Automatic calibration of electrode arrays for dexterous neuroprostheses: a review

Background. Electrode arrays can simplify the modulation of shape, size, and position for customized stimulation delivery. However, the intricacy in achieving the desired outcome stems from optimizing for the myriad of possible electrode combinations and stimulation parameters to account for varying physiology across users. Objective. This study reviews automated calibration algorithms that perform such an optimization to realize hand function tasks. Comparing such algorithms for their calibration effort, functional outcome, and clinical acceptance can aid with the development of better algorithms and address technological challenges in their implementation. Methods. A systematic search was conducted across major electronic databases to identify relevant articles. The search yielded 36 suitable articles; among them, 14 articles that met the inclusion criteria were considered for the review. Results. Studies have demonstrated the realization of several hand function tasks and individual digit control using automatic calibration algorithms. These algorithms significantly improved calibration time and functional outcomes across healthy and people with neurological deficits. Also, electrode profiling performed via automated algorithms was very similar to a trained rehabilitation expert. Additionally, emphasis must be given to collecting subject-specific a priori data to improve the optimization routine and simplify calibration effort. Conclusion. With significantly shorter calibration time, delivering personalized stimulation, and obviating the need for an expert, automated algorithms demonstrate the potential for home-based rehabilitation for improved user independence and acceptance.


Introduction
Several intrinsic factors that account for varying neurophysiology affect the accuracy and reliability of electrode placement to elicit the desired muscle response [1]. Moreover, electrodes tend to displace away from the motor points during forearm movements, which can obstruct the selective targeting of muscles. Furthermore, changes to the relative position of stimulation sites about the forearm surface also affect stimulation performance [2], cause discomfort [3], and induce muscle fatigue [4]. In addition to the exasperate process of donning the system, the need for recalibration with every session and the difficulty in identifying ideal stimulation sites were common reasons for users discontinuing Functional electrical stimulation (FES) therapy [5,6].
Wearable neuroprostheses overcome these limitations by employing electrode arrays, wherein electrodes are distributed spatially over the forearm muscles. Their shape over the stimulation area (virtual electrodes) is dynamically adjusted. Modulating each electrode entity for its location, shape, and size offers selective activation and easy reconfigurability to acquire the best outcome [7,8]. Nevertheless, electrode arrays have several inherent challenges regarding setup time, strategies to identify suitable virtual electrode (VE) configurations, reducing discomfort, and user integration. Also, the inter-subject variability due to never depth, fat thickness, and other intrinsic factors influence the overall stimulation Any further distribution of this work must maintain attribution to the author-(s) and the title of the work, journal citation and DOI.
outcome. Hence, it remains an optimization problem to identify suitable electrode combinations and stimulation parameters to customize stimulation delivery that can elicit the desired response [3,9].
The standard approach to finding a suitable VE configuration involves manual testing of every single electrode across all subjects. This calibration process involves selecting an electrode or a combination of electrodes in an array and varying the stimulation parameters to record the output responses. Ideally, this routine looks for an electrode that evokes maximum muscle response with minimal discomfort. Although searching for these sites for every individual seems reliable, such a routine is time-consuming. Moreover, defining the stimulation patterns for every individual can be laborious and requires extensive medical training.
Recent advances in fabrication technology have enabled high-resolution electrode arrays, improving selectivity [5,10]. Consequently, the scanning process becomes increasingly complex with many possible stimulation sites. Thus, there is a demand for automated algorithms as an alternative to a timeconsuming manual brute-force search to identify VE configurations. Manual intervention for electrode profiling increases the setup time. It needs expert validation, which can impede the users from using the device independently. Also, the stimulation sites identified via electrode profiling vary across users and use sessions. The need to compensate for these variations further instigates the requirement for fast and reliable scanning routines for automated electrode calibration.
Simultaneously activating multiple electrodes in an array (desired VE configuration) placed over the target muscle can coordinate the stimulation of more than one muscle to realize complex hand function tasks. Automated algorithms identify optimal VE configuration by examining the outcome measures, especially joint angles, from a subset of tested configurations [9,11,12]. For a static outcome response with fixed target joint angles involving postures, optimal electrode configurations are identified via automated algorithms without continuous sensor feedback. Similarly, for a dynamic outcome response involving manipulation tasks, a controller is implemented; that uses continuous sensor feedback to compensate for errors in the outcome.
Similar to applications involving hand function, the efficacy of automated calibration has been investigated for managing foot drop. Notably, [6] demonstrated the automated setup of an array stimulator to produce results broadly comparable to a clinician's setup. Similarly, [7] presented a novel decision support system based on an automated calibration that selectively induced dorsiflexion and plantarflexion of the foot. Foot drop correction is predominantly achieved by simulating the muscles for dorsiflexion and eversion; thus, the optimization space is relatively small. However, selective targeting is arduous for hand function tasks as the forearm has tightly packed musculature and higher degrees of freedom.
Patients with neurological deficits prefer assistive technology that is less cumbersome and personalizable. Considering the intrinsic factors and variations imparted during the donning process, automated algorithms can significantly reduce setup time and improve user independence and the acceptability of FES systems. Thus, the main objective of this study is to assess the efficacy of automated calibration algorithms for hand function restoration. In this regard, existing implementations that perform automated electrode profiling were reviewed. The significance of this review is to understand these implementations, which can aid with better algorithm design to improve their overall performance and clinical efficacy.

Methods
Relevant articles were identified from major electronic databases, including Google Scholar, PubMed, Scopus, IEEE Xplore, Web of Science, Springer, MED-LINE, and Cochrane. The articles were searched using the following keywords: 'Functional electrical stimulation', 'Hand function', 'multi-pad electrode', 'Electrode array', 'Virtual electrode', 'Calibration', and 'Selectivity'. Since electrode arrays and calibration algorithms are contemporary to FES research, relevant articles were searched between January 2000-Dec 2022.
An initial search for articles was done only based on the title and the abovementioned keywords. Subsequently, key articles were selected for inclusion based on their abstract and then their full-text content. All bibliographies from these key articles were further examined to identify any missing articles that might not have been found through the database search. The articles were selected based on the inclusion criteria: (1) Included studies must have used transcutaneous (non-invasive) stimulation to realize hand function tasks.
(2) Included studies must have performed an automated calibration procedure to identify suitable VE configurations or stimulation parameters.
(3) Included studies must have reported the algorithmic implementation of the calibration procedure.
(4) Included studies must have reported the performance outcome while achieving their targeted hand function tasks.
Transcutaneous stimulation, as a non-invasive technique, allows for the easy application of electrode arrays. However, they are susceptible to repositioning, affecting overall stimulation performance. Thus, it was critical to assess the impact of calibration algorithms on transcutaneous stimulation; hence, studies that used invasive means of stimulation were excluded. Similarly, for clinical translation, the reliability of calibration algorithms must be assessed across cohorts; thus, single-subject case studies were excluded.
The PRISMA guidelines were followed throughout the study. Overall, 365 articles were found through a database search, of which 127 were duplicates. Duplicate articles were identified and removed by processing the search results in a reference manager. The full-text screening was conducted on 36 eligible articles, which resulted in 14 articles being included for review (figure 1). Among them, [12] performed both semi-and fully automatic calibration in the same study to evaluate their preference. Regardless of these being two distinct methods, they were separately considered for the review.
The included studies were systematically analyzed based on their objective, cohort type, hardware specification, calibration algorithms, and performance outcomes. Table 1 summarizes the study design and hardware details for studies included in this review. These studies demonstrate the efficacy of automated calibration algorithms for hand function tasks across healthy (n = 75) and patient (n = 20) populations. The patient population included people with spinal cord injury (n = 6) and stroke (n = 14). These studies demonstrated individual and coordinated control of digits and the wrist to complete activities of daily living (ADL).

Results
The hardware setup included electrode arrays, sensors, and stimulators. The sensor systems drove the feedback loop and the calibration algorithms optimized stimulation delivery to achieve the desired outcome. Accordingly, controllable factors that influenced the overall stimulation delivery, including stimulation waveform (amplitude, frequency, and pulse width), stimulation type (bipolar and monopolar), electrode properties (size, shape, and hydrogel layers), inter-electrode distance (IED) and electrode configuration (location of electrodes in an array) were optimized.
The reported algorithms (table 1) identified appropriate electrode configuration and stimulation parameters across electrode arrays with sizes varying from 6 to 78 elements. Each element on the array had a surface area between 80 to 490 mm 2 and was 10 to 20 mm apart (IED). Most studies (n = 10) leveraged monopolar stimulation; herewith, every element on the array had a common return electrode. The surface area of the return electrodes was higher and often placed at the distal third of the forearm (close to the wrist). The electrode arrays were either screen printed (n = 8), textile-based (n = 2), or off-the-shelf electrodes integrated into a fabric sleeve (n = 2). An additional layer of thin (<1 mm) and highly resistive (1100 Ωcm) hydrogel layer was used to improve the stimulation comfort. These hydrogel layers were used as a single sheet covering the entire sleeve or cut to fit individual electrodes in the array. While the stimulation waveform (monophasic/biphasic) and frequency (32 ± 10 Hz) were fixed, the pulse width (286 ± 94 μs) and intensity were varied.  For a given stimulation, the primary outcome was digit or wrist movements, which were quantified as joint angles (q) or muscle contractions. Joint angles were measured using flexible goniometers, accelerometers integrated into inertial measurement units (IMUs), and motion capture systems. Here, the sampling rates for q varied from 10 to 1000 Hz. Electromyography (EMG) signals characterized muscle contraction, quantified using twitch responses and M-wave signals. Table 2 summarizes electrode calibration algorithms, their parameters, and their outcome. Studies opted for both monophasic and biphasic stimulation with varying stimulation frequency (20 to 50 Hz), pulse width between (150 to 500 μs), and amplitude (2 to 50 mA). The reported frequency and pulse width were in the typical range to stimulate intrinsic and extrinsic muscles for hand function tasks. Most studies optimized for the desired outcome while minimizing the stimulation amplitude. While painful levels of stimulation stopped the optimization search, the minimum amplitude was set to motor thresholds that were obtained a priori. The criteria for a desired outcome were based on target poses with an acceptable range of .
q And factors like selectivity, accuracy, and success rate quantified the overall outcome. Across all studies, using optimization routines, these algorithms identified suitable electrode configurations to achieve desired hand movements from 16 to 306 possible combinations. Notably, most studies were able to identify more than one optimal configuration. These additional configurations can be leveraged for subsequent recalibration and to mitigate the onset of muscle fatigue. Furthermore, calibration algorithms helped with achieving fine digit control with good accuracy [16,17]. Similarly, [11] was able to selectively stimulate intrinsic and extrinsic muscles, showing the efficacy for a high level of personalization and stimulation performance.
Notably, [14] demonstrated a reliable calibration method using fewer sensors (n = 3). Whereas [3] and [18] performed electrode calibration via an electrophysiologically driven approach. The desired outcome was evaluated by both joint angles and muscle contraction (using EMG) [12] assessed the clinical acceptance and practicability of calibration algorithms when using a semi-automatic and fully automatic approach. By evaluating hand opening/closing among stroke patients, the study reported high user acceptance for both methods, with no clear preference between the two. Here, the semi-automatic approach was supervised by an expert; thus, by utilizing humanin-the-loop optimization, it was 25% faster than the fully automatic approach.
As in figure 2, the following steps were involved in implementing these calibration algorithms. The first step ① was collecting a priori information on specific stimulation parameters and the stimulation site. These included motor threshold, pain threshold, and motor point locations. To normalize functional outcomes, range of motion as , q muscle contraction levels using EMG, and grip forces were captured accordingly. These parameters were critical to constrain the possible combinations in the parametric search space. Secondly ②, a search routine was conducted by accounting for individual specific a priori information.
Here, their stimulation parameters were varied for specific elements in the electrode array, and their outcome responses were recorded. The outcome responses were live sensor data on joint angles or muscle responses. This search routine was repeated for a few trials to capture longitudinal and spatial variations. Also, the search routine was stopped if the user felt any discomfort. Ultimately, this search routine mapped the electrode configuration and stimulation parameters to the desired outcome. Lastly, for any desired outcome, an optimization algorithm ③ performs a search over the parametric space to yield a target response. Here, the objective of the optimization routine was to minimize the cost function, i.e., the target error. Similarly, for machine learning-based algorithms, the optimization was to reduce the training error [14]. Optimization routines identified more than one optimal set of electrode configuration and stimulation parameters that yielded a desired response. The time taken for this optimization routine varied from 2 to 15 min across all studies. Additional time is also involved in acquiring a priori information (table 2). While the reliability of these calibration algorithms was poorly reported, it can be inferred that there was a lower longitudinal variability and a higher inter-and intra-subject variability.
In addition to generic optimization, studies also deployed interpolation [12,13], iterative learning control [30], and machine learning-based methods [14,15]. As an alternative to manual search, [12,13] proposes a feedback-control-assisted approach. Here, the position of VEs within an array can be modified. Then, an interpolation function estimates neighboring elements surrounding that array and their stimulation parameters. This approach has been debuted to improve user integration and acceptance of calibration algorithms. Similarly, [30] proposes iterative learning control (ILC) to achieve faster and more accurate postural control. Here, ILC combines data from the previous iteration with a dynamic model linking FES and resulting motion. Control inputs are then sequentially updated to reduce tracking errors. [14] trained artificial neural networks (ANN) to classify different hand movements based on accelerometer data on twitch response. By comparing its performance against gold-standard goniometric data, the study demonstrates the viability of using a minimum number of sensors for calibration tasks. Likewise, [15] proposes a recurrent fuzzy neural network (RFNN) for FES-controlled hand movements. The model takes in electrode configuration and stimulation parameters as input and maps it to the position of the wrist and digits. Utilizing the linguistic interpretability of fuzzy logic and an ANN to drive the feedback loop, the RFNN model could predict the output response for a given parametric input.

Discussion
FES systems aid with the recuperation of lost hand function by activating target muscle groups [19]. Furthermore, the advent of electrode arrays has streamlined this process of dynamic muscle activation to achieve complex hand function tasks for ADL. Nevertheless, compensating for variability amongst users to identify optimal stimulation sites and parameters is still an open challenge and is being actively researched. In this regard, calibration algorithms automate the process of identifying personalized stimulation sites and parameters. Such automation can significantly reduce clinicians' time and effort. Additionally, improving users' independence to use FES systems in the comfort of their homes. Through a systemic search of the literature, this review has identified suitable studies demonstrating such automated calibration algorithms for hand function tasks. Figure 2(a) illustrates the generic system architecture for wearable neuroprostheses aimed at hand function. This system includes user-control interfaces, a multichannel stimulator, routing circuits, a stimulation electrode array, sensors systems, and a controller. While selective activation of target muscles depends on the resolution of the electrode array, control over the stimulation waveform depends on the capabilities of the stimulator. Thus, it is critical to understand these hardware capabilities, as they influence the development of electrode calibration algorithms.

Hardware identification
Most commercial stimulators have limited channels that allow for a customized stimulation waveform. Hence routing circuits are used to direct these channels to specific electrodes in an array. For more information on FES stimulators, refer [20,21]. Commercially available stimulators like the RehaStim TM allow low-level hardware control to derive highly customized stimulation waveforms and for channel selection [22]. Implementing such hardware control with software like LabVIEW allows for streamlined hardware integration and algorithm development [11].
Electrode arrays have seen improvements with advances in fabrication technology via screen printing [10,23] and textile-based [5]. Screen printing offers a scalable and cost-effective method to fabricate highly personalized electrode arrays. As such, most studies reviewed in this study utilized screen printing. Although screen printing can produce high-resolution arrays, having more electrodes complicates calibration and demands additional switching circuits [24]. Thus, it is essential to identify the smallest size for an electrode array without compromising the resolution needed to achieve a specific functional outcome. Additionally, guidelines on electrode size, shape, and IED specific to electrode array design for forearm muscles can be inferred from existing literature [25,26].
Furthermore, feedback from sensors attached to the hand is also critical for automatic calibration, as they aid in mapping stimulation input to an outcome response. Grasp control cannot operate in an open loop configuration, as it will rely on the operator's decisions and will be prone to error. Thus, sensor systems provide a feedback loop during grasping, wherein the kinetic and kinematic feedback extends digit control to hand manipulation tasks. These sensors fall into three main types that quantify kinetics (grip force), kinematics (joint motion), and electrophysiology (muscle contraction), figure 2(a). As in table 1, studies have utilized sensors to measure joint movement and quantify muscle contraction using EMG. While joint movements obtained through a motion capture system can be reliable, this is only practical for a clinical setting. Wearable sensorized gloves that embed IMUs or flexible goniometric sensors are often used for ambulatory settings. They can also be lightweight and easily donned on and off [27]. These sensors are mounted on the joints of each digit to capture all degrees of freedom of a human hand. To obviate the need for such complex sensor systems, [14] has demonstrated using fewer sensors for electrode array calibration and control. Nevertheless, obtaining accurate kinetic or kinematic responses is difficult for people with neuromuscular deficits. Here, electrophysiological responses are a viable alternative. As such, electrodes to capture electrophysiological signals can also be integrated into the electrode array [3]. Integrating sensors and stimulation electrodes into a single array makes the system less cumbersome and easy to use.
In addition to the above sensors, user-control interfaces allow the wearer to send commands to control the stimulation hardware to achieve desired grasps. These interfaces can range from simple switches to complex brain-computer interfaces using Electroencephalography [28].
Calibration algorithms for electrode profiling Optimization routines are integral to automatic calibration algorithms, as their objective is to find a satisfactory solution iteratively. Mapping algorithms identify personalized stimulation sites and parameters that compensate for user variability. These algorithms aid in achieving a specific hand response by varying a set of input parameters. To achieve a specific hand function, first, user-initiated inputs are obtained. Based on the type of grasp pattern required, the electrode configuration and stimulation parameters are automatically adjusted to achieve desired contraction levels. Out of several combinations, to find the optimal parameters, the elicited grasp patterns are compared and compensated against the target grasp. Furthermore, during grasp control, the user must command the grasp intuitively. Accordingly, studies have implemented several control strategies that facilitated grasp control based on user command. Specifications of the electrode calibration routine and its outcome are summarized in table 2. It can be inferred from these studies that calibration algorithms can extract suitable electrode configurations and stimulation parameters to elicit ADL-based grasps.
Although each study has its own implementation of the calibration algorithm, they were able to achieve the desired grasp.
Furthermore, most studies reported both intersubject and intra-subject variations pertaining to stimulation parameters and electrode configurations. Also, these parameters were markedly different between healthy participants and people with motor deficits [29]. This can be attributed to the varying physiology due to the underlying condition. Additionally, inter-subject variations were also attributed to the position of electrodes with respect to the forearm, i.e., forearm movements can displace the stimulation sites, needing to recalibrate the VE configuration [2].
To achieve faster and more accurate posture control, [30] demonstrated a model-based control approach that finds optimal stimulation sites. This approach addresses the limitations of lacking an explicit plant model that can learn from experience. Utilizing iterative learning control, which uses previous iteration data together with a system model, it sequentially updates the control signal and reduces error until preferred tracking is achieved. Similarly, [31] demonstrates a calibration procedure that uses Boolean satisfiability, an SAT-based constraint solver, to drive the calibration procedure from earlier observations. This method does not need any prior assumptions about the location of stimulation sites or electrode configuration.
Lastly, [13] presents a feedback-control-assisted manual search strategy that enables the therapist to conveniently modify a FE within an array for a desired outcome. Similarly, [12] preferred a semi-automatic approach as the search strategy. They observed faster search duration when compared to a fully automated approach. Also, they advocate such a semi-automatic approach could further reduce calibration time as repeated calibration on a patient will only require minor position adjustments for respective VE configurations.
Optimizing calibration routines As in figure 2(b), the primary steps to run the optimization routine involve collecting a priori information. They represent user-specific baseline information that is necessary to minimize the search space and time involved in the calibration effort. Primarily, this includes motor point locations, range of motion, motor and sensory thresholds. Based on this preliminary information, electrode configuration and stimulation parameters are varied to map the desired stimulation outcome. Additionally, factors like muscle recruitment and fatigue must be considered for advanced hand function tasks. Ideally, these characterizations can help to deliver a highly selective, comfortable, and desired muscle contraction for specific grasp outcomes. Information on electrode configuration includes indexing a specific electrode in an array, IED between two electrodes, and indexing a few electrodes to change the shape and size of a VE configuration. While collating all this data is a manual and exhaustive procedure, most of this information can be obtained from current literature. Stimulation zones can help to identify potential electrode locations for a desired muscle response from forearm anthropometry [2]. Such zones have been demonstrated to have a high probability of muscle activation. Moreover, stimulation zones can significantly simplify mapping routines considering the symmetricity of motor point locations. For a dataset compiling manual motor point locations of healthy subjects, refer [32]. As such, optimal stimulation parameters for forearm muscles can be extracted from table 2 and other studies [1,2,33,34]. Also, most studies in this review identified more than one optimal electrode configuration for a target response. By alternatively switching between these configurations to get the same response, the effects of fatigue can be compensated [35].

Performance and expectations
Patients with neurological deficits prefer assistive technology that is less cumbersome and personalizable. Automated calibration algorithms simplify the setup and control of the device. This allows a nonexpert to use the device for home-based rehabilitation. It allows easy repositioning, and the system can be calibrated effortlessly after donning and doffing. Deploying a reliable and fast scanning routine for automated electrode profiling can significantly improve user comfort and acceptability of FES systems for everyday use.
The following guidelines must be considered while developing automated calibration algorithms.

Usability
The primary aim of calibration algorithms is to identify personalized stimulation sites and parameters that compensate for user variability. To demonstrate clinical validity, these algorithms should be comparable to manual calibration performed by a physician [2]. They should also integrate well with user-control interfaces that allow users to control the stimulation outcome easily. Factors like extensive setup procedures, lack of customization, and non-user-evaluated interfaces may lead to poor acceptance. These algorithms should also retain the previous calibration and allow for user-initiated recalibration for short-term drifts. The user could be frustrated if these recalibrations are to be performed too often. Further to this, [12] recommends different levels of user integration in FES systems such that the search strategy can be chosen based on the users' preferences and applications.

Safety and comfort
As an automated process, calibration algorithms would not have feedback on user-perceived discomfort. These procedures can be painful to users, and discomfort during stimulation is one of the main reasons for discontinuing the FES system. Thus, userperceived discomfort or pain during the stimulation and setup must also be considered. Moreover, the use of hydrogels can improve the situation. Nevertheless, when targeting deeper fibers, the requisite for a higher stimulation threshold activates more sensory fibers that can be painful to users. As in [3], electrophysiologically-driven strategies can be deployed to detect optimal stimulation patterns with relatively low current intensities. For safety, there should be mechanisms to stop the search if the user feels uncomfortable. Also, the search space for parametric optimization should be within safe limits.

Calibration time
The optimization routines reportedly vary from 2 to 15 min across studies. While this is still acceptable for initial calibration, everyday calibration after donning and doffing should be significantly shorter. Future algorithms should use existing literature to obtain information on motor point locations and stimulation parameters to constrain the search space and to fasten the calibration time.

Accuracy
Optimization routines within calibration algorithms should derive highly accurate outcomes. Its performance in terms of individual-specific accuracy and specificity during algorithm development must be reviewed. Additionally, the success rate can be a good predictor for the validity of these algorithms to be deployed across subjects.

Reliability
Several physiological factors influence the variability of stimulation sites and parameters required to elicit a target response. While most reported studies show that there is a high inter-and intra-subject variations, the automated algorithms were able to compensate for it. Accordingly, systematic assessments should be conducted to assess the algorithms' reliability in intersubject, intra-subject, and longitudinal variations.

Conclusion
This study has comprehensively reviewed automated calibration algorithms aimed toward hand function tasks. Electrode arrays offer a high level of personalization. Thus, their adoption in the rehabilitation and assistive technology communities has been increasing. Automatic calibration algorithms being integral to such systems, significantly shorten calibration time, deliver personalized stimulation, and obviate the need for expert calibration. Thus, the development of automated algorithms demonstrates the potential for home-based rehabilitation for improved user independence and acceptance.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.