This study was undertaken to gain a better understanding of the countercurrent heat exchange of thermally significant blood vessels in skeletal muscle by measuring the vascular structure and flow in an exteriorized rat spinotrapezius muscle and estimating the enhancement in the effective thermal conductivity of the muscle. Detailed anatomic measurements of the number density and length of countercurrent vessel pairs between 45 and 165 μm diameter were obtained. Moreover, diameter and blood flow in the 1A to 3A vessels were measured for muscles in which pharmacological vasoactive agents were introduced, allowing one to vary the local blood flow Peclet number from 1 to 18 in the major feeding arteries. These combined measurements have been used to estimate the range of possible enhancement in the effective thermal conductivity of the tissue. The newly derived conduction shape factor in Zhu et al. [23] for countercurrent vessels in two-dimensional tissue preparations was used in this analysis. Our experimental data indicated that the value of this conduction shape factor was about one-third to two-thirds the value for two countercurrent vessels of the same size and spacing in an infinite medium. The experiment also revealed that the Weinbaum–Jiji expression for keff was valid for the spinotrapezius muscle when the largest vessels were less than 195 μm diameter. A fivefold increase in keff was predicted for 195 μm diameter vessels. Vasoregulation was also shown to have a dramatic effect on keff. A tissue that exhibits only small increases in keff due to countercurrent convection in its vasoconstricted state can exhibit a more than fivefold increase in Keff in its vasodilated state.
Correction to: thermal conductivity of porous sintered metal powder and the Langmuir shape factor
