Heat and Mass Transfer

, Volume 55, Issue 8, pp 2199–2208 | Cite as

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

  • Ali Kabiri
  • Mohammad Reza TalaeeEmail author


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.



Series counter


Time (s)


Cylindrical coordinate (mm)


Cylindrical coordinate (mm)


Radius of catheter (mm)


Outer radius of biological tissue (mm)


Height of affected area (mm)


Constant of proportionality


volumetric rate of heating (Wm−3)


experimental power function


Reference power (J)


Temperature (°C )


Blood temperature (°C )


Reference temperatures (°C )


Initial temperatures (°C )


Tissue specific heat (JKg−1 ° C−1)


Blood specific heat (JKg−1 ° C−1)


Convection coefficient (Wm−2 ° C−1)


Heat propagation speed (ms−1)

Greek symbols


Dimensionless coordinate


Dimensionless coordinate


Tissue density (Kgm−3)


Thermal diffusivity (m2s−1)


Thermal conductivity (Wm−1 ° C−1)


Blood density (Kgm−3)


Thermal relaxation time (s)


Blood perfusion rate (s−1)


Microwaves rate of absorption (m−1)


Dimensionless temperature


Dimensionless time


Dimensionless constant


Dimensionless heat source


Dimensionless constant


Compliance with ethical standards

Conflict of intrest

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


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Railway EngineeringIran University of Science and Technology (IUST)TehranIran

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