Tissue Heat Conduction in Millisecond-Picosecond Ranges

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 picosecond 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.
In a small tissue volume element of a homogeneous medium, the 1D heat conduction is given by
where is density (), the specific heat (), and the thermal conductivity of the tissue (). Analytical solution of the 1D heat conduction equation gives:
where and are determined by the boundary and initial conditions. Both of these solutions show the same general trend in temperature distribution vs. depth of tissue and in temperature distribution vs. time.
  • Contributed by: Muhamad Hamdi and Yusof Munajat
  • (Biophysics Department, University of Riau, Indonesia and Physics Department, University of Technology Malaysia, Johor Bahru)


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshots 1, 2, 3, and 4: Skin tissue shows heat conduction (with maximum tissue depth and time steps ) with a small temperature change gradually approaching zero. It is thinner than fat tissue () but thicker than tumor () or muscle tissue (), correlated with the contrasting tissue structures.
[1] H. Ilham, Introduction to Biophysics, 1st ed., Pekanbaru, Riau, Indonesia: RUEDC-Press, 2007.
[2] M. Hamdi, Y. Munajat, R. K. R. Ibrahim, and R. A. Rahman, "Terahertz Radiation Field Regime Absorption in Cancer-Health Tissue for Medical Application," presentation given at The 4th International Conference & Workshop on Basic and Applied Science (2013), Johor Bahru, Malaysia.
[3] M. Hamdi, "Investigation on Bio-Electromagnetic Field of Terahertz Radiation Behaviors at the Interface of Brain-Fat Tissue," Journal of Innovation and Entrepeneurship, 1(2), 2012 pp. 86–95.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+