What determines the caliber of axonal branches? We pursue the hypothesis that the axonal caliber has evolved to minimize signal propagation delays, while keeping arbor volume to a minimum. We show that for a general cost function the optimal diameters of mother (do) and daughter (d], d2 ) branches at a bifurcation obey h a ranc mg aw: e envatIOn re les on t e fact that the conduction speed scales with the axon diameter to the power V (v = 1 for myelinated axons and V = 0.5 myelinated axons). We test the branching law on the available experimental data and find a reasonable agreement.
d v+2 d v+2 d v+2 Th d " 0 = ] + 2