Biomedical Engineering Reference

In-Depth Information

The measurement technique consists of inserting the therm-

istor probe of nominal radius
a
into a target and allowing

an initial period of thermal equilibration. Then, a current is

supplied to the thermistor with a control to maintain a con-

stant temperature rise of the probe above the initial baseline,

=−

problems in biotechnology
, ed. J.C. Chato, 16-25, New York,

ASME.

Chato, J.C. 1980. Heat transfer in blood vessels,
J. Biomech. Engr.

102:110-118.

Chen, M.M. and Holmes, K.R. 1980. Microvascular contributions

in tissue heat transfer,
Ann. N.Y. Acad. Sci.
335:137-143.

Diller, K.R. 1990a. A simple procedure for determining the spa-

tial distribution of cooling rates within a specimen during

cryopreservation I. analysis,
Proc. Inst. Mech. Engrs, J. Engr.

in Med.
204:179-187.

Diller, K.R. 1990b. Coefficients for solution of the analytical freez-

ing equation in the range of states for rapid solidification of

biological systems,
Proc. Inst. Mech. Engrs, J. Engr. in Med.

204:199-202.

Diller, K.R. 1992. Modeling of bioheat transfer processes at high

and low temperatures,
Adv. Heat Trans.
22:157-357.

Diller K.R., Valvano, J.W., and Pearce, J.A. 2005. Bioheat transfer,

in
The CRC handbook of mechanical engineering, 2nd ed.
,

ed. F. Kreith and Y. Goswami, 4-282-4-361, Boca Raton,

CRC Press.

Howell, J.R. 1982.
Catalogue of radiation configuration factors
,

New York, McGraw Hill.

Incroprera, F.P., DeWitt, D.P., Bergman, T.L. et al. 2007.

Fundamentals of heat and mass transfer,
6th ed., Hoboken,

NJ, Wiley.

Kays, W.M., Crawford, M.F., and Weigand, B. 2004.
Convective

heat and mass transfer
, 4th ed., New York, McGraw Hill.

Morse, P.M. and Feshback. H. 1953.
Methods of theoretical physics,

Parts I and II
, New York, McGraw Hill.

Pennes, H.H. 1948. Analysis of tissue and arterial blood tem-

peratures in the resting forearm.
J. Appl. Physiol.
1:92-122

(republished on 50th anniversary in 1998.
J. Appl. Physiol.

85:5-34.)

Roemer, R.B. 1990. Thermal dosimetry, in
Thermal dosimetry

and treatment planning
, ed. M. Gautherie, 119-208, Berlin,

Springer.

Roselli, R.J. and Diller, K.R. 2011.
Biotransport principles and

applications,
New York, Springer.

Shrivastava, D. and Roemer, R.B. 2006. Readdressing the issue of

thermally significant blood vessels using a countercurrent

vessel network,
J. Biomech. Engr.
128:210-216.

Siegel, R. and Howell, J.R. 2002.
Thermal radiation heat transfer,

4th ed. New York, Taylor & Francis.

Valvano, J.W. 1992. Temperature measurement,
Adv. Heat Trans
.

22:359-436.

Valvano, J.W., Allen, J.T., and Bowman, H.F. 1984. The simulta-

neous measurement of thermal conductivity, thermal dif-

fusivity, and perfusion in small volume of tissue,
J. Biomech.

Engr
. 106:198-191.

Wissler, E.H. 1998. Pennes' 1948 paper revisited.
J. Appl. Physiol.

85:35-41.

Wissler, E.H. 2008. A quantitative assessment of skin blood flow

in humans.
Eur. J. Appl. Physiol
. 104:145-157.

TTT
o
. The Pennes equation is applied in spherical coordi-

nates to model the transient temperatures in the probe and in

the surrounding tissue:

1
2

+

−

∂

∂

T

t

∂

∂

T

r

∂

∂

ABt

a

+

p

p

2

ρ

c

=

k

r

for
r
<
(1.96)

pp

p

4

r

2

π

3

−ω

∂

∂

T

t

∂

∂

∂

∂

T

r

(

)

t

2

t

(1.97)

ρ

c

=

k

r

cT T

−

for

r <a

tt

t

bb

b

t

r

where the subscripts
p
and
t
refer to the probe and tissue. The

constants
A
and
B
are characteristics of the heating regime

applied to the thermistor. The initial power input to the therm-

istor to maintain
T
p
at a constant value is maximal, followed

by a decline to a steady state value in which there is an equi-

librium between the heating of the thermistor and the rate of

loss by conduction in the tissue and convection to perfused

blood. The solution of Equations 1.96 and 1.97 is complex, and

for details the reader may reference Valvano (1992) and Diller

et al. (2005).

Currently, there is no method to quantify simultaneously the

major three parameters: the intrinsic tissue thermal conductiv-

it y,
k
m
, the tissue thermal diffusivity, α
m
, and perfusion, ω. Either

the knowledge of
k
m
is required prior to the perfusion measure-

ment, or even when
k
m
is measured in the presence of perfusion,

the thermal diffusivity cannot be measured.

acknowledgments

This chapter was prepared with support from NSF Grant No.

CBET 0966998 and the Robert and Prudie Leibrock Professorship

in Engineering.

references

Balasubramaniam, T.A. and Bowman, H.F. 1977. Thermal

conductivity and thermal diffusivity of biomaterials: A

simultaneous measurement technique,
J. Biomech. Engr
.

99:148-154.

Bejan, A. 2004.
Convection heat transfer
, Hoboken, NJ, Wiley.

Carslaw, H.S. and Jaeger, J.C. 1959.
Conduction of heat in solids,

2nd ed
., London, Oxford University Press.

Charney, C.K. 1992. Mathematical models of bioheat transfer,

Adv. Heat Trans.
22:19-155.

Chato, J.C. 1968. A method for the measurement of thermal

properties of biologic materials, in
Symposium on thermal