While the anisotropic behavior of the complex composite myocardial tissue has been well characterized in recent years, the compressibility of the tissue has not been rigorously investigated to date. In the first part of this study, we present experimental evidence that passive-excised porcine myocardium exhibits volume change. Under tensile loading of a cylindrical specimen, a volume change of 4.1±1.95% is observed at a peak stretch of 1.3. Confined compression experiments also demonstrate significant volume change in the tissue (loading applied up to a volumetric strain of 10%). In order to simulate the multiaxial passive behavior of the myocardium, a nonlinear volumetric hyperelastic component is combined with the well-established Holzapfel–Ogden anisotropic hyperelastic component for myocardium fibers. This framework is shown to describe the experimentally observed behavior of porcine and human tissues under shear and biaxial loading conditions. In the second part of the study, a representative volumetric element (RVE) of myocardium tissue is constructed to parse the contribution of the tissue vasculature to observed volume change under confined compression loading. Simulations of the myocardium microstructure suggest that the vasculature cannot fully account for the experimentally measured volume change. Additionally, the RVE is subjected to six modes of shear loading to investigate the influence of microscale fiber alignment and dispersion on tissue-scale mechanical behavior.

References

References
1.
LeGrice
,
I. J.
,
Smaill
,
B. H.
,
Chai
,
L. Z.
,
Edgar
,
S. G.
,
Gavin
,
J. B.
, and
Hunter
,
P. J.
,
1995
, “
Laminar Structure of the Heart: Ventricular Myocyte Arrangement and Connective Tissue Architecture in the Dog
,”
Am. J. Physiol.
,
269
(
2
), pp.
H571
H582
.
2.
Demer
,
L. L.
, and
Yin
,
F. C.
,
1983
, “
Passive Biaxial Mechanical Properties of Isolated Canine Myocardium
,”
J. Physiol.
,
339
(
1
), pp.
615
630
.
3.
Dokos
,
S.
,
Smaill
,
B. H.
,
Young
,
A. A.
, and
LeGrice
,
I. J.
,
2002
, “
Shear Properties of Passive Ventricular Myocardium
,”
Am. J. Physiol.
,
283
(
6
), pp.
H2650
H2659
.
4.
Sommer
,
G.
,
Schriefl
,
A. J.
,
Andrä
,
M.
,
Sacherer
,
M.
,
Viertler
,
C.
,
Wolinski
,
H.
, and
Holzapfel
,
G. A.
,
2015
, “
Biomechanical Properties and Microstructure of Human Ventricular Myocardium
,”
Acta Biomater.
,
24
, pp.
172
192
.
5.
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
,
2009
, “
Constitutive Modelling of Passive Myocardium: A Structurally Based Framework for Material Characterization
,”
Philos. Trans. A
,
367
(
1902
), pp.
3445
3475
.
6.
Nolan
,
D. R.
, and
McGarry
,
J. P.
,
2016
, “
On the Compressibility of Arterial Tissue
,”
Ann. Biomed. Eng.
,
44
(
4
), pp.
993
1007
.
7.
Yossef
,
O. E.
,
Farajian
,
M.
,
Gilad
,
I.
,
Willenz
,
U.
,
Gutman
,
N.
, and
Yosibash
,
Z.
,
2017
, “
Further Experimental Evidence of the Compressibility of Arteries
,”
J. Mech. Behav. Biomed. Mater.
,
65
, pp.
177
189
.
8.
Vossoughi
,
J.
,
Vaishnav
,
R. N.
, and
Patel
,
D. J.
, 1980, “
Compressibility of the Myocardial Tissue
,” Advances in bioengineering, Van C. Mow, ed., Bioengineering Division, American Society of Mechanical Engineers, New York, pp. 45–48.
9.
Ashikaga
,
H.
,
Coppola
,
B. A.
,
Yamazaki
,
K. G.
,
Villarreal
,
F. J.
,
Omens
,
J. H.
, and
Covell
,
J. W.
,
2008
, “
Changes in Regional Myocardial Volume During the Cardiac Cycle: Implications for Transmural Blood Flow and Cardiac Structure
,”
Am. J. Physiol.
,
295
(
2
), pp.
H610
H618
.
10.
Göktepe
,
S.
,
Acharya
,
S. N. S.
,
Wong
,
J.
, and
Kuhl
,
E.
,
2011
, “
Computational Modeling of Passive Myocardium
,”
Int. J. Numer. Method. Biomed. Eng.
,
27
(
1
), pp.
1
12
.
11.
Soares
,
J. S.
,
Li
,
D. S.
,
Lai
,
E.
,
Gorman
,
J. H.
, III,
Gorman
,
R. C.
, and
Sacks
,
M. S.
,
2017
,
Modeling of Myocardium Compressibility and Its Impact in Computational Simulations of the Healthy and Infarcted Heart
,
Springer
,
Cham, Switzerland
, pp.
493
501
.
12.
Ahmadzadeh
,
H.
,
Freedman
,
B. R.
,
Connizzo
,
B. K.
,
Soslowsky
,
L. J.
, and
Shenoy
,
V. B.
,
2015
, “
Micromechanical Poroelastic Finite Element and Shear-Lag Models of Tendon Predict Large Strain Dependent Poisson's Ratios and Fluid Expulsion Under Tensile Loading
,”
Acta Biomater.
,
22
, pp.
83
91
.
13.
Vaughan
,
T. J.
,
Voisin
,
M.
,
Niebur
,
G. L.
, and
McNamara
,
L. M.
,
2015
, “
Multiscale Modeling of Trabecular Bone Marrow: Understanding the Micromechanical Environment of Mesenchymal Stem Cells During Osteoporosis
,”
ASME J. Biomech. Eng.
,
137
(
1
), p.
011003
.
14.
Dowling
,
E. P.
,
Ronan
,
W.
, and
McGarry
,
J. P.
,
2013
, “
Computational Investigation of In Situ Chondrocyte Deformation and Actin Cytoskeleton Remodelling Under Physiological Loading
,”
Acta Biomater.
,
9
(
4
), pp.
5943
5955
.
15.
Sun
,
W.
,
Chaikof
,
E. L.
, and
Levenston
,
M. E.
,
2008
, “
Numerical Approximation of Tangent Moduli for Finite Element Implementations of Nonlinear Hyperelastic Material Models
,”
ASME J. Biomech. Eng.
,
130
(
6
), p.
061003
.
16.
Nolan
,
D. R. R.
,
Gower
,
A. L. L.
,
Destrade
,
M.
,
Ogden
,
R. W. W.
, and
McGarry
,
J. P. P.
,
2014
, “
A Robust Anisotropic Hyperelastic Formulation for the Modelling of Soft Tissue
,”
J. Mech. Behav. Biomed. Mater.
,
39
, pp.
48
60
.
17.
Yeoh
,
O. H.
,
1993
, “
Some Forms of the Strain Energy Function for Rubber
,”
Rubber Chem. Technol.
,
66
(
5
), pp.
754
771
.
18.
Nolan
,
D. R. R.
, and
McGarry
,
J. P. P.
,
2016
, “
On the Correct Interpretation of Measured Force and Calculation of Material Stress in Biaxial Tests
,”
J. Mech. Behav. Biomed. Mater.
,
53
, pp.
187
199
.
19.
Stoker
,
M. E.
,
Gerdes
,
A. M.
, and
May
,
J. F.
,
1982
, “
Regional Differences in Capillary Density and Myocyte Size in the Normal Human Heart
,”
Anat. Rec.
,
202
(
2
), pp.
187
191
.
20.
Yin
,
F. C.
,
Chan
,
C. C.
, and
Judd
,
R. M.
,
1996
, “
Compressibility of Perfused Passive Myocardium
,”
Am. J. Physiol.
,
271
(
5 Pt. 2
), pp.
H1864
H1870
.
21.
Hein
,
S.
,
Arnon
,
E.
,
Kostin
,
S.
,
Schönburg
,
M.
,
Elsässer
,
A.
,
Polyakova
,
V.
,
Bauer
,
E. P.
,
Klövekorn
,
W.-P.
, and
Schaper
,
J.
,
2003
, “
Progression From Compensated Hypertrophy to Failure in the Pressure-Overloaded Human Heart
,”
Circulation
,
107
(
7
), pp. 984–991.
22.
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.
,
61
(
1–3
), pp.
1
48
.
23.
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
,
2015
, “
On the Tension–Compression Switch in Soft Fibrous Solids
,”
Eur. J. Mech. A
,
49
, pp.
561
569
.
24.
Ronan
,
W.
,
Deshpande
,
V. S.
,
McMeeking
,
R. M.
, and
McGarry
,
J. P.
,
2012
, “
Numerical Investigation of the Active Role of the Actin Cytoskeleton in the Compression Resistance of Cells
,”
J. Mech. Behav. Biomed. Mater.
,
14
, pp.
143
157
.
25.
Li
,
K.
,
Ogden
,
R. W.
, and
Holzapfel
,
G. A.
,
2016
, “
Computational Method for Excluding Fibers Under Compression in Modeling Soft Fibrous Solids
,”
Eur. J. Mech. A
,
57
, pp.
178
193
.
26.
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.
27.
Pope
,
A. J.
,
Sands
,
G. B.
,
Smaill
,
B. H.
, and
LeGrice
,
I. J.
,
2008
, “
Three-Dimensional Transmural Organization of Perimysial Collagen in the Heart
,”
Am. J. Physiol.
,
295
(
3
), pp. H1243–H1252.
28.
Böl
,
M.
,
Ehret
,
A. E.
,
Leichsenring
,
K.
, and
Ernst
,
M.
,
2015
, “
Tissue-Scale Anisotropy and Compressibility of Tendon in Semi-Confined Compression Tests
,”
J. Biomech.
,
48
(
6
), pp.
1092
1098
.
29.
Vaughan
,
T. J.
, and
McCarthy
,
C. T.
,
2011
, “
Micromechanical Modelling of the Transverse Damage Behaviour in Fibre Reinforced Composites
,”
Compos. Sci. Technol.
,
71
(
3
), pp.
388
396
.
30.
Adham
,
M.
,
Gournier
,
J. P.
,
Favre
,
J. P.
,
De La Roche
,
E.
,
Ducerf
,
C.
,
Baulieux
,
J.
,
Barral
,
X.
, and
Pouyet
,
M.
,
1996
, “
Mechanical Characteristics of Fresh and Frozen Human Descending Thoracic Aorta
,”
J. Surg. Res.
,
64
(
1
), pp.
32
34
.
31.
Stemper
,
B. D.
,
Yoganandan
,
N.
,
Stineman
,
M. R.
,
Gennarelli
,
T. A.
,
Baisden
,
J. L.
, and
Pintar
,
F. A.
,
2007
, “
Mechanics of Fresh, Refrigerated, and Frozen Arterial Tissue
,”
J. Surg. Res.
,
139
(
2
), pp.
236
242
.
32.
Simon
,
B. R.
,
Kaufmann
,
M. V.
,
McAfee
,
M. A.
, and
Baldwin
,
A. L.
,
1996
,
Porohyperelastic Theory and Finite Element Models for Soft Tissues With Application to Arterial Mechanics
,
Springer
,
Dordrecht, The Netherlands
, pp.
245
261
.
33.
Liu
,
Y. H.
,
Bahn
,
R. C.
, and
Ritman
,
E. L.
,
1992
, “
Dynamic Intramyocardial Blood Volume: Evaluation With a Radiological Opaque Marker Method
,”
Am. J. Physiol.
,
263
(
3
), pp.
H963
H967
.
34.
van der Ploeg
,
C. P.
,
Dankelman
,
J.
, and
Spaan
,
J. A.
,
1993
, “
Functional Distribution of Coronary Vascular Volume in Beating Goat Hearts
,”
Am. J. Physiol.
,
264
(
6
), pp. H770–H776.https://www.physiology.org/doi/pdf/10.1152/ajpheart.1993.264.3.H770
35.
Reynolds
,
N. H.
, and
McGarry
,
J. P.
,
2015
, “
Single Cell Active Force Generation Under Dynamic Loading—Part II: Active Modelling Insights
,”
Acta Biomater.
,
27
, pp.
251
263
.
36.
McEvoy
,
E.
,
Deshpande
,
V. S.
, and
McGarry
,
P.
,
2017
, “
Free Energy Analysis of Cell Spreading
,”
J. Mech. Behav. Biomed. Mater.
,
74
, pp. 283–295.
37.
Reynolds
,
N. H.
,
Ronan
,
W.
,
Dowling
,
E. P.
,
Owens
,
P.
,
McMeeking
,
R. M.
, and
McGarry
,
J. P.
,
2014
, “
On the Role of the Actin Cytoskeleton and Nucleus in the Biomechanical Response of Spread Cells
,”
Biomaterials
,
35
(
13
), pp.
4015
4025
.
38.
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
, pp.
220
236
.
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