# Shape correction function

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The '''shape correction function''' is a ratio of the surface area of a growing organism and that of an [isomorph](/source/isomorph) as function of the volume. The shape of the isomorph is taken to be equal to that of the organism for a given reference volume, so for that particular volume the surface areas are also equal and the shape correction function has value one.

For a volume <math>V</math> and reference volume <math>V_d</math>, the shape correction function <math>M(V)</math> equals:<ref>{{Cite book|last=Kooijman|first=S. A. L. M. |title=Dynamic energy budget theory for metabolic organisation|date=2010|publisher=Cambridge University Press |isbn=978-0-511-64011-7|edition=3rd |location=Cambridge|oclc=535951807}}</ref>
* [V0-morph](/source/V0-morph)s: <math>M(V) = (V/V_d)^{-2/3}</math>
* [V1-morph](/source/V1-morph)s: <math>M(V) = (V/V_d)^{1/3}</math>
* [Isomorph](/source/Isomorph)s: <math>M(V) = (V/V_d)^0 = 1</math>

Static mixtures between a V0 and a V1-morph can be found as: <math>M(V) = w(V/V_d)^{-2/3} + (1-w)(V/V_d)^{1/3}</math> for <math>0<w<1</math>

The shape correction function is used in [Dynamic Energy Budget](/source/Dynamic_Energy_Budget) theory to correct equations for [isomorph](/source/isomorph)s to organisms that change shape during growth. The conversion is necessary for accurately modelling food (substrate) acquisition and mobilization of reserve for use by metabolism.

==References==
{{reflist}}

{{DEFAULTSORT:Shape Correction Function}}
Category:Developmental biology
Category:Metabolism

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