1.
MODELING UPPER ARM TRAUMA USING FINITE
ELEMENT ANALYSIS
By
Caroline Ashford, Brooke Burns, Connor McDermott, and Maggie Shilling
Dr. Cullinane
Biomedical Research
April 11th, 2014

2.
INTRODUCTION
Each year in the United States, six million men and women are victims of domestic violence
(Domestic Violence Resource Center, 2013). The presence of bruising can be an indicator of
abuse, particularly in locations where accidental occurrence is infrequent (Arkbarnia and
Campbell, 2005). Bruising in soft connective tissue occurs when a load from blunt trauma
exceeds the ultimate strength of capillaries (Huang et al., 2012). Minimal research of bruising at
the capillary level inhibits effective abuse diagnosis. Determining the failure threshold of
capillaries and investigating the mechanism under which they fail may eventually enable
physicians to better differentiate and diagnose abuse.
When capillaries fail, blood pools into the surrounding tissue, resulting in discoloration,
minor swelling, and pain (Kumar et. al., 2009;; DiMaio and DiMaio, 2001). Shear stress and
hydraulic induced tensile stress are two hypothesized modes of capillary failure. Shear stress
occurs when a region of tissue containing a capillary bed resists two opposing forces acting in
parallel planes;; resulting in shear strain (Tang et al., 2013). Hydraulic induced tensile stress in
bruising is defined as when a capillary deforms under high pressure and forces blood outside the
compression zone (Tang et al., 2013). The blood being forced at high pressure from one area to
another acts analogously to that of water in a hose;; stress is applied to a capillary in the
compression zone and blood disperses from the area of impact like water rushing from one end
of a hose to another as a truck runs over it. Pressure, known as tensile stress, builds around the
capillary wall and at the capillary’s bifurcations;; this balloons the capillary and increases its
surface area (Tang et al., 2013). When the pressure on the capillary wall exceeds the failure
threshold, bruising occurs (Tang et al., 2013). In bruise models, the blood in a capillary has been
modeled as an incompressible solid (Tang et al., 2013). Because blood does not naturally

3. behave as an incompressible solid, the capillary responds differently to applied loads. The failure
mechanism of a capillary modeled with a fluid is hypothesized to differ from that of a capillary
modeled with an incompressible solid.
Finite Element Analysis solves complex systems of problems as a series of discrete
finite parts through mathematical analysis (Huang et al., 2012). The results of forces applied to a
capillary modeled through ANSYS Workbench® 15.0 precisely demonstrate the true mechanical
behavior of a capillary (Tang, et al. 2013). A mesh generated through FEA divides the model into
subregions that are connected through nodes. As the regions become smaller, the simple
approximation number becomes more precise, resulting in an exact solution. The model can
then be solved for maximum principal stress and maximum shear strain. The stress and strain
magnitudes are displayed as scaled colors on the model, which represent different degrees of
trauma (Huang, et al. 2012).
Knowledge of bruising at the capillary level is limited despite the fact that bruising can be
a primary clinical indicator of abuse (Akbarnia and Campbell, 2005). Currently, the only evidence
of abuse involving bruising is the presence and placement of bruises. The mechanism in which
a capillary fails can help indicate if and how a victim was abused, and thus can assist in abuse
arrest decisions. Modeling upper arm trauma through Finite Element Analysis will characterize
bruising at the capillary level, and subsequently, abuse.
MATERIALS AND METHODS
A capillary bed and arm were modeled using Finite Element Analysis through ANSYS
Workbench® 15.0. When constructing the capillary two primary branches were swept from the
origins and connected to a base by the spline tool. These branches were further bifurcated.The
model was then mirrored to create a complete capillary bed and material properties of a capillary

4. wall were assigned. The diameters of the capillary bed’s internal and external walls were
0.007mm and 0.008mm, respectively. The length of the capillary bed was 0.1 mm. The mesh of
the capillary bed contained 102,000 elements and 200,000 nodes (Figure 1).
A cross section of an arm inferior to the deltoid tuberosity was modeled through
SolidWorks® and transferred onto ANSYS Workbench® 15.0. The image used for this model
was of a 59 year-­old female cadaver from the Visible Human Project. Actual measurements of
the cross-­section were unavailable, so the upper-­arm circumference of eighteen random
females, aged 50-­67 years old, were recorded in a community survey. The average arm
thickness was 292.1 mm. Relative thicknesses of the skin, adipose, muscle, and bone
sublayers of the Visible Human Project image were then measured through ImageJ®. The arm
thickness obtained through ImageJ® was compared to the thickness of the average female arm,
x̅=292.1 mm, and a ratio was found. Using the ratio, the estimated thicknesses of the skin,
adipose, muscle, and bone sections were then calculated. The thicknesses of the adipose,
muscle, bone, and bone marrow sections were 276.31 mm, 220.40 mm, 50.89 mm, and 29.77
mm respectively (Table 1).
The sublayers of skin, adipose, muscle tissue, and bone, modeled through SolidWorks®,
were separately extruded from the center to a length of 200mm. This model was then
transferred to ANSYS Workbench® 15.0 and non-­linear hyperelastic material properties of skin,
adipose and muscle tissue were separately assigned. The bone section was modeled as a fixed
support. Modeling hyper-­elastic properties better characterizes capillary failure because the
mechanical properties of an arm are represented in each tissue layer. The model of the arm
contained 81,000 elements and 150,000 nodes (Figure 2).
Because the thickness of a capillary is 0.017% of the thickness of an arm, four-­level
hierarchical sub-­models, along with the different layers of the arm, skin, adipose, muscle tissue,

5. and bone, were represented in the global model. The muscle was sectioned into three
sub-­models, the smallest containing the capillary bed. Using ANSYS Fluent, a fluid-­based finite
element analysis sub-­program, a blood-­simulating fluid was embedded into the capillary model.
Loads less than and equal to 8.4x104
Pa were applied to the model over multiple simulations,
causing the capillary to deform and fail.
Table 1: Dimensions of Modeled Arm and Capillary
Name Circumference (mm) Length (mm)
Global Arm 292.1 100
Skin 292.1 100
Adipose 276.31 100
Muscle 220.4 100
Bone 50.89 100
Bone Marrow 29.77 100
Capillary Internal: 0.044
External: 0.051
.2
Table 2: Physical and Linear Elastic Material Properties (as used in ANSYS Workbench®
15.0):
Name Density (kg/mm^3) Young’s Modulus
(MPa)
Poisson’s Ratio
Skin 1.05e-­6 0.035 0.48
Adipose 9.196e-­7 0.02442 0.49
Muscle 1.06e-­6 0.077 0.37
Capillary wall 1e-­6 0.37 0.495
*numbers for material properties values referenced from (Huang et al., 2012).

6.
Figure 1: 3D Capillary Model with Generated Mesh
Image 3: 3D Global Model of Female Arm with Generated Mesh

7. RESULTS
A model of an arm and embedded capillary bed were successfully created and loaded with a
force of ___ over 10cm2
. The model of the global arm consisted of sublayers of skin, adipose,
muscle tissue, and bone, was 200mm in length, and contained 81,000 elements and 150,000
nodes (Figure 2). The diameters of the capillary bed’s internal and external walls were 0.007mm
and 0.008mm, respectively. The length of the capillary bed was 0.1 mm. The mesh of the
capillary bed contained 102,000 elements and 200,000 nodes (Figure 1).
The capillary was embedded with a blood-­simulating fluid, modeled through ANSYS
Fluent (Figure 1) and the arm was loaded with varying forces of ____Pa. The model was solved
for maximum principal stress and maximum shear strain, which were displayed through varying
colors on the solved model (Figure 2.1). Values exceeding 8.4x104
Pa indicated the capillary
failure threshold. The maximum principal stress recorded in the solved model was ___. The
locations of peak stress included_____.
DISCUSSION
A model of a 0.2mmbyX mirror image capillary bed, consisting of eight branches, was
successfully incorporated into a global arm model consisting of skin, adipose, muscle, and a
bone-­representing fixed support. Different loads were applied to the model and peak stress
occurred under the impact zone, as well as at the junctions of the capillary. The shear strain did
not exceed the ultimate strength of capillaries, as hypothesized.
The model was successfully tested for hydraulic-­induced tensile stress and shear
stress. ANSYS Fluent was successfully run and realistically simulated blood flow in the capillary
bed. As predicted, the blood in the capillary bed pooled into one area.The capillary failure
threshold was 8.4 X 104
Pa at a loading rate of ___.

8. This study hypothesized that the capillary would be more sensitive to loading when
modeled with a blood-­simulating fluid. This is due to the viscoelasticity of blood and its inability to
compress fluid. Because an incompressible solid has properties similar to those of wet clay, a
capillary modeled with an incompressible solid responds to loading in a way which allows more
time for the simulated blood to move away from the area of impact. When modeling a capillary
through ANSYS Fluent, the blood-­simulating fluid is forced to move from the impact zone to a
new area in less time. The velocity at which the blood disperses is faster than that of an
incompressible solid. This creates an increase in stress upon the capillary wall and makes it
more sensitive to loading.

9. References:
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