Bruising, the result of capillary failure due to trauma, is a common indication of abuse. However, the etiology of capillary failure has yet to be determined as the scale change from tissue to capillary represents several orders of magnitude. As a first step toward determining bruise etiology, we have developed a multilevel hierarchical finite element model (FEM) of a portion of the upper human arm using a commercial finite element tool and a series of three interconnected hierarchical submodels. The third and final submodel contains a portion of the muscle tissue in which a single capillary is embedded. Nonlinear, hyperelastic material properties were applied to skin, adipose, muscle, and capillary wall materials. A pseudostrain energy method was implemented to subtract rigid-body-like motion of the submodel volume experienced in the global model, and was critical for convergence and successful analyses in the submodels. The deformation and hoop stresses in the capillary wall were determined and compared with published capillary failure stress. For the dynamic load applied to the skin of the arm (physiologically simulating a punch), the model predicted that approximately 8% volume fraction of the capillary wall was above the reference capillary failure stress, indicating bruising would likely occur.

References

References
1.
Pierce
,
M. C.
, and
Bertocci
,
G.
,
2008
, “
Injury Biomechanics and Child Abuse
,”
Annu. Rev. Biomed. Eng.
,
10
, pp.
85
106
.10.1146/annurev.bioeng.9.060906.151907
2.
Gayzik
,
F. S.
,
Hoth
,
J. J.
,
Daly
,
M.
,
Meredith
,
J. W.
, and
Stitzel
,
J. D.
,
2007
, “
A Finite Element-Based Injury Metric for Pulmonary Contusion: Investigation of Candidate Metrics Through Correlation With Computed Tomography
,”
Stapp Car Crash J.
,
51
, pp.
189
209
.
3.
Wong
,
B.
,
Kieser
,
J.
,
Ichim
,
I.
,
Swain
,
M.
,
Livingstone
,
V.
,
Waddell
,
N.
, and
Taylor
,
M.
,
2008
, “
Experimental Simulation of Non-Ballistic Wounding by Sharp and Blunt Punches
,”
Forensic Sci., Med., Pathol.
,
4
(
4
), pp.
212
220
.10.1007/s12024-008-9042-z
4.
Whittle
,
K.
,
Kieser
,
J.
,
Ichim
,
I.
,
Swain
,
M.
,
Waddell
,
N.
,
Livingstone
,
V.
, and
Taylor
,
M.
,
2008
, “
The Biomechanical Modelling of Non-Ballistic Skin Wounding: Blunt-Force Injury
,”
Forensic Sci., Med., Pathol.
,
4
(
1
), pp.
33
39
.10.1007/s12024-007-0029-y
5.
Smit
,
R. J. M.
,
Brekelmans
,
W. A. M.
, and
Meijer
,
H. E. H.
,
1998
, “
Prediction of the Mechanical Behavior of Nonlinear Heterogeneous Systems by Multi-Level Finite Element Modeling
,”
Comput. Methods Appl. Mech. Eng.
,
155
(
1–2
), pp.
181
192
.10.1016/S0045-7825(97)00139-4
6.
Ghosh
,
S.
,
Lee
,
K.
, and
Raghavan
,
P.
,
2001
, “
A Multi-Level Computational Model for Multi-Scale Damage Analysis in Composite and Porous Materials
,”
Int. J. Solids Struct.
,
38
(
14
), pp.
2335
2385
.10.1016/S0020-7683(00)00167-0
7.
Jenny
,
P.
,
Lee
,
S. H.
, and
Tchelepi
,
H. A.
,
2003
, “
Multi-Scale Finite-Volume Method for Elliptic Problems in Subsurface Flow Simulation
,”
J. Comput. Phys.
,
187
(
1
), pp.
47
67
.10.1016/S0021-9991(03)00075-5
8.
Wang
,
T. H.
, and
Lai
,
Y.-S.
,
2005
, “
Submodeling Analysis for Path-Dependent Thermomechanical Problems
,”
ASME J. Electron. Packag.
,
127
(
2
), pp.
135
140
.10.1115/1.1869513
9.
Huang
,
L.
,
2012
, “
A Multi-Level Hierarchical Finite Element Model for Capillary Failure in Soft Tissue
,” M.S. thesis, Biomechanical University of Massachusetts Amherst, Amherst.
10.
Ackerman
,
M. J.
,
Spitzer
,
V. M.
, and
Scherzinger
,
A. L.
,
1995
, “
The Visible Human Data Set: An Image Resource for Anatomical Visualization
,”
Medinfo.
,
8
(
Pt. 2
), pp.
1195
1198
.
11.
Looman
,
D.
,
2007
, “
Submodeling in ANSYS Workbench
,”
ANSYS Adv.
,
1
(
2
), pp. 34–36.
12.
Hsiang-Chen
,
H.
,
Yu-Chia
,
H.
,
Hui-Yu
,
L.
,
Chang-Lin
,
Y.
, and
Yi-Shao
,
L.
,
2006
, “
Application of Submodeling Technique to Transient Drop Impact Analysis of Board-Level Stacked Die Packages
,”
8th Electronics Packaging Technology Conference
, EPTC '06, pp. 34–36.
13.
Toupin
,
R. A.
,
1965
, “
Saint-Venant's Principle
,”
Arch. Ration. Mech. Anal.
,
18
(
2
), pp.
83
96
.10.1007/BF00282253
14.
Goodier
,
J. N.
,
1934
, “
An Analogy Between Slow Motions of a Viscous Fluid in Two Dimensions, and Systems of Plane Stress
,”
Philos. Mag. Ser.
,
17
(
113
), pp.
554
576
.
15.
Zou
,
H.
,
Schmiedeler
,
J. P.
, and
Hardy
,
W. N.
,
2007
, “
Separating Brain Motion Into Rigid Body Displacement and Deformation Under Low-Severity Impacts
,”
J. Biomech.
,
40
(
6
), pp.
1183
1191
.10.1016/j.jbiomech.2006.06.018
16.
Liu
,
Y.
,
Kerdok
,
A.
, and
Howe
,
R.
,
2004
, “
A Nonlinear Finite Element Model of Soft Tissue Indentation,
” Medical Simulation,
S.
Cotin
, and
D.
Metaxas
, eds.,
Springer
,
Berlin/Heidelberg
, pp.
67
76
.
17.
Jijun
,
S.
,
Haitian
,
Z.
, and
Tongtong
,
G.
,
2009
, “
The Study of Mechanical Properties on Soft Tissue of Human Forearm in Vivo
,”
3rd International Conference on Bioinformatics and Biomedical Engineering
, ICBBE.
18.
William
,
M.
, and
Vannah
,
D. S. C.
,
1996
, “
Indentor Tests and Finite Element Modeling of Bulk Muscular Tissue in Vivo
,”
J. Rehabil. Res. Develop.
,
33
, pp.
239
252
.
19.
Ranga
,
A.
,
Mongrain
,
R.
,
Biadilah
,
Y.
, and
Cartier
,
R.
,
2007
, “
A Compliant Dynamic FEA Model of the Aortic Valve
,” 12th IFToMM World Congress, Besançon, France.
20.
Otten
,
E.
, and
Hulliger
,
M.
,
1995
, “
A Finite-Elements Approach to the Study of Functional Architecture in Skeletal Muscle
,”
Zoology
,
98
, pp.
233
242
.
21.
Yucesoy
,
C. A.
,
Koopman
,
B. H. F. J. M.
,
Huijing
,
P. A.
, and
Grootenboer
,
H. J.
,
2002
, “
Three-Dimensional Finite Element Modeling of Skeletal Muscle Using a Two-Domain Approach: Linked Fiber-Matrix Mesh Model
,”
J. Biomech.
,
35
(
9
), pp.
1253
1262
.10.1016/S0021-9290(02)00069-6
22.
Lemos
,
R. R.
,
Epstein
,
M.
,
Herzog
,
W.
, and
Wyvill
,
B.
,
2004
, “
A Framework for Structured Modeling of Skeletal Muscle
,”
Comput. Methods Biomech. Biomed. Eng.
,
7
(
6
), pp.
305
317
.10.1080/10255840412331317398
23.
Böl
,
M.
, and
Reese
,
S.
,
2007
, “
A New Approach for the Simulation of Skeletal Muscles Using the Tool of Statistical Mechanics
,”
Materialwiss. Werkstofftech.
,
38
(
12
), pp.
955
964
.10.1002/mawe.200700225
24.
Comley
,
K.
, and
Fleck
,
N.
,
2012
, “
The Compressive Response of Porcine Adipose Tissue From Low to High Strain Rate
,”
Int. J. Impact Eng.
,
46
, pp.
1
10
.10.1016/j.ijimpeng.2011.12.009
25.
Liu
,
Y.
, and
Liu
,
W. K.
,
2006
, “
Rheology of Red Blood Cell Aggregation by Computer Simulation
,”
J. Comput. Phys.
,
220
(
1
), pp.
139
154
.10.1016/j.jcp.2006.05.010
26.
Shergold
,
O. A.
,
Fleck
,
N. A.
, and
Radford
,
D.
,
2006
, “
The Uniaxial Stress Versus Strain Response of Pig Skin and Silicone Rubber at Low and High Strain Rates
,”
Int. J. Impact Eng.
,
32
(
9
), pp.
1384
1402
.10.1016/j.ijimpeng.2004.11.010
27.
Bosboom
,
E. M. H.
,
Hesselink
,
M. K. C.
,
Oomens
,
C. W. J.
,
Bouten
,
C. V. C.
,
Drost
,
M. R.
, and
Baaijens
,
F. P. T.
,
2001
, “
Passive Transverse Mechanical Properties of Skeletal Muscle Under in Vivo Compression
,”
J. Biomech.
,
34
(
1
), pp.
1365
1368
.10.1016/S0021-9290(01)00083-5
28.
Randeberg
,
L. L.
,
Winnem
,
A. M.
,
Langlois
,
N. E.
,
Larsen
,
E. L. P.
,
Haaverstad
,
R.
,
Skallerud
,
B.
,
Haugen
,
O. A.
, and
Svaasand
,
L. O.
,
2007
, “
Skin Changes Following Minor Trauma
,”
Lasers Surg. Med.
,
39
(
5
), pp.
403
413
.10.1002/lsm.20494
29.
West
,
J. B.
,
Tsukimoto
,
K.
,
Mathieu-Costello
,
O.
, and
Prediletto
,
R.
,
1991
, “
Stress Failure in Pulmonary Capillaries
,”
J. Appl. Physiol.
,
70
, pp.
1731
1742
.
You do not currently have access to this content.