ANZIAM  J.  45 (2003), 27-34
Derivation of the probability density function for ultimate muscle pH in slaughtered animals

A. B. Pleasants
  AgResearch
  Private Bag 3123
  Hamilton
  New Zealand
    tony.pleasants@agresearch.co.nz
G. C. Wake
  Department of Mathematics and Statistics
  The University of Canterbury
  Private Bag 4800
  Christchurch
  New Zealand
    graeme.wake@canterbury.ac.nz
and
C. C. Daly
  AgResearch
  Private Bag 3123
  Hamilton
  New Zealand
    clyde.daly@agresearch.co.nz


Abstract
We consider the form of the probability density function for the ultimate muscle pH in slaughtered animals. Muscle pH in slaughtered animals is dependent on a biochemical process which forms lactic acid from the breakdown of glycogen stored in the muscle at slaughter. The relationship between glycogen and muscle pH after slaughter is expressed as a pair of coupled differential equations. The solution of this system for the equilibrium muscle pH as time $\to\infty$ gives the form of the probability density for the ultimate muscle pH. When the initial density for the muscle glycogen is normal, the density for the ultimate muscle pH is shown to be approximately a mixed normal density.
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