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Journal of Motor Behavior
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Variation of Isometric Response Force in the Rat Andrew B. Slifkina; Suzanne H. Mitchella; Jasper Brenera a State University of New York, Stony Brook, USA Online publication date: 14 July 2010
To cite this Article Slifkin, Andrew B. , Mitchell, Suzanne H. and Brener, Jasper(1995) 'Variation of Isometric Response
Force in the Rat', Journal of Motor Behavior, 27: 4, 375 — 381 To link to this Article: DOI: 10.1080/00222895.1995.9941725 URL: http://dx.doi.org/10.1080/00222895.1995.9941725
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Journal of Motor Behavior, 1995, Vol. 27, No. 4, 375-381
Variation of Isometric Response Force in the Rat
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Andrew B. Slifkin Suzanne H. Mitchell and Jasper Brener State University of New York at Stony Brook
ABSTRACT. Hungry, unrestrained rats (N= 7)were rewarded for pressing a response beam in excess of 11 different force requirements. Changes in peak force production as a function of peak force requirement were examined by analyses of the first four moments of distributions of peak response forces: constant error,
sures: constant error, the within-subject standard deviation, and the coefficient of variation for peak force (the standard deviation divided by the mean). When humans are required to generate monoarticulate isometric forces, mean peak force increases as a linear function of the requirement (e.g., Mintz & Notteman, 1965) but the slope of the line usually is less than one and the y intercept is greater than zero. This function reflects variations in the constant error, which is positive at low requirements, has been projected to reach zero at 50% maximum voluntary peak force, and becomes negative thereafter (Newell, Carlton, & Hancock, 1984). This range efecf (e.g., Weiss, 1955) may reflect the lower and upper biomechanical limits on force production imposed by the engaged effector system. Thus, overshooting at the lower force requirement may result from difficulty in counteracting the inertia of the limb, whereas undershooting at the upper requirement may be a result of the proximity of the requirement to the subject's maximum voluntary peak force. Across a full range of force requirements, the within-subject standard deviation of peak response force increases according to a negatively accelerating exponential function (e.g., Newell & Carlton, 1985; Newell et al., 1984; Sherwood, Schmidt, & Walter, 1988'). Therefore, peak force variability is not proportional to mean peak force: Coefficients of variation decline as a negatively accelerating function of mean peak force. As the range of peak forces becomes truncated by the increasing proximity of the force requirement (environmental constraint) to the upper biome-
the within-subject standard deviation, skewness, and kurtosis. Results were similar to those previously obtained with human subjects: Constant error was positive at low and negative at high force requirements, the within-subject standard deviation increased as a negatively accelerating function of force requirement, and skewness and kurtosis were positive at low force requirements and decreased to negative values at the highest increments. Additional analyses of response kinetics indicated that rats, like humans, meet increasing force requirements by altering the rate of rise of force. The performance similarities suggest that common processes are engaged by the human and rat motor control systems to solve the problem of generating forces that are appropriate to the prevailing environmental constraints.
Key words: isometric, kinetic, peak force, rats, variability
S
tudies of force control typically require subjects to adjust the peak force of their responses to peak force targets that are presented to them. The extent to which response forces meet target requirements is reflected by the distribution of peak response forces compiled from repeated trials under the same peak force requirement. The characteristics of these distributions, which have been shown to vary systematically as a function of force requirement (Carlton & Newell, 1993),can be viewed as the products of organismic and environmental constraints (e.g.. Newell, 1986; Riccio, 1993). As such, they are potentially useful in revealing factors that limit ability to produce forces of different magnitudes. Inferences regarding factors that influence force production have typically been based on three dependent mea-
Correspondence address: Jasper Brener, Psychology Department, SUNY at Stony Brook, Stony Brook, NY I 1794-2SOO.
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A. 6. Slifkin, S. H. Mitchell, & J. Brener
chanical constraint (intrinsic constraint: maximum voluntary peak force), relative variability (the coefficient of variation) declines. The operation of the upper constraint on the within-subject standard deviation function is evident at 65% maximum voluntary peak force, as it essentially ceases to increase with further increases in target levels (e.g. Newell & Carlton, 1985; Newell et al., 1984; Sherwood et al., 1988). Because these functions were found to be nonlinear, the impulse variability and speed-accuracy theorieswhich predict that increases in force variability should be linear and proportional to increases in the force requirement (viz., Schmidt, Zelaznik, Hawkins, Frank. & Quinn, 1979Fwere modified (e.g., Schmidt, 1988). Although a brief report (Filion. Fowler. & Notterman. 1969) reported similarities for humans and rhesus monkeys in relative variability? as a function of peak force requirement, to our knowledge no other examinations of force variability in animals other than humans have been reported. With a view to comparing the processes of force production in the rat with those that have been demonstrated in the human, the current report examines changes in distributions of isometric peak response forces as a function of peak force requirements in hungry rats. The procedure employed, which is analogous to the Method of Adjustment used in psychophysical and human force variability studies (Newell et al., 1984), allowed food-deprived, unrestrained rats to earn food rewards by pressing a rigid response beam in excess of experimenter-specified force criteria. According to Newell and Hancock (1984), the first two moments (the constant error and within-subject standard deviation) of a distribution of response forces do not, in many cases, provide a full description of motor performance. When these statistics are reported alone, the reader is left to assume that the population from which the sample statistics are drawn is normally distributed. Information regarding the third (skewness) and fourth (kurtosis) moments is needed for a more complete description of performance (Newell & Hancock. 1984). Taking account of changes in kurtosis and skewness may aid in describing variation in ability as a function of task difficulty. Skewness or the degree of a distribution's asymmetry is positive when the range of scores above the median is greater than the range of scores below the median. When the range of scores below the median is greater than the range above the median, skewness is negative. A normal or symmetrical distribution takes on a skewness value of zero. Kurtosis represents a distribution's peakedness; highly peaked or leptokurtic distributions take on positive values and flatter than normal or platykurtic distributions take on negative values. The kurtosis value associated with the peakedness of a normal distribution is zero. Failure to report skewness and kurtosis in the motor control, and especially the force variability, literature is surprising because systematic shifts in these measures as a function of increasing force requirements were present in data published over a century ago by Fullerton and Catell
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( 1892). Following analyses of Fullerton and Catell's data, Newell et al., (1984, p. 148) provided predictions of changes in skewness and kurtosis as a function of force requirement. In a subsequent report, Newell and Carlton (1985, p. 236) found similarities between their data and those of Fullerton and Catell: "Namely, at low force levels there is positive skewness and a modicum of leptokurticness with the distribution approximating normality at 50% of maximum, leading to negative skewness at high force levels with a modicum of platykurticness." These observations could imply that the intrinsic and environmental constraints exert an equal influence at the 50% maximum requirement so that the distribution is symmetrical, with skewness taking on a value of zero. It is also likely that the kurtosis function is influenced by these force production limits: Forces become more broadly distributed as the distance increases between easy-to-produce response forces and those necessary to meet higher force requirements. A common assumption has been that characteristics of responses are normally distributed across levels of task difficulty and that this property of the distribution results from the intrinsic stochasticity of the measured characteristic (e.g., Fitts, 1954). However, observations of systematic changes in skewness and kurtosis (Newell & Carlton, 1985; Newell et al., 1984; Newell, Carlton, Kim, & Chung, 1993; Newell & Hancock, 1984) as a function of task requirement indicate that these variations in the form of the distribution are determined by potentially identifiable intrinsic and environmental constraints (experimental contingencies) on force production. Therefore, a more complete view of the factors influencing force production may be provided by taking account of all four moments of force distributions. and, accordingly, all four moments were assessed in the analyses undertaken here.
Method Subjects
Seven naive male black-hooded rats weighing between 364 g and 423 g (M = 399 g) at the start of the experiment were drawn from the colony maintained in the psychology department at the University of Hull. All animals were maintained at between 85% and 90% of their preexperimental body weights by supplemental feeding with standard lab chow following each experimental session. Apparatus
The experimental environment used in this experiment was identical to that previously described by Brener and Mitchell (1989) and Mitchell and Brener (1991). It consisted of a Plexiglas box, 18 cm (wide) x 28.3 cm (deep) x 16 cm (high). Three aluminum force beams, designed to the specifications given by Notterman and Mintz ( 1965). were mounted on the front panel. In this experiment. only the leftmost beam was active: Responses on the central and right-hand beam had no effect and were not recorded. Journal of Motor Behavior
Response Force in the Rat
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Force applied to the beam was sampled continuously at 100 Hz by an 8-bit analog-to-digital ( A D )converter by a Cromemco Z-2D microcomputer. Force was measured in units of 0.625 g. We programmed the computer to calculate and record the response parameters described below and to apply the reinforcement criterion. Note that only beam presses that exceeded a peak force of 2.50 g, designated as the recognition criterion. were classified as responses. We adopted this measure to distinguish the animals' activities from spurious signals induced by, for example, amplifier drift. If the force criterion for reinforcement was achieved during the course of the beam press. then on beam release, a fixed amount of liquid food was delivered into a small food cup directly below the beam. This liquid food consisted of one part Build-Up, a commercially available dietary supplement manufactured by Carnation, diluted with three parts water. The volume of each food reward was 33.33 pL and had an energy value of 37 calories (155 J). Simultaneously with each food delivery, a 30-ms click was sounded in the box. Feedback (click and food) was delayed until response termination. This prevented the animals from using external feedback to regulate force production (e.g., Schmidt, 1988). The food delivery mechanism consisted of a 10-mL glass syringe mounted in a Plexiglas assembly and driven by a stepper motor. This device was positioned outside the soundattenuated chamber in which the experimental box was housed. When conditions for reinforcement had been fulfilled, the computer delivered a series of pulses to the stepper motor, which resulted in the delivery of a fixed amount of liquid food to the food cup. Procedi4r-r During training, only responses made at the left beam with a peak force greater than 5.625 g were reinforced. No response shaping was employed. Instead, rats were simply placed in the experimental chamber when the experimental contingencies were operating. Rats were said to have learned the beam-pressing response when they earned 100 reinforcers within 60 min. Throughout the experiment, sessions were terminated when 100 reinforcers were earned or 60 niin had passed. Rats were allowed to acquire the beam-pressing response for 16 consecutive days (sessions), during which they earned food for responses exceeding the training criterion of 5.625 g. On the next day, and on every 7th day thereafter, the peak force requirement was augmented by an additional 5 g. This continued until rats had experienced 10 upward shifts in the peak force requirement. Thus, including the response acquisition phase, a total of 1 1 peak force criteria, ranging from 5.625 g to 55.625 g, were imposed. Each rat completed 6 days under each peak force condition, and only data from the 16th day of acquisition and the 6th day of each of the following conditions were submitted to the analyses presented here. Changes in response kinetics as a function of days within peak force conditions have previously been reported by Mitchell and Brener (1991). December 1995, Vol. 27, No. 4
Data Analvsis Dependent variables of interest included the first four moments of the distribution of peak response forces. The first moment was expressed as the average constant error (Schmidt, 1988, p. 58). or the difference between mean peak force and the peak force criterion for each subject under each condition. The second, third, and fourth moments were, respectively, the within-subject standard deviation, the skewness, and the kurtosis of the distribution. The coefficient of variation for peak force was calculated by dividing the within-subject standard deviation by the mean peak force. This measure of relative variability has been used to test for departures from proportionality in the relationship between the within-subject standard deviation and mean peak force. We carried out additional analyses of time to peak force and the average rate of rise of force to determine how these variables were involved in the regulation of peak force over conditions. On each response, the average rate of rise of force was calculated by dividing the peak force by the time to peak force. For each variable, we used a one-way analysis of variance (ANOVA) to test for differences among the 1 I levels of force. When differences were significant, functions relating changes in the dependent variable to increases in the peak force requirement were described either by linear regression or power functions, depending on which description accounted for the greater proportion of variance ($) in the dependent variable.
Results Constant Error As illustrated in the top panel of Figure I , group mean constant error (CE) was positive at the initial criteria, close to zero at the median criterion (30.625 g). and negative at the higher criteria. This systematic and significant decrease in constant error, F( 10, 60) = 8.18, p < .001, as a function of peak force criterion (PFCRIT) was well described by the following linear regression equation:
CE = -0.30(PFCRIT) + 7.90; r(9) = -.99, p < .001. ( I )
Peak Force Variability Overall, changes in the within-subject standard deviation (SD) as a function of peak force requirement were significant, F( 10, 60) = 16.78, p < .001. As shown in the middle panel of Figure I , the value of this variable increased systematically from the first to the median requirement (30.625 g) and remained relatively stable thereafter. This relationship was well described by the following power function, indicating that the average within-subject standard deviation for peak force increased as a negatively accelerating exponential function of the peak force criterion: SD = 4.67(PFCRIT)"3X;r(9) = .98, p < .001.
(2)
The proportionality of the within-subject standard deviation to the mean peak force was examined by analyses of
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A. B. Slifkin, S. H. Mitchell, & J. Brener
the coefficients of variation (CVs).As illustrated in the bottom panel of Figure 1 and confirmed by ANOVA, coefficients of variation for peak force fell significantly across the range of forces, F( 10, 60) = 12.74, p c .001; the relationship was well described, as follows, by a linear regression formula: CV = -0.OO6(PFCRIT) + 0.797; 49) = -.95, p < .001. (3)
Skewness and Kurtosis As can be seen in Figure 2, at the lower force levels skewness was positive and declined in a systematic linear fashion, reaching a negative level only at the final force requirement (55.625 g), F(I0, 60) = 24.62, p c .OOI. This relationship was well described by the following linear regression formula:
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Skewness = -0.04I (PFCRIT) + 1.96; 49) = -.98, p < .001. (4) Kurtosis also declined significantly, but according to a negatively accelerating function over the range of force levels, F( 10.60) = 8.03, p c .OOI.As shown in Figure 2, at the initial increments there is evidence of high leptokurticness, which drops sharply across the first five force levels. From the fifth to seventh requirement, distribution peakedness is close to normal, and at subsequent requirements, distributions take on a modicum of platykurticness. The following power function described these data well: Kurtosis = 24.14(PFCRIT)4.s’ - 3; 49) = -.97. p c .OOI .3 ( 5 )
0 1 : : : : : : : : : : : l’O1
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Determinants of Peak Force
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ANOVA indicated that time to peak force did not change significantly as a function of increases in the peak force requirement for reinforcement, F( 10, 60) = I .63, p > .05, whereas the rate of rise of force, F(10, 60) = 22.33, p < .OO I , and mean peak force, F( 10, 60) = 44.25, p < .001, increased significantly. The regression equations for the rate of rise of force and mean peak force are, respectively:
0.01:
Rate of Rise of Force = 64.45 + 5.83(PFCRIT); r(9) = .99,p c .001. (6) Peak Force = 7.90 + 0.70(PFCRIT); 49) = .999, p < .001. (7) It is clear from the top and bottom panels of Figure 3 that
increases in peak force are strongly determined by the rate of rise of force and not by time to peak force.
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Peak Force Requirement (9) FIGURE 1. Measures of variability as a function of peak force requirement. Top, average constant error (CE); midand bottom, dle, the within-subject standard deviation (SD); the coefficient of variation (CV)for peak force. Each data point represents an average based on the performance means of all subjects under each condition. Constant error and the within-subject standard deviation for peak force are expressed in grams (g). The coefficient of variation for peak force is expressed in standardized units. Average constant error is the difference between the mean peak force and the peak force requirement (Schmidt. 1988, p. 58). The coefficient of variation for peak force was calculated by dividing the within-subject standard deviation for peak force by the mean peak force. Symbols represent means. and lines represent the best-fitting function (see text for details).
Discussion Variations in the characteristics of isometric beam presses in rats revealed remarkable similarities to those already found in humans. First, a typical range effect was found (Figure I , top panel); mean peak force exceeded the low requirements but fell below the higher requirements (e.g., Jenkins, 1947; Newell et al., 1984; Weiss. 1955). Second, 378
the within-subject standard deviation for peak force could be described as a negatively accelerating exponential function of the requirement (Figure 1, middle panel) (e.g., Newell et al., 1984; cf. Figure 2.3b in Carlton & Newell, 1993). Third, and as a consequence of these results, there Journal of Motor Behavior
Response Force in the Rat
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Peak Force Requirement (9) FIGURE 2. Changes in distribution shape as a function of peak force requirement: skewness and kurtosis. Values of both variables are expressed in standardized units, and deviations from zero indicate departures from normality. Symbols represent averages of performance means across subjects. Lines represent the best-fitting function (see text for detai Is).
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F‘eak Force Requirement (9) FIGURE 3. Changes in response kinetics as a function of peak force requirement. Top, peak force measured in grams (g); bottom, time to peak force measured in milliseconds
(ms); and the average rate of rise of force measured in grams per second (g/s). The average rate of rise of force was calculated for each response by dividing the peak force by the time to peak force. Symbols represent means, and lines represent the best-fitting function (see text for details).
December 1995, Vol. 27, No. 4
was a decrease in the coefficients of variation for peak force across the levels of force studied. Unlike the equivalent function for humans (e.g., Jenkins, 1947), the coefficients of variation did not decrease at a negatively accelerating rate. This may have occurred because peak force requirements below 5.625 g were absent, or because exposure to this requirement was longer (16 days) compared with the subsequent requirements (6 days) or both. Fourth, the skewness values found here at the lowest and highest requirements are similar to those reported by Newell and Carlton (1985). In their study, skewness took on a value of 1.18 when the initial peak force requirement was based on 2.5% of the subject’s maximum voluntary force and -0.47 when the final requirement was based on 90% of the subject’s maximum voluntary force. Although force requirements were not assigned on the basis of a percentage of maximum voluntary peak force in the current study, the skewness value at the lowest force level (5.625 g) was 1.85, and at the highest (55.625 g), -0.25 (Figure 2). Fifth, kurtosis (Figure 2) did show “a high degree of leptokurticness” initially and “a modicum of platykurticness” at the higher force levels (Newell et al., 1984, p. 148). Sixth, although rats were free to modulate the rate of rise of force and time to peak force independently or in combination to meet the increasing peak force requirements, like cats (Ghez & Vicario, 1978) and humans (e.g., Freund & Budingen, 1978; Gordon & Ghez, 1987) rats engaged a pufse-height control policy to modulate peak response force (Figure 3). It is tempting to infer the percent maximum voluntary peak force on the basis of the results presented. Newell et al. ( 1984) projected that the peak force requirement corresponding to a constant error of zero should be located at 50% of subjects’ maximum voluntary peak force, with the within-subject standard deviation reaching a ceiling at 65% maximum voluntary peak force. In the current experiment, constant error was equal to zero between the 25.625-g and 30.625-g (the median) requirement and the within-subject standard deviation for peak force began to become asymptotic at the 30.625-g peak force requirement. This suggests that 30.625 g is close to the rats’ force midrange and 55.625 g is close to the maximum peak force. Confirmation of this inference would require the use of an experimental procedure analogous to those used in the human studies (e.g., Newell & Carlton, 1985) for determining maximum voluntary peak force in the rat. The observed similarities in the distributions of peak forces occurred despite substantial differences in the procedures under which the rat and human subjects responded. In particular, the information, motivation, and permissible biomechanical degrees of freedom for force production differed in the procedures to which the two species were submitted. First, in the human studies visual stimuli provided precise information about the peak force requirement in effect (e.g., Sherwood & Schmidt, 1980), whereas no stimuli were 379
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Slifkin
used here to signal requirement changes for rats. Also, within an experimental session each force requirement has typically been presented to subjects in a block of trials, with the presentation of different peak force requirements randomized across blocks (e.g., Newell & Carlton, 1985; Sherwood & Schmidt, 1980). On the other hand, rats were exposed to each peak force condition over a number of experimental sessions, and the force requirement increased with each successive condition change. Furthermore, knowledge of results in the human studies has either been verbal (e.g., Newell & Carlton, 1988; Noble & Bahrick, 1956)or has allowed comparisons of generated force-time curves against criterion curves (e.g., Carlton, Kim, Liu, & Newell, 1993; Newell & Carlton, 1985). In contrast, exteroceptive feedback for rats was binary: Food delivery accompanied by a simultaneous click followed responses exceeding the peak force requirement and was withheld when responses were equal to or below the criterion. Second, unlike the protocols of human studies, we used food-deprived rats, because it is assumed that procuring food to satisfy an immediate biological need was the primary goal of subjects in the present experiment, with adjustment of response kinetics an implicit and secondary goal. For humans, the kinetic goal of responding was primary: Namely, accuracy in meeting peak force targets was made explicit in verbal instructions or was implicit in the information (target display and knowledge of results) presented to them. Third, in the human studies on force production, forces were generated mainly through elbow flexion or extension (e.g., Gordon & Ghez, 1987; Newell & Carlton, 1988; Sherwood & Schmidt, 1980), with each action involving only a single degree of freedom. In contrast to the seated human subjects, subjects in the current experiment reared up on their hind limbs and executed responses with a forelimb to operate the beam, following which they assumed a fourlegged posture to retrieve the reward from the food tray. Hence, for rats, the muscles and joints contributing to peak force production were not held constant and involved many degrees of freedom. In light of the differences between species and experimental conditions, it appears that the similarities between rat and human performance are unrelated to informational or motivational conditions or permissible degrees of freedom. Instead performance appears to be attributable to common processes engaged by both the human and rat motor control systems to solve the problem of generating forces that are appropriate to the prevailing environmental constraints. The further identification of these processes may be aided by the development of a rat model of force variability. which would facilitate investigations of the neural circuitry, physiology. and biological constraints (e.g.. biomechanical, neuromuscular, central, energetic) implicated in force production. ACKNOWLEDGMENT This research was partly supported by National Institutes of Health grant ROI HL42366 and a Sigma Xi Grant-in-Aid of
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Research awarded, respectively, to Jasper Brener and Andrew B. Slifkin. We would like to thank William Guethlein for his programming assistance.Andrew B. Slifkin is now at the Department of Exercise and Sport Science, the Pennsylvania State University. Suzanne H. Mitchell is now at the Department of Psychology, the University of New Hampshire.
NOTES I . In a task requiring subjects to generate isotonic contractions, Sherwood et al. (1988) found that the within-subject standard deviation for torque, analogous to the within-subject standard deviation for peak force in isometric tasks, essentially stabilized beyond 65% maximum voluntary torque. 2. Filion et al. (1969) as well as Mintz and Notterman (1965) used a measure of relative variability, a Weber ratio analogue, calculated by dividing the within-subject standard deviation by the peak force requirement instead of the mean peak force. 3. A condition of power function description is that the values to be described must exceed 0. Therefore, it was necessary to add a constant to each observed kurtosis value, and 3 was added here. Most researchers and statistical packages subtract 3 so that a normal distribution’s kurtosis and skewness is represented, more intuitively, by 0. Thus, the calculation of Equation 5 was based on the uncorrected kurtosis values, where normality is represented by 3 and not 0. Then, by subtracting 3 from predictions provided by Equation 5, the best-fitting function for the reported data (see Figure 2) was generated.
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