Exp Brain Res (2011) 212:359–369 DOI 10.1007/s00221-011-2735-7

R ES EA R C H A R TI CLE

The rate of force development scaling factor (RFD-SF): protocol, reliability, and muscle comparisons Maria Bellumori · Slobodan Jaric · Christopher A. Knight

Received: 11 February 2011 / Accepted: 15 May 2011 / Published online: 9 June 2011 © Springer-Verlag 2011

Abstract Performing a set of isometric muscular contractions to varied amplitudes with instructions to generate force most rapidly reveals a strong linear relationship between peak forces (PF) achieved and corresponding peak rates of force development (RFD). The slope of this relationship, termed the RFD scaling factor (RFD-SF), quantiWes the extent to which RFD scales with contraction amplitude. Such scaling allows relative invariance in the time required to reach PF regardless of contraction size. Considering the increasing use of this relationship to study quickness and consequences of slowness in older adults and movement disorders, our purpose was to further develop the protocol to measure RFD-SF. Fifteen adults (19– 28 years) performed 125 rapid isometric contractions to a variety of force levels in elbow extensors, index Wnger abductors, and knee extensors, on 2 days. Data were used to determine (1) how the number of pulses aVects computation of the RFD-SF, (2) day-to-day reliability of the RFDSF, and (3) the nature of RFD-SF diVerences between diverse muscle groups. While sensitive to the number of pulses used in its computation (P < .05), RFD-SF was reliable when computed with >50 pulses (ICC > .7) and more so with 100–125 pulses (ICC = .8–.92). Despite diVerences in size and function across muscles, RFD-SF was generally

M. Bellumori · S. Jaric · C. A. Knight (&) Department of Kinesiology and Applied Physiology, University of Delaware, 541 S. College Ave, Newark, DE 19716, USA e-mail: [email protected] M. Bellumori e-mail: [email protected] S. Jaric e-mail: [email protected]

similar (i.e., only 8.5% greater in elbow extensors than in index Wnger abductors and knee extensors; P = .049). Results support this protocol as a reliable means to assess how RFD scales with PF in rapid isometric contractions as well as a simple, non-invasive probe into neuromuscular health. Keywords Neuromuscular · Physical function · Measurement · Assessment · Power · Motor control · Muscle

Introduction Physical quickness is a movement quality of widespread interest in sport, aging, falls, pathology, and rehabilitation. Under the instructions to produce isometric muscular force pulses most rapidly (Wierzbicka et al. 1991) and across a range of submaximal amplitudes, there is a positive linear relationship between the peak force (PF) of a pulse and the corresponding rate of force development (RFD). Such scaling results in relative invariance in the time required to achieve peak force regardless of the strength of the muscular contraction. Among contextually varied publications related to the scaling of RFD with respect to PF (e.g., Gordon and Ghez 1987; Ghez and Vicario 1978a, b; Mirkov et al. 2004; van Cutsem and Duchateau 2005; Klass et al. 2008), the paper by Freund and Budingen (1978) provides the most relevant background for the present paper. Not only was their elegant work among the Wrst to describe this relationship in humans, but it also demonstrated apparent consistency across muscle groups and robustness of the scaling despite initiation of contractions from nonzero baseline force levels. According to Freund and Budingen (1978), “the independence of time of contraction of skeletal

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muscles from the Wnal force level or angle of movement is regarded as representing a necessary condition for the synchrony of synergistic muscle action”. Related to the degrees of freedom problem (Bernstein 1967), Gordon and Ghez (1987) suggest that this “regulation of rise time around a preset value simpliWes accurate control of response amplitude by reducing the number of variables that must be controlled”. As a result, the rise time of muscle force should be pre-set instead of separately modulated, which could considerably simplify control of intended mechanical output. For more extensive coverage of the related literature and a test of the generalizability of this speed-control hypothesis to weightlifting, see also Enoka (1983). In some publications, the PF-RFD relationship has been quantiWed using a single linear regression equation to describe aggregated data from multiple subjects, with informative Wndings related to adaptations to power training (van Cutsem et al. 1998) and diVerences between age groups (Klass et al. 2008). However, the prior work by Freund and Budingen (1978) and its clinical application to the symptom of bradykinesia in Parkinson’s disease (Wierzbicka et al. 1991) demonstrated that quantiWcation of the PF-RFD relationship at the unit of the individual also has high utility. When computed for the individual, the slope of the linear PF-RFD relationship can be treated as a dependent measure that we term the RFD scaling factor (RFD-SF) in the remainder of this paper. Consistent with the remarks of Wierzbicka et al. (1991), we anticipate that the RFD-SF is a measure with high potential to inform rehabilitation researchers and human movement scientists about the important feature of movement initiation and the quickness of force production. The RFD-SF measure is appealing because (1) it can be used to quantify the quick force production across the full continuum of force amplitudes, and (2) the resulting units of this measure (s¡1) make it mathematically independent of strength and therefore size of the muscle group of interest. This latter feature facilitates comparisons between individuals and between muscle groups with respect to the underlying neuromuscular determinants of quickness. Furthermore, while it is important to consider muscle factors including Wber type and shortening velocity (e.g., Korhonen et al. 2006; Harridge et al. 1996) together with the inXuence of elastic tissues (e.g., Bojsen-Moller et al. 2005), the RFD-SF also reXects neural and neuromuscular factors. Pre-motorneuronal determinants of quickness include the discharge of red nucleus neurons, which is known to correlate with movement velocity and/or the rate of change in force (Ghez and Vicario 1978a; Burton and Onoda 1978; Gibson et al. 1985; Mewes and Cheney 1994). More peripheral determinants of quickness include features of the neural stimulation of muscle (Brown and

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Cooke 1981; Aagaard et al. 2002) and the underlying high initial motor unit Wring rates (van Cutsem et al. 1998; van Cutsem and Duchateau 2005; Klass et al. 2008). Therefore, considering the potential utility of the RFD-SF and its potential neural and neuromuscular correlates, the purpose of this project was to further develop the methodology for its measurement. The Wrst aim of this study was to determine how many pulses are necessary to compute a stable RFD-SF. To address this aim, we oversampled the PF-RFD relationship and computed the RFD-SF from random subsets of 25–125 pulses. The second aim was to assess the test– retest reliability of the RFD-SF. Intra-class correlation coeYcients (ICCs) were computed from data obtained on two test sessions separated by 48 h. The third aim was to determine whether the RFD-SF is a general characteristic of an individual that might be consistent or correlated among diVerent muscles. RFD-SF was compared across three diverse muscle groups: elbow extensors, index Wnger abductors, and knee extensors. It was hypothesized that although RFD-SF may diVer across the three muscle groups, due to diVerences in their musculoskeletal anatomy, morphology, and function, the RFD-SF taken from the diVerent muscle groups would be correlated.

Methods Similar to the methods used by others (Freund and Budingen 1978; Wierzbicka et al. 1991; Klass et al. 2008), the RFD-PF relationship was computed from sets of several rapid isometric contractions (pulses) performed across a full range of amplitudes. The linear regression parameters (slope, R2, y-intercept) were calculated for each individual subject, and the slope (RFD-SF) was the main dependent measure of interest. Although meaningful information may be available in the y-intercept and R2 data, the present paper maintains a succinct focus on the RFD-SF, as has been done in related literature. Reliability of RFD-SF was assessed using intra-class correlation (ICC) and a test–retest design (Safrit 1976). RFD-SF was compared between tests separated by 48 h and across the elbow extensors, index Wnger abductors, and knee extensors in a within subjects design. These muscle groups were chosen for their diversity, functional relevance, and prevalence in mechanistic and rehabilitation research. Knee extension is especially relevant in walking and fall prevention. Elbow extension is a primary action in the upper extremity utilized frequently during daily activity and also relevant to preventing a fall. Index Wnger abduction was chosen to represent a small and dexterous muscle group.

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Subjects Subjects were 15 young adults (7 men, mean (SD) age = 23.1 (1.6) years, height = 178.6 (5.9) cm, mass = 85.5 (17.7) kg; 8 women, mean age = 22.8 (3.6) years, height = 165.3 (6.0) cm, mass = 61.8 (7.0) kg). Of the subjects, 10 were right-handed and 5 were left-handed. Exclusion criteria included injury to the left leg, arm or hand within the past 6 months that required medical treatment, low back pain, uncontrolled hypertension, arthritis, or osteoporosis. All participants signed an institutionally approved document of informed consent. Procedures Each subject was tested during two sessions separated by 48 h. Testing included the recording of isometric force pulses from the left limbs during isometric knee extension, elbow extension, and index Wnger abduction. Prior to testing in each muscle group, three 3-s isometric maximal voluntary contractions (MVC) were completed with 60 s of rest between each trial. MVC was deWned as the greatest value of the three maximal attempts and was used to provide visual biofeedback of force as a percentage of maximal force (%MVC). Although the PF-RFD relationship will be discussed using the language of “force”, strength and peak rates of contraction are reported as joint torques using the measured perpendicular distance from the joint center to the point of force application on each transducer. The RFD-SF protocol The same protocol was followed for each of the three muscles tested. Subjects were instructed to produce individual isometric force pulses in a manner to achieve peak force as quickly as possible and then relax instantly. The timing of pulses was cued by verbal “go” commands from the experimenter that were approximately 2 s apart (Fig. 2a). Subjects were explicitly instructed not to target the force levels requested because targeting slows the rate of force production (Gordon and Ghez 1987). Subjects practiced until they felt comfortable with the task and could perform discrete force pulses as instructed. This apparently healthy sample did not demonstrate any diYculty producing discrete and smooth force pulses. After practice, subjects completed Wve trials consisting of at least Wve brief pulses to each of Wve approximate amplitudes (20, 40, 60, 80, 100% MVC), resulting in a total of at least 125 pulses. This number of pulses was selected to intentionally oversample the PF-RFD relationship, allowing us to test the stability of the RFD-SF as computed from diVerent sized subsets of pulses (Aim 1). Subjects rested for 60 s between trials. The force levels were pre-

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sented in a balanced order across subjects. Visual feedback of force was provided to the subjects as a vertical bar graph, on a computer screen placed at eye level. Including the informed consent process, the full protocol was completed within 1 h per subject. All subjects were tested by the same experimenter to eliminate a potential source of variance. Isometric elbow extensors forces were recorded with the subjects in a standing position and while holding an instrumented wooden pole (SM-50, Interface Inc., Scottsdale, AZ, USA; Fig. 1a). Subjects stood with their backs against a wall with their shoulder in a neutral position and elbow Xexed at 90°. While holding the device like a ski pole, subjects produced pulses by rapidly pushing the pole downward against the Xoor. Index Wnger abductor forces were obtained with subjects seated comfortably on a standard height oYce chair with the palmar surface of their left hand resting on the force measuring device at standard table height. Isometric index Wnger abductor forces were recorded from a strain gauge force transducer (MB-10, Interface Inc., Scottsdale, AZ, USA; Fig. 1b). The index Wnger was oriented perpendicular to the measurement axis of the force transducer and secured with a small segment of hook and loop fastener. An adjustable block of wood held the thumb at approximately 80° with respect to the index Wnger. Isometric knee extensors forces were obtained with the subjects seated on a custom bench and their distal leg aYxed to a strain gauge force transducer (SM-250, Interface Inc., Scottsdale, AZ, USA; Fig. 1c). Subjects were seated in an upright position with back support, and both the hip and knee Xexed at approximately 110°. The force transducer was coupled to the bench using a ball joint to allow some freedom of knee extensors direction without imparting oV-axis forces on the transducer. The transducer was coupled to the distal leg with a 9.7-cm wide rigid plastic cuV made from a bisected piece of polyvinyl chloride (PVC) pipe. With a Wrm rubber pad and small section of cloth surrounding the leg, the cuV was secured by 5-cm wide hook and loop fastener. These materials were selected to minimize the eVect of material compression on measures related to movement initiation (Corcos et al. 1992). Knee extensors pulses were performed isometrically to mimic a rapid forward kick. Data acquisition A Grass Instruments Model 15LT (West Warwick, RI, USA) bioampliWer system was used to amplify and Wlter (low-pass cutoV at 30 Hz, ¡6 dB) signals from each of the three force transducers. Analog signals were digitized at 200 Hz using a 16-bit acquisition board (PowerDaq Series, United Electronics Industries, Walpole, MA, USA). Data acquisition and the visual display of force were controlled using Dasylab software (Measurement Computing Corporation, Norton, MA, USA).

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Fig. 1 a Isometric elbow extension (EE) forces were recorded from the subjects in a standing position and while holding an instrumented pole. Subjects stood with their shoulder in a neutral position and elbow Xexed at 90°. Subjects were tested with their backs against a wall. b Isometric index Wnger abduction (IFA) forces were recorded from subjects while seated comfortably in a standard height oYce chair with the palmar surface of their left hand resting on the force measuring device at standard table height. The index Wnger was oriented perpen-

dicular to the measurement axis of the force transducer and held against it with a small segment of hook and loop fastener. An adjustable block of wood held the thumb at approximately 80° with respect to the index Wnger. c Subjects were seated on a custom bench for measurement of isometric knee extension (KE) forces. Knee and hip angles were both approximately 110°. The force transducer was coupled to the distal leg with a 9.7-cm wide rigid plastic cuV made from a bisected piece of PVC plumbing supply

Data reduction

Statistical analysis

Data were processed by a single investigator using custom software (van Rossum 2011) to obtain corresponding PF and peak RFD measures from each pulse (Fig. 2a, b). The RFD time series was computed from the force recording using the Wnite diVerence method over overlapping 0.1-s intervals (Winter 1990). Based on pilot analyses, this method of preparing the RFD signal provided RFD-SF results that were comparable to those from RFD computation using time to peak force and peak amplitude, as performed by Freund and Budingen (1978). Results are also comparable to diVerentiation of the force recording after low-pass Wltering with a 5-Hz cutoV frequency. Although these approaches smooth the RFD signal and do not capture the greatest instantaneous RFD between movement initiation and peak force, they prevent the ampliWcation of noise that occurs with diVerentiation of the untreated recording. Within the Wve trials, Wve muscular contractions to each force level (20, 40, 60, 80, 100% MVC) resulted in 125 measurements for each muscle during both testing sessions. Subsets of pulses were obtained using random selection. For all subjects, muscle groups, and subsets of pulses, linear regression equations were computed to describe the PF-RFD relationship. The slope of the regression equation (Fig. 2d, rate of force development-scaling factor; RFD-SF) was the dependent measure of interest in the analysis of number of pulses (Aim 1), day-to-day reliability (Aim 2), and between-muscle comparisons (Aim 3).

R statistical software (R Development Core Team 2010) was used to extract random subsets of pulses, to generate regression parameters, and for statistical tests. Intra-class correlation coeYcients were calculated to determine the day-to-day reliability of RFD-SF as computed from diVerent numbers of pulses (Safrit 1976). SpeciWcally, using the mean squares (MS) from a days-by-subjects randomized analysis of variance, ICC was computed as (MSsubjects ¡ MSdays £ subjects)/MSsubjects. Repeated measures analysis of variance was used to test diVerences between days and muscle groups. When making comparisons of R2 as a dependent measure, the Fischer z’ transform was used to normalize these data. Pearson’s product moment correlation coeYcients (r) were calculated to describe associations between diVerent muscles and relationships between PF-RFD parameters and potential covariates (strength and body mass).

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Results Strength The observed strength measures for each joint (Table 1, peak torque) were consistent with published values, taking into consideration the diVerences in gender distributions between the present and the former experiments [index Wnger abductors: (Carroll et al. 2002); elbow extensors:

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Fig. 2 a Sample recording of rapid pulses to a variety of amplitudes. b Corresponding rate of force development computed using the Wnite diVerence method and overlapping .1-s intervals of the force recording (Winter 1990). c Overlaid force pulses from one subject demonstrating the relative invariance of time to peak force, as observed by Freund and Budingen (1978). d PF-RFD plot with data points taken from the peaks (circled in a and b) of each force pulse and corresponding RFD

Table 1 Mean (SD) peak torque (PT), rate of torque development (RTD), and rate of force development-scaling factors (RFD-SF) by muscle group and gender (8 females, 7 males)

Muscle

Gender

PT (Nm)

RTD (Nm/s)

RFD-SF

Elbow extensors

Female

27.6 (5.5)

260.3 (58.0)

8.60 (.75)

Male

45.4 (6.26)

482.9 (51.7)

9.35 (.67)

t = 5.8, P < .001

t = 7.9, P < .001

t = 1.99, P = .07

Female

.91 (.25)

9.3 (3.03)

8.16 (.97)

Male

1.46 (.18)

15.1 (1.31)

8.03 (.74)

t = 5.0, P < .001

t = 4.9, P < .001

t = .31, P = .76

Index Wnger abductors

Knee extensors

Female

121.4 (27.7)

1,043 (259)

7.75 (1.52)

Male

163.2 (48.4)

1,635 (411)

8.54 (.81)

t = 2.01, P = .07

t = 3.3, P = .008

t = 1.28, P = .23

(Gabriel et al. 2001); knee extensors: (Cohen et al. 2010; Berger et al. 2010)]. For elbow extensors and knee extensors (muscle groups with published RFD values), the observed maximal rates of torque development were also within expected ranges, after estimating conversions from force to torque in some cases [elbow extensors: (Mirkov et al. 2004); knee extensors: (Cohen et al. 2010; Thorlund et al. 2009)]. The PF-RFD relationship The results from 15 subjects and 3 muscle groups indicated strong linear PF-RFD relationships (average R2 = 0.96, P < .01) summarized by the equation RFD = RFD-SF * PF + y-intercept (Fig. 2d). RFD-SF and

R2 values had low variability while the y-intercept was relatively close to zero and more variable (coeYcient of variation: RFD-SF = .121, R2 = .042, Y-intercept = .822). The range of observed RFD-SF values was 5.65– 10.21 s¡1. For each of the muscle groups, the y-intercept was signiWcantly greater than zero (elbow extensors: t = 7.65, P < .001, knee extensors: t = 3.04, P = .008, index Wnger abductors: t = 5.38, P < .001). Although signiWcantly diVerent from zero, the relative magnitude of the average y-intercept (32.6% MVC/s) was quite small, representing only 2.7% of the range of RFD values (maximum RFD = 1,210% MVC/s). Freund and Budingen (1978) reported a similarly small y-intercept that was approximately 1% of their RFD range, based on estimates of the range in their Fig. 1.

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Table 2 Mean (SD) regression parameters of the PF-RFD relationship for each muscle at each test Test

Muscle

RFD-SF

R2

Y-intercept

1

Elbow extensors

8.9 (.7)

.97 (.05)

44.4 (25.7)

Index Wnger abductors

8.2 (.8)

.97 (.03)

32.3 (23.7)

1.2 (0.4)

12.0 (3.8)

Knee extensors

8.3 (1.2)

.96 (.04)

28.5 (37.9)

140.9 (43.1)

1,319 (446)

2

PT (Nm) 35.9 (10.8)

RTD (Nm/s) 364.2 (126.6)

Elbow extensors

8.8 (.9)

.98 (.03)

52.1 (25.1)

38.4 (12.5)

Index Wnger abductors

8.5 (.7)

.98 (.03)

18.3 (25.5)

1.2 (.3)

375.6 (142.2) 11.6 (3.5)

Knee extensors

8.5 (1.3)

.97 (.03)

20.3 (36.8)

140.8 (48.0)

1,406 (645)

Peak torque (PT) and rate of torque development (RTD) values are means of the peak values achieved by each subject

Gender Table 1 presents mean (SD) data for MVC, maximum RFD and the RFD-SF for women (n = 8) and men (n = 7) separately. Although statistical tests of the gender eVect were performed, these results are provided cautiously due to the small sample sizes within genders. With the exception of knee extensors, strength and rate of torque development results were less for women whereas there was little evidence of gender diVerences in RFD-SF. The absence of a gender diVerence is consistent with the assumption that the RFD-SF quantiWes the scaling of RFD with PF as a property of neuromuscular control, rather than as a matter of muscle mass or strength. RFD-SF versus strength Within the three muscle groups, there were weak, non-signiWcant correlations (r < .36, P > .1) between regression parameters (RFD-SF, R2, y-intercept) and both absolute (MVC, Nm) and relative strength (Nm/kg). Mean (SD) regression parameters of the PF-RFD relationship for each muscle on each day as well as mean (SD) strength and maximum RFD values can be found in Table 2. Number of pulses and reliability A non-signiWcant interaction between muscle group and the number of pulses used to compute RFD-SF indicated that the eVects of number of pulses on the RFD-SF did not vary by muscle group (F8,112 = .401, P = .918). There was a signiWcant eVect of number of pulses (F4,56 = 3.977, P = .007) with systematic increases in RFD-SF as more pulses were used in its calculation (Fig. 3, top). Qualitatively, the RFDSF measure appears most stable in all muscle groups when 75 or more pulses are used. Trend analysis indicated that there was a signiWcant linear trend in this relationship (F1,29 = 5.307, P = .029) and evidence of a quadratic trend that suggests a plateau (F1,29 = 3.022, P = .093). Pairwise comparisons indicated that RFD-SF scaling factors computed from 75, 100, or 125 pulses were not signiWcantly

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diVerent from each other (all P > .3) and that RFD-SF values computed from 25 or 50 pulses were signiWcantly less than those from computed from 75 pulses (all P < .034). To evaluate the reliability of the RFD-SF protocol, subjects were tested on 2 days separated by 48 h. With a minimum of 50 pulses, intra-class correlation coeYcients were all greater than .7, and 100 pulses or more resulted in ICCs greater than .8 (Fig. 3, bottom). RFD-SF values computed from 100 pulses were used for all subsequent comparisons and correlations (Aims 2 and 3). Muscle group and day comparisons There was no signiWcant interaction between muscle group and day for RFD-SF (F2,28 = 2.5, P = .12). There was a signiWcant eVect of muscle group (F2,28 = 3.373, P = .049) for which Tukey’s post hoc comparisons indicated that the RTD-SF for elbow extensors was greater than both of the other two muscle groups (Fig. 3, top, P < .05). There was no signiWcant eVect of day on RFD-SF (F1,14 = 1.47, P = .25). We similarly analyzed the regression R2 (Fisher transformed), considering it a measure of consistency of performance within a testing session and perhaps an indicator of learning. For R2, there was no signiWcant interaction between muscle group and day (F2,28 = .46, P = .64), and there were no signiWcant diVerences between muscles (F2,28 = .33, P = .72) or between days (F1,14 = 2.3, P = .15). Muscle–muscle correlations To investigate whether the RFD-SF is a characteristic that describes an individual, we assessed the correlations between the three muscle groups. RFD-SFs from the upper extremity (elbow extensors and index Wnger abductors) had the strongest correlation (r = .60, P < .05). Correlations between knee extensors and index Wnger abductors (r = .34, P = .22) and knee extensors and elbow extensors (r = .33, P = .23) were less strong. For comparison, correlations were also computed for measures of muscle strength (MVC, Nm). As with RFD-SF, strength measures taken

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they possess the greatest and least variance, respectively. In the between-subjects design, experiments would be adequately powered to detect 10% diVerences with 34 (knee extensors) or 11 (elbow extensors) subjects per group. In the within-subject’s design, 12 (knee extensors) and 6 (elbow extensors) subjects are estimated for adequate power to detect a 10% diVerence.

Discussion The purpose of this project was to further develop the protocol to assess quick force production across a continuum of force levels that are relevant to activities of daily living. Using rates of force development and peak forces from a set of rapid isometric force pulses, linear regression provides a single variable that we term the rate of force development scaling factor (RFD-SF). Addressing three aims, the present results indicate that (1) the number of pulses used to compute RFD-SF is an important methodological consideration, (2) RFD-SF has good reliability, and (3) statistically signiWcant diVerences between RFD-SF measures from diverse muscle groups might be considered small. Number of pulses

Fig. 3 Top Mean (SE) rate of force development scaling factor (RFDSF) calculated from 25 to 125 force pulses within each subject for each of three muscle groups (elbow extensors = EE, index Wnger abductors = IFA, knee extensors = KE). Within the signiWcant muscle factor, homogenous subsets are marked by a continuous horizontal line (P < .05, Tukey). Bottom Corresponding intraclass correlation coeYcients (ICC) computed for test–retest reliability on 2 days separated by 48 h

from the upper extremity had the greatest correlation (elbow extensors vs. index Wnger abductors: r = .75, P = .001; knee extensors vs. index Wnger abductors: r = .08, P = .78; elbow extensors vs. knee extensors: r = .44, P = .10). Sample size estimation To guide future research utilizing RFD-SF as a dependent measure, we used values computed from 100 pulses to perform hypothetical sample size estimates using G*Power (Erdfelder et al. 1996) for the detection of 10% diVerences between subjects (t test, two-tailed,  = .05, 1¡ = .8) and within subjects (paired t test, two-tailed,  = .05, 1¡ = .8, correlation = .7). These estimates were based on day 1 results from knee extensors and elbow extensors because

Regarding Aim 1, it is clear that the number of pulses used in computing the RFD-SF is an important consideration and should be standardized across groups or experimental conditions, due to the increases in this value when more pulses are used. When designing this experiment, we contemplated the potential for fatigue that might occur due to oversampling of force pulses. Subjects were periodically asked whether they felt any localized fatigue in the muscle group being tested and none was reported. After setup, 125 pulses were recorded from a single muscle group within approximately 10 min. Perhaps with a modiWed schedule of rest periods, this many pulses may not be problematic in the elderly or patients. Reliability Although signiWcantly diVerent from zero, the magnitude of y-intercepts corresponded to very few percent of the recorded maximum MVC/s quantity. Regarding Aim 2, intra-class correlation coeYcients for the RFD-SF computed from at least 50 pulses supported favorable reliability (>.7) with even higher ICCs (>.8) when 100 or more pulses were used. In accordance with Atkinson and Nevill’s (1998) criteria for “good” reliability being determined by ICCs greater than or equal to 0.7, it is suggested that a minimum of 50 pulses be performed to obtain reliable results

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(ICCs: elbow extensors = .80, index Wnger abductors = .72, knee extensors = .72). For the greatest statistical power, one would seek the best reliability conditions by utilizing more pulses in the computation of RFD-SF. However, if there is concern about time or fatigue, the greatest number of pulses may not be necessary to detect group or treatment diVerences. Using the present results from the most variable muscle group (a worst case scenario), our sample size estimation indicates that reasonable numbers of subjects are adequate to detect 10% diVerences in RFD-SF, in both within- and between-subjects designs. Furthermore, the diVerences reported in the literature suggest that the RFD-SF can vary by much more than 10% due to exercise training (van Cutsem et al. 1998), aging (Klass et al. 2008), or movement disorder (Wierzbicka et al. 1991). The stability of these measures is further supported by the lack of signiWcant diVerences between days even though one might expect the possible improvement (increased RFD-SF) due to experience with the task. The absence of a learning eVect may be due to the relative simplicity of the rapid isometric contractions, the apparent health of the subjects, and the eVectiveness of the brief practice period used before testing. In related projects that do not require oversampling, we adopted the practice of obtaining approximately 5–10% more pulses than the desired number. Although rare, subjects do sometimes make motor errors that are easily detected in visual inspection of pulses during data processing or as outlier data points in the resulting regression plots. It is important to detect and remove these pulses that do not represent the subject’s normative performance because linear regression can be quite sensitive (Cohen et al. 2003).

units of s¡1 and therefore is a measure that is independent of muscle strength and, therefore, muscle size. The similarity of RFD-SF across joints is perhaps an extension of Freund and Budingen’s (1978) early interpretation of the RFD-SF as a means to simplify timing of forces from synergistic muscles within a joint. If so, the underlying central determinants of the RFD-SF (Ghez and Vicario 1978a) are important contributors to coordination within rapid movements and important considerations in a variety of movement disorders. Although stronger relationships between the slopes from diVerent muscle groups were anticipated, the stronger correlation observed in the upper extremity (r = .6) and the Wnding that the remaining correlations were both positive (r » .3) partially supports the notion that the RFD-SF is a general characteristic of an individual. For a point of comparison, the correlation between strength measurements in these three muscle groups was also stronger in the upper extremity MVC correlations. Considering the youth and apparent health of our sample, a homogeneous sample may not have aVorded good opportunity to observe stronger correlations across muscle groups. In a sample of subjects that is more heterogeneous with respect to functional abilities, greater muscle–muscle correlations may exist and this would further support the interpretation of RFD-SF as an individual, rather than joint speciWc, characteristic. If true, the generalizability across muscle groups is favorable for clinical use. For example, RFD-SF taken from handgrip dynamometry may be informative on slowing in gait initiation or directional changes following perturbations. However, larger datasets and further inquiry are required to develop such assessment practices.

Muscle group considerations

Functional signiWcance of RFD-SF

Regarding Aim 3, RFD-SF (with 100 pulses) had favorable sensitivity to detect an 8.5% diVerence between muscle groups. The average RFD-SF was generally similar in three muscle groups ranging from 8.2 to 8.9 (minimum–maximum values = elbow extensors: 7.5–9.8, index Wnger abductors: 6.8–9.6, knee extensors: 5.9–9.8). Furthermore, the R2 values for the PF-RFD relationship were consistently high (>.91) in all subjects and all muscles, indicating that this scaling is a robust feature of the neuromuscular system. Even though the main eVect of muscle was signiWcant (P = .049), the 8.5% diVerence between elbow extensors (greatest RFD-SF) and index Wnger abductors (least RFDSF) might be considered relatively small with respect to their anatomical and functional diVerences, as well as compared to the large diVerences observed due to aging (Klass et al. 2008) and training (van Cutsem et al. 1998). Regarding the similarity of index Wnger abductors and knee extensors, recall that the slope of the PF-RFD relationship is in

Wierzbicka et al. (1991) demonstrated the clinical utility of the RFD-SF protocol by diVerentiating between subgroups of individuals with Parkinson’s disease and called for its further development. Caligiuri et al. (1998) also examined the scaling of movement velocity and movement amplitude in an attempt to diVerentiate between the psychomotor or neuromotor basis of motor retardation. The functional signiWcance of the RFD-SF in human movement is that it allows weak or strong muscular contractions to reach peak force with relative invariance (»100 ms in Fig. 2c), and this rule has been included among candidate solutions to the degrees of freedom problem (Bernstein 1967; Enoka 1983). Consider a hypothetical example in which RFD-SF is equal to zero. If a RFD of 200% MVC/s is observed during a 20% MVC contraction (Fig. 2), the peak force would be produced in approximately 100 ms. During a 60% MVC contraction with the same RFD, the time to achieve peak force would approximate 300 ms. Although the assumption

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of zero RFD-SF may be an excessive case, Wierzbicka et al. (1991) reported similar durations of time to peak force for more severely aVected individuals with Parkinson’s disease. To extend the relevance of the RFD-SF, consider the results from an inverted pendulum model of walking, which suggested that a reduction of response time to a perturbation from 265 ms (reported average of during-step fallers) to 175 ms can allow a 77% increase in safe walking velocity (van den Bogert et al. 2002). Even though the time to achieve peak force is only one component of total response time, an intervention that targets improvements in the RFD-SF would be one with beneWts across the full continuum of force levels. Finally, the attention should be also paid to two general properties of the studied relationship. First, of importance should be the remarkable linearity of the PF-RFD relationship that allows its measurement to be performed without exposing frail individuals to high force muscular contractions. This beneWts assessment in rehabilitation. Second, negligible y-intercepts suggest that a single variable (i.e., RFD-SF) could describe the muscle behavior during rapid exertion of forces of diVerent magnitudes both in routine muscle testing and, possibly, in daily activities. This would simplify both the analysis and modeling of complex human movements.

the same approach to group data, aggregating peak force and rate of force development values from multiple subjects and computing regression parameters for entire samples of subjects. For example, in response to 12 weeks of dynamic training, the aggregate RFD-SF value in Wve subjects increased 54.7% from 4.2 to 6.5 (van Cutsem et al. 1998). In an age-group comparison, Klass et al. (2008) also used the aggregate approach and documented an 88% diVerence in RFD-SF between the young (RFD-SF = 11.3) and elderly (RFD-SF = 6.0) in dorsiXexor contractions. These are very large eVect sizes. That these aggregate values diVer from those reported here (8.2–8.9) may be related to diVerences between muscle groups, the protocol, or details in the data analysis methodology such as Wltering approaches or the duration over which dF/dt derivatives were computed. Nonetheless, the values and trends observed across diVerent laboratories are more similar than not and the eVects of aging and exercise training oVer logical validity of the RFD-SF as a sensitive measure of neuromuscular function and its adaptation. While individual or aggregate calculation of the RFD-SF can be eVective in the appropriate context, the computation of the RFD-SF for individuals provides a dependent measure that can be used in conventional comparisons using analysis of variance or in correlations with other measures.

Central mechanisms

Simplicity

Existing literature demonstrates that high initial motor unit Wring rates are related to the production of rapid muscular contractions (Desmedt and Godaux 1978; Masakado et al. 1995; Garland and GriYn 1999) and speciWcally to the RFD-SF (van Cutsem et al. 1998; Klass et al. 2008; van Cutsem and Duchateau 2005). A reduction in the RFD-SF with Parkinson’s disease (Wierzbicka et al. 1991) suggests that the basal ganglia are involved, although the nature of the disease allows for the role of other structures within the body. In feline preparations in which the linear PF-RFD relationship was observed, Wring rates of neurons of the red nucleus were proportional to RFD (Ghez and Vicario 1978a). In macaque monkeys, the correlation between burst frequency of red nucleus neurons and movement velocity was r = .69 (Gibson et al. 1985). Taken together and considering what is known about central correlates of impairments in rapid arm movements (Berardelli et al. 1996), there are likely multiple neural determinants of the RFD-SF in addition to muscle properties such as Wber type and the potential inXuence of muscle mechanical factors.

Test sessions including oversampling of pulses in three diVerent muscles required less than 40 min per subject (including setup). This protocol represents a quick, easy, and non-invasive method of obtaining a measure that appears to be informative on important property of neuromuscular system. With the use of the instrumented pole that did not require any adjustment between individuals, elbow extensors measurement was reported by the subjects to be the easiest task while providing comparable regression parameters to knee extensors and index Wnger abductors and the highest reliability. However, there may be situations in which the dependency of this measure on adequate grip force or postural control is a relevant consideration. During testing, subjects stood with their backs against a wall.

Unit of observation Whereas the present work is focused on computing the RFD-SF for individuals, other research teams have applied

A magnitude independent measure One convenience of RFD-SF is that it carries the units of 1/s, with the same value resulting from measurements that are obtained in the units of the unconverted hardware voltages (Volts/s vs. Volts), forces (N/s vs. N), torque (Nm/s vs. Nm), or forces relative to strength (%MVC/s vs. %MVC). The independence of the RFD-SF from the absolute amplitude of muscular contractions facilitates comparisons

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across laboratories, muscle groups, and individuals with diVerent strength and/or body mass. Throughout data processing, all PF-RFD relationships were plotted in %MVC units to facilitate the detection of patterns in the RFD-SF results (or potential outliers) separately from diVerences in strength. Accordingly, a single investigator could sequentially examine all of the PF-RFD regression plots and easily visualize the full range of RFD-SFs in the sample. We recommend this approach.

Conclusion Based on these results, the rate of force development scaling factor (RFD-SF) is a simple and reliable measure of the feature of movement typically described as quickness. With a standardized protocol, RFD-SF should be comparable across laboratories. Indeed, despite some variance in methodological details, there already exists some consistency in the PF-RFD slopes from other labs (Freund and Budingen 1978; van Cutsem et al. 1998; Klass et al. 2008) and the clinical utility of this method was substantiated by the report of reduced RFD-SF in Parkinson’s disease (Wierzbicka et al. 1991). RFD-SF may prove in future experiments to be a valid measure of neuromuscular function that has stronger relationships to some aspects of motor function than standard tests of MVC or maximal RFD. Both the future use of the evaluated protocol in routine testing and general understanding of the observed phenomena could beneWt from the future research of its mechanical and neural control mechanisms. Acknowledgments The project described was supported by Grant Number 1R21AR060659-01A2 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases. The content is solely the responsibility of the authors and does not necessarily represent the oYcial views of the National Institute of Arthritis and Musculoskeletal and Skin Diseases or the National Institutes of Health.

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