Abstract

Skin tissue is a complex heterogeneous material abundant with fibers. Various models capturing its anisotropy, nonlinearity, and viscoelasticity have been developed. However, the existence of multiple fiber families and their differences have been largely ignored. Furthermore, inhomogeneous deformation over the thickness is observed in the skin under shear deformation, which the traditional skin models do not predict. In this paper, we propose that two fiber families with distinct mechanical and structural properties exist in the skin within the framework of a general structure tensor-based constitutive strain energy model. Our constitutive model considers fiber families’ distinct properties and the consequent inhomogeneous deformation in the skin, showing good agreement with in vivo measurements of human face skin.

References

1.
Jor
,
J. W. Y.
,
Parker
,
M. D.
,
Taberner
,
A. J.
,
Nash
,
M. P.
, and
Nielsen
,
P. M. F.
,
2013
, “
Computational and Experimental Characterization of Skin Mechanics: Identifying Current Challenges and Future Directions
,”
Wiley Interdiscip. Rev.: Syst. Biol. Med.
,
5
(
5
), pp.
539
556
.
2.
Evans
,
S. L.
, and
Holt
,
C. A.
,
2009
, “
Measuring the Mechanical Properties of Human Skin in Vivo Using Digital Image Correlation and Finite Element Modelling
,”
J. Strain Anal. Eng. Des.
,
44
(
5
), pp.
337
345
.
3.
Chen
,
S.-Y.
,
Chen
,
S.-U.
,
Wu
,
H.-Y.
,
Lee
,
W.-J.
,
Liao
,
Y.-H.
, and
Sun
,
C.-K.
,
2010
, “
In Vivo Virtual Biopsy of Human Skin by Using Noninvasive Higher Harmonic Generation Microscopy
,”
IEEE J. Sel. Top. Quantum Electron.
,
16
(
3
), pp.
478
492
.
4.
Pensalfini
,
M.
,
Weickenmeier
,
J.
,
Rominger
,
M.
,
Santoprete
,
R.
,
Distler
,
O.
, and
Mazza
,
E.
,
2018
, “
Location-Specific Mechanical Response and Morphology of Facial Soft Tissues
,”
J. Mech. Behav. Biomed. Mater.
,
78
(
1
), pp.
108
115
.
5.
Ducourthial
,
G.
,
Affagard
,
J.
,
Schmeltz
,
M.
,
Solinas
,
X.
,
Lopez-Poncelas
,
M.
,
Bonod-Bidaud
,
C.
,
Rubio-Amador
,
R.
, et al
,
2019
, “
Monitoring Dynamic Collagen Reorganization During Skin Stretching with Fast Polarization-Resolved Second Harmonic Generation Imaging
,”
J. Biophotonics
,
12
(
5
), p.
e201800336
.
6.
Lynch
,
B.
,
Bancelin
,
S.
,
Bonod-Bidaud
,
C.
,
Gueusquin
,
J.-B.
,
Ruggiero
,
F.
,
Schanne-Klein
,
M.-C.
, and
Allain
,
J.-M.
,
2017
, “
A Novel Microstructural Interpretation for the Biomechanics of Mouse Skin Derived From Multiscale Characterization
,”
Acta Biomater.
,
50
(
1
), pp.
302
311
.
7.
Lynch
,
B.
,
Bonod-Bidaud
,
C.
,
Ducourthial
,
G.
,
Affagard
,
J.-S.
,
Bancelin
,
S.
,
Psilodimitrakopoulos
,
S.
,
Ruggiero
,
F.
,
Allain
,
J.-M.
, and
Schanne-Klein
,
M.-C.
,
2017
, “
How Aging Impacts Skin Biomechanics: a Multiscale Study in Mice
,”
Sci. Rep.
,
7
(
1
), p.
13750
.
8.
Bancelin
,
S.
,
Lynch
,
B.
,
Bonod-Bidaud
,
C.
,
Ducourthial
,
G.
,
Psilodimitrakopoulos
,
S.
,
Dokládal
,
P.
,
Allain
,
J.-M.
,
Schanne-Klein
,
M.-C.
, and
Ruggiero
,
F.
,
2015
, “
Ex Vivo Multiscale Quantitation of Skin Biomechanics in Wild-Type and Genetically-Modified Mice Using Multiphoton Microscopy
,”
Sci. Rep.
,
5
(
1
), p.
17635
.
9.
Bancelin
,
S.
,
Lynch
,
B.
,
Bonod-Bidaud
,
C.
,
Dokládal
,
P.
,
Ruggiero
,
F.
,
Allain
,
J. M.
, and
Schanne-Klein
,
M. C.
,
2019
, “Combination of Traction Assays and Multiphoton Imaging to Quantify Skin Biomechanics,”
Methods in Molecular Biology
, pp.
145
155
.
10.
Jor
,
J. W. Y.
,
Nielsen
,
P. M. F.
,
Nash
,
M. P.
, and
Hunter
,
P. J.
,
2011
, “
Modelling Collagen Fibre Orientation in Porcine Skin Based upon Confocal Laser Scanning Microscopy
,”
Skin Res. Technol.
,
17
(
2
), pp.
149
159
.
11.
Laurent
,
A.
,
Mistretta
,
F.
,
Bottigioli
,
D.
,
Dahel
,
K.
,
Goujon
,
C.
,
Nicolas
,
J. F.
,
Hennino
,
A.
, and
Laurent
,
P. E.
,
2007
, “
Echographic Measurement of Skin Thickness in Adults by High Frequency Ultrasound to Assess the Appropriate Microneedle Length for Intradermal Delivery of Vaccines
,”
Vaccine
,
25
(
34
), pp.
6423
6430
.
12.
Ní Annaidh
,
A.
,
Bruyère
,
K.
,
Destrade
,
M.
,
Gilchrist
,
M. D.
,
Maurini
,
C.
,
Otténio
,
M.
, and
Saccomandi
,
G.
,
2012
, “
Automated Estimation of Collagen Fibre Dispersion in the Dermis and its Contribution to the Anisotropic Behaviour of Skin
,”
Ann. Biomed. Eng.
,
40
(
8
), pp.
1666
1678
.
13.
Gerhardt
,
L.-C.
,
Schmidt
,
J.
,
Sanz-Herrera
,
J. A.
,
Baaijens
,
F. P. T.
,
Ansari
,
T.
,
Peters
,
G. W. M.
, and
Oomens
,
C. W. J.
,
2012
, “
A Novel Method for Visualising and Quantifying Through-Plane Skin Layer Deformations
,”
J. Mech. Behav. Biomed. Mater.
,
14
(
1
), pp.
199
207
.
14.
Jayyosi
,
C.
,
Affagard
,
J.-S.
,
Ducourthial
,
G.
,
Bonod-Bidaud
,
C.
,
Lynch
,
B.
,
Bancelin
,
S.
,
Ruggiero
,
F.
, et al
,
2017
, “
Affine Kinematics in Planar Fibrous Connective Tissues: an Experimental Investigation
,”
Biomech. Model. Mechanobiol.
,
16
(
4
), pp.
1459
1473
.
15.
Lim
,
J.
,
Hong
,
J.
,
Chen
,
W. W.
, and
Weerasooriya
,
T.
,
2011
, “
Mechanical Response of pig Skin Under Dynamic Tensile Loading
,”
Int. J. Impact Eng.
,
38
(
2–3
), pp.
130
135
.
16.
Remache
,
D.
,
Caliez
,
M.
,
Gratton
,
M.
, and
Dos Santos
,
S.
,
2018
, “
The Effects of Cyclic Tensile and Stress-Relaxation Tests on Porcine Skin
,”
J. Mech. Behav. Biomed. Mater.
,
77
(
1
), pp.
242
249
.
17.
Ní Annaidh
,
A.
,
Bruyère
,
K.
,
Destrade
,
M.
,
Gilchrist
,
M. D.
, and
Otténio
,
M.
,
2012
, “
Characterization of the Anisotropic Mechanical Properties of Excised Human Skin
,”
J. Mech. Behav. Biomed. Mater.
,
5
(
1
), pp.
139
148
.
18.
Ottenio
,
M.
,
Tran
,
D.
,
Ní Annaidh
,
A.
,
Gilchrist
,
M. D.
, and
Bruyère
,
K.
,
2015
, “
Strain Rate and Anisotropy Effects on the Tensile Failure Characteristics of Human Skin
,”
J. Mech. Behav. Biomed. Mater.
,
41
(
1
), pp.
241
250
.
19.
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
.
20.
Khatam
,
H.
,
Liu
,
Q.
, and
Ravi-Chandar
,
K.
,
2014
, “
Dynamic Tensile Characterization of pig Skin
,”
Acta Mech. Sin.
,
30
(
2
), pp.
125
132
.
21.
Kumaraswamy
,
N.
,
Khatam
,
H.
,
Reece
,
G. P.
,
Fingeret
,
M. C.
,
Markey
,
M. K.
, and
Ravi-Chandar
,
K.
,
2017
, “
Mechanical Response of Human Female Breast Skin Under Uniaxial Stretching
,”
J. Mech. Behav. Biomed. Mater.
,
74
(
1
), pp.
164
175
.
22.
Tonge
,
T. K.
,
Atlan
,
L. S.
,
Voo
,
L. M.
, and
Nguyen
,
T. D.
,
2013
, “
Full-Field Bulge Test for Planar Anisotropic Tissues: Part I—Experimental Methods Applied to Human Skin Tissue
,”
Acta Biomater.
,
9
(
4
), pp.
5913
5925
.
23.
Diab
,
M.
,
Kumaraswamy
,
N.
,
Reece
,
G. P.
,
Hanson
,
S. E.
,
Fingeret
,
M. C.
,
Markey
,
M. K.
, and
Ravi-Chandar
,
K.
,
2020
, “
Characterization of Human Female Breast and Abdominal Skin Elasticity Using a Bulge Test
,”
J. Mech. Behav. Biomed. Mater.
,
103
(
1
), p.
103604
.
24.
Hollenstein
,
M.
,
Ehret
,
A. E.
,
Itskov
,
M.
, and
Mazza
,
E.
,
2011
, “
A Novel Experimental Procedure Based on Pure Shear Testing of Dermatome-cut Samples Applied to Porcine Skin
,”
Biomech. Model. Mechanobiol.
,
10
(
5
), pp.
651
661
.
25.
Batisse
,
D.
,
Bazin
,
R.
, and
Baldeweck
,
T.
,
2002
, “
Influence of age on the Wrinkling Capacities of Skin
,”
Skin. Res. Technol.
,
8
(
3
), pp.
148
154
.
26.
Escoffier
,
C.
,
de Rigal
,
J.
,
Rochefort
,
A.
,
Vasselet
,
R.
,
Leveque
,
J.-L.
, and
Agache
,
P. G.
,
1989
, “
Age-Related Mechanical Properties of Human Skin: An In Vivo Study
,”
J. Invest. Dermatol.
,
93
(
3
), pp.
353
357
.
27.
Salter
,
D. C.
,
Mcarthur
,
H. C.
,
Crosse
,
J. E.
, and
Dickens
,
A. D.
,
1993
, “
Skin Mechanics Measured in Vivo Using Torsion: a new and Accurate Model More Sensitive to age, sex and Moisturizing Treatment
,”
Int. J. Cosmet. Sci.
,
15
(
5
), pp.
200
218
.
28.
Bismuth
,
C.
,
Gerin
,
C.
,
Viguier
,
E.
,
Fau
,
D.
,
Dupasquier
,
F.
,
Cavetier
,
L.
,
David
,
L.
, and
Carozzo
,
C.
,
2014
, “
The Biomechanical Properties of Canine Skin Measured in Situ by Uniaxial Extension
,”
J. Biomech.
,
47
(
5
), pp.
1067
1073
.
29.
Lim
,
K. H.
,
Chew
,
C. M.
,
Chen
,
P. C. Y.
,
Jeyapalina
,
S.
,
Ho
,
H. N.
,
Rappel
,
J. K.
, and
Lim
,
B. H.
,
2008
, “
New Extensometer to Measure in Vivo Uniaxial Mechanical Properties of Human Skin
,”
J. Biomech.
,
41
(
5
), pp.
931
936
.
30.
Kvistedal
,
Y. A.
, and
Nielsen
,
P. M. F.
,
2004
, “
Investigating Stress-Strain Properties of in-Vivo Human Skin Using Multiaxial Loading Experiments and Finite Element Modeling
,”
Proceedings of the 26th Annual International Conference of the Ieee Engineering in Medicine and Biology Society
, Vol.
1–7
, pp.
5096
5099
.
31.
Flynn
,
C.
,
Taberner
,
A.
, and
Nielsen
,
P.
,
2011
, “
Measurement of the Force-Displacement Response of in Vivo Human Skin Under a Rich set of Deformations
,”
Med. Eng. Phys.
,
33
(
5
), pp.
610
619
.
32.
Flynn
,
C.
,
Taberner
,
A. J.
,
Nielsen
,
P. M. F.
, and
Fels
,
S.
,
2013
, “
Simulating the Three-Dimensional Deformation of in Vivo Facial Skin
,”
J. Mech. Behav. Biomed. Mater.
,
28
(
1
), pp.
484
494
.
33.
Coutts
,
L.
,
Bamber
,
J.
, and
Miller
,
N.
,
2013
, “
Multi-Directional in Vivo Tensile Skin Stiffness Measurement for the Design of a Reproducible Tensile Strain Elastography Protocol
,”
Skin Res. Technol.
,
19
(
1
), pp.
E37
E44
.
34.
Delalleau
,
A.
,
Josse
,
G.
,
Lagarde
,
J.-M.
,
Zahouani
,
H.
, and
Bergheau
,
J.-M.
,
2006
, “
Characterization of the Mechanical Properties of Skin by Inverse Analysis Combined with the Indentation Test
,”
J. Biomech.
,
39
(
9
), pp.
1603
1610
.
35.
Zahouani
,
H.
,
Pailler-Mattei
,
C.
,
Sohm
,
B.
,
Vargiolu
,
R.
,
Cenizo
,
V.
, and
Debret
,
R.
,
2009
, “
Characterization of the Mechanical Properties of a Dermal Equivalent Compared with Human Skin in Vivo by Indentation and Static Friction Tests
,”
Skin Res. Technol.
,
15
(
1
), pp.
68
76
.
36.
Pailler-Mattei
,
C.
,
Bec
,
S.
, and
Zahouani
,
H.
,
2008
, “
In Vivo Measurements of the Elastic Mechanical Properties of Human Skin by Indentation Tests
,”
Med. Eng. Phys.
,
30
(
5
), pp.
599
606
.
37.
Diridollou
,
S.
,
Patat
,
F.
,
Gens
,
F.
,
Vaillant
,
L.
,
Black
,
D.
,
Lagarde
,
J. M.
,
Gall
,
Y.
, and
Berson
,
M.
,
2000
, “
In Vivo Model of the Mechanical Properties of the Human Skin Under Suction
,”
Skin Res. Technol.
,
6
(
4
), pp.
214
221
.
38.
Rosado
,
C.
,
Antunes
,
F.
,
Barbosa
,
R.
,
Fernando
,
R.
,
Estudante
,
M.
,
Silva
,
H. N.
, and
Rodrigues
,
L. M.
,
2017
, “
About the in Vivo Quantitation of Skin Anisotropy
,”
Skin Res. Technol.
,
23
(
3
), pp.
429
436
.
39.
Hendriks
,
F. M.
,
Brokken
,
D.
,
Oomens
,
C. W. J.
,
Bader
,
D. L.
, and
Baaijens
,
F. P. T.
,
2006
, “
The Relative Contributions of Different Skin Layers to the Mechanical Behavior of Human Skin in Vivo Using Suction Experiments
,”
Med. Eng. Phys.
,
28
(
3
), pp.
259
266
.
40.
Delalleau
,
A.
,
Josse
,
G.
,
Lagarde
,
J.-M.
,
Zahouani
,
H.
, and
Bergheau
,
J.-M.
,
2008
, “
A Nonlinear Elastic Behavior to Identify the Mechanical Parameters of Human Skin in Vivo
,”
Skin Res. Technol.
,
14
(
2
), pp.
152
164
.
41.
Sutradhar
,
A.
, and
Miller
,
M. J.
,
2013
, “
In Vivo Measurement of Breast Skin Elasticity and Breast Skin Thickness
,”
Skin Res. Technol.
,
19
(
1
), pp.
E191
E199
.
42.
Flynn
,
C.
,
Taberner
,
A.
, and
Nielsen
,
P.
,
2011
, “
Mechanical Characterisation of in Vivo Human Skin Using a 3D Force-Sensitive Micro-Robot and Finite Element Analysis
,”
Biomech. Model Mechanobiol.
,
10
(
1
), pp.
27
38
.
43.
Ogden
,
R. W.
,
1972
, “
Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids
,”
Proc. Math. Phys. Eng. Sci.
,
326
(
1567
), pp.
565
584
.
44.
Ban
,
E.
,
Wang
,
H.
,
Franklin
,
J. M.
,
Liphardt
,
J. T.
,
Janmey
,
P. A.
, and
Shenoy
,
V. B.
,
2019
, “
Strong Triaxial Coupling and Anomalous Poisson Effect in Collagen Networks
,”
Proc. Natl. Acad. Sci. U. S. A.
,
116
(
14
), pp.
6790
6799
.
45.
Soares
,
J. S.
,
Zhang
,
W.
, and
Sacks
,
M. S.
,
2017
, “
A Mathematical Model for the Determination of Forming Tissue Moduli in Needled-Nonwoven Scaffolds
,”
Acta Biomater.
,
51
(
1
), pp.
220
236
.
46.
Avazmohammadi
,
R.
,
Hill
,
M. R.
,
Simon
,
M. A.
,
Zhang
,
W.
, and
Sacks
,
M. S.
,
2017
, “
A Novel Constitutive Model for Passive Right Ventricular Myocardium: Evidence for Myofiber-Collagen Fiber Mechanical Coupling
,”
Biomech. Model. Mechanobiol.
,
16
(
2
), pp.
561
581
.
47.
Lanir
,
Y.
,
1983
, “
Constitutive Equations for Fibrous Connective Tissues
,”
J. Biomech.
,
16
(
1
), pp.
1
12
.
48.
Agianniotis
,
A.
,
Rezakhaniha
,
R.
, and
Stergiopulos
,
N.
,
2011
, “
A Structural Constitutive Model Considering Angular Dispersion and Waviness of Collagen Fibres of Rabbit Facial Veins
,”
Biomed. Eng. Online
,
10
(
1
), p.
18
.
49.
Ateshian
,
G. A.
,
Rajan
,
V.
,
Chahine
,
N. O.
,
Canal
,
C. E.
, and
Hung
,
C. T.
,
2009
, “
Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena
,”
J. Biomech. Eng.
,
131
(
6
), p.
061003
.
50.
Sacks
,
M. S.
,
2003
, “
Incorporation of Experimentally-Derived Fiber Orientation Into a Structural Constitutive Model for Planar Collagenous Tissues
,”
J. Biomech. Eng.
,
125
(
2
), pp.
280
287
.
51.
Gasser
,
T. C.
,
Ogden
,
R. W.
, and
Holzapfel
,
G. A.
,
2006
, “
Hyperelastic Modelling of Arterial Layers with Distributed Collagen Fibre Orientations
,”
J. R. Soc. Interface
,
3
(
6
), pp.
15
35
.
52.
Pandolfi
,
A.
, and
Holzapfel
,
G. A.
,
2008
, “
Three-dimensional Modeling and Computational Analysis of the Human Cornea Considering Distributed Collagen Fibril Orientations
,”
J. Biomech. Eng.
,
130
(
6
), p.
061006
.
53.
Lu
,
T.
,
Chen
,
Z.
,
Qi
,
H. J.
, and
Wang
,
T. J.
,
2018
, “
A Micro-Structure Based Constitutive Model for Anisotropic Stress–Strain Behaviors of Artery Tissues
,”
Int. J. Solids Struct.
,
139–140
(
1
), pp.
55
64
.
54.
Holzapfel
,
G. A.
,
2000
,
Nonlinear Solid Mechanics : A Continuum Approach for Engineering
,
Wiley
,
Chichester
.
55.
Holzapfel
,
G. A.
,
Gasser
,
T. C.
, and
Ogden
,
R. W.
,
2000
, “
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
,”
J. Elast. Phys. Sci. Solids
,
61
(
1
), pp.
1
48
.
56.
Holzapfel
,
G. A.
,
Niestrawska
,
J. A.
,
Ogden
,
R. W.
,
Reinisch
,
A. J.
, and
Schriefl
,
A. J.
,
2015
, “
Modelling non-Symmetric Collagen Fibre Dispersion in Arterial Walls
,”
J. R. Soc. Interface
,
12
(
106
).
57.
Holzapfel
,
G. A.
,
Ogden
,
R. W.
, and
Sherifova
,
S.
,
2019
, “
On Fibre Dispersion Modelling of Soft Biological Tissues: a Review
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
475
(
2224
), p.
20180736
.
58.
Holzapfel
,
G. A.
, and
Weizsäcker
,
H. W.
,
1998
, “
Biomechanical Behavior of the Arterial Wall and its Numerical Characterization
,”
Comput. Biol. Med.
,
28
(
4
), pp.
377
392
.
You do not currently have access to this content.