Mechanics of feline soleus: II design and validation of a mathematical model

Brown, Ian E.; Scott, Stephen H.; Loeb, Gerald E.

doi:10.1007/bf00124244

Cited by 107 publications

(92 citation statements)

References 31 publications

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“…Some of the data were analyzed by constructing lengthtension curves during whole or partial muscle stimulation. The data were fit to Otten's equation (3,23) …”

Section: Methodsmentioning

confidence: 99%

Nonlinear summation of force in cat soleus muscle results primarily from stretch of the common-elastic elements

Sandercock

2000

Journal of Applied Physiology

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The complex connective tissue structure of muscle and tendon suggests that forces from two parts of a muscle may not summate linearly. This study measured the nonlinear summation of force (Fnl) in whole cat soleus during isometric and ramp movements. In six anesthetized cats, the soleus was attached to a servomechanism to control muscle length and record force. The ventral roots were divided into two bundles, each innervating about half the soleus; thus the two parts could be stimulated alone or together. In all experiments, Fnl was small (<6% of maximum tetanic tension). Peak Fnl occurred during changes in muscle force, either as a result of imposed muscle movement or the onset or offset of a stimulus train. The data were fit to a model in which both parts of the muscle were assumed to stretch to a common elasticity. The servomechanism was programmed to compensate for reduced stretch of the common elasticity during partial compared with whole muscle activation. These compensatory movements showed how the model could account for most, but not all, of Fnl.

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“…Some of the data were analyzed by constructing lengthtension curves during whole or partial muscle stimulation. The data were fit to Otten's equation (3,23) …”

Section: Methodsmentioning

confidence: 99%

Nonlinear summation of force in cat soleus muscle results primarily from stretch of the common-elastic elements

Sandercock

2000

Journal of Applied Physiology

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“…Therefore, stiffness of the leg could be altered without sensory feedback as a response to the altered loading condition (landing velocity) and due to the changed working range of the muscles [force-length and force-velocity curve (e.g. Brown et al, 1996)]. …”

Section: Control Strategy By Stiffness Adjustment Process?mentioning

confidence: 99%

Running on uneven ground: leg adjustment to vertical steps and self-stability

Grimmer

Ernst

Günther

et al. 2008

Journal of Experimental Biology

112

133

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SUMMARYHuman running is characterized by comparably simple whole-body dynamics. These dynamics can be modelled with a point mass bouncing on a spring leg. Theoretical studies using such spring-mass models predict that running can be self-stable. In simulations, this self-stability allows for running on uneven ground without paying attention to the ground irregularities. Whether humans actually use this property of the mechanical system in such an irregular environment is, however, unclear. One way to approach this question is to study how the leg stiffness in stance and the leg orientation in flight are changed in response to ground perturbations. Here, for 11 human subjects we studied two consecutive contacts during running on uneven ground with a force plate of adjustable height (step of +5, +10 and +15 cm). We found that runners adjust their leg stiffness to the height of a vertical step. The adjustment is characterized by a 9% increase in leg stiffness in preparation for the perturbation and by a systematic decrease in proportion to the step height. At the highest vertical step (+15 cm), leg stiffness was reduced by about 26%. We also observed that the angle of attack decreased from 68 deg. to 62 deg. with increasing ground height. These leg adjustments are in accordance with the predictions of a stable spring-mass system. Furthermore, we could describe the identified leg forces and leg compressions with a simple spring-mass simulation for a given body mass, leg stiffness, angle of attack and initial conditions. We compared the experimental findings with the self-stabilizing properties of the spring-mass model, and discuss how humans use a combination of strategies that include purely mechanical self-stabilization and active neuromuscular control. Finally, beyond self-stability, we suggest that control may apply to smooth centre of mass kinematics.

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“…2). The form of the intrafusal fiber model was also influenced by recent improvements in the modeling of extrafusal mechanics Brown et al 1996bBrown et al , 1999.…”

Section: The Intrafusal Fiber Modelmentioning

confidence: 99%

“…2). The form of the intrafusal fiber model was also influenced by recent improvements in the modeling of extrafusal mechanics Brown et al 1996bBrown et al , 1999.BACKGROUND. The linear spindle model suggested by McMahon (1984) makes no distinction between different intrafusal fibers, but rather the fibers are lumped together into one spindle model.…”

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confidence: 99%

Mathematical Models of Proprioceptors. I. Control and Transduction in the Muscle Spindle

Mileusnic¹,

Brown²,

Lan³

et al. 2006

Journal of Neurophysiology

Self Cite

180

181

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. We constructed a physiologically realistic model of a lower-limb, mammalian muscle spindle composed of mathematical elements closely related to the anatomical components found in the biological spindle. The spindle model incorporates three nonlinear intrafusal fiber models (bag 1 , bag 2 , and chain) that contribute variously to action potential generation of primary and secondary afferents. A single set of model parameters was optimized on a number of data sets collected from feline soleus muscle, accounting accurately for afferent activity during a variety of ramp, triangular, and sinusoidal stretches. We also incorporated the different temporal properties of fusimotor activation as observed in the twitchlike chain fibers versus the toniclike bag fibers. The model captures the spindle's behavior both in the absence of fusimotor stimulation and during activation of static or dynamic fusimotor efferents. In the case of simultaneous static and dynamic fusimotor efferent stimulation, we demonstrated the importance of including the experimentally observed effect of partial occlusion. The model was validated against data that originated from the cat's medial gastrocnemius muscle and were different from the data used for the parameter determination purposes. The validation record included recently published experiments in which fusimotor efferent and spindle afferent activities were recorded simultaneously during decerebrate locomotion in the cat. This model will be useful in understanding the role of the muscle spindle and its fusimotor control during both natural and pathological motor behavior. I N T R O D U C T I O NThe muscle spindle is a sense organ found in most vertebrate skeletal muscles. In a typical mammalian lower limb muscle, several tens (or even hundreds) of muscle spindles can be found lying in parallel with extrafusal fibers and experiencing length changes representative of muscle length changes (Barker 1962;Eldred et al. 1962). The spindle has been found to play a dominant role both in kinesthesia and in reflexive adjustments to perturbations (Hulliger 1984;Matthews 1981). Its sensory transducers (primary and secondary afferents) provide the CNS with information about the length and velocity of the muscle in which the spindle is embedded. The spindle provides the main source of proprioceptive feedback for spinal sensorimotor regulation and servocontrol. At the same time that the spindle supplies the CNS with afferent information, it also receives continuous control through specialized fusimotor efferents (static and dynamic fusimotor efferents) whose task is to shift the spindle's relative sensitivities over the wide range of lengths and velocities that occur in various natural tasks (Banks 1994;Matthews 1962).The spindle consists of three types of intrafusal muscle fibers: long nuclear bag 1 and bag 2 fibers and shorter chain fibers ( Fig. 1A) (Boyd et al. 1977). Typically, one bag 1 , one bag 2 , and about four to 11 chain fibers lie in parallel within a spindle (Boyd and Smith 1984). The bag 1 ...

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Mechanics of feline soleus: II design and validation of a mathematical model

Cited by 107 publications

References 31 publications

Nonlinear summation of force in cat soleus muscle results primarily from stretch of the common-elastic elements

Nonlinear summation of force in cat soleus muscle results primarily from stretch of the common-elastic elements

Running on uneven ground: leg adjustment to vertical steps and self-stability

Mathematical Models of Proprioceptors. I. Control and Transduction in the Muscle Spindle

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