Proceedings of the 2014 IEEE/SICE International
Symposium on System Integration, Chuo University,
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Similarities and Differences in Manual Stretching ofPhysical Therapists for Equinovarus
Naomi Yamada, Shogo Okamoto, Hiroshi Okumura, Yoji Yamada, Kaoru Isogai, and Keisuke Kawakami
Abstract— For equinovarus, a foot condition commonly suffered as a side effect of stroke, sustained muscle stretching is
the primary form of treatment, most of which is manually
performed by physical therapists (PTs). It is important to
identify variations in the execution of manual stretching techniques by PTs for the standardization of therapeutic techniques.
In this study, manual stretching motions performed by three
PTs on one stroke survivor were analyzed in terms of footposture and the force and torque applied to the diseased
foot, which were measured through a motion capture system
and instrumented foot brace. Statistical analyses based on
the principal component analysis showed that many of thestretching motions of the PTs were similar in that they served tocontrol the deformed foot. However, individual differences wereobserved in the force applied to the heel and the inversion andeversion torque around the ankle, suggesting that individual
PTs may stretch different muscle groups. Furthermore, there
are potential differences in the efficiency of stretching technique
execution among PTs.

I. INTRODUCTION
Equinovarus is one of the major side effects developedin the foot on the paralyzed side of the body of stroke
survivors. Owing to this symptom, the plantar flexors of thefoot become overly excited, and human postural control isimpaired during standing and walking [1], [2]. As shown in
Fig. 1, unintended plantar flexion and inversion of the footresult. The gait stability decreases because of the marginalcontact between the ground and the deformed sole [3]. An
epidemic study reported that approximately 30% of stroke
survivors have a foot deformity [4]. These issues typicallycontinue after discharge and diminish the ability to performdaily activities and the quality of life [5].
For equinovarus, common treatment is stretching of the
spastic muscles of the foot. Sustained stretching prevents thechronic shortening and hyperexcitation of these muscles andmaintains a healthy range of joint motion [6], [7], [8]. Somevariations exist in the clinical stretching for equinovarus
foot. Some studies compared the effects of static and cyclic
stretching, and others discussed whether or not the torqueapplied to the foot during stretching should be constant [7],[9]. According to these studies, both static and cyclic stretching were effective for decreasing joint stiffness. However,N.Yamada and K. Kawakami are with the Department of Physicaland Occupational Therapy, Graduate School of Health Sciences, Nagoya
University, 1-1-20, Daikominami, Higashi-ku, Nagoya, Japan.
S. Okamoto, H. Okumura, Y. Yamada and K. Isogai are with the
Department of Mechanical Science and Engineering, Graduate School ofEngineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Japan
K. Isogai is also with the Department of Physical Therapy, Facultyof Health and Medical, Tokoha University, 1230, Miyakoda-cho, Kita-ku,
Hamamatsu, Japan.

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Fig. 1.

Equinovarus. Right foot: deformed. Left foot: healthy.

static stretching led to greater relaxation of deformed foottorques than cyclic stretching did. Whereas some have studied effective stretching techniques for equinovarus regarding
the strength and duration of stretching, thus far, few studies
have focused on the complexity of the foot joint. There haverarely been studies on the directions of torques applied to thefoot and their time course during stretching. The purpose of
stretching is to stretch muscles and tendons running througha three-dimensional body structure. In particular, the ankle
consists of multiple degrees of freedom in motion and several
related muscles. Hence, the direction of stretching is very
important, and so are its strength and duration.
In clinical rehabilitation, a large part of stretching treatments for equinovarus is manually performed by physicaltherapists. They typically stretch the spastic or shortened
muscles of the foot in its dorsal direction by applying asufficiently strong force on the foot sole. They must be sure
to maintain control of foot during inversion/eversion andadduction/abduction motions. Because motions of the ankle
around its multiple axes affect each other, directions andtimings of forces, which are applied to the foot by therapists,
depend on and are regulated by the muscles related toequinovarus. Furthermore, in order to smooth the movementof the ankle joint during stretching, some therapists pull theheel of the subject and decrease the pressures between bones
in the ankle joint. Despite their complexity, the techniquesof stretching are not quantitatively described, and physicaltherapists learn them experimentally. Hence, the effectivenessof manual stretching motions for equinovarus often relies on
the execution of individual therapists, and there are potential
differences in the execution of stretching techniques among
therapists.
In this study, the kinematic and force properties of manual490

stretching motions for treatment of the equinovarus foot ofa stroke survivor were investigated, and the similarities anddifferences in execution among the therapists were identified.
The patient wore an instrumented brace on his diseased
foot, which was developed for this study, through which
each therapist stretched the related muscles. The results ofthis study are helpful for identifying individual differencesin stretching techniques for equinovarus and contributing totheir standardization.
II. EXPERIMENTThis study was approved by the Institutional Review Boardof Graduate School of Engineering, Nagoya University.

Fig. 2. Foot brace with two force sensors. A patient wore the brace on his
diseased foot through a sock. A PT held the heel grip and placed his/her
forearm against the forearm cuff.

A. SubjectsylThree male PTs with at least three years of experience
in rehabilitation for stroke survivors and one male stroke
survivor at Brunnstrom Recovery Stage IV were invited toparticipate in this experiment. The experimental proceduresand purposes were explained in both written and verbal form
to the participants, and all of them signed a written informed
consent agreement.

zlΣl

The patient wore the shoe brace on his left paralyzed footand lay relaxed on a bed. Each PT stretched the patient’s
foot through the brace. The PTs were instructed to performthe stretching as they did in a clinical setting. One trialof stretching lasted ten seconds, and in a single set of theexperiment, three trials were repeated with a rest periodof five seconds between trials. In total, three sets wereconducted for each therapists, with a one-minute break after
each set.

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Σf
xl

zf

xf

yf

zf

C. Experimental task

: Foot brace: Markerys

B. Measurement method and experimental system
The main part of the experimental apparatus was an
instrumented shoe brace through which PTs stretched thepatient’s ankle, as shown in Fig. 2. Generally, in order tostretch the ankle plantar flexors, PTs push the plantar surface
using their forearms while gripping the heel of the patient.
Hence, forces applied to both the forefoot and heel were
measured by installing three- and six-axial force sensors on
the forefoot and heel of the shoe brace, respectively. The shoebrace was fastened to the patient’s foot using fabric bands,
and the gaps between the foot and brace were filled withrubber plates and sponges to tightly fix them while avoiding
possible pain. This tightening allowed the therapists to apply
sufficient forces to the brace as they clinically do for the barefoot of patient.
A three-dimensional motion capture system (VENUS3D,
Nobby Tech. Ltd., Japan) was used for measuring the stretching motion, which also allowed for synchronization of theforce sensors and cameras. The system recorded the positionsof reflective markers attached to the patient’s thigh and braceat the rate of 120 Hz.

yf

Σf

zs

xf
Fig. 3.

Σs xs

Coordinate systems (Σl , Σ f , and Σs )D. Coordinate systems
Seven reflective markers were used for the motion capturesystem. Two markers were placed on the anterior border ofthe patient’s tibia shin bone. One marker was also attached on
the bone’s medial surface. The shoe brace had four markers
attached, as shown in Fig. 3. Two of them were located on thefrontal part, and the other two markers were on the medial
part of the brace.
Using these markers, two coordinate systems were defined:
lower leg (Σl ) and foot (Σ f ), as shown in Fig. 3. The origin of
the lower leg system was set to the position of the proximal
marker among those attached on the anterior border of thetibia bone. The direction of the X axis (xxl ) was set along theanterior border of the tibia bone. z l and y l were defined along
and orthogonal to the frontal plane, respectively, based on
the markers on the tibia bone. The foot’s coordinate system
was defined such that its basic axes were parallel to thoseof Σl in the basic human standing posture. x f was definedas perpendicular to the plantar surface, and y f was along
the longitudinal direction of the brace. The origin of thefoot system was placed on the frontal medial marker of theshoe brace. Furthermore, the coordinate system of the sixaxial force sensor (Σs ) was fixed on the sensor’s position andalong the posture of Σ f .

491

Transitional phase

Keeping phaseFig. 4. Two phases of stretching. In the transitional phase, the deformed
foot is placed in the flexed posture. In the keeping phase, the ankle flexors
are stretched with strong forces.

multidimensional data, an extended vector composed of thefollowing nine variables was prepared: l θx , l θy , l θz , f fx , f fy ,f f , f m , f m , and f m . Each of these variables had stanzxyz
dardized one hundred values. Hence, the extended vector was
defined as v = (l θ Tx l θ Ty l θ Tz f f Tx f f Ty f f Tz f m Tx f m Ty f m Tz )T ,which had a length of 900. This extended vector was used foreach stretching. Since twenty-five valid trials of stretchingwere acquired, with two out of twenty-seven trials beingD) of all stretchingconsidered invalid, the data matrix (Dbecame 900 × 25 in size. A principal component analysis
was applied on D .

E. Data analysis
1) Three types of data to be analyzed: In the analysis, thefollowing three types of data were used: foot posture, footforce, and torques applied to the foot brace.
The foot posture was defined as the roll-pitch-yaw angles
between the lower leg and foot coordinate systems. For thisend, we computed the rotation matrix l R f between the twocoordinate systems, and decomposed it into roll, pitch, andyaw angles. This process is described as follows:l

Ry (l θy )RRx (l θx ),R f = [l x f l y f l z f ] = R z (l θz )R(1)

where l θx , l θy , and l θz are the roll, pitch, and yaw angles,
respectively, of the foot from the viewpoint of the tibia
coordinate system.
The six-axial torque sensor on the heel output three force
components ( f f x , f f y , f f z ) and moments ( f m x , f m y , f m z ).
As described before, these force and torque values wereexpressed from the viewpoint of the foot coordinate system.
Note that it was not possible to acquire the outputs fromanother force sensor on the forefoot owing to a problem ofelectronic circuits; therefore, data from the forefoot sensor
was not used in the analysis.
2) Segmentation of stretching into two phases: As shownin Fig. 4, a single foot stretching was split into two phases:transitional and keeping. The transitional phase spans fromthe beginning of the stretching to the point at which thefoot was dorsiflexed. The keeping phase is the period during
which the muscles and tendons affected by equinovarus were
continuously stretched with relatively large manual forces.
A border between these two phases was defined using theacceleration of the dorsi/plantarflexion angle of the foot.
When this angular acceleration reached its minimum value,
the transition phase ended and the keeping phase started. The
focus of this study was on the transitional phase in the latter
analysis.
3) Principal component analysis of motion and force data:
The time-sequential data was downsampled to the lengthof 100 because individual PTs performed foot stretching attheir own preferential paces, so each stretching differed in
duration. The downsampling was conducted according tolength(xr ), i = 1, . . . , 100, (2)100where xr was for the data before the downsampling and xd
was for after. We applied a principal component analysis on
the downsampled data. To analyze the time-sequential andxd [i] = xr [i × ∆] s.t. ∆ =978-1-4799-6943-2/14/$31.00 ©2014 IEEE

III. RESULT
Valid data obtained in this experiment were the forces andmoments measured using the six-axial force sensor and thecoordinates of the seven reflective markers attached to thelower leg of the patient and the shoe brace. Therefore, thesedata were analyzed in the transitional phase.
A. Sample of stretching-related posture, force, and torqueAs an example, the averages of foot position, force, andmoment from one PT are shown in Fig. 5. These are the results of the dynamics between the foot of the patient and thetherapist. In terms of the foot posture, the main motions were
dorsiflexion (around the Z axis) and abduction (around the Xaxis). There was little deformation of inversion/eversion in
the patient’s foot. For this PT, the forces were applied along
all three directions, and their absolute values increased as the
100% mark of the cycle was approached. As for the moment,
the dorsiflexion moment (around the Z axis) was remarkable,
whereas the other components were relatively minor. Thechange in the Z moment was as much as 700 mN·m,
while those in the X and Y moments were approximately
200 mN·m at most.
B. Results of principal component analysis
From the principal component analysis, two principal
components were acquired, with the contribution ratios ofeach component being 64.0% and 22.0%. Fig. 6 shows theprimary and secondary components for the foot posture,force, and torque. Note that all variables appear equallysignificant in terms of magnitudes; however, this is because
they were standardized before the analyses.
1) Principal components of foot posture (roll-pitch-yaw
angles): As described above, the foot posture mainly varied around the Z axis (dorsi/plantar flexion) and the X
axis (ad/abduction), whereas its change around the Y axis
(e/inversion) was minuscule. As shown in Fig. 6 (top), theprimary and secondary components of the foot posture werelargely similar to each other in terms of their profiles. Thissuggests that the profiles of the foot posture did not varysignificantly among the trials and PTs. The angle around theZ axis gradually increased in both the primary and secondary
components, indicating that the foot was monotonically
flexed to the dorsal direction. Also, the foot was continuously
abducted because the angle around the X axis constantly
decreased during the entire stretching phase.

492

l

θx (+/-: adduction/abduction)
θy (+/-: eversion/inversion)lθz (+/-: dorsiflexion/plantarflexion)

1

1

䢢

Normalized posture (-)

l

Posture (rad)

0.5

0

䢢

0.5

l

θx (1)lθy (1)0l-0.5

θx (2)lθy (2)

l
䢢

20
40
60
80
Cycle in transitional phase (%)

100sfx (+/-: distal/proximal direction)
fy (+/-: fore/rear direction)s
fz (+/-: medial/lateral direction)

Normalized force (-)

Force (N)

10

20
40
60
80
Cycle in transitional phase (%)

100

1

s

15

θz (2)

䢢

-0.5
0

20

-1
0

θz (1)

l

䢢

5
0

䢢

0.5

s

fx (1)sfy (1)0sfz (1)sfx (2)-0.5sfy (2)

s

-5
0

800

-1
0

fz (2)

䢢

20
40
60
80
Cycle in transitional phase (%)

100

s

20
40
60
80
Cycle in transitional phase (%)

1

mx (+/-: adduction/abduction)
my (+/-: eversion/inversion)smz (+/-: dorsiflexion/plantarflexion)

100

䢢

䞉

600

Normalized moment (-)

Moment (mN m)

s

400
䢢

200
0

0.5

s

mx (1)smy (1)0smz (1)smx (2)-0.5s

my (2)

s

-200
0

-1
0

mz (2)

䢢

20
40
60
80
Cycle in transitional phase (%)

100

Fig. 5. Average torques and forces applied to the foot and its postureduring the stretching performed by one PT. Top: posture. Middle: force.
Bottom: moment. Posture and moment: X (+/-: adduction/abduction), Y(+/-: eversion/inversion), Z (+/-: dorsiflexion/plantarflexion). Force: X (+/-:
distal/proximal direction), Y (+/-: fore/rear direction), Z (+/-: medial/lateral
direction).

2) Principal components of force applied to rear foot: As
shown in Fig. 6 (middle), for the force along the X axis, thefirst principal component decreased continuously, whereas
its secondary component increased. This indicates that theheel was pushed in some trials, but pulled in the other trials
during stretching. In terms of the force along the Y axis,
the first principal component increased constantly, whereas
the second component started to increase in the last partof the cycle. The trials differed in terms of when the Yaxis forces started changing. For the Z-axis force, the firstcomponent decreased continuously. On the other hand, thesecond component began to decrease at 40-50% of the cycle.
There might have been a variation in the onsets of the Z-axis
forces among the trials.

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20
40
60
80
Cycle in transitional phase (%)

100

Fig. 6. Results of principal component analysis. x(1), y(1), and z(1) are theprimary components, and x(2), y(2), and z(2) are the secondary components.

3) Principal components of moment around rear foot:As described before, the changes in the moments around theX (ab/adduction) and Y (e/inversion) axes were somewhat
minor, but the profiles of the Y-axial moments were very
different in the primary and secondary components. As
shown in Fig. 6 (bottom), its primary component continuously decreased, whereas its secondary component behaved
oppositely, indicating that substantial differences in Y-axial
moments existed among the trials, the PTs, or both.
The moment around the Z axis (dorsi/plantarflexion) was
larger than the moments around the other two axes in Fig. 5(bottom). Its first component increased significantly, whereas
its secondary component started increasing at approximately
40% of the cycle. This suggests that the dorsiflexion moment
varied among the trials or PTs in terms of how it increased,
but it basically increased for all of the trials.

493

IV. D ISCUSSION ON INDIVIDUAL DIFFERENCES IN

15

STRETCHING

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5
0

PT1
PT2

−5

PT3

−10
−15
0

Fig. 7.

20
40
60
80
Cycle in transitional phase (%)

100

Average X-axial heel forces for individual PTs.

600

Moment (mN m)

The results of the principal component analysis of thestretching showed similarities and differences in the execution of stretching techniques among the therapists. According
to the primary component of forces (Fig. 6 middle), which
represents the general trends of stretching, PTs gradually
increased their forces on the heel grip to the toe side (+Y )and lateral direction (−Z). Also, as shown in the bottom
panel of Fig. 6, the ankle was continuously dorsiflexed(around +Z). These are consistent with the changes in thefoot posture shown in Fig. 6 (top), indicating that the footwas primarily abducted and dorsiflexed during the transition
phase. Since equinovarus causes hypertonia in the ankle
flexors and plantar flexion, inversion, and adduction of thefoot, it is reasonable to assert that the PTs provided stretchingsuch that these foot deformations were alleviated.
In contrast, the secondary component represents the difference among PTs or trials. Notably, the X-axis component of
the force applied to the heel showed clearly distinguishedtrends. Its secondary component monotonically increased,
whereas its primary component monotonically decreased.
Such a difference in the principal components clearly appears
in the average values of the X-axial force of each PT(Fig. 7). PT1 and PT3 applied the X-axis force in the positive
direction, indicating that they pulled the heel. In contrast,
the X-axis force of PT2 was negative, indicating that hepushed the patient’s heel. Therefore, it is presumed that PT2
applied a larger force to the forefoot in order to dorsiflex
the ankle joint than the other PTs did, although it was notpossible to acquire the force values on the forefoot owing toan electronic problem. Such stretching by PT2 is consideredinefficient in terms of energy loss because the forces applied
to the heel and forefoot oppose each other.
Furthermore, the profiles of the Y-axial (eversion/inversion) moment significantly differ between the
primary and secondary components. Its primary component
gradually decreased, whereas its secondary component did
the opposite. As shown in Fig. 8, such a difference can beseen in the average Y-axial moments among the three PTs.
PT3 apparently applied large eversion torques on the foot.
On the other hand, those of PT1 and PT2 were negligible
or even inversion torques. This difference in eversion andinversion torques applied to the foot potentially leads to thedifference in the groups of muscles being stretched. Whether
or not such a difference is important for the stretching
against equinovarus remains to be determined in a future
study.
In this experiment, since the period of transitional phasevaried either among each trial or PTs, the obtained data
was downsampled for analysis. Owing to this process, it
was not possible to discuss the dynamics of stretching. The
analysis of such dynamics is left for a future study, althoughstretching usually does not involve quick but slow joint
movements.

Force (N)

10

400

・

PT1

200

PT2
PT3

0

−200
0

Fig. 8.

20
40
60
80
Cycle in transitional phase (%)

100

Average torques around Y axis for individual PTs.

V. CONCLUSION
Execution of manual stretching techniques for equinovarus
inherently varies among PTs, owing to the musculoskeletal
complexity of the human ankle joint. In this study, theperformances of manual stretching by PTs for treatment of
the equinovarus of a stroke survivor were investigated. PTs
stretched the deformed foot of the patient as they usually didin their clinical scenes through an instrumented shoe braceworn on the patient’s foot. A motion capture system andmultiaxis load cells acquired kinematic and force profiles
during stretching. The collected data were processed basedon a principal component analysis to identify the similarities
and differences of the stretching techniques among the PTs.
All PTs commonly transferred the diseased foot such thatthe symptomatic deformation (plantar flexion and adduction)of the foot was corrected. On the other hand, there wereindividual differences in the force applied to the heel andthe magnitude of the eversion moment. In particular, one
PT pushed the heel in the proximal direction, while theother two PTs pulled it during stretch. Furthermore, one PT
apparently applied eversion moments to the ankle, whereas
the others did not. These differences could potentially be
used to define levels of efficiency in stretching technique
execution. The next step is to identify an effective stretching
technique by revealing how the individual’s execution affects494

the therapeutic outcome. We will study further with sufficientnumbers of patients and PTs to acquire statistically valid
data.
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