Biomedical Engineering Reference
In-Depth Information
Fig. 3.32
Schematic flow-chart of a single-criteria shape parameter optimization process
The diagram, Fig.
3.31
, schematically illustrates the iterative process of the
inverse problem for material parameter optimization.
Signs and symbols used in Fig.
3.31
:
Referring to the employed constitutive material equations used for character-
ization of tissue and foam material, N is the order of the series expansion, a and m
are variables of the parameter vector p; the quantities F
exp
i
and u
exp
;
F
sim
i
i
;
u
si
i
are
force and displacement outputs of simulation (superscript sim) and experiment
(superscript exp); U
k
is a scalar objective function value; n is the order of series
expansion in objective function evaluation, and it is equal to the compared number
of data pairs; subscript k increments the parameter vector (iteration number); p with
respect to N subscripts the single parameters; tol
a
, tol
b
are tolerance values for
program
termination
at
good
convergence
(i),
and
check
of
stagnancy
of
improvement of the objective function value, (ii), respectively.
Signs and symbols used in Fig.
3.32
:
The u
i
are spatial coordinates of the body support which are to be optimized
regarding their spatial position; S
i
represents the particular stress component at
tissue material point i, S
i
is the mean of all considered S
i
to obtain one repre-
sentative scalar value.
