Page 65 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

42 BIOMECHANICS OF THE HUMAN BODY

axial temperature distribution in the limb showed that the Weinbaum-Jiji bioheat equation provided
very good agreement with the three-equation model for downstream vascular generations that are
located in the outer layer in the limb muscle, while the Pennes model yielded better description of
heat transfer in the upstream vessel generations. Considering that vessels bifurcate from approxi-
mately 1000 μm in the first generation to 150 μm in the last generation, one finds that the Pennes
source term, which was originally intended to represent an isotropic heat source in the capillaries, is
shown to describe instead the heat transfer from the largest countercurrent vessels, more than 500 μm
in diameter. The authors concluded that this was largely attributed to the capillary bleed-off from the
large vessels in these tissue regions. The capillary bleed-off appeared to result in a heat source type
of behavior that matches the Pennes perfusion term. The Weinbaum-Jiji model, on the other hand
significantly overestimated the countercurrent heat exchange in the tissue region containing larger
blood vessels. The validity of the Weinbaum-Jiji equation requires that the ratio of the thermal equi-
libration length L of the blood vessel to its physical length L be less than 0.2. This criterion was
e
found to be satisfied for blood vessels less than 300 μm in diameter under normothermic conditions.

2.3.3 Heat Transfer Models of the Whole Body

As outlined above, due to the complexity of the vasculature, continuum models appear more favor-
able in simulating the temperature field of the human body. In the Pennes bioheat equation, blood
temperature is considered to be the same as the body core temperature; in the Weinbaum-Jiji bioheat
equation, on the other hand, the effect of the blood temperature serves as the boundary condition of
the simulated tissue domain. In either continuum model (Pennes or Weinbaum-Jiji), blood tempera-
ture is an input to the governing equation of the tissue temperature. However, in situations in which
the blood temperature is actively lowered or elevated, both continuum models seem inadequate to
account for the tissue-blood thermal interactions and to accurately predict the expected body tem-
perature changes.
The human body has limited ability to maintain a normal, or euthermic, body temperature. The
vasculature facilitates the redistribution and transfer of heat throughout the body preserving a steady
core temperature for all vital organs and making the human body relatively insensitive to environ-
mental temperature changes. In extreme situation such as heavy exercise or harsh thermal environ-
ment, the body temperature can shift to a high or low level from the normal range. Active control of
body temperature is increasingly employed therapeutically in several clinical scenarios, most com-
monly to protect the brain from the consequences of either primary (i.e., head trauma, stroke) or sec-
ondary injury (i.e., after cardiac arrest with brain hypoperfusion). Mild to moderate hypothermia,
during which brain temperature is reduced to 30 to 35°C, has been studied, among others, as an
adjunct treatment for protection from cerebral ischemia during cardiac bypass injury (Nussmeier,
2002), carotid endarterectomy (Jamieson et al., 2003), and resection of aneurysms (Wagner and
Zuccarello, 2005), and it is also commonly employed in massive stroke and traumatic brain injury
patients (Marion et al., 1996, 1997). Even mild reductions in brain temperature as small as 1°C and
importantly, the avoidance of any hyperthermia, can substantially reduce ischemic cell damage
(Clark et al., 1996; Wass et al., 1995) and improve outcome (Reith et al., 1996). It seems that either
the Pennes or Weinbaum-Jiji bioheat equation alone is unable to predict how the body/blood tem-
perature changes during those situations.
Understanding the blood temperature variation requires a theoretical model to evaluate the over-
all blood-tissue thermal interaction in the whole body. The theoretical models developed by Wissler
and other investigators (Fu, 1995; Salloum, 2005; Smith, 1991; Wissler, 1985) similarly introduced
the whole body as a combination of multiple compartments. The majority of the previously pub-
lished studies introduced a pair of countercurrent artery and vein with their respective branching
(flow system) in each compartment and then modeled the temperature variations along this flow sys-
tem to derive the heat transfer between the blood vessels and tissue within each flow segment. The
accuracy of those approaches of applying a countercurrent vessel pair and their subsequent branches
has not been verified by experimental data. Such an approach is also computationally intensive,
although the models are capable of delineating the temperature decay along the artery and the
rewarming by the countercurrent vein.