Clinical treatments of skeletal muscle weakness are hindered by a lack of an approach to evaluate individual muscle force. Intramuscular pressure (IMP) has shown a correlation to muscle force in vivo, but patient to patient and muscle to muscle variability results in difficulty of utilizing IMP to estimate muscle force. The goal of this work was to develop a finite element model of whole skeletal muscle that can predict IMP under passive and active conditions to further investigate the mechanisms of IMP variability. A previously validated hypervisco-poroelastic constitutive approach was modified to incorporate muscle activation through an inhomogeneous geometry. Model parameters were optimized to fit model stress to experimental data, and the resulting model fluid pressurization data were utilized for validation. Model fitting was excellent (root-mean-square error or RMSE <1.5 kPa for passive and active conditions), and IMP predictive capability was strong for both passive (RMSE 3.5 mmHg) and active (RMSE 10 mmHg at in vivo lengths) conditions. Additionally, model fluid pressure was affected by length under isometric conditions, as increases in stretch yielded decreases in fluid pressurization following a contraction, resulting from counteracting Poisson effects. Model pressure also varied spatially, with the highest gradients located near aponeuroses. These findings may explain variability of in vivo IMP measurements in the clinic, and thus help reduce this variability in future studies. Further development of this model to include isotonic contractions and muscle weakness would greatly benefit this work.

References

References
1.
Emery
,
A. E. H.
,
2002
, “
The Muscular Dystrophies
,”
Lancet
,
359
(
9307
), pp.
687
695
.
2.
Morley
,
J. E.
,
Abbatecola
,
A. M.
,
Argiles
,
J. M.
,
Baracos
,
V.
,
Bauer
,
J.
,
Bhasin
,
S.
,
Cederholm
,
T.
,
Stewart Coats
,
A. J.
,
Cummings
,
S. R.
,
Evans
,
W. J.
,
Fearon
,
K.
,
Ferrucci
,
L.
,
Fielding
,
R. A.
,
Guralnik
,
J. M.
,
Harris
,
T. B.
,
Inui
,
A.
,
Kalantar-Zadeh
,
K.
,
Kirwan
,
B. A.
,
Mantovani
,
G.
,
Muscaritoli
,
M.
,
Newman
,
A. B.
,
Rossi-Fanelli
,
F.
,
Rosano
,
G. M. C.
,
Roubenoff
,
R.
,
Schambelan
,
M.
,
Sokol
,
G. H.
,
Storer
,
T. W.
,
Vellas
,
B.
,
von Haehling
,
S.
,
Yeh
,
S. S.
, and
Anker
,
S. D.
,
2011
, “
Sarcopenia With Limited Mobility: An International Consensus
,”
J. Am. Med. Dir. Assoc.
,
12
(
6
), pp.
403
409
.
3.
Go
,
S. A.
,
Jensen
,
E. R.
,
O'Connor
,
S. M.
,
Evertz
,
L. Q.
,
Morrow
,
D. A.
,
Ward
,
S. R.
,
Lieber
,
R. L.
, and
Kaufman
,
K. R.
,
2017
, “
Design Considerations of a Fiber Optic Pressure Sensor Protective Housing for Intramuscular Pressure Measurements
,”
Ann. Biomed. Eng.
,
45
(
3
), pp.
739
746
.
4.
Davis
,
J.
,
Kaufman
,
K. R.
, and
Lieber
,
R. L.
,
2003
, “
Correlation Between Active and Passive Isometric Force and Intramuscular Pressure in the Isolated Rabbit Tibialis Anterior Muscle
,”
J. Biomech.
,
36
(
4
), pp.
505
512
.
5.
Ward
,
S. R.
,
Davis
,
J.
,
Kaufman
,
K. R.
, and
Lieber
,
R. L.
,
2007
, “
Relationship Between Muscle Stress and Intramuscular Pressure During Dynamic Muscle Contractions
,”
Muscle and Nerve
,
36
(
3
), pp.
313
319
.
6.
Sejersted
,
O. M.
, and
Hargens
,
A. R.
,
1995
, “
Intramuscular Pressures for Monitoring Different Tasks and Muscle Conditions
,”
Adv. Exp. Med. Biol.
,
384
, pp.
339
350
.
7.
Hill
,
A. V.
,
1938
, “
The Heat of Shortening and the Dynamic Constants of Muscle
,”
Proc. R. Soc. B. Biol. Sci.
,
126
(
843
), pp.
136
195
.
8.
Lieber
,
R. L.
,
2010
,
Skeletal Muscle Structure, Function, and Plasticity
,
Lippincott Williams and Wilkins
,
Philadelphia, PA
.
9.
Huijing
,
P. A.
,
1999
, “
Muscle as a Collagen Fiber Reinforced Composite: A Review of Force Transmission in Muscle and Whole Limb
,”
J. Biomech.
,
32
(
4
), pp.
329
345
.
10.
Wheatley
,
B. B.
,
Odegard
,
G. M.
,
Kaufman
,
K. R.
, and
Haut Donahue
,
T. L.
,
2017
, “
A Validated Model of Passive Skeletal Muscle to Predict Force and Intramuscular Pressure
,”
Biomech. Model. Mechanobiol.
,
16
(
3
), pp.
1011
1022
.
11.
Lieber
,
R. L.
, and
Blevins
,
F. T.
,
1989
, “
Skeletal Muscle Architecture of the Rabbit Hindlimb: Functional Implications of Muscle Design
,”
J. Morphol.
,
199
(
1
), pp.
93
101
.
12.
Wang
,
K.
,
McCarter
,
R.
,
Wright
,
J.
,
Beverly
,
J.
, and
Ramirez-Mitchell
,
R.
,
1993
, “
Viscoelasticity of the Sarcomere Matrix of Skeletal Muscles. The Titin-Myosin Composite Filament is a Dual-Stage Molecular Spring
,”
Biophys. J.
,
64
(
4
), pp.
1161
1177
.
13.
Meyer
,
G. A.
,
McCulloch
,
A. D.
, and
Lieber
,
R. L.
,
2011
, “
A Nonlinear Model of Passive Muscle Viscosity
,”
ASME J. Biomech. Eng.
,
133
(
9
), p.
091007
.
14.
Proske
,
U.
, and
Morgan
,
D. L.
,
1999
, “
Do Cross-Bridges Contribute to the Tension During Stretch of Passive Muscle?
,”
J. Muscle Res. Cell Motil.
,
20
(
5–6
), pp.
433
442
.
15.
Gillies
,
A. R.
, and
Lieber
,
R. L.
,
2011
, “
Structure and Function of the Skeletal Muscle Extracellular Matrix
,”
Muscle Nerve
,
44
(
3
), pp.
318
331
.
16.
Meyer
,
G. A.
, and
Lieber
,
R. L.
,
2011
, “
Elucidation of Extracellular Matrix Mechanics From Muscle Fibers and Fiber Bundles
,”
J. Biomech.
,
44
(
4
), pp.
771
773
.
17.
Hodgson
,
J. A.
,
Chi
,
S.-W.
,
Yang
,
J. P.
,
Chen
,
J.-S.
,
Edgerton
,
V. R.
, and
Sinha
,
S.
,
2012
, “
Finite Element Modeling of Passive Material Influence on the Deformation and Force Output of Skeletal Muscle
,”
J. Mech. Behav. Biomed. Mater.
,
9
, pp.
163
183
.
18.
Yucesoy
,
C. A.
,
Koopman
,
B. H. F. J. M.
,
Huijing
,
P. A.
, and
Grootenboer
,
H. J.
,
2002
, “
Three-Dimensional Finite Element Modeling of Skeletal Muscle Using a Two-Domain Approach: Linked Fiber-Matrix Mesh Model
,”
J. Biomech.
,
35
(
9
), pp.
1253
1262
.
19.
Clemen
,
C. B.
,
Benderoth
,
G. E. K.
,
Schmidt
,
A.
,
Hübner
,
F.
,
Vogl
,
T. J.
, and
Silber
,
G.
,
2017
, “
Human Skeletal Muscle Behavior In Vivo: Finite Element Implementation, Experiment, and Passive Mechanical Characterization
,”
J. Mech. Behav. Biomed. Mater.
,
65
, pp.
679
687
.
20.
Oomens
,
C. W. J.
,
Maenhout
,
M.
,
van Oijen
,
C. H.
,
Drost
,
M. R.
, and
Baaijens
,
F. P.
,
2003
, “
Finite Element Modelling of Contracting Skeletal Muscle
,”
Philos. Trans. R. Soc. London B. Biol. Sci.
,
358
(
1437
), pp.
1453
1460
.
21.
Wheatley
,
B. B.
,
Odegard
,
G. M.
,
Kaufman
,
K. R.
, and
Haut Donahue
,
T. L.
,
2016
, “
A Case for Poroelasticity in Skeletal Muscle Finite Element Analysis: Experiment and Modeling
,”
Comput. Methods Biomech. Biomed. Eng.
,
20
(
6
), pp.
598
601
.
22.
Johansson
,
T.
,
Meier
,
P.
, and
Blickhan
,
R.
,
2000
, “
A Finite-Element Model for the Mechanical Analysis of Skeletal Muscles
,”
J. Theor. Biol.
,
206
(
1
), pp.
131
149
.
23.
Wheatley
,
B. B.
,
Morrow
,
D. A.
,
Odegard
,
G. M.
,
Kaufman
,
K. R.
, and
Haut Donahue
,
T. L.
,
2016
, “
Skeletal Muscle Tensile Strain Dependence: Hyperviscoelastic Nonlinearity
,”
J. Mech. Behav. Biomed. Mater.
,
53
, pp.
445
454
.
24.
Mohammadkhah
,
M.
,
Murphy
,
P.
, and
Simms
,
C. K.
,
2016
, “
The In Vitro Passive Elastic Response of Chicken Pectoralis Muscle to Applied Tensile and Compressive Deformation
,”
J. Mech. Behav. Biomed. Mater.
,
62
, pp.
468
480
.
25.
Ateshian
,
G. A.
,
Rajan
,
V.
,
Chahine
,
N. O.
,
Canal
,
C. E.
, and
Hung
,
C. T.
,
2009
, “
Modeling the Matrix of Articular Cartilage Using a Continuous Fiber Angular Distribution Predicts Many Observed Phenomena
,”
ASME J. Biomech. Eng.
,
131
(
6
), p.
061003
.
26.
Wheatley
,
B. B.
,
Odegard
,
G. M.
,
Kaufman
,
K. R.
, and
Donahue
,
T. L. H.
,
2016
, “
How Does Tissue Preparation Affect Skeletal Muscle Transverse Isotropy?
,”
J. Biomech.
,
49
(
13
), pp.
3056
3060
.
27.
Maas
,
S. A.
,
Ellis
,
B. J.
,
Ateshian
,
G. A.
, and
Weiss
,
J. A.
,
2012
, “
FEBio: Finite Elements for Biomechanics
,”
ASME J. Biomech. Eng.
,
134
(
1
), p.
011005
.
28.
Blemker
,
S. S.
,
Pinsky
,
P. M.
, and
Delp
,
S. L.
,
2005
, “
A 3D Model of Muscle Reveals the Causes of Nonuniform Strains in the Biceps Brachii
,”
J. Biomech.
,
38
(
4
), pp.
657
65
.
29.
Einat
,
R.
, and
Yoram
,
L.
,
2009
, “
Recruitment Viscoelasticity of the Tendon
,”
ASME J. Biomech. Eng.
,
131
(
11
), p.
111008
.
30.
Sjøgaard
,
G.
, and
Saltin
,
B.
,
1982
, “
Extra- and Intracellular Water Spaces in Muscles of Man at Rest and With Dynamic Exercise
,”
Am. J. Physiol.
,
243
(
3
), pp.
R271
R280
.
31.
Bartoo
,
M. L.
,
Popov
,
V. I.
,
Fearn
,
L. A.
, and
Pollack
,
G. H.
,
1993
, “
Active Tension Generation in Isolated Skeletal Myofibrils
,”
J. Muscle Res. Cell Motil.
,
14
(
5
), pp.
498
510
.
32.
Maganaris
,
C. N.
,
Baltzopoulos
,
V.
,
Ball
,
D.
, and
Sargeant
,
A. J.
,
2001
, “
In Vivo Specific Tension of Human Skeletal Muscle
,”
J. Appl. Physiol.
,
90
(
3
), pp.
865
872
.
33.
Wheatley
,
B. B.
,
Pietsch
,
R. B.
,
Haut Donahue
,
T. L.
, and
Williams
,
L. N.
,
2016
, “
Fully Non-Linear Hyper-Viscoelastic Modeling of Skeletal Muscle in Compression
,”
Comput. Methods Biomech. Biomed. Eng.
,
19
(
11
), pp.
1181
1189
.
34.
Pietsch
,
R.
,
Wheatley
,
B. B.
,
Haut Donahue
,
T. L.
,
Gilbrech
,
R.
,
Prabhu
,
R.
,
Liao
,
J.
, and
Williams
,
L. N.
,
2014
, “
Anisotropic Compressive Properties of Passive Porcine Muscle Tissue
,”
ASME J. Biomech. Eng.
,
136
(
11
), p.
111003
.
35.
Takaza
,
M.
,
Moerman
,
K. M.
,
Gindre
,
J.
,
Lyons
,
G.
, and
Simms
,
C. K.
,
2012
, “
The Anisotropic Mechanical Behaviour of Passive Skeletal Muscle Tissue Subjected to Large Tensile Strain
,”
J. Mech. Behav. Biomed. Mater.
,
17
, pp.
209
220
.
36.
Van Loocke
,
M.
,
Lyons
,
C. G.
, and
Simms
,
C. K.
,
2006
, “
A Validated Model of Passive Muscle in Compression
,”
J. Biomech.
,
39
(
16
), pp.
2999
3009
.
37.
Abraham
,
A. C.
,
Kaufman
,
K. R.
, and
Haut Donahue
,
T. L.
,
2012
, “
Phenomenological Consequences of Sectioning and Bathing on Passive Muscle Mechanics of the New Zealand White Rabbit Tibialis Anterior
,”
J. Mech. Behav. Biomed. Mater.
,
17
, pp.
290
295
.
38.
Van Ee
,
C. A.
,
Chasse
,
A. L.
, and
Myers
,
B. S.
,
2000
, “
Quantifying Skeletal Muscle Properties in Cadaveric Test Specimens: Effects of Mechanical Loading, Postmortem Time, and Freezer Storage
,”
ASME J. Biomech. Eng.
,
122
(
1
), pp.
9
14
.
39.
Fukunaga
,
T.
,
Roy
,
R. R.
,
Shellock
,
F. G.
,
Hodgson
,
J. A.
, and
Edgerton
,
V. R.
,
1996
, “
Specific Tension of Human Plantar Flexors and Dorsiflexors
,”
J. Appl. Physiol.
,
80
(
1
), pp.
158
165
.
40.
Erskine
,
R. M.
,
Jones
,
D. A.
,
Maganaris
,
C. N.
, and
Degens
,
H.
,
2009
, “
In Vivo Specific Tension of the Human Quadriceps Femoris Muscle
,”
Eur. J. Appl. Physiol.
,
106
(
6
), pp.
827
838
.
41.
Burkholder
,
T. J.
, and
Lieber
,
R. L.
,
2001
, “
Sarcomere Length Operating Range of Vertebrate Muscles During Movement
,”
J. Exp. Biol.
,
204
(
Pt. 9
), pp.
1529
1536
.http://jeb.biologists.org/content/204/9/1529
42.
Grasa
,
J.
,
Ramírez
,
A.
,
Osta
,
R.
,
Muñoz
,
M. J.
,
Soteras
,
F.
, and
Calvo
,
B.
,
2011
, “
A 3D Active-Passive Numerical Skeletal Muscle Model Incorporating Initial Tissue Strains. Validation With Experimental Results on Rat Tibialis Anterior Muscle
,”
Biomech. Model. Mechanobiol.
,
10
(
5
), pp.
779
787
.
43.
Jenkyn
,
T.
,
Koopman
,
B.
,
Huijing
,
P. A.
,
Lieber
,
R. L.
, and
Kaufman
,
K. R.
,
2002
, “
Finite Element Model of Intramuscular Pressure During Isometric Contraction of Skeletal Muscle
,”
Phys. Med. Biol.
,
47
(
22
), pp.
4043
4061
.
44.
Light
,
N.
, and
Champion
,
A. E.
,
1984
, “
Characterization of Muscle Epimysium, Perimysium and Endomysium Collagens
,”
Biochem. J
,
219
(
3
), pp.
1017
1026
.
45.
Lemos
,
R. R.
,
Epstein
,
M.
,
Herzog
,
W.
, and
Wyvill
,
B.
,
2004
, “
A Framework for Structured Modeling of Skeletal Muscle
,”
Comput. Methods Biomech. Biomed. Eng.
,
7
(
6
), pp.
305
317
.
46.
Yucesoy, C. A.
,
Koopman, B. H. F. J. M.
,
Grootenboer, H. J.
, and
Huijing, P. A.
, 2008, “
Extramuscular Myofascial Force Transmission Alters Substantially the Acute Effects of Surgical Aponeurotomy: Assessment by Finite Element Modeling
,”
Biomech. Model Mechanobiol.
,
7
(3), pp. 175–189.
47.
Khodaei
,
H.
,
Mostofizadeh
,
S.
,
Brolin
,
K.
,
Johansson
,
H.
, and
Osth
,
J.
,
2013
, “
Simulation of Active Skeletal Muscle Tissue With a Transversely Isotropic Viscohyperelastic Continuum Material Model
,”
Proc. Inst. Mech. Eng. H.
,
227
(
5
), pp.
571
580
.
48.
Hernández-Gascón
,
B.
,
Grasa
,
J.
,
Calvo
,
B.
, and
Rodríguez
,
J. F.
,
2013
, “
A 3D Electro-Mechanical Continuum Model for Simulating Skeletal Muscle Contraction
,”
J. Theor. Biol.
,
335
, pp.
108
118
.
49.
Rehorn
,
M. R.
, and
Blemker
,
S. S.
,
2010
, “
The Effects of Aponeurosis Geometry on Strain Injury Susceptibility Explored With a 3D Muscle Model
,”
J. Biomech.
,
43
(
13
), pp.
2574
2581
.
50.
Lu
,
Y. T.
,
Zhu
,
H. X.
,
Richmond
,
S.
, and
Middleton
,
J.
,
2010
, “
A Visco-Hyperelastic Model for Skeletal Muscle Tissue Under High Strain Rates
,”
J. Biomech.
,
43
(
13
), pp.
2629
2632
.
51.
Chi
,
S.
,
Hodgson
,
J.
,
Chen
,
J.
,
Reggie Edgerton
,
V.
,
Shin
,
D. D.
,
Roiz
,
R. A.
, and
Sinha
,
S.
,
2010
, “
Finite Element Modeling Reveals Complex Strain Mechanics in the Aponeuroses of Contracting Skeletal Muscle
,”
J. Biomech.
,
43
(
7
), pp.
1243
1250
.
52.
Rahemi
,
H.
,
Nigam
,
N.
, and
Wakeling
,
J. M.
,
2015
, “
The Effect of Intramuscular Fat on Skeletal Muscle Mechanics: Implications for the Elderly and Obese
,”
J. R. Soc. Interface
,
12
(
109
), p.
20150365
.
53.
Böl
,
M.
, and
Reese
,
S.
,
2008
, “
Micromechanical Modelling of Skeletal Muscles Based on the Finite Element Method
,”
Comput. Methods Biomech. Biomed. Eng.
,
11
(
5
), pp.
489
504
.
54.
Tang
,
C. Y.
,
Zhang
,
G.
, and
Tsui
,
C. P.
,
2009
, “
A 3D Skeletal Muscle Model Coupled With Active Contraction of Muscle Fibres and Hyperelastic Behaviour
,”
J. Biomech.
,
42
(
7
), pp.
865
872
.
55.
Yang
,
M.
, and
Taber
,
L. A.
,
1991
, “
The Possible Role of Poroelasticity in the Apparent Viscoelastic Behavior of Passive Cardiac Muscle
,”
J. Biomech.
,
24
(
7
), pp.
587
597
.
56.
Gindre
,
J.
,
Takaza
,
M.
,
Moerman
,
K. M.
, and
Simms
,
C. K.
,
2013
, “
A Structural Model of Passive Skeletal Muscle Shows Two Reinforcement Processes in Resisting Deformation
,”
J. Mech. Behav. Biomed. Mater.
,
22
, pp.
84
94
.
57.
Sleboda
,
D. A.
, and
Roberts
,
T. J.
,
2017
, “
Incompressible Fluid Plays a Mechanical Role in the Development of Passive Muscle Tension
,”
Biol. Lett.
,
13
(
1
), p. 20160630.
58.
Ateş
,
F.
,
Davies
,
B. L.
,
Chopra
,
S.
,
Coleman-Wood
,
K.
,
Litchy
,
W. J.
, and
Kaufman
,
K. R.
,
2018
, “
Intramuscular Pressure of Tibialis Anterior Reflects Ankle Torque But Does Not Follow Joint Angle-Torque Relationship
,”
Front. Physiol.
,
9
, p.
22
.
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