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Modeling skin cooling using optical windows and cryogens during laser induced hyperthermia in a multilayer vascularized tissue
Applied Thermal Engineering 89 (2015) 28e35
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Modeling skin cooling using optical windows and cryogens during laser induced hyperthermia in a multilayer vascularized tissue Rupesh Singh a, Koushik Das a, Junnosuke Okajima b, Shigenao Maruyama b, Subhash C. Mishra a, * a b
Department of Mechanical Engineering, Indian Institute of Technology Guwahati, India Institute of Fluid Science, Tohoku University, Japan
h i g h l i g h t s Skin surface cooled laser induced hyperthermia is studied. A multi-layer 2-D cylindrical tissue geometry is considered. Both Pennes and WeinbaumeJiji bioheat models are considered. Laser transport in the tissue is modeled using discrete ordinate method. Results for 4 optical windows and 2 cryogens for skin cooling are presented.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 December 2014 Accepted 4 June 2015 Available online 14 June 2015
This article deals with the spatial and the temporal evolution of tissue temperature during skin surface cooled laser induced hyperthermia. Three different skin surface cooling methodologies viz., optical window contact cooling, cryogenic spray cooling and cryogen cooled optical window contact cooling are considered. Sapphire, yttrium aluminum garnet, lithium tantalate, and magnesium oxide doped lithium niobate are the considered optical windows. The cryogens considered are liquid CO2 and R1234yf. Heat transfer in the multilayer skin tissue embedded with thermally significant blood vessels pairs is modeled using the Pennes and WeinbaumeJiji bioheat equations. WeinbaumeJiji bioheat equation is used for the vascularized tissue. Laser transport in the tissue is modeled using the radiative transfer equation. Axial and radial (skin surface) temperature distributions for different combinations of optical windows and cryogens are analyzed. Liquid CO2 cooled yttrium aluminum garnet is found to be the best surface cooling mechanism. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Bioheat transfer Laser induced hyperthermia Optical windows Cryogens Finite volume method Discrete ordinate method
1. Introduction Laser induced hyperthermia and thermal therapy are emerging as promising methods of treatment for many ailments like portwine stain, and diseases like malignant tumors [1e3]. During such procedures, light energy gets absorbed in tissue and the absorption starts from the skin surface in case of external laser irradiation. Therefore, the maximum thermal energy produced is in the skin and the tissue layers immediately below the skin surface (dermis and subcutaneous layers). The multilayer skin tissue is
* Corresponding author. E-mail address: [email protected] (S.C. Mishra). http://dx.doi.org/10.1016/j.applthermaleng.2015.06.006 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
composed of epidermis, the outermost layer, the intermediate dermis, and internal vascular tissue with layers of fat. The epidermis contains melanin which is characterized by high absorption of light, and is therefore most susceptible for thermal damage during laser heating of tissues [4,5]. In any externally irradiated hyperthermia procedure, principal aim is to provide treatment to target tissue while minimizing thermal damage to the skin surface. Therefore in any such procedures, which involve high temperatures, cooling the skin is desirable. Many methods of skin cooling during laser induced hyperthermia and thermal therapy have been proposed by researchers [6,7]. Optical window surface contact cooling and cryogenic spray cooling are widely used methods for the skin surface cooling. Contact type cooling using optical windows and spray type cooling using
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Nomenclature a r, rb ho ðtÞ k keff
vessel radius density of tissue and blood normalized heat transfer coefficient thermal conductivity of tissue effective thermal conductivity hb blood perfusion rate Qm metabolic heat generation rate Ta arterial blood temperature l wavelength u average blood velocity cp ,cpb specific heat capacity of tissue and blood hcryo(0,t) surface heat transfer coefficient ho,max maximum heat transfer coefficient Ic, max intensity ka absorption coefficient p scattering phase function n number of vessel pairs ssf shape factor ss scattering coefficient t non-dimensional time
cryogens has been studied by many researchers in detail [8e10]. Zenzie et al. [11] studied three different application procedures of cooling agent, viz. passive contact plate cooling, active contact plate cooling and spray cooling. Optical windows are transparent material with applications in laser optics, electronics, and medicine [12]. For applications in laser induced hyperthermia and thermal therapy procedures, optical windows are used for providing a highly conducting contact cooling material which passes most of light through it [6,13]. This provides a way of simultaneously heating the tissue deep inside from the surface while preventing thermal damage to top surface of skin [14,15]. For contact cooling application, sapphire is most preferred material because of its wide range of transparency from UV to IR wavelengths, high strength and high conductivity. Optical quality crystalline aluminum oxide or sapphire is characterized by very high thermal conductivity, approximately 23 W/m K, high stability and hardness. Sapphire also has high threshold for optical damage [13]. In the present study, three new optical materials with thermal conductivity comparable or greater than sapphire are examined for suitability for contact cooling applications. The new optical window materials viz. sapphire (Al2O3), yttrium aluminum garnet (YAG), lithium tantalate (LiTaO3), and magnesium oxide doped lithium niobate (MgO:LiNbO3), were selected based on their ability to pass light between wavelength range of medical lasers i.e. between 500 nm and 1200 nm [16e19]. Other important properties for selection were high conductivity, low reflection loss, stability, hardness, insolubility, non-toxicity, and high threshold for optical damage. Yttrium aluminum garnet is a synthetic, hard material with wide transparency range between UV and IR. Lithium Tantalate and Magnesium Oxide doped Lithium Niobate, apart from having high thermal conductivities, also exhibits wide range of transparent window ranging from UV to IR wavelengths. A theoretical assessment of suitability of these four materials for contact cooling application is done. Cryogenic liquids, also known as cryogens, have very low boiling point (typically less than 30 C) [20e22]. At low temperatures, cryogens are in their liquid state. When exposed to normal temperature and pressure conditions, cryogens expand into large volume of gas. For spray cooling, the scattering from the cryogen is
29
ignored, as desired results can be achieved by varying the laser power. The two cryogens selected in the present study are HFO1234yf or R1234yf (Boiling point 30 C) and liquid CO2 (Boiling point 57 C), and the selection criteria followed are low boiling point, low global warming potential and low toxicity [23].
2. Model and formulation In the present study a quantitative evaluation of skin surface cooling during laser induced hyperthermia and thermal therapy is performed. Schematic of the multilayer skin tissue with deep vascularized soft tissue is shown in Fig. 1a. The tissue consists of skin layer viz. epidermis, dermis, and fatty soft tissue. The fourth (bottom) layer of tissue is a vascularized tissue with embedded large blood vessel pairs. Heat transfer in the top three layer and the fourth (bottom) layer are modeled using the blood perfusion based Pennes bioheat equation [24] and blood velocity based WeinbaumeJiji bioheat equation, respectively. The computational geometry, shown in Fig. 2a, is a 2-D axisymmetric cylinder, with a 2-D planner solution space. The modeling of laser propagation and absorption in biological tissue is done by solving the radiative transfer equation (RTE) [25]. The 3-D control volume for solution of RTE is shown in Fig. 2b. A solver for collimated radiation modeling is developed using discrete ordinate method (DOM) [26]. The volumetric radiative source term, in the form of the divergence of radiative heat flux is incorporated in Pennes bioheat as well as WeinbaumeJiji models. With radiative information computed using the discrete ordinate method, the bioheat energy equations are solved using the finite volume method (FVM) [27]. Laser of wavelengths of 1064 nm, irradiated on top surface of 2D cylindrical tissues geometry is considered. To the best of our knowledge, this is the first time when a set of radiative transfer equation for laser transport and light absorption, along with Pennes bioheat equation for blood perfused tissue, and WeinbaumeJiji bioheat equation for vascularized deep tissue is applied in conjunction. Also for numerical study of skin surface cooling, both optical window contact and cryogenic spray types, this is first attempt to model a realistic real-time scenario of laser heating of multilayer skin with deep seated tissue embedded with thermally significant blood vessels. A perfect contact between the skin and optical window is assumed for all cases of contact cooling. In practice, a near perfect contact can be achieved by applying high conductive gels on the skin. For a 2-D axisymmetric cylindrical geometry, Pennes bioheat equation is given by,
rcp
" # vT 1 v vT v2 T ¼k r þ 2 þ hb rb cpb ðTa TÞ þ Qm vt r vr vr vz
(1)
where rb and cpb are the density and the specific heat of blood, respectively. r, cp and k are the density, the specific heat, and the thermal conductivity of the tissue, respectively. With arterial blood temperature Ta ,hb is the blood perfusion rate and Qm is the volumetric metabolic heat generation rate. For the 2-D cylindrical geometry (Figs. 1 and 2a), the WeinbaumeJiji (WJ) model can be expressed as,
rc
vT 1 v vT v vT ¼ rkeff þ keff þ Qm vt r vr vr vz vz
(2)
where r, c, keff and Qm are the density, the specific heat, the effective thermal conductivity and the volumetric metabolic heat generation rate of the tissue, respectively. The effective thermal
30
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Fig. 1. Laser irradiated multilayer tissue geometry with (a) optical window contact, (b) cryogenic spray, and (c) cryogen cooled optical window contact cooling systems.
conductivity of the tissue is a function of different tissue-blood vessel configurations, and is given by [28],
"
keff
2 n prb cb a2 u ¼k 1þ 2 k ssf
# (3)
In Eq. (3), k, n, rb, cb, a and u are the thermal conductivity of the tissue, the number of vessel pairs crossing control volume surface per unit area, the density of blood, the specific heat of blood, the vessel radius and the average blood velocity in the counter current vessel pairs, respectively. For two parallel vessels with uniform surface temperature, embedded in a very large medium of tissue the shape factor ssf provides the information of resistance to the heat transfer and is given by [28,29].
ssf ¼
p cosh1 ðl=2aÞ
(4)
where l is the center to center spacing between the vessel pairs.
Both conduction and volumetric radiation has to be considered when a tissue is subjected to a laser (collimated radiation) with intensity Ic, max. In such a case, when the volumetric radiative source term, i.e., the divergence of radiative heat flux V$qr is accounted, the Pennes bioheat equation takes the form,
" # vT 1 v vT v2 T r þ 2 þ hb rb cpb ðTa TÞ þ Qm V$qr rcp ¼ k vt r vr vr vz (5) Similarly, in the WeinbaumeJiji equation, radiation to appears as a volumetric term, and accordingly the WJ bioheat model gets modified to
rc
vT 1 v vT v vT ¼ rkeff þ keff V$qr þ Qm vt r vr vr vz vz
(6)
The left (r ¼ 0, z) boundary of the computational domain (Fig. 2a) is the central axis of the cylinder and have symmetry boundary
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
31
Fig. 2. Schematic of (a) 2-D concentric cylindrical enclosure with cylindrical coordinate system and computational domain and (b) 3-D control volume needed for marching in angular space.
condition
vT vr
ðr¼0;zÞ
¼ 0 : The right (r ¼ R,z) boundary, which is the
outer surface of the cylinder and the bottom (r,z ¼ Z) surface i.e., the core body, are at isothermal condition. The top (r,z ¼ 0) boundary of the tissue is exposed to optical window of cryogenic spray. The optical window in case of contact cooling or the skin surface in case of direct spray cooling is considered under convective cooling condi tion, i.e., kvT ¼ hðT Tf Þ : A dynamic heat transfer coefvz ðr;z¼ZÞ
ficient relation is used for cryogen spray cooling. This relation (Eq. (7)) gives a time dependent effect of cryogen spray [21]
ho ðtÞ
¼
8 t > > < hcryo ð0; tÞ 1:0 0:35ðt 1Þ ¼ 0:3 0:002ðt 3Þ > ho;max > : 0:2 0:0125ðt 8Þ
t 1:0 1:0 < t 3:0 3:0 < t 8:0 8:0 < t (7)
ho ðtÞ
where is the normalized convection heat transfer coefficient, hcryo(0,t) is the surface heat convection coefficient, t is the nondimensional time, and ho,max is the maximum heat transfer coefficient during cryogenic spray. Although this relation is experimentally available for cryogen R134a [30,31], it is assumed that this relation is applicable to R1234yf and liquid CO2. The radiative transfer is governed by the radiative transfer equation and is given by [26]
Z
vI ss ¼ bI þ ka Ib þ vs 4p
0 0 0 I U p U; U dU
(8)
0
U ¼4p
where s is the distance in the direction bs , ka is the absorption coefficient, ss is the scattering coefficient, and p is the scattering phase function. With the calculated values of radiative components, the divergence of radiative heat flux is calculated using,
sT 4 G V$qr ¼ ka 4p p
(9)
For the modeling of heat transfer in the present geometry, Eq. (5) and Eq. (6) are numerically solved using FVM following the procedure stated in Ref. [27]. The radiative information of the tissue in the form of V$qr, is obtained by solving Eq. (7) and Eq. (8) using the DOM procedure. The detailed solution procedure of DOM is omitted for brevity and can be found in Ref. [26]. 3. Results and discussion The surface cooling mechanism is adopted in the present study only considers active by means of either keeping constant isothermal condition of optical window material or forced convective condition with extremely low temperature cryogen. Table 1 gives the thermal and physical properties of different layers of skin tissue and vascularized tissue. The effective thermal conductivity of vascularized tissue is calculated using Eqs. (3) and (4). The thickness for epidermis, dermis, soft tissue, and vascularized tissue considered are 100 mm, 2.0 mm, 2.4 mm, and 3.0 mm, respectively. The optical window is taken as 0.5 mm thick while the radius of the cylindrical geometry is taken as 3.0 mm. Table 2 lists the optical properties of different layers tissue at laser wavelength of l ¼ 1064 nm [2,5]. Table 3 provides the
Table 1 Thermo-physical properties of skin and vascularized tissues. Thermo-physical properties
Epidermis
Dermis
Soft tissue
Vascularized tissue
k (W/m K) rtissue (kg/m3) cp (J/kg,K) Qm (W/m3) h (1/s)
0.24 1190.0 3590.0 368.0 1.0 107
0.45 1116.0 3300.0 368.0 1.25 103
0.628 1000.0 4187.0 1190.0 3.0 103
0.5441 (Using WJ model) 1000.0 4187.0 1190.0 0.0 100
32
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
thermophysical properties of optical windows considered in the presented study. The thermophysical properties of cryogens are not considered for simulation for simplification, and only the dynamic time dependent convective effect by cryogen spray is considered. Laser power of 4 W with 1.0 mm beam radius is used for irradiation top surface of cylindrical geometry with optical window Table 2 Optical Properties of skin and vascularized tissue. Optical properties
Epidermis
Dermis
Soft tissue
Vascularized tissue
Extinction coefficient b(1/m) Scattering albedo, u
8592.0
8286.0
1100.0
1100.0
0.9586
0.994
0.963
0.963
Table 3 Thermo-physical properties of optical window materials. Material/properties
Density r (kg/m3)
Specific heat capacity cp (J/Kg K)
Thermal conductivity k (W/m K)
Sapphire YAG Lithium tantalate Magnesium oxide doped lithium niobate
3970.0 4560.0 7460.0 4640.0
419.0 590.0 430.0 628.0
22.21 14.0 46.0 38.0
placed on top surface. Fig. 3aed shows centerline temperature for different time level of exposure with different optical windows. With continuous wave laser exposure for time level ranging from 50 ms to 5 s, temperature evolution in multilayer tissue can be observed to be slightly different for four different optical windows at short time level. However as exposure time increases, this distinction in temperature profile is less (Fig. 3aed). A zoomed-in comparative centerline temperature profiles near the skin surface is presented in Fig. 4aeb. For short time level of laser exposure, i.e. 50 ms (Fig. 4a) and 100 ms (Fig. 4b), result shows that for other conditions remaining constant, YAG performs well in comparison to other optical windows. Fig. 4c shows a comparative centerline temperature profile at exposure time of 1 s. In Fig. 4c, a centerline temperature profile of tissue with sapphire window under no laser exposure is presented for providing a reference of how temperature evolves under 1 s exposure. Fig. 5a and b shows a skin surface (top layer of epidermis) temperature profile for different optical windows as contact cooling materials. Fig. 5a shows a comparison of skin surface temperature at laser exposure time of 0.5 s, and it can be seen that YAG provides maximum cooling. However at time level of 1 s and above this difference in skin temperature is less, as evident in Fig. 5b. This suggests that for short pulse laser irradiation with contact cooling, YAG may provide a better surface cooling than other optical windows. Fig. 6a and b shows the centerline temperature distribution of multilayer skin tissue (Fig. 1b) when cooled with cryogen spray
Fig. 3. Centerline temperature of skin tissue for different time of laser exposure with (a) Sapphire, (b) YAG, (c) Lithium tantalate, and (d) MgO: Lithium niobate.
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
33
Fig. 4. Comparison of centerline temperature for different optical windows with laser exposure time of (a) 50 ms, (b) 100 ms, and (c) 1 s.
R1234yf and liquid CO2, respectively. Fig. 6c shows surface temperature of laser irradiated multilayer skin tissue (Fig. 1b) for two cryogens, namely R1234yf and liquid CO2. Liquid CO2 having low boiling point than R1234yf, and hence a low surface temperature can be observed in Fig. 6c for liquid CO2 as cryogen.
Cryogen cooled optical window contact cooling as shown in Fig. 1c, is the third method of surface cooling in the present study. With a laser exposure time of 0.5 s on liquid CO2 precooled optical windows, skin surface temperature of multilayer tissue is presented in Fig. 7a. Fig. 7b shows surface temperature of skin with
Fig. 5. Skin surface temperature at laser exposure time of (a) 0.5 s, and (b) 1.0 s, for different optical window cooling.
34
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Fig. 6. Centerline temperature of skin when cooled with cryogen spray (a) R1234yf, and (b) liquid CO2, and (c) surface temperature of skin with two cryogen at different exposure times.
four different optical windows cooled with liquid CO2 for a laser exposure time of 1 s. In both Fig. 7a and b it is evident that for short time of laser irradiation, the combination of liquid CO2 and YAG provides better
cooling of skin surface. A 2-D temperature contour of 5 s laser exposure with liquid CO2 cooled YAG optical window is presented in Fig. 8. Maximum temperature is well inside the tissue while preventing overheating the skin surface, as can be seen in Fig. 8.
Fig. 7. Surface temperature of skin with liquid CO2 cryogen cooled optical window at laser exposure time of 0.5 s.
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Fig. 8. A 2-D temperature contour of liquid CO2 cooled YAG optical window during contact cooling of skin at laser exposure time of 5 s. Laser power of 4 W with 1 mm beam radius is used.
4. Conclusions A comparison of four different optical window material performances for surface contact cooling during laser induced hyperthermia is presented. A set of two equation for bioheat transfer modeling, namely, Pennes bioheat equation for blood perfused tissue and WeinbaumeJiji bioheat equation for tissue with embedded large blood vessel pairs, are solved in conjunction with radiative transfer equation. The radiative transfer equation was used for modeling light transport and energy deposition in the optical window and tissue. A comparative study was presented for two different cryogen with low global warming potential viz. R1234yf and liquid CO2, for spray cooling during laser induced hyperthermia. A dynamic heat transfer coefficient relation was used for cryogen spray cooling. Finally a combined cryogen - optical window cooling strategy was presented for all combination of cryogens and optical window materials. The combination of liquid CO2 and yttrium aluminum garnet was found to be more effective for short duration laser exposure hyperthermia procedures.
References [1] D. Li, Y.L. He, G.X. Wang, Y.X. Wang, Z.X. Ying, A new model of selective photothermolysis to aid laser treatment of port wine stains, Chin. Sci. Bull. 58 (2013) 416e426. [2] D. Li, G.X. Wang, Y.L. He, W.J. Wu, B. Chen, A three-temperature model of selective photothermolysis for laser treatment of port wine stain containing large malformed blood vessels, Appl. Therm. Eng. 65 (2014) 308e321.
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[3] M.K. Loze, C.D. Wright, Temperature distributions in laser-heated biological tissue with application to birthmark removal, J. Biomed. Opt. 6 (2001) 74e85. [4] A.N. Bashkatov, E.A. Genina, V.I. Kochubey, V.V. Tuchin, Optical properties of human skin, subcutaneous and mucous tissues in the wavelength range from 400 to 2000nm, J. Phys. D Appl. Phys. 38 (2005) 2543e2555. [5] T. Lister, P.A. Wright, P.H. Chappell, Optical properties of human skin, J. Biomed. Opt. 17 (2012) 90901e90915. [6] G.B. Altshuler, H.H. Zenzie, A.V. Erofeev, M.Z. Smirnov, R.R. Anderson, C. Dierickx, Contact cooling of the skin, Phys. Med. Biol. 44 (1999) 1003e1023. [7] T.Y. Cheng, C. Herman, Analysis of skin cooling for quantitative dynamic infrared imaging of near-surface lesions, Int. J. Therm. Sci. 86 (2014) 175e188. [8] L.O. Svaasand, L.L. Randeberg, G. Aguilar, B. Majaron, S. Kimel, E.J. Lavernia, J.S. Nelson, Cooling efficiency of cryogen spray during laser therapy of skin, Lasers Surg. Med. 32 (2003) 137e142. [9] B.S. Patel, Z.H. Zaidi, The suitability of sapphire for laser windows, Meas. Sci. Technol. 10 (1999) 146. [10] Z. Zhou, B. Chen, Y. Wang, L. Guo, G. Wang, An experimental study on pulsed spray cooling with refrigerant R-404a in laser surgery, Appl. Therm. Eng. 39 (2012) 29e36. [11] H.H. Zenzie, G.B. Altshuler, M.Z. Smirnov, R.R. Anderson, Evaluation of cooling methods for laser dermatology, Lasers Surg. Med. 26 (2000) 130e144. [12] J. Kim, Spray cooling heat transfer: the state of the art, Int. J. Heat Fluid Flow 28 (2007) 753e767. [13] B. Anvari, T.E. Milner, B.S. Tanenbaum, J.S. Nelson, A comparative study of human skin thermal response to sapphire contact and cryogen spray cooling, IEEE Trans. Biomed. Eng. 45 (1998) 934e941. [14] B. Anvari, T.E. Milner, B.S. Tanenbaum, S. Kimel, L.O. Svaasand, J.S. Nelson, Selective cooling of biological tissues: application for thermally mediated therapeutic procedures, Phys. Med. Biol. 40 (1995) 241e252. [15] B. Anvari, T.E. Milner, B.S. Tanenbaum, S. Kimel, L.O. Svaasand, J.S. Nelson, A theoretical study of the thermal response of skin to cryogen cooling and pulsed laser irradiation: implications for the treatment of port wine stain, Phys. Med. Biol. 40 (1995) 1451e1465. [16] F. Gervais, V. Fonseca, Lithium tantalate (LiTaO3), in: Handbook of Optical Constants of Solids, vol. III, Academic Press, San Diego, 1998, pp. 777e805. [17] E.D. Palik, Lithium niobate (LiNbO3), in: Handbook of Optical Constants of Solids, vol. I, Academic Press, San Diego, 1998, pp. 695e702. [18] W.J. Tropf, Yttrium aluminum garnet (Y3Al5O12), in: Handbook of Optical Constants of Solids, vol. III, Academic Press, San Diego, 1998, pp. 963e986. [19] W.J. Tropf, M.E. Thomas, Aluminum oxide (Al2O3) revisited, in: Handbook of Optical Constants of Solids, vol. III, Academic Press, San Diego, 1998, pp. 653e682. [20] S.S. Hsieh, H.H. Tsai, Thermal and flow measurements of continuous cryogenic spray cooling, Arch. Dermatol. Res. 298 (2006) 82e95. [21] D. Li, B. Chen, W.J. Wu, G.X. Wang, Y.L. He, Multi-scale modeling of tissue freezing during cryogen spray cooling with R134a, R407c and R404a, Appl. Therm. Eng. (2014) 1e12, http://dx.doi.org/10.1016/j.applthermaleng.2014.03.034. [22] J.H. Torres, J.S. Nelson, B.S. Tanenbaum, T.E. Milner, D.M. Goodman, B. Anvari, Estimation of internal skin temperatures in response to cryogen spray cooling: implications for laser therapy of port wine stains, IEEE J. Sel. Top. Quant. 5 (1999) 1058e1066. [23] R.A. Perkins, M.L. Huber, Measurement and correlation of the thermal conductivity of 2,3,3,3-Tetrafluoroprop-1-ene (R1234yf) and trans-1,3,3, 3tetrafluoropropene (R1234ze(E)), J. Chem. Eng. Data 56 (2011) 4868e4874. [24] A. Bhowmik, R. Singh, R. Repaka, S.C. Mishra, Conventional and newly developed bioheat transport models in vascularized tissues: a review, J. Therm. Biol. 38 (2013) 107e125. [25] M.F. Modest, Radiative Heat Transfer, third ed., Academic Press, New York (, 2013. [26] S.C. Mishra, R. Singh, P. Agarwal, C.H. Krishna, Analysis of radiative transport in a 2-D cylindrical participating medium subjected to collimated radiation, Numer. Heat Transf. A 66 (2014) 884e903. [27] H.K. Versteeg, W. Malalasekera, An Introduction to Computational Fluid Dynamics, the Finite Volume Method, Longman Group Limited, New York (, 1995. [28] S. Weinbaum, L.M. Jiji, A new simplified bioheat equation for the effect of blood flow on local average tissue temperature, J. Biomech. Eng. Trans. ASME 107 (1985) 131e139. [29] J.C. Chato, Heat transfer to blood vessels, J. Biomech. Eng. Trans. ASME 102 (1980) 110e118. [30] G. Aguilar, G.X. Wang, J.S. Nelson, Effect of spurt duration on the heat transfer dynamics during cryogen spray cooling, Phys. Med. Biol. 48 (2003) 2169e2181. [31] W. Franco, J. Liu, G.X. Wang, J.S. Nelson, G. Aguilar, Radial and temporal variations in surface heat transfer during cryogen spray cooling, Phys. Med. Biol. 50 (2005) 387e397.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research paper
Modeling skin cooling using optical windows and cryogens during laser induced hyperthermia in a multilayer vascularized tissue Rupesh Singh a, Koushik Das a, Junnosuke Okajima b, Shigenao Maruyama b, Subhash C. Mishra a, * a b
Department of Mechanical Engineering, Indian Institute of Technology Guwahati, India Institute of Fluid Science, Tohoku University, Japan
h i g h l i g h t s Skin surface cooled laser induced hyperthermia is studied. A multi-layer 2-D cylindrical tissue geometry is considered. Both Pennes and WeinbaumeJiji bioheat models are considered. Laser transport in the tissue is modeled using discrete ordinate method. Results for 4 optical windows and 2 cryogens for skin cooling are presented.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 December 2014 Accepted 4 June 2015 Available online 14 June 2015
This article deals with the spatial and the temporal evolution of tissue temperature during skin surface cooled laser induced hyperthermia. Three different skin surface cooling methodologies viz., optical window contact cooling, cryogenic spray cooling and cryogen cooled optical window contact cooling are considered. Sapphire, yttrium aluminum garnet, lithium tantalate, and magnesium oxide doped lithium niobate are the considered optical windows. The cryogens considered are liquid CO2 and R1234yf. Heat transfer in the multilayer skin tissue embedded with thermally significant blood vessels pairs is modeled using the Pennes and WeinbaumeJiji bioheat equations. WeinbaumeJiji bioheat equation is used for the vascularized tissue. Laser transport in the tissue is modeled using the radiative transfer equation. Axial and radial (skin surface) temperature distributions for different combinations of optical windows and cryogens are analyzed. Liquid CO2 cooled yttrium aluminum garnet is found to be the best surface cooling mechanism. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Bioheat transfer Laser induced hyperthermia Optical windows Cryogens Finite volume method Discrete ordinate method
1. Introduction Laser induced hyperthermia and thermal therapy are emerging as promising methods of treatment for many ailments like portwine stain, and diseases like malignant tumors [1e3]. During such procedures, light energy gets absorbed in tissue and the absorption starts from the skin surface in case of external laser irradiation. Therefore, the maximum thermal energy produced is in the skin and the tissue layers immediately below the skin surface (dermis and subcutaneous layers). The multilayer skin tissue is
* Corresponding author. E-mail address: [email protected] (S.C. Mishra). http://dx.doi.org/10.1016/j.applthermaleng.2015.06.006 1359-4311/© 2015 Elsevier Ltd. All rights reserved.
composed of epidermis, the outermost layer, the intermediate dermis, and internal vascular tissue with layers of fat. The epidermis contains melanin which is characterized by high absorption of light, and is therefore most susceptible for thermal damage during laser heating of tissues [4,5]. In any externally irradiated hyperthermia procedure, principal aim is to provide treatment to target tissue while minimizing thermal damage to the skin surface. Therefore in any such procedures, which involve high temperatures, cooling the skin is desirable. Many methods of skin cooling during laser induced hyperthermia and thermal therapy have been proposed by researchers [6,7]. Optical window surface contact cooling and cryogenic spray cooling are widely used methods for the skin surface cooling. Contact type cooling using optical windows and spray type cooling using
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Nomenclature a r, rb ho ðtÞ k keff
vessel radius density of tissue and blood normalized heat transfer coefficient thermal conductivity of tissue effective thermal conductivity hb blood perfusion rate Qm metabolic heat generation rate Ta arterial blood temperature l wavelength u average blood velocity cp ,cpb specific heat capacity of tissue and blood hcryo(0,t) surface heat transfer coefficient ho,max maximum heat transfer coefficient Ic, max intensity ka absorption coefficient p scattering phase function n number of vessel pairs ssf shape factor ss scattering coefficient t non-dimensional time
cryogens has been studied by many researchers in detail [8e10]. Zenzie et al. [11] studied three different application procedures of cooling agent, viz. passive contact plate cooling, active contact plate cooling and spray cooling. Optical windows are transparent material with applications in laser optics, electronics, and medicine [12]. For applications in laser induced hyperthermia and thermal therapy procedures, optical windows are used for providing a highly conducting contact cooling material which passes most of light through it [6,13]. This provides a way of simultaneously heating the tissue deep inside from the surface while preventing thermal damage to top surface of skin [14,15]. For contact cooling application, sapphire is most preferred material because of its wide range of transparency from UV to IR wavelengths, high strength and high conductivity. Optical quality crystalline aluminum oxide or sapphire is characterized by very high thermal conductivity, approximately 23 W/m K, high stability and hardness. Sapphire also has high threshold for optical damage [13]. In the present study, three new optical materials with thermal conductivity comparable or greater than sapphire are examined for suitability for contact cooling applications. The new optical window materials viz. sapphire (Al2O3), yttrium aluminum garnet (YAG), lithium tantalate (LiTaO3), and magnesium oxide doped lithium niobate (MgO:LiNbO3), were selected based on their ability to pass light between wavelength range of medical lasers i.e. between 500 nm and 1200 nm [16e19]. Other important properties for selection were high conductivity, low reflection loss, stability, hardness, insolubility, non-toxicity, and high threshold for optical damage. Yttrium aluminum garnet is a synthetic, hard material with wide transparency range between UV and IR. Lithium Tantalate and Magnesium Oxide doped Lithium Niobate, apart from having high thermal conductivities, also exhibits wide range of transparent window ranging from UV to IR wavelengths. A theoretical assessment of suitability of these four materials for contact cooling application is done. Cryogenic liquids, also known as cryogens, have very low boiling point (typically less than 30 C) [20e22]. At low temperatures, cryogens are in their liquid state. When exposed to normal temperature and pressure conditions, cryogens expand into large volume of gas. For spray cooling, the scattering from the cryogen is
29
ignored, as desired results can be achieved by varying the laser power. The two cryogens selected in the present study are HFO1234yf or R1234yf (Boiling point 30 C) and liquid CO2 (Boiling point 57 C), and the selection criteria followed are low boiling point, low global warming potential and low toxicity [23].
2. Model and formulation In the present study a quantitative evaluation of skin surface cooling during laser induced hyperthermia and thermal therapy is performed. Schematic of the multilayer skin tissue with deep vascularized soft tissue is shown in Fig. 1a. The tissue consists of skin layer viz. epidermis, dermis, and fatty soft tissue. The fourth (bottom) layer of tissue is a vascularized tissue with embedded large blood vessel pairs. Heat transfer in the top three layer and the fourth (bottom) layer are modeled using the blood perfusion based Pennes bioheat equation [24] and blood velocity based WeinbaumeJiji bioheat equation, respectively. The computational geometry, shown in Fig. 2a, is a 2-D axisymmetric cylinder, with a 2-D planner solution space. The modeling of laser propagation and absorption in biological tissue is done by solving the radiative transfer equation (RTE) [25]. The 3-D control volume for solution of RTE is shown in Fig. 2b. A solver for collimated radiation modeling is developed using discrete ordinate method (DOM) [26]. The volumetric radiative source term, in the form of the divergence of radiative heat flux is incorporated in Pennes bioheat as well as WeinbaumeJiji models. With radiative information computed using the discrete ordinate method, the bioheat energy equations are solved using the finite volume method (FVM) [27]. Laser of wavelengths of 1064 nm, irradiated on top surface of 2D cylindrical tissues geometry is considered. To the best of our knowledge, this is the first time when a set of radiative transfer equation for laser transport and light absorption, along with Pennes bioheat equation for blood perfused tissue, and WeinbaumeJiji bioheat equation for vascularized deep tissue is applied in conjunction. Also for numerical study of skin surface cooling, both optical window contact and cryogenic spray types, this is first attempt to model a realistic real-time scenario of laser heating of multilayer skin with deep seated tissue embedded with thermally significant blood vessels. A perfect contact between the skin and optical window is assumed for all cases of contact cooling. In practice, a near perfect contact can be achieved by applying high conductive gels on the skin. For a 2-D axisymmetric cylindrical geometry, Pennes bioheat equation is given by,
rcp
" # vT 1 v vT v2 T ¼k r þ 2 þ hb rb cpb ðTa TÞ þ Qm vt r vr vr vz
(1)
where rb and cpb are the density and the specific heat of blood, respectively. r, cp and k are the density, the specific heat, and the thermal conductivity of the tissue, respectively. With arterial blood temperature Ta ,hb is the blood perfusion rate and Qm is the volumetric metabolic heat generation rate. For the 2-D cylindrical geometry (Figs. 1 and 2a), the WeinbaumeJiji (WJ) model can be expressed as,
rc
vT 1 v vT v vT ¼ rkeff þ keff þ Qm vt r vr vr vz vz
(2)
where r, c, keff and Qm are the density, the specific heat, the effective thermal conductivity and the volumetric metabolic heat generation rate of the tissue, respectively. The effective thermal
30
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Fig. 1. Laser irradiated multilayer tissue geometry with (a) optical window contact, (b) cryogenic spray, and (c) cryogen cooled optical window contact cooling systems.
conductivity of the tissue is a function of different tissue-blood vessel configurations, and is given by [28],
"
keff
2 n prb cb a2 u ¼k 1þ 2 k ssf
# (3)
In Eq. (3), k, n, rb, cb, a and u are the thermal conductivity of the tissue, the number of vessel pairs crossing control volume surface per unit area, the density of blood, the specific heat of blood, the vessel radius and the average blood velocity in the counter current vessel pairs, respectively. For two parallel vessels with uniform surface temperature, embedded in a very large medium of tissue the shape factor ssf provides the information of resistance to the heat transfer and is given by [28,29].
ssf ¼
p cosh1 ðl=2aÞ
(4)
where l is the center to center spacing between the vessel pairs.
Both conduction and volumetric radiation has to be considered when a tissue is subjected to a laser (collimated radiation) with intensity Ic, max. In such a case, when the volumetric radiative source term, i.e., the divergence of radiative heat flux V$qr is accounted, the Pennes bioheat equation takes the form,
" # vT 1 v vT v2 T r þ 2 þ hb rb cpb ðTa TÞ þ Qm V$qr rcp ¼ k vt r vr vr vz (5) Similarly, in the WeinbaumeJiji equation, radiation to appears as a volumetric term, and accordingly the WJ bioheat model gets modified to
rc
vT 1 v vT v vT ¼ rkeff þ keff V$qr þ Qm vt r vr vr vz vz
(6)
The left (r ¼ 0, z) boundary of the computational domain (Fig. 2a) is the central axis of the cylinder and have symmetry boundary
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
31
Fig. 2. Schematic of (a) 2-D concentric cylindrical enclosure with cylindrical coordinate system and computational domain and (b) 3-D control volume needed for marching in angular space.
condition
vT vr
ðr¼0;zÞ
¼ 0 : The right (r ¼ R,z) boundary, which is the
outer surface of the cylinder and the bottom (r,z ¼ Z) surface i.e., the core body, are at isothermal condition. The top (r,z ¼ 0) boundary of the tissue is exposed to optical window of cryogenic spray. The optical window in case of contact cooling or the skin surface in case of direct spray cooling is considered under convective cooling condi tion, i.e., kvT ¼ hðT Tf Þ : A dynamic heat transfer coefvz ðr;z¼ZÞ
ficient relation is used for cryogen spray cooling. This relation (Eq. (7)) gives a time dependent effect of cryogen spray [21]
ho ðtÞ
¼
8 t > > < hcryo ð0; tÞ 1:0 0:35ðt 1Þ ¼ 0:3 0:002ðt 3Þ > ho;max > : 0:2 0:0125ðt 8Þ
t 1:0 1:0 < t 3:0 3:0 < t 8:0 8:0 < t (7)
ho ðtÞ
where is the normalized convection heat transfer coefficient, hcryo(0,t) is the surface heat convection coefficient, t is the nondimensional time, and ho,max is the maximum heat transfer coefficient during cryogenic spray. Although this relation is experimentally available for cryogen R134a [30,31], it is assumed that this relation is applicable to R1234yf and liquid CO2. The radiative transfer is governed by the radiative transfer equation and is given by [26]
Z
vI ss ¼ bI þ ka Ib þ vs 4p
0 0 0 I U p U; U dU
(8)
0
U ¼4p
where s is the distance in the direction bs , ka is the absorption coefficient, ss is the scattering coefficient, and p is the scattering phase function. With the calculated values of radiative components, the divergence of radiative heat flux is calculated using,
sT 4 G V$qr ¼ ka 4p p
(9)
For the modeling of heat transfer in the present geometry, Eq. (5) and Eq. (6) are numerically solved using FVM following the procedure stated in Ref. [27]. The radiative information of the tissue in the form of V$qr, is obtained by solving Eq. (7) and Eq. (8) using the DOM procedure. The detailed solution procedure of DOM is omitted for brevity and can be found in Ref. [26]. 3. Results and discussion The surface cooling mechanism is adopted in the present study only considers active by means of either keeping constant isothermal condition of optical window material or forced convective condition with extremely low temperature cryogen. Table 1 gives the thermal and physical properties of different layers of skin tissue and vascularized tissue. The effective thermal conductivity of vascularized tissue is calculated using Eqs. (3) and (4). The thickness for epidermis, dermis, soft tissue, and vascularized tissue considered are 100 mm, 2.0 mm, 2.4 mm, and 3.0 mm, respectively. The optical window is taken as 0.5 mm thick while the radius of the cylindrical geometry is taken as 3.0 mm. Table 2 lists the optical properties of different layers tissue at laser wavelength of l ¼ 1064 nm [2,5]. Table 3 provides the
Table 1 Thermo-physical properties of skin and vascularized tissues. Thermo-physical properties
Epidermis
Dermis
Soft tissue
Vascularized tissue
k (W/m K) rtissue (kg/m3) cp (J/kg,K) Qm (W/m3) h (1/s)
0.24 1190.0 3590.0 368.0 1.0 107
0.45 1116.0 3300.0 368.0 1.25 103
0.628 1000.0 4187.0 1190.0 3.0 103
0.5441 (Using WJ model) 1000.0 4187.0 1190.0 0.0 100
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R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
thermophysical properties of optical windows considered in the presented study. The thermophysical properties of cryogens are not considered for simulation for simplification, and only the dynamic time dependent convective effect by cryogen spray is considered. Laser power of 4 W with 1.0 mm beam radius is used for irradiation top surface of cylindrical geometry with optical window Table 2 Optical Properties of skin and vascularized tissue. Optical properties
Epidermis
Dermis
Soft tissue
Vascularized tissue
Extinction coefficient b(1/m) Scattering albedo, u
8592.0
8286.0
1100.0
1100.0
0.9586
0.994
0.963
0.963
Table 3 Thermo-physical properties of optical window materials. Material/properties
Density r (kg/m3)
Specific heat capacity cp (J/Kg K)
Thermal conductivity k (W/m K)
Sapphire YAG Lithium tantalate Magnesium oxide doped lithium niobate
3970.0 4560.0 7460.0 4640.0
419.0 590.0 430.0 628.0
22.21 14.0 46.0 38.0
placed on top surface. Fig. 3aed shows centerline temperature for different time level of exposure with different optical windows. With continuous wave laser exposure for time level ranging from 50 ms to 5 s, temperature evolution in multilayer tissue can be observed to be slightly different for four different optical windows at short time level. However as exposure time increases, this distinction in temperature profile is less (Fig. 3aed). A zoomed-in comparative centerline temperature profiles near the skin surface is presented in Fig. 4aeb. For short time level of laser exposure, i.e. 50 ms (Fig. 4a) and 100 ms (Fig. 4b), result shows that for other conditions remaining constant, YAG performs well in comparison to other optical windows. Fig. 4c shows a comparative centerline temperature profile at exposure time of 1 s. In Fig. 4c, a centerline temperature profile of tissue with sapphire window under no laser exposure is presented for providing a reference of how temperature evolves under 1 s exposure. Fig. 5a and b shows a skin surface (top layer of epidermis) temperature profile for different optical windows as contact cooling materials. Fig. 5a shows a comparison of skin surface temperature at laser exposure time of 0.5 s, and it can be seen that YAG provides maximum cooling. However at time level of 1 s and above this difference in skin temperature is less, as evident in Fig. 5b. This suggests that for short pulse laser irradiation with contact cooling, YAG may provide a better surface cooling than other optical windows. Fig. 6a and b shows the centerline temperature distribution of multilayer skin tissue (Fig. 1b) when cooled with cryogen spray
Fig. 3. Centerline temperature of skin tissue for different time of laser exposure with (a) Sapphire, (b) YAG, (c) Lithium tantalate, and (d) MgO: Lithium niobate.
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
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Fig. 4. Comparison of centerline temperature for different optical windows with laser exposure time of (a) 50 ms, (b) 100 ms, and (c) 1 s.
R1234yf and liquid CO2, respectively. Fig. 6c shows surface temperature of laser irradiated multilayer skin tissue (Fig. 1b) for two cryogens, namely R1234yf and liquid CO2. Liquid CO2 having low boiling point than R1234yf, and hence a low surface temperature can be observed in Fig. 6c for liquid CO2 as cryogen.
Cryogen cooled optical window contact cooling as shown in Fig. 1c, is the third method of surface cooling in the present study. With a laser exposure time of 0.5 s on liquid CO2 precooled optical windows, skin surface temperature of multilayer tissue is presented in Fig. 7a. Fig. 7b shows surface temperature of skin with
Fig. 5. Skin surface temperature at laser exposure time of (a) 0.5 s, and (b) 1.0 s, for different optical window cooling.
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R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Fig. 6. Centerline temperature of skin when cooled with cryogen spray (a) R1234yf, and (b) liquid CO2, and (c) surface temperature of skin with two cryogen at different exposure times.
four different optical windows cooled with liquid CO2 for a laser exposure time of 1 s. In both Fig. 7a and b it is evident that for short time of laser irradiation, the combination of liquid CO2 and YAG provides better
cooling of skin surface. A 2-D temperature contour of 5 s laser exposure with liquid CO2 cooled YAG optical window is presented in Fig. 8. Maximum temperature is well inside the tissue while preventing overheating the skin surface, as can be seen in Fig. 8.
Fig. 7. Surface temperature of skin with liquid CO2 cryogen cooled optical window at laser exposure time of 0.5 s.
R. Singh et al. / Applied Thermal Engineering 89 (2015) 28e35
Fig. 8. A 2-D temperature contour of liquid CO2 cooled YAG optical window during contact cooling of skin at laser exposure time of 5 s. Laser power of 4 W with 1 mm beam radius is used.
4. Conclusions A comparison of four different optical window material performances for surface contact cooling during laser induced hyperthermia is presented. A set of two equation for bioheat transfer modeling, namely, Pennes bioheat equation for blood perfused tissue and WeinbaumeJiji bioheat equation for tissue with embedded large blood vessel pairs, are solved in conjunction with radiative transfer equation. The radiative transfer equation was used for modeling light transport and energy deposition in the optical window and tissue. A comparative study was presented for two different cryogen with low global warming potential viz. R1234yf and liquid CO2, for spray cooling during laser induced hyperthermia. A dynamic heat transfer coefficient relation was used for cryogen spray cooling. Finally a combined cryogen - optical window cooling strategy was presented for all combination of cryogens and optical window materials. The combination of liquid CO2 and yttrium aluminum garnet was found to be more effective for short duration laser exposure hyperthermia procedures.
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