Adherence of the Vascular Branching Geometry in the blue Crab, Callinectes Sapidus, to Murray's Cost-Optimized Model
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Authors
Marcinek, David
Issue Date
1993
Type
Thesis
Language
en_US
Keywords
Alternative Title
Abstract
Murray's Law predicts that there will be a radius cubed relationship
between the parent and daughter vessels of a branching system of vessels that
minimize the cost per volumetric flow. This cost-optimizing model has proven to
be a loose approximation of biological fluid transport systems as diverse as the
trophic systems of sponges and the closed circulatory systems of mammals. This
study examines this relationship in yet a third distinct group of animals, the
phylum Arthropoda. Molds of the vascular system of blue crabs, Callinectes
sapidus, were made by corrosion casting with modified Bateson's number 17.
Diameters were measured from these molds and used to calculate a junction
exponent for each branch point, which was then compared to the Murray's
predicted value of three. The exponents in the blue crab circulatory system
correspond well with Murray's ideal cost-optimized model. These findings are
significant for a number of reasons. (1) This study is the first quantitative
description of the branching geometry of an open circulatory system. (2) The
phylogenetic distance of arthropods from the animals previously studied,
sponges and mammals, as well as the distance between these two groups is
evidence for three independent evolutions of this branching relationship in
biological fluid transport systems. (3) The physiological characteristics of the
blue crab vasculature, such as the lack of cells in direct contact with the fluid and
the absence of arterial smooth muscle, raise questions as to the mechanism
animals use to maintain a relatively constant branching geometry throughout
their fluid transport system in the face of dynamic environmental conditions.
Description
v, 43 p.
Citation
Publisher
Kalamazoo College
License
U.S. copyright laws protect this material. Commercial use or distribution of this material is not permitted without prior written permission of the copyright holder.