create the summary of the findings "Methods
Subjects
Experiments were performed on 15 individuals with
paraplegic SCI (age: 34.60 ± 9.18 years; height:
169.80 ± 11.02 cm; weight: 70.86 ± 14.45 kg) and 15
able-bodied individuals (age: 30.66 ± 11.13 years;
height: 168.67±11.02 cm; weight: 67.10 ± 16 kg) as
control group.The subject population in this study was
a sample of convenience made up of the subjects who
were between the ages of 21 and 55 years. They were
consecutive subjects who agreed to participate and fulfilled the inclusion criteria. The subjects with SCI
(n=15) all had clinically stable lesions between the
neurological levels of T4–L1, signified by a lack of sensation and voluntary movement below the level of
injury. Considering the American Spinal Injury
Association (ASIA) Impairment Scale (AIS) for SCI,
patients were classified as having incomplete injury
(grade C, AIS-C). Patients with higher level injuries
were excluded to provide a group of patients with
similar physiological characteristics. In this study, SCI
occurred following motor vehicle accident, falls,
gunshot wounds, lifting heavy objects during a parade
and from Myelin degeneration. Detailed information
is provided in the Results section. Healthy subjects,
matched in age, were selected as control. All the subjects
signed an informed consent form approved by the
human subjects committee at the University of Social
Welfare and Rehabilitation Sciences before participating
in the study. Physical characteristics of the subjects in
each group are shown in Table 1.
Joghtaei et al. Passive knee stiffness and viscosity in individuals with SCI
The Journal of Spinal Cord Medicine 2015 VOL. 38 NO. 2 171
Passive pendulum test procedure
Passive pendulum testing is a means of acquiring passive
viscous-elastic parameters of the knee. The subject was
placed in a semi-upright sitting position (45°) with the
lower legs hanging over the edge of a chair (Fig. 1).
The thigh was tightened with a strap to make it stays
in a stationary condition. To avoid any modification
to the passive characteristic of the knee due to ankle
movements, a plastic ankle foot orthosis was used to
keep the ankle at 90°. The subject’s shank was raised
and held by the examiner with the knee in maximum
extension until the knee muscle was completely
relaxed. This may take about 10–15 seconds. Then the
subject’s leg was released and was allowed to swing
and oscillate freely between flexion and extension and
the leg movement was recorded until the shank
reaches its final resting position and stopped. The
viscous-elastic properties of the joint and surrounding
tissues, together with the mass of the moving foot and
leg, caused the leg to finally come to rest close to the
vertical position. Using a flexible twin axis electronic
goniometer (Model: SG110/A, Biometrics Ltd,
Newport, UK), movements of the leg were recorded
during a passive pendulum test. During testing procedure, the subject’s eyes were kept close using sleep
masks. The test was performed three times and the
mean value of three measurements was taken for the
analysis.
Measurements and estimations
There are several variables that could be derived from
kinematics of pendulum test. The following displacement and timing parameters were measured using the
Wartenberg’s technique8–12 (Fig. 2):
• Start angle, onset angle (OA)
• Resting angle (RA)
• First three peak flexion angles (F1, F2, F3)
• First three peak extension angles (E1, E2, E3)
• Amplitude of initial flexion (F1Amp = F1−OA)
• Amplitude of initial extension (E1Amp = F1−E1)
• Plateau amplitude (PA = RA−OA)
• Relaxation index (RI = F1Amp/PA)
• Extension relaxation index , (ERI = E1Amp/PA)
• Period of the first cycle (T)
Some kinematic data of knee motion and anthropometric measures were used to compute the viscosity
and stiffness. Knee stiffness (K) and viscosity (B) were
estimated by computing the damping ratio (ζ) and the
natural frequency (ωn) obtained from the test data
using the following equations reported by others8
:
ωn =

K′
J

= 2π
T
ζ = B
2 
JK′ √ =

(ln D)
2
4π2 + (ln D)
2

D = θ1
θ2
ωn = K′
J = 2π
T
The estimation for J and mass characteristics (m and l)
were obtained for the subjects according to Winter.18
Table 1 Demographic data of the subjects (mean±SD)
Variables Patients with paraplegia and SCI (n=15) Healthy subjects (n=15)
Age (years) 36.22 ± 11.16 30.16 ± 12.08
Weight (kg) 69.55 ± 17.61 65.83 ± 8.83
Height (m) 1.71 ± 0.15 1.7 ± 0.03
Sex Male (n = 8) 53.3% (n = 8) 53.3%
Female (n = 7) 46.7% (n = 7) 46.7%
Cause of SCI Motor vehicle accident (n = 9) 60% NA
Fall (n = 2) 13.33% NA
Gunshot (n = 1) 6.66% NA
Lifting heavy objects (n = 1) 6.66% NA
Myelin virus (n = 2) 13.33% NA
SD, standard deviation; NA, not applicable.
Figure 1 Passive pendulum test experiment.
Joghtaei et al. Passive knee stiffness and viscosity in individuals with SCI
172 The Journal of Spinal Cord Medicine 2015 VOL. 38 NO. 2
Figure 2 Pendulum test angular values for one healthy subject and two patients with paraplegic SCI. (A) Typical electrogoniometric
output during pendulum test in a healthy subject. (B, C) Pendulum test angular response for two patients with paraplegia.
Joghtaei et al. Passive knee stiffness and viscosity in individuals with SCI
The Journal of Spinal Cord Medicine 2015 VOL. 38 NO. 2 173
The values of viscosity (B) and stiffness (K) were
obtained as follows:
B = 2 × ζ × ωn × J K = K′ − mgl
2
where “J” is the sagittal moment of inertia applied to
the leg-foot complex rotation around the knee axis;
“m” is the leg-foot complex mass; “g” is the gravity
acceleration, and “l” is the leg-foot length from the
knee axis; “θ1” is the peak angle of one cycle; “θ2” is
the peak angle of the following cycle and “T” is the
period of one cycle. To assure reliability of measurements, the same examiner tested all participants.
The data were normalized by dividing the results of
moment of inertia, stiffness, and viscosity by the fifth
power of body stature according to the procedure previously described by others.7,8
Statistical analysis
Statistical analysis was performed using SPSS version
17.0 (SPSS Inc., Chicago, IL, USA). Multivariate analysis of variance (ANOVA) was used to compare the stiffness, viscosity, and kinematic data assessed during the
pendulum test in healthy subjects and those with paraplegic SCI. The alpha level was set at 0.05.
Results
The demographic data for two individual groups are displayed in Table 1. There was no statistically significant
difference in subjects’ age (P = 0.27), height (P = 0.87),
and weight (P = 0.51) among the two groups. Of the
subjects with SCI, nine were from motor vehicle accident, two from falls, one from gunshot wounds, one
lifting heavy objects during a parade, and two from
myelin degeneration secondary to, they claim, virus of
unknown origin. Of subjects with paraplegia, eight
were male and seven were female. Of the control
group, eight were male and seven female.
Pendulum test angular values for one control subject
and two subjects with paraplegic SCI as a sample are presented in Fig. 2. The plots for subjects with SCI showed
that not all persons with SCI respond the same way
during test. However, control subjects responded similarly.
Fig. 3 depicts the mean values of the first three peak
flexion and extension angles (F1, F2, F3, E1, E2, E3)
in subjects with and without SCI.
The results of the multivariate ANOVA for betweensubject effect in tested variables is shown in Table 2.
Descriptive statistics (mean ± SD) for some kinematic
data assessed during the pendulum test and comparison
between two groups are presented in Table 3.
There was significant difference in the stiffness
between healthy subjects and those with paraplegic
SCI (P = 0.01) (Table 3). The results indicated that subjects with SCI have significantly greater stiffness compared to able-bodied subjects. However, no significant
difference was found in the viscosity (P = 0.17)
between two groups (Table 3).
Except for F1Amp, all other displacement parameters
exhibited no statistically significant difference between
subjects with and without SCI (Table 3)."