Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma
Abstract
:Simple Summary
Abstract
1. Introduction
2. Mathematical MGT Bioheat Model
3. Formulation of the Problem
4. Solution in the Laplace Transform Space
5. Evaluation of the Thermal Damages
6. Numerical Results
- The classical Pennes bioheat transfer (CPBT) model can be obtained when we set .
- The Cattaneo–Vernotte Pennes bioheat transfer (CVPBT) model can be obtained when we put and take .
- The Pennes bioheat transfer model based on Green and Naghdi’s theory of type II (GNPBTII) can be obtained when the terms, including and are neglected.
- The Pennes bioheat transfer model based on Green and Naghdi’s theory of type III (GNPBTIII) can be obtained when the thermal relaxation time is neglected .
- The new MGTPBT model is attained when .
- The temperature distribution in the tumor and normal tissues is greatly influenced by the thermal factors and .
- Including the relaxation coefficient, in the CVPBT and MGTPBT models may mean that the temperature decrease is slowed down.
- The predictions of the GNPBTIII and MGTPBT models are incompatible.
- The magnitude is larger in the case of the GNPBTIII model than in the case of the MGTPBT model, although the graph shows similar results for both models.
- The thermoelastic results of the GNPBTIII model differ significantly from the GNPBTII model due to energy losses in the case of the first model.
- In contrast to previous modified bioheat models, the results of the GNPBTIII model of thermoelasticity indicate convergence with the results of the conventional CPBT model, which do not fade in heat rapidly within the tumor and normal tissues, respectively.
- The profiles of the temperature differences between the MGTPBT and CVPBT models were compared. It is clear from the figure that the behavior and convergence of the results of both models are quite similar, with only slight differences in magnitude.
- The blood temperature distribution slightly differed between the MGTPBT and GNPBTII models.
- Heat wave propagation may realistically predict the temperature distribution in living tissues. The cooling function of the blood circulation keeps the tissue temperature from increasing but does not affect the speed of the thermal diffusion. According to this new hypothesis, the relaxation coefficient will become a new measure of the efficiency of the vital heat transfer in living tissues.
- Transferring thermal energy away from the interface is difficult to apply. As a result, the temperature gradually decreases. It indicates that by lowering the relaxation coefficient, the heat transfer capacity of the medium can be increased.
7. Conclusions
- The rate of change of blood perfusion has a significant effect on the transfer of bioheat in a tumor and normal tissue. Because the skin temperature is higher than the arterial temperature, the blood perfusion acts as a cooling agent. The perfusion rate is proportional to the amount of heat energy extracted from the blood.
- The results were influenced by the relaxation durations used and the perfusion of the blood. It is also clear that more experimental research is needed to determine the delay times more accurately.
- It was found that the presence of a thermal relaxation time in the biothermal conduction equation significantly affects the temperature spread in a tumor and in normal tissue over time. As a result, having a thermal relaxation time reduces the temperature drop as well as the tissue depth.
- This MGT Pennes bioheat model adds some additional dimensions to the investigation of transient heat transfer mechanisms in biological systems.
- The propagation of thermal waves may provide a realistic prediction of the temperature distribution in living tissue.
- In the case of the MGT Pennes biothermal model, the temperature spreads with a finite speed in the tumor and the normal tissue instead of an infinite speed in the classical model.
- The relaxation parameter can be proposed as a novel measure of bioheat transfer efficiency in living tissues in the revolutionary MGT Pennes bioheat model.
- The findings reported here may be of value for the design of many biomedical and biomechanical application areas, including in healthy and diseased tissues, as well as for the development of theoretical knowledge of bioheat transfer in spherical tissue architecture.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ragab, M.; Abouelregal, A.E.; AlShaibi, H.F.; Mansouri, R.A. Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma. Biology 2021, 10, 1259. https://doi.org/10.3390/biology10121259
Ragab M, Abouelregal AE, AlShaibi HF, Mansouri RA. Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma. Biology. 2021; 10(12):1259. https://doi.org/10.3390/biology10121259
Chicago/Turabian StyleRagab, Mahmoud, Ahmed E. Abouelregal, Huda F. AlShaibi, and Rasha A. Mansouri. 2021. "Heat Transfer in Biological Spherical Tissues during Hyperthermia of Magnetoma" Biology 10, no. 12: 1259. https://doi.org/10.3390/biology10121259