Biomedical Engineering Reference
In-Depth Information
This circuit element can be included in a radiation network
model as appropriate to represent the effect of an interstitial
medium between radiating surfaces.
Note that in this analysis of radiation, all of the equivalent
electrical networks contain only resistors, and specifically there
are no capacitors. The explicit interpretation of this arrange-
ment is that all of the radiation processes considered are at
steady state such that no energy storage occurs. For our present
analysis, the mass of all radiating bodies has been neglected.
Since many thermal radiation processes are approximated as
surface phenomena, this is a reasonable assumption. Under
conditions that demand more comprehensive and sophisticated
analysis, this assumption may have to be relaxed, which leads to
a significant increase in the complexity of the thermal radiation
analysis.
occur, altering the temperatures of both the blood and the tissue.
Perfusion-based heat transfer interaction is critical to a number
of physiological processes such as thermoregulation and inflam-
mation. The blood/tissue thermal interaction is a function of
several parameters including the rate of perfusion and the vas-
cular anatomy, which vary widely among the different tissues,
organs of the body, and pathology. Diller et al. (2005) contains
an extensive compilation of perfusion rate data for many tissues
and organs and for many species.
The rate of perfusion of blood through different tissues and
organs varies over the time course of a normal day's activi-
ties, depending on factors such as physical activity, physiologi-
cal stimulus, circadian cycle, and environmental conditions.
Further, many disease processes are characterized by alterations
in blood perfusion, and some therapeutic interventions result
in either an increase or decrease in blood flow in a target tis-
sue. For these reasons, it is very useful in a clinical context to
know what the absolute level of blood perfusion is within a given
tissue. There are numerous techniques that have been devel-
oped for this purpose over the past several decades. In some of
these techniques, the coupling between vascular perfusion and
local tissue temperature is applied to advantage to assess the
flow through local vessels via inverse solution of equations that
model the thermal interaction between perfused blood and the
surrounding tissue.
Pennes (Pennes 1948; Wissler 1998) published the seminal
work on developing a quantitative basis for describing the ther-
mal interaction between tissue and perfused blood. His work
consisted of a series of experiments to measure temperature
distribution as a function of radial position in the forearms of
nine human subjects. A butt-junction thermocouple was passed
completely through the arm via a needle inserted as a tempo-
rary guideway, with the two leads exiting on opposite sides of the
arm. The subjects were unanesthetized so as to avoid the effects
of anesthesia on blood perfusion. Following a period of normal-
ization, the thermocouple was scanned transversely across the
mediolateral axis to measure the temperature as a function of
radial position within the interior of the arm. The environment
in the experimental suite was kept thermally neutral during the
experiments. Pennes's data showed a temperature differential of
three to four degrees between the skin and the interior of the
arm, which he attributed to the effects of metabolic heat genera-
tion and heat transfer with arterial blood perfused through the
microvasculature.
Pennes proposed a model to describe the effects of metabo-
lism and blood perfusion on the energy balance within tissue.
These two effects were incorporated into the standard thermal
diffusion equation, which is written in its simplified form as
1.3 Special Features of Heat transfer
in Biomedical Systems
Living tissues present a special set of complications for solving
heat transfer problems. Among the often-encountered issues
are: composite materials structures, anisotropic properties,
complex geometric shapes not amenable to convenient math-
ematical description, nonhomogeneously distributed internal
energy generation, constitutive properties that may change dra-
matically with temperature, nonlinear feedback control (such
as for thermoregulatory function), and a diffuse and complex
internal circulation of blood that has a significant effect on the
body's thermal state and energy distribution via convective heat
transfer. Plus, therapeutic, diagnostic, and prophylactic proce-
dures that are energy based, such as hyperthermia protocols,
frequently introduce intricate formulations for energy deposi-
tion in tissue as a function of time and position. This latter topic
is addressed in detail in other chapters throughout this text and
will not be discussed here except to note that the various energy
sources applied to create a state of hyperthermia are embod-
ied into the
Q
gen
term in the conservation of energy equation
(Equation 1.1). Neither does space allow us to discuss all of the
unique features of heat transfer in living tissues as listed before.
There are many more comprehensive analyses and presentations
of bioheat transfer to which the reader is directed (Charney 1992;
Diller 1992; Diller et al. 2005; Roemer 1990; Roselli and Diller
2011). Here we will discuss only two aspects of bioheat transfer
that are of greatest relevance to the design and application of
therapeutic hypothermia protocols: the influence of convective
flow of blood through blood vessels and the thermal properties
of living tissues, including local blood perfusion rates.
∂
∂
=⋅ +ρ ω−+
T
t
() (
)
1.3.1 Blood perfusion Effects
Bioheat transfer processes in living tissues are often influenced
by blood perfusion through the vascular network. When there
is a significant difference between the temperature of blood and
the tissue through which it flows, convective heat transport will
ρ
c
kT
c
TTQ
(1.95)
bb
met
b
where ω
b
is perfusion of blood through the microvasculature in
units of volume of blood flowing per unit time per unit of tissue
volume, and the subscript
b
denotes a property of blood.
