438 Computational Modelling of Biomechanics and Biotribology
enable knee exion; and an improved prosthesis–bone interface subject to
desirable bone remodelling behaviour. If we can formulate a function F ( X ),
that describes the objective that needs to be achieved, as a function of the
variables X , for example, minimum muscle exertion as a function of the con-
tribution of the individual muscle bellies to enable a loaded knee extension
from 90° exion to full extension, then the function F ( X ) is known as the
objective function.
Now consider the ideal case where we can obtain the rst order deriv-
ative, F ′( X ), of the function F ( X ). The maximum and minimum values of
F ( X ) will then be located at the values of X where F ′( ...