Several types of analyses in biomechanics require estimates of both muscle force and stiffness. Simulations were performed using the two-state cross-bridge Bond Distribution-Moment muscle model of Zahalak (1981), together with other parameters for passive elasticity and tendon compliance, to estimate instantaneous stiffness and to compare these estimates with the wide range of values reported in the literature. While the relatively simple cross-bridge theory appears to approximate the stiffness of skinned muscle fibers, the stiffness of a complete muscle-tendon unit become complex and non-linear due to relative changes in muscle-tendon length and interaction with activation and length dependent passive elastic components. It would appear that the variability in muscle stiffness values reported in the literature can be explained with the D-M approach.

1.
Bergmark, A., 1987, “Mechanical Stability of the Human Lumbar Spine,” Doctoral dissertation, Dept. of Solid Mechanics, Lund University, Lund, Sweden.
2.
Bergmark
A.
,
1989
, “
Stability of the Lumbar Spine: A Study in Mechanical Engineering
,”
Acta Orthop. Scand.
, Vol.
60
,
Suppl. (230)
, pp.
1
54
.
3.
Bobet
J.
,
Stein
R. B.
, and
Ogˇuzto¨reli
M. N.
,
1990
, “
Mechanisms Relating Force and High-Frequency Stiffness in Skeletal Muscle
,”
J. Biomech.
, Vol.
23
suppl. (1)
, pp.
13
21
.
4.
Brenner, B., 1990, “Muscle Mechanics and Biochemical Kinetics,” Molecular Mechanisms in Muscular Contraction, Topics in Molecular and Structural Biology, Vol. 13, J. M. Squire, ed., MacMillan Press, pp. 77–149.
5.
Crisco
J. J.
, and
Panjabi
M. M.
,
1991
The Intersegmental and Multisegmental Muscles of the Lumbar Spine: A Biomechanical Model Comparing Lateral Stabilizing Potential
,”
Spine
, Vol.
16
, pp.
793
799
.
6.
Ettema
G. J. C.
, and
Huijing
P. A.
,
1989
, “
Properties of the Tendinous Structures and Series Elastic Component of the EDL Muscle-Tendon Complex of the Rat
,
J. Biomech.
, Vol.
22
, pp.
1209
1215
.
7.
Gordon
A. M.
,
Huxley
A. F.
, and
Julian
F. J.
,
1966
, “
The Variation in Isometric Tension with Sarcomere Length in Vertebrate Muscle Fibres
,”
J. Physiol.
, Vol.
184
, pp.
170
192
.
8.
Grillner
S.
,
1972
, “
The Role of Muscle Stiffness in Meeting the Changing Postural and Locomotor Requirements for Force Development by the Ankle Extensors
,”
Acta Physiol. Scand.
, Vol.
86
, pp.
92
108
.
9.
Huxley, A. F., 1957, “Muscle Structure and Theories of Contraction,” Progress in Biophysics and Biophysical Chemistry, J. A. V. Butler and B. Katz, eds., A Pergamon Press Book, The MacMillan Company, New York, pp. 6–318.
10.
Joyce
G. C.
, and
Rack
M. H.
,
1969
, “
Isotonic Lengthening and Shortening Movements of Cat Soleus Muscle
,”
J. Physiol.
, Vol.
204
, pp.
475
491
.
11.
Julian
F. J.
, and
Sollins
M. R.
,
1975
, “
Variation of Muscle Stiffness with Force at Increasing Speeds of Shortening
,”
J. Gen. Physiol.
, Vol.
66
, pp.
287
302
.
12.
Julian
F. J.
, and
Morgan
,
1981
, “
Variations of Muscle Stiffness With Tension During Tension Transients and Constant Velocity Shortening in the Frog
,”
J. Physiol.
, Vol.
319
, pp.
193
2103
.
13.
Lacquaniti
F.
,
Licata
F.
, and
Soechting
J. F.
,
1982
, “
The Mechanical Behaviour of the Human Forearm in Response to Transient Perturbations
,”
Bio. Cybern
, Vol.
44
, pp.
35
46
.
14.
Lensel-Corbeil
G.
, and
Goubel
F.
,
1990
, “
Series Elasticity in Frog Sartorius Muscle Subjected to Stretch-Shortening Cycles
,”
J. Biomech.
, Vol.
23
, pp.
121
126
.
15.
Ma, S.-P., 1988, “Activation Dynamics for the Distribution-Moment Model of Muscle,” D.Sc. Dissertation, Dep. Mech. Eng., Washington, University.
16.
Ma
S.-P.
, and
Zahalak
G. I.
,
1991
, “
A Distribution-Moment Model of Energetics in Skeletal Muscle
,”
J. Biomech.
, Vol.
24
, pp.
21
35
.
17.
McGill
S. M.
,
1992
, “
A Myoelectrically Based Dynamic Three-Dimensional Model to Predict Loads on Lumbar Spine Tissues During Lateral Bending
,”
J. Biomech.
, Vol.
25
, pp.
395
414
.
18.
Proske
U.
, and
Morgan
D. L.
,
1984
, “
Stiffness of Cat Soleus Muscle and Tendon During Activation of Part of Muscle
,”
J. Neurophysiol.
, Vol.
52
, pp.
459
468
.
19.
Rack
P. M. H.
, and
Westbury
D. R.
,
1974
, “
The Short Range Stiffness of Active Mammalian Muscle and Its Effect on Mechanical Properties
,”
J. Physiol.
, Vol.
240
, pp.
331
350
.
20.
Stein
R. B.
, and
Gordon
T.
,
1986
, “
Nonlinear Stiffness-Force Relationship in Whole Mammalian Skeletal Muscles
,”
Can. J. Physiol. Pharmacol
, Vol.
64
, pp.
1236
1244
.
21.
Sugi
H.
, and
Tsuchiya
T.
,
1988
, “
Stiffness Changes During Enhancement and Deficit of Isometric Force by Slow Length Changes in Frog Skeletal Muscle Fibres
,”
J. Physiol.
, Vol.
407
, pp.
215
229
.
22.
Winters
J. M.
,
Stark
L.
, and
Seif-Naraghi
A. H.
,
1988
, “
An Analysis of the Sources of Musculoskeletal System Impedance
,”
J. Biomech.
, Vol.
21
, pp.
1011
1025
.
23.
Winters, J. M., 1990, “Hill-Based Muscle Models: A Systems Engineering Perspective,” Multiple Muscle Systems: Biomechanics and Movement Organization, J. M. Winters and S.L-Y. Woo, eds. Springer-Verlag, pp. 70–93.
24.
Woittiez
R. D.
,
Huijing
P. A.
,
Boom
H. B. K.
, and
Rozendal
R. H.
,
1984
, “
A Three-Dimensional Muscle Model: A Quantified Relation Between Form and Function of Skeletal Muscles
,”
J. Morphol.
, Vol.
182
, pp.
95
113
.
25.
Zahalak
G. I.
,
1981
, “
A Distribution-Moment Approximation for Kinetic Theories of Muscular Contraction
,”
Math. Biosc.
, Vol.
55
, pp.
89
114
.
26.
Zahalak
G. I.
,
1986
, “
A Comparison of the Mechanical Behaviour of the Cat Soleus Muscle with a Distribution-Moment Model
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
108
, pp.
131
140
.
27.
Zahalak, G. I., 1990, “Modelling Muscle Mechanics (and Energetics), Multiple Muscle Systems: Biomechanics and Movement Organization, J. M. Winters and S.L-Y. Woo eds., Springer-Verlag, pp. 1–23.
28.
Zahalak
G. I.
, and
Ma
S.-P.
,
1990
, “
Muscle Activation and Contraction: Constitutive Relations Based on Directly on Cross-Bridge Kinetics
,”
ASME JOURNAL OF BIOMECHANICAL ENGINEERING
, Vol.
112
, pp.
52
62
.
29.
Zajac
F. E.
,
1989
, “
Muscle and Tendon: Properties, Models, Scaling, and Application to Biomechanics and Motor Control
,”
Crit. Rev. Biomed. Eng.
, Vol.
17
, pp.
359
411
.
This content is only available via PDF.
You do not currently have access to this content.