Biomedical Engineering Reference
In-Depth Information
Fig. 7.4
(
A
), (
B
) cross-bridge cycling rates used in the model; (
C
) free energy profiles found by
optimization of the mathematical model
(b) parameters describing Ca
2
+
—induced activation of the actomyosin complex and
rate constants of the actomyosin complex state transformation reactions.
As a first step in the optimization, (b) parameters were optimized at different sets
of parameters (a) by minimization of the different residual functions. After that, the
best fit was picked out and all (a) and (b) parameters were optimized again. For find-
ing the parameters for describing the rate constants between biochemical states we
predescribed the shape of these functions. The relationship between rate constants
pairs (Eq. (
7.1
)) declare that only one rate constants from the pair is independent.
The shapes of the functions are shown at the Figs.
7.4
(A) and (B).
To obtain the optimal model parameters we considered three fitting protocols.
Simulation for isometric contraction were fitted against experimental data. The max-
imal total stress in isometric contraction was used for fitting the end-systolic points
for isotonic contraction. And the linear relationship between SSA and ATP con-
sumption was fitted against a pre-described linear line for all considered contraction
types.
7.4 Results and Discussion
We considered three different type of contractions: isometric, isotonic and phys-
iological. Under 'physiologic' contraction we mean the isotonic contraction until
the minimal half sarcomere length is reached and isometric contraction after that
moment.
