Solution Of Bioheat Transfer Equation Research Articles

Effect of dispersion state of the magnetic Fe3O4 nanoparticles on the thermal distribution in Hyperthermia

Introduction: Magnetic nanoparticle (MNP) hyperthermia is a promising cancer treatment approach. It is based on the evidence that by injecting MNPs such as Fe3O4 in the tumor and subjecting them to an alternating magnetic field, they release heat, generating temperatures up to 42°C that can kill cancer cells by apoptosis, usually with lowest damage to normal tissue. In previous work the temperature distribution of an ordinary tumor over the different sizes of Fe3O4 MNPs with uniform dispersion in tumor was performed. The objective of this work is to evaluate the thermal distribution of MNPs in the tumor tissue using random and array geometries due to dispersion states of the inclusions. Materials and Methods: The bio heat transfer equation (BHTE) formulated by Pennes, describes thermal processes in the human body. Since finding the exact solution of BHTE for a complex system like tumor tissue is a challenging issue, so finite element method in the COMSOL Multiphysics software is used to capture more details in predicting the temperature distribution in tumor tissue during the hyperthermia therapy. Producing the random and array numbers for distribution of the MNPs into the tumor tissue was carried out with MATLAB software. Fe3O4 MNPs with the size of 100 nm with different distributions in the tumor were simulated and the temperature distribution of the tumor and normal tissue was calculated, taking into account the thermal conductivity, density, and heat capacity. Results: The distribution of temperature in the tumor depends on Fe3O4 MNPs distribution. Uniform distribution of MNPs has appropriate distribution in the tumor and normal tissue around it. And also the agglomeration of MNPs in the tumor tissue leads to non-uniformity of the temperature distribution of the inclusions. Conclusion: In this research, the temperature distribution of an ordinary tumor over the different distributions (random and array) of Fe3O4 MNPs was investigated via the finite element method. The bio heat transfer equation was used to calculate the thermal processes in the tumor and normal tissues around it. It should be taken into account the distribution states of the MNPs into the tumor tissue and its subsequently effects on the thermal distribution. Finally, results showed that uniform distribution of the magnetic nanoparticles into the tumor tissue exhibited more appropriated results.

Estimation of temperature distribution in biological tissue by using solutions of bioheat transfer equation

AbstractA living body has a system for maintaining its temperature. We have investigated the heat transfer characteristics common to each organ and therapy using heat transfer. The one‐dimensional bioheat transfer equation with bioheat generation was converted into a dimensionless form and solved by Laplace transformation on the assumption that biological tissue is homogeneous. A dimensionless steady‐state solution and transient solution were derived analytically. These solutions can represent the characteristics of the temperature distribution common to each organ. Comparison with numerical solutions has confirmed that these solutions can be applied to estimate the temperature distribution of inhomogeneous biological tissue. It is proved that the size of the region where temperature change occurs, the steady‐state thermal penetration depth, is decided by biological properties. Furthermore, the time needed to reach a steady state, or the time it takes for biological tissue to reach a steady state, is calculated by using these solutions. Additionally, a temperature chart was proposed for each organ or tissue. This chart can serve as a guideline for medical doctors in formulating thermal therapy. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(6): 374– 386, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20210

Estimation of Temperature Distribution in Biological Tissue by Using Solutions of Bioheat Transfer Equation

A living body has a system to maintain its own temperature. We have investigated the heat transfer characteristic common to each organ and therapy. One-dimensional bioheat transfer equation with bioheat generation was transformed to dimensionless form and solved by Laplace transformation on the assumption that biological tissue is homogeneous. Dimensionless steady state solution and transient solution were derived analytically. These solutions can be represented temperature distribution of organ. It is confirmed that these solutions can be applied to estimate temperature distribution of inhomogeneous biological tissue by comparison with numerical solution. It is proved that the size of region where temperature change occurs, steady state thermal penetration depth, is decided by biological properties. Furthermore reaching time to steady state, or the time that biological tissue becomes steady state, is calculated by using these solutions. Additionally temperature chart was proposed for each organs or tissue. This temperature chart can be guideline for medical doctors in the thermal therapy.