Tissue Heat Conduction in Millisecond-Picosecond Range

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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 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.


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 versus depth of tissue and in temperature distribution versus time.


Contributed by: Muhamad Hamdi and Yusof Munajat (September 2015)
Biophysics Department, University of Riau, Indonesia 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. Kamarulzaman Raja Ibrahim, and R. A. Rahman, "Terahertz Radiation Field Regime Absorption in Cancer-Health Tissue for Medical Application," Proceedings of Fourth International Conference & Workshops on Basic and Applied Science & Eleventh Regional Annual Fundamental Science Symposium (ICOWOBAS-RAFSS 2013), Senai, Johor Bahru, Malaysia, September 3–5, 2013 pp. 286–291. www.ibnusina.utm.my/links/icowobasrafss2013proceedings/ICOWOBASRAFSS2013Proceedings.pdf.

[3] M. Hamdi, " Investigation on Bio-electromagnetic Field of Terahertz Radiation Behaviors at the Interface of Brain-Fat Tissue," Asian Journal of Innovation and Entrepreneurship, 1(2), 2012. journal.uii.ac.id/index.php/inovasi_kewirausahaan/article/view/2826.

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