Skip to main content
SpringerLink
Log in

Theoretical investigation of thermal wave model of microwave ablation applied in prostate Cancer therapy

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

This paper presents an hyperbolic Pennes bioheat equation in cylindrical coordinate for modeling the Microwave Ablation (MWA) applied in prostate cancer. Due to recent reports, the number of patients of prostate cancer is growing by 15 million in the world each year. Since, it is shown that application of uniform microwave in prostate area of different patients may produce different temperature, the Pennes bioheat equation is considered to study the effect of perfusion term on produced temperature profiles. The solution method is Eigen value method which results in a closed form solution. The hyperbolic behavior of temperature profiles under high heat release against Fourier model is shown. Results show the importance of tissue perfusion term in estimation of temperature profiles and establish that the thermal tissue damage is expected to initiate from 1 to 3 mm above the catheter surface and to promote up to 7 mm. The solutions can be applied as a verification branch for other numerical works and can be very useful to reduce uncertainty about MWA treatments and improve the reliability of clinical protocols giving insight to the Surgeons.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

n :

Series counter

t :

Time (s)

r :

Cylindrical coordinate (mm)

z :

Cylindrical coordinate (mm)

r i :

Radius of catheter (mm)

r o :

Outer radius of biological tissue (mm)

H :

Height of affected area (mm)

A t :

Constant of proportionality

Q :

volumetric rate of heating (Wm−3)

P :

experimental power function

P r :

Reference power (J)

T :

Temperature (°C )

T b :

Blood temperature (°C )

T m :

Reference temperatures (°C )

T 0 :

Initial temperatures (°C )

c t :

Tissue specific heat (JKg−1 ° C−1)

c b :

Blood specific heat (JKg−1 ° C−1)

h :

Convection coefficient (Wm−2 ° C−1)

w :

Heat propagation speed (ms−1)

η :

Dimensionless coordinate

ζ :

Dimensionless coordinate

ρ t :

Tissue density (Kgm−3)

α t :

Thermal diffusivity (m2s−1)

κ t :

Thermal conductivity (Wm−1 ° C−1)

ρ b :

Blood density (Kgm−3)

τ q :

Thermal relaxation time (s)

ω b :

Blood perfusion rate (s−1)

β :

Microwaves rate of absorption (m−1)

θ :

Dimensionless temperature

τ :

Dimensionless time

γ :

Dimensionless constant

ψ :

Dimensionless heat source

ψ 0 :

Dimensionless constant

References

  1. Kundu B (2016) Exact analysis for propagation of heat in a biological tissue subject to different surface conditions for therapeutic applications. Appl Math Comput 285:204–216

    MathSciNet  MATH  Google Scholar 

  2. Talaee MR, Kabiri A (2017) Analytical solution of hyperbolic bioheat equation in spherical coordinates applied in radiofrequency heating. J Mech Med Biol 17(04):1750072

    Article  Google Scholar 

  3. Deshazer G, Prakash P, Merck D, Haemmerich D (2017) Experimental measurement of microwave ablation heating pattern and comparison to computer simulations. Int J Hyperth 33(1):74–82

    Article  Google Scholar 

  4. Lin SM, Li CY (2017) Semi-analytical solution of bioheat conduction for multi-layers skin subjected to laser heating and fluid cooling. J Mech Med Biol 17(02):1750029

    Article  Google Scholar 

  5. Ghosh S, Gupta DD, Chakraborty S, Das SK (2013) Superparamagnetic nanoparticle assisted hyperthermia and cooling protocol for optimum damage of internal carcinoma using computational predictive model. Heat Mass Transf 49(9):1217–1229

    Article  Google Scholar 

  6. Lv Y, Zou Y, Yang L (2012) Theoretical model for thermal protection by microencapsulated phase change micro/nanoparticles during hyperthermia. Heat Mass Transf 48(4):573–584

    Article  Google Scholar 

  7. Ramadhyani S, Abraham JP, Sparrow EM (2009) A mathematical model to predict tissue temperatures and necrosis during microwave thermal ablation of the prostate. Adv Num Heat Trans 3:345–371

    Google Scholar 

  8. Abraham JP, Sparrow EM, Ramadhyani S (2007) Numerical simulation of a BPH thermal therapy—a case study involving TUMT. J Biomech Eng 129(4):548–557

    Article  Google Scholar 

  9. Lopresto V, Pinto R, Farina L, Cavagnaro M (2017) Microwave thermal ablation: effects of tissue properties variations on predictive models for treatment planning. Med Eng Phys 46:63–70

    Article  Google Scholar 

  10. Liu D, Brace CL (2017) Numerical simulation of microwave ablation incorporating tissue contraction based on thermal dose. Phys Med Biol 62(6):2070

    Article  Google Scholar 

  11. Anvari B, Rastegar S, Motamedi M (1994) Modeling of intraluminal heating of biological tissue: implications for treatment of benign prostatic hyperplasia. IEEE Trans Biomed Eng 41(9):854–864

    Article  Google Scholar 

  12. He X, McGee S, Coad JE, Schmidlin F, Iaizzo PA, Swanlund DJ et al (2004) Investigation of the thermal and tissue injury behavior in microwave thermal therapy using a porcine kidney model. Int J Hyperth 20(6):567–593

    Article  Google Scholar 

  13. Loyd D, Karlsson M, Erlandsson BE, Sjödin JG, Ask P (1997) Computer analysis of hyperthermia treatment of the prostate. Adv Eng Softw 28(6):347–351

    Article  Google Scholar 

  14. Bernardi P, Cavagnaro M, Lin JC, Pisa S, Piuzzi E (2004) Distribution of SAR and temperature elevation induced in a phantom by a microwave cardiac ablation catheter. IEEE Trans Micro Theory Techniq 52(8):1978–1986

    Article  Google Scholar 

  15. Navarro MC, Burgos J (2017) A spectral method for numerical modeling of radial microwave heating in cylindrical samples with temperature dependent dielectric properties. Appl Math Model 43:268–278

    Article  MathSciNet  Google Scholar 

  16. Schramm W, Yang D, Haemmerich D (2006). Contribution of direct heating, thermal conduction and perfusion during radiofrequency and microwave ablation. In Engineering in Medicine and Biology Society, 2006. EMBS'06. 28th Annual International Conference of the IEEE (pp. 5013–5016). IEEE

  17. Wren J (2004) Microwave thermotherapy of prostatic enlargement-analysis of radiometric thermometry using a hybrid bio-heat equation. Comput Methods Biomech Biomed Eng 7(3):177–185

    Article  Google Scholar 

  18. Wu X, Liu B, Xu B (2016) Theoretical evaluation of high frequency microwave ablation applied in cancer therapy. Appl Therm Eng 107:501–507

    Article  Google Scholar 

  19. Wang T, Zhao G, Qiu B (2015) Theoretical evaluation of the treatment effectiveness of a novel coaxial multi-slot antenna for conformal microwave ablation of tumors. Int J Heat Mass Transf 90:81–91

    Article  Google Scholar 

  20. Chaichanyut, M., & Tungjitkusolmun, S. (2016). Microwave Ablation Using Four-Tine Antenna: Effects of Blood Flow Velocity, Vessel Location, and Total Displacement on Porous Hepatic Cancer Tissue. Computational and Mathematical Methods in Medicine, 2016

  21. Gao H, Wu S, Wang X, Hu R, Zhou Z, Sun X (2017) Temperature simulation of microwave ablation based on improved specific absorption rate method compared to phantom measurements. Comput Assis Surg 22(sup1):9–17

    Article  Google Scholar 

  22. Tung MM, Trujillo M, Molina JL, Rivera MJ, Berjano EJ (2009) Modeling the heating of biological tissue based on the hyperbolic heat transfer equation. Math Comput Model 50(5–6):665–672

    Article  MathSciNet  MATH  Google Scholar 

  23. Lee HL, Lai TH, Chen WL, Yang YC (2013) An inverse hyperbolic heat conduction problem in estimating surface heat flux of a living skin tissue. Appl Math Model 37(5):2630–2643

    Article  MathSciNet  MATH  Google Scholar 

  24. Molina JAL, Rivera MJ, Berjano E (2014) Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study. Proc R Soc A 470(2172):20140547

    Article  MathSciNet  MATH  Google Scholar 

  25. Ezzat MA, AlSowayan NS, Al-Muhiameed ZI, Ezzat SM (2014) Fractional modelling of Pennes’ bioheat transfer equation. Heat Mass Transf 50(7):907–914

    Article  Google Scholar 

  26. Kumar D, Singh S, Rai KN (2016) Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat source. Heat Mass Transf 52(6):1089–1107

    Article  Google Scholar 

  27. Kumar A, Kumar S, Katiyar VK, Telles S (2017) Phase change heat transfer during cryosurgery of lung cancer using hyperbolic heat conduction model. Comput Biol Med 84:20–29

    Article  Google Scholar 

  28. Atefi G, Talaee MR (2011) Non-fourier temperature field in a solid homogeneous finite hollow cylinder. Arch Appl Mech 81(5):569–583

    Article  MATH  Google Scholar 

  29. Talaee MR, Atefi G (2011) Non-Fourier heat conduction in a finite hollow cylinder with periodic surface heat flux. Arch Appl Mech 81(12):1793–1806

    Article  MATH  Google Scholar 

  30. Talaee MR, Kabiri A, Khodarahmi R (2018) Analytical solution of hyperbolic heat conduction equation in a finite medium under pulsatile heat source. Iran J Sci Technol, Trans Mech Eng 42(3):269–277

    Article  Google Scholar 

  31. Talaee MR, Kabiri A (2017) Exact analytical solution of bioheat equation subjected to intensive moving heat source. J Mech Med Biol 17(05):1750081

    Article  Google Scholar 

  32. Talaee M, Alizadeh M, Bakhshandeh S (2014) An exact analytical solution of non-Fourier thermal stress in cylindrical shell under periodic boundary condition. Eng Solid Mech 2(4):293–302

    Article  Google Scholar 

  33. Asmar NH (2016) Partial differential equations with Fourier series and boundary value problems. Courier Dover Publications

  34. Henriques FC Jr, Moritz AR (1947) Studies of thermal injury: I. The conduction of heat to and through skin and the temperatures attained therein. A theoretical and an experimental investigation. Am J Pathol 23(4):530

    Google Scholar 

  35. Bhowmick P, Coad JE, Bhowmick S, Pryor JL, Larson T, De La Rosette J, Bischof JC (2004) In vitro assessment of the efficacy of thermal therapy in human benign prostatic hyperplasia. Int J Hyperth 20(4):421–439

    Article  Google Scholar 

  36. Van de Sompel D, Kong TY, Ventikos Y (2009) Modelling of experimentally created partial-thickness human skin burns and subsequent therapeutic cooling: a new measure for cooling effectiveness. Med Eng Phys 31(6):624–631

    Article  Google Scholar 

  37. Ahmadikia H, Moradi A, Fazlali R, Parsa AB (2012) Analytical solution of non-Fourier and Fourier bioheat transfer analysis during laser irradiation of skin tissue. J Mech Sci Technol 26(6):1937–1947

    Article  Google Scholar 

  38. Mitra K, Kumar S, Vedevarz A, Moallemi MK (1995) Experimental evidence of hyperbolic heat conduction in processed meat. J Heat Transf 117(3):568–573

    Article  Google Scholar 

  39. Wootton JH, Ross AB, Diederich CJ (2007) Prostate thermal therapy with high intensity transurethral ultrasound: the impact of pelvic bone heating on treatment delivery. Int J Hyperth 23(8):609–622

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Railway Engineering, Iran University of Science and Technology (IUST), Tehran, 16846-13114, Iran

    Ali Kabiri & Mohammad Reza Talaee

Authors
  1. Ali Kabiri
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Reza Talaee
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Reza Talaee.

Ethics declarations

Conflict of intrest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kabiri, A., Talaee, M.R. Theoretical investigation of thermal wave model of microwave ablation applied in prostate Cancer therapy. Heat Mass Transfer 55, 2199–2208 (2019). https://doi.org/10.1007/s00231-019-02562-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-019-02562-9

Search

Navigation