ENERGY OPTIMIZATION AND BIFURCATION ANGLES IN THE MICROCIRCULATION

Our purpose was to examine the relationship between bifurcation angle and energy optimization in the arteriolar microcirculation. We measure d bifurcation angles and diameters for sequential branches along a thi rd-order feed arteriole (25 mu m) in the superfused cremaster muscle o f anesthetized (pentobarbital, 70 mg/kg) Golden hamsters (N = 51). Pre dicted bifurcation angles were calculated using the diameter data in a model designed to minimize total energy or using four different model s each designed to minimize a specific energy cost (vessel wall surfac e area, vascular volume, wall shear stress, power losses), these model s each assuming constant viscosity and that branching occurs with perf ect space filling (i.e. junction exponent, x, = 3). The range of the p redicted bifurcation angles for any model was small (+/-10 degrees), a nd they were not different for the sequential junctions along the feed arteriole, where the observed angles significantly decreased in angle along the feed (first junction, 115 +/- 4.4 degrees; second, 88 +/- 5 .2 degrees; third, 76 +/- 4.8 degrees; and last, 57 +/- 3.4 degrees). We next corrected for a nonconstant viscosity by using our in vivo tub e hematocrit data and a published relationship among diameter, tube he matocrit, and apparent viscosity. Again assuming that x = 3, the total energy minimization model now predicted that the bifurcation angle wa s always obtuse and not different for the sequential branches along th e feed arteriole (first, 125 +/- 3.3 degrees; second, 124 +/- 3.4 degr ees; third, 120 +/- 6.6 degrees; and last, 132 +/- 2.7 degrees); the p redicted angles were not correlated with the observed angles (r = 0.25 ). Using the geometric resistance (diameters) and the angles measured in vivo, and assuming constant viscosity, we next calculated the value of x for each of the bifurcation junctions for each of the four model s described above. The average value of x was not equal to 3 for any o f the four models. The value of x decreased along the feed arteriole ( first to last branch) from 2.7 +/- 0.26 to 1.6 +/- 0.22 (surface) and from 4.2 +/- 0.36 to 2.9 +/- 0.23 (volume), and x increased along the feed from 3.0 +/- 0.35 to 15.5 +/- 2.6 (shear stress) and from 40 +/- 31 to 82 +/- 49 (power loss). These calculations suggest that both cha nging viscosity and a changing value for the junction exponent are lik ely important when examining the energy optimization within the arteri olar microcirculation. (C) 1995 Academic Press, Inc.