An improved analytical model for heat flow in cancerous tumours to avoid thermal injuries during hyperthermia

Abstract

The present study highlights an analytical hybrid scheme consisted of a shift of variables and finite integral transform for analysing a local thermal non-equilibrium (LTNE) bioheat model. This model can have utilised to be a betterment of prediction of the temperature field in the localised hyperthermia therapy (LHT) for the treatment of cancer patients. As the hyperthermia treatment is only the application in living tissues, an appropriate initial condition for the therapeutic thermal response is proposed instead of a constant temperature taken in the previous studies based on the 1-D heat flow. The present analysis suggests the therapeutic exposure time of 7776.8s (2.16 h) with constant heat flux and the exposure time of 10969.9s (3.06 h) with a sinusoidal heat flux within the usual temperature range of the hyperthermia (in a combination of thermal ablation and medium temperature hyperthermia) to be more effective in the treatment protocol. The presented results show that fatal injuries (tissue trauma, thermal burn, etc.) of internal organs might be possible to avoid by the current therapeutic condition. Therefore, this study may nullify the adverse effect of the existing model with the constant heating and consequently, the repercussion of the several therapeutic variables is to estimate with the development of a thermal profile for the suitability of a therapeutic condition. On the other hand, the present study well matches with the published analysis in case of both the theoretical and experimental (live tissues of the pig due to unavailability of real-time data on the human body) studies and it found the maximum deviation of the thermal response as 2.26% and 2.66%, respectively.

Keywords

Local thermal non-equilibrium model hyperthermia thermal response hybrid scheme

Get full access to this article

View all access options for this article.

References

Mallorya

Goginenib

Jonesc

, et al. Simone II CB. Therapeutic hyperthermia: The old, the new, and the upcoming. Crit Rev Oncol Hematol 2016; 97: 56–64.

Issels

RD.

Hyperthermia adds to chemotherapy. Eur J Cancer 2008; 44: 2546–2554.

Chu

Dupuy

DE.

Thermal ablation of tumours: biological mechanisms and advances in therapy. Nat Rev Cancer 2014; 14: 199–208.

Pfeiffer

Cold

Rose

Cytotoxic treatment of metastatic breast cancer: which drugs and drug combinations to use?

Acta Oncologica 2009; 31: 219–224.

Heldin

Rubin

Pietras

, et al. High interstitial fluid pressure – an obstacle in cancer therapy. Nat Rev Cancer 2004; 4: 806–813.

Minchinton

Tannock

IF.

Drug penetration in solid tumours. Nat Rev Cancer 2006; 6: 583–592.

Van der Zee

. Heating the patient: a promising approach? Ann Oncol 2002; 13(8): 1173–1184.

Habash

RWY

Bansal

Krewski

, et al. Thermal therapy, part 2: hyperthermia techniques. Crit Rev Biomed Eng 2006; 34(6): 491–542.

Harima

Nagata

Harima

, et al. Arandomized clinical trial of radiation therapy versus thermoradiotherapy in stage IIIB cervical carcinoma. Int J Hyperthermia 2001; 25: 338–343.

10.

Consiglieri

Continuum models for the cooling effect of blood flow on thermal ablation techniques. Int J Thermophysics 2012; 33: 864–884.

11.

Sudharsan

EYK

. Parametric optimization for tumour identification: Bioheat equation using ANOVA and the Taguchi method. Proc IMechE, Part H: J Engineering in Medicine 2000; 214(5): 50–512.

12.

EYK

Sudharsan

. An improved three-dimensional direct numerical modelling and thermal analysis of a female breast with tumour. Proc IMechE, Part H: J Engineering in Medicine 2001; 215(1): 25–37.

13.

EYK

Sudharsan

. Effect of blood flow, tumour and cold stress in a female breast: A novel time-accurate computer simulation. Proc IMechE, Part H: J Engineering in Medicine 2001; 215(4): 393–404.

14.

Pennes

HH.

Analysis of tissue and arterial blood temperature in the resting forearm. J Appl Physiol 1948; 1: 93–122.

15.

Cattaneo

A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus 1958; 247: 431–433.

16.

Vernotte

Les Paradoxes de la theorie continue de l’equation de la chaleur. Compte Rendus 1958; 246: 3154–3155.

17.

Tzou

DY.

A unified field approach for heat conduction from macro- to micro-scales. ASME J Heat Transf 1995; 117: 8–16.

18.

Fazlali

Ahmadikia

Analytical solution of thermal wave models on skin tissue under arbitrary periodic boundary conditions. Int J Thermophysics 2013; 34: 139–159.

19.

Moradi

Ahmadikia

Numerical study of the solidification process in biological tissue with blood flow and metabolism effects by the dual phase lag model. Proc IMechE, Part H: J Engineering in Medicine 2012; 226(5): 406–416.

20.

Capek

Henys

Barsa

Performance of radiofrequency ablation used for metastatic spinal tumor: Numerical approach. Proc IMechE, Part H: J Engineering in Medicine 2017; 231(9): 814–820.

21.

Jiji

LM.

Heat conduction. 3rd ed. Berlin: Springer, 2009.

22.

Xuan

Roetzel

Bioheat transfer equation of human thermal system. Chem Eng Tech 1997; 20: 268–276.

23.

Khaled

A-R

Vafai

The role of porous media in modeling flow and heat transfer in biological tissues. Int J Heat Mass Transf 2003; 46: 4989–5003.

24.

Zhang

Generalized dual-phase lag bioheat equations based on non-equilibrium heat transfer in living biological tissues. Int J Heat Mass Transf 2009; 52: 4829–4834.

25.

Afrin

Zhou

Zhang

, et al. Numerical simulation of thermal damage to living biological tissues induced by laser irradiation based on a generalized dual phase lag model. Num Heat Transf A Appl 2012; 61(7): 483–501.

26.

Yuan

Yang

C-S

Liu

S-F.

Temperature analysis of a biological tissue during hyperthermia therapy in the thermal non-equilibrium porous model. Int J Therm Sci 2014; 78: 124–131.

27.

Hooshmand

Moradi

Kherzy

Bioheat transfer analysis of biological tissues induced by laser irradiation. Int J Therm Sci 2015; 90: 214–223.

28.

Jasiński

Majchrzak

Turchan

Numerical analysis of the interactions between laser and soft tissues using generalized dual-phase lag equation. Appl Math Model 2016; 40: 750–762.

29.

Monte

Haji-Sheikh

Bio-heat diffusion under local thermal non-equilibrium conditions using dual-phase lag-based Green’s functions. Int J Heat Mass Transf 2017; 113: 1291–1305.

30.

Introduction to skin biothermomechanics and thermal pain. London, New York: Science Press Beijing and Springer-Verlag Berlin Heidelberg, 2011.

31.

Dutta

Kundu

A revised approach for an exact analytical solution for thermal response in biological tissues significant in therapeutic treatments. J Therm Biol 2017; 66: 33–48.

32.

Dutta

Kundu

Two-dimensional closed-form model for temperature in living tissues for hyperthermia treatments. J Therm Biol 2018; 71: 41–51.

33.

Dutta

Kundu

Thermal wave propagation in blood perfused tissues under hyperthermia treatment for unique oscillatory heat flux at skin surface and appropriate initial condition. Heat Mass Transf 2018; 54(11): 3199–3217.

34.

Kundu

Exact analysis of propagation of heat in biological tissue subject to different surface conditions for therapeutic applications. Appl Math Comput 2016; 285: 204–216.

35.

Nakayama

Kuwahara

A general bioheat transfer model based on theory of porous media. Int J Heat Mass Transf 2008; 51: 3190–3199.

36.

Minkowycz

Haji-Sheikh

Vafai

On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: the Sparrow number. Int J Heat Mass Transf 1999; 42: 3373–3385.

37.

Kumar

Singh

Rai

KN.

Analysis of classical Fourier, SPL and DPL heat transfer modeling biological tissues in presence of metabolic and external heat source. Heat Mass Transf 2016; 52: 1089–1107.

38.

Abdel-Hamid

Modelling non-Fourier heat conduction with periodic thermal oscillation using the finite integral transform. Appl Math Model 1999; 23: 899–914.

39.

Cotta

Naveira-Cotta

, et al. Hybrid integral transforms analysis of the bioheat equations with variable properties. Int J Therm Sci 2010; 49: 1510–1516.

40.

Liu

K-C

and Chen Y-S. Analysis of heat transfer and burn damage in a laser irradiated living tissue with the generalized dual-phase-lag model. Int J Therm Sci 2016; 103: 1–9.

41.

Andreozzi

Brunese

Iasiello

, et al. Modeling heat transfer in tumors: a review of thermal therapies. Annal Biomed Engg 2018; 47: 676–693.

42.

Ware

Nguyen

Law

, et al. A new mild hyperthermia device to treat vascular involvement in cancer surgery. Sci Rep 2017; 7(11299): 1–14.

43.

Tang

McGoron

AJ.

Increasing the rate of heating: a potential therapeutic approach for achieving synergistic tumour killing in combined hyperthermia and chemotherapy. Int J Hyperthermia 2013; 29(2): 145–155.