3-D Heat Equation Numerical Solution

Solution to the three-dimensional heat equation using alternating direction implicit (ADI) method
Updated 13 Mar 2019

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This function solves the three-dimensional Pennes Bioheat Transfer (BHT) equation in a homogeneous medium using Alternating Direction Implicit (ADI) method. The code has been developed for High-Intensity Focused Ultrasound (HIFU) treatments in tissue, but it can be applied to other heating problems as well. If desired, the solution takes into account the perfusion rate, thermal conductivity and specific heat capacity of tissue.


ADI_method.pdf - Written down numerical solution to heat equation using ADI method
solve_heat_equation_implicit_ADI.m - Code for the numerical solution using ADI method
thomas_algorithm.m - Fast algorithm for solving tridiagonal matrices
comparison_to_analytical_solution.m - An example code for comparing the solutions from ADI method to an analytical solution with different heating and cooling durations

Created by:

Visa Suomi

Cite As

Visa Suomi (2024). 3-D Heat Equation Numerical Solution (https://www.mathworks.com/matlabcentral/fileexchange/59336-3-d-heat-equation-numerical-solution), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2018a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

- Checked compatibility with Matlab R2018a and above
- Fixed bug in thermal dose calculation (time step changed from seconds to minutes)
- Time step is now given as an input variable for the ADI method

- The outputs are now given as 4-D matrices for temperature and thermal dose over time
- Perfusion rate is given now in units 1/s and new blood parameters are required
- Determination of suitable time step changed
- New calculation progress bar added
- Description updated