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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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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