Tissue Heat Conduction in Millisecond-Picosecond Ranges

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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 (September 2015)
(Biophysics Department, University of Riau, Indonesia and Physics Department, University of Technology Malaysia, Johor Bahru)
Open content licensed under CC BY-NC-SA



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.

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