bioheatExact
Compute exact solution to Pennes' bioheat equation in homogeneous media.
Syntax
T = bioheatExact(T0, S, material, dx, t) T = bioheatExact(T0, S, [D, P, Ta], dx, t)
Description
bioheatExact
calculates the exact solution to Pennes' bioheat equation in a homogeneous medium on a uniform Cartesian grid using a Fourier-based Green's function solution assuming a periodic boundary condition [1]. The function supports inputs in 1D, 2D, and 3D. The exact equation solved is given by
dT/dt = D * d^2T/dx^2 - P * (T - Ta) + S
where the coefficients are defined below. Pennes' bioheat equation is often given in the alternative form
P0 * C0 * dT/dt = Kt * d^2T/dx^2 - Pb * Wb * Cb * (T - Ta) + Q T: temperature [degC] C0: tissue specific heat capacity [J/(kg.K)] P0: tissue density [kg/m^3] Kt: tissue thermal conductivity [W/(m.K)] Pb: blood density [kg/m^3] Wb: blood perfusion rate [1/s] Ta: blood arterial temperature [degC] Cb: blood specific heat capacity [J/(kg.K)] Q: volume rate of heat deposition [W/m^3]
In this case, the function inputs are calculated by
D = Kt / (P0 * C0); P = Pb * Wb * Cb / (P0 * C0); S = Q / (P0 * C0);
If the perfusion coefficient P
is set to zero, bioheatExact
calculates the exact solution to the heat equation in a homogeneous medium.
[1] Gao, B., Langer, S., & Corry, P. M. (1995). Application of the time-dependent Green's function and Fourier transforms to the solution of the bioheat equation. International Journal of Hyperthermia, 11(2), 267-285.
Inputs
T0 |
matrix of the initial temperature distribution at each grid point [degC] | ||||||
S |
matrix of the heat source at each grid point [K/s] | ||||||
material |
material coefficients given as a three element vector in the form: material = [D, P, Ta] , where
|
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dx |
grid point spacing [m] | ||||||
t |
time at which to calculate the temperature field [s] |
Outputs
T |
temperature field at time t [degC] |
See Also
kWaveDiffusion