scholarly journals An Approach for Simulation of the Muscle Force Modeling It by Summation of Motor Unit Contraction Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Rositsa Raikova ◽  
Hristo Aladjov ◽  
Jan Celichowski ◽  
Piotr Krutki
Keyword(s):  
Muscle Force ◽  
Cumulative Effect ◽  
Motor Units ◽  
Medial Gastrocnemius ◽  
Size Principle ◽  
Firing Patterns ◽  
Force Modeling ◽  
The Individual ◽  
Whole Muscle ◽  
Medial Gastrocnemius Muscle

Muscle force is due to the cumulative effect of repetitively contracting motor units (MUs). To simulate the contribution of each MU to whole muscle force, an approach implemented in a novel computer program is proposed. The individual contraction of an MU (the twitch) is modeled by a 6-parameter analytical function previously proposed; the force of one MU is a sum of its contractions due to an applied stimulation pattern, and the muscle force is the sum of the active MUs. The number of MUs, the number of slow, fast-fatigue-resistant, and fast-fatigable MUs, and their six parameters as well as a file with stimulation patterns for each MU are inputs for the developed software. Different muscles and different firing patterns can be simulated changing the input data. The functionality of the program is illustrated with a model consisting of 30 MUs of rat medial gastrocnemius muscle. The twitches of these MUs were experimentally measured and modeled. The forces of the MUs and of the whole muscle were simulated using different stimulation patterns that included different regular, irregular, synchronous, and asynchronous firing patterns of MUs. The size principle of MUs for recruitment and derecruitment was also demonstrated using different stimulation paradigms.

Activation of type-identified motor units during centrally evoked contractions in the cat medial gastrocnemius muscle. III. Muscle-unit force modulation

1996 ◽  
Vol 75 (1) ◽  
pp. 51-59 ◽  
Author(s):  
K. E. Tansey ◽  
A. K. Yee ◽  
B. R. Botterman
Keyword(s):  
Firing Rate ◽  
Motor Unit ◽  
Muscle Force ◽  
Motor Units ◽  
Medial Gastrocnemius ◽  
Rate Variation ◽  
Unit Force ◽  
Rate Modulation ◽  
Force Modulation ◽  
Whole Muscle

1. The aim of this study was to examine the extent of muscle-unit force modulation due to motoneuron firing-rate variation in type-identified motor units of the cat medial gastrocnemius (MG) muscle, and to investigate the contribution of muscle-unit force modulation to whole-muscle force regulation. The motoneuron discharge patterns recorded from 8 pairs of motor units during 12 smoothly graded muscle contractions evoked by stimulation of the mesencephalic locomotor region (MLR) were used to reactivate those units in isolation to estimate what their force profiles would have been like during the evoked whole-muscle contractions. 2. For most motor units, muscle-unit force modulation was similar to motoneuron firing-rate modulation, in that muscle-unit force increased over a limited range (120-600 g) of increasing whole-muscle tension and was then maintained at a near maximal (> 70%) output level as muscle force continued to rise. Most muscle units also decreased their force outputs over a slightly larger range of declining whole-muscle force before relaxing. This second finding was best explained by the counterclockwise hysteresis recorded in the motor units' frequency-tension (f-t) relationships. 3. In those instances when whole-muscle force fluctuated just above the recruitment threshold of a motor unit, a substantial percentage (10-25%) of the change in whole-muscle force could be accounted for by force modulation in that motor unit alone. This finding suggested that few motor units in the pool were simultaneously simultaneously undergoing force modulation. To evaluate this possibility, the extent of parallel muscle-unit force modulation within the 8 pairs of simultaneously active motor units was evaluated. As with parallel motoneuron firing-rate modulation, the extent of parallel muscle-unit force modulation was limited to unit pairs of the same physiological type and recruitment threshold. In several instances, pairs of motor units displayed parallel motoneuron firing-rate modulation but did not show parallel muscle-unit force modulation because of the nature of the motor units' f-t relationships. 4. The limited extent of parallel muscle-unit force modulation seen in these experiments implies that the major strategy for force modulation in the cat MG muscle, involving contractions estimated to reach 30-40% of maximum, may be motor-unit recruitment rather than motor-unit firing-rate variation with resulting force modulation. Given, however, that the majority of motor units are already recruited at these output levels (< 40%), it is proposed that motor-unit firing-rate variation with resulting force modulation may take over as the major muscle force modulating strategy at higher output levels.

scholarly journals A model of the rat medial gastrocnemius muscle based on inputs to motoneurons and on an algorithm for prediction of the motor unit force

2018 ◽  
Vol 120 (4) ◽  
pp. 1973-1987 ◽  
Author(s):  
R. Raikova ◽  
J. Celichowski ◽  
S. Angelova ◽  
P. Krutki
Keyword(s):  
Motor Unit ◽  
Input Data ◽  
Gastrocnemius Muscle ◽  
Muscle Force ◽  
Motor Units ◽  
Contractile Properties ◽  
Medial Gastrocnemius ◽  
Physiological Data ◽  
Excitation Signal ◽  
Medial Gastrocnemius Muscle

The muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties. During movements, MUs develop unfused tetani, which result from summation of twitch-shape responses to individual stimuli, which are variable in amplitude and duration. The aim of the study was to develop a realistic muscle model that would integrate previously developed models of MU contractions and an algorithm for the prediction of tetanic forces. The proposed model of rat medial gastrocnemius muscle is based on physiological data: excitability and firing frequencies of motoneurons, contractile properties, and the number and proportion of MUs in the muscle. The MU twitches were modeled by a six-parameter analytical function. The excitability of motoneurons was modeled according to a distribution of their rheobase currents measured experimentally. Processes of muscle force regulation were modeled according to a common drive hypothesis. The excitation signal to motoneurons was modeled by two form types: triangular and trapezoid. The discharge frequencies of MUs, calculated individually for each MU, corresponded to those recorded for rhythmic firing of motoneurons. The force of the muscle was calculated as the sum of all recruited MUs. Participation of the three types of MUs in the developed muscle force was presented at different levels of the excitation signal to motoneurons. The model appears highly realistic and open for input data from various skeletal muscles with different compositions of MU types. The results were compared with three other models with different distribution of the input parameters.NEW & NOTEWORTHY The proposed mathematical model of rat medial gastrocnemius muscle is highly realistic because it is based strictly on experimentally determined motor unit contractile parameters and motoneuron properties. It contains the actual number and proportion of motor units and takes into consideration their different contributions to the whole muscle force, depending on the level of the excitation signal. The model is open for input data from other muscles, and additional physiological parameters can also be included.

scholarly journals Effect of synchronization of firings of different motor unit types on the force variability in a model of the rat medial gastrocnemius muscle

2020 ◽  
Author(s):  
Rositsa Raikova ◽  
Vessela Krasteva ◽  
Piotr Krutki ◽  
Hanna Drzymała-Celichowska ◽  
Katarzyna Kryściak ◽  
...  
Keyword(s):  
Root Mean Square ◽  
Gastrocnemius Muscle ◽  
Motor Units ◽  
Medial Gastrocnemius ◽  
Force Variability ◽  
Mean Square ◽  
Synchronization Index ◽  
The Mean ◽  
Whole Muscle ◽  
Medial Gastrocnemius Muscle

AbstractOscillations of muscle force, observed as physiological tremors, rely upon the synchronized firings of active motor units (MUs). This study aimed to investigate the effects of synchronizing the firings of three types of MUs on force development using a mathematical model of the rat medial gastrocnemius muscle. The model was designed based on the actual proportion and physiological properties of MUs and motoneurons innervating the muscle. The isometric muscle and MU forces were simulated by a model predicting non-synchronized firing of a pool of 57 MUs (including eight slow, 23 fast resistant to fatigue, and 26 fast fatigable) to ascertain a maximum excitatory signal when all MUs were recruited into the contraction. The mean firing frequency of each MU depended upon the twitch contraction time, whereas the recruitment order was determined according to increasing forces (the size principle). The synchronization of firings of individual MUs was simulated using four different modes and inducing the synchronization of firings within three time windows (± 2, ± 4, and ± 6 ms) for four different combinations of MUs. The synchronization was estimated using two parameters, the correlation coefficient and the cross-interval synchronization index. The four scenarios of synchronization increased the values of the root-mean-square, range, and maximum force in correlation with the increase of the time window. Greater synchronization index values resulted in higher root-mean-square, range, and maximum of force outcomes for all MU types as well as for the whole muscle output; however, the mean spectral frequency of the forces decreased, whereas the mean force remained nearly unchanged. The range of variability and the root-mean-square of forces were higher for fast MUs than for slow MUs; meanwhile, the relative values of these parameters were highest for slow MUs, indicating their important contribution to muscle tremor, especially during weak contractions.Author summaryThe synchronization of firings of motor units (MUs), the smallest functional elements of skeletal muscle increases fluctuations in muscle force, known as physiological tremor, which can disturb high-precision movements. In this study, we adopted a recently proposed muscle model consisting of MUs of three different types (fast fatigable, fast resistant to fatigue, and slow) to study four different scenarios of MU synchronization during a steady level of excitatory input to motoneurons. The discharge patterns were synchronized between pairs of MUs by shifting in time individual pulses, which occurred within a short time interval, and a degree of synchronization was then estimated. The increased synchronization index resulted in increased force variability for all MU types as well as for the whole muscle output; however, the mean force levels remained nearly unchanged, whereas the frequencies of the force oscillations were decreased. The absolute range of force variability was higher for fast than for slow MUs, indicating their dominant influence on muscle tremor at strong contractions, but the highest relative increase in force variability was observed for synchronized slow MUs, indicating their significant contribution to tremor during weak contractions, in which only slow MUs are active.

Damage to different motor units from active lengthening of the medial gastrocnemius muscle of the cat

2002 ◽  
Vol 92 (3) ◽  
pp. 1104-1110 ◽  
Author(s):  
C. L. Brockett ◽  
D. L. Morgan ◽  
J. E. Gregory ◽  
U. Proske
Keyword(s):  
Gastrocnemius Muscle ◽  
Motor Units ◽  
Medial Gastrocnemius ◽  
Optimum Length ◽  
Time To Peak ◽  
Slow Twitch ◽  
Fast Twitch ◽  
Whole Muscle ◽  
Medial Gastrocnemius Muscle ◽  
Anesthetized Cat

Slow-twitch motor units in the medial gastrocnemius muscle of the anesthetized cat were found to have an average optimum length for active tension that was 0.8 ± 0.5 (SE) mm longer than the whole muscle optimum. For fast-twitch units (time to peak < 50 ms), the average optimum was 1.3 ± 0.3 mm shorter than the whole muscle optimum. After the muscle had been subjected to 10 stretches while maximally activated, beginning at the whole muscle optimum length, the optimum lengths of the 27 fast-twitch motor units shifted significantly further in the direction of longer muscle lengths (mean 4.3 ± 0.3 mm) than for the eight slow-twitch units (2.1 ± 0.4 mm). A shift in the muscle's length-tension relation was interpreted as being due to sarcomere disruption. Statistical analysis showed that a motor unit's optimum length for a contraction, relative to the whole muscle optimum, was a better indicator of the unit's susceptibility to damage from active lengthenings than was motor unit type.

Activity and motor unit size in partially denervated rat medial gastrocnemius

1994 ◽  
Vol 76 (6) ◽  
pp. 2663-2671 ◽  
Author(s):  
L. J. Einsiedel ◽  
A. R. Luff
Keyword(s):  
Motor Unit ◽  
Gastrocnemius Muscle ◽  
Motor Units ◽  
Ventral Root ◽  
Treadmill Walking ◽  
Medial Gastrocnemius ◽  
Unit Size ◽  
Partial Denervation ◽  
Motoneuron Activity ◽  
Medial Gastrocnemius Muscle

The aim of the study was to determine whether increased motoneuron activity induced by treadmill walking would alter the extent of motoneuron sprouting in the partially denervated rat medial gastrocnemius muscle. An extensive partial denervation was effected by unilateral section of the L5 ventral root, and it is very likely that all units remaining in the medial gastrocnemius were used in treadmill walking. Rats were trained for 1.5 h/day and after 14 days were walking at least 1 km/day. Motor unit characteristics were determined 24 days after the partial denervation and were compared with units from partially denervated control (PDC) animals and with units from normal (control) animals. In PDC rats, force developed by slow, fast fatigue-resistant, and fast intermediate-fatigable motor units increased substantially compared with control animals; that of fast-fatigable units did not increase. In partially denervated exercised animals, force developed by slow and fast-fatigue-resistant units showed no further increase, but fast-intermediate- and fast-fatigable units showed significant increases compared with those in PDC animals. The changes in force were closely paralleled by changes in innervation ratios. We concluded that neuronal activity is an important factor in determining the rate of motoneuron sprouting.

Fast-to-Slow Conversion Following Chronic Low-Frequency Activation of Medial Gastrocnemius Muscle in Cats. II. Motoneuron Properties

1997 ◽  
Vol 77 (5) ◽  
pp. 2605-2615 ◽  
Author(s):  
John B. Munson ◽  
Robert C. Foehring ◽  
Lorne M. Mendell ◽  
Tessa Gordon
Keyword(s):  
Gastrocnemius Muscle ◽  
Low Frequency ◽  
Motor Units ◽  
Input Resistance ◽  
Medial Gastrocnemius ◽  
Excitatory Postsynaptic Potential ◽  
Chronic Stimulation ◽  
General Hypothesis ◽  
Slow Type ◽  
Medial Gastrocnemius Muscle

Munson, John B., Robert C. Foehring, Lorne M. Mendell, and Tessa Gordon. Fast-to-slow conversion following chronic low-frequency activation of medial gastrocnemius muscle in cats. II. Motoneuron properties. J. Neurophysiol. 77: 2605–2615, 1997. Chronic stimulation (for 2–3 mo) of the medial gastrocnemius (MG) muscle nerve by indwelling electrodes renders the normally heterogeneous MG muscle mechanically and histochemically slow (type SO). We tested the hypothesis that motoneurons of MG muscle thus made type SO by chronic stimulation would also convert to slow phenotype. Properties of all single muscle units became homogeneously type SO (slowly contracting, nonfatiguing, nonsagging contraction during tetanic activation). Motoneuron electrical properties were also modified in the direction of type S, fatigue-resistant motor units. Two separate populations were identified (on the basis of afterhyperpolarization, rheobase, and input resistance) that likely correspond to motoneurons that had been fast (type F) or type S before stimulation. Type F motoneurons, although modified by chronic stimulation, were not converted to the type S phenotype, despite apparent complete conversion of their muscle units to the slow oxidative type (type SO). Muscle units of the former type F motor units were faster and/or more powerful than those of the former type S motor units, indicating some intrinsic regulation of motor unit properties. Experiments in which chronic stimulation was applied to the MG nerve cross-regenerated into skin yielded changes in motoneuron properties similar to those above, suggesting that muscle was not essential for the effects observed. Modulation of group Ia excitatory postsynaptic potential (EPSP) amplitude during high-frequency trains, which in normal MG motoneurons can be either positive or negative, was negative in 48 of 49 chronically stimulated motoneurons. Negative modulation is characteristic of EPSPs in motoneurons of most fatigue-resistant motor units. The general hypothesis of a periphery-to-motoneuron retrograde mechanism was supported, although the degree of control exerted by the periphery may vary: natural type SO muscle appears especially competent to modify motoneuron properties. We speculate that activity-dependent regulation of the neurotrophin-(NT) 4/5 in muscle plays an important role in controlling muscle and motoneuron properties.

Motor-unit recruitment in the decerebrate cat: several unit properties are equally good predictors of order

1991 ◽  
Vol 66 (4) ◽  
pp. 1127-1138 ◽  
Author(s):  
T. C. Cope ◽  
B. D. Clark
Keyword(s):  
Motor Unit ◽  
Rank Order ◽  
Motor Units ◽  
Afferent Input ◽  
Medial Gastrocnemius ◽  
Size Principle ◽  
Recruitment Pattern ◽  
Decerebrate Cat ◽  
Recruitment Order ◽  
Stimulation Of

1. Recruitment order was studied in pairs of motor units of the medial gastrocnemius (MG) muscle of decerebrate cats with the use of dual microelectrode recording from intact ventral root filaments. Excitation was provided by stretch of MG, stretch of synergists [lateral gastrocnemius (LG), plantaris (PL), and soleus (SOL) muscles] or electrical stimulation of the caudal cutaneous sural (CCS) nerve. Motor units were characterized by axonal conduction velocity (CV), tetanic tension (Pmax), twitch contraction time (CT), and fatigue index (FI). 2. Consistent with the recruitment pattern described by others, most often in relation to either CV or Pmax, the first unit of a pair to be recruited by MG stretch was typically the one with the lower CV and Pmax, and the higher FI and CT. The proportion of pairs that agreed in rank order of each property and recruitment order was as follows: for CT, 94%; for CV, 87%; for Pmax, 84%; and for FI, 75%. With a single marginal exception (CT vs. FI), no motor-unit property proved to be significantly better than the others at predicting recruitment (G test; P greater than 0.05). 3. In all 11 tested pairs containing one slow (type S) and one fast (type F) unit, the S was more easily recruited by stretch. Type F units divided into groups with high (type FR), low (type FF), and intermediate (type FInt) values for FI were recruited in order from FR to FInt to FF in 8/11 pairs. Thus our findings were similar to earlier demonstrations that recruitment proceeds in order by type. 4. Stretch of MG synergists usually recruited units in the same order as MG stretch. In two S-S pairs, recruitment order was switched with synergist stretch. 5. Stimulation of the CCS nerve was generally excitatory to the MG units sampled. Most unit pairs were recruited by CCS stimulation in the same order as by MG stretch, but, for 6 of 39 pairs, CCS stimulation switched the order produced by stretch. Thus, whereas sural afferent input can preferentially excite some units over others as suggested by Kanda et al., that effect is not widespread or selective for unit type under these conditions. 6. Assuming that all MG motor units cooperate as a single functional pool in homonymous stretch reflexes, we support others in concluding that a motoneuron's recruitment threshold is not strictly determined by its size. However, our data do not distinguish other schemes that predict recruitment order more accurately than the size principle.(ABSTRACT TRUNCATED AT 400 WORDS)

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