2. Orthosis design

In order to more fully comprehend the upper-limb needs and challenges survivors of neurological events face, and to determine a target end user, the authors conducted informal customer discovery conversations with 153 members of the ecosystem (60 survivors, 30 caregivers, and 63 medical providers) as part of the National Science Foundation I-Corps Program. This customer discovery helped bridge the knowledge gap regarding the generic information and standard of care that is common to the medical community but unbeknownst to many engineers. Discussions with survivors and caregivers yielded additional insights into the unique experiences of individuals from their own perspectives. The authors then realized upper-limb patients fell into two populations: spastic/toned (stiff, clenched hands) and flaccid (limp hands). For the subsequently described body of work, the authors chose to focus on a simple technological solution for the first category of patients. This group struggles to open their hands due to involuntary clenching, or “freezing” of the hands in a curled position, and needs help stretching on a regular basis to relieve their manual tone. Based on the information collected from the customer discovery, the authors developed a set of design constraints and then prototyped a powered wrist-hand stretching orthosis to aid in recovery. The set of design constraints and features derived from customer discovery are as follows:

1. 1. Easy to don and doff. Since the patients’ hands are stiff, ease of donning is essential. They are unable to control their fingers and must manually push them into position, making individual finger motion practically impossible and often requiring the help of a caregiver in a procedure that can last several minutes. Ideally, a patient could singlehandedly put the orthosis on his hand or remove it in less than 1 min.

2. 2. Dynamic: flexible and comfortable. Many patients complained that their static splints are painful due to the constant aggressive stretch, so they need something comfortable or they will not wear it. And since common a side effect of neurological impairment is reduced sensation in the affected limb, preventing abrasion is critical to prevent skin damage and infection.

3. 3. Therapeutic stretching. All patients need to stretch their hands to prevent contractures and regain function. To alleviate the mental and physical burdens of constantly opening and closing their hands, and because most patients lack voluntary control, the orthosis should cyclically stretch the affected hand.

4. 4. Intelligent: intuitive control and sensory feedback. Any device for a neurologically impaired person must be easy to use and safe. Powering and controlling the device should be simple, and force or pressure monitoring should prevent overextension of joints.

5. 5. Affordable. As most neuro patients are no longer able to maintain a full-time job and often require caregiver assistance, they also face financial challenges. A device should be as low cost as possible so they can afford it, ideally below 100 USD.

6. 6. Portable: lightweight and untethered. In order for a patient to easily transport and use a device, it must be unchained from external equipment. Furthermore, the proportion of weight on the distal limb should be minimized (ideally <0.5 kg) in order to reduce the required torque to lift the arm and hand, with heavier components located more proximally.

For this prototype, the authors chose to prioritize the first three design constraints: easy to don and doff, flexible and comfortable, and therapeutic stretching. The other design constraints (intelligent, affordable, and portable) will be addressed in future work as the project develops. The orthosis prototype, shown in Figure 1, has a very different form than others in literature. It is essentially an inflatable, intentionally shaped vessel with hook and loop fastener straps. Designing for flexibility and comfort necessitated a soft robotics approach. The vessel is made of nylon coated with TPU, and the stitching and ¼” tubing inlet are sealed with a commercial sealant to prevent leaks. Designed to fit the 50th percentile male hand, but easily scalable to other sizes, the prototype is an hourglass shape 30 cm long, 19 cm wide at the widest part, and 12 cm wide at the narrowest part when deflated. The simple structure facilitates the ease of donning in a way that a standard glove with individual fingers would not. There is one strap for the forearm, two straps for the fingers, and one strap for the thumb. The straps utilize hook and loop fasteners for secure, adjustable positioning and ease of donning and doffing. The finger straps’ placement falls on the metacarpophalangeal (MCP) and proximal interphalangeal (PIP) joints of the hand in order to encourage finger extension, as recommended by occupational therapists consulted during the design process. Positioning the finger straps on the joints naturally causes the forces from the straps to intersect the joints, eliminating any torque that would be created by a lever arm, and counteracting (by flattening the fingers) the torque created by the force from the vessel on the fingers. This keeps the knuckles and therefore the links of the fingers in as close contact as possible to the orthosis surface, allowing the fingers to uncurl as the orthosis inflates. The hourglass shape is designed to minimize wasted air while applying sufficient force to open the hand and support the wrist. This wrist support is essential because a patient with spastic hands typically experiences wrist contraction as well, and therefore needs to extend the wrist joint simultaneously with the thumb and fingers. The entire prototype weighs only 63 g, far below the distal weight limit of 500 g and the minimum of other published research prototypes at 120 g (Rahman, Reference Rahman2000). Furthermore, it is quite inexpensive with materials under 5 USD and simply sewn together.

Figure 1. Stretching orthosis prototype. the photos, clockwise from top left, show the prototype with (a) straps unfastened, (b) straps fastened, (c) flat hand, donned, (d) clenched hand, dorsal view, (e) clenched hand, angled view, and (f) clenched hand, palmar view.

At present, the prototype is actuated via an air compressor, powered through a DC power supply, and controlled through a computer interface, as explained in section 3.1 Pressure Testing. This allows for testing device functionality and evaluating the primary design features in a timely manner. A photo of the inflated prototype with dimensions is shown in Figure 2.

Figure 2. Inflated orthosis dimensions. The inflated orthosis is on the bottom, and dimensions to certain points are on the top diagram, profile view. The points are: (A) shrink distance of the center due to inflation, (B) the widest point of the hourglass (see Figure 1 a–c), (C) narrowest point of the hourglass (see Figure 1 a–c), and (D) wrist strap. The left end is the distal end, and the right is proximal.

3. Experimental testing and results

Two neuro-patient test subjects were recruited from a brain injury rehabilitation clinic through the recommendation of an occupational therapist. One subject was an elderly male just over a year post-stroke, who displayed medium hand spasticity (tone). The other subject survived a traumatic brain injury (TBI) nearly 2 years prior and had a lower tone as perceived by the authors. Details about each subject are shown in Table 1. The baseline Modified Ashworth Scores (MAS) for each subject was assessed separately for the digits (fingers and thumb) and wrist by the clinic and are reported on a 0 (best) to 4 (worst) scale. The study was approved by the Vanderbilt University Institutional Review Board, study number 221203, and all subjects provided informed consent to participate.

Table 1. Test subject information

Each subject came separately to the lab to test the orthosis. Three types of tests were performed: donning and doffing, grip force, and cyclic stretching. The full sequence of events for each session is enumerated below, and the tests are specified in a graphic in Figure 3. Video footage of the testing is available here.

1. 1. Allow the subject to acclimate to the orthosis;

2. 2. Measure initial resting and maximum grip forces;

3. 3. Don orthosis (time);

4. 4. Measure inflation pressure required to open hand;

5. 5. Cyclically inflate/deflate orthosis to stretch hand;

6. 6. Doff orthosis (time);

7. 7. Interview subject for feedback;

8. 8. Measure final resting and maximum grip forces;

9. 9. Optional: Cyclically inflate/deflate orthosis to stretch the hand on a longer cycle.

Figure 3. Testing sequence. This graphic outlines the experimental protocol for subject testing.

3.1. Donning and doffing

The donning and doffing tests consisted simply of the subject strapping the orthosis on their arm and then removing it. After an acclimation period, during which a subject could “practice” with the orthosis until he verbalized readiness for testing, each subject was timed for the procedures and observed to determine if he could complete them independently. Both subjects were able to don and doff the orthosis without assistance. Their donning and doffing times are listed in Table 2.

Table 2. Donning and doffing times

3.2. Pressure testing

The authors constructed a setup to regulate and measure air pressure in the orthosis during the experiments. A diagram of this setup is shown in Figure 4. An air line was connected to a Festo proportional directional control valve (MPYE-5-M5–010-B), powered by a 24 V DC supply and controlled by Simulink Real-Time via a Humusoft data acquisition card (MF634). The valve was connected to an analog pressure sensor (Festo SDE-16-10 V/20 mA), which was attached to the orthosis via ¼” pneumatic tubing. First, a pressure regulator on the pressure supply line was opened, and then the pressure was slowly and manually increased to inflate the prototype until the subject’s hand opened (see Figure 5). The regulator was then set as the desired peak pressure for the open loop cyclic stretching tests.

Figure 4. Experimental setup. This block diagram shows the experimental setup. The arrows indicate the flow of power (red, solid), signal (green, dotted), and air (blue, dashed) for device inflation.

Figure 5. Hand stretching cycle. The first photo shows a spastic hand, and the remaining three show how the hand opens as the orthosis inflates.

The primary cyclic stretching test involved five, 1-min sessions in which the prototype was inflated and deflated over a 4-s cycle of sinusoidal valve orifice position. The subjects alternated between 1 min of stretching and 1 min of resting for a total of five sets. During the test, each subject was carefully observed and communicated with to ensure his hand was not in pain. At the suggestion of the occupational therapist, an additional (optional) test was appended to the protocol, using a longer cycle (3 min of a 12-s cycle biased toward inflated: 8 s inflate, 4 s deflate). With Subject 1, five sets of this were intended to be completed, but during the fourth set, he complained of hand soreness where the stitching on the straps contacted his skin, so the test was discontinued, and Subject 2 was not asked to participate in this supplemental test during his visit.

Pressures required for the orthosis prototype to open each subject’s hands are shown in Table 3. A higher tone corresponded to higher opening pressure.

Table 3. Opening pressures

For each subject, during the main cyclic stretching test, the orthosis took approximately three cycles to fully inflate, at which point it continued cycling at a steady state. Performance averages over 10 steady-state stretching cycles are shown for each subject for the first and last (fifth) 1-min session in Figure 6. One can see that the performance consistency increased between the first and last tests as each subject’s hand relaxed, suggesting that the orthosis can facilitate consistent, repeatable motion.

Figure 6. Stretching pressures. These figures show the average air pressure in the orthosis over 10 cycles for (a) the first one-minute interval, and (b) the last (fifth) one-minute interval. Subject 1’s curve is green, and Subject 2’s curve is red. The gray bands indicate ± 1 standard deviation from the means. The standard deviation bands are too small to be seen on the fifth session (b) for both subjects, indicating that consistency increased between the first and last intervals.

3.3. Grip force

Grip force testing was conducted at the beginning and end of each session to see if stretching the hand affected grip force. Force was measured with a digital hand dynamometer and reported in kilograms. Two types of forces were measured: “resting” grip force to determine the tension in the affected hand, and maximum grip force to quantify how much force the subject could voluntarily exert with the same hand. Resting and maximum grip forces before and after stretching are shown in Table 4 for each injured subject and each session. Subject 1 was tested twice because no significant grip force reduction was observed after the original session. The hand dynamometer does not register forces less than 1 kg, so any force below that threshold is indicated as “< 1”.

Table 4. Grip force before and after stretching

In order to estimate the maximum possible forces the orthosis could endure, a strong, healthy subject was also tested. This subject was a 25-year-old male rock climber selected for his superior grip strength. First, his maximum grip strength was measured with the hand dynamometer. After resting, he was then instructed to don the orthosis and clench it in his fist as tightly as possible, while the inflation pressure was slowly increased until either the prototype ruptured or the hand opened. When testing maximum pressure with a strong healthy subject, the prototype withstood the subject’s grip. It inflated to 35 psi without rupturing, at which point the subject complained of pressure from the edge of the strap against his hand, and the test was discontinued. The maximum grip force of this strong healthy subject was 55 kgf and is included in Table 4.

4. Mathematical modeling

A lumped parameter model was developed to describe the compliance of the hand (quantify the stiffness of the fingers) based on the experimental kinematic data and orthosis pressure. This model will be useful for determining joint stiffness as a metric to quantify and monitor patient improvement over time. Ideally, joint stiffness would decrease as the patient consistently performs therapeutic stretching and exercises for recovery. This model is two-dimensional (in the sagittal plane) and discretizes the hand as rigid links that are sequentially connected and able to rotate in the plane in the presence of applied and internal forces and moments. This simplification is justified because the finger diameter is sufficiently smaller than the hand length and depth. This model is derived by lumping all four fingers as one and only considering the three segments of this lumped finger along with the palm. In particular, we treat each link as having a center of mass and a rotational moment of inertia corresponding to a slender rod. Each link is tied to its neighboring links with rotational springs and damping terms to represent angular compliance and resistance. As the orthosis inflates, each link is subject to a normal force. This is modeled as an equivalent external force and is computed by the product of the equivalent pressure-induced force and resultant area (product of link length and depth of lumped finger/wrist system), applied at the center of each link. The coordinate system and free-body diagram of the system are shown in Figure 7.

Figure 7. WHO modeling diagram. this diagram shows the 4-link model of the hand, along with states used to represent this system. The inflated orthosis is depicted in red along with the resultant pressure forces acting at the center of each link. The forearm link ( $ {L}_1 $ ) is grounded and not shown in this diagram.

In this work, we use a maximal generalized coordinate representation to describe the system. The states q for this model for links i = 2–5 include:

(1) $$ q={\left[{x}_2,{y}_2,{\theta}_2,\dots, {x}_5,{y}_5,{\theta}_5\right]}^T $$

where $ {x}_i $ and $ {y}_i $ are the position of the respective link center, and $ {\theta}_i $ is the link angle with respect to a global frame as shown in Figure 7. The dynamics of the system are derived using a constrained Lagrangian approach. Consider a set of constraints of the form $ \phi (q)=0 $ representing the constraints that tie the links together at the joints. The associated Lagrangian L is given by $ L=T-V+{\phi}^T\lambda $ , where T is the total kinetic energy of the system, V is the total potential energy, $ \phi $ is the set of constraint equations, and $ \lambda $ is the vector of Lagrange multipliers. The dynamics of the system are formulated as:

(2) $$ \frac{d}{dt}\left(\frac{\partial L}{\partial {\dot{q}}_i}\right)-\frac{\partial L}{\partial {q}_i}+\sum \limits_{j=1}^8{\lambda}_j\frac{\partial {\phi}_j}{\partial {q}_i}=0 $$

There are a total of 8 constraints in this system. There are six constraints that ensure link-to-link continuity by relating the positions of consecutive centers of masses. These equations describe the hinge point ahead of the center of mass of the $ {i}^{th} $ link, and behind the $ {\left(i+1\right)}^{th} $ link as the same points and are given as:

(3) $$ {x}_i+\frac{L_i\cos \left({\theta}_i\right)}{2} + \frac{L_{i+1}\cos \left({\theta}_{i+1}\right)}{2}-{x}_{i+1}=0 $$

(4) $$ {y}_i+\frac{L_i\sin \left({\theta}_i\right)}{2} + \frac{L_{i+1}\sin \left({\theta}_{i+1}\right)}{2}-{y}_{i+1}=0 $$

To pin one end of $ {L}_2 $ to the origin of the coordinate system, $ {x}_2 $ and $ {y}_2 $ are each constrained such that:

(5) $$ {x}_2-\frac{L_2\cos \left({\theta}_2\right)}{2}=0 $$

(6) $$ {y}_2-\frac{L_2\sin \left({\theta}_2\right)}{2}=0 $$

The system of equations can be formulated in matrix form as follows:

(7) $$ M\ddot{q}+{A}^T\lambda =F $$

Here M is the diagonal inertia matrix containing link masses and moments of inertia, A is the sparse constraint matrix given by $ A=\frac{\partial \phi }{\partial q} $ of size 8×12, and F collects all internal and external generalized forces and torques. For a detailed derivation of this model, refer to (Rucker, Reference Rucker2022). Baumgarte stabilization (Baumgarte, Reference Baumgarte1972) was implemented to ensure constraints were numerically enforced over simulation runtime. Without such an enforcement scheme, constraint equations may be violated due to the accumulation of integration truncation errors (Flores, Reference Flores2011; Haizman, Reference Haizman2007). The stabilized constraints were derived by differentiating the set of original constraint equations twice:

$$ {\displaystyle \begin{array}{l}\phi (q)=0,\\ {}\dot{\phi}(q)=\frac{\partial \phi }{\partial q}=A(q)\dot{q}=0,\\ {}\ddot{\phi}(q)=A(q)\ddot{q}+\dot{A}(q)\dot{q}=0,\end{array}} $$

and incorporating them into a stable 2nd order dynamic relationship that rapidly brings any constraint violations to zero by choosing appropriately fast and damped parameters $ \zeta $ and $ {\omega}_N $ :

$$ \ddot{\phi}(q)+2{\zeta \omega}_N\dot{\phi}(q)+{\omega}_N^2\phi (q)=0 $$

(8) $$ A(q)\ddot{q}=-\dot{A}(q)\dot{q}+2{\zeta \omega}_N\dot{\phi}(q)+{\omega}_N^2\phi (q)=0 $$

The combined set of equations (7) and (8) describe the evolution of the states (1) and are solved simultaneously:

(9) $$ \left[\begin{array}{cc}M& {A}^T\\ {}A& 0\end{array}\right]\left[\begin{array}{c}\ddot{q}\\ {}\lambda \end{array}\right]=\left[\begin{array}{c}F\\ {}\gamma \end{array}\right]. $$

Here, $ \gamma =-A\left(\dot{q}\right)\ddot{q}-2{\zeta \omega}_NA(q)\dot{q}-{\omega}_N^2\phi (q) $ and F is the sum of internal $ \left({F}_{int}\right) $ and external ( $ {F}_{ext} $ ) generalized forces. In particular, the generalized internal torques in F are of the form:

$$ {F}_{\theta_{i,\mathit{\operatorname{int}}}}={K}_i\left({\theta}_i-{\theta}_{i-1}-{\theta}_{i,i-1,0}\right)+{K}_{i+1}\left({\theta}_{i+1}-{\theta}_i-{\theta}_{i+1,i,0}\right)-B{\dot{\theta}}_i $$

Here $ {K}_i $ is the rotational spring constant of the $ {i}^{th} $ joint and B is a damping coefficient implemented for faster convergence. The $ {K}_i\left({\theta}_i-{\theta}_{i-1}-{\theta}_{i,i-1,0}\right) $ term reflects the rotational spring torque generated from the deviation of the proximal joint from its equilibrium position, given by the constant $ {\theta}_{i,i-1,0} $ . Similarly, $ {K}_{i+1}\left({\theta}_{i+1}-{\theta}_i-{\theta}_{i+1,i,0}\right) $ represents the rotational spring torque from the distal joint. The generalized external forces (due to the orthosis) in F are given by:

$$ {F}_{x_{i,\mathit{\operatorname{ext}}}}=-{F}_{orth,i}\sin \left({\theta}_i\right) $$

$$ {F}_{y_{i,\mathit{\operatorname{ext}}}}=-{F}_{orth,i}\cos \left({\theta}_i\right) $$

The external force for link $ i,{F}_{orth,i} $ , is a product of the pressure in the orthosis and the effective area that contacts the orthosis at each link. These forces are applied normally to each link, and their effective contact areas are given in Table 5.

Table 5. Effective contact area

The goal of this modeling work is to determine the rotational spring constants $ {K}_i $ of each joint. This was done by numerically integrating the system of equations (9) in MATLAB 2022b using the ode15s solver with an initial random set of $ {K}_i $ (all set to 1 Nm/rad). The configuration error, e, defined as the difference between the desired and steady-state joint angle values (after all dynamics settle), was used to find a new set of $ {K}_i $ iteratively until the sum of squared errors fell below a certain threshold (set at 0.05) as follows:

(10) $$ {K}_{i, new}={K}_{i, old}- Ce $$

where C is a positive constant, proportional to the magnitude of ( $ {K}_{i, old}\Big) $ to help with convergence. The intuition for the negative sign is that if the error is positive, the current joint needs to be less stiff to reach the desired angle. It should be pointed out that this has no physical interpretation, per se; it is merely a numerical method for finding the joint stiffnesses that match the simulation’s configuration to the physically observed configuration. The initially curled hand position is set as the spring equilibrium position for each link. As the orthosis inflates, the links straighten to a final position. The orthosis is modeled as a constant-perimeter balloon constrained maximally to the inflation dimensions (see Figure 2).

To first validate this modeling approach, and verify that it yields reasonable stiffness values, a mechanical hand was designed, 3D-printed, and integrated with springs with known stiffness values (see Figure 8).

Figure 8. Mechanical hand. This figure shows the phantom hand prototype, constructed of 3D-printed ABS links, connected by revolute joints with torsional springs of known stiffnesses.

It was empirically observed that the inflated orthosis does not provide additional force on the hand beyond a certain angle, due to the fact that the surface is convex when inflated. In particular, this effect is more significant on the distal joints. A healthy subject’s joint angles resting on the orthosis were used to estimate an “offset” angle for each link (i.e., the orthosis does not provide a force on any link that is larger than a certain, empirically derived angle). This effect was modeled as a linear decrease in the pressure exerted by the orthosis from the initial configuration of each link to the estimated offset angle. For example, an offset angle of $ \alpha >0 $ modifies $ {F}_{orth,i} $ to:

(11) $$ {F}_{orth,i}=P\frac{\left({\theta}_i+\alpha \right)}{\left({\theta}_{i,0}+\alpha \right)}{A}_{e,i} $$

Here P is the gauge pressure in the orthosis, $ {\theta}_{i,0} $ is the initial angle of the joint and $ {A}_{e,i} $ is the effective area of the corresponding joint. The term $ \left(\frac{\theta_i+\alpha }{\theta_{i,0}+\alpha}\right)=1 $ at the initial joint configuration $ {\theta}_i={\theta}_{i,0} $ and represents the maximum force applied to the joint. When $ {\theta}_i=-\alpha $ , the expression reduces to 0 and describes the scenario when the orthosis is unable to exert any additional force on the joint. Note $ {\theta}_i<0 $ for all angles as shown in Figures 9 and 11. Offset angle values of 10, 30, 30, and 45 degrees were used for the wrist, MCP, PIP, and DIP joints respectively, and we find there is reasonable agreement between the simulation and the experimental configuration of the mechanical hand, as shown in Figure 9. The average rotation error is 4.1 deg (magnitude of 1.2, 3.5, 4.3, and 7.6 deg for each joint, from the wrist to the DIP, respectively).

Figure 9. Simulation results of final configuration static matching of the 3D printed mechanical hand. Known spring constants are used to show the predicted and actual mechanical hand configuration. The average rotation error is 4.1 deg (magnitude of 1.2, 3.5, 4.3, and 7.6 deg for each joint, from the wrist to the DIP, respectively).

After validating the modeling approach on the mechanical hand, the analysis was then extended to determine joint stiffnesses of a test subject’s impaired hand. Using photographs from Subject 1’s testing, the link lengths and initial and final relative link angles were determined (see Figure 10 for an example). The mass of the hand was estimated to be 0.5 kg (corresponding to the 50th percentile male hand mass), with the weight distributed between the palm and fingers at a 60:40 ratio and the finger segments’ mass proportional to length. These values were used in combination with the measured inflation pressure of the orthosis (5 psig) to simulate the hand opening and determine joint stiffnesses.

Figure 10. Subject dimensions. This figure shows the segment data for a subject’s hand prior to stretching. The black line is a known distance of 100 mm used for calibration, and the red lines indicate link lengths (forearm $ {L}_1 $ , dorsal palm $ {L}_2 $ , proximal finger segment $ {L}_3 $ , middle segment $ {L}_4 $ , and final segment $ {L}_5 $ ).

Figure 11 plots the experimental starting configuration in black, the experimental (desired) final configuration in blue, and the simulation match based on the iteratively-derived spring constants in red. Here the average rotation error is 0.7 deg (0.2, 1.5, 0.39, and 0.59 deg for each joint, from the wrist to the DIP, respectively).

Figure 11. Simulation results of final configuration static matching for a patient’s hand. The controller can drive the simulation (red dashed line) from the starting configuration (black) of the closed hand to the final (blue) configuration by identifying sufficiently accurate joint stiffness values. Here the average rotation error is 0.7 deg (0.2, 1.5, 0.39, and 0.59 deg for each joint, from the wrist to the DIP, respectively).

Simulation results indicate joint stiffness decreasing from proximal to distal for this patient-specific data. The relative angle changes for each joint, as well as the stiffness values, are shown in Table 6. Angle changes are all negative due to the hand straightening.

Table 6. Joint angles and stiffnesses