Enhancing Two-Dimensional Control via Single-Channel Haptic Feedback: A Multi-dimensional Encoding Strategy

Enhancing Two-Dimensional Control via Single-Channel Haptic Feedback: A Multi-dimensional Encoding Strategy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Enhancing Two-Dimensional Control via Single-Channel Haptic Feedback: A Multi-dimensional Encoding Strategy T R Benigni, A Pena, S Kuntaegowdanahalli, J J Abbas, R Jung This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7189693/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract Haptic feedback elicits sensations of touch to communicate information to the user. Recent developments in virtual reality and sensory prostheses have demonstrated the need for systems that can provide more information than the simple vibrotactor in your phone. A novel multidimensional encoding approach allows for percepts of signal intensity and flutter frequency in a single distal location using transcutaneous neural stimulation. In this study we aimed to determine if these percepts are able to convey useful information to participants performing motor control tasks and if they perform better than a typical intensity-only modulation approach. Eleven participants performed three types of tasks to assess the efficacy of multidimensional stimulation. The first set included discrete matching tasks, where participants had to differentiate between thirteen combinations of flutter frequency and intensity. In the other two sets, participants had to differentiate between simultaneous changes in the percepts. Participants in this study could correctly identify all discrete percept combinations and follow the changes in the percepts better than chance. Performance in the discrete task using a multidimensional approach showed increased information transfer compared to the individual modulation of intensity or flutter frequency. These results suggest that multidimensional encoding is a promising approach for increasing information throughput in sensory feedback systems. Hence, such an approach might improve upon conventional methods of providing graded percepts, creating more informative tactile percepts for haptic feedback through peripheral nerve stimulation. Physical sciences/Engineering Biological sciences/Neuroscience non-invasive electrical stimulation peripheral nerve stimulation information transfer encoding approaches haptics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Haptic feedback delivered through vibration or electrical stimulation has been shown to enhance performance in teleoperation, increase immersion in virtual environments [ 1 , 2 ], and improve functional outcomes for users of myoelectric prostheses [ 3 , 4 ]. However, not all feedback methods are equally effective across applications. In virtual reality and prosthetic use, limitations such as latency between stimulation and perception [ 5 , 6 ], and difficulty distinguishing between graded percepts [ 7 ], can reduce the effectiveness of haptic systems by limiting the amount of information conveyed. To evaluate the utility of haptic feedback, researchers have employed various task paradigms. Object discrimination tasks assess functional relevance in prosthetic and virtual environments [ 8 – 10 ], while matching tasks evaluate how well users can grade percepts by aligning them with visual targets [ 11 ]. Center-out tasks, where users respond to changes in stimulation by moving a cursor, have been used to measure perceptual resolution and tracking ability [ 12 , 13 ]. Electrical stimulation of peripheral nerves can evoke distally referred sensations with percepts felt in limb regions distal to the stimulation site [ 14 , 15 ]. These sensations are often somatotopically matched; for example, stimulating the ulnar nerve at the elbow can elicit percepts in the missing ring and little fingers of individuals with transradial amputations [ 16 ]. These percepts can be modulated by adjusting stimulation parameters such as pulse width, amplitude, or frequency within comfortable ranges [ 17 ]. We recently developed a multidimensional encoding approach that simultaneously modulates two stimulation parameters to deliver distinct, co-located percepts: flutter frequency (5–25 Hz) via interburst interval (IBI) modulation, and intensity via charge rate (QR) modulation [ 18 – 22 ]. This method uses repeated bursts of stimulation pulses, with IBI controlling the perceived frequency and QR determined by the number and duration of pulses within each burst, controlling intensity. Prior studies suggest that conveying multiple, independently gradable percepts can enhance task performance and increase information transfer [ 20 , 23 – 28 ]. Building on this, we hypothesized that a multidimensional encoding strategy, modulating flutter frequency through IBI and intensity through QR, would enable participants to perform motor tasks with accuracy significantly above chance. To evaluate this, participants completed a series of perceptual-motor tasks while receiving stimulation mapped to a two-dimensional percept space: the horizontal axis represented flutter frequency, and the vertical axis represented intensity. In a discrete matching task, participants matched stimulation-evoked percepts to visual targets in this space. A second task assessed their ability to track simultaneous changes in both percepts using a modified center-out paradigm. Finally, we examined whether performance declined when stimulation began at high intensity levels, a phenomenon known as amplitude dropout [ 29 ]. We also compared the information transfer achieved using the multidimensional encoding approach to that of a conventional intensity-only encoding method [ 14 , 25 , 30 ]. Our results demonstrate that participants can reliably differentiate and track multidimensional percepts, suggesting that this approach may offer a more effective means of delivering haptic feedback. Results Sensory characterization Eleven participants (n = 11) received repeated bursts of electrical stimulation to their median nerve through non-invasive stimulating electrodes placed on the wrist using a channel-hopping interleaved pulse scheduling (CHIPS) strategy [ 19 ]. Each participant reported receiving comfortable distal sensations in the area innervated by the median nerve. Local sensations under the electrodes were not reported once calibration was completed. After calibration, a stimulation pulse amplitude (PA) of 1794 ± 401 µA, a comfortable pulse width (PW) range of 469– 699 µs, and a pulse frequency (PF) range of 62–180 Hz was found for each of the eleven participants. These three parameters modulated together were found to provide reliable percepts of intensity following the charge rate model. Participants were also able to perceive a range of flutter frequencies by discriminating the off time or interburst interval between bursts. Participants performed the entire three-hour session without having to re-adjust the calibrated parameters. Thus, using the multidimensional encoding approach, all participants were able to perceive the two simultaneous percepts of flutter frequency and intensity. Participants could identify multiple points in the percept space better than chance. In a discrete matching task participants matched elicited percepts of flutter frequency, intensity, or both dimensions to different visual targets in the percept space (Fig. 5 a). In the first of three iterations, only the flutter frequency percept was modulated by changing the IBI of stimulation and participants had to match the elicited flutter frequency percept to four targets in the percept space. For the second iteration, only the intensity of the percept was modulated by changing the QR and participants had to match the elicited intensity of the percept to four targets in the percept space. In the third set, both the flutter frequency and intensity of the percepts were changed by modulating the interburst interval and the charge rate simultaneously, and participants matched the elicited percepts to five targets distributed across the percept space. Chi-squared analysis of all three discrete tasks showed that participants could match the elicited percepts to all discrete percept targets provided to them better than chance (p < 0.0001 per task) as seen in Fig. 1 a. In the task where participants differentiated flutter frequency percepts, the highest average correct percentage obtained was 88% ± 9%, and the lowest was 53% ± 25%, for flutter frequency values of 80% and 60% of the maximum flutter frequency. The highest p-value was (p = 0.008), during the task where only the intensity of the stimulation was modulated. Participants performed with the highest average correct percentage of 95% ± 12.5%, and the lowest of 60% ± 28.2%, for intensity values of 20%, and 60% of each participant’s QR range, respectively. t-tests for each intensity target compared to chance showed significantly better performance with all p-values < 0.003. As illustrated in Fig. 1 b, in the discrete matching task where both percepts were modulated, participants successfully matched the elicited flutter frequency and intensity of the percepts to their corresponding targets. The highest average correct percentage in this task was 91% ± 10% and the lowest was 73% ± 24%, for (80%, 80%) and (50%, 50%) relative to the maximum IBI and QR range, respectively. In the tasks where both the elicited flutter frequency and intensity are modulated, all p-values < 0.0001. Participants could detect simultaneous changes in elicited flutter frequency and intensity better than chance. A modified center-out task, which we termed a ‘change-in-direction’ task, was used to assess how well participants could detect changes in the interburst interval that modulated the flutter frequency percept and the charge rate that modulated the intensity percept. When performing the change-in-direction task where only the IBI was modulated, participants were able to correctly track the changes with an average correct response rate of 97% ± 0.06% in either an increasing or decreasing direction ( p < 0.0001). Increases in the QR were detected with 100% accuracy after training, while decreases were detected with 91% ± 19% accuracy. As seen in Fig. 2 a when both the interburst interval and charge rate were changed simultaneously, participants were still able to follow the changes in the percept better than chance, with a lowest average correct percentage of 68% ± 27% when detecting simultaneous decreases in elicited flutter frequency and intensity percepts, and the highest average correct detection percentage of 89% ± 25% when detecting increases in both. All participants could detect the changes better than chance (Fig. 2 b). Multidimensional encoding had significantly greater information transfer than intensity or flutter frequency modulation. The information transfer using a multidimensional encoding approach was significantly higher than when using flutter frequency or intensity modulation alone as seen in Fig. 1 c. Flutter frequency modulation alone transmitted an average of 1.74 bits ± 0.1, intensity modulation transmitted 1.76 bits ± 0.05, and the multidimensional modulation transmitted 2.16 bits ± 0.11. Results of an ANOVA comparing the three encoding approaches called for a post hoc test ( F = 61.37, p < 0.001). The results of a Tukey’s post hoc analysis showed that the information transfer with a multidimensional encoding approach is significantly greater than both flutter frequency and intensity modulation alone p < 0.001 for both comparisons. Detecting changes in the stimulation parameters was significantly harder when starting at a high intensity and slow flutter. In another task, participants were asked to track changes in stimulation trains which started at three combinations of the maximum and minimum IBI and QR ranges as seen in Fig. 3 c. The first (Bottom-Left) had the largest IBI possible and QR set to just above the participants threshold, the second (Top-Left) had the largest IBI possible but QR set at just below each participant’s maximum comfort intensity, and the third (Bottom-Right) had the smallest IBI possible and QR set to just above the participant’s threshold. Participants were able to detect changes in the elicited percept in all three iterations of the extremes-in task better than chance regardless of the starting position as seen in Fig. 3 a; (χ 2 = 68.31, p < 0.0001) for the Bottom-Left task, (χ 2 = 82.73, p < 0.0001) for the Bottom-Right task, and (χ 2 = 68.31, p < 0.0001) for the Top-Left task. ANOVA showed a significant difference in performance in the three extremes-in tasks ( F = 7.95, p = 0.02). A Tukey’s post hoc analysis showed that performance in the Top-Left extremes-in task was significantly worse than the Bottom-Left extremes-in task ( p = 0.01) and the Bottom-Right extremes-in task p = 0.002 as seen in Fig. 3 b. These results reflect qualitative responses obtained through a verbal survey on task preference during the experimental sessions. Six out of the eleven participants reported the Bottom-Right extremes-in as their preferred task; five out of the eleven preferred the Bottom-Left. No participants indicated that the Top-Left extremes-in task was their preferred task. Discussion This study evaluated whether a multidimensional encoding strategy, modulating flutter frequency via interburst interval (IBI) and intensity via charge rate (QR), could effectively convey haptic feedback during motor control tasks. The findings support the following hypothesis: participants can reliably identify and track percepts across a two-dimensional space and perform significantly above chance in all tasks. Notably, the multidimensional approach enabled participants to distinguish between thirteen discrete percept combinations and detect changes across seventeen dynamic conditions, demonstrating robust perceptual resolution. The multidimensional encoding approach significantly increased information throughput compared to conventional intensity- or frequency-only modulation. Information transfer exceeded 2 bits per trial, surpassing the typical 1.5–2-bit ceiling reported for unimodal haptic feedback systems [24,31]. These results align with prior findings from microneurography and intraneural stimulation studies [25,32,33]. and suggest that combining independently gradable percepts can enhance the bandwidth of sensory feedback delivered through a single stimulation channel. While participants could detect changes in percepts across all tested conditions, performance declined when stimulation began at high intensity and low flutter frequency. This reduction is consistent with the phenomenon of amplitude dropout, where decreases in stimulation amplitude impair the ability to perceive changes in other perceptual dimensions [34], In our study, detection accuracy dropped to ~50% when intensity decreased from a high starting point, compared to ~85% when only frequency changed. These findings suggest that encoding strategies should avoid initiating feedback at high intensity levels when tracking multiple percepts, particularly in applications such as prosthetic control where sensor values vary dynamically. The discrete matching task was performed without visual feedback during the response phase, which may have introduced motor control errors unrelated to perceptual discrimination. Although this constraint was applied uniformly across conditions, it likely added unnecessary difficulty. Future studies could incorporate visual guidance or alternative response modalities to isolate perceptual accuracy more effectively. Additionally, while the study accounted for several sources of bias, such as randomization, delayed response windows [35], and double blinding [7], it did not explicitly control response strategies like “counting” or pattern recognition [36]. However, a secondary analysis consisting of a set of paired t-tests comparing early and late trials found no significant performance differences, suggesting that such biases did not meaningfully affect outcomes in this study. All participants were naïve to peripheral nerve stimulation and completed the tasks within a single session. Although training was sufficient to reach intra-session performance plateaus, longer-term studies are needed to assess learning effects and retention [29,37]. One participant’s remark, “With experience, this would be functional,” highlights the potential intuitiveness of the multidimensional encoding scheme. The participant cohort was relatively young, which may have positively influenced performance, particularly in joystick-based tasks known to correlate negatively with age [38]. However, prior research suggests that older adults can acquire similar motor skills with extended training [39]. Future work should explore the usability of this approach across age groups and over longitudinal timelines [40]. Unlike prior studies that used force-matching tasks with the contralateral hand [11,31,41], this study employed a joystick-based matching paradigm to maintain consistency across encoding conditions. While effective for comparative analysis, this method may limit generalizability to real-world applications. Future work should evaluate how this encoding strategy performs in functional tasks such as object manipulation with a myoelectric prosthesis or virtual grasping environments. Importantly, this study was conducted in participants with intact peripheral nerves. Although transcutaneous stimulation has been shown to elicit percepts in individuals with amputation [22,31,42], the information transfer achievable in such populations remains unreported. Given the potential for somatotopically matched, distally referred sensations to improve prosthesis embodiment and control [15,31,43,44], future studies should assess whether the benefits of multidimensional encoding extend to users with limb loss. In summary, this work showed that a multidimensional encoding approach might be a feasible method of conveying haptic feedback. Results from this study show, for the first time, that participants could detect multiple different flutter frequencies and intensity values and changes to both flutter frequency and intensity with a greater information transfer than conventional approaches. This shows that this encoding approach could be a suitable method for conveying enhanced haptic feedback. The results also illustrate that intensity and flutter frequency, when linearly mapped to orthogonal directions, can be interpreted as two independent dimensions. The ability to relate the percepts to two independent values implies that this encoding approach could help provide a participant with improved peripheral nerve-based haptic feedback. Performance in actual functional tasks, such as an object discrimination task with a myoelectric prosthesis or a virtual box-and-blocks task, would still need to be assessed before concluding if this encoding approach has functional benefits in conveying haptic feedback. Methods Human Subjects Six male and five female participants without limb abnormalities, with an average age of 25.2 ± 7.5 years were recruited to take part in this study. Ethical approval for the study protocol was obtained through the University of Arkansas Institutional Review Board (IRB # 2201379281) and all research was performed in accordance with relevant guidelines/regulations. Participants were recruited for a single three-hour data collection session. Informed consent was obtained from all participants to conduct the study and to publish the information/image(s) in an online open access publication. Experiment Setup A multi-channel bio-stimulator (TDT IZ2-16H, Tucker-Davis Technologies, Alachua, FL USA) delivered charge-balanced, current-controlled biphasic, cathodic-first, rectangular pulses. To avoid local discomfort around the stimulating electrodes, a CHIPS strategy was employed [19]. The median nerve was targeted transcutaneously via four small, self-adhesive gel electrodes, two 15 mm by 20 mm stimulating electrodes and two 20 mm by 25 mm return electrodes (Rhythmlink International LLC, Columbia, SC, #STCUL15026, and STCUS25026,) placed around the left wrist. The stimulating electrodes were placed on the ventral aspect of the wrist approximately 3 cm from the distal radial crease, while the return electrodes were on the dorsal side. A small amount of current was sent through the electrodes to ensure they provided a distally referred sensation in the areas of the hand innervated by the median nerve. Low current (< 2500 µA for 500 µs) pulses were sent at 5 Hz while the participant reported if and where they perceived a sensation to ensure the electrode location elicited distally referred sensations. Participants sat at a table with a display monitor placed in front of them to convey instructions [21], with their left arm on a cushioned support pad, with their medial side in contact with the pad. Depending on the task, they used their right hand to manipulate a control knob during the parameter calibration or a custom joystick during the experimental tasks as seen in Figure 4b. Experimental control software, written in Python 3 (version 3.11.3), managed the organization and execution of the experiments while storing the collected data. A custom stimulation control module was developed on the Synapse Software (version 96, Tucker-Davis Technologies (TDT), Alachua, FL USA) to control the stimulator. Encoding approach As illustrated in Figure 4a, periodic bursts of stimulation pulses were provided with each burst period consisting of a constant burst duration (BD) of 40 ms, constant interphase gap of 100 µs, and an inter-burst interval (IBI) modulated between 10-160 ms to convey flutter frequencies between 5-20 Hz. A charge-rate (QR) encoding approach for intensity modulation was used to provide graded intensity percepts [18,22]. To change QR, the intraburst pulse frequency (PF) and the pulse width (PW) were modulated along their comfortable ranges, while the pulse amplitude (PA) was kept constant. Calibration A participant-controlled calibration routine was used to find comfortable suprathreshold sensations. This approach was described in detail in other reports [9]. A strength-duration (SD) curve was generated to obtain the threshold of perceivable sensations. PA thresholds were collected for five different PWs between 200 -700 µs with a 100 µs step at a low PF (5 Hz). Participants were given control of a knob; the PA delivered increased when the knob was rotated clockwise. Thresholds were defined as when participants begin to perceive a sensation. Each test PW was presented at least twice in random order. Responses were fitted to the Lapicque-Weiss's model to obtain the SD curve [7]. From each participants’ SD curve, a stimulation PA above the linear region of the curve was selected for the rest of the study. Typically, the PA was set at ~25% above the threshold at a PW of 500 µs [9]. To find the PW limits participants rotated the knob, which modulated PW between a range of 100-800 µs. For the lower limit of the PW, participants were instructed to find the PW where they reliably perceived a sensation; for the upper limit, they were asked to stay below a PW that led to an uncomfortable percept. For the PF limits, participants found the lowest possible frequency that was not perceived as pulsating, and then the highest frequency level at which the perceived intensity did not change. Percept space Each experimental task was represented in a two-dimensional percept space as seen in Figure 4b. The horizontal direction was mapped inversely to the range of the IBI and therefore linear to the flutter frequency percept. The vertical direction was mapped linearly to the intensity percept, by increasing QR. Participants were given control of the joystick which moved a cursor on the screen in front of them. They were told that moving the cursor in the horizontal direction modulated the flutter frequency of the perceived sensation while the vertical direction modulated its intensity. An exploratory training phase was used to introduce the two perceived dimensions. In the following sections, the tasks are defined in terms of flutter frequency and intensity percepts. Training. For each novel task, participants first completed a target-matching task with visual feedback, where elicited percepts were represented by a target on the screen as seen in Figure 5. This was followed by a training phase with delayed visual feedback. During training, participants performed a trial without visual feedback [14]. Upon completion, the target and the final joystick cursor position were displayed. Training trials consisted of three randomly presented repetitions of all targets for each task. Training continued until participants completed the task without errors or reached a performance plateau, defined as three consecutive sessions in which the number of correct responses had a minimal variation (±1 correct response). Discrete Control Task. To assess participants’ ability to identify combinations of flutter frequency and intensity percepts, and differences in information transfer, a matching task was performed. Participants were asked to match the perceived flutter frequency and intensity to a target within the percept space (Figure 5a). At the start of each trial, participants positioned the cursor at a starting location that varied by task version. They then received a 1.5-second stimulation pulse train corresponding to a target in the parameter space. After the stimulation ended, they moved the joystick to where they believed the target was and pressed a button to confirm their selection. A response was considered correct if it fell within ±10% of the target value. The percentage of correctly identified targets was recorded, and individual performance was used to determine information transfer [7,34]. Information transfer quantifies how well sensory information is used for task performance, reflecting sensorimotor integration. It accounts for factors such as memory and signal clarity and is measured in bits [7,45]. Three versions of the discrete matching task were conducted as shown in Figure 5a. In the first, only the flutter frequency percept was modulated, with four targets set at 20%, 40%, 60%, and 80% relative to the maximum IBI, while the QR remained constant at 50% of each participant’s range. In the second, only the intensity percept was modulated, with the same four target values set relative to each participant’s QR range, while IBI remained at a constant 50% of its maximum. In the third version, both IBI and QR varied, with five targets set at (20%, 20%), (20%, 80%), (50%, 50%), (80%, 20%), and (80%, 80%) with respect to the maximum IBI and each participant’s QR range, respectively. Center-out Control Task. To assess participants' ability to identify changes in both the flutter frequency and intensity percepts, a variation of the center-out task was performed [13]. At the start of each trial, the joystick and cursor were positioned at the center of the percept space as shown in Figure 5b. The stimulation was provided such that the percept began at 50% of the maximum of both the flutter frequency and intensity. Then, the IBI (horizontal axis) and QR (vertical axis) changed in one of eight directions, corresponding to all combinations of ±x and ±y, with each change being a ± 30% shift in IBI relative to the maximum or the QR relative to each participant’s range. These changes occurred at a constant rate over 1.5 seconds. Participants moved the joystick along one of the eight directions and pressed a button at the final position. Each stimulation train lasted 3.5 seconds: one second at the initial stimulation value, 1.5 seconds of gradual change, and one additional second at the final stimulation target. The percentage of correctly identified targets was recorded. The center-out task had three versions. In the first, QR changed along the -y and +y directions leading to changes in the elicited intensity. In the second, only IBI changed along the -x and +x directions, changing the elicited flutter frequency. This was done to help participants learn to detect changes in specific dimensions. In the final version, QR and IBI were modulated, with targets shifting in the following directions: (-x, +y), (+x, +y), (-x, -y), and (-x, +y). Extremes-in Control Task. To determine whether an intensity drop, starting from a higher QR and moving to a lower QR, affects participants' ability to detect changes in the elicited percepts, a modified center-out task was performed. As shown in Figure 5c, the task had three starting points based on their position in the percept space. The first (Bottom-Left) had the largest IBI possible and QR set to just above the participant’s threshold , the second (Top-Left) had the largest IBI possible but QR set at just below each participant’s maximum comfort intensity, and the third (Bottom-Right) had the smallest IBI possible and QR set to just above the participant’s threshold. In each trial, stimulation began at one of these starting points and remained constant for one second. Then, the percept changed in one of three ways; only the QR, only the IBI, or both simultaneously. The parameters changed by ± 30% at a constant rate over 1.5 seconds, with the direction of change tied to the starting point. After reaching the new state, stimulation remained constant there for an additional second. Participants moved the joystick along one of three directions and pressed a button once they reached their final position. The percentage of correctly identified targets was recorded. After completing all three extremes-in tasks, participants conducted a verbal survey to say which task they preferred. Study Protocol The study protocol began with a calibration phase, followed by center-out tasks, starting with the intensity-only version and then the flutter-frequency-only version. Next, participants completed either all three versions of the discrete control task or all three versions of the extremes-in task in a randomly determined order. Training for each task was provided just before data collection. Statistical Analysis Statistical analysis was conducted using the SciPy library in Python 3 and R software. Normality was assessed with the Shapiro-Wilk test. One-tailed t-tests or Mann-Whitney tests compared each target's performance to chance, which was set at 33%, 25%, and 20% for tasks with three, four, and five targets, respectively. ANOVAs assessed inter-task differences, with significance set at α = 0.05 unless otherwise specified. When post-hoc analysis was needed, Tukey's test was performed. Chi-square tests evaluated whether overall task performance exceeded chance. Data are presented as mean ± standard deviation. Declarations Acknowledgments This research was supported by a grant from the Department of Defense US Army Joint Warfighter Medical Research Program (JWMRP) (W81XWH1910839). Additionally, TB received partial funding through an I 3 R Graduate Research Assistantship. Data Availability Statement The data that support the findings of this study are openly available at the following: https://doi.org/10.5061/dryad.1rn8pk12q Additional Information The authors declare no competing interests. Funding Research supported by the Department of Defense US Army Medical Research Acquisition Activity, Joint Warfighter Medical Research Program (JWMRP) grant number W81XWH1910839. Author Contribution T R Benignicollected and analyzed the data as well as drafted the manuscript. T R Benigni, A Pena, S Kuntaegowdanahalli all contributed to the development of the encoding approach. All authors contributed to the experimental design. J J Abbasand R Jungoversaw all aspects of the research. All authors have reviewed the manuscript and have read and approved the final manuscript. References Tanacar, N. T., Mughrabi, M. H., Batmaz, A. U., Leonardis, D. & Sarac, M., The impact of haptic feedback during sudden, rapid virtual interactions. 2023 WHC , 64-70 (2023). Gibbs, J. K., Gillies, M. & Pan, X., A comparison of the effects of haptic and visual feedback on presence in virtual reality. Int J Hum Comput Stud 157 , 102717 (2022). 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Cite Share Download PDF Status: Under Review Version 1 posted Reviewers invited by journal 09 Dec, 2025 Editor assigned by journal 31 Jul, 2025 Editor invited by journal 30 Jul, 2025 Submission checks completed at journal 28 Jul, 2025 First submitted to journal 27 Jul, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7189693","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":557506608,"identity":"7417561c-c1d8-4aca-b9a5-e15baded7956","order_by":0,"name":"T R Benigni","email":"","orcid":"","institution":"University of Arkansas","correspondingAuthor":false,"prefix":"","firstName":"T","middleName":"R","lastName":"Benigni","suffix":""},{"id":557506609,"identity":"8599a310-2307-4ad9-8413-be5998f8b792","order_by":1,"name":"A Pena","email":"","orcid":"","institution":"University of 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13:25:02","extension":"html","order_by":29,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":134080,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/7b23b0d0f95391b0221b576e.html"},{"id":98429308,"identity":"817e1885-d0c4-4182-a286-21701cd53a75","added_by":"auto","created_at":"2025-12-17 16:43:12","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":290921,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eDetection of discrete intensity and flutter frequency targets.\u003c/em\u003e (\u003cstrong\u003ea\u003c/strong\u003e) Group average (n = 11) correct response percentage for each target in the discrete control task where only the flutter frequency or intensity of the percept was modulated. On the horizontal axis, the stimulation parameters which elicited the percept relative to their respective maximum is labeled. Each target's average response rate is compared to the chance response rate (25%). Asterisks indicate the results of a t-test. *** = \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001. (\u003cstrong\u003eb\u003c/strong\u003e) Group average correct response rate for the multidimensional discrete task. In this task, both the intensity and frequency of the percepts were modulated for each target. The stimulation parameters used of each of the target's relative to the maximum (IBI, QR) is labeled on the horizontal axis. Each target's average response rate is compared to the chance response rate (20%). Asterisks indicate results of a t-test. ** = \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01, *** = \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001 (\u003cstrong\u003ec\u003c/strong\u003e) The information transfer rate for each of the discrete tasks. On the horizontal axis is the name of the discrete task assessed: flutter frequency (F), intensity (I), and multidimensional (M). An ANOVA was used to discover significant differences between the groups indicated by the asterisks. ** = \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01, *** = \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.001\u003c/p\u003e","description":"","filename":"Figure1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/39af5346d77c5a8870d1ec53.jpg"},{"id":98074007,"identity":"c9de8556-1934-4157-85cb-5ddb8fc8a98a","added_by":"auto","created_at":"2025-12-12 13:25:00","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":188123,"visible":true,"origin":"","legend":"\u003cp\u003eDetection of simultaneous interburst interval and charge rate changes. (\u003cstrong\u003ea\u003c/strong\u003e) Confusion matrix quantifying overall performance in the center-out task. During the center-out task, participants were asked to differentiate among stimulation trains that started at 50% of both the IBI and QR ranges and changed towards the maximum or minimum of the IBI and QR ranges simultaneously modulating the elicited percepts. Participants followed the elicited percept by moving a cursor inside the stimulation parameter space. The vertical axis of the matrix shows the actual final stimulation parameters of the stimulation train (IBI% and QR% of ranges respectively). The horizontal axis shows the final stimulation parameters of the target the participants gave as a response. Each block represents the frequency of responses provided by all participants presented with a stimulation train (actual), and how they classified (perceived) those stimulation trains. (\u003cstrong\u003eb\u003c/strong\u003e) The average correct (n = 11) response percentage for each final target compared to chance (25% correct). t-tests or Mann-Whitney tests were used to determine whether there was a significant difference compared to chance (*** = p \u0026lt; 0.001)\u003c/p\u003e","description":"","filename":"Figure2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/7bfbcb328545727400d06338.jpg"},{"id":98074001,"identity":"277f10c6-c671-4c91-84ba-f5307f8eb3f1","added_by":"auto","created_at":"2025-12-12 13:25:00","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":359991,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eParticipants could detect changes at the IBI and QR limits. \u003c/em\u003e(a) Three confusion matrices for each corner in the extremes-in tasks. The title of each confusion matrix indicates the starting point for each task. Bottom-Left corresponds to the slowest flutter frequency and lowest intensity (10%, 10% of the flutter frequency and intensity ranges respectively) percept elicited. Top-Left corresponds to the slowest flutter frequency but the highest intensity (10%, 100%), Bottom-Right corresponded to the fastest flutter frequency and lowest intensity (100%, 10%). The final frequency and intensity target in the extremes-in task is on the vertical axis. The horizontal axis shows the perceived final intensity and frequency target. Each block represents the frequency of responses provided by all participants when they were presented with a stimulation train (actual) and classified (perceived). (b) Group average (n = 11) correct response percentage of the three tested extremes with SD. An ANOVA and subsequent Tukey's were conducted to find any significant difference between tasks (*= \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.05, ** = \u003cem\u003ep\u003c/em\u003e \u0026lt; 0.01)\u003c/p\u003e","description":"","filename":"Figure3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/0e3382c8796da71790373562.jpg"},{"id":98428368,"identity":"368e39bd-6195-44b2-bb91-2669672cbcf4","added_by":"auto","created_at":"2025-12-17 16:41:57","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":224419,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eMultidimensional encoding approach andexperimental setup during data collection. \u003c/em\u003e(\u003cstrong\u003ea\u003c/strong\u003e) A stimulation burst encoding approach was used to convey a percept of flutter frequency and intensity. The flutter frequency was modulated by changing the interburst interval (IBI) inside the burst period (BP). BP consists of the IBI and the burst duration (BD), BD remained constant while the IBI was varied. The intensity of the percept was modulated by changing the number and duration of biphasic, cathode-first rectangular pulses within each burst following the charge rate model. (\u003cstrong\u003eb\u003c/strong\u003e) Electrodes are placed on the left arm which rests on a pad. The right hand is used to manipulate a joystick to move a cursor inside a percept space during the performance of the discrete control, center-out, and extremes-in tasks. The horizontal axis of the percept space is linearly mapped to increasing flutter frequency, while the vertical axis is linearly mapped to increasing percept intensity.\u003c/p\u003e","description":"","filename":"Figure4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/178f2ffea54b9daf290326b3.jpg"},{"id":98074005,"identity":"54f81612-1544-4e4a-ac40-cbc48968d54c","added_by":"auto","created_at":"2025-12-12 13:25:00","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":359185,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eVisual display of the nine experimental tasks.\u003c/em\u003e Nine experimental tasks were performed in this study. The cursor's position (small dot) shows the initial point where participants were instructed to start each specific task. (\u003cstrong\u003ea\u003c/strong\u003e) In the discrete tasks, a 1.5-second stimulation train conveying a constant percept equivalent to the target's position was given to the participant. Participants were instructed to move the cursor to one of the possible targets. In (\u003cstrong\u003eb\u003c/strong\u003e) the center-out and (\u003cstrong\u003ec\u003c/strong\u003e) extremes-in tasks, the percept changed at a constant rate over the course of three and a half seconds from the origin point to a final target percept. Once the stimulation had stopped, participants moved the cursor to one of the final targets. In (\u003cstrong\u003ea\u003c/strong\u003e) and (\u003cstrong\u003eb\u003c/strong\u003e) three versions of the task were performed, in two versions, only the intensity or flutter frequency of the target was modulated. In the third version, the target's intensity and flutter frequency was modulated multidimensionally. In (\u003cstrong\u003ec\u003c/strong\u003e) Bottom-left, Top-Left and Bottom-Right refer to the initial values used during that version of the extremes-in task.\u003c/p\u003e","description":"","filename":"Figure5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/3dbd40bddb4f34bfdc4d959a.jpg"},{"id":98444539,"identity":"64bab928-3dbb-4a1c-91a8-511ec630d036","added_by":"auto","created_at":"2025-12-17 17:16:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1935782,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7189693/v1/2590e292-af67-4fc6-826d-44f66f9f99da.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhancing Two-Dimensional Control via Single-Channel Haptic Feedback: A Multi-dimensional Encoding Strategy","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHaptic feedback delivered through vibration or electrical stimulation has been shown to enhance performance in teleoperation, increase immersion in virtual environments [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], and improve functional outcomes for users of myoelectric prostheses [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. However, not all feedback methods are equally effective across applications. In virtual reality and prosthetic use, limitations such as latency between stimulation and perception [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e], and difficulty distinguishing between graded percepts [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e], can reduce the effectiveness of haptic systems by limiting the amount of information conveyed.\u003c/p\u003e\u003cp\u003eTo evaluate the utility of haptic feedback, researchers have employed various task paradigms. Object discrimination tasks assess functional relevance in prosthetic and virtual environments [\u003cspan additionalcitationids=\"CR9\" citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], while matching tasks evaluate how well users can grade percepts by aligning them with visual targets [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Center-out tasks, where users respond to changes in stimulation by moving a cursor, have been used to measure perceptual resolution and tracking ability [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eElectrical stimulation of peripheral nerves can evoke distally referred sensations with percepts felt in limb regions distal to the stimulation site [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. These sensations are often somatotopically matched; for example, stimulating the ulnar nerve at the elbow can elicit percepts in the missing ring and little fingers of individuals with transradial amputations [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. These percepts can be modulated by adjusting stimulation parameters such as pulse width, amplitude, or frequency within comfortable ranges [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eWe recently developed a multidimensional encoding approach that simultaneously modulates two stimulation parameters to deliver distinct, co-located percepts: flutter frequency (5\u0026ndash;25 Hz) via interburst interval (IBI) modulation, and intensity via charge rate (QR) modulation [\u003cspan additionalcitationids=\"CR19 CR20 CR21\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. This method uses repeated bursts of stimulation pulses, with IBI controlling the perceived frequency and QR determined by the number and duration of pulses within each burst, controlling intensity.\u003c/p\u003e\u003cp\u003ePrior studies suggest that conveying multiple, independently gradable percepts can enhance task performance and increase information transfer [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan additionalcitationids=\"CR24 CR25 CR26 CR27\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. Building on this, we hypothesized that a multidimensional encoding strategy, modulating flutter frequency through IBI and intensity through QR, would enable participants to perform motor tasks with accuracy significantly above chance.\u003c/p\u003e\u003cp\u003e To evaluate this, participants completed a series of perceptual-motor tasks while receiving stimulation mapped to a two-dimensional percept space: the horizontal axis represented flutter frequency, and the vertical axis represented intensity. In a discrete matching task, participants matched stimulation-evoked percepts to visual targets in this space. A second task assessed their ability to track simultaneous changes in both percepts using a modified center-out paradigm. Finally, we examined whether performance declined when stimulation began at high intensity levels, a phenomenon known as amplitude dropout [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eWe also compared the information transfer achieved using the multidimensional encoding approach to that of a conventional intensity-only encoding method [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Our results demonstrate that participants can reliably differentiate and track multidimensional percepts, suggesting that this approach may offer a more effective means of delivering haptic feedback.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003e\u003cem\u003eSensory characterization\u003c/em\u003e\u003c/p\u003e\u003cp\u003eEleven participants (n\u0026thinsp;=\u0026thinsp;11) received repeated bursts of electrical stimulation to their median nerve through non-invasive stimulating electrodes placed on the wrist using a channel-hopping interleaved pulse scheduling (CHIPS) strategy [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Each participant reported receiving comfortable distal sensations in the area innervated by the median nerve. Local sensations under the electrodes were not reported once calibration was completed. After calibration, a stimulation pulse amplitude (PA) of 1794\u0026thinsp;\u0026plusmn;\u0026thinsp;401 \u0026micro;A, a comfortable pulse width (PW) range of 469\u0026ndash; 699 \u0026micro;s, and a pulse frequency (PF) range of 62\u0026ndash;180 Hz was found for each of the eleven participants. These three parameters modulated together were found to provide reliable percepts of intensity following the charge rate model. Participants were also able to perceive a range of flutter frequencies by discriminating the off time or interburst interval between bursts. Participants performed the entire three-hour session without having to re-adjust the calibrated parameters. Thus, using the multidimensional encoding approach, all participants were able to perceive the two simultaneous percepts of flutter frequency and intensity.\u003c/p\u003e\u003cp\u003e\u003cem\u003eParticipants could identify multiple points in the percept space better than chance.\u003c/em\u003e\u003c/p\u003e\u003cp\u003e In a discrete matching task participants matched elicited percepts of flutter frequency, intensity, or both dimensions to different visual targets in the percept space (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003ea). In the first of three iterations, only the flutter frequency percept was modulated by changing the IBI of stimulation and participants had to match the elicited flutter frequency percept to four targets in the percept space. For the second iteration, only the intensity of the percept was modulated by changing the QR and participants had to match the elicited intensity of the percept to four targets in the percept space. In the third set, both the flutter frequency and intensity of the percepts were changed by modulating the interburst interval and the charge rate simultaneously, and participants matched the elicited percepts to five targets distributed across the percept space.\u003c/p\u003e\u003cp\u003eChi-squared analysis of all three discrete tasks showed that participants could match the elicited percepts to all discrete percept targets provided to them better than chance (p\u0026thinsp;\u0026lt;\u0026thinsp;0.0001 per task) as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea. In the task where participants differentiated flutter frequency percepts, the highest average correct percentage obtained was 88% \u0026plusmn; 9%, and the lowest was 53% \u0026plusmn; 25%, for flutter frequency values of 80% and 60% of the maximum flutter frequency. The highest p-value was (p\u0026thinsp;=\u0026thinsp;0.008), during the task where only the intensity of the stimulation was modulated. Participants performed with the highest average correct percentage of 95% \u0026plusmn; 12.5%, and the lowest of 60% \u0026plusmn; 28.2%, for intensity values of 20%, and 60% of each participant\u0026rsquo;s QR range, respectively. t-tests for each intensity target compared to chance showed significantly better performance with all p-values\u0026thinsp;\u0026lt;\u0026thinsp;0.003. As illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, in the discrete matching task where both percepts were modulated, participants successfully matched the elicited flutter frequency and intensity of the percepts to their corresponding targets. The highest average correct percentage in this task was 91% \u0026plusmn; 10% and the lowest was 73% \u0026plusmn; 24%, for (80%, 80%) and (50%, 50%) relative to the maximum IBI and QR range, respectively. In the tasks where both the elicited flutter frequency and intensity are modulated, all p-values\u0026thinsp;\u0026lt;\u0026thinsp;0.0001.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cem\u003eParticipants could detect simultaneous changes in elicited flutter frequency and intensity better than chance.\u003c/em\u003e\u003c/p\u003e\u003cp\u003e A modified center-out task, which we termed a \u0026lsquo;change-in-direction\u0026rsquo; task, was used to assess how well participants could detect changes in the interburst interval that modulated the flutter frequency percept and the charge rate that modulated the intensity percept. When performing the change-in-direction task where only the IBI was modulated, participants were able to correctly track the changes with an average correct response rate of 97% \u0026plusmn; 0.06% in either an increasing or decreasing direction (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001). Increases in the QR were detected with 100% accuracy after training, while decreases were detected with 91% \u0026plusmn; 19% accuracy. As seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea when both the interburst interval and charge rate were changed simultaneously, participants were still able to follow the changes in the percept better than chance, with a lowest average correct percentage of 68% \u0026plusmn; 27% when detecting simultaneous decreases in elicited flutter frequency and intensity percepts, and the highest average correct detection percentage of 89% \u0026plusmn; 25% when detecting increases in both. All participants could detect the changes better than chance (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cem\u003eMultidimensional encoding had significantly greater information transfer than intensity or flutter frequency modulation.\u003c/em\u003e\u003c/p\u003e\u003cp\u003eThe information transfer using a multidimensional encoding approach was significantly higher than when using flutter frequency or intensity modulation alone as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. Flutter frequency modulation alone transmitted an average of 1.74 bits\u0026thinsp;\u0026plusmn;\u0026thinsp;0.1, intensity modulation transmitted 1.76 bits\u0026thinsp;\u0026plusmn;\u0026thinsp;0.05, and the multidimensional modulation transmitted 2.16 bits\u0026thinsp;\u0026plusmn;\u0026thinsp;0.11. Results of an ANOVA comparing the three encoding approaches called for a post hoc test (\u003cem\u003eF\u003c/em\u003e\u0026thinsp;=\u0026thinsp;61.37, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001). The results of a Tukey\u0026rsquo;s post hoc analysis showed that the information transfer with a multidimensional encoding approach is significantly greater than both flutter frequency and intensity modulation alone \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001 for both comparisons.\u003c/p\u003e\u003cp\u003e\u003cem\u003eDetecting changes in the stimulation parameters was significantly harder when starting at a high intensity and slow flutter.\u003c/em\u003e\u003c/p\u003e\u003cp\u003e In another task, participants were asked to track changes in stimulation trains which started at three combinations of the maximum and minimum IBI and QR ranges as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. The first (Bottom-Left) had the largest IBI possible and QR set to just above the participants threshold, the second (Top-Left) had the largest IBI possible but QR set at just below each participant\u0026rsquo;s maximum comfort intensity, and the third (Bottom-Right) had the smallest IBI possible and QR set to just above the participant\u0026rsquo;s threshold.\u003c/p\u003e\u003cp\u003eParticipants were able to detect changes in the elicited percept in all three iterations of the extremes-in task better than chance regardless of the starting position as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea; (χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;68.31, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001) for the Bottom-Left task, (χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;82.73, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001) for the Bottom-Right task, and (χ\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;68.31, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.0001) for the Top-Left task. ANOVA showed a significant difference in performance in the three extremes-in tasks (\u003cem\u003eF\u0026thinsp;=\u003c/em\u003e\u0026thinsp;7.95, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.02). A Tukey\u0026rsquo;s post hoc analysis showed that performance in the Top-Left extremes-in task was significantly worse than the Bottom-Left extremes-in task (\u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.01) and the Bottom-Right extremes-in task \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.002 as seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb. These results reflect qualitative responses obtained through a verbal survey on task preference during the experimental sessions. Six out of the eleven participants reported the Bottom-Right extremes-in as their preferred task; five out of the eleven preferred the Bottom-Left. No participants indicated that the Top-Left extremes-in task was their preferred task.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study evaluated whether a multidimensional encoding strategy, modulating flutter frequency via interburst interval (IBI) and intensity via charge rate (QR), could effectively convey haptic feedback during motor control tasks. The findings support the following hypothesis: participants can reliably identify and track percepts across a two-dimensional space and perform significantly above chance in all tasks. Notably, the multidimensional approach enabled participants to distinguish between thirteen discrete percept combinations and detect changes across seventeen dynamic conditions, demonstrating robust perceptual resolution.\u003c/p\u003e\n\u003cp\u003eThe multidimensional encoding approach significantly increased information throughput compared to conventional intensity- or frequency-only modulation. Information transfer exceeded 2 bits per trial, surpassing the typical 1.5–2-bit ceiling reported for unimodal haptic feedback systems [24,31]. These results align with prior findings from microneurography and intraneural stimulation studies [25,32,33]. and suggest that combining independently gradable percepts can enhance the bandwidth of sensory feedback delivered through a single stimulation channel.\u003c/p\u003e\n\u003cp\u003eWhile participants could detect changes in percepts across all tested conditions, performance declined when stimulation began at high intensity and low flutter frequency. This reduction is consistent with the phenomenon of amplitude dropout, where decreases in stimulation amplitude impair the ability to perceive changes in other perceptual dimensions [34], In our study, detection accuracy dropped to ~50% when intensity decreased from a high starting point, compared to ~85% when only frequency changed. These findings suggest that encoding strategies should avoid initiating feedback at high intensity levels when tracking multiple percepts, particularly in applications such as prosthetic control where sensor values vary dynamically.\u003c/p\u003e\n\u003cp\u003eThe discrete matching task was performed without visual feedback during the response phase, which may have introduced motor control errors unrelated to perceptual discrimination. Although this constraint was applied uniformly across conditions, it likely added unnecessary difficulty. Future studies could incorporate visual guidance or alternative response modalities to isolate perceptual accuracy more effectively.\u003c/p\u003e\n\u003cp\u003eAdditionally, while the study accounted for several sources of bias, such as randomization, delayed response windows [35], and double blinding [7], it did not explicitly control response strategies like “counting” or pattern recognition [36]. However, a secondary analysis consisting of a set of paired t-tests comparing early and late trials found no significant performance differences, suggesting that such biases did not meaningfully affect outcomes in this study. \u003c/p\u003e\n\u003cp\u003eAll participants were naïve to peripheral nerve stimulation and completed the tasks within a single session. Although training was sufficient to reach intra-session performance plateaus, longer-term studies are needed to assess learning effects and retention [29,37]. One participant’s remark, “With experience, this would be functional,” highlights the potential intuitiveness of the multidimensional encoding scheme.\u003c/p\u003e\n\u003cp\u003eThe participant cohort was relatively young, which may have positively influenced performance, particularly in joystick-based tasks known to correlate negatively with age [38]. However, prior research suggests that older adults can acquire similar motor skills with extended training [39]. Future work should explore the usability of this approach across age groups and over longitudinal timelines [40]. \u003c/p\u003e\n\u003cp\u003eUnlike prior studies that used force-matching tasks with the contralateral hand [11,31,41], this study employed a joystick-based matching paradigm to maintain consistency across encoding conditions. While effective for comparative analysis, this method may limit generalizability to real-world applications. Future work should evaluate how this encoding strategy performs in functional tasks such as object manipulation with a myoelectric prosthesis or virtual grasping environments.\u003c/p\u003e\n\u003cp\u003eImportantly, this study was conducted in participants with intact peripheral nerves. Although transcutaneous stimulation has been shown to elicit percepts in individuals with amputation [22,31,42], the information transfer achievable in such populations remains unreported. Given the potential for somatotopically matched, distally referred sensations to improve prosthesis embodiment and control [15,31,43,44], future studies should assess whether the benefits of multidimensional encoding extend to users with limb loss. \u003c/p\u003e\n\u003cp\u003eIn summary, this work showed that a multidimensional encoding approach might be a feasible method of conveying haptic feedback. Results from this study show, for the first time, that participants could detect multiple different flutter frequencies and intensity values and changes to both flutter frequency and intensity with a greater information transfer than conventional approaches. This shows that this encoding approach could be a suitable method for conveying enhanced haptic feedback. The results also illustrate that intensity and flutter frequency, when linearly mapped to orthogonal directions, can be interpreted as two independent dimensions. The ability to relate the percepts to two independent values implies that this encoding approach could help provide a participant with improved peripheral nerve-based haptic feedback. Performance in actual functional tasks, such as an object discrimination task with a myoelectric prosthesis or a virtual box-and-blocks task, would still need to be assessed before concluding if this encoding approach has functional benefits in conveying haptic feedback.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cem\u003eHuman Subjects\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eSix male and five female participants without limb abnormalities, with an average age of 25.2 ± 7.5 years were recruited to take part in this study. Ethical approval for the study protocol was obtained through the University of Arkansas Institutional Review Board (IRB # 2201379281) and all research was performed in accordance with relevant guidelines/regulations. Participants were recruited for a single three-hour data collection session. Informed consent was obtained from all participants to conduct the study and to publish the information/image(s) in an online open access publication. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eExperiment Setup\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eA multi-channel bio-stimulator (TDT IZ2-16H, Tucker-Davis Technologies, Alachua, FL USA) delivered charge-balanced, current-controlled biphasic, cathodic-first, rectangular pulses. To avoid local discomfort around the stimulating electrodes, a CHIPS strategy was employed [19]. The median nerve was targeted transcutaneously via four small, self-adhesive gel electrodes, two 15 mm by 20 mm stimulating electrodes and two 20 mm by 25 mm return electrodes (Rhythmlink International LLC, Columbia, SC, #STCUL15026, and STCUS25026,) placed around the left wrist. The stimulating electrodes were placed on the ventral aspect of the wrist approximately 3 cm from the distal radial crease, while the return electrodes were on the dorsal side. A small amount of current was sent through the electrodes to ensure they provided a distally referred sensation in the areas of the hand innervated by the median nerve. Low current (\u0026lt; 2500 µA for 500 µs) pulses were sent at 5 Hz while the participant reported if and where they perceived a sensation to ensure the electrode location elicited distally referred sensations. \u003c/p\u003e\n\u003cp\u003eParticipants sat at a table with a display monitor placed in front of them to convey instructions [21], with their left arm on a cushioned support pad, with their medial side in contact with the pad. Depending on the task, they used their right hand to manipulate a control knob during the parameter calibration or a custom joystick during the experimental tasks as seen in Figure 4b. Experimental control software, written in Python 3 (version 3.11.3), managed the organization and execution of the experiments while storing the collected data. A custom stimulation control module was developed on the Synapse Software (version 96, Tucker-Davis Technologies (TDT), Alachua, FL USA) to control the stimulator.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eEncoding approach\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eAs illustrated in Figure 4a, periodic bursts of stimulation pulses were provided with each burst period consisting of a constant burst duration (BD) of 40 ms, constant interphase gap of 100 µs, and an inter-burst interval (IBI) modulated between 10-160 ms to convey flutter frequencies between 5-20 Hz. A charge-rate (QR) encoding approach for intensity modulation was used to provide graded intensity percepts [18,22]. To change QR, the intraburst pulse frequency (PF) and the pulse width (PW) were modulated along their comfortable ranges, while the pulse amplitude (PA) was kept constant. \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eCalibration\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eA participant-controlled calibration routine was used to find comfortable suprathreshold sensations. This approach was described in detail in other reports [9]. A strength-duration (SD) curve was generated to obtain the threshold of perceivable sensations. PA thresholds were collected for five different PWs between 200 -700 µs with a 100 µs step at a low PF (5 Hz). Participants were given control of a knob; the PA delivered increased when the knob was rotated clockwise. Thresholds were defined as when participants begin to perceive a sensation. Each test PW was presented at least twice in random order. Responses were fitted to the Lapicque-Weiss's model to obtain the SD curve [7]. From each participants’ SD curve, a stimulation PA above the linear region of the curve was selected for the rest of the study. Typically, the PA was set at ~25% above the threshold at a PW of 500 µs [9]. To find the PW limits participants rotated the knob, which modulated PW between a range of 100-800 µs. For the lower limit of the PW, participants were instructed to find the PW where they reliably perceived a sensation; for the upper limit, they were asked to stay below a PW that led to an uncomfortable percept. For the PF limits, participants found the lowest possible frequency that was not perceived as pulsating, and then the highest frequency level at which the perceived intensity did not change. \u003c/p\u003e\n\u003cp\u003ePercept space\u003c/p\u003e\n\u003cp\u003eEach experimental task was represented in a two-dimensional percept space as seen in Figure 4b. The horizontal direction was mapped inversely to the range of the IBI and therefore linear to the flutter frequency percept. The vertical direction was mapped linearly to the intensity percept, by increasing QR. Participants were given control of the joystick which moved a cursor on the screen in front of them. They were told that moving the cursor in the horizontal direction modulated the flutter frequency of the perceived sensation while the vertical direction modulated its intensity. An exploratory training phase was used to introduce the two perceived dimensions. In the following sections, the tasks are defined in terms of flutter frequency and intensity percepts. \u003c/p\u003e\n\u003cp\u003eTraining.\u003c/p\u003e\n\u003cp\u003eFor each novel task, participants first completed a target-matching task with visual feedback, where elicited percepts were represented by a target on the screen as seen in Figure 5. This was followed by a training phase with delayed visual feedback. During training, participants performed a trial without visual feedback [14]. Upon completion, the target and the final joystick cursor position were displayed. Training trials consisted of three randomly presented repetitions of all targets for each task. Training continued until participants completed the task without errors or reached a performance plateau, defined as three consecutive sessions in which the number of correct responses had a minimal variation (±1 correct response). \u003c/p\u003e\n\u003cp\u003e\u003cem\u003eDiscrete Control Task.\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eTo assess participants’ ability to identify combinations of flutter frequency and intensity percepts, and differences in information transfer, a matching task was performed. Participants were asked to match the perceived flutter frequency and intensity to a target within the percept space (Figure 5a).\u003c/p\u003e\n\u003cp\u003eAt the start of each trial, participants positioned the cursor at a starting location that varied by task version. They then received a 1.5-second stimulation pulse train corresponding to a target in the parameter space. After the stimulation ended, they moved the joystick to where they believed the target was and pressed a button to confirm their selection. A response was considered correct if it fell within ±10% of the target value. The percentage of correctly identified targets was recorded, and individual performance was used to determine information transfer [7,34].\u003c/p\u003e\n\u003cp\u003eInformation transfer quantifies how well sensory information is used for task performance, reflecting sensorimotor integration. It accounts for factors such as memory and signal clarity and is measured in bits [7,45]. \u003c/p\u003e\n\u003cp\u003eThree versions of the discrete matching task were conducted as shown in Figure 5a. In the first, only the flutter frequency percept was modulated, with four targets set at 20%, 40%, 60%, and 80% relative to the maximum IBI, while the QR remained constant at 50% of each participant’s range. In the second, only the intensity percept was modulated, with the same four target values set relative to each participant’s QR range, while IBI remained at a constant 50% of its maximum. In the third version, both IBI and QR varied, with five targets set at (20%, 20%), (20%, 80%), (50%, 50%), (80%, 20%), and (80%, 80%) with respect to the maximum IBI and each participant’s QR range, respectively.\u003c/p\u003e\n\u003cp\u003eCenter-out Control Task.\u003c/p\u003e\n\u003cp\u003eTo assess participants' ability to identify changes in both the flutter frequency and intensity percepts, a variation of the center-out task was performed [13]. At the start of each trial, the joystick and cursor were positioned at the center of the percept space as shown in Figure 5b. The stimulation was provided such that the percept began at 50% of the maximum of both the flutter frequency and intensity. Then, the IBI (horizontal axis) and QR (vertical axis) changed in one of eight directions, corresponding to all combinations of ±x and ±y, with each change being a ± 30% shift in IBI relative to the maximum or the QR relative to each participant’s range. These changes occurred at a constant rate over 1.5 seconds. Participants moved the joystick along one of the eight directions and pressed a button at the final position. Each stimulation train lasted 3.5 seconds: one second at the initial stimulation value, 1.5 seconds of gradual change, and one additional second at the final stimulation target. The percentage of correctly identified targets was recorded.\u003c/p\u003e\n\u003cp\u003eThe center-out task had three versions. In the first, QR changed along the -y and +y directions leading to changes in the elicited intensity. In the second, only IBI changed along the -x and +x directions, changing the elicited flutter frequency. This was done to help participants learn to detect changes in specific dimensions. In the final version, QR and IBI were modulated, with targets shifting in the following directions: (-x, +y), (+x, +y), (-x, -y), and (-x, +y). \u003c/p\u003e\n\u003cp\u003eExtremes-in Control Task.\u003c/p\u003e\n\u003cp\u003eTo determine whether an intensity drop, starting from a higher QR and moving to a lower QR, affects participants' ability to detect changes in the elicited percepts, a modified center-out task was performed. As shown in Figure 5c, the task had three starting points based on their position in the percept space. The first (Bottom-Left) had the largest IBI possible and QR set to just above the participant’s threshold , the second (Top-Left) had the largest IBI possible but QR set at just below each participant’s maximum comfort intensity, and the third (Bottom-Right) had the smallest IBI possible and QR set to just above the participant’s threshold. \u003c/p\u003e\n\u003cp\u003eIn each trial, stimulation began at one of these starting points and remained constant for one second. Then, the percept changed in one of three ways; only the QR, only the IBI, or both simultaneously. The parameters changed by ± 30% at a constant rate over 1.5 seconds, with the direction of change tied to the starting point. After reaching the new state, stimulation remained constant there for an additional second. \u003c/p\u003e\n\u003cp\u003eParticipants moved the joystick along one of three directions and pressed a button once they reached their final position. The percentage of correctly identified targets was recorded. After completing all three extremes-in tasks, participants conducted a verbal survey to say which task they preferred.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eStudy Protocol\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eThe study protocol began with a calibration phase, followed by center-out tasks, starting with the intensity-only version and then the flutter-frequency-only version. Next, participants completed either all three versions of the discrete control task or all three versions of the extremes-in task in a randomly determined order. Training for each task was provided just before data collection.\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eStatistical Analysis\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003eStatistical analysis was conducted using the SciPy library in Python 3 and R software. Normality was assessed with the Shapiro-Wilk test. One-tailed t-tests or Mann-Whitney tests compared each target's performance to chance, which was set at 33%, 25%, and 20% for tasks with three, four, and five targets, respectively. ANOVAs assessed inter-task differences, with significance set at α = 0.05 unless otherwise specified. When post-hoc analysis was needed, Tukey's test was performed. Chi-square tests evaluated whether overall task performance exceeded chance. Data are presented as mean ± standard deviation.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was supported by a grant from the Department of Defense US Army Joint Warfighter Medical Research Program (JWMRP) (W81XWH1910839). Additionally, TB received partial funding through an I\u003csup\u003e3\u003c/sup\u003eR Graduate Research Assistantship.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are openly available at the following:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ehttps://doi.org/10.5061/dryad.1rn8pk12q\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eResearch supported by the Department of Defense US Army Medical Research Acquisition Activity, Joint Warfighter Medical Research Program (JWMRP) grant number W81XWH1910839.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eT R Benignicollected and analyzed the data as well as drafted the manuscript.\u0026nbsp;T R Benigni,\u0026nbsp;A Pena,\u0026nbsp;S Kuntaegowdanahalli all contributed to the development of the encoding approach. All authors contributed to the experimental design.\u0026nbsp;J J Abbasand\u0026nbsp;R Jungoversaw all aspects of the research. All authors have reviewed the manuscript and have read and approved the final manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eTanacar, N. T., Mughrabi, M. H., Batmaz, A. U., Leonardis, D. \u0026amp; Sarac, M., The impact of haptic feedback during sudden, rapid virtual interactions. \u003cem\u003e2023 WHC\u003c/em\u003e, 64-70 (2023).\u003c/li\u003e\n\u003cli\u003eGibbs, J. 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S., Haptic identification of stiffness and force magnitude. \u003cem\u003eHAPTICS 2008\u003c/em\u003e, 87-91 (2008).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"non-invasive electrical stimulation, peripheral nerve stimulation, information transfer, encoding approaches, haptics","lastPublishedDoi":"10.21203/rs.3.rs-7189693/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7189693/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHaptic feedback elicits sensations of touch to communicate information to the user. Recent developments in virtual reality and sensory prostheses have demonstrated the need for systems that can provide more information than the simple vibrotactor in your phone. A novel multidimensional encoding approach allows for percepts of signal intensity and flutter frequency in a single distal location using transcutaneous neural stimulation. In this study we aimed to determine if these percepts are able to convey useful information to participants performing motor control tasks and if they perform better than a typical intensity-only modulation approach. Eleven participants performed three types of tasks to assess the efficacy of multidimensional stimulation. The first set included discrete matching tasks, where participants had to differentiate between thirteen combinations of flutter frequency and intensity. In the other two sets, participants had to differentiate between simultaneous changes in the percepts. Participants in this study could correctly identify all discrete percept combinations and follow the changes in the percepts better than chance. Performance in the discrete task using a multidimensional approach showed increased information transfer compared to the individual modulation of intensity or flutter frequency. These results suggest that multidimensional encoding is a promising approach for increasing information throughput in sensory feedback systems. Hence, such an approach might improve upon conventional methods of providing graded percepts, creating more informative tactile percepts for haptic feedback through peripheral nerve stimulation.\u003c/p\u003e","manuscriptTitle":"Enhancing Two-Dimensional Control via Single-Channel Haptic Feedback: A Multi-dimensional Encoding Strategy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-12 13:24:53","doi":"10.21203/rs.3.rs-7189693/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewersInvited","content":"","date":"2025-12-09T06:41:27+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-07-31T10:08:00+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-07-30T18:11:59+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-07-28T04:39:29+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-07-27T23:06:38+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b24a7f1c-f945-49a8-839c-714c3ce3eb91","owner":[],"postedDate":"December 12th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":59335359,"name":"Physical sciences/Engineering"},{"id":59335360,"name":"Biological sciences/Neuroscience"}],"tags":[],"updatedAt":"2025-12-12T13:24:54+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-12 13:24:53","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7189693","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7189693","identity":"rs-7189693","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}