Accepted Manuscript Title: The validity and reliability of modelled neural and tissue properties of the ankle muscles in children with cerebral palsy Author: Lizeth H Sloot Marjolein M van der Krogt Karin L. de Gooijer-van de Groep Stijn van Eesbeek Jurriaan de Groot Annemieke I. Buizer Carel Meskers Jules G Becher Erwin de Vlugt Jaap Harlaar PII: DOI: Reference:
S0966-6362(15)00447-6 http://dx.doi.org/doi:10.1016/j.gaitpost.2015.04.006 GAIPOS 4466
To appear in:
Gait & Posture
Please cite this article as: Sloot LH, Krogt MM, Groep KLG-v, van Eesbeek S, de Groot J, Buizer AI, Meskers C, Becher JG, de Vlugt E, Harlaar J, The validity and reliability of modelled neural and tissue properties of the ankle muscles in children with cerebral palsy, Gait and Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The validity and reliability of modelled neural and tissue properties of the ankle muscles in children with cerebral palsy Lizeth H Sloot1, Marjolein M van der Krogt1 , Karin L. de Gooijer-van de Groep2 , Stijn van Eesbeek3 ,
Department of Rehabilitation Medicine, MOVE research institute Amsterdam, VU University Medical
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1
ip t
Jurriaan de Groot2, Annemieke I. Buizer1, Carel Meskers1, Jules G Becher1, Erwin de Vlugt3, Jaap Harlaar1
us
Center, Amsterdam, The Netherlands
Department of Rehabilitation Medicine, Leiden University Medical Center, Leiden, The Netherlands
3
Faculty of Mechanical Engineering, Delft University of Technology, Delft, The Netherlands
M
an
2
Acknowledgements
Ac ce p
Keywords:
te
d
This research was financially supported by Grant 10733 from the Dutch Technology Foundation STW.
1. Muscle stiffness
2. Muscle spasticity 3. Cerebral palsy 4. Biomechanics
5. Rehabilitation
Research highlights: •
Modelled neuromuscular ankle parameters were validated in patients with CP
•
Tissue and neural parameters and variability differed between patients and controls
Page 1 of 30 1
Between-trial and between-day repeatability was medium to good
•
A large variability in tissue and neural contributions was found in patients
Ac ce p
te
d
M
an
us
cr
ip t
•
Page 2 of 30 2
Abstract
2
Spastic cerebral palsy (CP) is characterized by increased joint resistance, caused by a mix of increased tissue
3
stiffness, as well as involuntary reflex and background muscle activity. These properties can be quantified
4
using a neuromechanical model of the musculoskeletal complex and instrumented assessment. The
5
construct validity of the neuromechanical parameters was examined (i.e. the internal model validity, effect of
6
knee angle, speed and age, sensitivity to patients versus controls, spasticity severity and treatment), together
7
with the repeatability. We included 38 children with CP and 35 controls. A motor driven footplate applied
8
two slow (5 °/s) and two fast (100 °/s) rotations around the ankle joint, at two different knee angles. Ankle
9
angle, torque and EMG of the gastrocnemius (GA), soleus (SO) and tibialis anterior (TA) muscle were used to
10
optimize a nonlinear neuromuscular model. Outcome measures were tissue stiffness, reflex and background
11
activity for GA, SO and TA. The internal model validity showed medium to high parameter confidence and
12
good model fits. All parameter could discriminate between patients with CP and controls according to CP
13
pathology. Other measures of external model validity (effect of test position, speed and age) showed
14
behavior along the lines of current knowledge of physiology. GA/SO background activity was sensitive to
15
spasticity severity, but reflex activity was not. Preliminary data indicated that reflex activity was reduced
16
after spasticity treatment. The between-trial and -day repeatability was moderate to good. The large
17
variance between patients in the ratio of stiffness and neural resistance indicates that the method could
18
potentially contribute to patient-specific treatment selection.
Ac ce p
te
d
M
an
us
cr
ip t
1
Page 3 of 30 3
19 Introduction
2
Spastic cerebral palsy (CP) is characterized by increased joint resistance to motion, which is caused by neural
3
as well as tissue impairments 1. Among the neural impairments are increased reflex activity (i.e. a velocity
4
dependent increase in muscle tone or spasticity 2), co-contraction, and non-stretch related contractions (i.e.
5
background activation) 3, 4. The tissue impairments comprise altered visco-elastic properties of connective
6
tissues, muscle or tendon 4. The discrimination between neural and tissue impairments largely guides the
7
selection of treatments that aim to reduce joint resistance. In case of suspected neural origin, muscle
8
activation can be reduced by botulinum toxin (BTX-A) or selective dorsal rhizotomy (SDR) 5, 6, while suspected
9
tissue impairments can be treated by corrective casting or splinting 7. Thus, objective quantification of
cr
us
an
neuromechanical joint parameters could contribute to patient specific treatment in CP.
12
Current clinical assessment of joint resistance is based on manual testing of the resistance to slow and/or
13
fast movements, such as the Ashworth and Tardieu-like tests. These clinical tests do not allow for objective
14
quantification, because they are found to be subjective, of low resolution, and limited in discriminating
15
neural and tissue components 8-10. Instrumented manual measurements have been shown to result in an
16
increased precision 11-13. Nevertheless, these manual tests still lack standardization of exerted force and
17
movement velocity, while spasticity is known to be force- and velocity dependent 13.
te
Ac ce p
18
d
11
M
10
ip t
1
19
Neuromuscular modelling combined with motorized assessment has been demonstrated to quantitatively
20
distinguish between reflex activity and tissue viscoelasticity around the ankle in stroke patients and patients
21
with CP 14, 15. However, previous models only tested in the dorsiflexion direction and did not include the
22
tissue properties of the major antagonist (tibialis anterior), even though its field of activity could overlap with
23
those of a shortened triceps surae muscle. In addition, they modelled the lumped properties of the triceps
24
surae and were thus unable to distinguish between the contribution of the soleus and gastrocnemius. These
Page 4 of 30 4
models did not take any non-stretch related background activity into account 3, 4. Finally, the validity of the
26
model has not yet been established in young children with CP, but only in adolescents, while the
27
impairments of these children worsen during growth and are thus often assessed and treated before the end
28
of their growth.
ip t
25
29
Therefore, the aim of the study was to present an extended motorized assessment protocol (to separate
31
between soleus and gastrocnemius) combined with an extended neuromuscular ankle model (including
32
antagonists and estimation of background activity); and to assess the construct validity and repeatability of
33
derived neural and tissue parameters. For construct validity, i.e. the extent to which the results correspond
34
with current knowledge of the neuromuscular ankle system in CP by a lack of a true gold standard 16, 17, we
35
examined the internal model validity (parameter confidence and model fit), and external model validity
36
(effect of two different test positions, movement speed, and age; patients versus controls; spasticity
37
severity, and treatment).
38
te
d
M
an
us
cr
30
Methods
2
Subjects
3
We included a convenience sample of 38 children with CP (10.5±2.9 yr; 16 GMFCS-I, 16 GMFCS-II, 6 GMFCS-
4
III; 18 male) and 35 typically developing children (10.1±2.7 yr, 15 male). Patients were included if they were
5
between 6 and 18 years old, had a clinical diagnosis of spastic uni- or bilateral CP and excluded if they were
6
not able to extent their knee to 20° knee flexion, had additional medical problems interfering with joint
7
neuromechanical characteristics, or severe cognitive deficits interfering with participation in the study.
8
Informed consent was provided and the study was approved by the local medical ethics committee.
Ac ce p
1
9 10
Procedures
Page 5 of 30 5
All children were measured at the ankle dynamometer. In a random subset of 29 patients (10.3±3.3 yr), the
12
spasticity score (SPAT) was collected and subdivided into a low (SPAT 0 and 1, n=16) and high (SPAT 2+, n=13)
13
spasticity severity group 18. Four patients (12.3±1.5 yr, GMFCS I-III) were measured before and after
14
treatment (2 received BTX-A in the gastrocnemius muscles and 2 underwent SDR). To assess repeatability,
15
12 patients (9.8±3.1 yr; GMFCS I-II) were measured on two occasions, 9.0±7.3 days apart, without any
16
treatment in between.
cr
ip t
11
us
17 Instrumentation
19
Subjects were seated in an adjustable chair, with a fixed 120º hip angle and the knee adjusted to 20° and 70°
20
flexion (figure 1). In patients, the foot of the most affected leg was fixed in an adjustable footplate that
21
allowed for talus repositioning, i.e. correction of ab/adduction and pro/supination of the forefoot with
22
respect to the talus and calcaneus for an optimal fixation (figure 1) 19. In controls, the right foot was fixed in a
23
rigid footplate. The footplates were motor driven and applied rotations around the ankle joint in the sagittal
24
plane (MOOG, Nieuw Vennep, The Netherlands). The axes of the ankle (talo crural joint) and the motor were
25
visually aligned by minimizing knee translation during rotating. EMG electrodes (Ø 15mm, 24mm inter-
26
electrode distance) were placed on the tibialis anterior (TA), soleus (SO), gastrocnemius medialis and lateralis
27
(together GA) muscles according to SENIAM guidelines 20. Angular displacement, foot reaction torque and
28
muscle activity (Porti7, TMSi B.V., The Netherlands) were measured at 1024 Hz. EMG was high-pass filtered
29
(bi-directional 3rd order Butterworth at 20 Hz), rectified and low-pass filtered (uni-directional 4th order Bessel
30
filter at 20 Hz) to obtain the envelope. The angle and torque data were identically low-pass filtered and all
31
data were resampled to 128 Hz.
Ac ce p
te
d
M
an
18
32 33
Measurement protocol
34
The ankle angle offset was calibrated by measuring the position of the footplate corresponding to 30 º ankle
35
plantar flexion, which was determined by goniometry. The passive ankle range of motion (ROM) was Page 6 of 30 6
determined by imposing an age- and disorder-dependent maximal flexion and extension torque (Appendix
37
A). Next, two repetitions of ramp-and-hold rotations were imposed at 15 and at 100 º/s, starting at a random
38
time instant to prevent anticipation and with at least 20s rest between measurements. Subjects were
39
instructed to remain relaxed and not resist any motion during the measurements. The measurements were
40
performed at both 20° and 70° knee flexion, conform clinical testing 18. The outcomes at these angles are
41
from here on referred as SO and GA/SO, because the soleus is expected to be the dominant muscle at 70°
42
knee flexion, since the gastronemii are too short to generate force 21. TA properties were included for both
43
angles, but examined at 20° knee flexion.
us
cr
ip t
36
an
44 Neuromuscular model
46
Ankle angle and EMG signals were cropped from start to stop of the dorsal and plantar flexion movement
47
and used as an input to the nonlinear neuromuscular model. For each trial, the model estimated the passive
48
stiffness and neural torques around the ankle by optimizing the quadratic difference between the modelled
49
and recorded total ankle torque (Appendix B). This extended model comprised TA passive stiffness
50
parameters (enabled by the inclusion of movement towards plantar flexion), relaxation between the bi-
51
directional movements, and age scaling of physiological parameters, while it did not include viscosity and
52
inertia (Appendix B). A total of 10 model parameters were optimized, including four passive tissue
53
parameters (two exponential shape parameters and muscle slack lengths), five neural parameters related to
54
the activation dynamics (four EMG gains and the neural filter frequency), as well as an offset torque to
55
account for the relaxation between the dorsal and plantar flexion curves (Appendix C).
Ac ce p
te
d
M
45
56 57
The passive stiffness and neural torques estimated by the optimized model were used to determine the
58
outcome parameters (figure 2). Tissue ‘stiffness’ was expressed as the limitation in ankle rotation due to
59
passive resistance during the slow trials, being the flexion angle corresponding to 3 Nm of stiffness torque
60
(dorsiflexion for TS and plantar flexion for TA) , subtracted from the highest measured angles in all subjects Page 7 of 30 7
(60° for TS and 80° for TA) for better comparison. Reflex and background activity were calculated from the
62
fast trials. Background activity torque was the minimum muscle activation measured over the entire trial
63
related to force via the Hill type muscle model (Appendix B). The reflex activity torque was the total neural
64
torque subtracted by the background torque. Reflex and background activity were both parameterized by
65
the root-mean-square (rms) of their corresponding torque. All modelling and analyses were performed in
66
Matlab (The Mathworks Inc., Natick MA).
cr
ip t
61
us
67 Statistics
69
To examine the internal model validity, we determined the standard error of the mean (SEM) of the
70
parameter estimation, with low values representing high parameter confidence 14. The goodness of the
71
model fit was represented by the variance accounted for (VAF) 14. VAF values lower than 90% were discarded
72
from the analysis (a total of 3 trials) for possible poor fixation or misalignment of the motor and ankle. For
73
external model validity, the effects of knee angle, movement velocity and age were examined using sign-rank
74
tests and Spearman’s correlation coefficients. Median differences between patients and controls and
75
between low and high spasticity groups was examined using rank-sum tests; differences in variance between
76
patients and controls using Levene’s tests. The (preliminary) effect of spasticity treatment was evaluated
77
using sign-rank tests. To determine the reliability for the patients, data were checked for any systematic
78
difference using the sign rank tests. The between-trial and -day repeatability were examined using intra class
79
correlation coefficients (ICC, 2-way mixed model), the standard error of measurement (SEM) and the smallest
80
detectable difference (SDD) 22. Statistics were performed using IBM SPSS statistics 20 and Matlab.
Ac ce p
te
d
M
an
68
81 1
Results
2
Internal model validity
Page 8 of 30 8
3
SEM values were less than 0.1% for 6 out of 10 parameters, but were high for the slack length parameters of
4
both TS and TA (125% and 40%), the neural filter frequency f0 (19%) and the relaxation offset (104%)
5
(Appendix C). Median VAF value was 98.7 (IQR = 1.3).
ip t
6 External model validity
8
Stiffness changed with knee angle, with a 9.80% increase in GA/SO compared to SO stiffness and a 4.5%
9
decrease for TA at the same angles (both p
S0966-6362(15)00447-6 http://dx.doi.org/doi:10.1016/j.gaitpost.2015.04.006 GAIPOS 4466
To appear in:
Gait & Posture
Please cite this article as: Sloot LH, Krogt MM, Groep KLG-v, van Eesbeek S, de Groot J, Buizer AI, Meskers C, Becher JG, de Vlugt E, Harlaar J, The validity and reliability of modelled neural and tissue properties of the ankle muscles in children with cerebral palsy, Gait and Posture (2015), http://dx.doi.org/10.1016/j.gaitpost.2015.04.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
The validity and reliability of modelled neural and tissue properties of the ankle muscles in children with cerebral palsy Lizeth H Sloot1, Marjolein M van der Krogt1 , Karin L. de Gooijer-van de Groep2 , Stijn van Eesbeek3 ,
Department of Rehabilitation Medicine, MOVE research institute Amsterdam, VU University Medical
cr
1
ip t
Jurriaan de Groot2, Annemieke I. Buizer1, Carel Meskers1, Jules G Becher1, Erwin de Vlugt3, Jaap Harlaar1
us
Center, Amsterdam, The Netherlands
Department of Rehabilitation Medicine, Leiden University Medical Center, Leiden, The Netherlands
3
Faculty of Mechanical Engineering, Delft University of Technology, Delft, The Netherlands
M
an
2
Acknowledgements
Ac ce p
Keywords:
te
d
This research was financially supported by Grant 10733 from the Dutch Technology Foundation STW.
1. Muscle stiffness
2. Muscle spasticity 3. Cerebral palsy 4. Biomechanics
5. Rehabilitation
Research highlights: •
Modelled neuromuscular ankle parameters were validated in patients with CP
•
Tissue and neural parameters and variability differed between patients and controls
Page 1 of 30 1
Between-trial and between-day repeatability was medium to good
•
A large variability in tissue and neural contributions was found in patients
Ac ce p
te
d
M
an
us
cr
ip t
•
Page 2 of 30 2
Abstract
2
Spastic cerebral palsy (CP) is characterized by increased joint resistance, caused by a mix of increased tissue
3
stiffness, as well as involuntary reflex and background muscle activity. These properties can be quantified
4
using a neuromechanical model of the musculoskeletal complex and instrumented assessment. The
5
construct validity of the neuromechanical parameters was examined (i.e. the internal model validity, effect of
6
knee angle, speed and age, sensitivity to patients versus controls, spasticity severity and treatment), together
7
with the repeatability. We included 38 children with CP and 35 controls. A motor driven footplate applied
8
two slow (5 °/s) and two fast (100 °/s) rotations around the ankle joint, at two different knee angles. Ankle
9
angle, torque and EMG of the gastrocnemius (GA), soleus (SO) and tibialis anterior (TA) muscle were used to
10
optimize a nonlinear neuromuscular model. Outcome measures were tissue stiffness, reflex and background
11
activity for GA, SO and TA. The internal model validity showed medium to high parameter confidence and
12
good model fits. All parameter could discriminate between patients with CP and controls according to CP
13
pathology. Other measures of external model validity (effect of test position, speed and age) showed
14
behavior along the lines of current knowledge of physiology. GA/SO background activity was sensitive to
15
spasticity severity, but reflex activity was not. Preliminary data indicated that reflex activity was reduced
16
after spasticity treatment. The between-trial and -day repeatability was moderate to good. The large
17
variance between patients in the ratio of stiffness and neural resistance indicates that the method could
18
potentially contribute to patient-specific treatment selection.
Ac ce p
te
d
M
an
us
cr
ip t
1
Page 3 of 30 3
19 Introduction
2
Spastic cerebral palsy (CP) is characterized by increased joint resistance to motion, which is caused by neural
3
as well as tissue impairments 1. Among the neural impairments are increased reflex activity (i.e. a velocity
4
dependent increase in muscle tone or spasticity 2), co-contraction, and non-stretch related contractions (i.e.
5
background activation) 3, 4. The tissue impairments comprise altered visco-elastic properties of connective
6
tissues, muscle or tendon 4. The discrimination between neural and tissue impairments largely guides the
7
selection of treatments that aim to reduce joint resistance. In case of suspected neural origin, muscle
8
activation can be reduced by botulinum toxin (BTX-A) or selective dorsal rhizotomy (SDR) 5, 6, while suspected
9
tissue impairments can be treated by corrective casting or splinting 7. Thus, objective quantification of
cr
us
an
neuromechanical joint parameters could contribute to patient specific treatment in CP.
12
Current clinical assessment of joint resistance is based on manual testing of the resistance to slow and/or
13
fast movements, such as the Ashworth and Tardieu-like tests. These clinical tests do not allow for objective
14
quantification, because they are found to be subjective, of low resolution, and limited in discriminating
15
neural and tissue components 8-10. Instrumented manual measurements have been shown to result in an
16
increased precision 11-13. Nevertheless, these manual tests still lack standardization of exerted force and
17
movement velocity, while spasticity is known to be force- and velocity dependent 13.
te
Ac ce p
18
d
11
M
10
ip t
1
19
Neuromuscular modelling combined with motorized assessment has been demonstrated to quantitatively
20
distinguish between reflex activity and tissue viscoelasticity around the ankle in stroke patients and patients
21
with CP 14, 15. However, previous models only tested in the dorsiflexion direction and did not include the
22
tissue properties of the major antagonist (tibialis anterior), even though its field of activity could overlap with
23
those of a shortened triceps surae muscle. In addition, they modelled the lumped properties of the triceps
24
surae and were thus unable to distinguish between the contribution of the soleus and gastrocnemius. These
Page 4 of 30 4
models did not take any non-stretch related background activity into account 3, 4. Finally, the validity of the
26
model has not yet been established in young children with CP, but only in adolescents, while the
27
impairments of these children worsen during growth and are thus often assessed and treated before the end
28
of their growth.
ip t
25
29
Therefore, the aim of the study was to present an extended motorized assessment protocol (to separate
31
between soleus and gastrocnemius) combined with an extended neuromuscular ankle model (including
32
antagonists and estimation of background activity); and to assess the construct validity and repeatability of
33
derived neural and tissue parameters. For construct validity, i.e. the extent to which the results correspond
34
with current knowledge of the neuromuscular ankle system in CP by a lack of a true gold standard 16, 17, we
35
examined the internal model validity (parameter confidence and model fit), and external model validity
36
(effect of two different test positions, movement speed, and age; patients versus controls; spasticity
37
severity, and treatment).
38
te
d
M
an
us
cr
30
Methods
2
Subjects
3
We included a convenience sample of 38 children with CP (10.5±2.9 yr; 16 GMFCS-I, 16 GMFCS-II, 6 GMFCS-
4
III; 18 male) and 35 typically developing children (10.1±2.7 yr, 15 male). Patients were included if they were
5
between 6 and 18 years old, had a clinical diagnosis of spastic uni- or bilateral CP and excluded if they were
6
not able to extent their knee to 20° knee flexion, had additional medical problems interfering with joint
7
neuromechanical characteristics, or severe cognitive deficits interfering with participation in the study.
8
Informed consent was provided and the study was approved by the local medical ethics committee.
Ac ce p
1
9 10
Procedures
Page 5 of 30 5
All children were measured at the ankle dynamometer. In a random subset of 29 patients (10.3±3.3 yr), the
12
spasticity score (SPAT) was collected and subdivided into a low (SPAT 0 and 1, n=16) and high (SPAT 2+, n=13)
13
spasticity severity group 18. Four patients (12.3±1.5 yr, GMFCS I-III) were measured before and after
14
treatment (2 received BTX-A in the gastrocnemius muscles and 2 underwent SDR). To assess repeatability,
15
12 patients (9.8±3.1 yr; GMFCS I-II) were measured on two occasions, 9.0±7.3 days apart, without any
16
treatment in between.
cr
ip t
11
us
17 Instrumentation
19
Subjects were seated in an adjustable chair, with a fixed 120º hip angle and the knee adjusted to 20° and 70°
20
flexion (figure 1). In patients, the foot of the most affected leg was fixed in an adjustable footplate that
21
allowed for talus repositioning, i.e. correction of ab/adduction and pro/supination of the forefoot with
22
respect to the talus and calcaneus for an optimal fixation (figure 1) 19. In controls, the right foot was fixed in a
23
rigid footplate. The footplates were motor driven and applied rotations around the ankle joint in the sagittal
24
plane (MOOG, Nieuw Vennep, The Netherlands). The axes of the ankle (talo crural joint) and the motor were
25
visually aligned by minimizing knee translation during rotating. EMG electrodes (Ø 15mm, 24mm inter-
26
electrode distance) were placed on the tibialis anterior (TA), soleus (SO), gastrocnemius medialis and lateralis
27
(together GA) muscles according to SENIAM guidelines 20. Angular displacement, foot reaction torque and
28
muscle activity (Porti7, TMSi B.V., The Netherlands) were measured at 1024 Hz. EMG was high-pass filtered
29
(bi-directional 3rd order Butterworth at 20 Hz), rectified and low-pass filtered (uni-directional 4th order Bessel
30
filter at 20 Hz) to obtain the envelope. The angle and torque data were identically low-pass filtered and all
31
data were resampled to 128 Hz.
Ac ce p
te
d
M
an
18
32 33
Measurement protocol
34
The ankle angle offset was calibrated by measuring the position of the footplate corresponding to 30 º ankle
35
plantar flexion, which was determined by goniometry. The passive ankle range of motion (ROM) was Page 6 of 30 6
determined by imposing an age- and disorder-dependent maximal flexion and extension torque (Appendix
37
A). Next, two repetitions of ramp-and-hold rotations were imposed at 15 and at 100 º/s, starting at a random
38
time instant to prevent anticipation and with at least 20s rest between measurements. Subjects were
39
instructed to remain relaxed and not resist any motion during the measurements. The measurements were
40
performed at both 20° and 70° knee flexion, conform clinical testing 18. The outcomes at these angles are
41
from here on referred as SO and GA/SO, because the soleus is expected to be the dominant muscle at 70°
42
knee flexion, since the gastronemii are too short to generate force 21. TA properties were included for both
43
angles, but examined at 20° knee flexion.
us
cr
ip t
36
an
44 Neuromuscular model
46
Ankle angle and EMG signals were cropped from start to stop of the dorsal and plantar flexion movement
47
and used as an input to the nonlinear neuromuscular model. For each trial, the model estimated the passive
48
stiffness and neural torques around the ankle by optimizing the quadratic difference between the modelled
49
and recorded total ankle torque (Appendix B). This extended model comprised TA passive stiffness
50
parameters (enabled by the inclusion of movement towards plantar flexion), relaxation between the bi-
51
directional movements, and age scaling of physiological parameters, while it did not include viscosity and
52
inertia (Appendix B). A total of 10 model parameters were optimized, including four passive tissue
53
parameters (two exponential shape parameters and muscle slack lengths), five neural parameters related to
54
the activation dynamics (four EMG gains and the neural filter frequency), as well as an offset torque to
55
account for the relaxation between the dorsal and plantar flexion curves (Appendix C).
Ac ce p
te
d
M
45
56 57
The passive stiffness and neural torques estimated by the optimized model were used to determine the
58
outcome parameters (figure 2). Tissue ‘stiffness’ was expressed as the limitation in ankle rotation due to
59
passive resistance during the slow trials, being the flexion angle corresponding to 3 Nm of stiffness torque
60
(dorsiflexion for TS and plantar flexion for TA) , subtracted from the highest measured angles in all subjects Page 7 of 30 7
(60° for TS and 80° for TA) for better comparison. Reflex and background activity were calculated from the
62
fast trials. Background activity torque was the minimum muscle activation measured over the entire trial
63
related to force via the Hill type muscle model (Appendix B). The reflex activity torque was the total neural
64
torque subtracted by the background torque. Reflex and background activity were both parameterized by
65
the root-mean-square (rms) of their corresponding torque. All modelling and analyses were performed in
66
Matlab (The Mathworks Inc., Natick MA).
cr
ip t
61
us
67 Statistics
69
To examine the internal model validity, we determined the standard error of the mean (SEM) of the
70
parameter estimation, with low values representing high parameter confidence 14. The goodness of the
71
model fit was represented by the variance accounted for (VAF) 14. VAF values lower than 90% were discarded
72
from the analysis (a total of 3 trials) for possible poor fixation or misalignment of the motor and ankle. For
73
external model validity, the effects of knee angle, movement velocity and age were examined using sign-rank
74
tests and Spearman’s correlation coefficients. Median differences between patients and controls and
75
between low and high spasticity groups was examined using rank-sum tests; differences in variance between
76
patients and controls using Levene’s tests. The (preliminary) effect of spasticity treatment was evaluated
77
using sign-rank tests. To determine the reliability for the patients, data were checked for any systematic
78
difference using the sign rank tests. The between-trial and -day repeatability were examined using intra class
79
correlation coefficients (ICC, 2-way mixed model), the standard error of measurement (SEM) and the smallest
80
detectable difference (SDD) 22. Statistics were performed using IBM SPSS statistics 20 and Matlab.
Ac ce p
te
d
M
an
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Results
2
Internal model validity
Page 8 of 30 8
3
SEM values were less than 0.1% for 6 out of 10 parameters, but were high for the slack length parameters of
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both TS and TA (125% and 40%), the neural filter frequency f0 (19%) and the relaxation offset (104%)
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(Appendix C). Median VAF value was 98.7 (IQR = 1.3).
ip t
6 External model validity
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Stiffness changed with knee angle, with a 9.80% increase in GA/SO compared to SO stiffness and a 4.5%
9
decrease for TA at the same angles (both p
