Key words
muscle - force - velocity - power - quadriceps - linear regression
Introduction
Isokinetic dynamometry has often been recognized as the gold standard method for testing
muscle mechanical capacities in healthy and physically active individuals, as well
as in those recovering from injuries or other medical conditions [5]
[15]
[18]. However, similar to other functional tests that typically provide a single testing
outcome [13], the interpretation of the results obtained from isokinetic dynamometry has always
been somewhat challenging to interpret regarding particular mechanical properties
of the tested muscles, such as their capacities to produce high levels of the force,
velocity and power (i.e. the product of force and velocity) outputs. The authors have
interpreted the recorded forces and torques rather arbitrarily, with regard to either
the observed capacities of the tested muscles or the outcomes of the applied rehabilitation
and training interventions [1]
[6]
[17]. Most of the authors at least implicitly agree that the tests conducted at low joint
angular velocities or even isometric conditions predominantly reveal muscle ‘strength’
(i.e. force), while high angular velocities predominantly reveal muscle power [20]
[25]. As a result, routine testing procedures often include several joint velocities,
where 60°/s and 180°/s could be considered as the standard values [6]
[20]
[29]. However, it is also known that the maximum power is typically obtained at high
angular velocities outside the standard testing ranges, while the maximum velocity
is even higher [26]. As a consequence, despite some attempts [19], the isokinetic tests conducted at standard angular velocities neither discern between
muscle force and power-producing capacities, nor allow for assessment of maximum velocity.
A solution of the problem discussed could be based on the muscle force-velocity relationship.
Namely, although the typical force-velocity relationship of in vitro muscles should
be curvilinear [10], the loaded functional multi-joint movements (e. g., jumping, running, cycling,
lifting, throwing) typically display a strong and linear force-velocity relationship
of the tested muscles [13]
[27]. Parameters of such a relationship directly reveal the maximum force, velocity and
power-producing capacities, theoretically, of the tested muscles, and the results
are not only reliable but are also at least moderately valid [7]
[13]
[23]. Conversely, the force-velocity relationship of individual muscles tested by means
of isokinetic dynamometry has often been considered to be curvilinear [4]
[11]
[24]
[28]. However, most of the available data sets suggest that the ‘curvilinearity’ could
mainly originate from the inclusion of the relatively high isometric force, while
the ranges of angular velocities typically applied provide an approximately linear
relationship between the measured force and velocity [4]
[6]
[8]
[12]
[24]
[28]. Moreover, if the force-velocity relationship of individual muscle groups proves
to be strong and approximately linear within a wide range of angular velocities, a
similar approach to the recently proposed ‘2-load method’ could be applied in routine
testing [14]
[30]. Specifically, it has been shown that the functional movements tested under only
2 distinctive loads could provide almost identical outcomes as the same movements
tested under variety of external loads that inevitably require regression modeling,
as well as a prolonged and fatigue-prone testing procedure. Since the standard isokinetic
testing is typically conducted at prescribed joint angular velocities instead of under
different external loads, the isokinetic test conducted at only 2 distinctive angular
velocities could also differentiate between the force, velocity and power-producing
capacities of the muscle tested.
To address both the presented problems and gaps in the literature, we tested the knee
extensors’ concentric force within a wide range of knee angular velocities. Note that
the concentric contraction of knee extensors is the most frequently applied isokinetic
test in the literature. The first aim of the study was to evaluate the shape and strength
of the force-velocity relationships obtained. The second aim was to explore the concurrent
validity of the 2-velocity method, based on the results obtained from only the typically
applied 60°/s and 180°/s velocities, with respect to the standard linear regression
method based on a wide range of the tested angular velocities. The results related
to the first aim are expected to contribute to our understanding of the mechanical
properties of knee extensors. The results related to the second aim, however, could
encourage development of a simple ‘2-velocity method’ for assessment of the force-velocity
relationship, based on only 2 tested angular velocities, that could differentiate
between the force, velocity and power-producing capacities of knee extensors and,
possibly, other individual muscles.
Methods
Participants
Since we preferred a homogeneous group of participants,13 healthy female students
of physical education (age 21±2 years, body mass 64±7 kg, height 172±7 cm; data presented
as mean±SD) were recruited through word of mouth and fliers posted at the School of
Sport and Physical Education. All of them were physically active through their academic
curriculum, which typically consisted of about 10 h a week of on average moderate
physical activity. They were neither active athletes nor did they suffer from neurological
diseases or recent injuries. The study was conducted in accordance with the Declaration
of Helsinki and meets the ethical standards of the journal [9]. All participants signed informed consent forms approved by the institution’s Ethics
Committee.
Testing procedures
All measurements were performed in the university research laboratory, using a Kin-Com
AP125 isokinetic dynamometer (Chatex Corp., Chattanooga, Tennessee, USA). Following
a standardized 10-min warm-up consisting of 5 min of cycling and 5 min of callisthenic
and dynamic stretching, the participants were seated in an upright position and fixed
to the testing apparatus with the straps around the pelvis, thigh, and malleoli. The
axis of rotation of the dynamometer was aligned with the lateral femoral condyle.
The same experienced examiner supervised all of the tests. A detailed explanation
and qualified demonstration were provided prior to each test along with a standardized
verbal encouragement. Participants were asked to complete 2 to 3 submaximal practice
repetitions prior to each test series.
Maximum muscle force was tested under both isokinetic and isometric conditions. The
isometric test was performed first, and it later served for the assessment of the
concurrent validity of the maximum force obtained from the force-intercept of the
force-velocity regression model applied to the results of the isokinetic tests. The
isometric test was conducted at an angle of 120° of knee extension (180° corresponds
to full extension) [15]. Participants were instructed to extend the knee “as fast and as hard as possible”
[2]. 2 maximal contractions were performed with a 30 s inter-contraction rest.
The range of motion was from 90° to 170° of knee extension for the isokinetic trials
[3]. To obtain the force-velocity relationship from a wide range of force and velocity
data, we conducted isokinetic tests at 5 angular velocities in the following order:
30, 60, 120, 180 and 240°/s. Note that to extend the interval of the tested velocities,
we added both a lower (i.e. 30°/s) and higher velocity (240°/s) to the most frequently
applied range of 60–180°/s of the knee angular velocities [6]
[20]
[29]. 2 experimental trials were performed as hard as possible at each velocity, and
the trial with the highest peak force was used for further analysis. All subjects
were able to reach the preset angular velocities including the highest ones. The rests
were 30 s between the trials and 60 s between 2 consecutive velocities. A real-time
visual feedback of the force-time curve was available during the strength assessment
[2]
[15]. Since the participants were without previous experience with isokinetic testing,
a brief familiarization procedure was conducted prior to the data collection consisting
of 5 trials performed at different testing velocities.
Data acquisition and analyses
The force-time curves were recorded at 500 Hz and low-pass filtered (5 Hz) using a
second-order (zero-phase lag) Butterworth filter. In addition to both the peak and
average muscle force assessed at each angular velocity, we also recorded the maximum
isometric strength (Fmax) within the same knee angle interval. Since force was directly recorded, in order
to assess the force-velocity relationships, the selected angular velocity (in rad/s)
was transformed into a linear velocity (m/s) by multiplying it with the length of
individual lever arms. Force-velocity relationships were assessed both by fitting
a linear regression through the force and velocity data obtained from all 5 angular
velocities (linear regression method) and by drawing a line through the force and
velocity data obtained only from the 60 and 180°/s angular velocities (2-velocity
method). The force-velocity relationships of both methods were extrapolated to determine
the maximum force (F0; force-intercept) and maximum velocity (V0; velocity-intercept), as well as the slope of the relationship (a=F0/V0). Finally, the maximum power was calculated from the product of F0 and V0 (P0=F0×V0/4).
None of the sets of recorded forces deviated from normality (all P>0.05; Kolmogorov-Smirnov
test). Student’s paired-sample t-test was used to test the differences between the
same parameters obtained from the linear regression and 2-velocity method, while the
relationship between them was tested by means of Pearson’s correlations. The same
correlations were used to assess the relationship between the 2-load method parameters
F0 and the directly measured maximum isometric force Fmax. Standard errors of estimate were calculated for each individual set of data with
respect to the values predicted by the corresponding linear regressions. Data were
analyzed using SPSS 20.0 software (SPSS Inc. Chicago, IL, USA). Alpha was set at 0.05.
Results
[Fig. 1] depicts both the peak and averaged values of force and velocity data averaged across
the subjects. Although the angular velocities were fixed, somewhat different individual
lever arms resulted in a certain variance of the calculated velocity. However, of
utmost importance here is that although the data were obtained from a wide range of
velocities, the linear regression method revealed exceptionally strong relationships
for both sets of variables.
Fig. 1 Averaged across the subject peak (squares; solid line) and averaged (circles; dashed
line) knee extensor forces and velocities that served for the assessment of the force-velocity
relationships (error bars indicate SD). Fmax depicts the recorded maximum isometric force that was not included in the regression
modeling.
While [Fig. 1] shows the force-velocity relationships obtained from the data averaged across the
subjects, the same relationships were also obtained from each individual set of data
(see the solid line shown in [Fig. 2] as an example) by using the linear regression method. The median correlation coefficients
were 0.978 (range 0.960–0.990) and 0.991 (0.982–0.998) for the peak and averaged force
and velocity values, respectively, suggesting strong individual relationships. The
same conclusion could be derived from the relatively low individual standard errors
of estimate. They specifically revealed 23.1N (13.1–31.8N) for peak force and 11.2N
(5.1–16.6N) for averaged force (data presented as mean and range). However, the force-velocity
relationship was also obtained by applying the 2-velocity method. Simply stated, the
relationship was obtained by drawing a line through the data obtained from only the
60 and 180°/s values (see the dashed line in [Fig. 2]). Of utmost importance here is that the lines obtained by applying the linear regression
and 2-velocity models almost overlap.
Fig. 2 A representative set of individual data that illustrates a high level of correspondence
between the outcomes of the linear regression method (solid line; all 5 data points
included) and the 2-velocity method (dashed line; only the data indicated by solid
squares included).
The comparison of the individual parameters of force-velocity relationships obtained
by means of the individual linear regression method and the corresponding 2-velocity
method is presented in [Fig. 3]. Of importance here is not only that there were no significant differences in their
magnitudes (all P>43; paired t-tests), but also that the magnitudes were strongly
related (0.76<R<0.97; all P<0.001; [Fig. 3]).
Fig. 3 The parameters of force-velocity relationships (data averaged across the subjects;
means with SD error bars) obtained from the peak and averaged force and velocity data
through the linear regression and 2-velocity method. The correlations between the
outcomes of the 2 models are indicated in parentheses (all p<0.001).
Finally, note that the recorded maximum isometric force Fmax=647±114N (the value indicated by arrow in [Fig. 1]) was not only well above the F0 of the relationship observed from averaged, but also from the F0 observed form the peak force and velocity data (see [Fig. 1] for illustration). Nevertheless, the correlation of Fmax with the F0 obtained from the linear regression method and from the 2-velocity method was 0.80
and 0.84 for the relationships obtained from the peak force, and 0.80 and 0.68 for
the relationships obtained from the average force values, respectively (all P≤0.01).
Discussion
The aims of the study were to evaluate the shape and strength of the force-velocity
relationship of knee extensors tested by means of isokinetic dynamometry, as well
as to explore the concurrent validity of a simple 2-velocity method applied on the
same set of the data. In general, the first and rather novel finding was that the
observed force-velocity relationships were strong and approximately linear. Consequently,
we also found that the virtually identical force-velocity relationships could be also
observed by using the ‘2-velocity method’ based on testing knee extensors at only
2 standard angular velocities of 60 and 180°/s.
Regarding the first aim, it should be noted that the tests were conducted within a
wide range of velocities as compared to most of the standard testing procedures [6]
[17]. Nevertheless, both sets of variables revealed strong and linear force-velocity
relationships of the tested knee extensors. Although a visual inspection of the relationships
observed from the peak force and velocity data indicate that the relationship could
be slightly curvilinear, note that the linear regression method applied on either
the averaged or individual force-velocity relationships revealed nearly perfect relationships.
Therefore, the present study adds to the evidence that the force-velocity relationship
of single-joint functional tasks could be approximately linear [13]
[27]. However, it should be also noted that the directly recorded maximum isometric force
Fmax was well above the F0 predicted by the applied linear regressions. Therefore, our findings are clearly
in line with those reporting a relatively high level of Fmax that motivated the authors to at least implicitly assume that the force-velocity
relationship of individual muscle submitted to standard isokinetic testing could be
generally curvilinear [4]
[11]
[24]
[28]. Neither our study nor the studies of other authors that revealed the same observation
provide the data that could help to elucidate the discussed phenomenon. Therefore,
so far we can only speculate whether the observed difference between the predicted
and recorded maximum isometric force originate either from the shape of force-velocity
relationship, or the differences in the level of muscle activation, or the differences
in knee angles that provide maximum isokinematic and isometric force, or from something
else.
Regarding the second aim of the study, the data revealed a high level of agreement
between the force-velocity relationship parameters obtained from the linear regression
method and the 2-velocity method. Note also that the selected angular velocities of
60 and 180°/s have been routinely applied in a number of standard isokinetic testing
procedures [6]
[20]
[29]. Therefore, similar to the 2-load method applied on loaded functional movements
[14], the 2-velocity method could also considerably simplify and shorten the assessment
of the force-velocity relationship of individual muscles tested by means of isokinetic
dynamometry. Note that the same outcomes can be observed through the force-velocity
relationship (i.e. where force is directly measured, while the preselected angular
velocity recalculated into linear velocity; the method applied in the present study)
and by the torque-angular velocity relationship (the torque is directly measured and
the angular velocity is preselected). Namely, the known lever arm allows for a simple
conversion of force-velocity into torque-angular velocity relationship, and vice versa.
The high level of agreement between the 2 methods is comparable to the level of agreement
observed from 4 different functional tests when the force-velocity relationship of
the tested muscles was observed from a number of loading conditions using a linear
regression model and from just 2 loads, i.e. the ‘2-load method’ [30]. Of particular interest could be that the 2-velocity method could also reveal valid
indices of maximum force (i.e. F0), velocity (V0) and power (P0)-producing capacities of knee extensors and possibly other muscles. The present data
already suggest a high concurrent validity of F0 with respect to the directly recorded Fmax. Finally, note also that the relationship slope (a=F0/V0) also depicts the ‘force-velocity profile’ that needs to be optimized to maximize
a particular movement performance [21]
[22].
Within the present study we intentionally selected a homogeneous sample of participants
and focused on a single but most frequently tested muscle. Therefore, regarding the
directions of future research, of utmost importance could be conducting a similar
evaluation on other muscles routinely tested by means of isokinetic dynamometry, as
well as on diverse populations. If obtained, the strong linearity similar to the one
observed in the present study could allow for a generalization of the present finding
to the entire muscular system and, consequently, establishing the 2-velocity method
as a the standard procedure for isokinetic testing. In addition, the reliability and
concurrent validity of the force-velocity relationship parameters (and, consequently,
of the 2-velocity method parameters) would certainly require further evaluation. A
potential bias of the fixed order of velocities that has been often applied in routine
testing procedures also deserves attention in future studies. Finally, a routine use
of the 2-velocity method in the future would inevitably require evaluation of methodological
elements of the applied procedures such as the standardization of the joint angles
[16] and the selection of particular angular velocities.
We conclude that when isometric force is excluded, the force-velocity relationship
of knee extensors tested by means of isokinetic dynamometry could be strong and linear
even when it is tested within a wide range of knee angular velocities. That finding
allows for a novel approach to the elaborate assessment of the mechanical capacities
of knee extensors (i.e. the 2-velocity method) where only 2 trials performed at distinctive
angular velocities could allow for discerning between the muscle force, velocity and
power-producing capacities. Finally, if future research reveals a similar shape of
the force-velocity relationship of other muscles, the 2-velocity method could be developed
into a standard method for elaborate isokinetic testing of muscle mechanical properties
for both clinical and non-clinical purposes.
