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Heat treatment modelling using strongly continuous semigroups.

Alaeddin Malek1, Ghasem Abbasi1

  • 1Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran.

Computers in Biology and Medicine
|April 28, 2015
PubMed
Summary
This summary is machine-generated.

This study presents an analytical solution for bioheat transfer using a non-Fourier thermal wave model. The findings offer precise simulations for thermal therapies like cancer hyperthermia and laser surgery.

Keywords:
Analytical solutionSemigroup theoryTemperature controlThermal therapyThermal wave

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Area of Science:

  • Biomedical Engineering
  • Mathematical Modeling
  • Heat Transfer

Background:

  • Bioheat transfer is crucial for understanding thermal therapies.
  • Non-Fourier heat conduction models are necessary for short-time or high-intensity heating.
  • Existing numerical methods can yield physically unrealistic results.

Purpose of the Study:

  • To develop an exact analytical solution for the non-Fourier bioheat transfer model.
  • To investigate thermal wave propagation in biological tissues under various heating conditions.
  • To provide a stable and accurate simulation method for therapeutic applications.

Main Methods:

  • Utilized strongly continuous semigroup theory and variational methods.
  • Formulated an abstract differential equation and its infinitesimal generator.
  • Proposed a contraction semigroup proven to be exponentially stable.

Main Results:

  • Developed an exact analytical solution for the non-Fourier bioheat transfer equation.
  • Simulated thermal effects for skin burning and thermal therapy across 10 models.
  • Demonstrated the absence of numerical oscillations, unlike traditional numerical methods.

Conclusions:

  • The proposed analytical solution provides accurate and stable simulations for bioheat transfer.
  • This method enhances the understanding and application of thermal therapies.
  • The semigroup approach offers a robust framework for non-Fourier heat transfer problems.