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AcfObpoce »nicuical Research Laboratory Aerospace Medical Div, Air Force Systems Command i"- '»<""
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3 IN
I. KOO" TITLE
BIODYNAMIC MODELING AND SCALING: ANTHROPOMORPHIC DUMMIES, ANIMALS AND MAN
«. OESCRIPTIVt NOIII (Trp' ol rtpori mnd inrlu./». </.(.«;
> tuTHOmii (rift nmmt, mUdlm Iniiimi, /••> n«m«>
M. Kornhauser
*. REPORT OA Tl
December 1971
15
7«. TOTAL NO. OP PXCS
2L 76. NO. OP «t'l
22
*. PAOJCCT NO. 7231
j •«. OniClNATOR'S REPORT NUMS£A<*|
AMRL-TR-71-2S Paper No 6
lib. OTHER REPORT NOiSi (Any other numbtem tfitt mmf i« jiu.-.d f/lla report)
10. DISTRIBUTION STATEMENT
Approved for public release; distribution unlimited
II. SUPPLEMENTARY NOTES 12. ^PON^OHINW W.talTA«Y A C ~ . V I T Y
Aerospace Medical Researcn Laboratory Aerospace Medical D.v, Air Force Syste: Command, Wright-PattersonAF3, CH45-F
U. ABSTRACT
The Symposium on Biodynamics Models and Their Applications took place in Dayton, Ohio, on 26-28 October 1970 under the sponsorship of the National /•cademy of Sciences - National Research Council, Committee on Hearing, Bioacoustics, and Biomechanics; the National Aeronautics and Space Administration; and the Aerospace Medical Research Laboratory, Aerospace Medical Division, United States Air Fcrce. Most technical area's discussed included application of biodynamic mcceis for the establishment of environmental exposure limits, models for interpretation of ar.irr.ai, dummy, and operational experiments, mechanical characterization of living tissue and isolated organs, models to describe man's response to impact, blast, and acous- tic energy, and performance in biodynamic environments.
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PAPER NO. 6 ¥\D-'~)HOL|H3
BIODYNAMIC MODELING AND SCALING: ANTHROPOMORPHIC DUMMIES, ANIMALS AND MAN
M. Kornhauser
Consulting Services Wynnewood, Pennsylvania
«- ABSTRACT
£ After a brief outline of the applications and methods of biomechanics and the major sources of biodynamics data, this paper reviews the status of mathematical modeling, physical modeling (dummies) and scaling of models and damage levels.
Biomechanics data required for preparing mathematical models, as well as for adjusting and validating the computer programs, are found to be insufficient for computational applications. Because of this paucity of supporting data, computer models are in general oversimplified and rudi- mentary, despite the availability of adequate computational techniques used in the aerospace industry.
Physical models and the requirements for dynamic similarity are discussed. Although quantitative simulation is warranted under some cir- cumstances, anthropomorphic dummies are expected to be of most value as visual aids and for purposes of demonstrating kinematic relationships between man and vehicle.
Scaling from dummies to man and from animals to man is difficult to justify theoretically because of differences in structure, size and modes of failure. However, damage scaling in terms of the inputs (G and delta-V) required for failure, is shown to be accurate enough for purposes of rough approximation.
The mathematical model approach, with proper validation, is concluded to offer ultimately the greatest promise of accurate quantitative prediction.
171
INTRODUCTION
Biomechanics is an interdisciplinary blending of the biomedical and
the physical sciences applied to the effects of dynamic mechanical environments
on living organisms. In its broadest terms, biomechanics covers a wide
range of mechanical environments such as shock and vibration, acoustic
inputs, air blast, underwater explosion effects, etc. ; as well as applications
to a variety of organisms. The discussions of this paper are restricted to
the narrower subject of the effects of whole body impact or deceleration
(not direct impact of projectiles, etc. ) on man and other animals.
The primary purpose of biomechanics is to predict response and
injury, via the following route:
(1) Input - Definition of the force application or input to the
biological system, spatially and in terms of its time history. In many cases
the loading system is coupled to the biomechanical system, for example in
the cases of vehicular crashes, and it may become necessary to define inputs
to the entire vehicle-man coupled system.
(2) Response - Observation, analysis or prediction of the response
of the organism to the inputs. In the cases of analysis and prediction, it is
necessary to obtain some kind of biomechanical definition, or model, of the
organism and to subject this model to the mechanical inputs.
(3) Failure - Observation, analysis or prediction of failure, damage,
or injury to the organism. For purposes of prediction, it becomes necessary
to determine the various mechanisms of injury and to ascertain whether one
or more mechanisms have been excited to the point of failure.
(4) Prediction - Prediction of response and failure of the animal,
or another animal, to other inputs.
The latter three steps are discussed further in this paper in terms
of the methods employed, an evaluation of accomplishments to date, and
recommendations for the future.
172
METHODS OF BIOMECHANICS
Four broad sources of data are employed to assist in the process
of prediction human response and injury:
(1) Results of experimentation on man and natural incidents
involving humans.
(2) Animal experimentation.
(3) Mathematical "experiments" with computer models.
(4) Physical experimentation with dummies.
Table 1 presents in capsule form the relative advantages and disad-
vantages of each approach to obtaining useful data.
The above listing of methods of obtaining data is generally in the
direction of less direct applicability to man (requiring more adjustment,
interpretation, or scaling) for numbers (2), (3), and (4), although their
sequence is not intended to be exact. Mathematical and physical models
are discussed below in terms of the sources of inaccuracy and methods of
application.
MATHEMATICAL MODELING
The process of mathematical modeling of the human body may be
compared directly with the similar process employed in the aerospace
industry to model a large aircraft or space structure. Table 2 lists the
main steps required to develop and validate a mathematical model.
Although the aerospace industry has matured and developed a
sophisticated technology of mathematical modeling, the biomechanics
community has not been able to justify complex models (because of the
paucity of the biomechanical data required for modeling and validation of
models) and only very recently has begun to adopt aerospace methods. The
best work has been done in the biomedical areas (1) and (3) of Table 2, but
the potentialities of the engineering areas (2) and (4) have not been ex-
ploited well.
173
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Much work has been done to define tissue and joint properties.
Without tabulating the actual properties, Table 3 lists some sources and
examples of the data available. Data of this kind must be available in order
to accomplish Step (1) of Table 2.
Step (2) of Table 2 involves formation of the system model, which may
be one or more organs, the entire body, the body plus restraints, etc. ,
depending on the application to be simulated. The human body is a structurally
complex system, composed of subsystems (organs, limbs, etc. ) made of
dissimilar materials and coupled to each other in complex ways. In certain,
loading regimes such as high frequency vibrations, grossly different trans-
mission properties of the bony skeleton and the "hydraulic" vascular system
will result in parallel structural systems responding out of phase, but
coupled throughout by interconnecting tissues. With lower frequency inputs,
however, the parallel systems may react essentially as one system. Modeling
such a system poses formidable challenges to the structural dynamics analyst
who is accustomed to modeling aerospace structures. He must learn to
select the significant breakdowns of mass, elasticity and damping in order
to construct the biodynamic model; and the selection techniques will be
somewhat different from those he has used for steel or titanium in plates,
shells, I beams, etc. However, the general methods of analysis are
identical, and the aerospace industry can provide a powerful tool for computer
modeling the complex human structure.
Hurty , Bamford and others develop a most fruitful method for
computer modeling of exceedingly complex structures. In the component
mode approach to modeling, the subsystems are first broken down to
whatever level of detail is required for adequate dynamic representation.
Experience and judgment are, of course, required to determine adequacy.
Besides, however, the subsystem may be tested experimentally to ascertain
whether enough modes have been represented, and how accurately. There
may, of course, turn out to be a limitation in computer capacity or running
time, which could force the modeler to split the subsystem into smaller
176
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subsystems. However, with a large machine which can handle of the order
of 100 elements comfortably, it should be possible to develop good dynamic
lumped models of each human organ as a subsystem. The subsystem program
is then run to obtain output modes. Subsystems are now tied together at
their physical points of connection to obtain overall system response to a
set of inputs. The final step is to go back to each subsystem to read out
its response (perhaps to failure) in its own modes.
The basic advantage of working in modal coordinates is economy.
The overall coupled system modes are approximately equal to the number of
subsystems times the modes represented in each subsystem. Therefore if
an average of 10 modes were found adequate to represent each of 10 different
subsystems, the coupled system program would have 100 elements. A
single program for all subsystems taken together could have required 1, 000
elements, which would have been prohibitive in size. Therefore the component
mode approach appears suitable for modeling the human body, with its
hundreds of bones and muscles.
A comment is in order on the question of continuum mechanics
programs vs. lumped parameter programs. There is really no difference
between these approaches if a fine enough breakdown of lumped parameters
is made. Stress wave behavior will be exhibited without an inordinate degree
of definition. A beam or column, for example, will require of the order of
10 subdivisions to exhibit minimum "continuous" properties.
Nonlinearities do pose a special problem in the component mode
approach, since the modes will shift with change in amplitude of input and
response. For example, it is known that a steady linear acceleration will
cause increased stiffness, less damping, and higher energy transmission
to internal organs when the human body is then subjected to vibration. It
is therefore necessary to adjust the subsystem modes to be consistent
with the response obtained, and this will be somewhat of an iterative process.
178
After the computer model has been assembled and exercised (step 3
of Table 2), it is desirable to make adjustments at all levels possible within 1,2 3
the system. Test data ' on modes, frequencies, etc. should be used to
validate and adjust the subsystem programs. Table 4 presents some data
on first mode frequencies.
Besides response data, static and dynamic failure data should be
employed to validate computer models. (Some of these data will be presented
below in a discussion of damage scaling). The end product is an adjusted and
validated computer program -which should provide some predictive value when
applied to a situation for which experimental data do not exist.
How well has the biomechanics rationale described above been applied
to the human body subjected to impact? The answer is, generally, in a
rudimentary and perfunctory fashion. A fair (but not complete) picture of
the history of computer models applied to human impact is presented in
Table 5, in chronological order.
The earlier models were oversimplified one-or-two degree of freedom
models, and they had limited predictive value. Some recent models (Turnbow,
McHenry and Naab) treated the man as a kinematic linkage without internal
flexibility, so that only external (to the body) loads could be determined.
Other more detailed models (Coermann, Starr) were still not fine enough
in breakdown to yield significant load and failure results within the human 13
body. Only the most recent work of Orne and Liu appears to have sufficient
detail to be a truly significant tool for predicting spinal response and failure.
Unfortunately, their model does not appear to have been adjusted by comparison
with experiment, and validation of its predictive utility remains to be
demonstrated.
To summarize the state of the art, it appears that only this year has
an (apparently) adequate model of the human spine been developed. Obviously,
much work remains in developing adequate models of the other human sub-
systems (limbs, organs, etc. ), and coupling them to finally obtain a good
system model of the human body.
179
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181
PHYSICAL MODELING AND SCALING
Table 1 summarizes the major advantages and limitations of using
dummies as biodynamic tools, and these will not be expanded in more detail.
Further, although it would be useful to discuss the practical problems of
material selection (physical simulation of properties) and model construction
(friction in joints, etc. ), the present discussion will be restricted to the
questions of scaling "laws" and what they predict about the adequacy of dummies
and animals to represent the human body.
27 Hudson presents a rather thorough discussion of scale model principles,
although he does not address the special problems of anthropomorphic dummies.
It is not appropriate to present here the theory of dimensional analysis and
dynamic similarity. Instead, the conclusions reached by Hudson and others
on the conditions required for dynamic similarity are presented in Table 6.
For dynamic similarity in general, it appears that geometric similarity
and identical material properties are required. Hudson, however, indicates
some structures for which complete geometric similarity is not required
and for which all material properties need not be identical. Likewise, Baker 30 31
and Westine and Horowitz and Nevill discuss modeling with dissimilar
materials, although the former require materials with similar stress-strain
curves while the latter use the area under the stress-strain as the correction
criterion. Thus it appears possible to justify relaxation of the requirements
for dynamic similarity under special circumstances .
Since humans and other animals are exceedingly complex structures,
it is not possible to justify simulation by dummies on any theoretical basis.
Only under very restrictive conditions, as for example when using kinematic
dummies (no flexibilities, but simply masses and linkages with correct
moments of inertia) to find motions and loads on restraint systems, can
physical models serve useful quantitative purposes. As tools for purposes
of visualization, or for demonstrating kinematic relationships of human and
vehicle dynamics, anthropomorphic dummies are very helpful.
182
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The scaling difficulties mentioned above apply, of course, to animal-
to-human comparisons. Structure and size differences present serious
obstacles to quantitative scaling. However, as with dummies, animal experi-
mentation is invaluable in uncovering responses and failure mechanisms which
often suggest similar qualitative behavior of human.
An invaluable animal-to-man correlation approach is to work with
non-human primates of similar construction and to scale directly to man. This
approach, of course, allows experimentation with primates which would not
be permitted with humans. Besides this direct scaling for clinical purposes,
the primate-series experimentation offers exciting possibilities for measuring
tissue and organ properties and responses required for developing and validating
computer models, which models may later be scaled for applications to humans.
DAMAGE SCALING
Despite the differences in structure which precludes any rationale
for scaling between animals and man, it has been possible to do some fairly
successful scaling based on the inputs required to produce damage. This is
even more surprising when one considers the different modes of failure
possible with any animal and man. Table 7 presents some modes of damage
and the inputs required to produce them.
The two main input parameters found most useful for scaling purposes
are acceleration level, or number of g's, and velocity change, delta-v. There
exists a background of structural dynamics technology (see, for example, 42
Kornhauser ) which presents the rationale for employing these two parameters
to characterize the input shock, even though some not-quite-second-order
effects are omitted (rise time, pulse shape, etc. ), and the two parameters
do indeed prove useful in presenting animal survival data. Kornhauser and 43
Gold show the following very approximate scaling laws for a wide range of
animal sizes:
G = 40/L Eq. (1)
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185
where L is a characteristic length (in feet) in the direction of acceleration, and
27 < delta v < 53 fps Eq. (2)
for all animals tested to date.
The first scaling law makes sense if animal tissues have approximately
equal densities and strengths. If the tissues behave as fluids with the density
of water, then the pressure produced by 1 g of acceleration is equal to about
1/2 psi per foot of "depth". Equation (1) above would then be equivalent to
the statement that animal structures can withstand about 20 psi of pressure,
induced by inertia loading of the tissues.
The second law shows the relative invariance of the delta-v required
to produce injury, over a wide variety of animals from mice to men. At first
glance this is most surprising, because of differences in size and structure. 42
However, size in itself may be explained away, since Kornhauser shows
that delta-v is almost constant for uniform beams of any size, with small
variations to account for different boundary conditions or methods of support.
Structural differences, unfortunately, are not that easy to rationalize since
beams and shells with concentrated masses may have much lower delta-v
for failure than uniform beams.
Despite structural differences, there is a mechanism for explaining
why animal delta-v's are not too different; namely, Darwinian natural selection.
Land animals live in an environment which produces falls from various heights,
and impact tolerance should be a definite factor in survivability and natural
selection. By this token, of course, the tree-dwelling creatures would be
expected to survive higher delta-v's than surface dwellers. To test this
hypothesis, Table 8 separates various animals into these two groups. Some
correlation does show, but not enough to be conclusive. Perhaps some impact
testing offish would reveal whether or not Darwinian selection has had much
to do with the existing delta-v tolerances of animals.
186
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187
CONCLUSIONS
(1) Because of the paucity of biomechanical data required for modeling
and validation of analytical models and for definition of failure points, bio-
mechanical models have been rudimentary. Sophisticated computer modeling
techniques are available, however, for modeling the most complex biological
systems.
(2) Scaling of anthropomorphic dummy data is seldom justifiable on
a theoretical basis, but some quantitative results of a kinematic (rather than
deformational) nature may be obtained. Dummy experimentation is therefore
of greatest value in producing kinematic data as well as qualitative data.
(3) Animal-to-man scaling is most fruitful with primates, and this
suggests the value of developing and validating primate computer models in
order to help in validating the human analytical models.
188
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3. Rodden, W. P. "A Method for Deriving Structural Influence Coefficients from Ground Vibration Tests" AIAA Journal, 5, 5, May 1967, 991-1000
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REFERENCES (Continued)
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16. Hurty, W. C. "Dynamic Analysis of Structural Systems using Component Modes", ALAA Journal, 3, 4, April 1965, 678-685
17. Bamford, R. M. "A Modal Combination Program for Dynamic Analysis of Structures", JPL, Pasadena, Calif., Aug. 1966
18. Hirsch, A. E. "Man's Response to Shock Motions", Navy Dept. , DTMB Report 1797, Jan. 1964, AD 436809
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20. Stech, E. L. and Payne, P. R. "Dynamic Models of the Human Body", AMRL-TR-66-157, Nov. 1969, AD 701383
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26. Kornhauser, M. "Impact Protection for the Human Structure" Proc. AAS, Western Regional Mtg. , Palo Alto, Calif. 1958
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REFERENCES (Continued)
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29. Heller, S. R. Jr. "Structural Similitude for Impact Phenomena" DTMB Report 1071, April 1952
30. Baker, W. E. and Westine, P. S. "Modeling the Blast Response of Structures using Dissimilar Materials", AIAA Journal, 7, 5, May 1969, 951-959
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33. Lombard, C. F. et al "Voluntary Tolerance of the Human to Impact Accelerations of the Head" J. Av. Medicine, 22, 2, 1951
34. Hirsch, A. E. "Current Problems in Head Protection", Head Injury Conf. Proc. , Lippincott, Philadelphia, 1966
35. Rayne, J. M. and Maslen, K. R. "Factors in the Design of Protective Helmets", J. Aviation Medicine, June 1969, 631-637
36. Gurdjian, E. S. et al "Observations on the Mechanism of Brain Concussion, Contusion, and Laceration" Surgery, Gynecology, and Obstetrics, 101, 1955
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38. von Gierke, H. E. "On the Dynamics of some Head Injury Mechanisms' Head Injury Conf. Proc. , Lippincott Co. , 1966
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191
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40. Evans, F. G. and Patrick, L. M. "Impact Damage to Internal Organs" Symp. on Impact Accel. Stress, Nov. 27-29, 1961, Brooks AFB, San Antonio, Texas
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192
