In section “Wrist rotation module prototype design” describes a previously developed prosthetic hand (Re-fill [40, 53]) and a wrist-rotation module prototype design applicable to subjects with a partial hand amputation. In section “Experiments for validation” consists of two experiments. Experiment 1 was conducted to verify the usability of the ADL of the proposed prosthetic hand using the wrist rotation module method, and a JHFT was conducted on an amputee subject. In addition, to validate the upper limb movement effectivity, we performed a reach-to-grasp task in Experiment 2, which represents the fundamental upper limb movement related to hand function. Here the muscle synergy and related motion analyses were compared between a control group and partial hand amputees with and without P/S during the reach-to-grasp task. Finally, Sect. “Data analysis and statistics” explains the data analysis and statistical methods used in the experiment in Sect. “Experiments for validation”.

Wrist rotation module prototype designPrevious work: Re-fill project

The common prosthetic hand could be customized by determining the shape and function of the amputee's remaining hand [19]. Our team developed and customized a prosthetic hand called a Re-fill for a partial hand amputee (Table 1) [40, 53]. The Re-fill consisted of the thumb and index finger parts (Fig. 1). The thumb and index finger are the passive and active joints, respectively. The index finger can be mainly driven by one linear actuator with 3DOF like the human index finger: distal, proximal interphalangeal, and metacarpophalangeal joints of the human index finger. Functionally, adaptation to the shape of an object is possible. Re-fill can perform hand grasping, holding, and releasing by opening and closing, which account for more than 70% of hand functions [26]. In addition, the straps could be worn easily and comfortably. Using the box and block test, the Re-fill validated its performance in moving eight blocks in 60 s.

Table 1 Characteristics of a partial hand amputee subjectFig. 1

Description of the proposed wrist rotation module prototype and the Re-fill (proposed prosthetic hand), and its wrist rotation motion

However, the amputee has been undergoing limited wrist rotation and reduced hand movement due to long-term internal plate fixation in both the fractured radius and ulnar bones after orthopedic surgery. He could flex or extend his wrist within a limited range of rotation. Therefore, we should consider designing a wrist-rotation module for enhanced hand function and efficient upper-limb movements without causing secondary damage. The characteristics of the amputee subjects (Table 1) were acquired to design a prosthetic hand and a wrist-rotation module applicable to the amputation hand.

Table 1. Characteristics of a Partial Hand Amputee Subject.

Specification for proposed wrist rotation module prototype

We proposed a wrist rotation module prototype for a partial hand amputee. The wrist-rotation module consisted of pronation and supination along the longitudinal axis of the anatomical transverse plane. We aimed to meet the two conditions for the wrist rotation module design for a partial hand amputee as mentioned in Sect. “Background”: (1) the prototype module’s axis of wrist rotation on the partial hand amputee allows the anatomical axis of the wrist rotation to be followed without interfering with the hand and the Re-fill, (2) low cost, small size, and design according to the required wrist rotation function (Table 2) [35].

Table 2 Required functions of proposed prototype

To satisfy the first condition for the wrist rotation module prototype design, it is important to know the anatomical structure of the wrist and forearm to determine the wrist rotation axis. Wrist rotation involves the distal radius wrapping around the ulna as the proximal radial head spins. Therefore, wrist rotation begins in the forearm (radial head), is transmitted to the wrist adjacent to the radius, and has a virtual axis centered on the third finger, based on the hand’s anatomy [26, 27, 54]. As a result, the thumb and index fingers produce a circular motion as the wrist rotates. Therefore, we applied a double parallelogram mechanism (DPM) to design a wrist-rotation module with a virtual axis aligned with the longitudinal axis [6, 55]. The DPM can move in a semicircular shape, similar to wrist rotation. A remote center (RC) can be formed at the center of the wrist to rotate the prosthetic finger without colliding with the residual hand. The wrist joint rotates along one axis based on the third finger and draws a semicircle based on the thumb (Fig. 1).

We confirmed functional range of motion (ROM), force, and speed for rotational motions in the wrist (the pronation and supination movements) to meet the second conditions in the proposed wrist rotation module in Table 2. The requirements for the wrist rotation module design were defined by human anthropometric data and the functional needs of activities of daily livings (ADLs), referencing previous research [26]. In Table 2, the first row, labeled 'Hand (thumb and index finger) and wrist joints,' was derived from anthropometric data by taking into account the height and weight of the participating amputees (Table 1) [26]. For the second to fourth rows, the 'Function ROM', 'Torque', and 'Speed' items, we chosen the information on the joint angles, forces, and speeds required for the ADLs as suggested by prior research [35]. It was made at a low cost and lightweight (500 g) to satisfy these conditions. Because a non-back-drivability mechanism is an essential requirement for prostheses [57], a lead-screw-based linear actuator (PLS-5030, Potenit Inc., Korea) was selected, and a slider-crank structure was used in consideration of space efficiency. We provided detailed information on slider crank systems in [40, 53].

The amputee is able to perform full supination motion and can rotate the wrist up to the neutral position (wrist rotation 0 deg), but full pronation is not possible. In the case of full pronation, the radius moves horizontally over the ulna, causing rotation of the longitudinal axis of the upper limb. Therefore, the RC axis to be created by the mechanism was determined to rotate based on the third finger of the amputee’s 3D-scanned hand model so that the DPM could perform supination and pronation movements.

Description of wrist rotation module prototype

The kinematics of the proposed mechanism is formulated based on parallelograms (Fig. 2). In order to select the location of RC, which is the axis of wrist rotation, the main link lengths were determined only \(_\) and \(_\) illustrated by the green line and blue line. As a result, DPM consisted of a pair of parallelograms of equal size and shape, forming a parallelogram with the RC as a defined vertex and all four sides of length \(_\). Following the shape changing parallelogram, \(_\), a rotation radius of DPM, is as follows.

Fig. 2

The kinematics of the proposed mechanism for wrist rotation module prototype

We measured the length from the wrist rotation axis to the furthest point of amputee’s residual hand to evade the collision between the DPM and the hand. As a result, the length of \(_\) which is same as \(_,\) and \(_\) was set to 25 mm and 10 mm to satisfy the small size of mechanism which can rotate without interfering with the hand.

According to these parameters, the angle of wrist rotation \(\theta\) has the same degree with \(\varnothing\), the angle between \(_\) and \(_\), which is an input angle of the crank slider. Therefore, the relation between \(\varnothing\) and \(\theta\) was obtained as follows:

$$\theta =\varnothing$$

(2)

\(\dot\) and \(\dot\) are the angular velocity of the crank input and the wrist rotation. \(_\) and \(_\) are the torque from the crank input and the wrist rotation.

Since, the force of wrist rotation from supination and pronation was generated by \(_\), the force \(f\) which pushed the coupler in normal direction at the middle of link, can be obtained as follows

\(_\) is the length of moment arm of \(_\). \(_\) was calculated in our previous work [40] as 0.3 Nm. As a result, \(f\) is 10N which satisfy the required force of wrist supination and pronation.

Through keyboard-input and a motion controller, we assign desired positions to the motor drive for the Re-fill and wrist rotation module, respectively (Fig. 3). The servo drive then calculates the torque required to manipulate the Re-fill and wrist rotation module, which is a position controller, and PWM amplifier provides the corresponding voltage to the motors in order to operate the prosthesis. In our previous research, our team developed the Re-fill [40] using myoelectrical input method. However, in this study, we opted for the more intuitive keyboard input method because the EMG-driven input approach could potentially influence that the muscle synergy patterns in the participated amputee [43].

Fig. 3

Operating and control principles for wrist rotation module and Re-fill

Experiments for validationParticipants

We recruited ten able-bodied right-handed subjects (8 males and 2 females) with a mean age of 25.5 ± 1.2 years, height of 174.3 ± 3.9 cm, and weight of 67.4 ± 10.8 kg, as well as one individual with a partially amputated hand (Table 1) to compare the effect of upper limb movement (muscle synergy and movement patterns). The inclusion criteria were as follows: (1) no orthopedic surgery or disease in the right upper extremity, (2) no neurological damage, and (3) no pain or abnormal sensations in the right upper extremity or hand. Participants voluntarily consented to participate in the experiment after receiving an explanation of its contents and procedures. This study was approved by the POSTECH Institutional Review Board (No. PIRB-2022-E012).

Experiment 1: Jebsen-Taylor hand function test

We used the Jebsen-Taylor hand function test (JHFT), a widely used assessment tool that measures a broad range of the uni-hand functions for ADL [51]. The JHFT consists of seven subsets: writing, simulated page-turning, lifting small objects, simulated feeding, stacking, and lifting large, lightweight, and heavy objects. The test is scored based on the time it takes to complete the task (units: seconds, maximum 120 s) and reflects speed rather than the performance quality. The JHFT allows compensatory movement of the trunk and shoulders during each task.

We prepared a standardized JHFT tool, including a pen and paper to record scores, a stopwatch or timer, and the JHFT manual. The participants sat comfortably and had their tested hands positioned on a table. We explained the test's purpose to the recruited amputee and provided instructions for each subset. According to the instructions, each subset was tested quickly and accurately. The examiner used a stopwatch to measure the time required to complete each task, and the scores were recorded. For consistency in the test, we requested that the subject maintain a seated posture while performing the tasks and asked whether they were permitted to make compensatory movements of their trunk and shoulders. Even then, we recorded 120 s for the tasks that he could not complete. The JHFT was repeated twice, and the fastest test was chosen. The test proceeded in the following order: the subject’s intact hand (left hand), an amputated hand (right hand) with only Re-fill without P/S, and finally an amputated hand (right hand) with Re-fill and with P/S (Fig. 4b).

Fig. 4

Description of the reach-to-grasp task. a All phases of the motions the reach-to-grasp task in the control group. b In phase 2, the partial hand amputee used only the Re-fill without P/S (left side), and a partial hand amputee used the Re-fill with P/S (right side). c Anatomical plane and defined joint motions

Experiment 2: reach-to-grasp task

The reach-to-grasp task (Fig. 4), including reach, grasp, transport, release, and return, can be defined as the most fundamental movement performed by the upper limbs [45]. We simultaneously investigated the muscle synergy and movement patterns in the upper limb according to the prosthetic hand with and without P/S in one person with a partially amputated hand during the reach-to-grasp task (Fig. 4b). To validate this, we compared a control group including 10 healthy subjects with muscle synergy and movement patterns while performing a reach-to-grasp task (Fig. 4a).

The reach-to-grasp task (Fig. 4) involved moving an object from the desk on which the participant was standing to the shelf on the same desk. For a consistent experimental environment, the desk's height was adjusted to be positioned in front of the pelvis (anterior superior iliac spine), considering the participant’s leg length. The position of the object on the desk and that on the shelf were fixed at designated locations. The object was placed on the sagittal plane of each arm approximately 10 cm from the subject.

The task can be divided into three phases (Fig. 4a) [43, 45]. Phase 1 involves reaching and grasping an object placed at a designated location on the table. Phase 2 requires transporting the picked object and releasing it onto the shelf on the table. Phase 3 engages regrasping the object and returning it to the table. All participants took the initial posture before Phase 1 and returned to the initial posture after Phase 3. Prior to initiating the motion, the initial posture was as follows: 0 degrees of the shoulder, 90 degrees of the elbow, and 90 degrees of wrist supination. The reach-to-grasp task was performed six times per set and repeated in four sets. At the end of each set, all subjects rested for at least 30 s. All the participants performed the reach-to-grasp motion 24 times under the guidance of an instructor. Participants completed the task to familiarize themselves with it before the experiment and performed it consistently. During the reach-to-grasp motion, participants were allowed to perform the movements as naturally as possible, and the initial posture at the beginning of the motion was maintained.

To analyze the muscle synergy using NMF [52, 58, 59], the surface electromyography (sEMG) sensors (Delsys Trigno EMG, Delsys, MA, USA) were attached to the muscles correlated in the reach-to-grasp task. We chose muscles based on two criteria: muscles used during the reach-to-grasp task [43, 58, 60–63] and muscles measurable by the amputee participating in our study. sEMG sensors were recorded for 14 muscles on the upper limb [63], which are the anterior deltoid (ADEL), posterior deltoid (PDEL), middle deltoid (MDEL), supraspinatus (SUFR), latissimus dorsi (LATD), pectoralis major (PECT), teres minor (TERE), infraspinatus (INFRA), biceps brachii (BIC), triceps brachii (TRI), pronator teres (PRO), supinator (SUPI), extensor digitorum (WEX), and flexor digitorum (WFLE). We followed SENIAM recommendations [64] for skin preparation and electrode placement [65]. Before performing the task, all participants completed a maximal voluntary contraction (MVC) test for each muscle to normalize the sEMG signal. A single clinically experienced examiner performed this test on all subjects to ensure the consistency of measurements. During the test of each muscle, the subject was asked to sit and position the arm for each muscle according to the examiner's instructions. All participants performed MVC five times on each muscle as performed by the examiner, with 30 s of rest between each contraction to prevent muscle fatigue.

Simultaneously, we acquired the kinematic data using an eight-camera motion capture system (VICON, Oxford Metrics Ltd., Oxford, UK) to analyze the upper limb movement patterns during the task. The motion capture system was acquired at 125 Hz. We targeted the shoulder, elbow, wrist joints, and the trunk to monitor upper limb kinematics. The set of markers is defined in the "Upper body modeling with Plug-in Gait" model provided by the motion capture system. The model utilized 17 reflective markers placed at anatomical locations [66,67,68,69]. Ten markers are attached to the torso [66]. Seven markers were attached to the right shoulder on the acromioclavicular joint, upper arm on the lower lateral 1/3 surface, lateral condylar of the elbow, lower arm on the lower lateral 1/3 surface, lateral/medial sides on the wrist, and 2nd finger. On the amputated hand wearing the prosthesis, two wrist markers (lateral and medial wrists) and an index finger marker were placed in the same position as the actual wrist joint. To obtain the angle, marker sets were attached following the guidelines of this model, and subsequently, the markers were captured using the system. After capturing, the joint angles were post-processed using the VICON NEXUS software (VICON, Oxford Metrics Ltd., Oxford, UK) based on the captured markers.

Data analysis and statisticsJHFT score

The JHFT is scored by measuring the completion time for each of the seven tasks. The subtest score equaled the number of seconds required to complete the task, and the maximum score for each subtest was 120. The total score was the sum of the scores from all subtests calculated separately for each hand. The lower the score, the better the participant’s hand function. We compared the JHFT scores between the intact side, the amputated side with only the Re-fill with P/S, and the amputated side without P/S. We compared the standardized JHFT scores (healthy people dominant/non-dominant hands) for age-specific healthy males [70].

Reach-to-grasp task for analysis of muscle synergy and its motion analysis

First, we analyzed the muscle synergy using NMF [59]. The sEMG signals were collected at 1000 Hz. We normalized the time from the start to the finish of the task (0 = start, 1 = finish). The following preprocessing steps were performed: band-pass filtering with a cut-off range of 20–450 Hz, notch filtering (cut-off: 60 Hz), rectification, low-pass filtering with a cut-off frequency of 2 Hz, and subtraction of the average when no movement occurred before the starting position. After sEMG preprocessing and subsequent data removal, the muscle synergy was extracted by applying the NMF algorithm. The NMF consists of the decomposition of multi-muscle sEMG signals into two matrices representing spatial muscle synergies (W, weighted muscle coefficient) and temporal muscle synergies (C, muscle activation pattern) [59]. Therefore, the decomposition of the sEMG signal into two matrices represents the control modules for the movement patterns, which are encoded in terms of the spatiotemporal neuromuscular strategy employed until the task is completed. The factorization of muscle activity is expressed as follows:

$$}}_=}}_\times }}_+},$$

(7)

where n is the number of muscles, and t is the number of time points. The initial matrix consisted of normalized sEMG data and the average of three cycles for each of the 14 muscles. E is a 14 × 501 matrix, W represents an n × m matrix, and m is the number of synergies and represents the muscle synergy. C is an m × t matrix that represents the activation coefficient, and e is the residual error matrix. For each subject, we repeated the analysis by varying the number of synergies between 1 and 14 and selected the least number of synergies fulfilling the global variance accounted for (gVAF > 90%) and VAF for each muscle (mVAF > 75%). VAF is 100% the coefficient of determination from the uncentered Pearson correlation coefficient [58, 71].

The upper limb movements during the reach-to-grasp task were evaluated and compared with the control group’s upper limb movements with and without wrist prostheses (P/S) in amputees. The trunk flexion/extension, trunk rotation, shoulder flexion/extension, shoulder abduction/adduction, shoulder internal/external rotation, elbow flexion/extension, wrist flexion/extension, and wrist pronation/supination were also assessed (Fig. 4c).

After obtaining the joint angles derived by Eular angles in VICON NEXUS, we redefined the angles to understand the changes in the joints during the task. We subtracted all calculated joint angles based on the defined initial posture. All participants were instructed to maintain this initial posture at the beginning. It as follows:

\(\theta\) is the joint angles. \(j\) represents each joint, \(m\) denotes the joint angles calculated across all task duration using VICON NEXUS. \(i\) denotes the initial value.

During the reach-to-grasp for each joint, we confirmed the angle change for each joint and compared and analyzed the angle change for the task. In addition, we aimed to quantify the compensatory movement using the joint angles of the control group subjects and amputee patients with and without P/S. Compensatory movement (CM) refers to a typical pattern that compensates for the loss of mobility in one part of the body. This is achieved by either underusing or overusing other parts of the body to achieve a final goal. To quantify the CM, we used normalization through the average difference between the maximum and minimum values (\(RO_\)) of each joint angle in all control group subjects of the control group during reach-to-grasp task. Then, the average value of each joint angle in the control group was subtracted from the average value of the body segment angles for subjects with and without the wrist rotation module configuration and each trial as follows:

$$CM=\frac__\right|}_},$$

(9)

where CM is the ratio of compensatory movement [28], \(RO_\) is the average ROM of all control group subjects in each α and \(n\) is the joint. \(_\) is the mean of the ROM for each joint all control group subjects, and \(_\) is the mean of \(ROM\) for two cases: Re-fill with P/S and Re-fill without P/S.

Statistics

For motion analysis, we calculated the average joint angle for each joint measured during the reach-to-grasp task using all trials and subjects in the control group. We also compared the muscle synergy with the control group to patients with P/S and patients without P/S. We prepared the data for statistical analysis using repeated the reach-to-grasp task (4 sets of 6 trials each set, totaling 24 trials). For the group of 10 subjects, we gathered data as follows: (10 subjects × 4 sets × 6 trials)/10 subjects = 24 trials. We analyzed the statistics between groups, taking into account the sample size of each group's dataset (control group N = 24 trials, with P/S N = 24 trials, and without P/S N = 24 trials).

The Wilcoxon rank-sum test was applied to confirm the differences between the control group 10 healthy subjects and the partial hand amputee with P/S, the control group and the partial hand amputee without P/S, and the cases with and without P/S. This was done using non-parametric tests. The Kruskal–Wallis test was applied to confirm the difference between the control group, the group with P/S, and the group without P/S. In addition, to determine the effect of the wrist rotation module on the amputees' upper limb movement, the CM ratio was calculated, and a non-parametric Wilcoxon rank-sum test was used for the with P/S and without P/S cases.

For the muscle synergy analysis, a partial hand amputee, both with and without P/S, was compared to a control group of 10 healthy subjects who participated in the study. The number of muscle synergies, as determined by VAF, was set based on a threshold (gVAF > 90%, mVAF > 75). When the number of muscle synergies was smae, the synergy vectors derived from NMF were compared. However, if the number of muscle synergies varied, the groups were considered distinct and thus were not compared. The statistical significance between each group (control, amputee with P/S, and amputee without P/S) was then verified. The Wilcoxon rank-sum test was employed for each muscle synergy vector to compare each muscle between the control and an amputee. All data comparisons were performed using MATLAB software (MATLAB 2021a Math; MathWorks Inc., MA, USA). Using statistical parametric mapping, the activation patterns were compared between the two groups (control vs. with P/S). Statistical significance was set at a p-value < 0.05.