Three algorithms for interpreting models consisting of ordinary differential equations: Sensitivity coefficients, sensitivity functions, global optimization

Lehman, Steven L.; Stark, Lawrence

doi:10.1016/0025-5564(82)90064-5

Cited by 169 publications

(39 citation statements)

References 14 publications

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“…However, initial forward velocity of the trunk segment was fixed at 0.615 m/sec. Muscle activation onset times, offset times, and amplitudes that minimized the objective function value were searched using a modification (Lehman and Stark, 1982;Winters et al, 1984) of the global optimization algorithm developed by Bremermann (1970). The optimization process was terminated when the value of the objective function had not improved more than 1% during 600 consecutive function evaluations.…”

Section: Figmentioning

confidence: 99%

Neuromusculoskeletal computer modeling and simulation of upright, straight‐legged, bipedal locomotion of Australopithecus afarensis (A.L. 288‐1)

Nagano

Umberger

Marzke

et al. 2004

American J Phys Anthropol

100

112

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The skeleton of Australopithecus afarensis (A.L. 288-1, better known as "Lucy") is by far the most complete record of locomotor morphology of early hominids currently available. Even though researchers agree that the postcranial skeleton of Lucy shows morphological features indicative of bipedality, only a few studies have investigated Lucy's bipedal locomotion itself. Lucy's energy expenditure during locomotion has been the topic of much speculation, but has not been investigated, except for several estimates derived from experimental data collected on other animals. To gain further insights into how Lucy may have walked, we generated a full three-dimensional (3D) reconstruction and forward-dynamic simulation of upright bipedal locomotion of this ancient human ancestor. Laser-scanned 3D bone geometries were combined with state-of-the-art neuromusculoskeletal modeling and simulation techniques from computational biomechanics. A detailed full 3D neuromusculoskeletal model was developed that encompassed all major bones, joints (10), and muscles (52) of the lower extremity. A model of muscle force and heat production was used to actuate the musculoskeletal system, and to estimate total energy expenditure during locomotion. Neural activation profiles for each of the 52 muscles that produced a single step of locomotion, while at the same time minimizing the energy consumed per meter traveled, were searched through numerical optimization. The numerical optimization resulted in smooth locomotor kinematics, and the predicted energy expenditure was appropriate for upright bipedal walking in an individual of Lucy's body size.

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Section: Figmentioning

confidence: 99%

Neuromusculoskeletal computer modeling and simulation of upright, straight‐legged, bipedal locomotion of Australopithecus afarensis (A.L. 288‐1)

Nagano

Umberger

Marzke

et al. 2004

American J Phys Anthropol

100

112

View full text Add to dashboard Cite

show abstract

“…A standardized method to evaluate model sensitivity has been employed in several studies (Lehman and Stark, 1982;Pandy, 1990;Winters and Stark, 1985). This method divides the normalized change in a model output by the normalized change in a model parameter.…”

Section: Introductionmentioning

confidence: 99%

Sensitivity of a Hill-based muscle model to perturbations in model parameters

Scovil

Ronsky

2006

Journal of Biomechanics

186

157

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“…A FFS was constructed based on the mean kinematic data of each cat. We then examined the changes in the maximal directions of these FFSs due to perturbations of ±50% to all nonzero muscle moment arms, perturbations of ±50% to the maximum force value for each muscle, and 1° perturbations to each joint angle (cf., Lehman and Stark, 1982;Scovil and Ronsky, 2006). In addition, we tested the influence of an externally applied moment limit, the use of the pseudoinverse of the full seven degree of freedom system Jacobian (J T ) + , and of scaling individual segment lengths to match the kinematic data.…”

Section: Sensitivity Analysismentioning

confidence: 99%

Biomechanical capabilities influence postural control strategies in the cat hindlimb

McKay

Burkholder

Ting

2007

Journal of Biomechanics

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During postural responses to perturbations, horizontal plane forces generated by the cat hindlimb are stereotypically directed either towards or away from the animal's center of mass, independent of perturbation direction. We used a static, three-dimensional musculoskeletal model of the hindlimb to investigate possible biomechanical determinants of this "force constraint strategy" (Macpherson, 1988). We hypothesized that directions in which the hindlimb can produce large forces are preferentially used in postural control. We computed feasible force sets (FFS) based on hindlimb configurations of three cats during postural equilibrium tasks (Jacobs and Macpherson, 1996) and compared them to horizontal plane postural force directions. The grand mean FFS was bimodal, with maxima near the posterior-anterior axis (−86±8° and 71±4°), and minima near the medial-lateral axis (177±8° and 8±8°). Postural force directions clustered near both maxima; there were no medial postural forces near the absolute minimum. However, the medians of the anterior and posterior postural force direction histograms in the right hindlimb were rotated counterclockwise from the FFS maxima (p<0.05; Wilcoxon signed-rank test). Because the posterioranterior alignment of the FFS is consistent with a hindlimb structure optimized for locomotion, we conclude that the biomechanical capabilities of the hindlimb strongly influence, but do not uniquely determine the force directions observed in the force constraint strategy. Forces used in postural control may reflect a balance between a neural preference for using forces in the directions of large feasible forces and other criteria, such as the stabilization of the center of mass, and muscular coordination strategies.

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Three algorithms for interpreting models consisting of ordinary differential equations: Sensitivity coefficients, sensitivity functions, global optimization

Cited by 169 publications

References 14 publications

Neuromusculoskeletal computer modeling and simulation of upright, straight‐legged, bipedal locomotion of Australopithecus afarensis (A.L. 288‐1)

Neuromusculoskeletal computer modeling and simulation of upright, straight‐legged, bipedal locomotion of Australopithecus afarensis (A.L. 288‐1)

Sensitivity of a Hill-based muscle model to perturbations in model parameters

Biomechanical capabilities influence postural control strategies in the cat hindlimb

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