The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics. [S0148-0731(00)00305-8]

1.
Lew
,
W. Y. W.
,
1987
, “
Influence of Ischemic Zone Size on Nonischemic Area Function in the Canine Left Ventricle
,”
Am. J. Physiol.
,
252
, pp.
H990–H997
H990–H997
.
2.
Nielsen
,
P. M. F.
,
Le Grice
,
I. J.
,
Smaill
,
B. H.
, and
Hunter
,
P. J.
,
1991
, “
Mathematical Model of Geometry and Fibrous Structure of the Heart
,”
Am. J. Physiol.
,
260
, pp.
H1365–H1378
H1365–H1378
.
3.
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
, pp.
464
472
.
4.
Demer
,
L. L.
, and
Yin
,
F. C. P.
,
1983
, “
Passive Biaxial Mechanical Properties of Isolated Canine Myocardium
,”
J. Physiol. (London)
,
339
, pp.
615
630
.
5.
Yin
,
F. C. P.
,
Strumpf
,
R. K.
,
Chew
,
P. H.
, and
Zeger
,
S. L.
,
1987
, “
Quantification of the Mechanical Properties of Noncontracting Canine Myocardium Under Simultaneous Biaxial Loading
,”
J. Biomech.
,
20
, pp.
577
589
.
6.
Smaill, B. H., and Hunter, P. J., 1991, “Structure and Function of the Diastolic Heart: Material Properties of Passive Myocardium,” in: Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function, L. Glass, P. J. Hunter, and A. D. McCulloch, eds., Springer-Verlag, New York, pp. 1–29.
7.
Novak
,
V. P.
,
Yin
,
F. C. P.
, and
Humphrey
,
J. D.
,
1994
, “
Regional Mechanical Properties of Passive Myocardium
,”
J. Biomech.
,
27
, pp.
403
412
.
8.
Guccione
,
J. M.
,
McCulloch
,
A. D.
, and
Waldman
,
L. K.
,
1991
, “
Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model
,”
ASME J. Biomech. Eng.
,
113
, pp.
42
55
.
9.
Omens
,
J. H.
,
MacKenna
,
D. A.
, and
McCulloch
,
A. D.
,
1993
, “
Measurement of Strain and Analysis of Stress in Resting Rat Left Ventricular Myocardium
,”
J. Biomech.
,
26
, pp.
665
676
.
10.
Omens
,
J. H.
,
May
,
K. D.
, and
McCulloch
,
A. D.
,
1991
, “
Transmural Distribution of Three-Dimensional Strain in the Isolated Arrested Canine Left Ventricle
,”
Am. J. Physiol.
,
261
, pp.
H918–H928
H918–H928
.
11.
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
, pp.
1167
1177
.
12.
Waldman
,
L. K.
,
Fung
,
Y. C.
, and
Covell
,
J. W.
,
1985
, “
Transmural Myocardial Deformation in the Canine Left Ventricle: Normal in Vivo Three-Dimensional Finite Strains
,”
Circ. Res.
,
57
, pp.
152
163
.
13.
Wicomb, W. N., and Cooper, D. K. C., 1990, “Storage of the Donor Heart.” in: The Transplantation and Replacement of Thoracic Organs, Cooper, D. K. C., and Novitsky, D., eds., Kluwer Academic, Boston, pp. 51–61.
14.
Mosher
,
T. B.
, and
Smith
,
M. B.
,
1990
, “
A DANTE Tagging Sequence for the Evaluation of Translational Sample Motion
,”
Magn. Reson. Med.
,
15
, pp.
334
339
.
15.
Creswell
,
L. L.
,
Moulton
,
M. J.
,
Wyers
,
S. G.
,
Pirolo
,
J. S.
,
Fishman
,
D. S.
,
Perman
,
W. H.
,
Myers
,
K. W.
,
Actis
,
R. L.
,
Vannier
,
M. W.
,
Szabo
,
B. A.
, and
Pasque
,
M. K.
,
1994
, “
An Experimental Method for Evaluating Constitutive Models of Myocardium in In-Vivo Hearts
,”
Am. J. Physiol.
,
267
, pp.
H853–H863
H853–H863
.
16.
Costa
,
K. D.
,
Hunter
,
P. J.
,
Rogers
,
J. R.
,
Guccione
,
J. M.
,
Waldman
,
L. K.
, and
McCulloch
,
A. D.
,
1996
, “
A Three-Dimensional Finite Element Method for Large Elastic Deformations of Ventricular Myocardium: Part I—Cylindrical and Spherical Coordinates
,”
ASME J. Biomech. Eng.
,
118
, pp.
452
463
.
17.
Okamoto, R. J., 1997, “Determining Mechanical Properties of Heart Muscle Using Epicardial Suction,” D.Sc. thesis, Washington University, St. Louis, MO.
18.
Moulton
,
M. J.
,
Creswell
,
L. L.
,
Actis
,
R. L.
,
Myers
,
K. W.
,
Vannier
,
M. W.
,
Szabo
,
B. A.
, and
Pasque
,
M. K.
,
1995
, “
An Inverse Approach to Determining Myocardial Material Properties
,”
J. Biomech.
,
28
, pp.
935
948
.
19.
Humphrey
,
J. D.
,
Strumpf
,
R. K.
, and
Yin
,
F. C. P.
,
1990
, “
Determination of a Constitutive Relation for Passive Myocardium: II. Parameter Estimation
,”
ASME J. Biomech. Eng.
,
112
, pp.
340
346
.
20.
Le Grice
,
I. L.
,
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
, pp.
H571–H582
H571–H582
.
21.
Kang
,
T.
,
Humphrey
,
J. D.
, and
Yin
,
F. C. P.
,
1996
, “
Comparison of Biaxial Mechanical Properties of Excised Endocardium and Epicardium
,”
Am. J. Physiol.
,
270
, pp.
H2169–H2176
H2169–H2176
.
22.
Humphrey
,
J. D.
,
Strumpf
,
R. K.
, and
Yin
,
F. C. P.
,
1990
, “
Biaxial Mechanical Behavior of Excised Ventricular Epicardium
,”
Am. J. Physiol.
,
259
, pp.
H101–H108
H101–H108
.
23.
Humphrey
,
J. D.
,
Strumpf
,
R. K.
, and
Yin
,
F. C. P.
,
1992
, “
A Constitutive Theory for Biomembranes: Application to Epicardial Mechanics
,”
ASME J. Biomech. Eng.
,
114
, pp.
461
466
.
24.
Kang
,
T.
, and
Yin
,
F. C. P.
,
1996
, “
The Need to Account for Residual Strains and Composite Nature of Heart Wall in Mechanical Analyses
,”
Am. J. Physiol.
,
271
, pp.
H947–H961
H947–H961
.
25.
Criscione
,
J. C.
,
Lorenzen-Schmidt
,
I.
,
Humphrey
,
J. D.
, and
Hunter
,
W. C.
,
1999
, “
Mechanical Contribution of Endocardium During Finite Extension and Torsion Experiments on Papillary Muscles
,”
Ann. Biomed. Eng.
,
27
, pp.
123
130
.
26.
May-Newman
,
K.
,
Omens
,
J. H.
,
Pavelec
,
R. S.
, and
McCulloch
,
A. D.
,
1994
, “
Three-Dimensional Transmural Mechanical Interaction Between the Coronary Vasculature and Passive Myocardium in the Dog
,”
Circ. Res.
,
74
, pp.
1166
1178
.
27.
May-Newman
,
K.
, and
McCulloch
,
A. D.
,
1998
, “
Homogenization Modeling for the Mechanics of Perfused Myocardium
,”
Prog. Biophys. Mol. Biol.
,
69
, pp.
463
481
.
28.
Omens
,
J. H.
, and
Fung
,
Y. C.
,
1990
, “
Residual Strain in Rat Left Ventricle
,”
Circ. Res.
,
66
, pp.
37
45
.
29.
Costa
,
K. D.
,
May-Newman
,
K.
,
Farr
,
D.
,
O’Dell
,
W. G.
,
McCulloch
,
A. D.
, and
Omens
,
J. H.
,
1997
, “
Three-Dimensional Residual Strain in Midanterior Canine Left Ventricle
,”
Am. J. Physiol.
,
273
, pp.
1968
1976
.
30.
Young, A. A., 1991, “Epicardial Deformation From Coronary Cineangiograms.” in: Theory of Heart: Biomechanics, Biophysics, and Nonlinear Dynamics of Cardiac Function, Glass, L., Hunter, J. P., and McCulloch, A. D., eds., Springer-Verlag, New York, pp. 175–207.
31.
O’Dell
,
W. G.
,
Moore
,
C. C.
,
Hunter
,
W. C.
,
Zerhouni
,
E. A.
, and
McVeigh
,
E. R.
,
1995
, “
Three-Dimensional Myocardial Deformations: Calculation With Displacement Field Fitting to Tagged MR Images
,”
Radiology
,
195
, pp.
829
835
.
32.
Moulton
,
M. J.
,
Creswell
,
L. L.
,
Downing
,
S. W.
,
Actis
,
R. L.
,
Szabo
,
B. A.
,
Vannier
,
M. W.
, and
Pasque
,
M. K.
,
1996
, “
Spline Surface Interpolation for Calculated 3-D Ventricular Strains From MRI Tissue Tagging
,”
Am. J. Physiol.
,
270
, pp.
H281–H297
H281–H297
.
33.
Young
,
A. A.
,
Axel
,
L.
,
Dougherty
,
L.
,
Bogen
,
D. K.
, and
Parenteau
,
C. S.
,
1993
, “
Validation of Tagging With MR Imaging to Estimate Material Deformation
,”
Radiology
,
188
, pp.
101
108
.
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