximum of the first type is higher than that of the secondtype. The second type of maximum is broader and easier to capturewith imaging systems that have a moderate frame rate, as highthermal contrast is available longer. The second type of thermalrecovery may be preferable in the clinical environment since theclinician will have sufficient time to capture the maximum thermalcontrast. A shorter cooling time could be more suitable for small,superficial lesions, which can be detected with a stronger thermalcontrast early in the thermal recovery phase. The dependence ofthermal recovery behavior on the cooling time thus provides thebasis for optimization. The choice of the cooling time, method, andtemperature will be ultimately determined by the availableequipment and the characteristics of the lesion being imaged.

The results suggest that it is feasible to apply a moderate tem-perature of about 20 �C to achieve effective skin cooling, with anacceptable cooling duration (<2 min) in a clinical setting. This levelof cooling is not likely to cause discomfort to the patient. Theduration of cooling can be further adjusted by considering thecharacteristics of the lesion to optimize thermal contrast for bettermeasurement data and improved clinical convenience.

Acknowledgments

This research was funded by the National Institutes of HealthNCI Grant No.R01CA161265, the National Science Foundation GrantNo. 0651981 and the Alexander and Margaret Stewart Trustthrough the Cancer Center of the Johns Hopkins University.

References

[1] SEER Stat Fact Sheets: Melanoma of the Skin, National Cancer Institute,Bethesda, MD, 2012.

[2] C.M. Balch, A.C. Buzaid, S.J. Soong, M.B. Atkins, N. Cascinelli, D.G. Coit,I.D. Fleming, J.E. Gershenwald, A. Houghton, J.M. Kirkwood, K.M. McMasters,M.F. Mihm, D.L. Morton, D.S. Reintgen, M.I. Ross, A. Sober, J.A. Thompson,J.F. Thompson, Final version of the american joint committee on cancerstaging system for cutaneous melanoma, J. Clin. Oncol. 19 (2001) 3635e3648.

[3] Skin Cancer Facts, Official website of skin cancer foundation, 2011.[4] K. Ammer, E.F. Ring, Standard procedures for infrared imaging in medicine, in:

J.D. Bronzino (Ed.), Biomedical Engineering Handbook, third ed., MedicalSystems and Devices, CRC Press, 2006, pp. 32-1e32-14.

[5] J. Cary, L. Kalisher, N. Sadowsky, B. Mikic, Thermal evaluation of breast diseaseusing local cooling, Radiology 115 (1975) 73e77.

[6] M.P. Cetingul, C. Herman, Quantification of the thermal signature of a mela-noma lesion, Int. J. Therm. Sci. 50 (2011) 421e431.

[7] C. Herman, M.P. Cetingul, Quantitative visualization and detection of skincancer using dynamic thermal imaging, J. Vis. Exp. 51 (2011) 2679.

[8] H.H. Pennes, Analysis of tissue and arterial blood temperatures in the restinghuman forearm, J. Appl. Physiol. 1 (1948) 93e122.

[9] I.A. Lubashevsky, V.V. Gafiychuk, Mathematical Description of the HeatTransfer in Living Tissue (Part 1), Adap-org/9911001, 2004.

[10] C.K. Charny, Mathematical models of bioheat transfer, Adv. Heat Trans. 22(1992) 19e155.

[11] H. Arkin, L.X. Xu, K.R. Holmes, Recent developments in modeling heat-transferin blood-perfused tissues, IEEE Trans. Biomed. Eng. 41 (1994) 97e107.

[12] J. Crezee, J. Mooibroek, J.J.W. Lagendijk, G.M.J. Vanleeuwen, The theoreticaland experimental evaluation of the heat-balance in perfused tissue, Phys.Med. Biol. 39 (1994) 813e832.

[13] M. Stanczyk, J.J. Telega, Modelling of heat transfer in biomechanics e a reviewpart I. Soft tissues, Acta Bioeng. Biomech. 4 (2002) 31e61.

[14] A.R.A. Khaled, K. Vafai, The role of porous media in modeling flow andheat transfer in biological tissues, Int. J. Heat Mass Transf. 46 (2003)4989e5003.

[15] M.P. Cetingul, C. Herman, A heat transfer model of skin tissue for the detectionof lesions: sensitivity analysis, Phys. Med. Biol. 55 (2010) 5933e5951.

[16] F. Xu, T.J. Lu, K.A. Seffen, E.Y.K. Ng, Mathematical modeling of skin bioheattransfer, Appl. Mech. Rev. 62 (2009).

[17] S. Mahjoob, K. Vafai, Analytical characterization of heat transport throughbiological media incorporating hyperthermia treatment, Int. J. Heat MassTransf. 52 (2009) 1608e1618.

[18] S. Mahjoob, K. Vafai, Analysis of bioheat transport through a dual layer bio-logical media, J. Heat Transfer-Transactions Asme 132 (2010).

[19] S. Mahjoob, K. Vafai, Analytical characterization and production of anisothermal surface for biological and electronic applications, J. Heat Transfer-Transactions Asme 131 (2009).

[20] S. Mahjoob, K. Vafai, Analysis of heat transfer in consecutive variable cross-sectional domains: applications in biological media and thermal manage-ment, J. Heat Transfer-Transactions Asme 133 (2011).

[21] J.G. Zaspel, H.M. Schnell, Cooling extensive burns: sprayed coolants canimprove initial cooling management - a thermography-based study, Burns 34(2008) 505e508.

[22] P. Axelrod, External cooling in the management of fever, Clin. Infect. Dis. 31(2000) S224eS229.

[23] C.H. Wyndham, N.B. Strydom, H.M. Cooke, J.S. Maritz, J.F. Morrison,P.W. Fleming, J.S. Ward, Methods of cooling subjects with hyperpyrexia,J. Appl. Phys. 14 (1959) 771e776.

[24] H.H. Zenzie, G.B. Altshuler, M.Z. Smirnov, R.R. Anderson, Evaluation of coolingmethods for laser dermatology, Lasers Surg. Med. 26 (2000) 130e144.

[25] R.G. Wheeland, Cutaneous Surgery, WB Saunders, Philadelphia, 1994.[26] B.A. Gilchrest, S. Rosen, J.M. Noe, Chilling port wine stains improves the

response to argon-laser therapy, Plast. Reconstr. Surg. 69 (1982) 278e283.[27] E. Armon, G. Laufer, New techniques for reducing the thermochemical dam-

age in the course of laser-surgery, Laser. Surg. Med. 7 (1987) 162e168.[28] C. Chess, Q. Chess, Cool laser optics treatment of large telangiectasia of the

lower extremities, J. Dermatol. Surg. Oncol. 19 (1993) 74e80.[29] B. Dreno, T. Patrice, P. Litoux, H. Barriere, The benefit of chilling in argon-laser

treatment of port-wine stains, Plast. Reconstr. Surg. 75 (1985) 42e45.[30] A.J. Welch, M. Motamedi, A. Gonzalez, Evaluation of cooling techniques for the

protection of the epidermis during Nd-YAG laser irradiation of the skin, in:S.N. Joffe (Ed.), Neodymium-yag Laser in Medicine and Surgery, Elsevier, New-York, 1983, pp. 195e204.

[31] A. Di Carlo, Thermography and the possibilities for its applications in clinicaland experimental dermatology, Clin. Dermatol. 13 (1995) 329e336.

[32] T.M. Buzug, S. Schumann, L. Pfaffmann, U. Reinhold, J. Ruhlmann, Functionalinfrared imaging for skin-cancer screening, Conf. Proc. IEEE Eng. Med. Biol.Soc. 1 (2006) 2766e2769.

[33] G.A. Santa Cruz, J. Bertotti, J. Marin, S.J. Gonzalez, S. Gossio, D. Alvarez,B.M. Roth, P. Menendez, M.D. Pereira, M. Albero, L. Cubau, P. Orellano,S.J. Liberman, Dynamic infrared imaging of cutaneous melanoma and normalskin in patients treated with BNCT, Appl. Radiat. Isot. 67 (2009) S54eS58.

[34] C. Herman, M.P. Cetingul, In-vivo detection of skin cancer using the dynamicinfrared imaging technique, J. Heat Trans-T. Asme 133 (8) (2011) 080910.

[35] A.S. Ahuja, K.N. Prasad, W.R. Hendee, P.L. Carson, Thermal conductivity anddiffusivity of neuroblastoma tumor, Med. Phys. 5 (1978) 418e421.

[36] S.B. Wilson, V.A. Spence, A tissue heat transfer model for relating dynamicskin temperature changes to physiological parameters, Phys. Med. Biol. 33(1988) 895e912.

[37] J. Werner, M. Buse, Temperature profiles with respect to inhomogeneity andgeometry of the human body, J. Appl. Physiol. 65 (1988) 1110e1118.

[38] D.A. Torvi, J.D. Dale, A finite-element model of skin subjected to a flash fire,J. Biomech. Eng-T. Asme 116 (1994) 250e255.

[39] F.A. Duck, Physical Properties of Tissue : a Comprehensive Reference Book,Academic Press, London, 1990.

[40] C.W. Song, A. Lokshina, J.G. Rhee, M. Patten, S.H. Levitt, Implication of bloodflow in hyperthermic treatment of tumors, IEEE Trans. Biomed. Eng. 31 (1984)9e16.

[41] J.W. Draper, J.W. Boag, Skin temperature distributions over veins and tu-mours, Phys. Med. Biol. 16 (1971) 645e656.

T.-Y. Cheng, C. Herman / International Journal of Thermal Sciences 86 (2014) 175e188188

[42] Z.S. Deng, J. Liu, Mathematical modeling of temperature mapping over skinsurface and its implementation in thermal disease diagnostics, Comput. Biol.Med. 34 (2004) 495e521.

[43] K.R. Pardasani, N. Adlakha, Exact solution to a heat-flow problem in peripheraltissue layers with a solid tumor in the dermis, Indian, J. Pure Appl. Math. 22(1991) 679e687.

[44] B.F. Jones, A reappraisal of the use of infrared thermal image analysis inmedicine, IEEE Trans. Med. Imaging. 17 (1998) 1019e1027.

[45] J. Steketee, Spectral emissivity of skin and pericardium, Phys. Med. Biol. 18(1973) 686e694.

[46] D.J. Watmough, P.W. Fowler, R. Oliver, The thermal scanning of a curvedisothermal surface: implications for clinical thermography, Phys. Med. Biol. 15(1970) 1e8.

[47] T.Y. Cheng, C. Herman, Involuntary motion tracking for medical dynamicinfrared thermography using a template-based algorithm, in: Proc. SPIEMedical Imaging 2013: Image Processing, 2013, p. 86692Q.

[48] T.Y. Cheng, C. Herman, Motion tracking in infrared imaging for quantitativemedical diagnostic applications, Infrared Phys. Technol. 62 (2014) 70e80.