Abstract
The combined force–length (F–L) properties of a muscle group acting synergistically at a joint are determined by several aspects of the F–L properties of the individual musculotendon units. Namely, misalignment of the optimal lengths of the individual muscles will affect the group F–L properties. This misalignment, which we named \(M_{\text{opt}}^{\text{MT}}\), arises from the properties of the muscles (i.e., optimum fiber length and pennation angle) and of their tendons (i.e., compliance and slack length). The aim of this study was to measure the F–L properties of kangaroo rat plantarflexors as a group and individually and determine the effects of \(M_{\text{opt}}^{\text{MT}}\) on the group F–L properties. Specifically, we performed a sensitivity analysis to quantify how \(M_{\text{opt}}^{\text{MT}}\) influences the tradeoff between maximizing the peak force vs. having a wider group F–L curve. In the kangaroo rat, we found that the optimal lengths of two bi-articular musculotendon units, the plantaris and the gastrocnemius, were misaligned by 1.8 mm, but this amount favored maximal peak force rather than increasing F–L curve width. Because we measured the misalignment in situ, we could directly assess the tradeoff between maximizing peak force vs. a wider F–L curve without making modeling assumptions about the individual muscle or tendon properties.
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Abbreviations
- F:
-
Force measured by servomotor (N)
- \(L^{\text{MT}}\) :
-
Musculotendon length equal to distance between origin of muscles and motor arm (mm)
- \(\Delta L^{\text{MT}}\) :
-
Change in musculotendon length (mm)
- FGRP :
-
Musculotendon force of the muscle group (N)
- \(F_{\text{a}}^{\text{GRP}}\) :
-
Active force of muscle group (N)
- \(F_{\text{p}}^{\text{GRP}}\) :
-
Passive force of muscle group (N)
- \(F_{\text{a}}^{\text{M}}\) :
-
Active force of muscle M (either gastrocnemius (GAS) or plantaris (PL)) (N)
- \(F_{\text{p}}^{\text{M}}\) :
-
Passive force of muscle M (N)
- \(F_{\text{o}}^{\text{GRP}}\) :
-
Maximum isometric force of the muscle group (N)
- \(F_{\text{o}}^{\text{M}}\) :
-
Maximum isometric force of the muscle M (N)
- \(L_{\text{o - GRP}}^{\text{MT}}\) :
-
Musculotendon length at maximum isometric force of muscle group (mm)
- \(L_{\text{o}}^{{{\text{MT}}^{ *} }}\) :
-
Initial musculotendon length, which is an estimation of \(L_{\text{o - GRP}}^{\text{MT}}\) (mm)
- \(L_{\text{o - M}}^{\text{MT}}\) :
-
Musculotendon length at maximum isometric force of muscle M (mm)
- \(L_{\text{o}}^{\text{M}}\) :
-
The length of muscle belly M at maximum isometric force of muscle M (mm)
- \(L_{\text{c}}^{\text{M}}\) :
-
Distance between the pair of sonometric crystals inserted into muscle M (mm)
- \(L_{\text{o - c}}^{\text{M}}\) :
-
Distance between crystal pair at maximum isometric force of muscle M (mm)
- \(\theta_{\text{f}}^{\text{M}}\) :
-
Pennation angle of muscle M (degrees)
- \(L_{\text{f}}^{\text{M}}\) :
-
Fiber length of muscle M (mm)
- \({\text{CSA}}^{\text{M}}\) :
-
Functional cross sectional area of muscle M (mm2)
- \(\sigma_{\max}\) :
-
Maximum isometric stress (kPa)
- \(L_{\text{s - M}}^{\text{T}}\) :
-
Slack length of the tendon of muscle M (mm)
- \(\varepsilon_{\text{max - M}}^{\text{T}}\) :
-
Tendon strain of muscle M at its maximum isometric force (%\(L_{\text{s - M}}^{\text{T}}\))
- \({\text{L}}^{\text{ac}}\) :
-
Relative displacement between the two muscle–tendon units (mm)
- \(M_{\text{opt}}^{\text{MT}}\) :
-
Distance between \(L_{\text{o - M}}^{\text{MT}}\) of two different muscles (mm)
- \(F_{\max}\) :
-
Maximum force of the F–L curve of muscle group calculated by model (N)
- W:
-
Width of the F–L curve of the muscle group calculated by model (mm)
References
Ackland, D. C., Y. C. Lin, and M. G. Pandy. Sensitivity of model predictions of muscle function to changes in moment arms and muscle-tendon properties: a Monte-Carlo analysis. J. Biomech. 45:1463–1471, 2012.
Biewener, A. A., and R. Blickhan. Kangaroo rat locomotion: design for elastic energy storage or acceleration? J. Exp. Biol. 140:243–255, 1988.
Biewener, A. A., R. Blickhan, A. K. Perry, N. C. Heglund, and C. R. Taylor. Muscle forces during locomotion in kangaroo rats: force platform and tendon buckle measurements compared. J. Exp. Biol. 137:191–205, 1988.
Dalton, B. H., M. D. Allen, G. A. Power, A. A. Vandervoort, and C. L. Rice. The effect of knee joint angle on plantar flexor power in young and old men. Exp. Gerontol. 52:70–76, 2014.
De Groote, F., A. Van Campen, I. Jonkers, and J. De Schutter. Sensitivity of dynamic simulations of gait and dynamometer experiments to hill muscle model parameters of knee flexors and extensors. J. Biomech. 43:1876–1883, 2010.
Fukashiro, S., M. Rob, Y. Ichinose, Y. Kawakami, and T. Fukunaga. Ultrasonography gives directly but noninvasively elastic characteristic of human tendon in vivo. Eur. J. Appl. Physiol. Occup. Physiol. 71:555–557, 1995.
Hasson, C. J., and G. E. Caldwell. Effects of age on mechanical properties of dorsiflexor and plantarflexor muscles. Ann. Biomed. Eng. 40:1088–1101, 2012.
Herzog, W. Skeletal muscle mechanics: questions, problems and possible solutions. J. Neuroeng. Rehabil. 14:1–17, 2017.
Hicks, J. L., T. K. Uchida, A. Seth, A. Rajagopal, and S. L. Delp. Is my model good enough? Best practices for verification and validation of musculoskeletal models and simulations of movement. J. Biomech. Eng. 137:020905, 2015.
Kawakami, Y., Y. Ichinose, and T. Fukunaga. Architectural and functional features of human triceps surae muscles during contraction. J. Appl. Physiol. 85:398–404, 1998.
Landin, D., M. Thompson, and M. Reid. Knee and Ankle joint angles influence the plantarflexion torque of the gastrocnemius. J. Clin. Med. Res. 7:602–606, 2015.
Lauber, B., G. A. Lichtwark, and A. G. Cresswell. Reciprocal activation of gastrocnemius and soleus motor units is associated with fascicle length change during knee flexion. Physiol. Rep. 2:e12044, 2014.
Maas, H., G. C. Baan, and P. A. Huijing. Muscle force is determined also by muscle relative position: isolated effects. J. Biomech. 37:99–110, 2004.
Maas, H., and T. G. Sandercock. Force transmission between synergistic skeletal muscles through connective tissue linkages. J. Biomed. Biotechnol. 1–9:2010, 2010.
Mendez, J., and A. Keys. Density and composition of mammalian muscle. Metabolism 9:184–188, 1960.
Olesen, A. T., B. R. Jensen, T. L. Uhlendorf, R. W. Cohen, G. C. Baan, and H. Maas. Muscle-specific changes in length-force characteristics of the calf muscles in the spastic Han-Wistar rat. J. Appl. Physiol. 117:989–997, 2014.
Powell, P. L., R. R. Roy, P. Kanim, M. A. Bello, and V. R. Edgerton. Predictability of skeletal muscle tension from architectural determinations in guinea pig hindlimbs. J. Appl. Physiol. 57:1715–1721, 1984.
Rajagopal, A., C. L. Dembia, M. S. DeMers, D. D. Delp, J. L. Hicks, and S. L. Delp. Full-body musculoskeletal model for muscle-driven simulation of human gait. IEEE Trans. Biomed. Eng. 63:2068–2079, 2016.
Rankin, J. W., K. M. Doney, and C. P. McGowan. Functional capacity of kangaroo rat hindlimbs: adaptations for locomotor performance. J. R. Soc. Interface 15:20180303, 2018.
Rassier, D. E., B. R. MacIntosh, and W. Herzog. Length dependence of active force production in skeletal muscle. J. Appl. Physiol. 86:1445–1457, 1999.
Rehwaldt, J. D., B. D. Rodgers, and D. C. Lin. Skeletal muscle contractile properties in a novel murine model for limb girdle muscular dystrophy 2i. J. Appl. Physiol. 123:1698–1707, 2017.
Rijkelijkhuizen, J. M., G. C. Baan, A. de Haan, C. J. de Ruiter, and P. A. Huijing. Extramuscular myofascial force transmission for in situ rat medial gastrocnemius and plantaris muscles in progressive stages of dissection. J. Exp. Biol. 208:129–140, 2005.
Rospars, J. P., and N. Meyer-Vernet. Force per cross-sectional area from molecules to muscles: a general property of biological motors. R. Soc. Open Sci. 3:160313, 2016.
Rugg, S. G., R. J. Gregor, B. R. Mandelbaum, and L. Chiu. In vivo moment arm calculations at the ankle using magnetic resonance imaging (MRI). J. Biomech. 23:495–501, 1990.
Schwaner, M. J., D. C. Lin, and C. P. McGowan. Jumping mechanics of desert kangaroo rats. J. Exp. Biol. 221:jeb186700, 2018.
Scovil, C. Y., and J. L. Ronsky. Sensitivity of a Hill-based muscle model to perturbations in model parameters. J. Biomech. 39:2055–2063, 2006.
Tijs, C., J. H. Van Dieën, G. C. Baan, and H. Maas. Three-dimensional ankle moments and nonlinear summation of rat triceps surae muscles. PLoS ONE 9:e111595, 2014.
Tijs, C., J. H. van Dieën, G. C. Baan, and H. Maas. Synergistic co-activation increases the extent of mechanical interaction between rat ankle plantar-flexors. Front. Physiol. 7:1–8, 2016.
Tijs, C., J. H. van Dieen, and H. Maas. No functionally relevant mechanical effects of epimuscular myofascial connections between rat ankle plantar flexors. J. Exp. Biol. 218:2935–2941, 2015.
Xiao, M., and J. Higginson. Sensitivity of estimated muscle force in forward simulation of normal walking. J. Appl. Biomech. 26:142–149, 2010.
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Work supported by Army Research Office #66554-EG (DCL and CPM) and National Science Foundation #1553550 (CPM).
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Javidi, M., McGowan, C.P. & Lin, D.C. The Contributions of Individual Muscle–Tendon Units to the Plantarflexor Group Force–Length Properties. Ann Biomed Eng 47, 2168–2177 (2019). https://doi.org/10.1007/s10439-019-02288-z
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DOI: https://doi.org/10.1007/s10439-019-02288-z