Related Experiment Video
Updated: Sep 11, 2025
04:35
Author Spotlight: Simulation and Analysis of the Temperature Rise of Ring Main Unit Equipment
Published on: July 5, 2024
2.0K
The Key Role of Thermal Relaxation Time on the Improved Generalized Bioheat Equation: Analytical Versus Simulated
Alexandra Maria Isabel Trefilov1, Mihai Oane1, Liviu Duta1
1National Institute for Laser, Plasma and Radiation Physics, 077125 Magurele, Romania.
Materials (Basel, Switzerland)
|August 14, 2025
Summary
This study develops an advanced analytical model for heat transfer in biological tissues, improving thermal therapy precision. The refined bioheat equation offers more realistic simulations for laser treatments.
Area of Science:
- Biomedical Engineering
- Thermal Physics
- Mathematical Modeling
Background:
- The Pennes bioheat equation is standard for tissue heat transfer but lacks analytical solutions.
- Existing models often use classical Fourier heat conduction, neglecting thermal relaxation times.
Purpose of the Study:
- To develop a novel 3D analytical model for heat transfer in biological tissues using MATHEMATICA.
- To refine the Pennes bioheat equation by incorporating non-Fourier heat transfer and localized heating.
- To derive closed-form analytical solutions for both classical and improved bioheat equations.
Main Methods:
- Developed a 3D analytical model in MATHEMATICA.
- Incorporated non-Fourier heat transfer (relaxation time) and Dirac functions.
- Validated the model using COMSOL Multiphysics simulations.
- Derived closed-form analytical solutions for enhanced bioheat equations.
Main Results:
- Achieved a generalized analytical model for bioheat transfer.
- Demonstrated agreement between analytical (MATHEMATICA) and numerical (COMSOL) results.
- Identified an optimal thermal relaxation time of 1.16 s for simulations.
- Investigated thermal exposure times from 0.01 s to 120 s.
Conclusions:
- The developed analytical model provides a more realistic simulation of heat transfer in biological tissues.
- The refined bioheat equation enhances understanding of thermal therapies, particularly laser irradiation.
- This work supports advancements in optimizing laser-based medical treatments and thermal therapies.
Related Concept Videos
02:46Quantifying Heat
56.0K
Thermal Energy Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a quantitative measure of “hot” or “cold”, which depends on the amount of thermal energy. When the atoms and molecules in an object are moving or vibrating quickly, they have a higher average kinetic energy (KE) (or higher thermal energy), and the object is perceived as “hot”, or it is described as being at a...
56.0K
01:27Thermal expansion and Thermal stress: Problem Solving
1.3K
San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in...
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in...
1.3K
01:16Thermal Sigmatropic Reactions: Overview
2.2K
Sigmatropic rearrangements are a class of pericyclic reactions in which a σ bond migrates from one part of a π system to another. These are intramolecular rearrangements where the total number of σ and π bonds remain unchanged.
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
Sigmatropic shifts are classified based on an order term [i, j ], where i and j indicate the number of atoms across which each end of the σ bond migrates. Below are examples of a [3,3] sigmatropic shift in...
2.2K
01:28Atomic Nuclei: Types of Nuclear Relaxation
386
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
386
01:11Temperature and Thermal Equilibrium
7.2K
Heat and temperature are essential concepts for everyone every day. The study of heat and temperature is part of an area of physics known as thermodynamics. It is not always easy to distinguish heat and temperature.
The concept of temperature has evolved from the common concepts of hot and cold. The scientific definition of temperature explains more than just our sense of hot and cold. Temperature is operationally defined as the quantity measured with a thermometer. Furthermore, temperature is...
The concept of temperature has evolved from the common concepts of hot and cold. The scientific definition of temperature explains more than just our sense of hot and cold. Temperature is operationally defined as the quantity measured with a thermometer. Furthermore, temperature is...
7.2K
01:20Mechanisms of Heat Transfer II
3.5K
In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...
3.5K