Brain Research, 171 (1979 349-354 © Flsevier/North-Holland Biomedical Press
349
Firing rate behavior of human motor units during isometric voluntary contraction: relation to unit size
A. WILLEM MONSTER Departments of Physiology and Rehabilitation Medicine, Temple University, Philadelphia, Pa. 19141 (u.s.A.)
(Accepted April 5th, 1979)
Changes in voluntary muscle force are brought about by adjustments in the recruitment and the firing rates of the motor unit population of the muscle. Over the normal functional range of contraction levels there is an orderly behavior of the units, both in terms of recruitment (size principleZ,7,1z), and, to a lesser extent13,18, in terms of adjustments in unit firing rates with changes in muscle force. Although controversy continues about the uniformity of motor unit responses for different types of inputs to different muscles (e.g. refs. 4 and 19), slowly changing voluntary isometric contractions appear to produce systematically organized and predictable unit behavior in forearm muscles 16. Strong support for the existence of systematic firing rate relationships among homonymous units during voluntary contraction is obtained when units are recorded in pairs15,16. It is found that for the large majority of units changes in firing rates among the two units of a pair (A fi and A fj for units i and j, respectively) are linearly related over the normal functional range of contraction levels16; (but see ref. 14). The trend in the slopes of the A fi-Af~ linear regression lines further suggests that larger size units increase their firing rates more rapidly, once recruited, than smaller units ~z. Size-dependent trends in unit behavior during volitional motoneuron pool activation in humans are, thus, consistent with data obtained by direct intracellular current stimulation of cat motoneurons 9; that is, large units (motoneurons with a low input impedance) have higher recruitment thresholds and greater firing rate gradients than smaller units (motoneurons with a higher input impedance). The extent of the size dependency in unit firing rate behavior during voluntary contraction of a human muscle is described here. The findings suggest an extension of the 'size principle '7 by concluding that not only the recruitment of a unit but also its firing rate behavior at levels of motoneuron pool excitability beyond that required for recruitment, is largely predictable on the basis of unit size. Fifty pairs of middle finger extensor digitorum communis (EDC) units from 6 normal male individuals of comparable strength were examined. Hand and forearm were stabilized with the EDC at the normal relaxed muscle length. Extensor force was measured isometrically at the tip of the first phalanx. Surface electrodes were placed
350
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Fig. 1. Firing rate responses of two EDC units (i and j) to changes in voluntary isometric force.
over the muscle to record the electromyogram (EMG). By manipulating two needle electrodes (Disa 13 K 83) two unit potentials were isolated so that they could be reliably and simultaneously recorded over a voluntary force range up to 500 g (approximately 50 To of maximum steady isometric forcel~). The strength of the voluntary contraction was slowly varied and mean firing rates were estimated for both units over successive one-second periods (Fig. 1). To minimize measurement errors due to adaptation on initiation of firing 1, units were discharged for a few seconds before rate measurements were made. Irregularity of firing was observed when a unit was discharging near recruitment threshold; any discharge interval > 2 5 ~o different from the running mean caused that one-second rate measurement to be discarded. Contractions lasted no longer than 30 sec, so as to prevent muscle fatigue; they were repeated 2 or 3 times at one-minute intervals. A unit's size was estimated by evoked response averaging of its twitch and/or surface E M G potential using the intramuscular unit potential as a trigger6,ZZ, 16. The results for 4 unit pairs from one experiment are shown in Fig. 2. Unit firing rates vary monotonically with total voluntary muscle force (Fig. 2A); the lines represent averages for a large number of data points that include both increasing and decreasing contractions. The arrows along the abscissa identify the thresholds of recruitment of the 8 units and the dashed line, marked F, represents the voluntary force level at which the force-firing rate gradient of each unit was determined in order to compose Fig. 3 (see below). The solid lines in Fig. 2B are the fi-fj relationships of the same 4 pairs (i.e. the firing rates of the two units of a pair are plotted against one another, rather than each against voluntary force, as in Fig. 2A). Individual measurement points (circles) are shown for 2 of the 4 pairs; pair 1, which consisted of two units of very similar force threshold and pair 2, two units which differed in force threshold
351
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Fig. 2. Mean firing rate behavior of 4 unit pairs (8 units) with slow changes in isometric voluntary force. The four pairs are identified by numbers (1), (2), (3) and (4). Arrows along the abscissa mark the (force) threshold of recruitment for each unit. The dashed line marks the force level (1~) at which gradient measurements were made on each unit to obtain the data in Fig. 3 ; A. Firing rates of the same units are replotted in B. The lowest threshold unit of a pair is in all cases called 'unit i' and is plotted along the abscissa. The fi--f~relationship is approximated for each pair by linear regression (solid lines), Measurement points are shown for pair I (circles) and 2 (triangles); open symbols mark decreasing contractions and filled symbols identify increasing contractions. by more than 200 g. The open symbols in Fig. 2B are measurements made during decreasing contractions and the filled symbols indicate increasing contractions. Note that: (1) the relationships are linear (more than 80 % of the unit pairs showed linear correlation coefficients >0.9); and (2)that the higher threshold (j) unit of each pair (plotted along the ordinate) increases its firing rate relatively more rapidly than the lower threshold (i) unit. Slope values for the linear regression lines in Fig. 2B were: 1.08, 1.75, 1.55, and 1.15 for pairs l, 2, 3, and 4, respectively. If the gradient value of the force-firing rate curve of each unit, at a given force level (~ = dashed line in Fig. 2A), is plotted against the unit's size, then a strong positive correlation between size and gradient is seen (Fig. 3). In interpreting the trend shown in Fig. 3, it is emphasized that the gradient values are all obtained at one force level (1~); this is necessary for a valid comparison among units, because the relationship between changes in total muscle force ( A F) and changes in motoneuron excitability (• E) varies with F (i.e. A f / % E = A f / A F x % F / A E ; A F / + E # constant). For instance, if gradient values of different units were compared at their respective recruitment force levels, then it would be concluded that larger units have smaller gradients than smaller units (e.g. ref. 3); however, this is more the result of the small number of units contributing to force production at the force levels at which small units are recruited, than of different sensitivity of different size units (motoneurons) to the same change in motoneuron pool excitability. It is the latter that is represented in Fig. 3. The choice of force level ~" influences the absolute values along the ordinate of Fig. 3 but this is arbitrary in terms of demonstrating the positive correlation between unit sizes and gradients; ~ was selected here so as to intersect as many force-firing rate curves as possible for the set of available data. For
352 .12
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Fig. 3. Relationships between the twitch size of a unit, obtained by spike-triggered averaging (16), and its firing rate-force gradient at ~" = 300 g of total voluntary force.
units j with recruitment threshold > F ( i . e . twitch size > 1 . 5 g; ref. 16, Fig. 4) the gradient at 1~ was estimated by extrapolating from its gradient at a higher force F' using the gradient values of a second unit i the firing rate of which was recorded over a force range that included both F and 1~' (i.e., grad i~j = regression slope j, i (from Fig. 2B) × grad l~i (from Fig. 2A). The observed linear rate changes among unit pairs (Fig. 2B) are interpreted as follows: if, during a change in voluntary effort, ak = induced change in synaptic drive of motoneuron pool input k and P~ = percentage synaptic connections of motoneuron i with input k (normalized, in some way, for density and spatial location on the cell) and Ci is the intrinsic 'firing rate-current' relationship of motoneuron i, then the rate change of unit i is Afi = Ci × {al × P1i @ az X pzi + . . . . }. This model makes numerous simplifying assumptions about the summation of different synaptic inputs and the nature of the cell population's 'firing rate-current' relationships. However, these assumptions are reasonable, based on presently available data and models (cf. refs. 8, 11 and 21). It follows from the above expression for • fi that the A fi-z~ fj relationship for paired units i and j can be linear only if either: (1) the P~ and P~ are the same for units i and j for k = 1, 2 . . . ; or (2) one input (e.g. am) strongly dominates the motoneuron pool's excitatory state under the conditions of the voluntary contraction experiment. In view of other data describing the consistency of the firing rate and recruitment behavior of homonymous units with different types of inputs modulating motoneuron pool excitability 2, it appears that (1) is the more likely of the two possibilities. If this is assumed, then it can be concluded that the range of gradient values for the units in Fig. 3 is closely related to the range of firing ratecurrent (Ci) values of the EDC motoneuron population. The remarkably wide range of
353 gradient values, as compared to that observed with constant current stimulation of cat gastrocnemius motoneurons (Fig. 3, ref. I0; Ci -- f-I), is attributed to a more selective sampling of large motoneurons in the animal study; close to the full range of unit sizes can be readily examined during voluntary contraction because of the size principle of recruitment. This (sampling bias) interpretation is supported by input impedance and fatigue resistance characteristics of the reported 1° gastrocnemius motoneuron sample as compared to the characteristics of the total population, reported by others 2°. Furthermore, whereas cellular mechanisms of firing rate regulation are likely to be quaBtatively the same, for different motoneuron pools in m a n y species (e.g. ref, 4) a number of experimental parameters, such as absolute cell size, cell geometry and type of activation, are potentially capable of producing quantitative differences in C~ values s. Inability to demonstrate in earlier human studiesla, 18 the correlation shown in Fig. 3 is attributed to: (1) sampling of an insufficient range of unit sizes; (2) non-paired recording (as a check on experimental artifacts such as cocontraction of other muscles which disturbs the force-firing rate curves, and transient effects such as gradual adaptation of the motoneuron firing rate with a 'steady' level of synaptic drive); (3) problems of unit size estimation because of a complex anatomical arrangement of unit-fibers; and (4) selection of less uniform muscles in terms of anatomy, unit types and diversity of functions served. Less consistent gradient-size relationships were obtained by us with the tibialis anterior (attributed to (3) and (4) above), and a virtual absence of gradient differences among units was found for the human soleus muscle (attributed to (1) and (3)). These relative differences among muscles are consistent with the metabolic and usage characteristics of their muscle fibers 17. In summary, the present experiment on extensor digitorum communis (EDC) m o t o r units suggests that, during voluntary contraction, systematic differences between different size E D C units exist not only for recruitment 16 but also for firing rate behavior. I f these differences are of synaptic origin or reflect intrinsic properties of the motoneuron cells themselves has not been established. Supported by N I H - N S 11574 N E U B
1 Baldissera, F. and Gustafsson, B., Firing behavior of a neurone model based on the after hyper. polarization conductance time course and algebraical summation. Adaptation and steady-state firing, Acta physiol, scan& 92 (1974) 27-47. 2 Clamann, H. P., Gillies, J. D. and Henneman, E., Effects of inhibitory inputs on critical firing level and rank order of motoneurons, J. Neltrophysiol., 37 (1974) 1350-1360. 3 Clark, R. W., Luschei, E. S. and Hoffman, D. S., Recruitment order, contractile characteristics and firing patterns of motor units in the temporalis muscle of monkeys, Exp. Neurol., 61 (1978) 31-52. 4 Davis, W. J., Functional significance of motoneuron size and soma position in swimmeret system of the lobster, 3". NeurophysioL, 34 (1971) 274-288. 5 Goldberg, L. J. and Defiler, B., Relationship among recruitment order, spike amplitude and twitch tension of single motor units in human masseter muscle, J. Neurophysiol., 40 (1978) 879-890. 6 Gydikov, A. and Kosarov, D., Volume conduction and the potentials from separate motor units in human muscle, Electromyography, 12 (1972) 127-147.
354 7 Henneman, E., Organization of the spinal cord. In V. B. Mountcastle (Ed.), Medical Physiology (12th edn.), Mosby, St. Louis, 1968, pp. 1717-1732. 8 Jack, J. B., Noble, D. and Tsien, R. W., Electrical Current Flow in Excitable Cells, Clarendon Press, Oxford, 1975. 9 Kernell, D., Input resistance, electrical excitability, and size of ventral horn cells in cat spinal cord, Science, 152 (1966) 1637-1640. 10 Kernell, D., Rhythmic properties of motoneurons innervating muscle fibers of different speed in gastrocnemius medialis of the cat, Brain Research, 160 (1979) 159-162. 11 Kernell, D. and Sjoholm, H., Repetitive impulse firing: comparison between neurone models based on 'voltage clamp equations' and spinal motorneurones, ,4cta physiol, scand., 87 (1973) 40-56. 12 Milner-Brown, H. S., Stein, R. B. and Yemm, R. S.,The orderly recruitment of human motor units during voluntary isometric contractions, J. Physiol. (Lond.), 230 (1973) 359-370. 13 Milner-Brown, H. S., Stein, R. B. and Yemm, R. S., Changes in firing rate of human motor units during linearly changing voluntary contractions, J. Physiol. (Lond.), 230 (1973) 371-390. 14 Monster, A. W., Two ranges in the firing rate response of volitionally activated low-threshold EDC motor units, Electroenceph. clin. neurophysiol., 17 (1977) 231-237. 15 Monster, A. W. and Chan, H., Firing rates of motor units during voluntary isometric contractions, Proc. Ann. Meet. Soc. Neurosci., Toronto, 1976, p. 184. 16 Monster, A. W. and Chan, H., Isometric force production by motor units of the extensor digitorum communis muscle in man, J. NeurophysioL, 40 (1977) 1432-1443. 17 Monster, A. W., Chan, H. and O'Connor, D., Activity patterns of human skeletal muscles: relation to muscle fiber type composition, Science, 200 (1978) 314-317. 18 Person, R. S. and Kudina, L. P., Discharge frequency and discharge pattern ot human motor units during voluntary contraction of muscle, Electroenceph. clin. NeurophysioL, 9 (1972) 471-483. 19 Stephens, J. A., Garnett, R. and Buller, N. P., Reversal of recruitment order of single motor units produced by cutaneous stimulation during voluntary contraction in man, Nature (Lond.), 272 (1978) 362-364. 20 Walmsley, B., Hodgson, J. A. and Burke, R. E., Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats, J. Neurophysiol., 41 (1978) 1203-1216. 21 Zucker, R. S., Theoretical implications of the size principle ofmotoneurone recruitment, J. theor. Biol., 38 (1973) 587-596.
349
Firing rate behavior of human motor units during isometric voluntary contraction: relation to unit size
A. WILLEM MONSTER Departments of Physiology and Rehabilitation Medicine, Temple University, Philadelphia, Pa. 19141 (u.s.A.)
(Accepted April 5th, 1979)
Changes in voluntary muscle force are brought about by adjustments in the recruitment and the firing rates of the motor unit population of the muscle. Over the normal functional range of contraction levels there is an orderly behavior of the units, both in terms of recruitment (size principleZ,7,1z), and, to a lesser extent13,18, in terms of adjustments in unit firing rates with changes in muscle force. Although controversy continues about the uniformity of motor unit responses for different types of inputs to different muscles (e.g. refs. 4 and 19), slowly changing voluntary isometric contractions appear to produce systematically organized and predictable unit behavior in forearm muscles 16. Strong support for the existence of systematic firing rate relationships among homonymous units during voluntary contraction is obtained when units are recorded in pairs15,16. It is found that for the large majority of units changes in firing rates among the two units of a pair (A fi and A fj for units i and j, respectively) are linearly related over the normal functional range of contraction levels16; (but see ref. 14). The trend in the slopes of the A fi-Af~ linear regression lines further suggests that larger size units increase their firing rates more rapidly, once recruited, than smaller units ~z. Size-dependent trends in unit behavior during volitional motoneuron pool activation in humans are, thus, consistent with data obtained by direct intracellular current stimulation of cat motoneurons 9; that is, large units (motoneurons with a low input impedance) have higher recruitment thresholds and greater firing rate gradients than smaller units (motoneurons with a higher input impedance). The extent of the size dependency in unit firing rate behavior during voluntary contraction of a human muscle is described here. The findings suggest an extension of the 'size principle '7 by concluding that not only the recruitment of a unit but also its firing rate behavior at levels of motoneuron pool excitability beyond that required for recruitment, is largely predictable on the basis of unit size. Fifty pairs of middle finger extensor digitorum communis (EDC) units from 6 normal male individuals of comparable strength were examined. Hand and forearm were stabilized with the EDC at the normal relaxed muscle length. Extensor force was measured isometrically at the tip of the first phalanx. Surface electrodes were placed
350
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',
;'"~
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"r':,:~!-
::r:,-'.!":'-=T:7~'~ "'~"."-"~"'--~_i_
VOLUNTARY FORCE ( i n GRAMS) I-,q-.--- I0 SECONDS
Fig. 1. Firing rate responses of two EDC units (i and j) to changes in voluntary isometric force.
over the muscle to record the electromyogram (EMG). By manipulating two needle electrodes (Disa 13 K 83) two unit potentials were isolated so that they could be reliably and simultaneously recorded over a voluntary force range up to 500 g (approximately 50 To of maximum steady isometric forcel~). The strength of the voluntary contraction was slowly varied and mean firing rates were estimated for both units over successive one-second periods (Fig. 1). To minimize measurement errors due to adaptation on initiation of firing 1, units were discharged for a few seconds before rate measurements were made. Irregularity of firing was observed when a unit was discharging near recruitment threshold; any discharge interval > 2 5 ~o different from the running mean caused that one-second rate measurement to be discarded. Contractions lasted no longer than 30 sec, so as to prevent muscle fatigue; they were repeated 2 or 3 times at one-minute intervals. A unit's size was estimated by evoked response averaging of its twitch and/or surface E M G potential using the intramuscular unit potential as a trigger6,ZZ, 16. The results for 4 unit pairs from one experiment are shown in Fig. 2. Unit firing rates vary monotonically with total voluntary muscle force (Fig. 2A); the lines represent averages for a large number of data points that include both increasing and decreasing contractions. The arrows along the abscissa identify the thresholds of recruitment of the 8 units and the dashed line, marked F, represents the voluntary force level at which the force-firing rate gradient of each unit was determined in order to compose Fig. 3 (see below). The solid lines in Fig. 2B are the fi-fj relationships of the same 4 pairs (i.e. the firing rates of the two units of a pair are plotted against one another, rather than each against voluntary force, as in Fig. 2A). Individual measurement points (circles) are shown for 2 of the 4 pairs; pair 1, which consisted of two units of very similar force threshold and pair 2, two units which differed in force threshold
351
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Fig. 2. Mean firing rate behavior of 4 unit pairs (8 units) with slow changes in isometric voluntary force. The four pairs are identified by numbers (1), (2), (3) and (4). Arrows along the abscissa mark the (force) threshold of recruitment for each unit. The dashed line marks the force level (1~) at which gradient measurements were made on each unit to obtain the data in Fig. 3 ; A. Firing rates of the same units are replotted in B. The lowest threshold unit of a pair is in all cases called 'unit i' and is plotted along the abscissa. The fi--f~relationship is approximated for each pair by linear regression (solid lines), Measurement points are shown for pair I (circles) and 2 (triangles); open symbols mark decreasing contractions and filled symbols identify increasing contractions. by more than 200 g. The open symbols in Fig. 2B are measurements made during decreasing contractions and the filled symbols indicate increasing contractions. Note that: (1) the relationships are linear (more than 80 % of the unit pairs showed linear correlation coefficients >0.9); and (2)that the higher threshold (j) unit of each pair (plotted along the ordinate) increases its firing rate relatively more rapidly than the lower threshold (i) unit. Slope values for the linear regression lines in Fig. 2B were: 1.08, 1.75, 1.55, and 1.15 for pairs l, 2, 3, and 4, respectively. If the gradient value of the force-firing rate curve of each unit, at a given force level (~ = dashed line in Fig. 2A), is plotted against the unit's size, then a strong positive correlation between size and gradient is seen (Fig. 3). In interpreting the trend shown in Fig. 3, it is emphasized that the gradient values are all obtained at one force level (1~); this is necessary for a valid comparison among units, because the relationship between changes in total muscle force ( A F) and changes in motoneuron excitability (• E) varies with F (i.e. A f / % E = A f / A F x % F / A E ; A F / + E # constant). For instance, if gradient values of different units were compared at their respective recruitment force levels, then it would be concluded that larger units have smaller gradients than smaller units (e.g. ref. 3); however, this is more the result of the small number of units contributing to force production at the force levels at which small units are recruited, than of different sensitivity of different size units (motoneurons) to the same change in motoneuron pool excitability. It is the latter that is represented in Fig. 3. The choice of force level ~" influences the absolute values along the ordinate of Fig. 3 but this is arbitrary in terms of demonstrating the positive correlation between unit sizes and gradients; ~ was selected here so as to intersect as many force-firing rate curves as possible for the set of available data. For
352 .12
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Fig. 3. Relationships between the twitch size of a unit, obtained by spike-triggered averaging (16), and its firing rate-force gradient at ~" = 300 g of total voluntary force.
units j with recruitment threshold > F ( i . e . twitch size > 1 . 5 g; ref. 16, Fig. 4) the gradient at 1~ was estimated by extrapolating from its gradient at a higher force F' using the gradient values of a second unit i the firing rate of which was recorded over a force range that included both F and 1~' (i.e., grad i~j = regression slope j, i (from Fig. 2B) × grad l~i (from Fig. 2A). The observed linear rate changes among unit pairs (Fig. 2B) are interpreted as follows: if, during a change in voluntary effort, ak = induced change in synaptic drive of motoneuron pool input k and P~ = percentage synaptic connections of motoneuron i with input k (normalized, in some way, for density and spatial location on the cell) and Ci is the intrinsic 'firing rate-current' relationship of motoneuron i, then the rate change of unit i is Afi = Ci × {al × P1i @ az X pzi + . . . . }. This model makes numerous simplifying assumptions about the summation of different synaptic inputs and the nature of the cell population's 'firing rate-current' relationships. However, these assumptions are reasonable, based on presently available data and models (cf. refs. 8, 11 and 21). It follows from the above expression for • fi that the A fi-z~ fj relationship for paired units i and j can be linear only if either: (1) the P~ and P~ are the same for units i and j for k = 1, 2 . . . ; or (2) one input (e.g. am) strongly dominates the motoneuron pool's excitatory state under the conditions of the voluntary contraction experiment. In view of other data describing the consistency of the firing rate and recruitment behavior of homonymous units with different types of inputs modulating motoneuron pool excitability 2, it appears that (1) is the more likely of the two possibilities. If this is assumed, then it can be concluded that the range of gradient values for the units in Fig. 3 is closely related to the range of firing ratecurrent (Ci) values of the EDC motoneuron population. The remarkably wide range of
353 gradient values, as compared to that observed with constant current stimulation of cat gastrocnemius motoneurons (Fig. 3, ref. I0; Ci -- f-I), is attributed to a more selective sampling of large motoneurons in the animal study; close to the full range of unit sizes can be readily examined during voluntary contraction because of the size principle of recruitment. This (sampling bias) interpretation is supported by input impedance and fatigue resistance characteristics of the reported 1° gastrocnemius motoneuron sample as compared to the characteristics of the total population, reported by others 2°. Furthermore, whereas cellular mechanisms of firing rate regulation are likely to be quaBtatively the same, for different motoneuron pools in m a n y species (e.g. ref, 4) a number of experimental parameters, such as absolute cell size, cell geometry and type of activation, are potentially capable of producing quantitative differences in C~ values s. Inability to demonstrate in earlier human studiesla, 18 the correlation shown in Fig. 3 is attributed to: (1) sampling of an insufficient range of unit sizes; (2) non-paired recording (as a check on experimental artifacts such as cocontraction of other muscles which disturbs the force-firing rate curves, and transient effects such as gradual adaptation of the motoneuron firing rate with a 'steady' level of synaptic drive); (3) problems of unit size estimation because of a complex anatomical arrangement of unit-fibers; and (4) selection of less uniform muscles in terms of anatomy, unit types and diversity of functions served. Less consistent gradient-size relationships were obtained by us with the tibialis anterior (attributed to (3) and (4) above), and a virtual absence of gradient differences among units was found for the human soleus muscle (attributed to (1) and (3)). These relative differences among muscles are consistent with the metabolic and usage characteristics of their muscle fibers 17. In summary, the present experiment on extensor digitorum communis (EDC) m o t o r units suggests that, during voluntary contraction, systematic differences between different size E D C units exist not only for recruitment 16 but also for firing rate behavior. I f these differences are of synaptic origin or reflect intrinsic properties of the motoneuron cells themselves has not been established. Supported by N I H - N S 11574 N E U B
1 Baldissera, F. and Gustafsson, B., Firing behavior of a neurone model based on the after hyper. polarization conductance time course and algebraical summation. Adaptation and steady-state firing, Acta physiol, scan& 92 (1974) 27-47. 2 Clamann, H. P., Gillies, J. D. and Henneman, E., Effects of inhibitory inputs on critical firing level and rank order of motoneurons, J. Neltrophysiol., 37 (1974) 1350-1360. 3 Clark, R. W., Luschei, E. S. and Hoffman, D. S., Recruitment order, contractile characteristics and firing patterns of motor units in the temporalis muscle of monkeys, Exp. Neurol., 61 (1978) 31-52. 4 Davis, W. J., Functional significance of motoneuron size and soma position in swimmeret system of the lobster, 3". NeurophysioL, 34 (1971) 274-288. 5 Goldberg, L. J. and Defiler, B., Relationship among recruitment order, spike amplitude and twitch tension of single motor units in human masseter muscle, J. Neurophysiol., 40 (1978) 879-890. 6 Gydikov, A. and Kosarov, D., Volume conduction and the potentials from separate motor units in human muscle, Electromyography, 12 (1972) 127-147.
354 7 Henneman, E., Organization of the spinal cord. In V. B. Mountcastle (Ed.), Medical Physiology (12th edn.), Mosby, St. Louis, 1968, pp. 1717-1732. 8 Jack, J. B., Noble, D. and Tsien, R. W., Electrical Current Flow in Excitable Cells, Clarendon Press, Oxford, 1975. 9 Kernell, D., Input resistance, electrical excitability, and size of ventral horn cells in cat spinal cord, Science, 152 (1966) 1637-1640. 10 Kernell, D., Rhythmic properties of motoneurons innervating muscle fibers of different speed in gastrocnemius medialis of the cat, Brain Research, 160 (1979) 159-162. 11 Kernell, D. and Sjoholm, H., Repetitive impulse firing: comparison between neurone models based on 'voltage clamp equations' and spinal motorneurones, ,4cta physiol, scand., 87 (1973) 40-56. 12 Milner-Brown, H. S., Stein, R. B. and Yemm, R. S.,The orderly recruitment of human motor units during voluntary isometric contractions, J. Physiol. (Lond.), 230 (1973) 359-370. 13 Milner-Brown, H. S., Stein, R. B. and Yemm, R. S., Changes in firing rate of human motor units during linearly changing voluntary contractions, J. Physiol. (Lond.), 230 (1973) 371-390. 14 Monster, A. W., Two ranges in the firing rate response of volitionally activated low-threshold EDC motor units, Electroenceph. clin. neurophysiol., 17 (1977) 231-237. 15 Monster, A. W. and Chan, H., Firing rates of motor units during voluntary isometric contractions, Proc. Ann. Meet. Soc. Neurosci., Toronto, 1976, p. 184. 16 Monster, A. W. and Chan, H., Isometric force production by motor units of the extensor digitorum communis muscle in man, J. NeurophysioL, 40 (1977) 1432-1443. 17 Monster, A. W., Chan, H. and O'Connor, D., Activity patterns of human skeletal muscles: relation to muscle fiber type composition, Science, 200 (1978) 314-317. 18 Person, R. S. and Kudina, L. P., Discharge frequency and discharge pattern ot human motor units during voluntary contraction of muscle, Electroenceph. clin. NeurophysioL, 9 (1972) 471-483. 19 Stephens, J. A., Garnett, R. and Buller, N. P., Reversal of recruitment order of single motor units produced by cutaneous stimulation during voluntary contraction in man, Nature (Lond.), 272 (1978) 362-364. 20 Walmsley, B., Hodgson, J. A. and Burke, R. E., Forces produced by medial gastrocnemius and soleus muscles during locomotion in freely moving cats, J. Neurophysiol., 41 (1978) 1203-1216. 21 Zucker, R. S., Theoretical implications of the size principle ofmotoneurone recruitment, J. theor. Biol., 38 (1973) 587-596.
