Abstract

Mild traumatic brain injury (mTBI), more colloquially known as concussion, is common in contact sports such as American football, leading to increased scrutiny of head protective gear. Standardized laboratory impact testing, such as the yearly National Football League (NFL) helmet test, is used to rank the protective performance of football helmets, motivating new technologies to improve the safety of helmets relative to existing equipment. In this work, we hypothesized that a helmet which transmits a nearly constant minimum force will result in a reduced risk of mTBI. To evaluate the plausibility of this hypothesis, we first show that the optimal force transmitted to the head, in a reduced order model of the brain, is in fact a constant force profile. To simulate the effects of a constant force within a helmet, we conceptualize a fluid-based shock absorber system for use within a football helmet. We integrate this system within a computational helmet model and simulate its performance on the standard NFL helmet test impact conditions. The simulated helmet is compared with other helmet designs with different technologies. Computer simulations of head impacts with liquid shock absorption predict that, at the highest impact speed (9.3 m/s), the average brain tissue strain is reduced by 27.6% ± 9.3 compared to existing helmet padding when tested on the NFL helmet protocol. This simulation-based study puts forth a target benchmark for the future design of physical manifestations of this technology.

References

1.
Hernandez
,
F.
,
Wu
,
L. C.
,
Yip
,
M. C.
,
Laksari
,
K.
,
Hoffman
,
A. R.
,
Lopez
,
J. R.
,
Grant
,
G. A.
,
Kleiven
,
S.
, and
Camarillo
,
D. B.
,
2015
, “
Six Degree-of-Freedom Measurements of Human Mild Traumatic Brain Injury
,”
Ann. Biomed. Eng.
,
43
(
8
), pp.
1918
1934
.10.1007/s10439-014-1212-4
2.
Harmon
,
K. G.
,
Drezner
,
J.
,
Gammons
,
M.
,
Guskiewicz
,
K.
,
Halstead
,
M.
,
Herring
,
S.
,
Kutcher
,
J.
,
Pana
,
A.
,
Putukian
,
M.
, and
Roberts
,
W.
,
2013
, “
American Medical Society for Sports Medicine Position Statement: Concussion in Sport
,”
Clin. J. Sport Med.
,
23
(
1
), pp.
1
18
.10.1097/JSM.0b013e31827f5f93
3.
Cassidy
,
J.
,
Carroll
,
L.
,
Peloso
,
P.
,
Borg
,
J.
,
von Holst
,
H.
,
Holm
,
L.
,
Kraus
,
J.
, and
Coronado
,
V. G.
,
2004
, “
Incidence, Risk Factors and Prevention of Mild Traumatic Brain Injury: Results of the WHO Collaborating Centre Task Force on Mild Traumatic Brain Injury
,”
J. Rehabil. Med.
, 36(Suppl. 43), pp. 28–60. 10.1080/16501960410023732
4.
Gennarelli
,
T. A.
,
1993
, “
Mechanisms of Brain Injury
,”
J. Emerg. Med.
,
11
(
Suppl. 1
), pp.
5
11
.https://pubmed.ncbi.nlm.nih.gov/8445204/
5.
Franz
,
E.
,
2017
, “
Biomechanics of Concussion, Traumatic Brain Injury, and Chronic Traumatic Encephalopathy in a Mouse Model of Closed-Head Impact
,”
J. Neurotrauma
,
34
(
13
), pp.
A105
A105
.
6.
O'Brien
,
W.
,
Franz
,
E.
,
Chancellor
,
S.
,
Pietro
,
J.
,
Moncaster
,
J.
,
Anderson
,
A.
,
Minaeva
,
O.
,
Cleveland
,
R.
,
Moss
,
W.
, and
Goldstein
,
L.
,
2019
, “
Mouse Model of Closed-Head Impact Concussion and Chronic Traumatic Encephalopathy (CTE)
,”
J. Neurotrauma
,
36
(
13
), pp.
A101
A102
.
7.
Moore
,
D. F.
,
Radovitzky
,
R. A.
,
Shupenko
,
L.
,
Klinoff
,
A.
,
Jaffee
,
M. S.
, and
Rosen
,
J. M.
,
2008
, “
Blast Physics and Central Nervous System Injury
,”
Future Neurol.
,
3
(
3
), pp.
243
250
.10.2217/14796708.3.3.243
8.
Roth
,
T.
,
Nayak
,
D.
, and
Atanasijevic
,
T.
,
Koretsky
,
A. P.
,
Latour
,
L. L.
, and
McGavern
,
D. B.
2014
, “
Transcranial Amelioration of Inflammation and Cell Death After Brain Injury
,”
Nature
, 505(7482), pp.
223
228
.10.1038/nature12808
9.
Margulies
,
S. S.
, and
Thibault
,
L. E.
,
1992
, “
A Proposed Tolerance Criterion for Diffuse Axonal Injury in Man
,”
J. Biomech.
, 25(8), pp.
917
923
.10.1016/0021-9290(92)90231-o
10.
Ommaya
,
A.
,
Hirsch
,
A.
,
Flamm
,
E.
, and
Mahone
,
R. H.
,
1966
, “
Cerebral Concussion in the Monkey: An Experimental Model
,”
Science
, 153(3732), pp.
211
212
.10.1126/science.153.3732.211
11.
Meaney
,
D. F.
, and
Smith
,
D. H.
,
2011
, “
Biomechanics of Concussion
,”
Clin. Sports Med.
,
30
(
1
), pp.
19
31
.10.1016/j.csm.2010.08.009
12.
Daneshvar
,
D. H.
,
Nowinski
,
C. J.
,
McKee
,
A. C.
, and
Cantu
,
R. C.
,
2011
, “
The Epidemiology of Sport-Related Concussion
,”
Clin. Sports Med.
,
30
(
1
), pp.
1
17
.10.1016/j.csm.2010.08.006
13.
Casson
,
I. R.
,
Viano
,
D. C.
,
Powell
,
J. W.
, and
Pellman
,
E. J.
,
2010
, “
Twelve Years of National Football League Concussion Data
,”
Sports Health
,
2
(
6
), pp.
471
483
.10.1177/1941738110383963
14.
Marar
,
M.
,
McIlvain
,
N. M.
,
Fields
,
S. K.
, and
Comstock
,
R. D.
,
2012
, “
Epidemiology of Concussions Among United States High School Athletes in 20 Sports
,”
Am. J. Sports Med.
,
40
(
4
), pp.
747
755
.10.1177/0363546511435626
15.
Kontos
,
A. P.
,
Elbin
,
R. J.
,
Fazio-Sumrock
,
V. C.
,
Burkhart
,
S.
,
Swindell
,
H.
,
Maroon
,
J.
, and
Collins
,
M. W.
,
2013
, “
Incidence of Sports-Related Concussion Among Youth Football Players Aged 8-12 Years
,”
J. Pediatr.
,
163
(
3
), pp.
717
720
.10.1016/j.jpeds.2013.04.011
16.
Colello
,
R. J.
,
Colello
,
I. A.
,
Abdelhameid
,
D.
,
Cresswell
,
K. G.
,
Merchant
,
R.
, and
Beckett
,
E.
,
2018
, “
Making Football Safer: Assessing the Current National Football League Policy on the Type of Helmets Allowed on the Playing Field
,”
J. Neurotrauma
,
35
(
11
), pp.
1213
1223
.10.1089/neu.2017.5446
17.
Giudice
,
J. S.
,
Park
,
G.
,
Kong
,
K.
,
Bailey
,
A.
,
Kent
,
R.
, and
Panzer
,
M. B.
,
2019
, “
Development of Open-Source Dummy and Impactor Models for the Assessment of American Football Helmet Finite Element Models
,”
Ann. Biomed. Eng.
,
47
(
2
), pp.
464
474
.10.1007/s10439-018-02155-3
18.
Cecchi
,
N. J.
,
Oros
,
T. J.
,
Ringhofer
,
J. J.
, and
Monroe
,
D. C.
,
2019
, “
Comparison of Head Impact Attenuation Capabilities Between a Standard American Football Helmet and Novel Protective Equipment That Couples a Helmet and Shoulder Pads
,”
Sports Eng.
,
22
(
3–4
), p.
16
.10.1007/s12283-019-0311-8
19.
Schallmo
,
M. S.
,
Weiner
,
J. A.
, and
Hsu
,
W.
,
2017
, “
Assessing Trends in the Epidemiology of Concussions Among High School Athletes
,”
Orthop. J. Sport. Med.
,
5
(
7_suppl. 6
), pp.
2325967117
S0043
.
20.
Lincoln
,
A. E.
,
Caswell
,
S. V.
,
Almquist
,
J. L.
,
Dunn
,
R. E.
,
Norris
,
J. B.
, and
Hinton
,
R. Y.
,
2011
, “
Trends in Concussion Incidence in High School Sports
,”
Am. J. Sports Med.
,
39
(
5
), pp.
958
963
.10.1177/0363546510392326
21.
Ramirez, B. J., and Gupta, V.,
2018
, “
Evaluation of Novel Temperature-Stable Viscoelastic Polyurea Foams as Helmet Liner Materials
,”
Materials Design
, 137, pp.
298
304
.10.1016/j.matdes.2017.10.037
22.
Dixon
,
J. C.
,
2008
,
The Shock Absorber Handbook
, The Atrium Southern Gate, John Wiley & Sons
,
Hoboken, NJ
.
23.
Bruneau
,
D.
,
2019
, “
Investigation of Head and Brain Response in Football Helmet Impacts Using a Finite Element Model of the Head and Neck With Active Muscle
,”
Master's thesis
, University of Waterloo, Waterloo, ON, Canada.http://hdl.handle.net/10012/14771
24.
Corrales
,
M. A.
,
Gierczycka
,
D.
,
Barker
,
J.
,
Bruneau
,
D.
,
Bustamante
,
M. C.
, and
Cronin
,
D. S.
,
2020
, “
Validation of a Football Helmet Finite Element Model and Quantification of Impact Energy Distribution
,”
Ann. Biomed. Eng.
, 48(1), pp.
1
21–
132
.10.1007/s10439-019-02359-1
25.
Decker
,
W.
,
Baker
,
A.
,
Ye
,
X.
,
Brown
,
P.
,
Stitzel
,
J.
, and
Gayzik
,
F. S.
,
2019
, “
Development and Multi-Scale Validation of a Finite Element Football Helmet Model
,”
Ann. Biomed. Eng.
, 48(1), pp. 258–270.10.1007/s10439-019-02345-
26.
Giudice
,
J. S.
,
Caudillo
,
A.
,
Mukherjee
,
S.
,
Kong
,
K.
,
Park
,
G.
,
Kent
,
R.
, and
Panzer
,
M. B.
,
2020
, “
Finite Element Model of a Deformable American Football Helmet Under Impact
,”
Ann. Biomed. Eng.
, 48(1), pp. 1524–1539.10.1007/s10439-020-02472-6
27.
National Football League (NFL), 2019, “
Helmet Laboratory Testing Performance Results—NFL Play Smart, Play Safe
,” National Football League, Canton, OH, accessed Oct. 10, 2019, https://www.playsmartplaysafe.com/resource/helmet-laboratory-testing-performance-results/
28.
Hoshizaki
,
T. B.
,
Post
,
A.
,
Kendall
,
M.
,
Cournoyer
,
J.
,
Rousseau
,
P.
,
Gilchrist
,
M. D.
,
Brien
,
S.
,
Cusimano
,
M.
, and
Marshall
,
S.
,
2017
, “
The Development of a Threshold Curve for the Understanding of Concussion in Sport
,”
Trauma
,
19
(
3
), pp.
196
206
.10.1177/1460408616676503
29.
Johnson
,
V. E.
,
Weber
,
M. T.
,
Xiao
,
R.
,
Cullen
,
D. K.
,
Meaney
,
D. F.
,
Stewart
,
W.
, and
Smith
,
D. H.
,
2018
, “
Mechanical Disruption of the Blood–Brain Barrier Following Experimental Concussion
,”
Acta Neuropathol.
,
135
(
5
), pp.
711
726
.10.1007/s00401-018-1824-0
30.
Gurdjian
,
E. S.
,
Lissner
,
H. R.
,
Evans
,
F. G.
,
Patrick
,
L. M.
, and
Hardy
,
W. G.
,
1961
, “
Intracranial Pressure and Acceleration Accompanying Head Impacts in Human Cadavers
,”
Surg. Gynecol. Obstet.
,
113
, pp.
185
–1
90
.https://pubmed.ncbi.nlm.nih.gov/13709837/
31.
Holbourn
,
A. H. S.
,
1943
, “
Mechanics of Head Injuries
,”
Lancet
,
242
(
6267
), pp.
438
441
.10.1016/S0140-6736(00)87453-X
32.
Hardy
,
W. N.
,
Mason
,
M. J.
,
Foster
,
C. D.
,
Shah
,
C. S.
,
Kopacz
,
J. M.
,
Yang
,
K. H.
,
King
,
A. I.
,
Bishop
,
J.
,
Bey
,
M.
,
Anderst
,
W.
, and
Tashman
,
S.
,
2007
, “
A Study of the Response of the Human Cadaver Head to Impact
,”
Stapp Car Crash J.
,
51
, pp.
17
80
.10.4271/2007-22-0002
33.
Medige
,
J.
, and
Medige
,
J.
,
1997
, “
Shear Properties of Human Brain Tissue
,”
ASME J. Biomech. Eng.
,
119
(
4
), pp.
423
432
.10.1115/1.2798289
34.
Arbogast
,
K. B.
,
Thibault
,
K. L.
,
Scott Pinheiro
,
B.
,
Winey
,
K. I.
, and
Margulies
,
S. S.
,
1997
, “
A High-Frequency Shear Device for Testing Soft Biological Tissues
,”
J. Biomech.
,
30
(
7
), pp.
757
759
.10.1016/S0021-9290(97)00023-7
35.
Bustamante
,
M. C.
,
Bruneau
,
D.
,
Barker
,
J. B.
,
Gierczycka
,
D.
,
Coralles
,
M. A.
, and
Cronin
,
D. S.
,
2019
, “
Component-Level Finite Element Model and Validation for a Modern American Football Helmet
,”
J. Dyn. Behav. Mater.
,
5
(
2
), pp.
117
131
.10.1007/s40870-019-00189-9
36.
Ouellet
,
S.
,
Cronin
,
D.
, and
Worswick
,
M.
,
2006
, “
Compressive Response of Polymeric Foams Under Quasi-Static, Medium and High Strain Rate Conditions
,”
Polym. Test.
,
25
(
6
), pp.
731
743
.10.1016/j.polymertesting.2006.05.005
37.
Sun
,
Y.
, and
Li
,
Q. M.
,
2018
, “
Dynamic Compressive Behaviour of Cellular Materials: A Review of Phenomenon, Mechanism and Modelling
,”
Int. J. Impact Eng.
,
112
, pp.
74
115
.10.1016/j.ijimpeng.2017.10.006
38.
Spinelli
,
D. J.
,
Plaisted
,
T. A.
, and
Wetzel
,
E. D.
,
2018
, “
Adaptive Head Impact Protection Via a Rate-Activated Helmet Suspension
,”
Mater. Des.
,
154
, pp.
153
169
.10.1016/j.matdes.2018.04.083
39.
Kurt
,
M.
,
Laksari
,
K.
,
Kuo
,
C.
,
Grant
,
G. A.
, and
Camarillo
,
D. B.
,
2017
, “
Modeling and Optimization of Airbag Helmets for Preventing Head Injuries in Bicycling
,”
Ann. Biomed. Eng.
,
45
(
4
), pp.
1148
1160
.10.1007/s10439-016-1732-1
40.
Newman
,
J. A.
,
2002
, “
Biomechanics of Head Trauma: Head Protection
,”
Accidental Injury
,
Springer
,
New York
, pp.
303
323
.
41.
Begley
,
M. R.
, and
Zok
,
F. W.
,
2014
, “
Optimal Material Properties for Mitigating Brain Injury During Head Impact
,”
ASME J. Appl. Mech.
,
81
(
3
), p. 031014.10.1115/1.4024992
42.
Greenwald
,
R. M.
,
Gwin
,
J. T.
,
Chu
,
J. J.
, and
Crisco
,
J. J.
,
2008
, “
Head Impact Severity Measures for Evaluating Mild Traumatic Brain Injury Risk Exposure
,”
Neurosurgery
,
62
(
4
), pp.
789
798
.10.1227/01.neu.0000318162.67472.ad
43.
Kleiven
,
S.
,
2007
, “
Predictors for Traumatic Brain Injuries Evaluated Through Accident Reconstructions
,”
Stapp Car Crash J
,
51
, pp.
81
114
.10.4271/2007-22-0003
44.
Rowson
,
S.
, and
Duma
,
S. M.
,
2011
, “
Development of the STAR Evaluation System for Football Helmets: Integrating Player Head Impact Exposure and Risk of Concussion
,”
Ann. Biomed. Eng.
,
39
(
8
), pp.
2130
2140
.10.1007/s10439-011-0322-5
45.
Versace
,
J.
,
1971
, “
A Review of the Severity Index
,”
SAE
Technical Paper No. 710881.10.4271/710881
46.
Rowson
,
S.
,
Duma
,
S. M.
,
Beckwith
,
J. G.
,
Chu
,
J. J.
,
Greenwald
,
R. M.
,
Crisco
,
J. J.
,
Brolinson
,
P. G.
,
Duhaime
,
A.-C.
,
McAllister
,
T. W.
, and
Maerlender
,
A. C.
,
2012
, “
Rotational Head Kinematics in Football Impacts: An Injury Risk Function for Concussion
,”
Ann. Biomed. Eng.
,
40
(
1
), pp.
1
13
.10.1007/s10439-011-0392-4
47.
Takhounts
,
E. G.
,
Craig
,
M. J.
,
Moorhouse
,
K.
,
McFadden
,
J.
, and
Hasija
,
V.
,
2013
, “
Development of Brain Injury Criteria (BrIC)
,”
SAE
Technical Paper No. 2013-22-0010.10.4271/2013-22-0010
48.
Gabler
,
L. F.
,
Crandall
,
J. R.
, and
Panzer
,
M. B.
,
2018
, “
Development of a Metric for Predicting Brain Strain Responses Using Head Kinematics
,”
Ann. Biomed. Eng.
,
46
(
7
), pp.
972
985
.10.1007/s10439-018-2015-9
49.
Laksari
,
K.
,
Fanton
,
M.
,
Wu
,
L. C.
,
Nguyen
,
T. H.
,
Kurt
,
M.
,
Giordano
,
C.
,
Kelly
,
E.
,
O'Keeffe
,
E.
,
Wallace
,
E.
,
Doherty
,
C.
,
Campbell
,
M.
,
Tiernan
,
S.
,
Grant
,
G.
,
Ruan
,
J.
,
Barbat
,
S.
,
Camarillo
,
D. B.
,
2018
, “
Multi-Directional Dynamic Model for Traumatic Brain Injury Detection
,”
J. Neurotrauma
, 37(7), pp.
982
993
.10.1089/neu.2018.6340
50.
Laituri
,
T. R.
,
Henry
,
S.
,
Pline
,
K.
,
Li
,
G.
,
Frankstein
,
M.
, and
Weerappuli
,
P.
,
2016
, “
New Risk Curves for NHTSA's Brain Injury Criterion (BrIC): Derivations and Assessments
,”
SAE
Technical Paper No. 2016-22-0012.10.4271/2016-22-0012
51.
Coats
,
B.
,
Eucker
,
S. A.
,
Sullivan
,
S.
, and
Margulies
,
S. S.
,
2012
, “
Finite Element Model Predictions of Intracranial Hemorrhage From Non-Impact, Rapid Head Rotations in the Piglet
,”
Int. J. Dev. Neurosci.
,
30
(
3
), pp.
191
200
.10.1016/j.ijdevneu.2011.12.009
52.
Takhounts
,
E. G.
,
Ridella
,
S. A.
,
Hasija
,
V.
,
Tannous
,
R. E.
,
Campbell
,
J. Q.
,
Malone
,
D.
,
Danelson
,
K.
,
Stitzel
,
J.
,
Rowson
,
S.
and
Duma
,
S.
,
2008
, “
Investigation of Traumatic Brain Injuries Using the Next Generation of Simulated Injury Monitor (SIMon) Finite Element Head Model
,”
SAE
Technical Paper No. 2008-22-0001.10.4271/2008-22-0001
53.
Rojanavanich
,
V.
, and
Stalnaker
,
R. L.
,
1988
, “
Parametric Studies of the Translational Head Injury Model
,” Proceedings of the International Research Council on the Biomechanics of Impact (
IRCOBI
), Bron, France, Sept., pp.
181
194
.http://www.ircobi.org/wordpress/downloads/irc1988/pdf_files/1988_13.pdf
54.
Rojanavanich
,
V.
, and
Stalnaker
,
R. L.
,
1989
, “
Sensitivity Analysis for the Translational Energy Criteria: Overall Injuries
,”
Proceedings of the International Research Council on the Biomechanics of Injury Conference
, Vol.
17
, Stockholm, Sweden, Sept. 13–15, pp.
13
26
.https://trid.trb.org/view/316308
55.
Gabler
,
L. F.
,
Joodaki
,
H.
,
Crandall
,
J. R.
, and
Panzer
,
M. B.
,
2018
, “
Development of a Single-Degree-of-Freedom Mechanical Model for Predicting Strain-Based Brain Injury Responses
,”
ASME J. Biomech. Eng.
,
140
(
3
), p.
031002
.10.1115/1.4038357
56.
Gabler
,
L. F.
,
Crandall
,
J. R.
, and
Panzer
,
M. B.
,
2019
, “
Development of a Second-Order System for Rapid Estimation of Maximum Brain Strain
,”
Ann. Biomed. Eng.
,
47
(
9
), pp.
1971
1981
.10.1007/s10439-018-02179-9
57.
Balandin
,
D.
,
Bolotnik
,
N.
,
Pilkey
,
W.
, and
Cetinkaya
,
C.
,
2001
, “
Optimal Protection From Impact, Shock, and Vibration
,”
Appl. Mech. Rev
,
54
(
5
), pp.
B78
B79
.10.1115/1.1399377
58.
Geiger, B., Horn, J.,
DeLullo
,
A.
,
Niessner
,
A.
, and
Long
,
L.
,
2006
, “
Optimal Path Planning of UAVs Using Direct Collocation With Nonlinear Programming
,”
AIAA
Paper No. 2006-6199.10.2514/6.2006-6199
59.
Vahid Alizadeh
,
H.
,
Helwa
,
M. K.
, and
Boulet
,
B.
,
2018
, “
Modeling, Analysis and Constrained Control of Wet Cone Clutch Systems: A Synchromesh Case Study
,”
Mechatronics
,
49
, pp.
92
104
.10.1016/j.mechatronics.2017.11.005
60.
Habets
,
L.
, and
Van Schuppen
,
J. H.
,
2004
, “
A Control Problem for Affine Dynamical Systems on a Full-Dimensional Polytope
,”
Automatica
,
40
(
1
), pp.
21
35
.10.1016/j.automatica.2003.08.001
61.
Funk
,
J.
, and
Crandall
,
J.
,
2017
, “
NFL Linear Impactor Helmet Test Protocol
,” Biomechanics Consulting Research LLC, Charlottesville, VA.
62.
Fanton
,
M.
,
Alizadeh
,
H. V.
,
Hawkes
,
E.
,
Kurt
,
M.
,
Cutkosky
,
M.
,
Mungal
,
G.
, and
Camarillo
,
D.
,
2018
, “
Constant-Force Shock Absorbers for Preventing Traumatic Brain Injury
,”
8th World Congress of Biomechanics
, Dublin, Ireland, July 8–12, No. O0986.
63.
Organization World Intellectual Property
,
2018
, “
Constant Force Impact Protection Device
,” Organization World Intellectual Property, New York, Standard No.
WO/2018/148753
.https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2018148753
64.
Young
,
L.
,
Chan
,
N.
, and
Ruchelsman
,
J.
,
2009
, “
Fluid Safety Liner
,” U.S. Patent No.
12/296,843
.https://patents.justia.com/patent/20090265839
65.
Archbold
,
J.
,
2013
, “
Impact Attenuating Bladder With Fluid Release Control Valve for Helmet Liner
,” U.S. Patent No. 283,506 A1.
66.
Cade
,
J. R.
, and
Greathouse
,
B. B.
,
1971
, “
Hydraulic Helmet
,” U.S. Patent No. 3,600,714.
67.
Fanton
,
M.
,
Alizadeh
,
H. V.
,
Domel
,
A. G.
,
Devlin
,
M.
,
Kurt
,
M.
,
Mungal
,
M. G.
,
Camarillo
,
D. B.
, and
Hawkes
,
E.
,
2020
, “
Variable Area, Constant Force Shock Absorption Motivated by Traumatic Brain Injury Prevention
,”
Smart Mater. Struct.
,
29
(
8
), p.
085023
.10.1088/1361-665X/ab905f
68.
LSTC,
2017
, “
Ls-Dyna® Keyword User's Manual, Volume II, Material Models: Mat_Hydraulic_Gas_Damper_Discrete_Beam
,” Livermore Software Technology Corporation, Livermore, CA.https://ftp.lstc.com/anonymous/outgoing/jday/manuals/LS-DYNA_manual_Vol_II_R7.1.pdf
69.
Biomechanics Consulting and Research, LC
,
2019
, “
Biocore Models of Football Helmets
,” Biocore, LLC, Charlottesville, VA, accessed Oct. 10, 2019, http://www.lstc.com/links_to_models
70.
Society of Automotive Engineers
,
2007
, “
Instrumentation for Impact Test—Part 1—Electronic Instrumentation
,”
SAE
Technical Report No. SAE J211/1. https://law.resource.org/pub/us/cfr/ibr/005/sae.j211-1.1995.pdf
71.
Kuo
,
C.
,
Wu
,
L.
,
Zhao
,
W.
,
Fanton
,
M.
,
Ji
,
S.
, and
Camarillo
,
D. B.
,
2018
, “
Propagation of Errors From Skull Kinematic Measurements to Finite Element Tissue Responses
,”
Biomech. Model. Mechanobiol.
,
17
(
1
), pp.
235
247
.10.1007/s10237-017-0957-8
72.
Rowson
,
S.
, and
Duma
,
S. M.
,
2013
, “
Brain Injury Prediction: Assessing the Combined Probability of Concussion Using Linear and Rotational Head Acceleration
,”
Ann. Biomed. Eng.
,
41
(
5
), pp.
873
882
.10.1007/s10439-012-0731-0
73.
Cheng
,
Z. Q.
,
Pilkey
,
W. D.
,
Crandall
,
J. R.
,
Bass
,
C. R.
, and
Darvish
,
K.
,
1999
, “
Limiting Performance of Helmets for the Prevention of Head Injury
,”
Shock Vib.
,
6
(
5–6
), pp.
299
320
.10.1155/1999/146458
74.
Ballantyne
,
E. L.
,
Little
,
D. J.
, and
Wetzel
,
E. D.
,
2017
, “
Rate-Activated Strapping for Improved Retention of Protective Eyewear During Impact
,”
Sports Eng.
,
20
(
3
), pp.
171
183
.10.1007/s12283-017-0226-1
75.
Elliott
,
M. R.
,
Margulies
,
S. S.
,
Maltese
,
M. R.
, and
Arbogast
,
K. B.
,
2015
, “
Accounting for Sampling Variability, Injury Under-Reporting, and Sensor Error in Concussion Injury Risk Curves
,”
J. Biomech.
,
48
(
12
), pp.
3059
3065
.10.1016/j.jbiomech.2015.07.026
76.
Heck
,
J. F.
,
Clarke
,
K. S.
,
Peterson
,
T. R.
,
Torg
,
J. S.
, and
Weis
,
M. P.
,
2004
, “
National Athletic Trainers' Association Position Statement: Head-Down Contact and Spearing in Tackle Football
,”
J. Athletic Train.
,
39
(
1
), pp.
101
111
.https://pubmed.ncbi.nlm.nih.gov/15085218/
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