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This is the accepted version of the manuscript published in Consciousness and Cognition.
https://doi.org/10.1016/j.concog.2016.08.019
Embodied prosthetic arm stabilizes body posture, while unembodied one perturbs it
Shu Imaizumia,b,c, Tomohisa Asaib, and Shinichi Koyamaa
a Graduate School of Engineering, Chiba University, 1-33 Yayoi, Inage, Chiba 263-8522, Japan.
b NTT Communication Science Laboratories, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan.
c Japan Society for the Promotion of Science, 5-3-1 Kojimachi, Chiyoda, Tokyo 102-0083, Japan.
Corresponding author
Shu Imaizumi
Present address: Graduate School of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo
153-8902, Japan.
Phone: +81-3-5454-6259
Fax: +81-3-5454-6979
Email: shuimaizumi@gmail.com
Abstract
Senses of ownership (this arm belongs to me) and agency (I am controlling this arm) originate from
sensorimotor system. External objects can be integrated into the sensorimotor system following long-term use,
and recognized as one's own body. We examined how an (un)embodied prosthetic arm modulates whole-body
control, and assessed the components of prosthetic embodiment. Nine unilateral upper-limb amputees
participated. Four frequently used their prosthetic arm, while the others rarely did. Their postural sway was
measured during quiet standing with or without their prosthesis. The frequent users showed greater sway
when they removed the prosthesis, while the rare users showed greater sway when they fitted the prosthesis.
Frequent users reported greater everyday feelings of postural stabilization by prosthesis and a larger sense of
agency over the prosthesis. We suggest that a prosthetic arm maintains or perturbs postural control, depending
on the prosthetic embodiment, which involves sense of agency rather than ownership.
Keywords
Self, Agency, Embodiment, Amputation, Upper-limb prosthesis, Postural control
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1. Introduction
1.1. Embodied sense of self and embodiment of external objects
Several recent psychological and neuroscientific studies suggest that the human sense of self is represented
within the body and sensorimotor system (Blanke, Slater, & Serino, 2015; Haggard, 2005; Tsakiris, 2010).
Such an embodied sense of self (Gallagher, 2000) consists of a sense of one's own body (i.e., sense of body
ownership: “this hand belongs to my body”) and a sense of one's own action (i.e., sense of agency: “I am
causing this action and controlling my body”). These two senses are conceptually (Gallagher, 2000),
behaviorally (Tsakiris, Prabhu, & Haggard, 2006), psychometrically (Longo, Schuur, Kammers, Tsakiris, &
Haggard, 2008), and neurally (Tsakiris, Longo, & Haggard, 2010) distinctive (but also interactive, see below).
In theory, the sense of body ownership is based on multisensory afferent inputs (e.g., visuo-tactile), which are
spatially and temporally congruent (Botvinick & Cohen, 1998; Kilteni, Maselli, Kording, & Slater, 2015). The
sense of agency stems from congruence between a motor prediction based on an internal forward model for
motor control and its predicted sensory feedback (Blakemore, Wolpert, & Frith, 2002; Wolpert, Ghahramani,
& Jordan, 1995). This non-conceptual “comparator” model has been used to elucidate the mechanism of sense
of agency (Blakemore et al., 2002; Tsakiris & Haggard, 2005a); it must be noted, however, that there are other
conceptual models as well (Chambon, Sidarus, & Haggard, 2014; Synofzik, Vosgerau, & Newen, 2008).
External objects (e.g., tools and fake body parts) can be incorporated into human body representation and
recognized as one's own body parts (i.e., embodied) when two main sensorimotor requirements are met. First,
continuous multisensory afferent inputs from an external object can elicit a sense of body-ownership toward it
(i.e., ownership-driven embodiment). An example of this is the rubber hand illusion (RHI), in which observers
watch a rubber hand being stroked while their own unseen hand is synchronously stroked, and start to feel as
if the rubber hand belongs to their own body (Botvinick & Cohen, 1998; Tsakiris & Haggard, 2005b). Second,
motor learning and internal model updates can occur due to short- and long-term use of an external proxy of
one's effector (e.g., tools) with one's voluntary action (Imamizu, Kuroda, Miyauchi, Yoshioka, & Kawato,
2003; Imamizu et al., 2000). This can be referred to as agency-driven embodiment and is exemplified by an
active version of the RHI, wherein synchronously acting visual feedback of one's own voluntary action, such
as a fake hand (Caspar, Cleeremans, & Haggard, 2015; Dummer, Picot-Annand, Neal, & Moore, 2009;
Kalckert & Ehrsson, 2012, 2014a, 2014b) or a hand video (Asai, 2016; Imaizumi & Asai, 2015; Tsakiris et al.,
2006) can lead to embodiment. Importantly, passive movement (Haggard, Clark, & Kalogeras, 2002) or
incongruent visual feedback (Franck et al., 2001) can eliminate or attenuate the sense of agency, and therefore
are unlikely to lead to embodiment of the proxy (Asai, 2016; Kalckert & Ehrsson, 2012). While the active
RHI has been used to examine embodiment for short time intervals, tool embodiment by long-term use has
been demonstrated by neurophysiological evidence in primates (Iriki, Tanaka, & Iwamura, 1996; Maravita &
Iriki, 2004) and by human behavioral evidence, such as improvements in tool control due to their
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incorporation into a plastic body representation (Cardinali et al., 2009; Jacobs, Bussel, Combeaud, &
Roby-Brami, 2009). The tools previously examined included a rake to grasp objects (Farnè & Làdavas, 2000),
a computer mouse (Bassolino, Serino, Ubaldi, & Ladavas, 2010), and a cane for blind people (Serino,
Bassolino, Farne, & Ladavas, 2007).
1.2. Embodied prosthetic limb and postural stabilization
Prosthetic limbs are another example of external objects capable becoming embodied, which can be observed
in our everyday environment. More than 94 % of amputees due to accidents and vascular disease use
prosthetic limbs (Pezzin, Dillingham, MacKenzie, Ephraim, & Rossbach, 2004). In amputees, prosthetic limbs
functionally help daily life activities, such as work and leisure pursuits, and have a social role in that they
compensate for the appearance of the missing limb (Murray, 2005). Consequently, the frequency of usage of
prosthetic limbs positively correlates with amputees' quality of life (Akarsu, Tekin, Safaz, Goktepe, &
Yazicioglu, 2013), suggesting that long-term use of prosthetic limbs has a positive effect on amputees' mental
health. In contrast, qualitative studies have pointed out that long-term use of prosthetic limbs also results in
psychological and physical effects, including embodiment (de Vignemont, 2007; Mills, 2013; Murray, 2004,
2008). Some studies have shown evidence of prosthesis embodiment using behavioral data. Fraser (1984)
compared movement trajectories of prosthetic and intact arms in a unilateral amputee who had used the
prosthesis more than ten years, and showed that the movements were comparable. The author claimed that this
may stem from the use of similar neural networks in the motor system, and that prosthetic limb can become a
part of a proficient user. Regarding body representations, long-term prosthetic arm users are likely to
overestimate their proprioceptively felt stump lengths, that is, their arm representation extends toward the tip
of prosthetic arm (McDonnell, Scott, Dickison, Theriault, & Wood, 1989). Furthermore, upper-limb
amputee’s peripersonal space can also expand so as to include the prosthetic arm when they wear their
prosthesis (Canzoneri, Marzolla, Amoresano, Verni, & Serino, 2013).
A prosthetic upper-limb incorporated into an amputee's body may affect motor control over the whole body in
addition to body representation. A recent qualitative study suggested that a prosthetic arm can maintain
amputees' body posture (Wijk & Carlsson, 2015). Prosthetic arms (both functional and aesthetic) can
compensate for asymmetric and/or disturbed body balance due to limb amputation, which may cause uneven
load and consequently back and neck pain. The authors pointed out that everyday activities, such as walking
and swimming, also benefit from stabilization engendered by use of an upper-limb prosthesis. Given this, it is
natural to think that a lower-limb prosthesis would play a similar role because the legs bear one's body weight
and generate one’s gait. Indeed, studies have investigated the effects of a lower-limb prosthesis resulting in a
perturbed postural control (Fernie & Holliday, 1978) and an asymmetric gait (Winter & Sienko, 1988).
Moreover, because walking with a unilateral lower-limb prosthesis is likely to rely more on the intact side and
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thus show an asymmetric gait pattern, long-term use of the lower-limb prosthesis may cause musculoskeletal
distortion (Gailey, Allen, Castles, Kucharik, & Roeder, 2008). In contrast, it remains unclear whether and how
an upper-limb prosthesis modulates amputees’ postural control and how the frequency of use and embodiment
of an upper-limb prosthesis affects postural modulation; the suggestion by Wijk and Carlsson (2015) has yet
to be empirically examined.
Human body posture is maintained by online comparison of the desired body parts' locations with their actual
locations on the basis of multisensory afferent information supplied by those body parts, that is, a feedback
system (Mergner & Rosemeier, 1998; Peterka, 2002; Peterka & Loughlin, 2004). Additionally, since the
feedback system is not sufficient to maintain posture, anticipatory motor control computed by internal forward
models is also used, that is, a feedforward system (Collins & de Luca, 1993; van der Kooij, Jacobs, Koopman,
& Grootenboer, 1999). Both systems need to sense the current location of body parts and their movement
sequence, although humans do not have organs by which to directly perceive these data. Instead, implicit body
representation can play a key role as a template of a balanced body and a reference for postural control (di
Fabio & Emasithi, 1997; Gurfinkel, Ivanenko, Levik, & Babakova, 1995). Thus, it is assumed that a coherent
body representation may be sufficient to maintain their body posture, even in amputees presumably with
altered afferent information due to the amputation. If so, a prosthetic arm may restore an amputee’s body
representation by being incorporated as a part of his or her body (de Vignemont, 2007; Mayer, Kudar, Bretz,
& Tihanyi, 2008), and consequently stabilize his or her body posture. Thus, we expected that amputees whose
prosthetic arm belongs to their body representation would show well-stabilized postural control, whereas
those whose prosthesis is not incorporated into their body would show relatively disturbed postural control
because the prosthesis can behave as a perturbation.
1.3. What makes a prosthesis embodied?
It is an open question as to which of the aforementioned ownership- and agency-driven embodiment
mechanisms is crucial for the embodiment of a prosthetic arm, or whether both mechanisms are essential. It
can be assumed that ownership-driven embodiment occurs due to the integration of visual information from
observing the prosthetic arm and tactile information from the stump touched by the prosthesis socket, much
like the RHI. For instance, a transient sense of ownership over a prosthetic hand can be elicited by passive
visuo-tactile stimulation of the stump and prosthesis (Ehrsson et al., 2008), or by using a robotic touch
interface (Marasco, Kim, Colgate, Peshkin, & Kuiken, 2011). In contrast, as previous findings regarding tool
embodiment have suggested (Bassolino et al., 2010; Serino et al., 2007), voluntary controlling tools, perhaps
including prosthetic arms, for a long period can lead to motor learning and updated internal models (Imamizu
et al., 2003; Imamizu et al., 2000); thus, this process should be essential for incorporation of a prosthetic arm
into the body representation, that is, agency-driven embodiment. In fact, behavioral evidence from motor
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imagery tasks suggests that prosthetic arms that are controlled like tools (i.e., functional and myoelectric) are
likely to be incorporated into the body representation (Nico, Daprati, Rigal, Parsons, & Sirigu, 2004).
Furthermore, in addition to studies suggesting the possibility of interactions between sense of agency and
body ownership (Kalckert & Ehrsson, 2012, 2014a; Tsakiris et al., 2006), research has shown that the sense of
agency itself can elicit and even overwrite body ownership toward external objects (Asai, 2016). Therefore, it
is possible that prosthetic embodiment is driven more by sense of agency than by ownership.
1.4. Current study
To examine whether and how an (un)embodied prosthesis stabilizes body posture, and what components of
prosthetic embodiment contribute to postural stabilization, we measured amputees' postural sway during quiet
upright stance with and without their prosthetic arm and assessed their subjective feelings toward their
prosthesis and its embodiment. Given that it has been suggested that long-term use is required for tools
(Bassolino et al., 2010; Serino et al., 2007) and prosthetic arms (Canzoneri et al., 2013) to be incorporated into
the body representation, we assumed that a prosthetic arm is more likely to be embodied in amputees who
frequently use the prosthesis rather than in those who rarely use it; thus, two groups of amputees were
compared in the experiment. We hypothesized that amputees who frequently use their prosthetic arm would
stabilize their body posture, that is, decrease postural sway when the prosthesis was attached, while those who
rarely use their prosthesis would show greater sway in this case, because the prosthesis would serve as a
perturbation. These group differences would likely be due to the different degree of prosthesis embodiment.
Thus, we also hypothesized that amputees who frequently use their prosthesis would report postural
stabilization due to it on a daily basis, to a far greater extent than those who rarely use their prosthesis.
Moreover, we posited that a sense of agency over the prosthetic arm, rather than a sense of ownership over it,
would be reported more by the amputees who frequently use their prosthesis than those who rarely use it,
because embodiment can be driven more by a sense of agency than by ownership.
The current study, to our knowledge, is the first attempt to empirically demonstrate the effect of embodiment
of external objects, including a prosthetic arm, on whole-body motor control (i.e., postural control). In
particular, we extend on previous findings of the effect of embodiment on manual movement (Fraser, 1984)
and proprioception (McDonnell et al., 1989). However, given that embodiment, which is subjectively
multifaceted (Longo et al., 2008), contains two main components (i.e., ownership and agency), we were
further interested in determining what sort of subjective experiences of prosthetic embodiment arise among
upper-limb amputees. We also attempted to clarify how ownership and agency towards prosthetic arms relate
to whole-body movement (measured as postural control), thus expanding on previous findings of how
proprioceptive recalibration (Botvinick & Cohen, 1998; Tsakiris & Haggard, 2005b) and actual hand
movement (Asai, 2015) toward a fake hand can occur with illusory ownership. Furthermore, by investigating
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how ownership and agency arise from a prosthetic arm—which is likely to be actively used for a long
period—the current study can help untangle the complex interaction of ownership and agency over fake body
parts, which remains controversial (Asai, 2016; Braun, Thorne, Hildebrandt, & Debener, 2014; Caspar et al.,
2015; Imaizumi & Asai, 2015; Kalckert & Ehrsson, 2012, 2014a, 2014b; Tsakiris et al., 2006).
2. Materials and methods
2.1. Participants
Nine males with unilateral upper-limb amputation (mean age 64.33 ± 11.65 years), naïve with respect to the
study purpose, participated in return for monetary compensation (Table 1). Each amputation occurred an
average of 41.30 ± 18.90 years before the current study and prosthesis use began shortly after the amputation
(self-reported). We recruited elderly amputees because we were interested in the effects of long-term use of a
prosthetic arm and frequency of usage. All participants reported good health other than the limb amputation
and all walked without a cane or other walking aid. They were recruited from Seibu College of Medical
Technology, Tokyo, Japan, which they have frequently visited as prosthetic-fitting models for educational
purposes. Written informed consent was obtained from each participant. The current study was conducted in
accordance with the principles of the Declaration of Helsinki, and was approved by the local ethical
committee of the Graduate School of Engineering, Chiba University.
The four participants listed at the top of Table 1 reported that they used their prosthesis even in their home;
their mean duration of prosthesis use was about 14 hours per day. The other five participants reported not
using their prosthesis at home and a mean usage duration of about an hour per day. Accordingly, we classified
the former four individuals as a “frequent use” group and the latter five as a “rare use” group. The durations of
prosthesis use significantly differed between the two groups (two-tailed t-test: t(7) = 7.78, p < 0.001, effect
size r = 0.95), while the other indices, namely age, body mass index, years since amputation, stump length,
and prosthesis weight did not significantly differ between the groups (ts(7) ≤ 1.96, ps ≥ 0.09, rs ≤ 0.60).
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Table 1. Clinical characteristics of participants. All were right-handed males.
Age
Body
mass
index
(kg/m2)
Years
since
amputation
Amputated
side
Residual
limb
length
(cm)
Reason for
amputation
Prosthetic arm
Use in
home
Frequency
of use
(hours/day)
Type and
weight (g)
Frequent-use group
72
21.88
33
Right
32
Trauma
Yes
12
Functional
(687)
66
34.13
43
Right
32
Vascular
Yes
12
Aesthetic
(663)
46
29.41
21
Right
42
Trauma
Yes
15
Myoelectric
(1056)
80
22.45
54
Left
29
Trauma
Yes
16
Functional
(592)
Mean
66.00
26.97
37.75
33.75
13.75
705.50
SD
14.51
5.88
14.08
5.68
2.06
241.78
Rare-use group
76
20.62
75
Left
8
Trauma
No
0
Aesthetic
(792)
50
29.30
17
Right
13
Trauma
No
0
Functional
(1084)
55
28.70
33
Right
18
Trauma
No
1
Functional
(1365)
67
23.65
60
Left
29
Trauma
No
1
Aesthetic
(518)
67
26.22
36
Right
37
Trauma
No
6
Aesthetic
(768)
Mean
63.00
25.70
44.20
21.00
1.40
905.40
SD
10.42
3.61
23.08
11.85
2.58
325.94
To ensure that we purely examined the embodiment of prosthetic arm and its effect on postural control in
comparing the two amputee groups, we confirmed whether more general, everyday experiences of an
embodied sense of self (i.e., ownership and agency) through one's body and actions were comparable between
the groups. The Embodied Sense of Self Scale (ESSS), which comprises three subscales—Ownership, Agency,
and Narrative—was used to assess the experiences of the corresponding aspects of sense of self on an
everyday basis (Asai, Kanayama, Imaizumi, Koyama, & Kaganoi, 2016). The Narrative subscale measures
how the self extends in time, including identity, autobiographical memory, and intentions for the future
(Gallagher, 2000). The Ownership score ranges from 9 to 45; the other two subscale scores range from 8 to 40.
Higher scores on all three subscales indicate more anomalous experiences of ownership, agency, and narrative
self. Moreover, we checked whether the two groups differed in terms of state and trait anxiety, which appear
to influence postural control (Hainaut, Caillet, Lestienne, & Bolmont, 2011; Wada, Sunaga, & Nagai, 2001),
by using the state and trait scales of the State-Trait Anxiety Inventory (STAI-S and STAI-T, respectively).
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The total score of each scale ranges from 20 to 80, with higher scores indicating greater state or trait anxiety,
respectively (Shimizu & Imae, 1981; Spielberger, Gorsuch, & Lushene, 1970). Participants completed these
questionnaires before the main experiment described below. The results, shown in Table 2, indicated that the
groups did not differ in terms of ESSS subscales, STAI-S, or STAI-T (ts(7) ≤ 1.14, ps ≥ 0.29, rs ≤ 0.28). We
must note that the ESSS data from these amputees has already been published as a part of our previous study
aimed at developing and validating the ESSS (Asai et al., 2016).
Table 2. Responses to the Embodied Sense of Self Scale (ESSS) and state and trait scales of the State-Trait
Anxiety Inventory (STAI-S and STAI-T) by the two amputee groups as well as the non-amputee controls (in
the follow-up experiment; see 3.3.).
ESSS
STAI-S
STAI-T
Ownership
Agency
Narrative
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Mean
SD
Frequent-use group (N = 4)
14.25
4.11
20.75
9.71
16.25
6.24
37.25
8.54
44.25
7.59
Rare-use group (N = 5)
18.80
7.01
16.40
6.10
16.60
5.81
37.20
11.32
41.00
11.11
Controls (N = 9)
15.56
5.94
18.00
7.71
16.22
4.84
32.00
5.83
37.56
7.06
2.2. Apparatus
Postural sway was measured using a force plate (Wii Balance Board, Nintendo, Kyoto, Japan), which tracked
the participant’s center of pressure displacement at 20 Hz without filtering. A custom program written in C#
using an open-source library (WiiMoteLib, http://wiimotelib.codeplex.com/) running on Windows 7 collected
and sent the data to a computer via a Bluetooth interface. The Wii Balance Board has been confirmed as valid
and reliable for postural-sway measurement (Clark et al., 2010), including in elderly people (Chang, Chang,
Lee, & Feng, 2013).
2.3. Procedures
2.3.1. Posturography
The participant stood erect on the force plate with his knees straight and hands down at his sides, either with
or without his prosthesis. First, the participant viewed an eye-level fixation point on the wall for 60 seconds
(eyes-open condition). Immediately afterward, he closed his eyes and remained standing for 60 seconds
(eyes-closed condition). The eyes-open and eyes-closed conditions were then repeated after the participant
removed/installed his prosthesis. The order of eyes open/closed conditions and with/without prosthesis
conditions was counterbalanced across participants. We followed previous recommendations regarding the
recording duration (Carpenter, Frank, Winter, & Peysar, 2001) and measurements for both eyes-open and
-closed conditions (Kapteyn et al., 1983).
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2.3.2. Questionnaire
To examine the extent to which the prosthesis behaved as if it were a part of their own body and/or a postural
stabilizer, participants answered nine questions regarding the components of embodiment of their prosthesis
on an everyday basis, using five-point Likert scales (Table 3). We developed these items partially based on a
semi-structured interview guide (Wijk & Carlsson, 2015) regarding incorporation into the body and a
questionnaire (Longo et al., 2008) regarding the components of embodiment of body-like objects (e.g., rubber
hand). Longo et al. psychometrically showed that embodiment can be divided into Ownership and Agency
(note that the authors included another component: Location). Items 1 and 2 addressed how prosthetic arm
stabilizes body posture and/or affects the body axis. Items 3 to 6 addressed the sense of ownership over the
prosthetic arm, including how the prosthetic arm is subjectively incorporated into one's body representation,
together with associated somatosensation (Gallagher, 2000). Items 7 to 9 queried the sense of agency over the
prosthetic arm, that is, the extent to which amputees can control their prosthesis by themselves, in the same
manner as an intact limb. We expected these items to receive higher scores in the frequent-use group, whose
prosthesis would be more firmly embodied, than the rare-use group. This questionnaire was completed
approximately three months after the postural measurements, to prevent the results of the postural
measurement from biasing the answers to the questionnaire.
Table 3. Questionnaire regarding the participant’s own prosthetic arm and its embodiment. Note the titles for
each item (italics) were not presented to the participants in the actual experiment.
Items
Five-point scales
1. Postural stabilizing: Do you feel that the balance of your body posture is stable
when you fit your prosthesis?
1: Never. 5: Always.
2. Biased body axis: Do you feel that your body axis biases toward the side of either
the intact or amputated limb?
1: Intact side. 3: Neither. 5: Amputated
side.
3. Incorporation: To what extent do you feel that your prosthesis is a part of your
body?
1: Not at all. 5: Entirely.
4. Habitual touch: Do you have a habit of unintentionally touching your prosthesis?
1: Never. 5: Always.
5. Haptics: Do you feel that, when something touches your prosthesis, it touches
your body?
1: Never. 5: Always.
6. Proprioception: To what extent do you perceive the orientation and location of
your prosthesis with your eyes closed?
1: Not at all. 5: Extremely.
7. Quickness: How quickly do you move your prosthesis when you intend to move
it?
1: Extremely slow. 5: Instantaneous.
8. Accuracy: How accurately do you move your prosthesis?
1: Not at all. 5: Accurate as intact side.
9. Difficulty: How difficult is it to move your prosthesis?
1: Extremely. 5: Easy as intact side.
2.4. Data analysis
For each participant, we analyzed the total path length, medio-lateral (ML) path length, and antero-posterior
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(AP) path length of the center of pressure displacements. Total path length was calculated as the sum of the
Euclidean distances between successive data points (i.e., 1200 points: data sampled at 20 Hz for 60 seconds).
ML and AP path lengths were calculated as the sum of ML or AP components of the Euclidean distances
between the data points, respectively. We chose three types of path length as posturographic indices for two
reasons. First, the total path length of the center of pressure displacements can have small intra-individual
variations and discriminate well experimental conditions and group differences, such as age, health status, and
visuo-proprioceptive inputs (Duarte & Freitas, 2010; Raymakers, Samson, & Verhaar, 2005). Second, ML and
AP postural control, which underlie ML and AP path lengths, are based on different biomechanical strategies
(Day, Steiger, Thompson, & Marsden, 1993; Winter, Prince, Frank, Powell, & Zabjek, 1996) and differently
affected by cognitive controls (Pellecchia, 2003) and states (Wada et al., 2001).
The total, ML, and AP path lengths for each condition were submitted to analysis of variance (ANOVA) with
two within-participants factors (Eyes: open, closed; Prosthesis: with, without) and a between-participants
factor (Frequency: frequent use, rare use) with partial eta squared (η2p) as the effect size (Cohen, 1988).
Responses for questionnaire items 1 and 2 were averaged into a composite score of Postural effect, to examine
group differences in terms of several components of prosthesis embodiment and to ensure that the prosthesis
was more strongly embodied in the frequent-use group than the rare-use group. Similarly, items 3, 4, 5, and 6
were averaged into an Ownership composite score, and items 7, 8, and 9 averaged into an Agency composite
(cf. Longo et al., 2008). Two-tailed t-tests were used to compare the two groups for each of these three
components, and each of the nine questionnaire items. Welch’s t and corrected degrees of freedom were used
when the data violated the homogeneity of variance assumption, in accordance with Levene's test. Effect sizes
were calculated as r for t-tests (Cohen, 1988). The significance level was set at p < 0.05.
3. Results
3.1. Posturography
Total, ML, and AP path lengths were calculated for each participant and submitted to ANOVAs, which
revealed a significant main effect of Eyes on total, ML, and AP path lengths (total: F(1,7) = 33.18, p = 0.001,
η2p = 0.83; ML: F(1,7) = 6.22, p = 0.04, η2p = 0.47; AP: F(1,7) = 39.54, p < 0.001, η2p = 0.85). These effects
indicated larger postural sway during the eyes-closed condition, consistent with reports that postural sway
increases with a lack of visual input (Edwards, 1946). However, the effects of Eyes did not interact with two
factors Prosthesis and Frequency for all path lengths (Fs ≤ 1.84, ps ≥ 0.22, η2ps ≤ 0.21). Therefore, we
collapsed the data across the eyes-open/closed conditions and analyzed these data using an ANOVA with a
within-participants factor (Prosthesis) and a between-participants factor (Frequency).
Figure 1 shows the total, ML, and AP path lengths for the two groups. For these three path lengths, we found
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no main effect of Prosthesis (total: F(1,7) = 2.25, p = 0.18, η2p = 0.24; ML: F(1,7) = 2.08, p = 0.19, η2p = 0.23;
AP F(1,7) = 3.90, p = 0.09, η2p = 0.36) or Frequency (total: F(1,7) = 2.31, p = 0.17, η2p = 0.25; ML: F(1,7) =
0.26, p = 0.63, η2p = 0.04; AP: F(1,7) = 3.01, p = 0.13, η2p = 0.30), while we found significant interactions
between Prosthesis and Frequency (total: F(1,7) = 25.69, p = 0.001, η2p = 0.79; ML: F(1,7) = 8.76, p = 0.02,
η2p = 0.56; AP: F(1,7) = 21.16, p = 0.002, η2p = 0.75). Simple main effects analyses revealed that total path
length significantly increased in the without-prosthesis condition compared to the with-prosthesis condition in
the frequent-use group (F(1,7) = 21.58, p = 0.002), while in the rare-use group, total path length significantly
decreased in the without-prosthesis condition (F(1,7) = 6.37, p = 0.04). Moreover, total path length
significantly increased in the frequent-use group compared to the rare-use group in the without-prosthesis
condition (F(1,14) = 4.91, p = 0.04). ML path length significantly decreased in the without-prosthesis
condition compared to the with-prosthesis condition in the rare-use group (F(1,7) = 9.67, p = 0.02). AP path
length significantly increased in the without-prosthesis condition compared to the with-prosthesis condition in
the frequent-use group (F(1,7) = 21.63, p = 0.002), and significantly increased in the frequent-use group
compared to the rare-use group in the without-prosthesis condition (F(1,14) = 6.12, p = 0.03).
Figure 1. (A) Total, (B) medio-lateral, and (C) antero-posterior path lengths for the frequent- (N = 4) and
rare-use (N = 5) groups. Error bars denote ±1 standard error of the mean. Asterisks indicate significant simple
main effects (*p < 0.05, **p < 0.01).
3.2. Questionnaire
Figure 2 shows the mean response to each of merged questionnaire items (i.e., the three composite variables
assessing prosthesis embodiment) by the frequent- and rare-use groups. Postural effect was significantly
higher in the frequent-use group (t(7) = 4.91, p = 0.002, r = 0.88). Ownership did not differ between the two
groups (t(7) = 1.26, p = 0.25, r = 0.43). Agency was significantly higher in the frequent-use group (Welch's
t(6.59) = 2.49, p = 0.04, r = 0.70).
12
Figure 2. Composite variables obtained from the questionnaire, which were averages of the following items:
Postural effect, items 1 and 2; Ownership, items 3, 4, 5, and 6; Agency, items 7, 8, and 9. These three
composites served as components of embodiment. Error bars denote 95% confidence intervals. Asterisks
indicate significant group differences (*p < 0.05, **p < 0.01).
Figure 3 shows the mean response to each of the nine questions by the frequent- and rare-use groups. The
responses for items 1 (Postural stabilizing), 2 (Biased body axis), and 4 (Habitual touch) were significantly
higher in the frequent-use group than the rare-use group (item 1: t(7) = 3.04, p = 0.02, r = 0.75; item 2: t(7) =
3.27, p = 0.01, r = 0.78; item 4: t(7) = 2.59, p = 0.04, r = 0.70). Significant group differences were not found
for the other items (ts ≤ 1.10, ps ≥ 0.31, rs ≤ 0.39; Welch's t for item 8 (Accuracy): t(3.00) = 2.61, p = 0.08, r
= 0.75).
Figure 3. Mean responses to the questionnaire on prosthesis embodiment. Error bars denote 95% confidence
intervals. Asterisks and a dagger indicate significant or near-significant group differences (* p < 0.05, † p <
13
0.10).
3.3. Follow-up experiment in non-amputee controls
One might argue that the different postural modulation found in the frequent- and rare-use groups was simply
an artifact of the abnormal postural control in our elderly amputees. Furthermore, one might ask whether and
how an external object fitted to the upper limb in non-amputee individuals (e.g., wrist weight) affects body
posture similarly to a prosthetic arm in amputees. We expected such an object would be unembodied, and
therefore would affect postural sway similarly to the prosthetic arm in the rare-use group.
To ensure that our nine amputees had normal postural control in terms of postural stability and visual
contribution to postural sway, and to elucidate the effect of an external object temporarily attached to the
upper limb on the postural sway, we conducted a follow-up experiment assessing postural sway in
non-amputee controls (nine males; mean age 66.89 ± 3.28 years; mean body mass index 24.59 ± 1.02 kg/m2:
these were comparable to the amputees, ts(16) ≤ 0.92, ps ≥ 0.37, rs ≤ 0.23). As in the main experiment (see
2.1.), we confirmed that the day-to-day experiences of ownership, agency, and narrative self (ESSS) and state
and trait anxiety (STAI-S and STAI-T) of the controls did not differ from those of the amputees (ts(16) ≤ 1.40,
ps ≥ 0.18, rs ≤ 0.33, see Table 2). The ESSS data from the controls has already been published as a part of our
previous validation study of this scale (Asai et al., 2016). The controls, who were naïve with respect to the
study purpose, gave written informed consent and participated in return for monetary compensation. Each
stood on the force plate and viewed an eye-level fixation point on the wall for 60 seconds. Afterward, they
closed their eyes and remained standing for 60 seconds. Then, the eyes-open and -closed conditions were
repeated after a wrist weight, as an alternative to the prosthetic arm, was attached to their right wrist using a
Velcro strap. The wrist weight (995 g) was comparable to the amputees' prostheses in terms of weight (mean
836.11 ± 275.93 g; one-sample t test: t(8) = 1.73, p = 0.12, r = 0.52). The order of eyes open/closed conditions
and with/without wrist-weight conditions was counterbalanced across the participants. We used the
aforementioned apparatus and analyzed the total, ML, and AP path lengths in the same manner as the main
experiment.
We compared posturographic data under eyes-open and eyes-closed conditions between amputees and
controls to ensure that amputation itself did not affect postural control and its visual contributions. Data from
the controls were collapsed across with/without wrist-weight conditions, and compared with those from the
amputees, the latter of which were collapsed across with/without-prosthesis conditions and frequent/rare-use
groups. ANOVAs with a within-participants factor Eyes (eyes-open, eyes-closed) and a between-participants
factor Amputation (amputees, controls) was performed on the total, ML, and AP path lengths (Figure 4). Eyes
had a significant main effects on the total, ML, and AP path lengths (total: F(1,16) = 53.48, p < 0.001, η2p =
14
0.77; ML: F(1,16) = 21.13, p < 0.001, η2p = 0.57; AP: F(1,16) = 56.22, p < 0.001, η2p = 0.78), indicating a
larger postural sway in eyes-closed conditions (Edwards, 1946). Importantly, the effect of Eyes did not
interact with Amputation (Fs(1,16) ≤ 3.34, ps ≥ 0.09, η2ps ≤ 0.17). Furthermore, there was no main effect of
Amputation on all three path lengths (Fs(1,16) ≤ 0.58, ps ≥ 0.46, η2ps ≤ 0.04). These results indicate that
amputee’s postural stability and visual contribution to postural control were comparable to those in controls.
Figure 4. (A) Total, (B) medio-lateral, and (C) antero-posterior path lengths for amputees (N = 9) and
non-amputee controls (N = 9). Error bars denote ±1 standard error of the mean. Asterisks indicate significant
main effects (**p < 0.01).
The total, ML, and AP path length data from the controls were submitted to ANOVAs with two
within-participants factors, namely Eyes (eyes-open, eyes-closed) and Wrist weight (with, without). As
expected, we found significant main effects of Eyes for all three path lengths (total: F(1,8) = 24.14, p = 0.001,
η2p = 0.75; ML: F(1,8) = 16.04, p = 0.004, η2p = 0.67; AP: F(1,8) = 25.31, p = 0.001, η2p = 0.76), indicating a
larger postural sway in eyes-closed condition. However, Eyes did not interact with Wrist weight for all path
lengths (Fs(1,8) ≤ 4.54, ps ≥ 0.07, η2ps ≤ 0.36). Importantly, there were no main effects of Wrist weight on
path lengths (Fs(1,8) ≤ 1.89, ps ≥ 0.21, η2ps ≤ 0.19). These results suggest that a temporary wrist weight did
not affect postural control in non-amputees, unlike the prosthetic arm in the amputees who frequently or rarely
used it. Figure 5 shows the data for the controls, collapsed across eyes-open and -closed conditions, for
comparison with those in two amputee groups (see Figure 1).
15
Figure 5. (A) Total, (B) medio-lateral, and (C) antero-posterior path lengths in the non-amputee controls.
Error bars denote ±1 standard error of the mean.
4. Discussion
4.1. Postural modulation by (un)embodied prosthetic upper-limb
Posturographic measurements during quiet upright stance indicated that unilateral upper-limb amputees who
frequently use their prosthesis (i.e., frequent-use group) showed larger postural sway without the prosthesis,
while those who rarely use it (i.e., rare-use group) showed smaller sway without the prosthesis (see 4.2 for
ML/AP directionality). Comparable posturographic data from non-amputee controls ruled out the possibility
that the apparent postural modulation by prosthesis derived from altered postural control due to aging and
amputation per se. These results suggest that a prosthetic arm can stabilize an amputee’s body posture if the
prosthesis is frequently used, but not if it is rarely used, consistent with a recent qualitative study (Wijk &
Carlsson, 2015).
It is probable that frequent and long-term prosthesis use can lead to embodiment of the prosthesis (de
Vignemont, 2007; Mills, 2013; Murray, 2004, 2008). This may be the case for our frequent-use group, whose
daily usage was longer than that of the rare-use group, but whose elapsed time since amputation was
comparable. It has been suggested that long-term tool use not only improves performance in terms of
controlling the tool, but also leads to incorporation of the tool into the body representation (Cardinali et al.,
2009; Maravita, Clarke, Husain, & Driver, 2002). Prosthetic arms in the frequent-use group may also have
been incorporated into their owner’s body representation, and consequently involved in the
feedback/feedforward postural control system (Peterka, 2002; van der Kooij et al., 1999), requiring coherent
body representation as a reference frame (di Fabio & Emasithi, 1997; Gurfinkel et al., 1995). In contrast, as
the prosthesis was presumably not embodied in the rare-use group, these individuals may be able to control
their posture even without a prosthesis; consequently, the presence of a prosthesis can perturb their posture.
Studies have shown that removal of an embodied object and placement of an unembodied object, other than
16
an (un)embodied prosthesis, can disturb postural control (see 4.2 for an exception). For instance, in normal
individuals, fitting an unembodied external object (e.g., wrist weight or backpack) perturbs the body posture
during upright stance (Al-Khabbaz, Shimada, & Hasegawa, 2008; Haddad et al., 2011). Furthermore, breast
augmentation (Mazzocchi, Dessy, Iodice, Saggini, & Scuderi, 2012), breast reduction (Mazzocchi, Dessy, di
Ronza, et al., 2012), and abdominoplasty (Iodice, Scuderi, Saggini, & Pezzulo, 2015) also increase postural
sway in the patients just after the surgery, although the postural control is gradually restored to normal
approximately 12 months after surgery. In the current study, since roughly forty years had elapsed since
amputation and the beginning of prosthesis use, we could not examine the time course of embodiment of the
prosthesis and its relationship with changes in postural control ability over a long period. A future longitudinal
study that enrolls participants just after the amputation could be used to address this issue.
4.2. Postural sway in medio-lateral and antero-posterior directions
Different effects of a prosthesis on postural sway were found in the ML and AP directions; the prosthesis
reduced postural sway for AP and total path lengths in the frequent-use group, while removal of the prosthesis
reduced postural sway for ML and total path lengths in the rare-use group. A possible biomechanical
explanation for the differences in ML and AP postural control is that ML balance is accomplished by hip
(abductor/adductor) control, whereas AP balance is accomplished by ankle (plantar/dorsiflexor) control (Day
et al., 1993; Gatev, Thomas, Kepple, & Hallett, 1999; Winter et al., 1996). However, what is the basis of the
differences in the two groups?
Two explanations can be proposed to account for the AP-specific postural effect in the frequent-use group.
The first is based on direction-specific motor representation. Several studies have suggested that imagery of
whole-body and upper-limb movements can increase postural sway (Boulton & Mitra, 2013; Grangeon,
Guillot, & Collet, 2011; Rodrigues et al., 2010). In particular, Boulton and Mitra (2013) reported that ML and
AP postural sway increase during imagery of ML- and AP-directional movements using the upper limb,
respectively. If the embodiment of the prosthetic arm in the frequent-use group was associated with the motor
representation of related movements using the upper limb, the removal of the prosthetic arm representing
AP-direction movements (e.g., grasping, and arm swinging for walking) might have unconsciously driven
motor imagery and consequently elicited postural sway in the AP direction. Indeed, one of the basic actions of
the upper limb is an arm swing in the AP direction during walking, which can stabilize the gait pattern
following external perturbation (Elftman, 1939; Marigold, Bethune, & Patla, 2003; Meyns, Bruijn, & Duysens,
2013). We assume that the more controllable prosthetic arm, which allows execution and/or representation of
arm swing, is likely to stabilize postural control in AP direction. A second explanation has its basis in more
cognitive aspects. It has been suggested that cognitive states (e.g., anxiety and emotion) selectively affect
postural sway in the AP direction (Brunye et al., 2013; Lelard et al., 2013; Wada et al., 2001). Moreover,
17
recent studies have demonstrated that a pleasant touch facilitates the illusion of body representation, that is,
the RHI (Crucianelli, Metcalf, Fotopoulou, & Jenkinson, 2013; van Stralen et al., 2014), and that anxiety
responses can be induced by threatening an artificial hand under the RHI (Ehrsson, Wiech, Weiskopf, Dolan,
& Passingham, 2007). These findings suggest a linkage between cognitive states and bodily responses. Thus,
although speculative, certain cognitive responses elicited by fitting/removal of embodied prosthetic arm may
relate to the AP-specific postural modulation in the frequent-use group.
In contrast, why was the ML-specific effect observed in the rare-use group? The rare-use group, who may
have a coherent body representation without their prosthetic arm, should be able to maintain their body
posture without the prosthesis. It can be assumed that the unembodied prosthesis unilaterally perturbed the
upright body posture in the rare-use group, and increased the ML postural sway as a result of compensation
for the perturbation. This assumption is supported by findings that physical loads imposed on the unilateral
side can serve as postural perturbations that increase postural sway in the ML direction (Haddad et al., 2011).
To test this explanation, the follow-up experiment investigated the effect of fitting an unembodied external
object (i.e., wrist weight) in non-amputee controls. It was expected that an increase in ML postural sway
would be found while the wrist weight was present. However, the wrist weight did not influence ML path
length, or the total and AP path lengths. This might suggest that our unilateral amputees in the rare-use group,
unlike controls, had an asymmetric body representation, which could be vulnerable to perturbation. This could
explain the ML postural sway induced by fitting the prosthetic arm, although the amputees' body
representations may be coherent without a prosthesis. Alternatively, we speculate that the different nature of
prosthetic arms and wrist weights might explain the different postural effects; that is, a prosthesis can be a tool
that is likely to be incorporated into the body and/or motor representation, while a wrist weight is not tool; it is
just placed onto the body.
4.3. Subjective measures of prosthesis embodiment and their relationship to postural control
We used a questionnaire based on previous studies (Longo et al., 2008; Wijk & Carlsson, 2015), in addition to
the frequency of prosthesis use, as an indicator of embodiment of the prosthetic arm, to examine how
subjectively reported prosthesis embodiment relates to postural control, and what subcomponents of
embodiment (cf. Longo et al., 2008) are important for prosthesis embodiment. The composite variable
Postural effect received higher scores in the frequent-use group, suggesting that the amputees who frequently
used their prosthesis found that it contributed to their postural control more than those who rarely used their
prosthesis. This was also the case for the single item 1 (Postural stabilization), that is, the frequent-use group
was more likely to report that the prosthesis stabilized their body posture. For single item 2 (Biased body axis),
the frequent-use group was more likely to report their body axis was biased toward the amputated side, while
the rare-use group found no such bias. It is probable that the body-axis bias toward the amputated side would
18
result in unbalanced posture when the prosthesis is removed, while wearing a prosthesis would perturb body
posture if the body axis is without bias. These results from the subjective measures are consistent with the
objective measures (i.e., posturography) indicating a decrease in postural sway following prosthesis fitment in
the frequent-use group, and by removal of the prosthesis in the rare-use group.
No group difference was found for the composite variable Ownership, while only the single item 4 (Habitual
touch) was higher in the frequent-use group. This implies that the sense of ownership over the prosthetic arm
is not a primary component of the prosthesis embodiment and a critical factor for postural modulation,
although the reported tendency to touch their prosthesis was possibly due to attentiveness and care toward the
prosthesis. In contrast, as for Agency, the frequent-use group showed more agreement with the items than the
rare-use group, suggesting that amputees who frequently use their prosthesis are more likely to feel that they
can control their prosthesis accurately, quickly, and/or easily, possibly due to motor learning and updated
internal models (Imamizu et al., 2003; Imamizu et al., 2000), similarly to long-term tool use (Bassolino et al.,
2010; Cardinali et al., 2009; Serino et al., 2007). These results suggest that an upper-limb prosthesis is
incorporated into the body representation not simply as an object to be owned and with which to have sensory
experiences, but as an effector or a tool to be used and controlled, which supports our hypothesis that
embodiment of a prosthetic arm can be driven more by a sense of agency than by a sense of ownership. This is
consistent with the idea that a prosthetic arm is originally an alternative to the effector (i.e., intact upper limb)
and the hand and arm are an actively moving interface with the external world (Baumgartner, 2001).
Furthermore, these findings may extend those on the interaction of sense of agency and body ownership,
which are generated by the active or passive movement of one’s own hand (Caspar et al., 2015; Kalckert &
Ehrsson, 2012, 2014a; Tsakiris et al., 2006).
We could not examine variability according to prosthesis type or the presence and movement of a phantom
limb, that is, awareness of the amputated limb (Kooijman, Dijkstra, Geertzen, Elzinga, & van der Schans,
2000). Since voluntary tool use is likely important for incorporation into a coherent body representation,
which may be required for stable postural control as a reference frame (di Fabio & Emasithi, 1997; Gurfinkel
et al., 1995), movable prostheses (e.g., functional and myoelectric) are more likely to be embodied than
non-movable prostheses (Nico et al., 2004). This idea is supported by previous findings in non-amputees,
which suggest that the sense of agency is a key determinant of body-ownership over external objects (Asai,
2016) and contributes to recalibration of the body representation while maintaining its coherence and unity
(Tsakiris et al., 2006). In the current study, although three amputees in the frequent-use group and two in the
rare-use group used a functional or myoelectric prosthesis, the small sample size did not allow us to examine
the effect of prosthesis type. Regarding phantom limb phenomena, eight of the nine amputees reported that
they still experienced a phantom limb, despite approximately forty years having elapsed since their
19
amputation. Moreover, two of the eight with phantom limbs reported that they could voluntarily move their
phantom limbs. As such, we could not examine the effects of the presence or movement of a phantom limb on
postural modulation by a prosthetic arm. A phantom limb can be perceived in terms of its shape, size, and
location (Longo, Long, & Haggard, 2012; Sumitani, Yozu, Tomioka, Yamada, & Miyauchi, 2010), to execute
an action (Osumi et al., 2015; Raffin, Giraux, & Reilly, 2012), and to generate a sense of agency (Imaizumi,
Asai, Kanayama, Kawamura, & Koyama, 2014), similarly to an intact limb. Thus, it is possible that the
embodiment of a prosthetic limb and the presence and movement of a phantom limb can interact, and the
interaction might interfere with the postural modulation effect of the prosthesis.
4.4. Limitations
The current study has three limitations of note. First, our sample size was small. Future studies should seek to
replicate our findings with larger samples. Additionally, further studies might examine the aforementioned
issues by enrolling amputees with various conditions, that is, movable or non-movable prosthesis users with
or without a phantom limb. Second, it should be noted that we did not verify the self-reported frequency of
prosthesis usage; for example, some individuals might have used their prosthesis with the reported frequency
since their amputation, while others might have adopted the reported frequency of use only recently. This
could confound our between-groups design that included frequent-use (embodied) and rare-use (unembodied)
groups. Finally, our findings are limited to unilateral upper-limb amputees. Thus, it remains unclear whether
and how a prosthesis modulates postural control in bilateral upper-limb amputees and how bilateral prostheses
are embodied. Given the asymmetries in weight and morphology, substantial differences between unilateral
and bilateral amputees can be anticipated.
4.5. Conclusions and outlook
The current findings from posturography and a questionnaire regarding prosthesis embodiment suggest that an
embodied prosthetic arm stabilizes amputees' body posture while an unembodied one perturbs it, and that
amputees should feel a sense of agency over their embodied prosthesis, rather than a sense of ownership over
it, to enable the prosthesis to stabilize their body posture. While care should be taken when drawing
conclusions from our small sample, the current study is, to our knowledge, the first empirical demonstration
of a recent qualitative suggestion regarding postural stabilization by upper-limb prosthesis (Wijk & Carlsson,
2015). Additionally, previous findings that long-term use of a prosthetic arm leads to prosthesis embodiment
based on evidence from motor trajectories of the upper limb (Fraser, 1984), proprioceptive upper-limb
dimensions (McDonnell et al., 1989), and peripersonal space (Canzoneri et al., 2013) are extended by our
findings that prosthesis embodiment, especially driven by a sense of agency, can modulate whole body
movement, that is, postural control.
20
Cortical plasticity sometimes causes maladaptive reorganization in somatosensory and motor cortices
following limb amputation, for example, phantom limbs and associated pain (Flor, Diers, & Andoh, 2013;
Flor, Nikolajsen, & Jensen, 2006), but also leads to adaptive changes, including the embodiment of prostheses
and tools, and their subsequent influence on postural control and kinematics. As we have suggested, it is
important for this adaptive embodiment that amputees becomes agents who voluntarily use and control their
prosthesis. To date, studies of postural control have generally overlooked the perspective of embodiment and
the sense of self, whereas very few studies on the sense of self have examined its relationship with whole
body movement, for example, gait (Kannape & Blanke, 2012; Kannape, Schwabe, Tadi, & Blanke, 2010).
Understanding prosthesis embodiment and its postural modulation can bridge these two research fields and
may provide a new perspective on rehabilitation. Previous studies of postural control and gait have primarily
focused on lower-limb amputees (Gailey et al., 2008), perhaps because the lower limb may have a more
important role for locomotion and weight-bearing activity. However, future studies and rehabilitation practice
should note that an upper-limb prosthesis can maintain an amputee’s body posture in order to prevent falls and
back/neck pains. New assessments using posturography might be derived that determine whether and how an
upper-limb prosthesis matches an amputee and is embodied by him or her, beyond consideration of the motor
efficiency of prosthetic control as an index of embodiment (Cardinali et al., 2009).
Acknowledgements
We would like to thank Takashi Nomura and Toshihiko Hayashi for their assistance with participant
recruitment and the reviewers for their helpful comments.
Funding
This work was supported by Grant-in-Aids for JSPS Fellows to SI (13J00943, 16J00411) from the Japan
Society for the Promotion of Science.
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