Indentation experiments offer a robust, fast, and repeatable testing method for evaluating the mechanical properties of the solid-state materials in a wide stiffness range. With the advantage of requiring a minimal sample preparation and multiple tests on a small piece of specimen, this method has recently become a popular technique for measuring the elastic properties of the biological materials, especially the brain tissue whose ultrasoft nature makes its mechanical characterization very challenging. Nevertheless, some limitations are associated with the indentation of the brain tissue, such as improper surface detection, negative initial contact force due to tip-tissue moisture interaction, and partial contact between the tip and the sample. In this study, an indirect indentation scheme is proposed to overcome the aforementioned difficulties. In this way, the indentation force is transferred from a sharp tip to the surface of the tissue slices via a rigid coverslip. To demonstrate the accuracy of this method, the linear viscoelastic properties of the white and gray matters of the bovine brain samples are measured by imposing small cyclic loads at different frequencies. The rate, regional, directional, and postmortem time dependence of the viscoelastic moduli are investigated and compared with the previous results from cyclic shear and monotonic experiments on the brain tissue. While findings of this research present a comprehensive set of information for the viscoelastic properties of the brain at a wide frequency range, the central goal of this paper is to introduce a novel experimentation technique with noticeable advantages for biomechanical characterization of the soft tissue.

References

References
1.
Cowin
,
S. C.
, and
Doty
,
S. B.
,
2007
,
Tissue Mechanics
,
Springer Science
,
New York
.
2.
Humphrey
,
J. D.
, and
O'Rourke
,
S. L.
,
2004
,
An Introduction to Biomechanics: Solids and Fluids, Analysis and Design
,
Springer
,
New York
.
3.
Fung
,
Y.-C.
,
1990
,
Biomechanics: Motion, Flow, Stress, and Growth
,
Springer
,
New York
.
4.
Chatelin
,
S.
,
Constantinesco
,
A.
, and
Willinger
,
R.
,
2010
, “
Fifty Years of Brain Tissue Mechanical Testing: From In Vitro to In Vivo Investigations
,”
Biorheology
,
47
(
5–6
), pp.
255
276
.
5.
Faul
,
M.
,
Xu
,
L.
,
Wald
,
M.
, and
Coronado
,
V.
,
2010
, “
Traumatic Brain Injury in the United States: Emergency Department Visits, Hospitalizations, and Deaths 2002–2006
,” U.S. Department of Health and Homan Services, Centers for Disease Control and Prevention (
CDC
), Atlanta, GA.
6.
Budday
,
S.
,
Raybaud
,
C.
, and
Kuhl
,
E.
,
2014
, “
A Mechanical Model Predicts Morphological Abnormalities in the Developing Human Brain
,”
Sci. Rep.
,
4
, p. 5644.
7.
Budday
,
S.
,
Steinmann
,
P.
, and
Kuhl
,
E.
,
2014
, “
The Role of Mechanics During Brain Development
,”
J. Mech. Phys. Solids
,
72
, pp.
75
92
.
8.
Kuhl
,
E.
,
2016
, “
Biophysics: Unfolding the Brain
,”
Nat. Phys.
,
12
(
6
), pp.
533
534
.
9.
Budday
,
S.
,
Steinmann
,
P.
, and
Kuhl
,
E.
,
2015
, “
Physical Biology of Human Brain Development
,”
Front. Cell. Neurosci.
,
9
, p. 257.
10.
Bayly
,
P.
,
Taber
,
L. A.
, and
Kroenke
,
C. D.
,
2014
, “
Mechanical Forces in Cerebral Cortical Folding: A Review of Measurements and Models
,”
J. Mech. Behav. Biomed. Mater.
,
29
, pp.
568
581
.
11.
Streitberger
,
K.-J.
,
Sack
,
I.
,
Krefting
,
D.
,
Pfüller
,
C.
,
Braun
,
J.
,
Paul
,
F.
, and
Wuerfel
,
J.
,
2012
, “
Brain Viscoelasticity Alteration in Chronic-Progressive Multiple Sclerosis
,”
PLoS One
,
7
(
1
), p.
e29888
.
12.
Murphy
,
M. C.
,
Huston
,
J.
, III,
Jack
,
C. R.
, Jr.,
Glaser
,
K. J.
,
Manduca
,
A.
,
Felmlee
,
J. P.
, and
Ehman
,
R. L.
,
2011
, “
Decreased Brain Stiffness in Alzheimer's Disease Determined by Magnetic Resonance Elastography
,”
J. Magn. Reson. Imaging
,
34
(
3
), pp.
494
498
.
13.
Streitberger
,
K.-J.
,
Wiener
,
E.
,
Hoffmann
,
J.
,
Freimann
,
F. B.
,
Klatt
,
D.
,
Braun
,
J.
,
Lin
,
K.
,
McLaughlin
,
J.
,
Sprung
,
C.
,
Klingebiel
,
R.
, and
Sack
,
I.
,
2011
, “
In Vivo Viscoelastic Properties of the Brain in Normal Pressure Hydrocephalus
,”
NMR Biomed.
,
24
(
4
), pp.
385
392
.
14.
Zhang
,
L.
,
Yang
,
K. H.
, and
King
,
A. I.
,
2001
, “
Comparison of Brain Responses Between Frontal and Lateral Impacts by Finite Element Modeling
,”
J. Neurotrauma
,
18
(
1
), pp.
21
30
.
15.
Ahmadzadeh
,
H.
,
Smith
,
D. H.
, and
Shenoy
,
V. B.
,
2014
, “
Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules During Axonal Stretch Injury: Predictions From a Mathematical Model
,”
Biophys. J.
,
106
(
5
), pp.
1123
1133
.
16.
Tallinen
,
T.
,
Chung
,
J.-Y.
,
Rosseau
,
F.
,
Girard
,
N.
,
Lefèvre
,
J.
, and
Mahadevan
,
L.
,
2016
, “
On the Growth and Form of Cortical Convolutions
,”
Nat. Phys.
,
12
(
6
), pp.
588
593
.
17.
Razavi
,
M. J.
,
Zhang
,
T.
,
Liu
,
T.
, and
Wang
,
X.
,
2015
, “
Cortical Folding Pattern and Its Consistency Induced by Biological Growth
,”
Sci. Rep.
,
5
, p. 14477.
18.
Miller
,
K.
, and
Chinzei
,
K.
,
2002
, “
Mechanical Properties of Brain Tissue in Tension
,”
J. Biomech.
,
35
(
4
), pp.
483
490
.
19.
Velardi
,
F.
,
Fraternali
,
F.
, and
Angelillo
,
M.
,
2006
, “
Anisotropic Constitutive Equations and Experimental Tensile Behavior of Brain Tissue
,”
Biomech. Model. Mechanobiol.
,
5
(
1
), pp.
53
61
.
20.
Pervin
,
F.
, and
Chen
,
W. W.
,
2009
, “
Dynamic Mechanical Response of Bovine Gray Matter and White Matter Brain Tissues Under Compression
,”
J. Biomech.
,
42
(
6
), pp.
731
735
.
21.
Rashid
,
B.
,
Destrade
,
M.
, and
Gilchrist
,
M. D.
,
2012
, “
Mechanical Characterization of Brain Tissue in Compression at Dynamic Strain Rates
,”
J. Mech. Behav. Biomed. Mater.
,
10
, pp.
23
38
.
22.
Prevost
,
T. P.
,
Balakrishnan
,
A.
,
Suresh
,
S.
, and
Socrate
,
S.
,
2011
, “
Biomechanics of Brain Tissue
,”
Acta Biomater.
,
7
(
1
), pp.
83
95
.
23.
Arbogast
,
K. B.
, and
Margulies
,
S. S.
,
1998
, “
Material Characterization of the Brainstem From Oscillatory Shear Tests
,”
J. Biomech.
,
31
(
9
), pp.
801
807
.
24.
Arbogast
,
K. B.
, and
Margulies
,
S. S.
,
1999
, “
A Fiber-Reinforced Composite Model of the Viscoelastic Behavior of the Brainstem in Shear
,”
J. Biomech.
,
32
(
8
), pp.
865
870
.
25.
Takhounts
,
E. G.
,
Crandall
,
J. R.
, and
Darvish
,
K.
,
2003
, “
On the Importance of Nonlinearity of Brain Tissue Under Large Deformations
,”
Stapp Car Crash J.
,
47
, pp.
79
92
.
26.
Nicolle
,
S.
,
Lounis
,
M.
, and
Willinger
,
R.
,
2004
, “
Shear Properties of Brain Tissue Over a Frequency Range Relevant for Automotive Impact Situations: New Experimental Results
,”
Stapp Car Crash J.
,
48
, pp. 239–258.
27.
Hrapko
,
M.
,
Van Dommelen
,
J.
,
Peters
,
G.
, and
Wismans
,
J.
,
2008
, “
The Influence of Test Conditions on Characterization of the Mechanical Properties of Brain Tissue
,”
ASME J. Biomech. Eng.
,
130
(
3
), p.
031003
.
28.
Feng
,
Y.
,
Okamoto
,
R. J.
,
Namani
,
R.
,
Genin
,
G. M.
, and
Bayly
,
P. V.
,
2013
, “
Measurements of Mechanical Anisotropy in Brain Tissue and Implications for Transversely Isotropic Material Models of White Matter
,”
J. Mech. Behav. Biomed. Mater.
,
23
, pp.
117
132
.
29.
Prange
,
M. T.
, and
Margulies
,
S. S.
,
2002
, “
Regional, Directional, and Age-Dependent Properties of the Brain Undergoing Large Deformation
,”
ASME J. Biomech. Eng.
,
124
(
2
), pp.
244
252
.
30.
Budday
,
S.
,
Nay
,
R.
,
de Rooij
,
R.
,
Steinmann
,
P.
,
Wyrobek
,
T.
,
Ovaert
,
T. C.
, and
Kuhl
,
E.
,
2015
, “
Mechanical Properties of Gray and White Matter Brain Tissue by Indentation
,”
J. Mech. Behav. Biomed. Mater.
,
46
, pp.
318
330
.
31.
Chen
,
F.
,
Zhou
,
J.
,
Li
,
Y.
,
Wang
,
Y.
,
Li
,
L.
, and
Yue
,
H.
,
2015
, “
Mechanical Properties of Porcine Brain Tissue in the Coronal Plane: Interregional Variations of the Corona Radiata
,”
Ann. Biomed. Eng.
,
43
(
12
), pp.
2903
2910
.
32.
Elkin
,
B. S.
,
Ilankova
,
A.
, and
Morrison
,
B.
,
2011
, “
Dynamic, Regional Mechanical Properties of the Porcine Brain: Indentation in the Coronal Plane
,”
ASME J. Biomech. Eng.
,
133
(
7
), p.
071009
.
33.
Elkin
,
B. S.
,
Ilankovan
,
A. I.
, and
Morrison
,
B.
, III
,
2011
, “
A Detailed Viscoelastic Characterization of the P17 and Adult Rat Brain
,”
J. Neurotrauma
,
28
(
11
), pp.
2235
2244
.
34.
Kaster
,
T.
,
Sack
,
I.
, and
Samani
,
A.
,
2011
, “
Measurement of the Hyperelastic Properties of Ex Vivo Brain Tissue Slices
,”
J. Biomech.
,
44
(
6
), pp.
1158
1163
.
35.
MacManus
,
D.
,
Pierrat
,
B.
,
Murphy
,
J.
, and
Gilchrist
,
M.
,
2015
, “
Dynamic Mechanical Properties of Murine Brain Tissue Using Micro-Indentation
,”
J. Biomech.
,
48
(
12
), pp.
3213
3218
.
36.
MacManus
,
D. B.
,
Pierrat
,
B.
,
Murphy
,
J. G.
, and
Gilchrist
,
M. D.
,
2016
, “
Mechanical Characterization of the P56 Mouse Brain Under Large-Deformation Dynamic Indentation
,”
Sci. Rep.
,
6
, p. 21569.
37.
Prevost
,
T. P.
,
Jin
,
G.
,
De Moya
,
M. A.
,
Alam
,
H. B.
,
Suresh
,
S.
, and
Socrate
,
S.
,
2011
, “
Dynamic Mechanical Response of Brain Tissue in Indentation In Vivo, In Situ and In Vitro
,”
Acta Biomater.
,
7
(
12
), pp.
4090
4101
.
38.
Van Dommelen
,
J.
,
Van der Sande
,
T.
,
Hrapko
,
M.
, and
Peters
,
G.
,
2010
, “
Mechanical Properties of Brain Tissue by Indentation: Interregional Variation
,”
J. Mech. Behav. Biomed. Mater.
,
3
(
2
), pp.
158
166
.
39.
Weickenmeier
,
J.
,
de Rooij
,
R.
,
Budday
,
S.
,
Steinmann
,
P.
,
Ovaert
,
T. C.
, and
Kuhl
,
E.
,
2016
, “
Brain Stiffness Increases With Myelin Content
,”
Acta Biomater.
,
42
, pp.
265
272
.
40.
Oliver
,
W. C.
, and
Pharr
,
G. M.
,
1992
, “
An Improved Technique for Determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,”
J. Mater. Res.
,
7
(
6
), pp.
1564
1583
.
41.
Herbert
,
E.
,
Oliver
,
W.
, and
Pharr
,
G.
,
2008
, “
Nanoindentation and the Dynamic Characterization of Viscoelastic Solids
,”
J. Phys. D: Appl. Phys.
,
41
(
7
), p.
074021
.
42.
Herbert
,
E.
,
Oliver
,
W.
,
Lumsdaine
,
A.
, and
Pharr
,
G. M.
,
2009
, “
Measuring the Constitutive Behavior of Viscoelastic Solids in the Time and Frequency Domain Using Flat Punch Nanoindentation
,”
J. Mater. Res.
,
24
(
3
), pp.
626
637
.
43.
Sneddon
,
I. N.
,
1965
, “
The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile
,”
Int. J. Eng. Sci.
,
3
(
1
), pp.
47
57
.
44.
Liu
,
K.
,
VanLandingham
,
M. R.
, and
Ovaert
,
T. C.
,
2009
, “
Mechanical Characterization of Soft Viscoelastic Gels Via Indentation and Optimization-Based Inverse Finite Element Analysis
,”
J. Mech. Behav. Biomed. Mater.
,
2
(
4
), pp.
355
363
.
45.
Laksari
,
K.
,
Shafieian
,
M.
, and
Darvish
,
K.
,
2012
, “
Constitutive Model for Brain Tissue Under Finite Compression
,”
J. Biomech.
,
45
(
4
), pp.
642
646
.
46.
Taylor
,
Z.
, and
Miller
,
K.
,
2004
, “
Reassessment of Brain Elasticity for Analysis of Biomechanisms of Hydrocephalus
,”
J. Biomech.
,
37
(
8
), pp.
1263
1269
.
47.
Franceschini
,
G.
,
Bigoni
,
D.
,
Regitnig
,
P.
, and
Holzapfel
,
G. A.
,
2006
, “
Brain Tissue Deforms Similarly to Filled Elastomers and Follows Consolidation Theory
,”
J. Mech. Phys. Solids
,
54
(
12
), pp.
2592
2620
.
48.
Samadi-Dooki
,
A.
,
Shodja
,
H. M.
, and
Malekmotiei
,
L.
,
2015
, “
The Effect of the Physical Properties of the Substrate on the Kinetics of Cell Adhesion and Crawling Studied by an Axisymmetric Diffusion-Energy Balance Coupled Model
,”
Soft Matter
,
11
(
18
), pp.
3693
3705
.
49.
Finan
,
J. D.
,
Fox
,
P. M.
, and
Morrison
,
B.
, III
,
2014
, “
Non-Ideal Effects in Indentation Testing of Soft Tissues
,”
Biomech. Model. Mechanobiol.
,
13
(
3
), pp.
573
584
.
50.
Suresh
,
S.
,
Nieh
,
T.-G.
, and
Choi
,
B.
,
1999
, “
Nano-Indentation of Copper Thin Films on Silicon Substrates
,”
Scr. Mater.
,
41
(
9
), pp.
951
957
.
51.
Bilston
,
L. E.
,
Liu
,
Z.
, and
Phan-Thien
,
N.
,
1997
, “
Linear Viscoelastic Properties of Bovine Brain Tissue in Shear
,”
Biorheology
,
34
(
6
), pp.
377
385
.
52.
Shuck
,
L.
, and
Advani
,
S.
,
1972
, “
Rheological Response of Human Brain Tissue in Shear
,”
J. Basic Eng.
,
94
(
4
), pp.
905
911
.
53.
Hrapko
,
M.
,
Van Dommelen
,
J. A.
,
Peters
,
G. W.
, and
Wismans
,
J. S.
,
2006
, “
The Mechanical Behaviour of Brain Tissue: Large Strain Response and Constitutive Modelling
,”
Biorheology
,
43
(
5
), pp.
623
636
.
54.
Catani
,
M.
, and
De Schotten
,
M. T.
,
2008
, “
A Diffusion Tensor Imaging Tractography Atlas for Virtual In Vivo Dissections
,”
Cortex
,
44
(
8
), pp.
1105
1132
.
55.
Gerstl
,
C.
,
Schneider
,
G. J.
,
Pyckhout-Hintzen
,
W.
,
Allgaier
,
J.
,
Richter
,
D.
,
Alegría
,
A.
, and
Colmenero
,
J.
,
2010
, “
Segmental and Normal Mode Relaxation of Poly(Alkylene Oxide)s Studied by Dielectric Spectroscopy and Rheology
,”
Macromolecules
,
43
(
11
), pp.
4968
4977
.
56.
Nusser
,
K.
,
Schneider
,
G. J.
,
Pyckhout-Hintzen
,
W.
, and
Richter
,
D.
,
2011
, “
Viscosity Decrease and Reinforcement in Polymer–Silsesquioxane Composites
,”
Macromolecules
,
44
(
19
), pp.
7820
7830
.
57.
Vlassak
,
J. J.
, and
Nix
,
W. D.
,
1993
, “
Indentation Modulus of Elastically Anisotropic Half Spaces
,”
Philos. Mag. A
,
67
(
5
), pp.
1045
1056
.
58.
Ferrer
,
I.
,
Santpere
,
G.
,
Arzberger
,
T.
,
Bell
,
J.
,
Blanco
,
R.
,
Boluda
,
S.
,
Budka
,
H.
,
Carmona
,
M.
,
Giaccone
,
G.
, and
Krebs
,
B.
,
2007
, “
Brain Protein Preservation Largely Depends on the Postmortem Storage Temperature: Implications for Study of Proteins in Human Neurologic Diseases and Management of Brain Banks: A BrainNet Europe Study
,”
J. Neuropathol. Exp. Neurol.
,
66
(
1
), pp.
35
46
.
59.
Gladwell
,
G. M. L.
, and
Iyer
,
K. R. P.
,
1974
, “
Unbonded Contact Between a Circular Plate and an Elastic Half-Space
,”
J. Elasticity
,
4
(
2
), pp.
115
130
.
You do not currently have access to this content.