Advances in three-dimensional (3D) printing are enabling the design and fabrication of tailored lattices with high mechanical efficiency. Here, we focus on conducting experiments to mechanically characterize lattice structures to measure properties that inform an integrated design, manufacturing, and experiment framework. Structures are configured as beam-based lattices intended for use in novel spinal cage devices for bone fusion, fabricated with polyjet printing. Polymer lattices with 50% and 70% porosity were fabricated with beam diameters of 0.41.0mm, with measured effective elastic moduli from 28MPa to 213MPa. Effective elastic moduli decreased with higher lattice porosity, increased with larger beam diameters, and were highest for lattices compressed perpendicular to their original build direction. Cages were designed with 50% and 70% lattice porosities and included central voids for increased nutrient transport, reinforced shells for increased stiffness, or both. Cage stiffnesses ranged from 4.1kN/mm to 9.6kN/mm with yielding after 0.360.48mm displacement, thus suggesting their suitability for typical spinal loads of 1.65kN. The 50% porous cage with reinforced shell and central void was particularly favorable, with an 8.4kN/mm stiffness enabling it to potentially function as a stand-alone spinal cage while retaining a large open void for enhanced nutrient transport. Findings support the future development of fully integrated design approaches for 3D printed structures, demonstrated here with a focus on experimentally investigating lattice structures for developing novel biomedical devices.

References

References
1.
Thompson
,
M. K.
,
Moroni
,
G.
,
Vaneker
,
T.
,
Fadel
,
G.
,
Campbell
,
R. I.
,
Gibson
,
I.
,
Bernard
,
A.
,
Schulz
,
J.
,
Graf
,
P.
, and
Ahuja
,
B.
,
2016
, “
Design for Additive Manufacturing: Trends, Opportunities, Considerations, and Constraints
,”
CIRP Ann. Manuf. Technol.
,
65
(
2
), pp.
737
760
.
2.
Deshpande
,
V. S.
,
Fleck
,
N. A.
, and
Ashby
,
M. F.
,
2001
, “
Effective Properties of the Octet-Truss Lattice Material
,”
J. Mech. Phys. Solids
,
49
(
8
), pp.
1747
1769
.
3.
Zheng
,
X.
,
Lee
,
H.
,
Weisgraber
,
T. H.
,
Shusteff
,
M.
,
DeOtte
,
J.
,
Duoss
,
E. B.
,
Kuntz
,
J. D.
,
Biener
,
M. M.
,
Ge
,
Q.
, and
Jackson
,
J. A.
,
2014
, “
Ultralight, Ultrastiff Mechanical Metamaterials
,”
Science
,
344
(
6190
), pp.
1373
1377
.
4.
Egan
,
P. F.
,
Shea
,
K. A.
, and
Ferguson
,
S. J.
,
2018
, “
Simulated Tissue Growth for 3D Printed Scaffolds
,”
Biomech. Model. Mechanobiol.
,
17
(
5
), pp.
1481
1495
.
5.
Wang
,
X.
,
Xu
,
S.
,
Zhou
,
S.
,
Xu
,
W.
,
Leary
,
M.
,
Choong
,
P.
,
Qian
,
M.
,
Brandt
,
M.
, and
Xie
,
Y. M.
,
2016
, “
Topological Design and Additive Manufacturing of Porous Metals for Bone Scaffolds and Orthopaedic Implants: A Review
,”
Biomaterials
,
83
, pp.
127
141
.
6.
de Wild
,
M.
,
Zimmermann
,
S.
,
Rüegg
,
J.
,
Schumacher
,
R.
,
Fleischmann
,
T.
,
Ghayor
,
C.
, and
Weber
,
F. E.
,
2016
, “
Influence of Microarchitecture on Osteoconduction and Mechanics of Porous Titanium Scaffolds Generated by Selective Laser Melting
,”
3D Printing Addit. Manuf.
,
3
(
3
), pp.
142
151
.
7.
Cheng
,
M.-Q.
,
Wahafu
,
T.
,
Jiang
,
G.-F.
,
Liu
,
W.
,
Qiao
,
Y.-Q.
,
Peng
,
X.-C.
,
Cheng
,
T.
,
Zhang
,
X.-L.
,
He
,
G.
, and
X.-y
,
L.
,
2016
, “
A Novel Open-Porous Magnesium Scaffold With Controllable Microstructures and Properties for Bone Regeneration
,”
Sci. Rep.
,
6
, p.
24134
.
8.
Paris
,
M.
,
Götz
,
A.
,
Hettrich
,
I.
,
Bidan
,
C. M.
,
Dunlop
,
J. W.
,
Razi
,
H.
,
Zizak
,
I.
,
Hutmacher
,
D. W.
,
Fratzl
,
P.
, and
Duda
,
G. N.
,
2017
, “
Scaffold Curvature-Mediated Novel Biomineralization Process Originates a Continuous Soft Tissue-to-Bone Interface
,”
Acta Biomater.
,
60
, pp.
64
80
.
9.
Egan
,
P.
,
Ferguson
,
S.
, and
Shea
,
K.
,
2017
, “
Design of Hierarchical 3D Printed Scaffolds Considering Mechanical and Biological Factors for Bone Tissue Engineering
,”
ASME J. Mech. Des.
,
139
(
6
), p.
061401
.
10.
Kengla
,
C.
,
Renteria
,
E.
,
Wivell
,
C.
,
Atala
,
A.
,
Yoo
,
J. J.
, and
Lee
,
S. J.
,
2017
, “
Clinically Relevant Bioprinting Workflow and Imaging Process for Tissue Construct Design and Validation
,”
3D Print. Addit. Manuf.
,
4
(
4
), pp.
239
247
.
11.
Sanz-Herrera
,
J.
,
García-Aznar
,
J.
, and
Doblaré
,
M.
,
2009
, “
A Mathematical Approach to Bone Tissue Engineering
,”
Phil. Trans. R. Soc. A: Math., Phys. Eng. Sci.
,
367
(
1895
), pp.
2055
2078
.
12.
Habib
,
F. N.
,
Nikzad
,
M.
,
Masood
,
S. H.
, and
Saifullah
,
A. B. M.
,
2016
, “
Design and Development of Scaffolds for Tissue Engineering Using Three-Dimensional Printing for Bio-Based Applications
,”
3D Print. Addit. Manuf.
,
3
(2), pp. 119–127.
13.
Arabnejad
,
S.
,
Johnston
,
R. B.
,
Pura
,
J. A.
,
Singh
,
B.
,
Tanzer
,
M.
, and
Pasini
,
D.
,
2016
, “
High-Strength Porous Biomaterials for Bone Replacement: A Strategy to Assess the Interplay Between Cell Morphology, Mechanical Properties, Bone Ingrowth and Manufacturing Constraints
,”
Acta Biomater.
,
30
, pp.
345
356
.
14.
Ashby
,
M.
,
2006
, “
The Properties of Foams and Lattices
,”
Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci.
,
364
(
1838
), pp.
15
30
.
15.
Ameta
,
G.
,
Lipman
,
R.
,
Moylan
,
S.
, and
Witherell
,
P.
,
2015
, “
Investigating the Role of Geometric Dimensioning and Tolerancing in Additive Manufacturing
,”
ASME J. Mech. Des.
,
137
(
11
), p.
111401
.
16.
Ravari
,
M. K.
,
Kadkhodaei
,
M.
,
Badrossamay
,
M.
, and
Rezaei
,
R.
,
2014
, “
Numerical Investigation on Mechanical Properties of Cellular Lattice Structures Fabricated by Fused Deposition Modeling
,”
Int. J. Mech. Sci.
,
88
, pp.
154
161
.
17.
Egan
,
P. F.
,
Gonella
,
V. C.
,
Engensperger
,
M.
,
Ferguson
,
S. J.
, and
Shea
,
K.
,
2017
, “
Computationally Designed Lattices With Tuned Properties for Tissue Engineering Using 3D Printing
,”
PLoS One
,
12
(
8
), p.
e0182902
.
18.
Egan
,
P. F.
,
Bauer
,
I.
,
Shea
,
K.
, and
Ferguson
,
S. J.
,
2018
, “
Integrative Design, Build, Test Approach for Biomedical Devices With Lattice Structures
,”
ASME
Paper No. DETC2018-85355.
19.
Chen
,
S.-H.
,
Tai
,
C.-L.
,
Lin
,
C.-Y.
,
Hsieh
,
P.-H.
, and
Chen
,
W.-P.
,
2008
, “
Biomechanical Comparison of a New Stand-Alone Anterior Lumbar Interbody Fusion Cage With Established Fixation Techniques—A Three-Dimensional Finite Element Analysis
,”
BMC Musculoskeletal Disord.
,
9
, p.
88
.
20.
Choi
,
K.-C.
,
Ryu
,
K.-S.
,
Lee
,
S.-H.
,
Kim
,
Y. H.
,
Lee
,
S. J.
, and
Park
,
C.-K.
,
2013
, “
Biomechanical Comparison of Anterior Lumbar Interbody Fusion: Stand-Alone Interbody Cage Versus Interbody Cage With Pedicle Screw Fixation—A Finite Element Analysis
,”
BMC Musculoskeletal Disord.
,
14
, p.
220
.
21.
Van de Kelft
,
E.
, and
Van Goethem
,
J.
,
2015
, “
Trabecular Metal Spacers as Standalone or With Pedicle Screw Augmentation, in Posterior Lumbar Interbody Fusion: A Prospective, Randomized Controlled Trial
,”
Eur. Spine J.
,
24
(
11
), pp.
2597
2606
.
22.
Lee
,
Y.-H.
,
Chung
,
C.-J.
,
Wang
,
C.-W.
,
Peng
,
Y.-T.
,
Chang
,
C.-H.
,
Chen
,
C.-H.
,
Chen
,
Y.-N.
, and
Li
,
C.-T.
,
2016
, “
Computational Comparison of Three Posterior Lumbar Interbody Fusion Techniques by Using Porous Titanium Interbody Cages With 50% Porosity
,”
Comput. Biol. Med.
,
71
, pp.
35
45
.
23.
Fradique
,
R.
,
Correia
,
T.
,
Miguel
,
S.
,
De Sa
,
K.
,
Figueira
,
D.
,
Mendonça
,
A.
, and
Correia
,
I.
,
2016
, “
Production of New 3D Scaffolds for Bone Tissue Regeneration by Rapid Prototyping
,”
J. Mater. Sci.: Mater. Med.
,
27
, p.
69
.
24.
Egan
,
P. F.
,
Moore
,
J. R.
,
Ehrlicher
,
A. J.
,
Weitz
,
D. A.
,
Schunn
,
C.
,
Cagan
,
J.
, and
LeDuc
,
P.
,
2017
, “
Robust Mechanobiological Behavior Emerges in Heterogeneous Myosin Systems
,”
Proc. Natl. Acad. Sci.
,
114
(
39
), pp.
E8147
E8154
.
25.
Egan
,
P.
,
Cagan
,
J.
,
Schunn
,
C.
,
Chiu
,
F.
,
Moore
,
J.
, and
LeDuc
,
P.
,
2016
, “
The D3 Methodology: Bridging Science and Design for Bio-Based Product Development
,”
ASME J. Mech. Des.
,
138
(8), p. 081101.
26.
Wang
,
L.
,
He
,
K.
,
Chen
,
Z.
, and
Yang
,
Y.
,
2017
, “
A Design Method for Orthopedic Plates Based on Surface Features
,”
ASME J. Mech. Des.
,
139
(
2
), p.
024502
.
27.
Wynn
,
D. C.
, and
Eckert
,
C. M.
,
2017
, “
Perspectives on Iteration in Design and Development
,”
Res. Eng. Des.
,
28
(
2
), pp.
153
184
.
28.
Hollister
,
S. J.
,
Flanagan
,
C. L.
,
Zopf
,
D. A.
,
Morrison
,
R. J.
,
Nasser
,
H.
,
Patel
,
J. J.
,
Ebramzadeh
,
E.
,
Sangiorgio
,
S. N.
,
Wheeler
,
M. B.
, and
Green
,
G. E.
,
2015
, “
Design Control for Clinical Translation of 3D Printed Modular Scaffolds
,”
Ann. Biomed. Eng.
,
43
(
3
), pp.
774
786
.
29.
Dong
,
G.
,
Tang
,
Y.
, and
Zhao
,
Y. F.
,
2017
, “
A Survey of Modeling of Lattice Structures Fabricated by Additive Manufacturing
,”
ASME J. Mech. Des.
,
139
(
10
), p.
100906
.
30.
Kang
,
H.
,
Hollister
,
S. J.
,
La Marca
,
F.
,
Park
,
P.
, and
Lin
,
C.-Y.
,
2013
, “
Porous Biodegradable Lumbar Interbody Fusion Cage Design and Fabrication Using Integrated Global-Local Topology Optimization With Laser Sintering
,”
ASME J. Biomech. Eng.
,
135
(
10
), p.
101013
.
31.
Taniguchi
,
N.
,
Fujibayashi
,
S.
,
Takemoto
,
M.
,
Sasaki
,
K.
,
Otsuki
,
B.
,
Nakamura
,
T.
,
Matsushita
,
T.
,
Kokubo
,
T.
, and
Matsuda
,
S.
,
2016
, “
Effect of Pore Size on Bone Ingrowth Into Porous Titanium Implants Fabricated by Additive Manufacturing: An In Vivo Experiment
,”
Mater. Sci. Eng.: C
,
59
, pp.
690
701
.
32.
Kopperdahl
,
D. L.
, and
Keaveny
,
T. M.
,
1998
, “
Yield Strain Behavior of Trabecular Bone
,”
J. Biomech.
,
31
(
7
), pp.
601
608
.
33.
Wilke
,
H. J.
,
Neef
,
P.
,
Caimi
,
M.
,
Hoogland
,
T.
, and
Claes
,
L. E.
,
1999
, “
New In Vivo Measurements of Pressures in the Intervertebral Disc in Daily Life
,”
Spine
,
24
(
8
), pp.
755
762
.
34.
Marini
,
G.
,
Studer
,
H.
,
Huber
,
G.
,
Püschel
,
K.
, and
Ferguson
,
S. J.
,
2016
, “
Geometrical Aspects of Patient-specific Modelling of the Intervertebral Disc: Collagen Fibre Orientation and Residual Stress Distribution
,”
Mech. Model. Mechanobiol.
,
15
(
3
), pp.
543
560
.
35.
Roohani-Esfahani
,
S.-I.
,
Newman
,
P.
, and
Zreiqat
,
H.
,
2016
, “
Design and Fabrication of 3D Printed Scaffolds With a Mechanical Strength Comparable to Cortical Bone to Repair Large Bone Defects
,”
Sci. Rep.
,
6
, p.
19468
.
36.
Mueller
,
J.
,
Shea
,
K.
, and
Daraio
,
C.
,
2015
, “
Mechanical Properties of Parts Fabricated With Inkjet 3D Printing Through Efficient Experimental Design
,”
Mater. Des.
,
86
, pp.
902
912
.
37.
Ligon
,
S. C.
,
Liska
,
R.
,
Stampfl
,
J.
,
Gurr
,
M.
, and
Mülhaupt
,
R.
,
2017
, “
Polymers for 3D Printing and Customized Additive Manufacturing
,”
Chem. Rev.
,
117
(
15
), pp.
10212
10290
.
38.
Alifui-Segbaya
,
F.
,
Varma
,
S.
,
Lieschke
,
G. J.
, and
George
,
R.
,
2017
, “
Biocompatibility of Photopolymers in 3D Printing
,”
3D Print. Addit. Manuf.
,
4
(
4
), pp.
185
191
.
39.
Barnawal
,
P.
,
Dorneich
,
M. C.
,
Frank
,
M. C.
, and
Peters
,
F.
,
2017
, “
Evaluation of Design Feedback Modality in Design for Manufacturability
,”
ASME J. Mech. Des.
,
139
(
9
), p.
094503
.
40.
Booth
,
J. W.
,
Alperovich
,
J.
,
Chawla
,
P.
,
Ma
,
J.
,
Reid
,
T. N.
, and
Ramani
,
K.
,
2017
, “
The Design for Additive Manufacturing Worksheet
,”
ASME J. Mech. Des.
,
139
(
10
), p.
100904
.
41.
Ahmed
,
M.
,
Islam
,
M.
,
Vanhoose
,
J.
, and
Rahman
,
M.
,
2017
, “
Comparisons of Elasticity Moduli of Different Specimens Made Through Three Dimensional Printing
,”
3D Print. Addit. Manuf.
,
4
(
2
), pp.
105
109
.
42.
Oropallo
,
W.
, and
Piegl
,
L. A.
,
2016
, “
Ten Challenges in 3D Printing
,”
Eng. Comput.
,
32
(
1
), pp.
135
148
.
43.
Kim
,
S.-Y.
,
Shin
,
Y.-S.
,
Jung
,
H.-D.
,
Hwang
,
C.-J.
,
Baik
,
H.-S.
, and
Cha
,
J.-Y.
,
2018
, “
Precision and Trueness of Dental Models Manufactured With Different 3-Dimensional Printing Techniques
,”
Am. J. Orthod. Dentofacial Orthop.
,
153
(
1
), pp.
144
153
.
44.
Lopez
,
F.
,
Witherell
,
P.
, and
Lane
,
B.
,
2016
, “
Identifying Uncertainty in Laser Powder Bed Fusion Additive Manufacturing Models
,”
ASME J. Mech. Des.
,
138
(
11
), p.
114502
.
45.
Kadkhodapour
,
J.
,
Montazerian
,
H.
,
Darabi
,
A. C.
,
Anaraki
,
A.
,
Ahmadi
,
S.
,
Zadpoor
,
A.
, and
Schmauder
,
S.
,
2015
, “
Failure Mechanisms of Additively Manufactured Porous Biomaterials: Effects of Porosity and Type of Unit Cell
,”
J. Mech. Behav. Biomed. Mater.
,
50
, pp.
180
191
.
46.
Limmahakhun
,
S.
,
Oloyede
,
A.
,
Sitthiseripratip
,
K.
,
Xiao
,
Y.
, and
Yan
,
C.
,
2017
, “
3D-Printed Cellular Structures for Bone Biomimetic Implants
,”
Addit. Manuf.
,
15
, pp.
93
101
.
47.
Smith
,
M.
,
Guan
,
Z.
, and
Cantwell
,
W.
,
2013
, “
Finite Element Modelling of the Compressive Response of Lattice Structures Manufactured Using the Selective Laser Melting Technique
,”
Int. J. Mech. Sci.
,
67
, pp.
28
41
.
48.
Weißmann
,
V.
,
Wieding
,
J.
,
Hansmann
,
H.
,
Laufer
,
N.
,
Wolf
,
A.
, and
Bader
,
R.
,
2016
, “
Specific Yielding of Selective Laser-Melted Ti6Al4V Open-Porous Scaffolds as a Function of Unit Cell Design and Dimensions
,”
Metals
,
6
(
7
), p.
166
.
49.
Wieding
,
J.
,
Fritsche
,
A.
,
Heinl
,
P.
,
Körner
,
C.
,
Cornelsen
,
M.
,
Seitz
,
H.
,
Mittelmeier
,
W.
, and
Bader
,
R.
,
2013
, “
Biomechanical Behavior of Bone Scaffolds Made of Additive Manufactured Tricalciumphosphate and Titanium Alloy Under Different Loading Conditions
,”
J. Appl. Biomater. Funct. Mater.
,
11
(3), pp. 159–166.
50.
Melancon
,
D.
,
Bagheri
,
Z.
,
Johnston
,
R.
,
Liu
,
L.
,
Tanzer
,
M.
, and
Pasini
,
D.
,
2017
, “
Mechanical Characterization of Structurally Porous Biomaterials Built Via Additive Manufacturing: Experiments, Predictive Models, and Design Maps for Load-Bearing Bone Replacement Implants
,”
Acta Biomater.
,
63
, pp.
350
368
.
51.
Mehdizadeh
,
H.
,
Somo
,
S. I.
,
Bayrak
,
E. S.
,
Brey
,
E. M.
, and
Cinar
,
A.
,
2015
, “
Design of Polymer Scaffolds for Tissue Engineering Applications
,”
Ind. Eng. Chem. Res.
,
54
, pp.
2317
2328
.
52.
Cramer
,
A. D.
,
Challis
,
V. J.
, and
Roberts
,
A. P.
,
2017
, “
Physically Realizable Three-Dimensional Bone Prosthesis Design With Interpolated Microstructures
,”
ASME J. Biomech. Eng.
,
139
(
3
), p.
031013
.
53.
Bashkuev
,
M.
,
Checa
,
S.
,
Postigo
,
S.
,
Duda
,
G.
, and
Schmidt
,
H.
,
2015
, “
Computational Analyses of Different Intervertebral Cages for Lumbar Spinal Fusion
,”
J. Biomech.
,
48
(
12
), pp.
3274
3282
.
54.
Tsai
,
P.-I.
,
Hsu
,
C.-C.
,
Chen
,
S.-Y.
,
Wu
,
T.-H.
, and
Huang
,
C.-C.
,
2016
, “
Biomechanical Investigation Into the Structural Design of Porous Additive Manufactured Cages Using Numerical and Experimental Approaches
,”
Comput. Biol. Med.
,
76
, pp.
14
23
.
55.
Abràmoff
,
M. D.
,
Magalhães
,
P. J.
, and
Ram
,
S. J.
,
2004
, “
Image Processing With ImageJ
,”
Biophotonics Int.
,
11
(7), pp.
36
42
.https://imagescience.org/meijering/publications/download/bio2004.pdf
56.
Busscher
,
I.
,
Ploegmakers
,
J. J.
,
Verkerke
,
G. J.
, and
Veldhuizen
,
A. G.
,
2010
, “
Comparative Anatomical Dimensions of the Complete Human and Porcine Spine
,”
Eur. Spine J.
,
19
(
7
), pp.
1104
1114
.
57.
Campoli
,
G.
,
Borleffs
,
M.
,
Yavari
,
S. A.
,
Wauthle
,
R.
,
Weinans
,
H.
, and
Zadpoor
,
A. A.
,
2013
, “
Mechanical Properties of Open-Cell Metallic Biomaterials Manufactured Using Additive Manufacturing
,”
Mater. Des.
,
49
, pp.
957
965
.
58.
Luxner
,
M. H.
,
Stampfl
,
J.
, and
Pettermann
,
H. E.
,
2005
, “
Finite Element Modeling Concepts and Linear Analyses of 3D Regular Open Cell Structures
,”
J. Mater. Sci.
,
40
(
22
), pp.
5859
5866
.
59.
Stanković
,
T.
,
Mueller
,
J.
, and
Shea
,
K.
,
2017
, “
The Effect of Anisotropy on the Optimization of Additively Manufactured Lattice Structures
,”
Addit. Manuf.
,
17
, pp.
67
76
.
60.
Diebels
,
S.
, and
Steeb
,
H.
,
2002
, “
The Size Effect in Foams and Its Theoretical and Numerical Investigation
,”
Proc. R. Soc. London A
,
458
(
2028
), pp.
2869
2883
.
61.
Maskery
,
I.
,
Aremu
,
A.
,
Parry
,
L.
,
Wildman
,
R.
,
Tuck
,
C.
, and
Ashcroft
,
I.
,
2018
, “
Effective Design and Simulation of Surface-Based Lattice Structures Featuring Volume Fraction and Cell Type Grading
,”
Mater. Des.
, 155, pp. 220–232.https://www.sciencedirect.com/science/article/pii/S026412751830443X
62.
Rohlmann
,
A.
,
Pohl
,
D.
,
Bender
,
A.
,
Graichen
,
F.
,
Dymke
,
J.
,
Schmidt
,
H.
, and
Bergmann
,
G.
,
2014
, “
Activities of Everyday Life With High Spinal Loads
,”
PLoS One
,
9
(
5
), p.
e98510
.
63.
Meza
,
L. R.
,
Zelhofer
,
A. J.
,
Clarke
,
N.
,
Mateos
,
A. J.
,
Kochmann
,
D. M.
, and
Greer
,
J. R.
,
2015
, “
Resilient 3D Hierarchical Architected Metamaterials
,”
Proc. Natl. Acad. Sci.
,
112
(
37
), pp.
11502
11507
.
64.
Maggi
,
A.
,
Li
,
H.
, and
Greer
,
J. R.
,
2017
, “
Three-Dimensional Nano-Architected Scaffolds With Tunable Stiffness for Efficient Bone Tissue Growth
,”
Acta Biomater.
,
63
, pp.
294
305
.
65.
Maggi
,
A.
,
Allen
,
J.
,
Desai
,
T.
, and
Greer
,
J. R.
,
2017
, “
Osteogenic Cell Functionality on 3-Dimensional Nano-Scaffolds With Varying Stiffness
,”
Extreme Mech. Lett.
,
13
, pp.
1
9
.
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