Biomedical Engineering Reference
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Fig. 7.2 Scheme of one possible set of free energy profiles and transition trajectory ( black solid
line ) from state where considered cross-bridge is in the weakly bound state with ATP attached to
myosin to weakly bound state without ATP attached to myosin. G 1 , G 2 , x and x 1 are parameters,
that are describing the minimum points of free energy profiles for state S 1 and S 2 . These parameters
were found by optimization
models have made the simplification and neglected microscopic details of cross-
bridge population distribution and instead describe it using average cross-bridge cy-
cling governed by ordinary differential equation (ODE) systems. However, we have
demonstrated that it is possible to use a Huxley-type model as a model describing
the contraction in the 3D finite element model of the left ventricle (Vendelin et al.,
2002 ). As a basis of actomyosin description in a 3D model, we used a model de-
veloped earlier on the basis Hill formalism (Vendelin et al., 2000 ). In that model,
a linear relationship between SSA and ATP consumption during one beat was repro-
duced together with several other properties of cardiac muscle. Actually, we used a
free energy profile of the actomyosin reaction that had two force producing states
of the cross-bridge at the same displacement configuration. Namely, the free energy
minimum was located at the same position relative to the binding site for the both
force producing states. However, the configuration of the cross-bridge is changed
during the stroke and to incorporate that into the model, the force producing states
should have different free energy minima locations (Eisenberg et al., 1980 ; Pate and
Cooke, 1989 ).
The aim of this work is to find the set of free energy profiles, with different
minimum positions for force producing states of the cross-bridge (Fig. 7.2 ) that
would allow one to replicate the linear dependence between oxygen consumption
and stress-strain area in cardiac muscle. First, we give a short description of the
theoretical formalism developed by Hill that allows us to link mechanical contrac-
tion and chemical energy consumption. Next, the model description and simulation
results are presented.
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