In this paper, a finite element model of the heart is developed to investigate the impact of different gravitational loadings of Earth, Mars, Moon, and microgravity on the cardiac shape and strain/stress distributions in the left ventricle. The finite element model is based on realistic 3D heart geometry, detailed fiber/sheet micro-architecture, and a validated orthotropic cardiac tissue model and constitutive relationship that capture the passive behavior of the heart at end-diastole. The model predicts the trend and magnitude of cardiac shape change at different gravitational levels with great fidelity in comparison to recent cardiac sphericity measurements performed during simulated reduced-gravity parabolic flight experiments. Moreover, the numerical predictions indicate that although the left ventricular strain distributions remain relatively unaltered across the gravitational fields and the strain extrema values occur at the same relative locations, their values change noticeably with decreasing gravity. As for the stress, however, both the magnitude and location of the extrema change with a decrease in the gravitational field. Consequently, tension regions of the heart on Earth can change into compression regions in space.

References

References
1.
Buckey
,
J. C.
, Jr.
,
Lane
,
L. D.
,
Levine
,
B. D.
,
Watenpaugh
,
D. E.
,
Wright
,
S. J.
,
Moore
,
W. E.
,
Gaffney
,
F. A.
, and
Blomqvist
,
C. G.
,
1996
, “
Orthostatic Intolerance After Spaceflight
,”
J. Appl. Physiol.
,
81
(
1
) pp.
7
18
.
2.
Watenpaugh
,
D. E.
,
2001
, “
Fluid Volume Control During Short-Term Space Flight and Implications for Human Performance
,”
J. Exp. Biol.
,
204
(
9
), pp.
3209
3215
.
3.
Smith
,
S. M.
,
Krauhs
,
J. M.
, and
Leach
,
C. S.
,
1997
, “
Regulation of Body Fluid Volume and Electrolyte Concentrations in Spaceflight
,”
Adv. Space Biol. Med.
,
6
, pp.
123
165
.10.1016/S1569-2574(08)60081-7
4.
Blomqvist
,
C. G.
,
1983
, “
Cardiovascular Adaptation to Weightlessness
,”
Med. Sci. Sports Exerc.
,
15
(
5
), pp.
428
431
.
5.
Summers
,
R. L.
,
Martin
,
D. S.
,
Meck
,
J. V.
, and
Coleman
,
T. G.
,
2005
, “
Mechanism of Spaceflight Induced Changes in Left Ventricular Mass
,”
Am. J. Cardiol.
,
95
, pp.
1128
1130
.10.1016/j.amjcard.2005.01.033
6.
Goldstein
,
M. A.
,
Edwards
,
R. J.
, and
Schroeter
,
J. P.
,
1992
, “
Cardiac Morphology After Conditions of Microgravity During COSMOS 2044
,”
J. Appl. Physiol.
,
73
, pp.
94S
100S
.
7.
Perhonen
,
M. A.
,
Franco
,
F.
,
Lane
,
L. D.
,
Buckey
,
J. C.
,
Blomqvist
,
C. G.
,
Zerwekh
,
J. E.
,
Peshock
,
R. M.
,
Weatherall
,
P. T.
, and
Levine
,
B. D.
,
2001
, “
Cardiac Atrophy after Bed Rest and Spaceflight
,”
J. Appl. Physiol.
,
91
, pp.
645
653
.
8.
Gould
,
K. L.
,
Lipscomb
,
K.
,
Hamilton
,
G. W.
, and
Kennedy
,
J. W.
,
1974
, “
Relation of Left Ventricular Shape, Function and Wall Stress in Man
,”
Am. J. Cardiol.
,
34
, pp.
627
634
.10.1016/0002-9149(74)90149-0
9.
Janz
,
R. F.
,
Kubert
,
B. R.
,
Pate
,
E. F.
, and
Moriarty
,
T. F.
,
1980
, “
Effect of Shape on Pressure-Volume Relationships of Ellipsoidal Shells
,”
Am. J. Physiol.
,
238
(
6
), pp.
H917
H926
.
10.
Summers
,
R. L.
,
Martin
,
D. S.
,
Platts
,
S. H.
,
Mercado-Young
,
R.
,
Coleman
,
T. G.
, and
Kassemi
,
M.
,
2010
, “
Ventricular Chamber Sphericity During Spaceflight and Parabolic Flight Intervals of Less than 1 G
,”
Aviat., Space Environ. Med.
,
81
(
5
), pp.
506
510
.10.3357/ASEM.2526.2010
11.
Yin
,
F.
,
1981
, “
Ventricular Wall Stress
,”
Circ. Res.
,
49
(
4
), pp.
829
842
.10.1161/01.RES.49.4.829
12.
Hunter
,
P. J.
, and
Smaill
,
B. H.
,
1988
, “
The Analysis of Cardiac Function: A Continuum Approach
,”
Prog. Biophys. Mol. Biol.
,
52
, pp.
101
164
.10.1016/0079-6107(88)90004-1
13.
Nash
,
M. P.
, and
Hunter
,
P. J.
,
2000
, “
Computational Mechanics of the Heart— From Tissue Structure to Ventricular Function
,”
J. Elast.
,
61
(
1–3
), pp.
113
141
.10.1023/A:1011084330767
14.
Smith
,
N. P.
,
Nickerson
,
D. P.
,
Crampin
,
E. J.
, and
Hunter
,
P. J.
,
2004
, “
Multiscale Computational Modelling of the Heart
,”
Acta Numer.
,
13
, pp.
371
431
.10.1017/S0962492904000200
15.
Costa
,
K. D.
,
Hunter
,
P. J.
,
Wayne
,
J. S.
,
Waldman
,
L. K.
,
Guccione
,
J. M.
, and
McCulloch
,
A. D.
,
1996
, “
A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: II—Prolate Spheroidal Coordinates
,”
ASME J. Biomech. Eng.
,
118
(
4
), pp.
464
472
.10.1115/1.2796032
16.
Mazhari
,
R.
, and
McCulloch
,
A.
,
2000
, “
Integrative Models for Understanding the Structural Basis of Regional Mechanical Dysfunction in Ischemic Myocardium
,”
Ann. Biomed. Eng.
,
28
(
8
), pp.
979
990
.10.1114/1.1308502
17.
Usyk
,
T. P.
,
Mazhari
,
R.
, and
McCulloch
,
A. D.
,
2000
, “
Effect of Laminar Orthotropic Myofiber Architecture on Regional Stress and Strain in the Canine Left Ventricle
,”
J. Elast.
61
(
1– 3
), pp.
143
164
.10.1023/A:1010883920374
18.
Guccione
,
J. M.
,
Costa
,
K. D.
, and
McCulloch
,
A.D.
,
1995
, “
Finite Element Stress Analysis of Left Ventricular Mechanics in the Beating Dog Heart
,”
J. Biomech.
,
28
(
10
), pp.
1167
1177
.10.1016/0021-9290(94)00174-3
19.
Bovendeerd
,
P. H. M.
,
Kroon
,
W.
, and
Delhaas
,
T.
,
2009
, “
Determinants of Left Ventricular Shear Strain
,”
Am. J. Physiol. Heart Circ. Physiol.
,
297
(
3
), pp.
H1058
H1068
.10.1152/ajpheart.01334.2008
20.
Bovendeerd
,
P. H. M.
,
1994
, “
Influence of Endocardial-Epicardial Crossover of Muscle Fibers on Left Ventricular Wall Mechanics
,”
J. Biomech.
,
27
(
7
), pp.
941
951
.10.1016/0021-9290(94)90266-6
21.
Bovendeerd
,
P. H. M.
,
Arts
,
T.
,
Huyghe
,
J. M.
,
Van Campen
,
D. H.
, and
Reneman
,
R. S.
, “
Dependence of Local Left Ventricular Wall Mechanics on Myocardial Fiber Orientation: A Model Study
,”
J. Biomech.
,
25
(
10
), pp.
1129
1140
.10.1016/0021-9290(92)90069-D
22.
Hunter
,
P. J.
,
Smaill
,
B. H.
,
Nielsen
,
P. M. F.
, and
Le Grice
,
I. J.
,
1997
, “
A Mathematical Model of Cardiac Anatomy
,”
Computational Biology of the Heart
,
A. V.
Panilov
and
A. V.
Holden
, eds.,
Wiley
,
New York
, pp.
172
215
.
23.
Nielson
,
P. M.
,
Le Grice
,
I. J.
, and
Hunter
,
P. J.
,
1991
, “
Mathematical Model of Geometry and Fibrous Structure of the Heart
,”
Am. J. Physiol.
,
260
, pp.
H1365
H1378
.
24.
LeGrice
,
I. J.
,
Hunter
,
P. J.
, and
Smaill
,
B. H.
,
1997
, “
Laminar Structure of The Heart: A Mathematical Model
,”
Am. J. Physiol.
,
272
(
5
), pp.
H2466
H2476
.
25.
Hunter
,
P. J.
,
McCulloch
,
A. D.
, and
ter Keurs
,
H. E. D. J.
,
1998
, “
Modelling the Mechanical Properties of Cardiac Muscle
,”
Prog. Biophys. Mol. Biol.
,
69
, pp.
289
331
.10.1016/S0079-6107(98)00013-3
26.
Malvern
,
L. E.
,
1969
,
Introduction to the Mechanics of a Continuous Media
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
27.
Suga
,
H.
,
Hayashi
,
T.
, and
Shirahata
,
M.
,
1981
, “
Ventricular Systolic Pressure Volume Area as Predictor of Cardiac Oxygen Consumption
,”
Am. J. Physiol.
,
240
,
H39
H44
.
28.
Janicki
,
K. S.
, and
Weber
,
K. T.
,
1980
, “
The Pericardium and Ventricular Interaction: Dispensability and Function
,”
Am. J. Physiol.
,
238
, pp.
H494
H503
.
29.
Fung
,
Y. C.
,
1993
,
Biomechamics: Mechanical Properties of Living Tissue
,
Springer
,
New York
.
30.
Dokos
,
S.
,
Smaill
,
B. H.
,
Young
,
A. A.
, and
LeGrice
,
I. J.
,
2002
, “
Shear Properties of Passive Ventricular Myocardium
,”
Am. J. Physiol. Heart Circ. Physiol.
,
283
, pp.
H2650
H2659
.
31.
Schmid
,
H.
,
Nash
,
M. P.
,
Young
,
A. A.
, and
Hunter
,
P. J.
,
2006
, “
Myocardial Material Parameter Estimation—A Comparative Study for Simple Shear
,”
ASME J. Biomech. Eng.
,
128
(
5
), pp.
742
750
.10.1115/1.2244576
32.
Holzapfel
,
G. A.
, and
Ogden
,
R. W.
,
2009
, “
Constitutive Modelling of Passive Myocardium: A Structurally Based Framework for Material Characterization
,”
Philos. Trans. R. Soc. London
,
Ser. A
,
367
, pp.
3445
3475
.10.1098/rsta.2009.0091
33.
Iskovitz
,
I.
, and
Kassemi
,
M.
,
2012
, “
Finite Element Implementation of an Orthotropic Material Model for Cardiac Tissue and its Local and Global Validation
,” submitted to Journal of Biomechanics.
34.
Holzapfel
,
G. A.
,
2000
,
Nonlinear Solid Mechanics: A Continuum Approach for Engineering
,
Wiley
,
Chichester, UK
.
35.
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
, pp.
1
48
.10.1023/A:1010835316564
36.
Simo
,
J. C.
,
Fox
,
D. D.
, and
Hughes
,
T. J. R.
,
1992
, “
Formulations of Finite Elasticity With Independent Rotations
,”
Comput. Methods Appl. Mech. Eng.
,
95
(
2
), pp.
277
288
.10.1016/0045-7825(92)90144-9
37.
Demer
,
L. L.
, and
Yin
,
F. C. P.
,
1983
, “
Passive Biaxial Mechanical Properties of Isolated Canine Myocardium
,”
J. Physiol.
,
339
, pp.
615
630
.
38.
McCulloch
,
A. D.
,
Smaill
,
B. H.
, and
Hunter
,
P. J.
,
1989
, “
Regional Left Ventricle Epicardial Deformation in the Passive Dog Heart
,”
Circ. Res.
,
64
, pp.
721
733
.10.1161/01.RES.64.4.721
39.
McCulloch
,
A. D.
,
Hunter
,
P. J.
, and
Smaill
,
B. H.
,
1992
, “
Mechanical Effects of Coronary Perfusion in the Passive Canine Left Ventricle
,”
Am. J. Physiol.
,
262
, pp.
H523
H530
.
40.
Bathe
,
K. J.
,
1996
,
Finite Element Procedures
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
41.
Flory
,
P. J.
,
1961
, “
Thermodynamic Relations for High Elastic Materials
,”
Trans. Faraday Soc.
,
57
, pp.
829
838
.10.1039/tf9615700829
42.
Sussman
,
T.
, and
Bathe
,
K. J.
,
1987
, “
A Finite-Element Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis
,”
Comput. Struct.
,
26
(
1–2
), pp.
357
409
.10.1016/0045-7949(87)90265-3
43.
Malkus
,
D. S.
, and
Hughes
,
T. J. R.
,
1978
, “
Mixed Finite Element Methods - Reduced and Selective Integration Techniques: A Unification of Concepts
,”
Comput. Methods Appl. Mech. Eng.
,
15
(
1
), pp.
63
81
.10.1016/0045-7825(78)90005-1
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