4.2. Outcome measures of pendulum test
Alongside development of technologies of implementation for pendulum test, numerous measures were suggested to classify the severity of spasticity as outcome measures. Wartenberg used the test qualitatively paying attention to irregularities in swinging time or the number of oscillations. suggested Resting position as his method’s outcome measure. After that, many measures were introduced that are summarized in Table 5.
Table 5
Main categories of outcome measures (parameters) that are suggested in the studies that used pendulum test
Signal | Category # | Parameter | Measure/Parameter Definition | Ref. |
Angle | 1 | Onset Ang | Angle at the start of test response | [18] |
A0 | Knee angle at the beginning of the test during maximal limb extension | [13, 38, 50] |
αs Initial angle | Initial Knee angle | [44] |
2 | F1 Ang | Angle at the end of initial movement into flexion | [18, 49] |
F1 Amp | F1 Ang – Onset Ang | [18, 49] |
Ex | First swing excursion: the difference between the starting angle (the position at which the examiner released the participant’s heel) and the first angle of reversal of the swinging limb | [53] |
P4 | First maximum of the oscillation | [33, 43] |
FAR | knee angle when shank motion first switched from flexion to extension | [17] |
A1 | The amplitude of the first swing Magnitude of first drop | [33, 35] |
ϕmax | The first maximum of the goniogram after releasing the leg. | [50] |
αp | The peak angle of the first swing | [44] |
Θ1 First reversal | First maximum of the oscillation | [6, 39] |
3 | E1 Ang | Angle at the end of initial movement into extension | [33] |
E1 Amp | F1 Ang – E1 Ang | [33] |
A2 | The angular change between the first minimum and second maximum | [45, 50] |
4 | Rest ang Rest Angle(RA) θr | Resting knee angle Knee angle at the end of oscillations. | [17, 6, 18, 35, 39] |
Plat Amp | Rest Ang – onset Ang | [18, 49] |
αf | Final position of the leg | [44] |
5 | Duration T | Duration of oscillations. Test duration | [6, 42] |
Relative Swing Time | The time between the peaks, Normalized to the height of the person | [16, 27] |
TFR | Time to first reversal: time interval between the start of shank motion and the first reversal from flexion to extension. | [17] |
Test Duration | Duration from onset Angle to rest angle | [18] |
6 | F | Frequency of oscillations Frequency of the swing | [35, 50] |
C1 Freq | Initial cycle frequency = 1/duration of E1 Ang | [18] |
N P2 | The number of sinusoidal waves produced by the swinging limb after the heel was released (minimum of 3 degrees) The Number of swings | [6, 33, 43, 46, 48] |
Ncyc | Number of cycles (full oscillations) was counted between start of motion and until the oscillation amplitudes is less than 3 degrees. | [39] |
7 | RI | Relaxation index: (starting angle – first angle) / (starting angle – resting angle) F1 Amp / Plat Amp Θ1 / θr | [26, 43, 48] [18] [6] |
ERI | Extension Relaxation index = E1 Amp/ Plat Amp | [18, 49] |
| Damping ratio. Defined as the ratio of the logarithmic decrement (δ) to the period; expressed in sec | [42] |
| Defined as the natural log of the second to fourth peak amplitude ratio | [42] |
P1 | Normalized relaxation index | [33, 43] |
P5 | Relaxation index at the half swing | [33, 43] |
P6 | Average relaxation index of 10 successive swings | [33] |
Ratio 1 Ratio R1 R1 ratio | Ratio 1: A1/(A1 − A2), where A1 is the amplitude of the first oscillation and A2 is the amplitude of the second oscillation. Ratio R1: A/B, where A is the amplitude of the first oscillation and B is the amplitude of the second oscillation. The amplitude of the first swing (A) divided by the amplitude of the rebound angle. | [17, 26, 32, 33, 52] |
Ratio 2 Ratio R2 R2 ratio | Ratio 2: A1/A0, where A0 is the final resting angle and A1 is the amplitude of the first oscillation. R2: first swing (A) divided by the amplitude of the final position (C). | [33, 34, 36, 16, 27, 45] |
R2n | The normalized relaxation index. R2n: A1/1.6A0 where A0 is the knee angle between the full extension (starting position) and the neutral knee joint angle (end position), and A1 is the difference between the starting angle and the maximum flexion | [33, 44, 50] |
8 | AUC P3 | Area Under Curve: area between the knee angle during oscillations and the resting angle; it is the integral of the absolute value of the knee angle | [17, 39] [33] |
Ptotal | The area between the goniogram and the time axis. | [50] |
Relative area difference | Relative difference |P + − P-|/Ptotal between the positive and negative areas and the total area between the goniogram and the neutral line starting from the first minimum | [50] |
9 | PT | Total pendulum Score (combination of multiple parameters) | [50] |
Angular Velocity | 1 | ωmax | The maximum angular velocity of the shank | [50] |
Vmax | maximal velocity of the first swing (°/s) | [16, 26, 27] |
F1 Vel | Maximum velocity during F1 Amp | [18] |
P7 | First maximum of the tachogram | [33] |
2 | VFR | Velocity to first reversal: VFR = FAR /TFR | [17, 39] |
3 | E1 Vel | Maximum velocity during E1 Amp | [18] |
P8 | First minimum the tachogram | [33] |
ωmin | The minimum angular velocity of the shank | [50] |
Angular Acceleration | 1 | F1 A/D ratio | Initial flexion acceleration/deceleration ratio = Max acceleration duration F1 Amp/ Max deceleration during F1 Amp | [18] |
First Maximum Acceleration | First Maximum Acceleration during flexion phase | [26] |
Max Acc on the rebound swing | Max Acceleration during extension phase | [26] |
The first mentioned set of outcome measures from pendulum test of spasticity on the knee were by Boczko et al.[25] in 1950s. During the following half a century, other than number of oscillations, test duration and peak angles, other measures such as relaxation index (RI) were introduced to have higher reliability. The most comprehensive works on outcome measures during this time were performed by Bajd et al.[33, 46, 47]and Stillman et al.[18]. Table 5 illustrates all categories of outcome measures that have been suggested in the literature of pendulum test of spasticity. The three main categories are parameters based on angle data, based on angular velocity, and finally based on angular acceleration. All the investigated studies have used outcome measures that are based on joint angle during the test. Almost half of the studies have used parameters that are based on angular data (Table 5). A considerable amount of the studies has used more than one category (Table 5).
Overall, the suggested parameters can be divided into two categories of primary and secondary measures. Primary measures are directly obtained from aspects of the collected data such as the peak value of an angle, or number of oscillations (for example the first six categories in Table 5 for parameters based on angle data). Secondary outcome measures are calculated or combined from the primary ones mainly to reduce the number of parameters and to come up with ones that are more sensitive or better illustrate level of spasticity.
Outcome measures that are based on angle data are divided into 9 categories in Table 5. Category #1 is based on the initial position of the extended knee in the test. Although 29% of studies (out of 17 that we have investigated) have used this category in their set of parameters, it is not an outcome measure of spasticity test by itself, but is mainly used in the calculation of other outcome measures. Second category is used by 71% of the studies and relies on the maximum flexion angle in the first swing after the leg release. Category #3 examines the max angle in the first rebound towards extension of the knee, which is used by 18% of the studies. Resting angle or the final position of the leg is category #4 and is used by 41% of the literature. Category #5 examines durations in the test, whether overall duration or the time between two specific points, and is used by 35% of the studies. Number of cycles or frequency is category #6 and is used by 59% investigators. In counting the oscillations, a threshold of three degrees is considered below which the oscillations are ignored. Frequency concept was either used as the inverse of the time duration for the first cycle, or as the ratio of the number of total cycles to the total time. Time and frequency categories could be based on angular velocity or acceleration during the test, but almost all the researchers have based them on the angle data. Categories #7–9 are secondary measures and are calculated from the previous categories. Category #7 examines the ratio of the amplitudes for various angles. Wide range of ratios have been suggested by researchers and almost all studies (94%) have used at least one such category of outcome measure. Most of the powerful and consistent outcome measure that were capable of identifying levels of spasticity were in this category[44, 45]. Category #8 uses area under the knee angle curve which considers positive and negative values for flexion and extension around the resting angle, and is used by 24% of the studies. Recently, Popovic et al. suggested a total score for pendulum test which takes many aspects of the angle cure into account and comes up with a final score[50]. This is category #9 in Table 5.
There are three categories of outcome measures in the angular velocity group. Category #1 uses the first maximum angular velocity in the flexion direction, and is used by 35% of the investigators. Category #2 relies on the average angular velocity in the first swing towards the flexion, and is used by 12% of the literature. Category #3 is based on the first maximum velocity in the rebound towards the knee extension, and is suggested by the 18% of the literature. Some of the researchers call this category the minimum velocity instead of maximum velocity in the opposite direction.
Few studies have used outcome metrics that rely on angular acceleration. Stillman et al.[18] suggested the ratio of maximum acceleration to maximum deceleration during the first swing towards flexion of the knee as their measure of spasticity. Maximum angular acceleration both in flexion and in extension phases are separately used as outcome measures by Brown et al.[26] in 1988.
As can be seen from the table, quite a lot of parameters have been suggested as outcome measures. However, it is not practical to use all of the suggested parameters, and unfortunately no study has compared all these parameters to provide a comprehensive subjective scale of strength/weakness points. None the less, some of the studies have chosen reasonable number of outcome measure (and some provided a rationale for their choice). Table 6 is the list of the main studies on the outcome measures of pendulum test that is used in this review.
Table 6
Sets of outcome measures that were proposed in each key study
# of used parameters | List of Parameters (Measures) | First author |
8 | p1-p8 (using A0, A1, A2, R1,R2,R2n) | Bajd [33] |
6 | Ex, RI, β, λ, t, n | Szopa[42] |
4 | p1, p2, p4, p5 | Yeh[43] |
1 | R2n index (using αf, αs, αp) | Vargas Luna [44] |
4 | RI, Test duration, Fang, Rest ang | Azevedo[41] |
2 | Ratio 1 & Ratio 2 | Bui[45] |
1 | PT score | Popovic-Maneski[50] |
2 | Ratio R1, Ratio R2 | Leslie[34] |
5 | Θ1, N, Duration, RI, θr | Greenan Fowler[6] |
4 | R2 ratio, R1 ratio, Vmax, Relative swing time | Nordmark[16] |
4 | First Reversal, AUC, VFR, Resting Angle | Bohannon[39] |
5 | FAR, IA, AUC, TFR, VFR | Sterpi[17] |
14 | On Ang, Rest Ang, F1 Ang, E1 Ang, F1 Amp, E1 Amp, plat Amp, RI, ERI, F1 Vel, E1 Vel, F1 A/D ratio, Duration, C1 Freq | Stillman[18] |
5 | F1 Amp, E1 Amp, plat Amp, RI, ERI | Tancredo[29] |
4 | RI, Vmax, First Maximum Acceleration, Max Acc on the rebound swing | Brown[26] |
3 | A0, A1, Resting Angle | He[35] |
6 | RI, ERI, F1Amp, E1Amp, Plat, Ncyc | Whelan[49] |
In the literature of the pendulum test for spasticity, there is no standard agreement between the researchers particularly in definition of the outcome measures. One main reason for this ambiguity is the different references used for measuring the knee angle. Overall, four key positions can be used as a reference: Horizontal plane, vertical plane, initial shank position, and final shank position in the test. Figure 3-a shows these four possible frames of reference for knee angle, along the first four categories of angle parameters in Table 5.
Most of the studies have used horizontal plane as their frame of reference[6, 16–18, 26, 29, 34, 42]. The second most popular frame of reference for angular movement is rest angle or the final position of the knee in the pendulum test[27, 33, 35, 36, 43, 50]. Some of the researchers have used the initial angle of the shank as their reference instead of horizontal plane[39, 45, 49]. No researcher has used vertical plane as their reference in knee angle measurement. One example of such ambiguity is A0 which depending on the reference is defined as “Final resting angle” [45] as well as “knee angle at the beginning of the test during maximal limb extension” [17, 35]. Similarly, differences can be observed in the definition of other spasticity measures such is definition of RI in[6, 18] and in[33, 43].
Figures 3-b illustrate two typical knee angle traces during a pendulum test. The bold trace corresponds to when the reference is the resting angle. Sections of knee angle trace, that parameters (angle outcome measures) in categories #1-#4 are extracted, are marked. The dotted trace corresponds to when the reference is horizontal plane. If the beginning of trace falls on the time axis, then the reference is initial angle.