A mathematical model for evaluation of forces in lower extremeties of the musculo-skeletal system

Seireg, A.; Arvikar, R.J.

doi:10.1016/0021-9290(73)90053-5

Cited by 295 publications

(93 citation statements)

References 18 publications

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“…Which optimization method is physiologically more reasonable and whether the cost functions used in these methods are actually minimized by the neuromuscular system are controversial [2,5,7,17,30,32]. Practically, prediction of load sharing based on biomechanical modeling can have several fold changes even when muscle parameters ( e g , the physiological cross sectional area (PCSA), fiber length and composition, pennation angle, insertion and origin sites, and moment arm) vary within normal anatomical ranges [4,18].…”

Section: Introductionmentioning

confidence: 99%

In vivo load sharing among the quadriceps components

Zhang

Wang

Nuber

et al. 2003

Journal Orthopaedic Research

120

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Knee extension is always performed with coordinated contractions of multiple quadriceps muscle components; however, how the load is shared among them under normal and pathological conditions is unclear. We hypothesized that: the absolute moment generated by each quadriceps component increases with the total knee extension moment; the relative contribution and its dependence on the total knee extension moment are different for different quadriceps components; and the centrally located large vastus intermedius (VI) is favored by the central nervous system at low levels of activation. Electrical stimulation was used to activate each quadriceps component selectively in six human subjects. The relationship between the knee extension moment gcnerated by an individual quadriceps component and the corresponding compound muscular action potential (M-wave) over various contraction levels was established for each quddriCepS component. This relationship was used to calibrate the corresponding EMG signal and determine load sharing among quadriceps components during submaximal isometric voluntary knee extension. The VI contributed the most (51.8-39.6'%) and vastus medialis the least (9.5-12.2%) to knee extension moment ( P < 0.05). As the knee extension moment increased, the relative contribution of the VI decreased (P = 0.017) while the relation contribution of the vastus lateralis and medialis increased (P < 0.012). The absolute moment generated by each quadriceps component always increased with the total knee extension moment (P < 0.002). Our in vivo approach determined subject-and condition-specific load sharing among individual muscles and showed that the central nervous system utilized the centrally located, uniarticular VI in submaximal isometric knee extension.

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Section: Introductionmentioning

confidence: 99%

In vivo load sharing among the quadriceps components

Zhang

Wang

Nuber

et al. 2003

Journal Orthopaedic Research

120

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“…Considering that direct measurements of individual muscle force cannot be performed noninvasively, numerous modeling approaches have been proposed for nonfatiguing tasks (5,13) since the first works published in the 1970s (33). However, due to muscle redundancy (i.e., in most tasks, there are more muscles involved than mechanical degrees of freedom), these models remain invalidated (33).…”

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confidence: 99%

Shear elastic modulus can be used to estimate an index of individual muscle force during a submaximal isometric fatiguing contraction

Bouillard

Hug

Guével

et al. 2012

Journal of Applied Physiology

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The present study was designed to determine whether fatigue alters the ability to estimate an index of individual muscle force from shear elastic modulus measurements ( experiment I), and to test the ability of this technique to highlight changes in load sharing within a redundant muscle group during an isometric fatiguing task ( experiment II). Twelve subjects participated in experiment I, which consisted of smooth linear torque ramps from 0 to 80% of maximal voluntary contraction (MVC) performed before and after an isometric fatigue protocol, beginning at 40% of MVC and stopped when the force production dropped below 30% of MVC. Although the relationships between modulus and torque were very similar for pre- and postfatigue [root mean square deviation (RMSdeviation) = 3.7 ± 2.6% of MVC], the relationships between electromyography activity level and torque were greatly altered by fatigue (RMSdeviation = 10.3 ± 2.6% of MVC). During the fatiguing contraction, shear elastic modulus provided a significantly lower RMSdeviation between measured torque and estimated torque than electromyography activity level (5.7 ± 0.9 vs. 15.3 ± 3.8% of MVC). Experiment II performed with eight participants consisted of an isometric knee extension at 25% of MVC sustained until exhaustion. Opposite changes in shear elastic modulus were observed between synergists (vastus medialis, vastus lateralis, and rectus femoris) of some participants, reflecting changes in load sharing. In conclusion, despite the fact that we did not directly estimate muscle force (in Newtons), this is the first demonstration of an experimental technique to accurately quantify relative changes in force in an individual human muscle during a fatiguing contraction.

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“…A similar static optimization problem has been treated with linear programming for ad hoc determination of minimum forces [85]- [87]. The problem is statically indeterminate (m > n), a circumstance which may cause some frustration in engineering approaches to the evaluation of forces [85]- [87].…”

Section: Discussionmentioning

confidence: 99%

“…The problem is statically indeterminate (m > n), a circumstance which may cause some frustration in engineering approaches to the evaluation of forces [85]- [87]. It is, however, very difficult to motivate why and how any such restrictions should be imposed.…”

Section: Discussionmentioning

confidence: 99%

Optimal coordination and control of posture and movements

Johansson

Fransson

Magnusson

2009

Journal of Physiology-Paris

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This paper presents a theoretical model of stability and coordination of posture and locomotion, together with algorithms for continuous-time quadratic optimization of motion control. Explicit solutions to the Hamilton-Jacobi equation for optimal control of rigid-body motion are obtained by solving an algebraic matrix equation. The stability is investigated with Lyapunov function theory and it is shown that global asymptotic stability holds. It is also shown how optimal control and adaptive control may act in concert in the case of unknown or uncertain system parameters. The solution describes motion strategies of minimum effort and variance. The proposed optimal control is formulated to be suitable as a posture and movement model for experimental validation and verification. The combination of adaptive and optimal control makes this algorithm a candidate for coordination and control of functional neuromuscular stimulation as well as of prostheses. Validation examples with experimental data are provided.

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A mathematical model for evaluation of forces in lower extremeties of the musculo-skeletal system

Cited by 295 publications

References 18 publications

In vivo load sharing among the quadriceps components

In vivo load sharing among the quadriceps components

Shear elastic modulus can be used to estimate an index of individual muscle force during a submaximal isometric fatiguing contraction

Optimal coordination and control of posture and movements

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