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Computer Simulation of Stair Falls to Investigate Scenarios in Child Abuse
Gina E. Bertocci, PhD;
Mary Clyde Pierce, MD;
Ernest Deemer, MS;
Fernando Aguel, BS
Arch Pediatr Adolesc Med. 2001;155:1008-1014.
ABSTRACT
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Objectives To demonstrate the usefulness of computer simulation techniques in the
investigation of pediatric stair falls. Since stair falls are a common falsely
reported injury scenario in child abuse, our specific aim was to investigate
the influence of stair characteristics on injury biomechanics of pediatric
stair falls by using a computer simulation model. Our long-term goal is to
use knowledge of biomechanics to aid in distinguishing between accidents and
abuse.
Methods A computer simulation model of a 3-year-old child falling down stairs
was developed using commercially available simulation software. This model
was used to investigate the influence that stair characteristics have on biomechanical
measures associated with injury risk. Since femur fractures occur in unintentional
and abuse scenarios, biomechanical measures were focused on the lower extremities.
Results The number and slope of steps and stair surface friction and elasticity
were found to affect biomechanical measures associated with injury risk.
Conclusions Computer simulation techniques are useful for investigating the biomechanics
of stair falls. Using our simulation model, we determined that stair characteristics
have an effect on potential for lower extremity injuries. Although absolute
values of biomechanical measures should not be relied on in an unvalidated
model such as this, relationships between accident-environment factors and
biomechanical measures can be studied through simulation. Future efforts will
focus on model validation.
INTRODUCTION
IN CHILD abuse cases, caregivers often falsely report common fall scenarios
such as stair falls as the underlying cause of injury. Unfortunately, it is
often difficult to determine the validity of caregiver-stated scenarios, since
so little is known regarding pediatric biomechanics and injury risk associated
with these relatively common falls. A better understanding of the influence
that specific fall-environment factors have on injury biomechanics in children
is needed. We propose that computer simulation can be used in evaluating the
effect that the fall environment has on biomechanical measures associated
with injury. With the use of computer simulation, a single characteristic
of the fall environment, eg, the type or construction of steps, can be altered
to investigate its influence on injury biomechanics and therefore injury potential.
In our study, we used computer simulation modeling to investigate the effect
of various stair characteristics on injury risk measures.
Studies such as those conducted by Lyons and Oates1
using case-specific biomechanical measures to evaluate injuries in children
who have fallen from a bed are needed to begin scientifically distinguishing
between unintentional and abusive injuries. In their study, injuries of 207
children who had fallen from beds or horizontal surfaces were classified by
body region and correlated to momentum (child mass x fall velocity)
of the child during the fall. Similar studies investigating the relationships
between types of injuries and the biophysics of pediatric free falls are also
available in the literature.2, 3, 4
Joffe and Ludwig5 evaluated 363 stair falls
in children aged 1 month to 19 years in an effort to better describe injuries
resulting from stair falls. Although a limited number of studies describing
relationships between the biophysics of a particular fall and associated injuries
in children exist, additional studies are greatly needed to advance the forensic
science to detect child abuse.
Femoral fractures are one of the most common fracture types associated
with child abuse in children 5 years and younger.6, 7, 8, 9, 10, 11, 12, 13
However, femoral fractures can also result from falls in young children, making
differentiation between abuse and unintentional injury mechanisms difficult
for clinicians. To begin developing a foundation to aid in delineating between
unintentional and abusive femur fractures, we propose using computer simulation
to investigate pediatric biomechanics associated with common falls. Since
femur fractures are common fractures associated with child abuse, and stair
falls are a common scenario falsely reported in child abuse, our study is
focused on the biomechanics of the upper leg during stair falls.
Fall characteristics and environment factors such as height of fall
and impact surface properties have been shown to influence injury risk in
pediatric and adult falls.2, 14, 15, 16, 17
Mott et al16 reported that children sustained
significant increases in injuries on playgrounds with concrete surfaces as
opposed to those with bark or rubber surfaces. Studies have also documented
height of falls from playground equipment as having significant influence
on injury risk and fracture incidence.14 The
study by Joffe and Ludwig5 of pediatric injuries
in stair falls found that falls involving fewer than 4 steps had a similar
incidence and severity of injury to those involving more than 4 steps. Case-based
studies such as these are needed to define relationships between characteristics
of the fall environment and corresponding injuries. Unfortunately, reconstruction
of the victim, the initial condition, and the fall environment are often difficult
to capture retrospectively. Computer simulation and modeling techniques offer
tools that can aid in the investigation of falls when data from real-world
scenarios are limited.
Computer simulation techniques have been used extensively in the prediction
of injury risk, particularly in motor vehicle crash analysis.18, 19
Recently, the Institute of Medicine has recommended an increase in the use
of computer simulation techniques to study injury mechanisms and to predict
injury risk.20 Computer simulation has allowed
engineers to economically study the influence of various factors on the risk
of injury in a given scenario. Once an experimentally validated simulation
model has been developed, savings can be realized through reduction in the
number of costly experimental tests needed to investigate slight permutations.
In our study, we used computer simulation to investigate the effects of number
of steps, stair-surface friction, stair-surface elasticity, and slope of steps
on key biomechanical measures of the upper leg that are associated with injury
risk.
MATERIALS AND METHODS
SIMULATION SOFTWARE
General-purpose mechanical computer simulation software (Working Model
3D; MSC.Working Knowledge, San Mateo, Calif) was used to develop a model of
a 3-year-old child stair fall. This rigid-body software is commonly used to
study the motion and interaction of mechanical linkages. Various 3-D geometric
shapes, joints, and mechanical constraints, eg, springs and dampers, are available
in the software to construct body segments or the fall environment. Inertial
properties of each model segment, eg, mass, center of gravity, and mass distribution,
can also be prescribed. Surface characteristics, including friction and elasticity,
which influence the contact between segments and the fall environment, also
can be specified in the model. Forces and torques of specified magnitude and
direction can be applied to the model segments and are used to establish initial
conditions of various body segments. These parameters, with the specified
inertial properties of the model segments and their surface characteristics
that influence interaction with the fall environment, dictate the motion and
response of the model. Simulations are controlled through equations of motion
defined by principles of physics and are not constrained by animation. Measurements
of force, rotational acceleration, linear acceleration, velocity, and self-defined
parameters can be measured and recorded for each segment throughout the simulation
event.
DEVELOPMENT OF FALL ENVIRONMENT AND 3-YEAR-OLD CHILD MODEL
Using various geometric shapes, stairs with a pitch (slope) of 8:8 (rise-run
or stair-height–depth) were constructed in the model (Figure 1). Stair-surface friction and elasticity variables were
also prescribed. The 3-year-old child model was constructed using ellipsoid
segments with mass and inertial properties matching that of the Hybrid III
3-year-old anthropometric test dummy (ATD). This ATD has been developed for
use in motor vehicle crash analysis and provides an approximation of a 50th-percentile
3-year-old child. In addition, the matching of model specifications to the
existing physical ATD will allow for future experimental validation of the
model. Anatomically equivalent joints with prescribed ranges of motion were
used for the hips, neck, shoulders, elbows, and knees. The ATD was placed
at the edge of the stairs in a crawling position, and gravity initiated the
forward movement.
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Figure 1. Simulation model of a stair fall
by a 3-year-old child. A, initial position; B, midfall; and C, final resting
position.
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SENSITIVITY ANALYSIS
Computer simulations are useful in evaluating the effects of the fall
environment on biomechanics or other injury outcomes through a process known
as parametric sensitivity analysis.18, 19, 21
Such an analysis varies by only 1 factor at a time while maintaining all others
constant, allowing us to study the effects of each separate parameter on fall
biomechanics. For example, the influence that the type of flooring may have
on fall biomechanics or injury outcome in a given fall can be investigated
by stepwise variation of floor surface stiffness while maintaining all other
model parameters constant.
The contact interface between the sole of a shoe and flooring or stair
surface can be characterized by resilience and friction properties of both
materials in contact. Friction, or slip resistance, between 2 contact surfaces
can be represented by the coefficient of friction (COF). Frictional properties
are also highly dependent on surface conditions (wet vs dry). For example,
hard rubber-soled shoes on a dry vinyl tile floor have a COF of near 1, whereas
the same shoe on a more slippery oil-coated surface has a COF of approximately
0.1.22 The resiliency or elasticity (stiffness)
of the shoe-surface interface can be defined by the coefficient of restitution
(COR). The COR can be further defined as the amount of energy that is absorbed
when 2 objects collide or come into contact. Shoe-surface contacts that are
resilient will have CORs that approach 1. Materials that absorb energy on
impact typically have low COR values. Examples of material COR values include
the following: wood, 0.50; rubber, 0.95; rock, 0.20; and clay, 0.02.23
The baseline stair-fall model was defined as 7 steps with a slope of
8:8 and midrange surface friction (COF = 0.5) and stair elasticity (COR =
0.50). To determine the sensitivity of ATD fall biomechanics to various environment
parameters, simulations were run in which 1 of the following parameters was
varied while all others were held constant: number of steps, slope of stairs,
stair-surface friction, and stair-surface elasticity. Starting with the baseline
model, simulations were conducted for 3, 7, 11, and 15 steps while maintaining
midrange stair friction and elasticity and an 8:8 stair slope. Simulations
were also run for a series of stair-surface frictions (defined by the COF)
ranging from a very slippery surface (COF = 0) to a nonslip surface (COF =
0.9) using the 7-step model and maintaining midrange surface elasticity. Next,
using the 7-step, 8:8 slope model with constant stair-surface friction, simulations
were conducted for varying stair elasticity (defined by the COR), ranging
from a soft, "bouncy" surface (COR = 1.00) to a hard, more rigid surface (COR
= 0). Finally, using the 7-step model with midrange surface friction and elasticity,
the slope of stairs was decreased from the baseline 8:8 to 8:10 and 8:12.
(Most building codes permit a stair slope of  8:12.) For all simulations,
biomechanical measures associated with upper leg injury risk were evaluated.
These measures included upper leg impact velocity with the steps, energy,
and momentum. All measures were made at the center of gravity of the upper
leg. Peak values of each variable were extracted for analysis.
RESULTS
Without experimental validation, results of simulations can only be
used to study relationships and trends among variables. Since our model has
not been experimentally validated, absolute values of biomechanical measures
will not be presented; instead only relationships between biomechanical measures
and fall-environment factors will be described. Figure 1 characterizes the initial and final conditions of the child
and the total body kinematics during the stair fall. Observation of the fall
dynamics showed that the upper leg may hit the steps several times during
a stair fall, with increasing contacts associated with falls involving more
steps. Our model also demonstrated a slightly asymmetrical fall pattern, which
can lead to differences in biomechanical measures associated with the right
and left legs.
NUMBER OF STEPS
All biomechanical measures were influenced by changes in the number
of steps. The impact velocity of the upper leg (speed with which the leg impacts
the steps) increased as the number of steps was increased in the model (Figure 2). When a 3-step fall was compared
with a 15-step fall, impact velocity of the upper leg increased 3-fold. As
much as a 7-fold increase was observed in the peak kinetic energy of the upper
leg when a 3-step fall was compared with a 15-step fall (Figure 3). Since momentum is a function of velocity, similar increases
in momentum are seen with increasing numbers of steps (Figure 4). Momentum of the upper leg is nearly 3 times greater in
the 15-step fall compared with the 3-step fall. These findings suggest that
potential for upper leg injury increases with increased number of steps.
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Figure 2. Impact velocity of upper leg vs
number of steps.
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Figure 3. Kinetic energy of upper leg vs
number of steps.
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Figure 4. Momentum of upper leg vs number
of steps.
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STAIR FRICTION
All biomechanical measures decreased with increases in stair friction.
Stair falls with a step COF of 0, representing a slippery surface, had higher
upper leg impact velocity, kinetic energy, and momentum compared with nonslip
stair surfaces (represented by a COF approaching 1). A step COF of 0 (slippery
surface) in a 7-step fall generated a peak impact velocity of the upper leg
that doubled the velocity found in the same fall with a nonslip surface (COF
= 0.9) (Figure 5). Kinetic energy
associated with the fall on a slippery surface (COF = 0) was 2 to 3.5 times
higher than that associated with a less slippery or nonslip surface (COF =
0.9) (Figure 6). Similarly, momentum
was nearly doubled for slippery stair surfaces (COF = 0) compared with surfaces
with only slightly greater friction (COF 0.2) in the 7-step fall (Figure 7). These findings suggest that slippery
stair surfaces tend to increase potential for upper leg injury in a stair
fall.
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Figure 5. Impact velocity of upper leg vs
coefficient of friction (COF).
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Figure 6. Kinetic energy of upper leg vs
coefficient of friction (COF).
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Figure 7. Momentum of upper leg vs coefficient
of friction (COF).
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STAIR ELASTICITY
The elasticity (COR) or stiffness of the stairs was found to influence
biomechanical measures. Kinetic energy decreased nearly 4-fold as COR was
increased from 0 to 1.00 (Figure 8).
Impact velocity and momentum also decreased slightly with increasing values
of COR (Figure 9 and Figure 10). These findings suggest that stairs constructed of highly
elastic materials tend to decrease risk for upper leg injuries in a stair
fall.
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Figure 8. Kinetic energy of upper leg vs
coefficient of restitution (COR) (elasticity).
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Figure 9. Impact velocity of upper leg vs
coefficient of restitution (COR) (elasticity).
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Figure 10. Momentum of upper leg vs coefficient
of restitution (COR) (elasticity).
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SLOPE OF STAIRS
The slope of the stairs was also found to influence all biomechanical
measures. In general, increases in the slope of stairs led to increases in
biomechanical measures. Kinetic energy increased nearly 4-fold as the stair
slope was increased from 8:12 to 8:8 (Figure
11). Momentum and velocity increased 2-fold with the same increase
in slope (Figure 12 and Figure 13). These findings suggest that
steeper stairs tend to increase injury risk of the upper leg in a stair fall.
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Figure 11. Kinetic energy of upper leg vs
slope of stairs (rise-run).
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Figure 12. Momentum of upper leg vs slope
of stairs (rise-run).
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Figure 13. Impact velocity of upper leg
vs slope of stairs (rise-run).
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COMMENT
Using computer simulation models of a 3-year-old pediatric stair fall,
we investigated the relationships between potential for upper leg injury and
various fall-environment factors. Findings indicate that stair characteristics
and the number of steps influence biomechanical outcome measures, and thus
injury potential. Simulations revealed that increasing the number of steps,
reducing stair friction (eg, slippery surface), decreasing stair stiffness
(eg, concrete stairs), or increasing stair slope tended to elevate biomechanical
measures increasing the potential for upper leg injury.
Our findings further suggest that characteristics of the fall environment
can play a key role in predicting likelihood of injury. In other words, one
stair fall is not the same as another, although they may have involved the
same number of steps. This concept illustrates the need for more detailed
investigation of fall scenes, especially when attempting to distinguish between
unintentional and abusive cases. Also, similar detail is needed when conducting
and reporting case-based epidemiological studies to correlate injuries to
particular fall types. For example, although the study by Joffe and Ludwig5 relates the number of steps to the incidence and severity
of pediatric injury, additional details of the fall environment and stair
characteristics are needed to build an accurate database of stair fall injuries.
(Joffe and Ludwig indicate that injury risk and severity were similar in stair
falls involving more than 4 steps and stair falls involving fewer than 4 steps,
without specification of stair characteristics.) Details of the victim's initial
position and stair characteristics, such as those investigated in this study
(surface friction, surface elasticity, and stair slope), must also be documented
to make definitive statements related to injuries resulting from particular
types of falls. As shown through simulations, characteristics of the fall
environment affect biomechanics and the potential for injury. That is, a 7-step
stair fall with a slippery or icy stair surface may have a higher potential
for producing injury than a 7-step stair fall with steps that have a nonslip
surface. Substantiating our findings, a report by Ellis24
proposes that stair-surface characteristics are 1 of 3 primary factors contributing
to stair falls.
Unfortunately, few studies correlate fall-environment characteristics
to injury type and severity that can be used as the basis for a pediatric
stair fall injury risk model. However, the study by Joffe and Ludwig5 proposes an injury mechanism model that suggests "that
stairway falls consist of an initial mild to moderately severe impact followed
by a series of low-energy non-injurious falls." They further state that "there
is no correlation between severity and number of steps fallen down" and that
"the absence of severe or numerous injuries in falling down a greater number
of steps is predicted by this model." Our simulation results do not agree
with such findings and are in conflict with a stair fall injury risk model
that is independent of the number of steps. Using our simulation model, we
have further shown that overall body injury potential would likely increase
with more steps, since total body velocity increases with the number of steps
(Figure 14). Our simulation results
support a model that reflects dependency of injury risk on the number of steps
and other stair characteristics (surface materials and slope). We speculate
that differences between our simulation-based model and the case-based model
of Joffe and Ludwig may be due in part to undocumented variations in stair
characteristics, eg, surface friction, surface elasticity, and stair slope.
However, our model predicts injury risk or the likelihood of injury, whereas
the model by Joffe and Ludwig was based on actual injury incidence. Our predictions
of increased injury risk, implied through changes in biomechanical measures,
may still be below injury tolerance levels and would not have been associated
with injury incidence. In other words, predicted increases in injury risk
may not reflect the difference between the absence or presence of injury or
differences in injury severity. Discrepancies in these limited studies further
justify the need for additional investigation in the area of stair fall biomechanics
and injury incidence in the development of a pediatric stair fall injury model.
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Figure 14. Total body velocity vs number
of steps for varying slopes (rise-run).
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Since community and government policies often dictate the design of
playgrounds, injury epidemiology studies of playground falls have been motivated
to document key environment details such as impact surface characteristics
and heights of playground equipment.14, 16
This type of detailed fall information and the associated injuries, occurring
in a controlled playground environment, have provided a foundation for correlating
playground injuries to the fall environment. These studies of playground injuries,
like our computer simulation stair fall study, document the importance that
subtle changes in the fall environment can have on injury potential.
The stair fall simulation model used in this study has not been experimentally
validated. Future plans for our study include conducting experimental trials
of stair falls for use in validating our model. Without experimental validation,
absolute values of biomechanical measures should not be relied on and simulation
results should only be used to study relationships between model parameters
and outcome measures.
CONCLUSIONS
This study illustrated the usefulness of computer simulation techniques
to investigate the influence of stair characteristics on pediatric injury
potential associated with a stair fall. Although a number of factors must
be considered when attempting to distinguish between injuries that have resulted
from unintentional actions or abuse, knowledge of the relationships between
the fall environment and injury potential is key to providing clinicians a
scientific basis for judgment. Findings of our study documented that stair
characteristics, eg, surface materials and slope, can play an important role
in the likelihood of upper leg injury risk. Such findings further highlight
the need to carefully document the details of the fall environment when conducting
pediatric injury epidemiology studies. Validated fall simulations, leveraged
with case-based injury studies, ultimately will aid in developing an empirical
injury model for use by clinicians in detecting child abuse.
AUTHOR INFORMATION
| Editor's Note:
With this article by Bertocci and colleagues, we take advantage of the
current capabilities of information technology. Computer modeling was used
to simulate children falling down stairs—the consequences of which are
commonly seen in our emergency departments. The effect of the number of stairs
and the steepness of them was examined in a series of computer simulations.
It is a dramatic example of how technology can be used to shed new
light on an age-old
problem. We welcome other such creative uses of information technology for
articles published in ARCHIVES.—Frederick P. Rivara, MD, MPH
To view the computer simulation, link to the file:
View Computer Simulation You will need Quick Time to view this video:
Download free copy of Quick Time |
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What This Study Adds
In child abuse cases, caregivers often falsely report common fall scenarios
such as stair falls as the underlying cause of injury. Unfortunately, it is
often difficult to determine the validity of caregiver-stated scenarios, since
so little is known regarding pediatric biomechanics and injury risk associated
with these relatively common falls. A better understanding of the influence
that specific fall environment factors have on injury biomechanics in children
is needed. Our long-term goal is to use knowledge of biomechanics to aid in
distinguishing between accidents and abuse. Our study demonstrated the usefulness
of computer simulation techniques for investigating the biomechanics of stair
falls. Using our simulation model, we determined that stair characteristics
have an effect on lower extremity injury potential.
Accepted for publication March 27, 2001.
This research was funded through grants from the Childrens' Hospital
of Pittsburgh (Pittsburgh, Pa), the Whitaker Foundation (Arlington, Va), and
the Centers for Disease Control and Prevention–Center for Injury Research
and Control (Atlanta, Ga).
A poster format abstract of this work was presented at the 2000 Pediatric
Academic Society Conference, Boston, Mass, May 12-16, 2000.
This work is dedicated to Frances Pierce, August 3, 1919, to December
21, 2000, Dr Pierce's mom and life inspiration.
Opinions expressed are those of the authors and do not necessarily reflect
those of the funding agencies.
From the Departments of Bioengineering (Dr Bertocci and Mssrs Deemer
and Aguel), Rehabilitation Science and Technology (Dr Bertocci and Mssrs Deemer
and Aguel), and Pediatrics (Drs Bertocci and Pierce), Childrens' Hospital
of Pittsburgh, University of Pittsburgh, Pittsburgh, Pa.
Corresponding author and reprints: Gina E. Bertocci, PhD, University
of Pittsburgh, Rehabilitation Science and Technology, 5044 Forbes Tower, Pittsburgh,
PA 15260 (e-mail: ginaber{at}pitt.edu).
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