0
Research Papers: Bio-Heat and Mass Transfer

Assessment of Thermal Damage During Skin Tumor Treatment Using Thermal Wave Model: A Realistic Approach

[+] Author and Article Information
A. K. Verma

School of Mechanical Sciences,
Indian Institute of Technology Bhubaneswar,
Bhubaneswar 752050, India
e-mail: akv11@iitbbs.ac.in

P. Rath

Mem. ASME
School of Mechanical Sciences,
Indian Institute of Technology Bhubaneswar,
Bhubaneswar 752050, India
e-mail: prath@iitbbs.ac.in

S. K. Mahapatra

Mem. ASME
School of Mechanical Sciences,
Indian Institute of Technology Bhubaneswar,
Bhubaneswar 752050, India
e-mail: swarup@iitbbs.ac.in

1Corresponding author.

Presented at the 2016 ASME 5th Micro/Nanoscale Heat & Mass Transfer International Conference. Paper No. MNHMT2016-6464.Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 15, 2016; final manuscript received February 16, 2017; published online March 7, 2017. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 139(5), 051102 (Mar 07, 2017) (9 pages) Paper No: HT-16-1389; doi: 10.1115/1.4036015 History: Received June 15, 2016; Revised February 16, 2017

In this study, a three-layered skin tissue has been modeled to assess the heat transfer characteristics in laser skin tumor–tissue interaction. A finite-volume-based two-dimensional numerical bioheat transfer model has been put together to study the damage prediction of healthy tissues by considering both Fourier and non-Fourier laws. The combination of the bioheat transfer equation with Fourier law forms the parabolic equation (Pennes model) and with the non-Fourier equation forms the hyperbolic equation (thermal wave model). In this paper, the laser source is provided on the outer layer of the skin to dismantle the undesired tumor region exemplified as inhomogeneity (tumor) present in the intermediate layer. Heat input through the laser source is on until it reaches the tumor-killing criteria. The heat transport equation has been discretized by the finite volume method (FVM). The finite-volume-based numerical model is developed in such a way that the non-Fourier model predictions can be obtained through conventional Fourier-based solver. The central difference scheme is adopted for discretizing the spatial derivative terms. An implicit scheme is applied to treat the transient terms in the model. For few cases of the hyperbolic problems, certain limitation for a chosen implicit scheme has also been addressed in this paper. The results are validated with the existing literatures. The evaluated results are based on both the Fourier and the non-Fourier model, to investigate the temperature distribution and thermal damage by ensuring irreversible thermal damage in the whole tumor region placed in the dermis layer. Thermal damage of the healthy tissue is found to be more in the time scale of the thermal wave model.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Xu, F. , and Lu, T. , 2011, Introduction to Skin Biothermomechanics and Thermal Pain, Springer, Berlin.
Mitra, K. , Kumar, S. , Vedavarz, A. , and Moallemi, M. K. , 1995, “ Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat,” ASME J. Heat Transfer, 117(3), pp. 568–573. [CrossRef]
Kaminski, W. , 1990, “ Hyperbolic Heat Conduction Equation for Materials With a Nonhomogeneous Inner Structure,” ASME J. Heat Transfer, 112(3), pp. 555–560. [CrossRef]
Richardson, A. W. , Imig, C. G. , Feucht, B. L. , and Hines, H. M. , 1950, “ The Relationship Between Deep Tissue Temperature and Blood Flow During Electromagnetic Irradiation,” Arch. Phys. Med. Rehabil., 31(1), pp. 19–25. [PubMed]
Roemer, R. B. , Oleson, J. R. , and Cetas, T. C. , 1985, “ Oscillatory Temperature Response to Constant Power Applied to Canine Muscle,” Am. J. Physiol., 249(2), pp. R153–R158. [PubMed]
Herwig, H. , and Beckert, K. , 2000, “ Experimental Evidence About the Controversy Concerning Fourier or Non-Fourier Heat Conduction in Materials With a Nonhomogeneous Inner Structure,” Heat Mass Transfer, 36(5), pp. 387–392. [CrossRef]
Graßmann, A. , and Peters, F. , 1999, “ Experimental Investigation of Heat Conduction in Wet Sand,” Heat Mass Transfer, 35(4), pp. 289–294. [CrossRef]
Roetzel, W. , Putra, N. , and Das, S. K. , 2003, “ Experiment and Analysis for Non-Fourier Conduction in Materials With Non-Homogeneous Inner Structure,” Int. J. Therm. Sci., 42(6), pp. 541–552. [CrossRef]
Banerjee, A. , Ogale, A. A. , Das, C. , Mitra, K. , and Subramanian, C. , 2005, “ Temperature Distribution in Different Materials Due to Short Pulse Laser Irradiation,” Heat Transfer Eng., 26(8), pp. 41–49. [CrossRef]
Jeong, S. W. , Liu, H. , and Chen, W. R. , 2003, “ Temperature Control in Deep Tumor Treatment,” Proc. SPIE, 5068, pp. 210–216.
Jiao, J. , and Guo, Z. , 2009, “ Thermal Interaction of Short Pulsed Laser Focused Beams With Skin Tissues,” Phys. Med. Biol., 54(13), pp. 4225–4241. [CrossRef] [PubMed]
Robinson, D. S. , Parel, J. M. , Denham, D. B. , Gonzalez-Cirre, X. , Manns, F. , Milne, P. J. , Schachner, R. D. , Herron, A. J. , Comander, J. , and Hauptmann, G. , 1998, “ Interstitial Laser Hyperthermia Model Development for Minimally Invasive Therapy of Breast Carcinoma,” J. Am. Coll. Surg., 186(3), pp. 284–292. [CrossRef] [PubMed]
Sajjadi, A. Y. , Mitra, K. , and Guo, Z. , 2013, “ Thermal Analysis and Experiments of Laser-Tissue Interactions: A Review,” Heat Transfer Res., 44(3–4), pp. 345–388. [CrossRef]
Dewhrist, M. W. , Viglianti, B. L. , Lora-Michiels, M. , Hoopes, P. J. , and Hanson, M. , 2003, “ Thermal Dose Requirement for Tissue Effect: Experimental and Clinical Findings,” Proc. SPIE, 4954, pp. 37–57.
Pennes, H. H. , 1948, “ Analysis of Tissue and Arterial Blood Temperature in the Resting Forearm,” J. Appl. Physiol., 1(2), pp. 93–122. [PubMed]
Yang, W. H. , 1993, “ Thermal (Heat) Shock Biothermomechanical Viewpoint,” ASME J. Biomed. Eng., 115(4B), pp. 617–621. [CrossRef]
Verma, A. K. , and Mahapatra, S. K. , 2016, “ Thermal Wave Model for Analysis of Multilayer Tissue Medium in Presence of Inhomogeneity in Laser Treatment,” ASME Paper No. MNHMT2016-6464.
Liu, J. , Chen, X. , and Xu, L. X. , 1999, “ New Thermal Wave Aspects on Burn Evaluation of Skin Subjected to Instantaneous Heating,” IEEE Trans. Biomed. Eng., 46(4), pp. 420–426. [CrossRef] [PubMed]
Shih, T.-C. , Yuan, P. , Lin, W.-L. , and Kou, H.-S. , 2007, “ Analytical Analysis of the Pennes Bioheat Transfer Equation With Sinusoidal Heat Flux Condition on Skin Surface,” Med. Eng. Phys., 29(9), pp. 946–953. [CrossRef] [PubMed]
Xu, F. , Seffen, K. A. , and Lu, T. J. , 2008, “ Non-Fourier Analysis of Biothermomechanics,” Int. J. Heat Mass Transfer, 51(9–10), pp. 2237–2259. [CrossRef]
Ahmadikia, H. , Fazlali, R. , and Moradi, A. , 2012, “ Analytical Solution of the Parabolic and Hyperbolic Heat Transfer Equations With Constant and Transient Heat Flux Conditions on Skin Tissue,” Int. Commun. Heat Mass Transfer, 39(1), pp. 121–130. [CrossRef]
Ströher, G. R. , and Ströher, G. L. , 2014, “ Numerical Thermal Analysis of Skin Tissue Using Parabolic and Hyperbolic Approaches,” Int. Commun. Heat Mass Transfer, 57, pp. 193–199. [CrossRef]
Askarizadeh, H. , and Ahmadikia, H. , 2015, “ Analytical Study on the Transient Heating of a Two-Dimensional Skin Tissue Using Parabolic and Hyperbolic Bioheat Transfer Equations,” Appl. Math. Modell., 39(13), pp. 3704–3720. [CrossRef]
Cattaneo, C. , 1958, “ A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation,” Comptes Rendus, 247, pp. 431–433.
Vernotte, P. , 1958, “ Paradoxes in Theory of Continuity for Heat Equation,” Comptes Rendus, 46(22), pp. 3154–3155.
Henriques, F. C. , and Moritz, A. R. , 1947, “ Study of Thermal Injury: I. The Conduction of Heat to and Through Skin and the Temperature Attained Therein. A Theoretical and an Experimental Investigation,” Am. J. Pathol., 23(4), pp. 531–549.
Moritz, A. R. , and Henriques, F. C. , 1947, “ Studies of Thermal Injury: II. The Relative Importance of Time and Surface Temperature in the Causation of Cutaneous Burns,” Am. J. Pathol., 23(5), pp. 695–720. [PubMed]
Henriques, F. C. , 1947, “ Study of Thermal Injuries—V: The Predictability and the Significance of Thermally Induced Rate Processes Leading to Irreversible Epidermal Injury,” Arch. Pathol., 43(5), pp. 489–502.
Diller, K. R. , 1992, “ Modeling of Bioheat Transfer Processes at High and low Temperatures,” Adv. Heat Transfer, 22, pp. 157–357.
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York.
Zhang, H. , 2008, “ Lattice Boltzmann Method for Solving the Bioheat Equation,” Phys. Med. Biol., 53(3), pp. N15–N23. [CrossRef] [PubMed]
Cohen, M. L. , 1977, “ Measurement of the Thermal Properties of Human Skin. A Review,” J. Invest. Dermatol., 69(3), pp. 333–338. [CrossRef] [PubMed]
Emery, A. F. , and Sekins, K. M. , 1982, “ The Use of Heat Transfer Principles in Designing Optimal Diathermy and Cancer Treatment Modalities,” Int. J. Heat Mass Transfer, 25(6), pp. 823–834. [CrossRef]
Xu, F. , Lu, T. J. , Seffen, K. A. , and Ng, E. Y. K. , 2009, “ Mathematical Modeling of Skin Bioheat Transfer,” ASME J. Appl. Mech. Rev., 62(5), p. 050801. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

A schematic representation of the physical domain (a) and computational domain (b)

Grahic Jump Location
Fig. 2

(a) Validation with the experimental results provided by Mitra et al. [2], (b) validation of the 1D work with Ref. [18] at x=0.00208 m, for Δt=0.1 s and oscillated solution for Δt=0.01 s, and (c) validation of the 2D code with Ref. [31] for transient temperature distribution along the symmetry line with heat source 100×t  W/m2 inside the tumor region

Grahic Jump Location
Fig. 3

(a) Grid-independent control volume test along the symmetry line (threshold temperature reaching time) and (b) time-independent test at the top surface center location of the whole domain

Grahic Jump Location
Fig. 4

Effect of thermal wave propagation on dimensionless temperature distribution for dimensionless heat flux qo*=6 along the lines A, B, C, and D around tumor cells (at threshold temperature reaching time)

Grahic Jump Location
Fig. 5

Effect of thermal wave propagation on dimensionless temperature distribution for dimensionless heat flux qo*=18 along the lines A, B, C, and D around tumor cells (at threshold temperature reaching time)

Grahic Jump Location
Fig. 9

At threshold temperature reaching time inside the tumor cell, indices a and b correspond to Vn=0  and 0.25, and 1, 2, and 3 correspond to dimensionless temperature distribution, dimensionless thermal damage parameter, and damaged region, respectively

Grahic Jump Location
Fig. 8

At dimensionless time t*=0.05, indices a and b correspond to Vn=0  and 0.25, and 1, 2, and 3 correspond to dimensionless temperature distribution, dimensionless thermal damage parameter, and damaged region, respectively

Grahic Jump Location
Fig. 7

At dimensionless time t*=0.03, indices a and b correspond to Vn=0  and 0.25, and 1, 2, and 3 correspond to dimensionless temperature distribution, dimensionless thermal damage parameter, and damaged region, respectively

Grahic Jump Location
Fig. 6

Dimensionless heat flux versus dimensionless time (threshold temperature reaching time)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In