# Tissue Heat Conduction in Millisecond-Picosecond Range

Tissue Heat Conduction in Millisecond-Picosecond Range

This Demonstration explores transient 1D heat conduction through several types of biological tissue in the millisecond to picosecond time range, based on theoretically derived analytical solutions. We are interested particularly in relaxation times of pulse propagation. The results for time intervals of one second or longer show a constant temperature or a steady state centered about one temperature. By contrast, millisecond to picoseconds time ranges display a small but significant temperature change as the depth varies from mm to a depth at which . You can select time intervals for several types of tissue (skin, fat, tumor, or muscle) to obtain temperature distributions as functions of tissue depth.

x=0

T=0°C

In a small tissue-volume element of a homogeneous medium, the 1D heat conduction is given by

ρ

t

c

t

∂T

∂t

κ

t

2

∂

∂

2

x

-3

m

where is density ( ), the specific heat ( ), and the thermal conductivity of the tissue ( ). Analytical solution of the 1D heat conduction equation gives:

ρ

t

kg

-3

m

c

t

nJ

-1

kg

-1

°C

κ

t

µW

-1

m

°C

T(x,t)=(A+B)

-t

κ

t

2

β

e

-iβx

e

iβx

e

and

T(x,t)=A

1

t

-4t

2

x

κ

t

e

where and are determined by the boundary and initial conditions. Both of these solutions show the same general trend in temperature distribution versus depth of tissue and in temperature distribution versus time.

A

B