PLoS supp. material by Hermann Cuntz
A quadratic diameter taper optimizes current transfer in cables from any point
to the root (Cuntz, Borst and Segev 2007, Theor Biol Med Model, 4:21, see figure).
For different cable lengths, different parameter sets can be derived to fit
the quadratic equation with distance x:
y = P1x2 + P2x + P3.
Each single triplet P corresponds to the best fit to a segment of a specific cable length
ldend. In order to map a quadratic diameter to a full tree,
each path from terminal to the root is compared to its closest value
in a predetermined set of ldend.
Then the quadratic equation parameters P are chosen according to ldend.
This is done for all paths from root to terminal points
and for each node the diameter is set to the average of all local diameters
of all paths leading through that node
P and ldend depend on the total leak and the minimal diameter:
these have to be adjusted by the parameters scale and offset respectively
The resulting tree diameter mapping compares well
with the original even though it is set merely by two parameters,
the scale and offset values.
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