We incorporated a three-dimensional generalization of the Huxley cross-bridge theory in a finite element model of ventricular mechanics to examine the effect of nonaxial deformations on active stress in myocardium. According to this new theory, which assumes that macroscopic tissue deformations are transmitted to the myofilament lattice, lateral myofilament spacing affects the axial fiber stress. We calculated stresses and deformations at end-systole under the assumption of strictly isometric conditions. Our results suggest that at the end of ejection, nonaxial deformations may significantly reduce active axial fiber stress in the inner half of the wall of the normal left ventricle (18–35 percent at endocardium, depending on location with respect to apex and base). Moreover, this effect is greater in the case of a compliant ischemic region produced by occlusion of the left anterior descending or circumflex coronary artery (26–54 percent at endocardium). On the other hand, stiffening of the remote and ischemic regions (in the case of a two-week-old infarct) lessens the effect of nonaxial deformation on active stress at all locations (9–32 percent endocardial reductions). These calculated effects are sufficiently large to suggest that the influence of nonaxial deformation on active fiber stress may be important, and should be considered in future studies of cardiac mechanics.

1.
Bagni
M. A.
,
Cecchi
G.
, and
Colomo
F.
,
1990
, “
Myofilament Spacing and Force Generation in Intact Frog Muscle Fibers
,”
Journal of Physiology
, Vol.
430
, pp.
61
75
.
2.
Blinks
J. R.
,
1965
, “
Influence of Osmotic Strength on Cross-Section and Volume of Isolated Single Muscle Fibers
,”
Journal of Physiology
, Vol.
177
, pp.
42
57
.
3.
Brenner
B.
,
1988
, “
Effect of Ca2+ on Cross-Bridge Turnover Kinetics in Skinned Single Rabbit Psoas Fibers: Implications for Regulation of Muscle Contraction
,”
Proc. National Academy of Sciences U.S.A.
, Vol.
85
, pp.
3265
3269
.
4.
Brenner
B.
, and
Yu
L. C.
,
1991
, “
Characterization of Radial Force and Radial Stiffness in Ca2+-Activated Skinned Fibers of the Rabbit Psoas Muscle
,”
Journal of Physiology
, Vol.
441
, pp.
703
718
.
5.
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: Part II—Prolate Spheroidal Polar Coordinates
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
118
, pp.
464
471
.
6.
Edman
K. A. P.
, and
Hwang
J. C.
,
1977
, “
The Force-Velocity Relationship in Skeletal Muscle Fibers at Varied Tonicity of the Extracellular Medium
,”
Journal of Physiology
, Vol.
269
, pp.
255
272
.
7.
Eringen, A. C., 1980, Mechanics of Continua, Kreiger, New York.
8.
Gill, P. E., Murray, W., and Wright, M. H., 1981, Practical Optimization, Academic Press, London.
9.
Gordon
A. M.
, and
Godt
R. E.
,
1970
, “
Some Effects of Hypertonic Solutions on Contraction and Excitation-Contraction Coupling in Frog Skeletal Muscles
,”
Journal of General Physiology
, Vol.
55
, pp.
254
274
.
10.
Guccione
J. M.
,
McCulloch
A. D.
, and
Waldman
L. K.
,
1991
, “
Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
113
, pp.
42
55
.
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
,”
Journal of Biomechanics
, Vol.
28
, pp.
1167
1177
.
12.
Gupta
K. B.
,
Ratcliff
M. B.
,
Fallert
M. A.
,
Edmunds
L. H.
, and
Bogen
D. K.
,
1994
, “
Changes in Passive Mechanical Stiffness of Myocardial Tissue With Aneurysm Formation
,”
Circulation
, Vol.
89
, pp.
2315
2326
.
13.
Horowitz
A.
,
Lanir
Y.
,
Yin
F. C. P.
,
Perl
M.
,
Sheinman
I.
, and
Strumpf
R. K.
,
1988
, “
Structural Three-Dimensional Constitutive Law for the Passive Myocardium
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
110
, pp.
200
207
.
14.
Howarth
J. V.
,
1958
, “
The Behavior of Frog Muscles in Hypertonic Solution
,”
Journal of Physiology
, Vol.
144
, pp.
167
175
.
15.
Huxley
A. F.
,
1957
, “
Muscle Structure and Theories of Contraction
,”
Progress in Biophysics and Biophysical Chemistry
, Vol.
7
, pp.
255
318
.
16.
Kawai
M.
, and
Schulman
M. I.
,
1985
, “
Crossbridge Kinetics in Chemically Skinned Rabbit Psoas Fibers When the Actin-Myosin Lattice Spacing is Altered by Dextran T-500
,”
Journal of Muscle Research and Cell Motility
, Vol.
6
, pp.
313
332
.
17.
Koch-Weser
J.
,
1963
, “
Influence of Osmolarity of Perfusate on Contractility of Mammalian Myocardium
,”
American Journal of Physiology
, Vol.
204
, pp.
957
963
.
18.
Krasner
B.
, and
Maugham
D.
,
1984
, “
The Relationship Between ATP Hydrolysis and Active Force in Compressed and Swollen Skinned Muscle Fibers of Rabbit
,”
Pflugers Archiv
, Vol.
400
, pp.
160
165
.
19.
Landesberg
A.
, and
Sideman
S.
,
1994
, “
Mechanical Regulation of Cardiac Muscle by Coupling Calcium Kinetics With Cross-Bridge Cycling: A Dynamic Model
,”
American Journal of Physiology
, Vol.
267
, pp.
H779–H795
H779–H795
.
20.
Mansson
A.
,
1993
, “
Tension Transients in Skeletal Muscle Fibers of the Frog at Varied Tonicity of the Extracellular Medium
,”
Journal of Muscle Research and Cell Motility
, Vol.
14
, pp.
15
25
.
21.
McCulloch
A. D.
,
Smaill
B. H.
, and
Hunter
P. J.
,
1989
, “
Regional Left Ventricular Epicardial Deformation in the Passive Dog Heart
,”
Circulation Research
, Vol.
64
, pp.
721
733
.
22.
Metzger
J. M.
, and
Moss
R. L.
,
1987
, “
Shortening Velocity in Skinned Single Muscle Fibers
,”
Biophysical Journal
, Vol.
52
, pp.
127
131
.
23.
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
,”
American Journal of Physiology
, Vol.
260
, pp.
H1365–H1378
H1365–H1378
.
24.
Novak
V. P.
,
Yin
F. C. P.
, and
Humphrey
J. D.
,
1994
, “
Regional Mechanical Properties of Passive Myocardium
,”
Journal of Biomechanics
, Vol.
27
, pp.
403
412
.
25.
Omens
J. H.
,
May
K. D.
, and
McCulloch
A. D.
,
1991
, “
Transmural Distribution of Three-Dimensional Strain in the Isolated Arrested Canine Left Ventricle
,”
American Journal of Physiology
, Vol.
261
, pp.
H918–H928
H918–H928
.
26.
Piazzesi
G.
,
Linari
M.
, and
Lombardi
V.
,
1994
, “
The Effect of Hypertonicity on Force Generation in Tetanized Single Fibers From Frog Skeletal Muscle
,”
Journal of Physiology
, Vol.
476
, pp.
531
546
.
27.
Pollack, G. H., 1990, Muscles and Molecules, Ebner and Sons, Seattle, WA.
28.
Rodriguez
E. K.
,
Omens
J. H.
,
Waldman
L. K.
, and
McCulloch
A. D.
,
1993
, “
Effect of Residual Stress on Transmural Sarcomere Length Distribution in Rat Left Ventricle
,”
American Journal of Physiology
, Vol.
264
, pp.
H1048–H1056
H1048–H1056
.
29.
Squire, J. M., 1986, Muscle: Design Diversity and Disease, Benjamin/Cummings, Menlo Park, CA.
30.
Streeter
D. D.
, and
Hanna
W. T.
,
1973
, “
Engineering Mechanics for Successive States in Canine Left Ventricular Myocardium: I. Cavity and Wall Geometry
,”
Circulation Research
, Vol.
33
, pp.
639
655
.
31.
Strumph
R. K.
,
Humphrey
J. D.
, and
Yin
F. C. P.
,
1993
, “
Biaxial Mechanical Properties of Passive and Tetanized Canine Diaphragm
,”
American Journal of Physiology
, Vol.
265
, pp.
H469–H475
H469–H475
.
32.
Suga
H.
, and
Sagawa
K.
,
1974
, “
Instantaneous Pressure-Volume Relationships and Their Ratio in the Excised, Supported Canine Left Ventricle
,”
Circulation Research
, Vol.
35
, pp.
117
126
.
33.
ter Keurs
H. E. D. J.
,
Rijnsburger
W. H.
,
van Heuningen
R.
, and
Nagelsmit
M. J.
,
1980
, “
Tension Development and Sarcomere Length in Rat Cardiac Trabeculae: Evidence of Length-Dependent Activation
,”
Circulation Research
, Vol.
46
, pp.
703
713
.
34.
Waldman
L. K.
,
Nossan
D.
,
Villarreal
F.
, and
Covell
J. W.
,
1988
, “
Relation Between Transmural Deformation and Local Myofiber Direction in Canine Left Ventricle
,”
Circulation Research
, Vol.
63
, pp.
550
562
.
35.
Zahalak
G. I.
, and
Ma
S. P.
,
1990
, “
Muscle Activation and Contraction: Constitutive Relations Based Directly on Cross-Bridge Kinetics
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
52
62
.
36.
Zahalak
G. I.
,
1996
, “
Non-axial Muscle Stress and Stiffness
,”
Journal of Theoretical Biology
, Vol.
182
, pp.
59
84
.
37.
Zahalak
G. I.
, and
Motabarzadeh
I.
,
1997
, “
A Reexamination of Calcium Activation in the Huxley Cross-Bridge Model
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
119
, pp.
20
29
.
38.
Zienkiewicz, O. C., and Morgan, K., 1982, Finite Elements and Approximation, University of Wales, Swansea, UK.
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