Thus, the optimal radius for a blood vessel when the minimum rate of
energy is required for steady flow is proportional to the 1/3 power of
Optimizing Branching Radii and
Now consider a bifurcation with a mother vessel with length
ro that branches into
daughter vessels with lengths and radii of 11, 12
and rl and r2, respectively, as shown in Fig. 5.4.2. It is assumed that the
vessels are lying in the same plane.
a bifurcating vascular branching junction.
vessel branches into two daughter vessels. Lumen radius, length and bifurcation angles
We have for the cost function that assumes optimum rate of energy
usage given by equation (5.4.1
The conservation of mass gives the equation of continuity of
which gives rise to the relation for the branching radii, from