View Full Version : SUMMARY: thermal conductivity of bone and cartilage

Smit, Th.h.
06-14-1999, 06:32 PM
Dear list subscribers,

four weeks ago I posted the following message:

"As a "bone specialist" in our department, I have been asked by a colleague
of mine to come up with numbers on the thermal conductivity of bone and
cartilage. However, I am not a specialist on thermal effects in bone and
cartilage, and I also had difficulties to find numbers in literature: I
found only two contradicting sources on the thermal conductivity of bone
(0.16-0.34 W/m/K and 1.16 W/m/K, which is really wide apart for biological
tissues which usually have 0.4-0.6 W/m/K; water, for example, has 0.6
W/m/K), and none for cartilage.

Who can give me the right numbers and -if possible- the right references?".

I received five responses, which were very helpful in finding more
literature, but did not definitively answer the original question, as values
really vary over a large range:
0.16-4.89 W/(mK) for bone. However, the lower values seem to be more
realistic, as these are presented more often and in the more recent
literature. Personally, I found the study by Biyikli et al. (1986) the
convincing one: in an elegant study, he found k=0.3 for fresh human femora.
I further think values of k>0.6 are somewhat suspect, because that is the
thermal conductivity of water.

With respect to cartilage, I did not receive any responses at all, but
Bowman et al. (1975) quotes some studies by Davis (1963; as quoted by
Benzinger et al., in Hardy (ed): Temperature: its measurement and control in
sience and industry, Krieger, Huntington, NY). Davis came up with numbers
varying from 1.37-2.76 W/(mK).

One paper that was not mentioned by the respondees (but was found
nonetheless), was by Huiskes (1980: Acta Orthopaedica Scandinavica, Suppl.
185); this includes a summary of values for bone found in literature (before
1980, obviously). For those who want to look further themselves, here are
the four responses (the fifth was in Dutch, and pointed at the study by
Biyikli mentioned above).

Mr. Smit:

Source: Chato, J.C.: Thermal Properties of Tissues., in R. Skalak and S.
Chien (eds,), HANDBOOK of BIOENGINEERING, McGraw Hill, N.Y., 1987, pp 9.1.

Table 9.2 of Dr. Chato's chapter on Thermal Properties of Tissues list the
Thermal Conductivity of bone as follows:

In vitro at room to body temperatures
Dry Bone and Bone Marrow @ 0.22W/(m x degree Celseus)

In vivo
Bone @ 0.3 - 3.1W/(m x degree Celseus) Note: Properties increase with
increased blood perfusion and water content.

Table 9.2 also list water @0.57 - 0.68W/(m x degree Celseus)

Dr. Chato's source for Table 9.2 is condensed from the following:
Chato, J.C.: A survey of thermal conductivity and diffusivity data on
biological materials, ASME Pap. No. 66-WA/HT-37,1966.

Chato, J.C.: Heat transfer in bioengineering, in B.T. Chao (ed.), Advanced
Heat Transfer, University of Illinois Press, Urbana, 1969, pp. 404-412.

Bowman, H.F., Cravalho,E.G., and Woods, M.: Theory, measurement, and
application of thermal properties of biomaterials, Annu. Rev. Biophysics.
Bioeng.,4, 43-80,1975

Chato, J.C.: Measurement of properties related to thermal behavior of
biological systems, in A. Shitzer and R.C. Eberhart (eds.), Heat Transfer in
Medicine and Biology: Analysis and Applications, Plenum Press, N.Y., 1985,
vol. 1. chap. 8, pp. 167-192 and vol. 2, App. 2, pp. 413-418.

I hope that this helps answer your questions!

Bill Pierce
Biomedical Engineer
Texas Scottish Rite Hospital for Children
Dallas, Texas
e-mail: biomech@airmail.net


Dear Theo Smit:

You may find information on the conductivity and other thermal properties
of bone and other tissues (but not of cartilage) in the following articles:

1. Bowman H.F. et al: Theoty, measurement and application of thermal
properties of biomaterials. Ann. Rev. Biophysics-Bioengineering 4: 43-80
1975. This is a comprehensive review with 319 references.

2. Biyikli S. et al: Measurement of thermal properties for human femora. J.
Biomed. Mater. Res. 20:1335-1345, 1986. This is probably one of the sources
that you have already.

3. Clattenberg R. et al: Thermal properties of cancellous bone. J. Biomed.
Mater. Res. 9: 169-182, 1975.

4. Chen H.L. et al: Specific heat of bone. Med. Biol. Eng. September 1976,
pp. 548-550.

Ariel Simkin
Ariel Simkin, PhD
Biomechanics Laboratory
Department of Orthopaedic Surgery
Hadassah University Hospital
Kiryat Hadassah, Jerusalem, Israel 91120.
Tel: 972 2 6757127 Fax: 972 2 6434434
email: ruskin@vms.huji.ac.il


Dear Theo,
> Your email was passsed to me this morning. I hope that the following
> may be of interest. I was asked this question by another researhcer
> recently, and also contacted a colleague at Bath University. We did
> not turn up any information about ligaments - even by reference to a
> book called"Physical Properties of tissues, by F A Duck, Academic
> PRess, 1990.
> I have a paper, however, in my collection called" Numerical analysis
> of electromagnetic hyperthermia of the human thorax". Medical &
> Biological Engineering & Computation, January 1988. pp50-56. Authors
> Zheng Lou, Wen-Jei Yang and T S Sandhu.
> They quote values used in the model that they describe in this paper:
> density = 1650 kg m-3
> cp = 1.43 kJ kg-1 K-1
> l = 1.46 W m-1 K-1
> This clearly supports the higher value that you have quoted in our
> email.
> If I hear of any data that contradicts this value I'll let you know.
> Kind regards,
> Andy Buxton,
> Senior Scientist,
> Protection&Performance Dept.
> Centre for Human Sciences
> Defence Evaluation & Research Agency


Theo Smit

I read your eamil regarding conductivity of tissue. I know one paper
providing some iformation on tissue conductivity. It is:

Werner J., Buse M. Temperature profiles with repect to inhomogeneity and
geometry of the human body, J.Appl.Physiol. 17-25 (1988)

I am very much interested in what you are doing. Please let me know some
detail information on your progject.

Xiaojiang Xu, Ph.D.(Dr.-Ing.)
Research Associate
HLHP Institute
211 MaxBellCenter
University of Manitoba
Winnipeg, MB


That's it! Thanks to all who responded, hope this helps.

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