Chapter 11 Human Head-Neck Dynamics
11.1 Human Head-Neck Dynamics
During the past 30 years, there has been an increasing interest in head/neck dynamics
during crashes or high acceleration environments. This interest stems from the high
incidence of injuries occurring in automobile accidents. Since most of the traffic
fatalities are the result of injuries to the head/neck system this has caused safety and
research engineers to focus their attention upon head/neck injury criteria and
head/neck protective devices. The major cause of these injuries are direct impact and
indirect impact (e.g., hyperextension or “whiplash” ) of the head/neck system during
crashes and periods of high acceleration. Whiplash is a result of a rapidly applied
displacement (and/or acceleration) field to the torso in the poster anterior direction
with the head and neck unrestrained. To be better able to understand these
phenomena, the primary concern of researchers has been the dynamics of the
head/neck system. These interests and concerns have stimulated the development of a
number of experimental studies of head/neck system dynamic response. These studies
have used both volunteers and dummies in a variety of acceleration configurations. A
summary of some of these experiments is contained in references [1-5].
In a paper, Huston, et al. [6] suggested that it may be possible to obtain analytical
simulation of head/neck dynamics by using a biodynamic computer model of the
human body head/neck system. Indeed, by using the SuperCrash Crash Victim
computer model [7], it is possible to duplicate experimental data. These encouraging
results are a motivating factor for the head/neck study summarized herein.
There have occurred significant advances in head/neck modeling in recent years.
These advances have changed from simple pendulum models to elaborate multibody
dynamics analysis models currently being used. References [8-20] provide details of
some efforts in this research. Although these efforts have been reasonably successful,
it is the opinion of this author that there has not yet been developed a comprehensive
and user-friendly head/neck model. However, the paragraphs of this chapter are
believed to provide an outline of an approach toward the development of such a
model. In this approach, a flexible and inexpensive technique that employs multibody
dynamics analysis is used to model and simulate head/neck system.
The head/neck system is modeled as a series of rigid bodies, representing the bones
1
and vertebrae, together with a system of nonlinear springs and dampers representing
the discs, ligaments, and muscles. A user-oriented computer software simulator, is
also developed. This software simulator is intended to be more user friendly and
reliable than the earlier simulators. It is believed that the simulator will also provide a
more comprehensive analysis of the head/neck system.
11.1.1 Methods
The head/neck system is modeled by nine segments representing the skull, vertebrae,
and torso, as shown in Figure 11.1.1 and springs and dampers representing the discs,
ligaments, and muscles. The segments are connected by spherical (ball and socket)
joints representing the connecting joints of the human frame. Nonlinear springs and
dampers are used between adjacent bodies to simulate the ligaments and muscles and
limit the range of motion. Values for the inertia and geometrical properties of the rigid
bodies are adjusted to match the actual human values. These data are obtained from
experimental measurements and other published data [21-25]. Table 11.1.1-11.1.4 list
the values of these parameters as they are used in the head/neck model. The
“reference point” refers to the connection point between a body and its connecting
lower-numbered body. The springs and dampers are placed between each adjacent
body. This model can have as many as 54 degrees of freedom (3 for the translation
and 3 for the orientation of the bodies relative to their adjacent bodies). Each joint has
an internal force and moment to constrain its relative motion. These forces and
moments may be modeled as springs and dampers taken in the form:
Fi  (k f x i  c f x i )
(i=1,2,3)
(11.1.1)
and
M i  (k m i  c m  i )
(i=1,2,3)
(11.1.2)
where Fi and Mi are typical force and moment components, xi and i represent
displacement and rotation variables. The force and damping constant, kf , cf have the
forms:
2
kf0
for x min  x  x max

k  k ( x  x )
for x  x max
and x  0
f1
max
 f 0
kf  
0
for x  x max
and x  0
 k  k (x  x )
for x  x min
and x  0
f1
min
 f0
0
for x  x min
and x  0

(11.1.3)
cf 0
for  min     max

c  c (   )
for    max
and   0
f1
max
 f 0
cf  
0
for    max
and   0
 c  c (   )
for    min
and   0
f1
min
 f0
0
for    min
and   0

(11.1.4)
where x, xmax, xmin and , max, min represent the values of the displacement and
rotation variables and its corresponding maximum and minimum values respectively
and where kf0, cf0, are spring and damping constant which can be applied throughout
the total range of motion of the joint. After the joint exceeds its maximum or
minimum allowable values the spring and damping increase depending upon the slope
(kf1, and cf1) and the excess values. The constant km and cm have similar forms (see
joint stop mechanism in Figure 11.1.2). The values of these parameters are very
difficult to obtain. The difficulty stems from the nonlinear behavior of the soft tissue.
Fortunately, such data is available from the many experiments conducted by Ewing, et
al [1-3]. The values of these parameters have been estimated with experimental data.
The model of Figure 11.1.1 can be considered as a general chain system, which is
defined to be a collection of rigid bodies arbitrarily assembled so that adjoining
bodies have at least one common point such that no closed loops are formed. For the
system shown in Figure 11.1.1, each body has six degrees of freedom and, hence, the
entire system has a total of 54 degrees of freedom and 54 generalized coordinates (27
for the translation and 27 for the rotation) need to be defined to describe the
configuration of the system. It is convenient to define these coordinates as relative
coordinates as opposed to absolute coordinates.
3
Let the variables xb (b= 1,...,54) be generalized coordinates representing the 54
possible degrees of freedom of the head/neck model in Figures 11.1.1. Upon
introducing these coordinates, the angular velocities of the bodies and the velocities of
their mass centers relative to an inertia frame may be expressed in the form:


k  kbm x b n om


and v k  v kbm x b n om
(11.1.5)

where the n om (m = 1,2,3) are mutually perpendicular unit vectors fixed relative to the
inertial frame, and where the kbm and the v kbm are components of the partial
angular velocity and partial velocity arrays as defined by Kane [26].
By differentiating equation (11.1.5) the angular accelerations of the bodies and their
mass center accelerations may be written in the form:


 kbm x b )n om
 k  (kbm x b  


and a k  (v kbmx b  v kbm x b )n om
(11.1.6)
Next, let the bodies of the model be subjected to a force field. Let the forces be

represented on a typical body Bk by a force passing Fk through G k together with a

couple having torque Tk . Then the generalized applied force Fb for the coordinate
x b may be written as:
Fb  v kbmFkm  kbmTkm
(11.1.7)



where Fkm and Tkm are the n om components of Fk and Tk .

Similarly, let the inertia forces of body Bk be represented by a force Fk* passing

through G k together with a couple having torque Tk* . Then the generalized inertia
4
force
for x b may be written as:
*
*
Fb*  v kbm Fkm
  kbmTkm
(11.1.8)



*
*
where Fkm
and Tkm
are the n om components of Fk* and Tk* . From Kane and


Levinson [19] we see that Fk* and Tk* may be expressed as:


Fk*  m k a k
(11.1.9)
and




Tk*  I k   k  k  (I k  k )
(11.1.10)
where m k is the mass of B k and I k is the central inertia dyadic of B k .
Finally, the equations of motion of a given head/neck model composed of rigid
interconnected segment could be obtained using Kane’s equations (Lagrange form of
d’Alembert principle)[26-27]. These equations are expressed as
Fb  Fb*  0
(11.1.11)
where Fb denotes the generalized active force and Fb* the generalized inertia force.
By substituting from Equations (11.1.5) through (11.1.10), Equations (11.1.11) may
be expressed as
A bp x p  B bp x p  C bpr x p x r  Fb ,
b = 1,…,54
(11.1.12)
where the coefficient of A bp , B bp , and C bpr are given by
5
A bp  m k v kbm v kpn  I kmn  kbm  kpn
 kpn
B bp  m k v kbm v kpm  I kmn  kbm 
and
C bpr  e rsm I ksn  kbm  kqr  kpn
(11.1.13)


where the I kmn are the n om , n on components of I k , e rsm represents the permutation
symbol.
In equation (11.1.12) the coefficients A bp , B bp , and C bpr represent the

contribution of the generalized inertia forces, Fb* . The generalized active forces, Fb
can be broken into two components (internal and external)
Fb  Fbint  Fbext
(11.1.14)
where the Fbint is the contribution of the joint forces and moments representing the
action of soft tissues, and the Fbext represents the externally applied forces and
moments such as the external loads, and contact forces on the head/neck model. The
modeling of the generalized active forces and moments will depend on the model at
hand. Generally, representation of soft tissues by springs and dampers one would
express their contribution for each segment in inertial frame by the generalized
coordinates and their time derivatives.
Equations (11.1.12) form a set of 54 simultaneous, second-order ordinary, nonlinear
differential equations determining the 54 generalized coordinates xb of the system. If
some of the xb are specified, then the equations become algebraic equations for the
unknown forces or moments associated with the specific xb. Since the coefficients Abp,
Bbp, ,Cbpr and Fb of these equations are algebraic functions of the physical parameters
6
and the generalized coordinates, the equations may be integrated numerically using a
standard integration algorithms. Such algorithms have been constructed and compiled
into a Fortran based computer program.
The input data required by the model consists of the following; (1) body segment
dimensions and physical constants of the head/neck model. These data consist of the
masses and the local components of their central inertia dyadic and the local
components of the vectors locating their mass centers and their connection joints. (2)
intervertebral disc material parameters. (3) input acceleration at B1 (torso). (4)
Numerical integration parameters. These data define the integration time and error
allowances.
The numerical integration then produces a time history of the linear and angular
displacements, velocities and accelerations of the mass centers of the bodies of the
head/neck model. These data are expressed relative to the inertial frame R.
11.1.2 Results
In the first stage of this study, a three-dimensional head/neck multibody system
simulator is developed. The simulator allows a wide range of application including
head/neck system response during impact and a high acceleration environment. There
is little experimental data available which can be used to check the preceding
analytical model. However, in an attempt to validate the model, a comparison was
performed between the model’s head center of gravity motion to that obtained by
Ewing, et al. [1] at the Naval Aerospace Medical research Laboratory for volunteer
sled test data. In the verification, a sled deceleration profile, the known motion
applied to the sled, shown in Figure 11.1.3 was input to the model’s torso (first body
B1). This deceleration profile is typical of those experienced by volunteers seated in a
moving sled which is brought to a sudden stop. The subject was firmly attached to a
sled seat. The seat was then accelerated. The restraint system consisted of the lap belts
and shoulder belts.
An acceleration applied to the thorax at B1(torso) is a reasonable representation of the
input to the subject produced by the sled. The head mass center angular acceleration,
angular velocity, and angular displacement were measured. These data then were
calculated using the model with approximately input. A comparison of the results is
shown in Figures 11.1.4-11.1.6. From the comparisons we can see that there is a very
good agreement between the experimental results and those predicted by the computer
7
model.
In the examples we can also examine the effect of protective helmet mass on
head/neck dynamics. The deceleration profile of Figure 11.1.7 was used as a
horizontal deceleration input for a head/neck model which was modified to simulate
the use of different helmet masses. The helmets were modeled by adjusted the head
mass and inertia in equation (11.1.12). The relative effect of 1.004 kg and a 2.150 kg
helmet on head angular acceleration and angular rotation were computed. The results
are shown in Figure 11.1.8 and 11.1.9. From the Figures it is seen that the helmet
mass slightly decreases the peak head angular acceleration, but it is markedly
increases the peak head angular rotation. This angular rotation could aggravate a
hyper flexion and hyperextension under a severe acceleration environment. These
examples show that these can exist potentially harmful inertia effects of protective
helmets in high-acceleration environment where there is no direct head impact.
11.1.3 Discussion
This modeling of the head/neck system, and its simulation, represents one of the most
sophisticated head/neck models available. However, further refinement of the model
is necessary as more experimental data becomes available. This would include
refinement of the soft tissue biomechanical properties. There are several applications
of head/neck models. First, a head/neck model which simulates gross-motion
head/neck dynamics can be used to determine dynamic forces on the head/neck and
upper torso during high acceleration environments so that protective design principles
can be incorporated into automobiles, motorcycles, and sports equipment. Also, the
parameters of the model can be scaled to accommodate different sizes of people.
11.1.4 Conclusions
The analysis shows that it is now possible to construct reliable multibody simulation
models of human head-neck dynamics. The model is three-dimensional with six
degrees of freedom at each joint. The model was also developed so that a close
correlation between the human head/neck anatomy and the model’s segments. Injury
in the head/neck region can be predicted in one of two ways with this model. The first
way is to take the force-time histories of each segment in the model. If the forces
levels then exceed the ultimate allowable forces, then injury can be predicted. The
other method of injury prediction is by using the Head Injury Criterion (HIC) [28].
The head’s linear acceleration obtained from the model can be used in the HIC. These
8
values would then given an indication of the possible levels of injury in the head.
The success of the modeling is due to recent advances in computer hardware and
software and new approaches in formulating the governing dynamical equations of
motion. The examples presented show the range of applicability of the model. Future
research with the model could include a study on the influences that headrest,
seatback angle, and airbags have on the dynamic response of the model, criteria for
injury of the head/neck system, and whiplash phenomenon. When this is done, the
model could be an effective tool for predicting injury in a variety of high acceleration
configuration environments.
9
Head (B9)
C1 (B8)
C2 (B7)
C3 (B6)
C4 (B 5)
C5 (B4)
C6 (B3)
Z
C7 (B2)
X
Torso (B1)
R (B0)
Figure 11.1.1 Head-Neck Model
10
Y
Y:k f,cf,km,cm
X:x,
Y0:kf0,cf0,kmo,cmo
slope:kf1,cf1,km1,cm1
slope
slope
Y0
Xmin
Xmax
X
Figure 11.1.2 Joint Stop Mechanism
11
Sled Acceleration
(m/sec/sec)
Time (msec)
10
0
-10 0
13
25
38
50
63
75
88 100 113 125 138 150 163 175 188 200 213 225 238 250
-20
-30
-40
-50
-60
-70
-80
Figure 11.1.3 Horizontal Deceleration profile from Test.
12
Angular Accleration
(rad/sec/sec)
exp
1500
model
1000
500
Time (msec)
0
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
-500
-1000
Figure 11.1.4 Comparison of Analytical Model and Experimental
Angular Acceleration of the Head.
13
Angular Velocity
(rad/sec)
exp
model
25
20
15
10
5
0
-5
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
-10
Time (msec)
Figure 11.1.5 Comparison of Analytical Model and Experimental
Angular Velocity of the Head.
14
Angular Displacement
(rad)
exp
model
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2 0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Tme(msec)
Figure 11.1.6 Comparison of Analytical Model and Experimental
Angular Displacement of the Head.
15
Deceleration Profile
(m/sec/sec)
120
100
80
60
40
20
0
-20 0
40
80
160
240
Time (msec)
Figure 11.1.7 Horizontal Deceleration profile.
16
Head Angular
Accleration
(rad/sec/sec)
without helmet
1.004 kg helmet
2.150 kg helmet
1500
1000
500
Time (msec)
0
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
-500
-1000
-1500
Figure 11.1.8 Head Angular Acceleration Comparison.
17
Head Angular Rotation
(Degrees)
without helmet
1.004 kg helmet
2.150 kg helmet
160
140
120
100
80
60
40
20
0
-20 0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Time (msec)
Figure 11.1.9 Head Angular Rotation Comparison.
18
Table 11.1.1 Mass of the Head/Neck System
Body
1
2
3
4
5
6
7
8
9
Torso
C7
C6
C5
C4
C3
C2
C1
Head
Number
Body
Label
Mass(kg) 49.14 0.25 0.25 0.25 0.25 0.25 0.25 0.25 4.38
19
Table 11.1.2 Mass Center Position of the Head/Neck System
Body
Body
Number
Label
Mass Center Position(m)
1
Torso
0.0
0.0
0.10
2
C7
0.0
0.0
0.007
3
C6
0.0
0.0
0.007
4
C5
0.0
0.0
0.007
5
C4
0.0
0.0
0.007
6
C3
0.0
0.0
0.007
7
C2
0.0
0.0
0.009
8
C1
0.0
0.0
0.009
9
Head
0.012
0.0
0.07
20
Table 11.1.3 Reference Point Position of the Head/Neck System
Body
Body
Number
Label
Reference Point Position (m)
1
Torso
0.0
0.0
0.0
2
C7
0.0
0.0
0.20
3
C6
0.0
0.0
0.015
4
C5
0.0
0.0
0.013
5
C4
0.0
0.0
0.013
6
C3
0.0
0.0
0.014
7
C2
0.0
0.0
0.014
8
C1
0.0
0.0
0.017
9
Head
0.0
0.0
0.018
21
Table 11.1.4 Inertia Matrices for the Head/Neck System
Body
Body
Number
Label
1
Torso
2
Ixx
Iyy
Izz (10-3 kg m2)
1243.0
1243.0
1243.0
C7
0.32
0.32
0.64
3
C6
0.22
0.22
0.44
4
C5
0.20
0.20
0.41
5
C4
0.19
0.19
0.37
6
C3
0.18
0.18
0.36
7
C2
0.20
0.20
0.39
8
C1
0.20
0.20
0.39
9
Head
18.1
21.5
14.2
22
11.2 Dynamics Modeling of Human Temporomandibular Joint During Whiplash
Rear-end impacts account for more than one third of vehicle accidents, and nearly
40% of these accidents produce whiplash injuries. During rear-end impact of a vehicle,
an occupant’s head is thrust rearward with respect to the vehicle in a typical whiplash
action. During this motion, complex dynamic forces act on the jaw bone. Researchers
have reported symptoms suggesting potential injury to the temporomandibular joint
following vehicle rear-end impact accidents [29-32]. Jaw postural mechanics have
also been proposed as a cause of temporomandibular joint injuries after a vehicle
rear-end impact accident. Weinberg and Lapointe hypothesized that opening the jaw
during impact injuries temporomandibular joint intracapsular tissues and causes
myofacial injury. These authors argued that with acceleration of the patient’s body
after a rear-end impact, the unsupported head accelerates less quickly and mandible
even more so than the cranium, resulting in rapid jaw opening with downward and
forward displacement of the disk relative to the condyle. Jeffrey A. et al. [33]
gathered data from 219 patients identifying temporomandibular joint dysfunction after
an vehicle accident. Viano [34] indicated that when the seatback angle increase
rapidly the probability of injuries also increase. Jeffrey et. al. [35] shown that
temporomandibular joint or masticatory muscle injury may be associated with varying
postural characteristics and impact events, including speed, direction of impact and
vehicular damage. Huang [36] using a computer model show that when the seatback
angle and impact velocity increases rapidly the probability of whiplash injury also
increase.
The dynamics of the head/neck system of an occupant involved in a rear-end impact
are not easily analyze. The jaw is even more difficult to analyze, since its dynamic
motion depends upon that of the head. The major cause of these injuries are direct
impact and indirect impact (e.g., hyperextension or “whiplash” ) of the head/neck
system during crashes and periods of high acceleration. Whiplash is a result of a
rapidly applied displacement (and/or acceleration) field to the torso in the poster
anterior direction with the head and neck unrestrained. To be better able to
understand these phenomena, the primary concern of researchers has been the
dynamics of the head/neck system.
In a paper, Huang [37] suggested that it may be possible to obtain analytical
simulation of head/neck dynamics by using a biodynamic computer model of the
human body head/neck system. Indeed, by using the SuperCrash model, a crash
victim computer simulator [38], it could be able to exhibit reasonable experimental
23
data. These encouraging results were a motivating factor for the head/neck study
summarized in this paper. There have occurred significant advances in head/neck
modeling in recent years. These advances have changed from simple pendulum
models to elaborate multibody dynamics analysis models currently being used.
References [39-51] provide details of some efforts in this research. But all these
works didn’t specifically discuss about temporomandibular joint. In this paper, an
attempt is made to use the computer to investigate the temporomandibular joint of the
occupant during rear-end impacts.
11.2.1 The Biodynamic Head/Neck/Jaw Model
During the past 30 years, there has been an increasing interest in head/neck dynamics
during crashes or high acceleration environments. This interest stems from the high
incidence of injuries occurring in automobile accidents. References [39-51] provide
details of some efforts in this research. In some of these modeling efforts, it was
shown that computer analyses using numerical schemes based on biodynamic models
of the head/neck have been successful in obtained results. It is possible to construct a
comprehensive three-dimensional head/neck model that can be calibrated and
validated with experimental data.
In this study, the head/neck/jaw system is modeled by ten segments representing the
skull, jaw, vertebrae, and torso, as shown in Figure 11.2.1. The torso and neck are
elliptical cylinders and head is a spherical. The jaw is represented by frustums of
elliptical cones. Nonlinear springs and dampers are used between adjacent bodies to
simulate the ligaments and muscles and limit the range of motion. Values for the
inertia and geometrical properties of the rigid bodies are adjusted to match the actual
human values. These data are obtained from experimental measurements and other
published data [52-57]. When the mandible is rotated, during whiplash, a
simultaneous translation is the result of biomechanical constraints. The mandible can
be modeled as a rigid body with a hinge joint for jaw opening and closing, and
including translation during jaw opening. Thus, in this model we can have as many as
55 degrees of freedom (3 for the translation and 3 for the orientation of the bodies
relative to their adjacent bodies, 1 for the orientation of the jaw relative to the head).
The kinematics of the head/neck/jaw model may be describer and defined in terms of
55 position and orientation variables as Table 11.2.1.
11.2.2 Simulation and Analysis
24
In this study, the motion of the head/neck/jaw model is restricted to motion in the X-Z
plane. The jaw is limited to rotate about its hinge 0 ~ 30. The jaw itself is modeled
as a rigid body with mass and inertia properties 1/20 that of the head itself. The jaw is
hinged to rotate about as axis parallel to the global Y-axis. The hinge point is located
0.025 m forward of and 0.089 m above the joint between the head and neck. The mass
center of the jaw is about 0.076 m forward of and 0.076 m below this hinge point, The
geometry of the jaw model is shown in Figure 11.2.2. The input crash environment
was simulated by using a range of impact severity from 4.2 ~ 9.6 m/s change in
velocity simulating rear-end impact. The rear-end impact event is solved for a time
interval from 0.00 seconds to 0.19 seconds. The results are shown in Figure 11.2.3 to
11.2.6.
11.2.3 Results and Discussion
In the Figure 11.2.3, we can see that, the relative angle between the head and jaw (jaw
opening angle) increase with the impact velocity. Figure 11.2.4 shows the acceleration
of jaw increase with increase in velocity. In 9.6 m/s impact induced a peak jaw
angular acceleration of 495 rad/s2. For 6.4 m/s and 4.2 m/s impact the peak jaw
angular accelerations are 258 rad/s2 and 90 rad/s2 respectively. This increased
acceleration significantly aggravates a dynamic force of jaw. Figure 11.2.5 displays
the predicted temporomandibular joint torques caused by the rotation of the mandible
about the medico-lateral axis during the rear-end impact. The positive slope of the
torques during the first period of the rear-end impact (0.00-0.13 s) illustrate the
tendency for jaw closing. The negative slope of the torques during the remaining
impact period indicated a tendency for jaw opening. Figure 12.2.6 illustrates time
series of the jaw mass center acceleration in space. The peak linear acceleration of the
jaw were: 14.7 g for the 9.2 m/s impact, 11.3g for the 6.4 m/s impact, and 5.8g for the
4.2 m/s impact. From the Figure, we can see that the acceleration of the jaw is
characterized by several peaks. For the 9.2 m/s case the maximum peak is about 14.7
g, and occurs after 0.14 seconds. Multiplying the peak acceleration by the jaw mass
(0.292 kg) yields a peak force on the jaw bone of 42.1 newtons. This force is applied
at the temporomandibular joint.
The hyperextension of the head and neck caused jaw opening. The term ‘whiplash’
defines a hyperextension injury to the soft tissues of the neck. Sudden forward
acceleration of a vehicle, such as rear-end impact results in a backward thrust of the
head on the relaxed musculature of the neck, thus causing violent hyperextension. The
model was developed so that a close correlation between the human head/neck/jaw
25
anatomy and the model’s segments. By this model, the motions and forces of the
temporomandibular joint that occur during whiplash are obtained. These data may be
obtained for a variety of vehicle impact conditions. The success of the modeling is
due to recent advances in computer and new approaches in formulating the governing
dynamical equations of motion.
11.2.4 Conclusions
The analysis shows that it is now possible to construct reliable multibody simulation
models of human head/neck/jaw to analysis dynamics of temporomandibular joint.
However, there are much more to be done before the model realize these benefits.
More data on what happens of the temporomandibular joint dysfunction during the
whiplash are needed to adjust the model parameters. Better modeling of the soft tissue,
disc condyle friction and tolerance limits of temporomandibular joint tissues are
needed. Finally, a better understanding of causal relationship between the joint forces
and torques during whiplash and the temporomandibular joint damage is needed.
Beyond this, criteria for injury need to be established. When this is done, the model
could serve as an effective tool predicting temporomandibular joint injury in a variety
of high accident configuration environments. It could then be used in the development
of safety devices.
26
X1,X2,X3
position of a reference point in B1, the torso, relative to
the reference point of the inertia frame
X4,X5,X6
orientation of a reference point in B1, the torso, relative
to the reference point of the inertia frame
X7,X8,X9
position of a reference point in B2, relative to B1.
X10,X11,X12 orientation of a reference point in B2, relative to B1.
X13,X14,X15 position of a reference point in B3, relative to B2.
X16,X17,X18 orientation of a reference point in B3, relative to B2.
X19,X20,X21 position of a reference point in B4, relative to B3.
X22,X23,X24 orientation of a reference point in B4, relative to B3.
X25,X26,X27 position of a reference point in B5, relative to B4.
X28,X29,X30 orientation of a reference point in B5, relative to B4.
X31,X32,X33 position of a reference point in B6, relative to B5.
X34,X35,X36 orientation of a reference point in B6, relative to B5.
X37,X38,X39 position of a reference point in B7, relative to B6.
X40,X41,X42 orientation of a reference point in B7, relative to B6.
X43,X44,X45 position of a reference point in B8, relative to B7.
X46,X47,X48 orientation of a reference point in B8, relative to B7.
X49,X50,X51 position of a reference point in B9, relative to B8.
X52,X53,X54 orientation of a reference point in B9, relative to B8.
X55
orientation of a reference point in B10, relative to B9.
Table 11.2.1 Variables of the Model
27
Head (B9)
Jaw (B10)
Z
C1 (B8)
C2 (B7)
C3 (B6)
C4 (B 5)
C5 (B4)
C6 (B3)
C7 (B2)
X
Torso (B1)
R (B0)
Figure 11.2.1 Head-Neck-Jaw Model
28
Temporomandibular Joint
0.076 m
0.089 m
Jaw Mass Center
Head/Neck Joint
0.076 m 0.025 m
Figure 11.2.2 Temporomandibular Joint Configuration
29
9.6m/s
Angle (head-jaw)
(degree)
6.4/m/s
4.2m/s
5
0
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190
-5
-10
Time (msec)
-15
-20
-25
Figure 11.2.3 Relative angle between the head and jaw.
Jaw Angular
Accleration
(rad/sec/sec)
600
9.6m/s
6.4m/s
4.2m/s
500
400
300
Time (msec)
200
100
0
-100 0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190
-200
-300
-400
Figure 11.2.4 Jaw Angular Acceleration.
30
Torque (head-jaw)
(N-m)
9.6m/s
4000
4.2m/s
6.4m/s
3000
2000
1000
0
-1000
0
10
20
30
40
50
60
70
80
90
100 110 120 130 140 150 160 170 180 190
-2000
-3000
-4000
Time (msec)
Figure 11.2.5 Torques (head-jaw).
Jaw Mass Center
Accleration
(g)
9.6m/s
6.4m/s
4.2m/s
16
14
12
10
Time (msec)
8
6
4
2
0
-2 0
10
20
30
40
50
60
70
80
90 100 110 120 130 140 150 160 170 180 190
Figure 11.2.6 Jaw Mass Center Acceleration.
31
11.3 Effect of Helmet Mass on Human Head/Neck Dynamics
It has been generally recognized that the most series injury to the motorcycle rider is
injury to the head/neck system. Recently there has been considerable interest in
helmet-head/neck dynamics during crashes and periods of high acceleration. This
interest is due in part to the widely accepted notion that as many as 60 percent of
motorcycle accident fatalities are the result of injury to the head/neck system. This
interest in helmet-head/neck dynamics has stimulated the development of a number
head/neck biodynamic models. The beneficial effects of protective helmets in
motorcycle crash are well documented [58-62]. Some have claimed that a helmet
which offers protection against head injury from direct impact, may actually
contribute to head/neck injury in indirect impact (e.g. whiplash) situations. Indeed,
some researchers have been used this point of view to persuade state legislatures to
withdraw mandatory motorcycle helmet laws.
It is the objective of this paper to quantitatively and qualitatively examine these
propositions. We will study the potential deleterious effects of the helmet mass and
inertia through increased head rotations and acceleration during high acceleration
periods. The head/neck computer simulation model as developed by S.C. Huang [63]
is used to perform the analysis.
11.3.1 Methods
During the past 20 years there has been an increasing awareness of safety issues in the
motorcycle rider. A literature review reveals several hundred references with excellent
surveys on crash simulation including discussions of head/neck modeling. In one of
these modeling efforts , Huston, et al. [64] suggested that it may be possible to obtain
analytical simulation of head/neck dynamics by using a biodynamic computer model
of the human head/neck system. Since the development of that model, there have been
advances in both multibody dynamics modeling and in the recording of experimental
data. In multibody dynamics, the past two decades have produced marked advances in
modeling with translation between bodies [65], and new kinematic methods for
description of the bodies motion have been developed. More experimental data have
been published [66-70].
Using the more flexible and inexpensive methodology and the improved
computational techniques in conjunction with experimental data, Huang [63]
developed a head/neck model (Fig. 11.1.1). The head/neck multibody system is
32
modeled in the form of an "open-chain" system. The model consists of a series of
rigid bodies representing the skull, vertebrae, and torso. These bodies are connected to
each other by nonlinear springs and dampers representing the disks, ligaments, and
muscles. The governing of equations of such systems may be studies by use of Kane's
equations and Huston's procedures [71,72], which have been shown to have distinct
advantages over other formulations, such as Newton's law or Lagrange's equations,
for the dynamics analysis of multibody systems [73]. The resulting equations are
developed in a form ideally suited for conversion into computer algorithms for
numerical development and analysis.
They have shown that the equations of motion may be written in the form
  F
a ijX
j
i
(i, j  1,2, . . N
. ,)
(11.3.1)
where N is the number of degrees of freedom of the system, X j are the generalized
 for the head/neck
coordinates, and a ij and Fi are in general functions of X j and X
j
system of Fig. 11.1.1, the number of degrees of freedom is 54. For given initial
conditions, the computer program solves these equations by means of a Runge-Kutta
integrator.
The anatomy of the head/neck system is divided into bones and soft tissue. The largest
and heaviest bone is the skull, the other bones of the head/neck system are seven
cervical vertebrae (C1-C7). Values for the inertia and geometrical properties of the
rigid bodies are adjusted to match the actual values. These data are obtained from
experimental measurements and other published data [74-78].
The segments are connected by spherical joints representing the connecting joints of
the human frame. Nonlinear springs and dampers are used between adjacent bodies to
simulate the ligaments and muscles and limit the range of motion. The joint
constraints limiting the relative motion of the segments are modeled as non-linear
character. The values of the various constants for the ligaments, disc, muscles and
joints are difficult to specify because of the non-linear behavior of the soft tissue
during dynamic loading. The spring and dampers produce forces and moments on and
between the vertebrae and the skull. These forces and moments may be modeled as
springs and dampers taken in the form.
33
11.3.2 Simulation
To simulate head/neck dynamics during a crash environment, the system of Fig.
11.1.1 was subjected to a horizontal deceleration pulse as shown in Fig. 11.3.1. This
deceleration profile is typical of those experienced by volunteers seated in a moving
sled which is brought to a sudden stop, as recorded by Ewing, et al. [66]. Figure
11.3.2 shows a comparison between the head angular acceleration predicted by the
model and that measured experimentally.
The deceleration pulse of Fig. 11.3.3 was then used as a horizontal deceleration input
for a head/neck model which was modified to simulate the use of different helmet
masses. The helmets were modeled by adjusted the head mass and inertia in
governing equations. The relative effect of 0.8 kg, 1.2 kg, and 1.6 kg helmet on head
angular acceleration and angular rotation were computed. The results are shown in
Figure 11.3.4 to 11.3.8.
11.3.3 Discussion and Conclusions
We can see from the results, the accelerations of mass center of head and neck (C4)
increase with the increase in helmet mass. As seen in Figure 11.3.6, the head mass
center peak accelerations of 1.6 kg helmet case is higher than that of 1.2 kg helmet
case by 36.8%, and 0.8 kg helmet case by 104.0%. Also the result show the neck (C4)
mass center peak accelerations of 1.6 kg helmet case is higher than that of 1.2 kg
helmet case by 60.0%, and 0.8 kg helmet case by 125.0%. In the Figure 11.3.7, we
can see that the angular rotation of head increase with the increase in helmet mass. As
seen in Figure 11.3.8, the head angular rotation of 1.6 kg helmet case is higher than
that of 1.2 kg helmet case by 19.9%, and 0.8 kg helmet case by 62.4%.
The results of this analysis show that helmet mass is a important factor affect human
head/neck injuries during motorcycle accident. The analysis show the peak
acceleration and angular rotation of head increase with the increasing of the helmet
mass. This angular rotation could aggravate a hyper flexion and hyperextension under
severe acceleration environment. The simulations shows that the potentially harmful
effects of protective helmets in high-acceleration environment where there is no direct
head impact.
34
Sled Acceleration
(m/sec/sec)
Time (msec)
10
0
-10 0
13 25 38 50 63 75 88 100 113 125 138 150 163 175 188 200 213 225 238 250
-20
-30
-40
-50
-60
-70
-80
Figure 11.3.1 Horizontal Deceleration Profile From Test.
Angular Accleration
(rad/sec/sec)
1500
exp
model
1000
500
Time (msec)
0
0
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
-500
-1000
Figure 11.3.2 Comparison of Analytical Model and Experimental
Angular Acceleration of the Head.
35
70
Acceleration (m/sec/sec)
60
50
40
30
20
10
0
0
50
100
150
200
250
Time (msec)
Figure 11.3.3 Horizontal Deceleration Profile
Head Acceleration(g)
30
0.8 kg
1.2 kg
25
1.6 kg
20
15
10
5
0
0
50
100
150
200
Time(msec)
Figure 11.3.4 Head Acceleration Comparison
36
Neck Acceleration(g)
25
0.8 kg
1.2 kg
1.6 kg
20
15
10
5
0
0
50
100
150
200
Time(msec)
Figure 11.3.5 Neck (C4) Acceleration Comparison
0.8 kg
30
1.2 kg
1.6 kg
Head Acceleration (g)
25
20
15
10
5
0
Neck (C4)
Head
Time(msec)
Figure 11.3.6 Peak Acceleration (Head and Neck (C4))
37
0.8 kg
1.2 kg
20
1.6 kg
0
0
20
40
60
80
100
120
140
160
180
200
-20
-40
Head rotation relative
to chest (degrees)
-60
-80
-100
-120
Time(msec)
Figure 11.3.7 Head Angular Rotation
0.8 kg
120
1.2 kg
1.6 kg
Angular Rotation (°)
100
80
60
40
20
0
Head
Time(msec)
Figure 11.3.8 Peak Angular Rotation (Head)
38
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