Fractal analysis and imaging of the proximal nephron cell.
Welling, D., J. Urani, L. Welling, and E. Wagner.
RESEARCH SERVICE, DEPT. VETERANS AFFAIRS MED. CTR., KANSAS CITY, MO
64128; DEPTS. OF PATHOLOGY AND PHYSIOLOGY, UNIV. OF KANSAS MED. CTR.,
KANSAS CITY, KS 66108; AND DEPT. OF PHYSICS, UNIV. OF MISSOURI,
KANSAS CITY, MO 64110
APStracts 2:0317C, 1995.
Cells of the S1 proximal renal tubule are examined to determine if
their peculiar shapes are a result of certain constructs of fractal
mathematics. Morphometric measurements of the cell perimeter are made
at several levels of cell height by measuring the intercellular
boundaries which appear on electron micrographs of tubule cross
sections. When the measurements are made over a range of scale
lengths, the fractal dimension, D, of the cell perimeter is found to
increase from 1.3 near the cell apex to 1.78 near the cell base. The
length of scale is found to range between 8 [mu]m and 0.4 [mu]m and
to represent the approximate dimensions of actual cell processes.
Fractal patterns that conform to the measured parameters are then
constructed from a fractal generator composed of bud-like formations
that originate near the cell apex and increase in number and decrease
in size with cell depth according to a fractal scaling. It is found
that the fractal rule of keeping a constant relative scale can be
maintained between budding processes but, to obtain patterns that
resemble biological structure, the processes must be positioned
randomly on the cell periphery. It is shown that when the relative
sizes of the buds decrease exponentially and their numbers increase
geometrically, the perimeter can grow to the correct length without
overlap. This suggests that patterns of the cell periphery
corresponding to different levels of cell height obey a law of scale
but occur randomly in a way that increases to high fractal dimension
or near plane-filling values at the cell base. The fractal patterns
that correspond to the measured fractal dimensions can be assembled
into a 3-dimensional model that closely resembles the known shape of
the proximal tubule cell.
Received 5 October 1994; accepted in final form 15 August 1995.
APS Manuscript Number C590-5.
Article publication pending Am. J. Physiol. (Cell Physiology).
ISSN 1080-4757 Copyright 1995 The American Physiological Society.
Published in APStracts on 23 September 1995.