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Research Papers

Modeling Skeletal Muscle Stress and Intramuscular Pressure: A Whole Muscle Active–Passive Approach

[+] Author and Article Information
Benjamin B. Wheatley

Department of Mechanical Engineering,
Bucknell University,
1 Dent Drive,
Lewisburg, PA 17837
e-mail: b.wheatley@bucknell.edu

Gregory M. Odegard

Department of Mechanical Enginering—
Engineering Mechanics,
Department of Materials
Science and Engineering,
Michigan Technological University,
1400 Townsend Drive,
Houghton, MI 49931

Kenton R. Kaufman

Department of Orthopedic Surgery,
Department of Physiology and Biomedical
Engineering Mayo Clinic,
200 First Street SW,
Rochester, MN 55906

Tammy L. Haut Donahue

Department of Mechanical Engineering,
School of Biomedical Engineering,
Colorado State University,
1374 Campus Delivery,
Fort Collins, CO 80523

1Corresponding author.

Manuscript received September 11, 2017; final manuscript received May 18, 2018; published online June 1, 2018. Assoc. Editor: Spencer P. Lake.

J Biomech Eng 140(8), 081006 (Jun 01, 2018) (8 pages) Paper No: BIO-17-1402; doi: 10.1115/1.4040318 History: Received September 11, 2017; Revised May 18, 2018

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.

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References

Emery, A. E. H. , 2002, “ The Muscular Dystrophies,” Lancet, 359(9307), pp. 687–695. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
Lieber, R. L. , 2010, Skeletal Muscle Structure, Function, and Plasticity, Lippincott Williams and Wilkins, Philadelphia, PA.
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
Gillies, A. R. , and Lieber, R. L. , 2011, “ Structure and Function of the Skeletal Muscle Extracellular Matrix,” Muscle Nerve, 44(3), pp. 318–331. [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
Einat, R. , and Yoram, L. , 2009, “ Recruitment Viscoelasticity of the Tendon,” ASME J. Biomech. Eng., 131(11), p. 111008. [CrossRef]
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. [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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 [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
Light, N. , and Champion, A. E. , 1984, “ Characterization of Muscle Epimysium, Perimysium and Endomysium Collagens,” Biochem. J, 219(3), pp. 1017–1026. [CrossRef] [PubMed]
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. [CrossRef]
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.
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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.
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. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Inhomogeneous finite element geometry of skeletal muscle, showing excitable (dark longitudinal constituent), passive (light longitudinal constituent), and aponeurosis/tendon (located at ends of tissue): (a) Whole New Zealand White Rabbit tibialis anterior muscle model and (b) cross-sectional view of the rabbit tibialis anterior model

Grahic Jump Location
Fig. 2

(a) Model fit to experimental stress under (a) passive stretch and (b) active isometric conditions. The corresponding experimental data and model predictions for IMP are shown under (c) passive stretch and (d) active isometric conditions. Physiological in vivo muscle lengths are highlighted in the top right inset of (d), showing model predictive capabilities. All experimental data presented as mean and standard deviation. Active data show the change in stress/pressure as a result of contraction, and are thus calculated as passive stress/pressure subtracted from total stress/pressure. Note that for muscle lengths below zero in (a) and (c), the tissue does not support passive tensile load, and thus slack occurs.

Grahic Jump Location
Fig. 3

Color maps of fully activated finite element model at optimal length after one second of maximum contraction. (a) Image of two-dimensional sagittal midbelly slice of the model showing fluid pressure distribution. (b) Image of two-dimensional coronal midbelly slice showing fluid pressure distribution. The distal region exhibited the highest variability in fluid pressure.

Grahic Jump Location
Fig. 4

Comparison of two models to experimental data (mean with standard deviation in gray) of rabbit tibialis anterior muscle subject to transverse extension. The current model assumes a ξtrans value of 15 kPa while previous modeling utilized 33 kPa. (a) Stress relaxation step of 0.1 strain ramp (shown left) and 300 s of relaxation (shown right). (b) Constant rate pull to 0.25 strain at a rate of 0.01 s−1.

Grahic Jump Location
Fig. 5

(a) The deformations resulting from passive stretch and active contraction both enact the Poisson effect, where the longitudinal strain (horizontal arrows) results in strain in the transverse plane (vertical arrows). As these deformations oppose each other, the result is a smaller resultant volumetric deformation, which yields low fluid pressurization. (b) Model transverse strains (x and y directions, as elongation occurs in the z direction) for three time points when stretched to optimal length, after initial ramp elongation, at the end of stress relaxation, and at maximum contraction. Passive elongation results in negative transverse strains, which is then counteracted by shortening due to active contraction.

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