Effect of a Body Part Action on Body Perception of the Other Inactive Body Part

The rubber hand illusion (RHI) is an illusory experience in which a fake rubber hand is felt as if it were one’s own hand when the visible fake and invisible real hands are stimulated synchronously. Although several studies have suggested contributions of action to body ownership using the RHI paradigm, the relationship between body ownership and agency has not yet been fully revealed. To better understand this relationship, the present study investigated the transfer of body ownership between body parts induced by a body part action. Using an RHI paradigm involving virtual reality, we tested whether a simple finger action of the dominant (active) hand can induce the embodiment of a virtual hand corresponding to the nondominant (inactive) hand. We evaluated the illusory experience, perceptual changes, and physiological changes during the experiment with a subjective questionnaire, crossmodal congruency effect measurement, and skin temperature measurement, respectively. The results demonstrated that the finger action induced the embodiment of both virtual hands, causing a significant increase in agency of the inactive hand. This suggests that the illusory experience induced by an active body part contributes to an increase in agency as well as body ownership over the virtual body of the other inactive body part.


I. INTRODUCTION
I N GENERAL, humans never doubt a sense of "my body (or body part) belongs to me" (i.e., the sense of body ownership) or "I am moving (or controlling) my body" (i.e., the sense of agency) [1] although they are not particularly aware in daily life. For instance, we never consider that our fingers and hands are tools or being moved by someone else when we play a piano or type at a keyboard by ourselves. Such awareness is normally robust but could deteriorate in higher brain dysfunction or psychiatric/neurological disorders. For instance, a detachment experience of one's self (or mind) and body is caused in depersonalization, suggesting the dissociation of body ownership from one's physical body [2]. Patients with chronic pain often report the experience as if their painful affected limb were considerably swollen or not a part of their own body [3], [4], [5]. In terms of agency, the sense of control over one's body actions is lost in the alien hand syndrome (which may be caused by damage to the corpus callosum) [6], [7] or schizophrenia (which shows distortions in perception, thoughts, behavior, etc.) [8], [9], [10]. Therefore, a scientific understanding of the underlying mechanism or the relationship between body ownership and agency may shed further light on the pathology of these diseases or disorders.
Body ownership is based on the integration of multisensory signals, whereas agency is grounded in the integration of efferent and afferent sensorimotor information [11], [12]. Thanks to contributions in experimental psychology and cognitive neuroscience, the senses of body ownership and agency can be now experimentally manipulated, even in healthy people. Since Botvinick and Cohen [13] discovered that a sensory conflict between visual and tactile cues of one's body allows the modulation of the sense of body ownership resulting in the rubber hand illusion (RHI) in which a fake rubber hand is felt as if it were one's own hand, synchronous visuotactile stimulation of artificial and real bodies have been frequently used to induce bodily illusions [14], [15], [16], [17], [18], [19], [20], [21]. The illusory experience is evaluated using a subjective questionnaire based on the well-established RHI questionnaire [13], and can be quantitatively measured with changes in perceived self-location (e.g., proprioceptive drift [15]), perceptual changes (e.g., crossmodal congruency effect (CCE) [22], [23]), and physiological changes (e.g., skin temperature [24], [25]) during the experiment. These quantitative data may be typically associated with the strength of the illusory experience. For instance, the sense of position of This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ the stimulated hand drifted significantly toward a fake rubber hand [15] or the skin temperature on the stimulated hand decreased significantly [24] when a strong RHI was induced, although a significant effect has not been always observed [26], [27]. The illusory experience has been discussed by analyzing the quantitative data as well as the questionnaire results between synchronous and asynchronous conditions because asynchronous visuotactile stimulation reduces or vanishes bodily illusions.
Furthermore, several studies using specific devices, virtual reality, or robotic setups have demonstrated that synchronous movements of artificial (or virtual) and real bodies allow the experimental manipulation of the sense of body ownership [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39]. For instance, Dummer et al. [28] performed an RHI experiment with hand movement and compared the strength of the RHI under active (i.e., participants could move a fake rubber hand together with their real hand), passive (i.e., the experimenter moved the fake hand together with the participants' hand), and asynchronous (i.e., the movement of the fake hand was disconnected from that of the participants' hand) conditions. The study found that an increase in agency enhanced the illusory experience. In contrast, Kalckert and Ehrsson [31] suggested a dissociation of body ownership and agency through a moving RHI experiment with movement of the index finger. In addition, Sanchez-Vives et al. [30] demonstrated that the virtual hand illusion (VHI), which uses the virtual hands instead of the fake rubber hands, can be induced by simply synchronizing movements of the visible virtual and invisible real hands. Our previous studies succeeded in implementing active self-touch, in which experimental participants could administer tactile stimulation to both artificial (or virtual) and real hands with a leader-follower robotic system and a haptic interface, in the RHI paradigm [40]. We demonstrated that our method using robotic stimulation and haptic feedback allows the participants to experience the RHI [40] and that voluntary self-touch enhances the embodiment of the virtual hand [27]. Our results suggest that agency could affect the sense of body ownership during self-touch. As mentioned above, body ownership and agency have been studied with various experimental conditions and setups. However, the underlying mechanism and relationship have not yet been fully elucidated. To clarify these, we take an approach stemming from cognetics, which is a multidisciplinary research method based on cognitive neuroscience and robotics [41].
Here, we experimentally investigated how changes in the body perception of an active body part affect that of the other inactive body parts, especially focusing on the transfer of body ownership between body parts, which has been discussed only under the visuotactile stimulation in a very few studies [15], [42]. Specifically, using an RHI paradigm involving virtual reality, we examined whether a simple up-and-down action with an index finger of the dominant hand could induce the embodiment of not only a virtual hand corresponding to the active dominant hand but also the other virtual hand corresponding to the inactive nondominant hand. The experimental setup was designed and developed by integrating virtual reality and robotic technologies and was fundamentally based on a cognetic approach [41]. Considering the role of sensorimotor signals in hand ownership [27], [28], [40], these signals may also contribute to body ownership over the inactive body part. Thus, we hypothesized that the embodiment of a virtual body induced by the movement of corresponding body part affects the illusory experience in the other inactive body part even if it does not move. In the present study, participants' experience and perceptual changes during the experiment were measured using a subjective questionnaire (adapted from the RHI questionnaire [13], [14], [31]) and CCE [22], [23], respectively. In addition, physiological changes due to the illusory experience were investigated by measuring the hand skin temperature with reference to a previous study [24] as a supplementary data. Using these data, we aim at proving the aforementioned hypothesis correct from various aspects, and opening the door to a new discussion about the relationship between body ownership and agency.

A. Participants
Twenty-two healthy participants (five females, two lefthanded, mean age 25.2±4.2 (20 to 34) years) were recruited for the experiment. This sample size was determined based on our previous related study [43] and alternative studies using the moving RHI [28], [31], [34] and VHI paradigms [30], [33], [39] to replicate similar illusory experiences. All participants had normal or corrected to normal vision, normal motor function, and no history of neurological or psychiatric conditions as assessed by self-report. The experimental protocol was formulated following the ethical guidelines for medical and health research involving human subjects established by the Ministry of Education, Culture, Sports, Science and Technology, Japan, which was based on the ethical standards laid down in the Declaration of Helsinki, and was approved by the Ethics Committees of the School of Engineering in The University of Tokyo and the Graduate School of Science and Engineering in Saitama University. All participants were not familiar with the bodily illusions and had no preliminary knowledge about the experimental procedure. They gave their written informed consent before beginning the experiment, and were reimbursed for their participation in the experiment with 1000 JPY per hour.

1) Sensing Device for Movement of Index Finger:
We designed a simple sensing device to capture rotational movement in the first joint (i.e., metacarpophalangeal (MP) joint) of the participants' dominant index finger during the experiment. Fig. 1 shows a schematic of the internal structure and a photograph of a participant's right hand wearing the device. The sensing device consisted of three 3-D-printed parts-sensor, rotational, and grip parts in Fig. 1(a)-mainly made of acrylonitrile butadiene styrene (ABS). Regarding the device structure, a finger support connected to a steel shaft can be easily fixed to the proximal phalanx of the participants' index finger with a hook-and-loop fastener (Velcro), as shown in Fig. 1(b). The finger support could rotate freely around the shaft due to the two ball bearings embedded in the sensor part. A tiny potentiometer (RDC506002A, ALPS Electric Company, Ltd.), embedded in the sensor part, was linked to the shaft and measured the rotational angle around the MP joint of the index finger; the resolution was less than 0.01 • . The position of the finger support (i.e., rotational center) could be individually modified by an adjuster for each experimental participant based on their hand size. A grip part was attached to the participants' palm by tightening a hook-andloop fastener, as shown in Fig. 1(b). During the experiment, the participants moved the MP joint of the dominant index finger while placing their elbows on mechanical armrests (CA-500, AREA) and grasping soft polyurethane cushions. To unify the conditions between the hands, the participants also wore the same device on their nondominant hand. As the weight of the entire device was approximately 35.4 g, the load when wearing the sensing device on the hands was negligible.
2) CCE Measurement System: To measure the CCE (the details are described in Section II-C2), four button-type vibrators (FM34F, Tokyo Parts Industrial Company, Ltd.) were attached to the tips of the thumbs and index fingers with hookand-loop fasteners, as shown in Fig. 1(b), which were used to produce vibrotactile stimuli in the CCE measurement. Flash of distractor light by light-emitting diodes (LEDs), which was presented prior to vibrotactile stimuli [22], was expressed by the color change of virtual spherical markers rendered on the thumbs and index fingers of the virtual hands. A custom-made foot switch device comprising of two pedal-type switches (MFKS-1, Kasuga Electric Works Ltd.) was placed under a toe and a heel of the participants' dominant foot. The participants were instructed to keep stepping the two pedals during the experiment, except the CCE measurement phase. The foot switch device was used to measure the participant's reaction time (RT) to the vibrotactile stimuli presented to their thumbs or index fingers.
3) Temperature Measurement Device: A real-time temperature measurement device was implemented throughout the experiment to measure changes in skin temperature on both hands. Specifically, an eight-channel thermocouple data logger (USB TC-08, Pico Technology) was applied to measure the skin temperature of the hands using seven type K thermocouples. One thermocouple was used to measure the room temperature exclusively, and the other six were used for the skin temperature measurements of the active and inactive hands; the specific locations on the hands are explained in Section II-C3. The resolution of the temperature measurement was 0.025 • C (range: −250 • C to 1370 • C) with the use of type K thermocouples.

4) Experimental Display:
The virtual hands were rendered as 3-D graphics using OpenGL and GLEW libraries (see Fig. 2) and displayed on a head-mounted display (HMD: HMZ-T1, Sony) to follow up our previous studies [40], [43]. The index finger of the virtual active hand could move up and down based on the movement of the participants' dominant index finger measured by the sensing device, whereas the index finger of the virtual inactive hand did not move even if the index finger of the nondominant hand moved. Based on the real-time angle data, the virtual index finger moved simultaneously with the movement of the real index finger under illusion condition (i.e., synchronous condition). In nonillusion condition (i.e., asynchronous condition), the movement  of the virtual index finger was delayed using the angle data buffered before a specific time (i.e., delay time). White noise was presented to the participants via headphones on the HMD to block out the ambient noise and sound from the hardware, as well as to relax the participants during the experiment. The white noise was programmed to be automatically played back and stopped at the beginning and end of the experiment, respectively. 5) Experimental Environment: Fig. 3 shows an experimental environment involving the experimental system consisting of the aforementioned devices. For input/output (I/O) control, a data acquisition device (NI PCIe-6323, National Instruments) implemented in a desktop computer was used to control activation of the vibrators as well as to capture finger and pedal actions. A GUI-enabled application was programmed with Visual C++ (Microsoft) to facilitate the experimenter to manage the experiment. The experimenter could quickly configure the experimental conditions, such as synchrony of finger action and parameters for CCE measurements, via the GUIs. Furthermore, the application allowed the experimenter to observe the experimental information on an LCD monitor in real time and to record the behavior and state of the participants, such as RT, movement of the index finger, and skin temperature. In the present study, the sampling time was set to 1 ms, which was a sufficient period for both I/O controls and rendering of the virtual scene.
C. Dependent Measures 1) Illusory Experience: We evaluated the subjective experiences of the participants during the experiment using a subjective questionnaire adapted from the classical RHI questionnaire [13], [14], [43]. The questionnaire items are listed in Table I and were presented to the participants in the same order between the experimental blocks. The first item (Q1: self-identification) was an illusion item designed to confirm the illusory experience, that is, the embodiment of the virtual hand. The second item (Q2: agency) was used to assess the agency of one's own behavior during the experiment. The other three items (Q3: self-identification, Q4: disembodiment, and Q5: illusory movement) were irrelevant to the bodily illusion, although they were similar to the illusion question. The answers to these three items are typically not affected by multisensory stimulation that causes bodily illusions, such as the RHI and full-body illusion (FBI) [13], [17], [34], [44]; therefore, Q3, Q4, and Q5 served as control items to assess potential suggestibility effects. Here, suggestibility means that all items are sometimes rated in the same manner for any reason, which should be removed from the analysis.
At the end of each experimental block, the participants were asked to answer to the questionnaire for the active and inactive hands with a seven-point Likert scale (−3: "I strongly disagree with the statement" to +3: "I strongly agree with the statement"). A score of 0 was considered a neutral rating allocated for an uncertain or undecidable experience. In our design, the ratings for the illusion and agency items in the synchronous condition should be significantly higher than 0 and those in the asynchronous condition when the participants experienced as if the virtual hands were their own hands and they were administering the movement of the virtual index finger; in the present study, these illusory experiences are termed illusory body ownership and agency over the virtual hands, respectively. Additionally, in the synchronous condition, the ratings for the illusion item should be significantly higher than those for the control items when the suggestibility effects were negligible.
2) Crossmodal Congruency Effect: When the multisensory information given to our body matches temporally and spatially, it results in the reduction of RT to a stimulus as a behavioral response. The CCE task is one of implicit measures to investigate the behavioral response [22], [23]. Visuotactile interference has been frequently used to measure the CCE as a difference in the RT to tactile stimuli between the incongruent (i.e., when visual and tactile stimuli are presented to the different body locations) and congruent (i.e., when the two stimuli are presented to the same body location) conditions. In a visuotactile CCE test, the RT increases in the incongruent condition due to the disruption caused by the spatial incongruency of visuotactile information, whereas it decreases in the congruent condition due to the visuotactile integration. The CCE could be modulated by the visuotactile stimulation to artificial (or virtual) and real bodies when the embodiment of artificial body is induced. This is because the spatial locations of the two bodies are perceived psychologically to be congruent although they are physically away. Since Pavani et al. [22] demonstrated that the CCE increased under an embodiment condition (where the visible artificial hands were aligned with the invisible participants' hands) compared to nonembodiment condition (where the artificial hands were misaligned or absent), the CCE has been used to assess the visuotactile integration related to the artificial or virtual body [32], [45], [46], [47]. In the present study, we also investigated the CCE during the experiment using a visuotactile CCE test to strengthen the result related to the embodiment of the virtual hands reported in the subjective questionnaire (i.e., rating for Q1). To perform a visuotactile CCE test, we used the CCE measurement system of Section II-B2 which allows to present pairs of visual distractors and vibrotactile stimuli to the thumbs and index fingers of the virtual and real hands, as well as to measure the RT to the vibrotactile stimuli at 1 ms sampling time.
In the present study, a visuotactile CCE test started 2.5 s after four virtual markers were displayed on the thumbs and index fingers of the virtual hands (see Fig. 4). One of the vibrators on the participants' fingers was randomly activated after one of the visual distractors (i.e., change of marker color) was randomly presented. At this time, the participants were asked to ignore the visual distractor presented prior to the vibrotactile stimulus and discriminate the location where they felt the vibrotactile stimulus by raising their toe (in the case of the index fingers) or heel (in the case of the thumbs) from the foot switch device as quickly as possible. The RT from the onset of vibration to the response was measured and recorded for each condition. The CCE was expressed as a difference between RTs under incongruent and congruent conditions (i.e., "congruent" was when both visual distractor and vibrotactile stimulus were given to the same fingers, otherwise "incongruent"). The CCE was also calculated for each distractor side (i.e., "same" was when both visual distractor and vibrotactile stimuli were presented to the same hand, otherwise "different"). In each CCE measurement, the color of a virtual marker changed from white to red for 100 ms, and then, a randomly selected vibrator was activated for 150 ms. The stimulus onset asynchrony (SOA) of 100 ms was chosen because previous studies demonstrated that the CCE is maximized for such an SOA [48], [49].
3) Skin Temperature: Some previous studies demonstrated that the skin temperature of the hand and back could decrease significantly when the RHI [24] and FBI [25] were induced, respectively. These results suggest that the cognitive processes that cause the misattribution of body ownership to the external object may confuse our body temperature regulation. Using the temperature measurement device described in Section II-B3, we also measured changes in the skin temperature on the active and inactive hands during the experiment to investigate physiological changes due to the illusory experience. The skin temperature was measured at three points based on a previous study on the RHI [24]. Specifically, the thermocouples were attached to centers of the metacarpal bones of the index and third fingers (i.e., points A and B) and the tip of the ulna (i.e., point C) with surgical tapes, as shown in Fig. 5. In the present study, the skin temperature was measured every 1 s under an experimental environment where the room temperature was controlled to be approximately 24 • C to 25 • C by an air conditioner.

D. Experimental Procedure
First, participants underwent a training session in which they could try the finger action of the real and virtual hands under both synchronous and asynchronous conditions following the manner instructed in the main experiment until the experimenter felt that the participants had fully understood the experimental procedure. Furthermore, a CCE test with 32 conditions (16 conditions (i.e., 16 pairs of visual distractors and vibrotactile stimuli) × 2 repetitions) was conducted to check if the participants could correctly perform the CCE test. We verified that the error rate was less than 15% for all participants. After the compatibility test, we also instructed the participants to perform a CCE test with 240 conditions (16 conditions × 15 repetitions) while gazing at only virtual markers displayed on the HMD (i.e., the virtual hands were not rendered) to obtain baseline CCEs. A short break for a few minutes was taken after half of the conditions were completed. Fig. 6 shows a flow chart of the main experiment. In each experimental trial, the participants, while in a sitting position, were asked to move their dominant index finger up and down for 60 s in the first trial and 15 s in subsequent eleven trials; a long period for the finger action was set in the first trial to promote the embodiment of the virtual hands in the synchronous condition at the beginning of experiment. In the asynchronous condition (i.e., nonillusion condition), a constant 500 ms delay time was applied to the movement of the index finger in the virtual active hand, which could be sufficient to suppress the illusory experience [50]. During the experiment, the participants were instructed to gaze at the virtual hands via the HMD as far as possible and were not allowed to move their nondominant hand. Once four virtual markers were displayed on the thumbs and index fingers of the virtual hands at the end of the finger action phase, the participants prepared for a subsequent visuotactile CCE test by immediately stopping their finger action. After 2.5 s of preparation, they performed the CCE test with four conditions randomly selected from 16 conditions following the procedure described in Section II-C2. In summary, an experimental trial consisted of a finger action phase for 60 or 15 s and a CCE test phase for 10 s, which was repeated twelve times in an experimental block, as shown in Fig. 6. Thus, each experimental block includes the CCE tests with a total of 48 conditions (16 conditions × 3 repetitions). At the end of each block, the participants were asked to answer the RHI questionnaire for both active and inactive hands based on their experience during the experiment. All participant performed a total of ten experimental blocks (five blocks for each condition), randomly changing the synchrony of the finger movement in the virtual active hand. As an experiment took for approximately 2 h, short breaks for a few minutes were taken appropriately during the experiment depending on the degree of fatigue in the participants.

E. Data Analysis
In the present study, 95% confidence interval (CI) was adopted; therefore, the level of statistical significance was defined as p < 0.05.
The mean ratings for the five questionnaire items, which are discrete variables, were analyzed using nonparametric tests (Friedman test and Wilcoxon signed-rank test) because Shapiro-Wilk tests reported several significant deviations from normal distributions in Q2 (inactive hand-asynchronous: W = 0.910, p = 0.046), Q3 (active hand-synchronous: W = 0.893, p = 0.022; inactive hand-asynchronous: W = 0.908, p = 0.043), Q4 (active hand-synchronous: W = 0.906, p = 0.040; inactive hand-synchronous: W = 0.904, p = 0.035), and Q5 (active hand-synchronous: W = 0.857, p = 0.005; active hand-asynchronous: W = 0.880, p = 0.012; inactive hand-synchronous: W = 0.826, p = 0.001; inactive handasynchronous: W = 0.856, p = 0.004). We first applied the Friedman test, which is a nonparametric version of one-way repeated measures analysis of variance (ANOVA), to the mean ratings for each questionnaire item. If significant in the illusion (Q1) and agency (Q2) items, the mean ratings were further analyzed using the two-tailed Wilcoxon signed-rank test (a nonparametric alternative to two-tailed t-test), and the level of significance was corrected for multiple comparisons with the Bonferroni method (i.e., corrected α = 0.05/6 = 0.0083). In the synchronous condition, suggestibility effects were evaluated by comparing the mean ratings for Q1 and Q2 with those for the control items (Q3, Q4, and Q5) using the twotailed Wilcoxon signed-rank test, which employed the level of significance corrected with the Bonferroni method (i.e., corrected α = 0.05/3 = 0.0167). Furthermore, the correlations of the ratings for Q1 and Q2 under the synchronous condition were statistically analyzed between the hands using the Pearson correlation coefficient (PCC).
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Regarding the results of CCE measurement, we began by analyzing mean RTs, which are continuous variables, using a three-way repeated measures ANOVA with withinparticipants factors of Synchrony (synchronous versus asynchronous), Congruency (congruent versus incongruent), and Distractor side (same versus different). Similar to previous CCE studies [43], [46], [47], [49], RTs in erroneous trials and below 0.2 s or over 1.5 s, which were considered preemptive or delayed responses, were removed from the analysis. The mean CCEs were further analyzed if the three-way interaction was significant. Specifically, first, the Dunnett's test was applied to verify whether the mean CCEs measured on the same distractor side were significantly higher than those in the baseline condition. After the analysis using a two-way repeated measures ANOVA with within-participants factors of Synchrony and Distractor side, the mean CCEs were further analyzed with a two-tailed t-test to investigate which comparisons between the four conditions involve significant differences; the level of significance was corrected for multiple comparisons with the Bonferroni method (i.e., corrected α = 0.05/6 = 0.0083). The Dunnett's test was used to analyze potential differences in mean CCEs between the first and all subsequent experimental blocks under both synchronous and asynchronous conditions to examine whether the CCE degraded by repetitive measurements [51]. As a new challenge, the CCE results were further investigated in each hand to confirm whether a similar CCE trend could be observed in both hands. We divided the CCE results into the active and inactive hands (in latter sections, they are termed active hand CCE and inactive hand CCE, respectively) based on the location, where the vibrotactile stimuli were applied. Specifically, the CCEs measured when the vibrotactile stimuli were applied to the thumb or index finger of the active hand were analyzed as active hand CCE, otherwise as inactive hand CCE. Similar to the analysis of CCEs in both hands, these CCEs were analyzed with a three-way repeated measures ANOVA with within-participants factors of Hand (i.e., active hand versus inactive hand), Synchrony, and Distractor side and a two-tailed t-test with a corrected α = 0.0083.
Using time-series graphs, the mean skin temperature on the real hands was first investigated to determine whether it had decreased significantly during the experiment in line with previous studies [24], [25]. The mean skin temperature was further analyzed between the synchronous and asynchronous conditions if distinguishable decreases were found in the graphs. Specifically, the difference in the mean skin temperature between the beginning and end of the experiment was calculated as a representative decrease in the skin temperature and analyzed using a two-tailed t-test.  For the results of Q1 (i.e., the embodiment of the virtual hand), significant differences were found in the mean ratings between the synchronous and asynchronous conditions (active hand: z = 4.110, p < 0.001; inactive hand: z = 3.924, p < 0.001). In the synchronous condition, there was a significant difference between the active and inactive hands (z = 2.956, p = 0.002). The Wilcoxon signed-rank test also reported significant differences in the mean ratings for Q2 (i.e., agency) between the synchronous and asynchronous conditions (active hand: z = 4.109, p < 0.001; inactive hand: z = 3.860, p < 0.001). In addition, the difference between the active and inactive hands was significant in the synchronous condition (z = 3.612, p < 0.001).

B. CCE Measurement
1) RT to Vibrotactile Stimulus: First, mean RTs were analyzed in a classical manner [22], [23], [32], [46]. The mean RTs and errors for all conditions are listed in Table II. A threeway repeated measures ANOVA for the mean RTs detected a significant main effect of Congruency (F(1, 21) = 145.225, p < 0.001, η 2 p = 0.874); there were no significant main

2) CCE in Both Hands (Classical CCE):
As the three-way interaction was significant in the mean RTs, we further analyzed the mean CCEs. Fig. 9 plots the mean CCEs in the synchronous (same side: 126±12 ms; different side: 49±5 ms) and asynchronous (same side: 114±13 ms; different side: 56± 6 ms) conditions. On the same distractor side, the Dunnett's test detected a significant difference between the synchronous and baseline conditions (t(21) = 2.814, p = 0.012), but not between the asynchronous and baseline conditions (t(21) = Regarding the influence of repetitive measurements on the CCE, the Dunnett's test did not report significant differences in the mean CCEs between the first and the other experimental blocks (see Fig. 10). These results indicate that the CCE measurements in the present study could have been performed without the influence of repetitive measurements, unlike the previous study [51].
3) CCEs in Active and Inactive Hands: Fig. 11(a) and (b) shows the mean CCEs in the active and inactive hands, that is, active hand CCEs and inactive hand CCEs, respectively. A three-way repeated measures ANOVA revealed a significant main effect of Distractor side (F(1, 21)

C. Changes in Skin Temperature
First, the mean room temperature and the SEMs during all experimental trials were 24.35 ± 0.28 • C and 24.38 ± 0.28 • C under the synchronous and asynchronous conditions, respectively. As changes in the mean room temperature from the beginning to the end of the experiment were only +0.04 • C in the synchronous condition and +0.05 • C in the asynchronous condition, the influence on the skin temperature measurements is negligible. Fig. 12 shows the trends of changes in the mean skin temperature at the three measurement points of Fig. 5 during the  Table III lists differences in the mean skin temperature between the beginning and end of the experiment at the three measurement points (i.e., T A , T B , and T C ) and the SEMs. The mean skin temperature differences were analyzed only at point C because those increased at points A and B. No significant differences between the synchronous and asynchronous conditions were detected in both active (t(21) = −0.819, p = 0.422) and inactive (t(21) = −0.515, p = 0.612) hands with the two-tailed t-test, indicating that the illusory experience did not affect changes in the skin temperature.

IV. DISCUSSION
First, for the subjective measure with the questionnaire, positive ratings were found only in the illusion (Q1) and agency (Q2) items when the experimental participants performed the finger action with their dominant hand under the synchronous condition. The mean ratings were also significantly higher than those in the asynchronous condition as well as those for the control items. These results suggest that the embodiment of the virtual hand was induced in both active (i.e., dominant) and inactive (i.e., nondominant) hands without the suggestibility effects. This result is in line with our hypothesis, although the illusory experience in the inactive hand was weaker than that in the active hand. Interestingly, the sense of agency also increased significantly in the inactive hand, although the inactive hand neither moved physically nor visually during the experiment. The correlation analysis revealed a significant correlation between body ownership and agency in both hands. According to our previous study [40], we can consider that the illusory body ownership of the virtual active hand was enhanced by the action (i.e., increase in agency) of the active hand. However, this interpretation cannot be adapted to the results in the inactive hand as it is because the participants never moved their nondominant hand during the experiment. The correlation analysis also reported a significant correlation in body ownership between the active and inactive hands but not in agency. In addition, the correlation was not significant between agency in the active hand and body ownership in the inactive hand. Therefore, these results imply that the increase in agency of the inactive hand was not directly associated with changes in the senses of body ownership and agency in the active hand, but was affected by the illusory body ownership of the inactive hand enhanced due to the actions of the active hand. We assume that the sense that the participants were not moving their nondominant hand was enhanced by the embodiment of the virtual inactive hand, resulting in an enhanced sense of agency in the inactive hand.
Regarding the CCE measurement, the results showed that only the mean CCE on the same side in the synchronous condition was significant, although there was no significant difference between the synchronous and asynchronous conditions. These results remained unchanged even if the results of the CCE measurements were analyzed by dividing them into the active and inactive hands. This implies that our CCE measurement reproduced previous CCE results related to the artificial or virtual body [22], [23], [32], [45], [46], [47] in both active and inactive hands. Hence, our CCE findings strengthen the results that the embodiment of the virtual hand was induced in both hands reported in the subjective questionnaire.
The skin temperature was measured under an experimental environment where the room temperature was well-controlled at around 24.5 • C. From the beginning to the end of the experiment, a 0.10 • C to 0.20 • C decrease in the skin temperature was observed at the tips of the ulna (i.e., point C in Fig. 5) in both active and inactive hands, but no significant differences were reported between the synchronous and asynchronous conditions. This suggests that the skin temperature of the hands was not modulated by the illusory experience in the present study, which does not correspond to the results in the previous studies [24], [25]. As the present study differs from their experimental design in several aspects, such as the behavior of participants (finger action in the present study versus no action in the previous study [24]), resolution of temperature measurement (0.025 • C versus approximately 0.20 • C in [24]), and measurement point (hand versus back in [25]), they could have affected the results of our skin temperature measurement. In particular, the finger action might have altered the significant decrease in the skin temperature in the active hand, and the illusory experience weaker than that in the active hand might not have been enough to cause significant physiological changes in the inactive hand.
In summary, our experimental results demonstrated that the illusory experience in the inactive hand was enhanced by the sense of body ownership in the active hand and suggested that the sense of agency in the inactive hand increased due to the enhanced illusory experience. This finding contrasts with some previous studies suggesting a dissociation between the senses of body ownership and agency [31], [47] and could lead to a new discussion of the relationship between body ownership and agency.

V. CONCLUSION
The main objective of the present study was to reveal how a body part action affects body perception in the other inactive body parts. We examined this with a well-established RHI paradigm that involved virtual reality and robotic technologies. Our results demonstrated that a simple body part action could induce the embodiment of a virtual body, even in the other inactive body part, suggesting a possibility of the transfer of body ownership between the body parts by some kind of body action. Furthermore, we observed a curious increase in agency of the inactive hand that could be induced by an increase in body ownership. Therefore, the present study successfully extended previous studies on the interaction between body ownership and agency [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39] as well as our previous studies [40], [43], suggesting that illusory experience in an active body part can modulate the sense of body ownership in the other inactive body parts which could also cause the increase in agency.
We believe that our findings may provide an important information for further understanding the relationship between body ownership and agency. In addition, our results, in particular, the increase in agency of the inactive hand by a simple action of the active hand may be helpful in studies on, for instance, rehabilitation of upper limb hemiplegia [52], phantom pain, and chronic pain in which the patients lose the normal ability to move or aware their hand. Further studies with VR-based platforms like our experimental system may provide novel and effective medical treatments to those diseases or disorders.