Biomedical Engineering Reference
In-Depth Information
the thorax and the part of the total body mass that is coupled to the thorax by
the vertebral column. The elements coupling masses
m
1
and
m
2
represent the
elasticity and viscous damping of the rib cage and thoracic viscera. Masses
m
1
and
m
2
are connected directly by a spring which represents the effective
elasticity of the rib cage and directly coupled viscera such as the heart. The
dashpot connecting the two masses represents thoracic damping derived,
for example, from air in the lungs and blood in the thoracic vasculature,
both of which flow during impact. The corresponding spring and damping
forces,
f(x
2
−
x
1
)
, are approximated by piecewise linear
functions. Viscoelastic structural elements (Kent et al., 2003a), such as
might be present in thoracic muscular tissue, are represented by the spring
(
k
2
) and dashpot (
c
2
) in a series configuration. The action of a restraint
system on the thorax is represented by a control force
u(t)
between mass
m
1
and the vehicle. The variables
x
v
,
x
1
,
x
2
,and
x
3
represent the displacements
with respect to an inertial reference frame (absolute displacements) of the
vehicle, mass
m
1
, mass
m
2
, and mass
m
3
, respectively. The magnitude of
the mass
m
3
is equal to zero. The limiting performance of the seat belt
force is investigated based on this model.
To measure thoracic injuries, the following injury criteria will be
employed (Eppinger et al., 1999): (a) the maximum chest compression;
(b) the maximum chest acceleration; (c) the maximum rate of the chest
compression; and (d) the maximum chest viscous response, which is the
instantaneous product of chest compression and rate of chest compression.
The maximum chest compression and the maximum rate of chest
compression represent strength criteria for ribs and are used to predict
the risk of the rib fracture. The maximum chest acceleration measures
the risk of acceleration-induced injuries, which are the visceral injuries
caused by high accelerations. The quantitative definitions of the thoracic
injury criteria and the tolerable ranges for them will be given in the next
section.
x
1
)
and
h(
x
2
−˙
˙
6.3.2
Statement of the Problem
For the model described above, the motion of the car and the occupant is
governed by the equations
m
1
x
1
=
u
+
f(x
2
−
x
1
)
+
h( x
2
−
x
1
)
+
k
2
(x
3
−
x
1
),
m
2
x
2
¨
=−
f(x
2
−
x
1
)
−
h(
x
2
˙
−˙
x
1
)
−
c
2
(
x
2
˙
−˙
x
3
),
(6.26)
m
3
x
3
¨
=−
k
2
(x
3
−
x
1
)
+
c
2
(
x
2
˙
−˙
x
3
),
x
v
=
¨
a(t),
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