Biomedical Engineering Reference
In-Depth Information
The presence of the identity matrices in this system makes it easy to solve for
u
k
+
1
β
λ
β
and
as
u
k
+
1
β
G
β α
u
k
+
1
=
g
β
−
,
α
β
+
(
M
β α
−
M
u
k
+
1
α
+
M
G
T
λ
β
=−
b
G
β α
)
g
β
−
α β
λ
α
ββ
ββ
and therefore condense (
11.3
) into a reduced system
u
k
+
1
α
λ
α
b
∞
g
∞
α
M
∞
−
G
∞
T
=
.
G
∞
0
11.3.3 Contact Handling
Contact handling is another important feature of our face model, in particular the
ability to handle contact between FE models and other FE models (e.g. tongue/lips
contacts) or rigid bodies (e.g. tongue/teeth contacts). In ArtiSynth, contact involving
FEmodels is based on interpenetration of the surface nodes. First, the surface meshes
of the respective bodies are intersected to determine which FE surface nodes are in-
terpenetrating. A constraining direction is then determined for each interpenetrating
node, based on the normal of the opposing face closest to that node (see Fig.
11.9
).
These directions are then used to form velocity constraints between the interpenetrat-
ing nodes and the opposing faces. These constraints are then added to system (
11.2
)
for the subsequent time step to prevent the resulting velocity from increasing the
interpenetration, and they are also used to solve for the nodal displacements required
to correct the initial interpenetration.
In principle, these nodal constraints should be unilateral constraints. However,
because they are relatively decoupled, it is usually possible to implement them as
temporary bilateral constraints for the duration of the next time step, with the con-
straints being removed after the time step if the computed impulse indicates that the
contact is trying to separate. This significantly improves computation time, since
bilateral constraints in (
11.2
) are much faster to solve than unilateral constraints.
11.4 Applications of Biomechanical Face Modeling
Biomechanical face modeling permits a wide range of applications, as discussed in
the introduction to this chapter. Thus far, we have focused our simulation studies
on coupled face-jaw actions. In particular, we have used simulations to analyze the
biomechanics of lip rounding and protrusion, lip closure, and facial expressions.
