Abstract

Total shoulder arthroplasty (TSA) is an effective treatment for glenohumeral (GH) osteoarthritis. However, it still suffers from a substantial rate of mechanical failure, which may be related to cyclic off-center loading of the humeral head on the glenoid. In this work, we present the design and evaluation of a GH joint robotic simulator developed to study GH translations. This five-degree-of-freedom robot was designed to replicate the rotations (±40 deg, accuracy 0.5 deg) and three-dimensional (3D) forces (up to 2 kN, with a 1% error settling time of 0.6 s) that the humeral implant exerts on the glenoid implant. We tested the performances of the simulator using force patterns measured in real patients. Moreover, we evaluated the effect of different orientations of the glenoid implant on joint stability. When simulating realistic dynamic forces and implant orientations, the simulator was able to reproduce stable behavior by measuring the translations of the humeral head of less than 24 mm with respect to the glenoid implant. Simulation with quasi-static forces showed dislocation in extreme ranges of implant orientation. The robotic GH simulator presented here was able to reproduce physiological GH forces and may therefore be used to further evaluate the effects of glenoid implant design and orientation on joint stability.

Introduction

As the population ages cases of shoulder osteoarthritis increase, leading to an increased demand for total shoulder arthroplasty (TSA). In 2007, about 650,000 shoulder prostheses were implanted in the U.S., representing a 3.7-fold increase over the last 14 years [1]. Following the increase in shoulder implantations along with the increased longevity of the population, the number of revision surgeries ramped up by 431% over the same time period [1]. Identifying the underlying causes of these prosthetic failures and developing new methods to enhance the implant quality and survival can thus improve the patients' quality of life and decrease medical costs.

The two main problems instigating a frequent need for revision surgeries after TSA are glenoid implant aseptic loosening followed by glenohumeral (GH) joint instability [2]. Aseptic loosening of the glenoid component is mainly associated with cyclic off-center GH joint loading with subluxation indexes greater than 5% posteriorly or anteriorly [3]. Glenohumeral subluxation is defined by the displacement of the humeral head relative to a centered position in the glenoid cavity [3], or more recently, to its position with respect to Friedman's scapular axis, termed scapulohumeral subluxation [4]. In the present study, due to the lack of an actual scapula in the robot, we used the GH definition of subluxation. Humeral head subluxation is usually measured as the eccentricity of the humeral head center relative to the midpoint of the glenoid cavity [37]. According to Walch's classification, osteoarthritic glenoids are labeled A to D depending on the level of static subluxation [3,5]. This two-dimensional measurement of the humeral head subluxation has been widely used. Recently, humeral head subluxation was measured relative to the scapula, first in two-dimensional [6], and then extended in 3D [4,7]. Subluxation can occur in any orientation, and may or may not be associated with rotator cuff tendon tears or osteoarthritis [8]. Rotator cuff muscle degeneration may induce joint instability and eventually asymmetric glenoid loading after anatomic TSA [911].

Over the last 20 years, numerical models have been developed to study the shoulder joint and its stability [1214]. Glenohumeral instability is generally evaluated by constraining the load and estimating GH reaction forces [15]. However, most of these models cannot quantify GH translations. To the best of our knowledge, there are only few studies [1620] that account for the GH translation in numerical modeling of shoulder stability. These numerical predictions are however limited by variations in glenoid implant deformation as well as the absence of stiction and friction.

The limitations of numerical modeling and the difficulties of in vivo measurements have led to in silico research with mechanical or robotic simulators. Commercial simulators or multistation shoulder joint simulators are used for wear simulation [21]. These simulators2 are able to reproduce a wide range of motions while applying realistic forces. However, such systems were designed for testing prostheses under stable conditions where it is not possible to push the prosthesis toward dislocation, i.e., an excessive translation of the humeral implant over the glenoid implant.

Several machines were built to apply physiologically relevant forces on shoulder prostheses to study GH stability, implant wear and aseptic loosening, or to evaluate the load and translations which result in GH subluxation [2123]. Favre et al. [24] designed a similar simulator with the ability to impose an incident angle on the humeral shaft to study the stability of reverse TSA and how to best position the implant to prevent dislocation. A mechanical simulator was also used with cadaveric shoulders to study the radial mismatch effect on subluxation load force [25] and translation after applying displacement forces on the deltoid and rotator cuff muscles of cadaveric samples [26]. Moreover, the contribution of the deltoid muscle to subluxation was also simulated, while varying the force levels (from 0 to 50 N), and the capsule condition (healthy, vented, and Bankart lesion) [27].

Even though all those robotic simulators can contribute to a better understanding of the shoulder function, none are able to provide a fully controlled and physiologically relevant simulation of GH instability after anatomic TSA. Cadaver-based experiments are unable to reproduce force and movement patterns of the GH joint. To address these issues, few bio-mimetic robots [2830] were built with modified structures to avoid experiencing joint instability. Moreover, due to their high structural complexity their control is challenging and reproducing the internal force patterns of an anatomical human shoulder while maintaining controlled movements would be complex and costly.

Fujie et al. [31] proposed to use actuators orthogonally placed around a diarthrodial joint, in order to have simpler control schemes and an improved accuracy during their simulations. Combining their simulator with cadaveric joints, they were able to evaluate the force exerted by most of the ligaments of the glenohumeral capsule during different levels of arm abduction [32]. However, this simulator was demonstrated to work only with low loads (200 N), whereas vivo measurements [33] displayed larger loads, raising beyond 500 N in most cases.

One of the main outcomes of a robotic simulator is to provide the surgeon with preoperative information for better TSA. Among different surgical features, glenoid implant orientation has already been proposed to balance potential eccentric loadings [3436]; however, there are currently no tools to determine if one orientation is more stable than another. In this study, to model and quantify prosthetic GH instability and dislocation, we aimed at developing a GH joint robotic simulator capable of controlling joint forces while measuring humeral head translations over the glenoid cavity in stable and unstable conditions by changing GH orientation. Different tests were performed with the robot to evaluate both its static and dynamic performances, its effectiveness in controlling physiological GH forces and to measure GH translations in normal and subluxation/dislocation conditions by changing the glenoid implant orientation.

Materials and Methods

Mechanical Structure and Actuation Design.

There is a large number of muscles of different sizes acting on the shoulder. Most large muscles can be split into subgroups of muscle fibers with similar functions. However, building a robotic simulator with a dozen of actuators pulling on strings to replicate the natural process is impractical. Moreover, we were interested in the measurement of GH subluxation, i.e., displacement due to the net force acting on the prosthesis. Therefore, our robot had to work directly with the net forces exerted by the combination of these muscles on the prosthesis. Consequently, the number of actuators and mechanical complexity were also reduced.

Usually, the referential frames of the humerus and scapula are defined following the International Society of Biomechanics standard [37]. However, in this study, the referential frames were slightly different in order to express directly the motions of the prosthetic components by the simulator measures. We considered 5 degrees-of-freedom (DoF) for the prosthetic GH joint, oriented with respect to the prosthetic humeral head: three translations (along X: anteroposterior; along Y: inferior–superior; and along Z: axial or mediolateral, with XY plane being parallel to the planar surface lying at the back of the metallic hemisphere, and Z being perpendicular to XY plane) and two rotations (internal–external α (around Y) and abduction–adduction β (around X)), applied sequentially (first α, second β), as shown in Fig. 1(a). By considering the prosthetic humeral head as perfectly spherical, we assumed its rotations about the axis of the glenoid implant had no effect on the position of the humeral head with respect to the scapula or the geometry of the joint. Therefore, this rotation was not simulated. The three forces that the humeral head exerts on the glenoid implant were actuated along the three axes (X, Y, Z). As shown in Fig. 1(b), the simulator presented rotated but equivalent axes with respect to the anatomical ones. The forces were expressed in the referential system of the prosthetic humeral head, and the humeral rotations were replicated by an equivalent reversed rotation of the glenoid implant. The (α = 0 deg, β = 0 deg) coordinate indicated the configuration at which the axis of the glenoid implant was aligned with the axis of the humeral head.

The robot was designed and simulated using solidworks (SOLIDWORKS®) (Fig. 1(b)). This process led to a final assembly of 177 components to form the robot as shown in Fig. 1(c).

Sensors and Actuators.

The axial compression was provided by an MTS Bionix® (MTS Systems Corporation, Eden Prairie, MN) load unit (dynamic and static load capacity of ±15 kN), which was completed by two smaller hydraulic cylinders (Custom Actuator Products, Inc., Plymouth, MN, (CAP) model: AA3/4X3-1-3-4M6(3)-1D; maximum compression 5.8 kN, maximum tension 4.4 kN) to account for the anterior–posterior and inferior–superior force components. These three hydraulic actuators (Hx, Hy, Hz) were equipped with position and force sensors. The position was measured through an embedded resistive sensor. Both translations are transmitted to the glenoid joint using four ball bearing rollers (Schneeberger AG, Roggwil, Switzerland, Wagen MNNL 12-G3) mounted on two linear rails (Schneeberger AG, Roggwil, Switzerland, Schiene MN 12-370-G3-V0). The precision for position measurement was of 25.4 μm.

In order to maintain the glenoid orientation even when the humeral head is applying a high load on the glenoid rim, strong rotary motors were needed. Considering that the forces should not exceed the most extreme cases found with the instrumented prosthesis [33] of 180% bodyweight, with an assumed bodyweight of 100 kg, the force should not exceed 1.8 kN. Placing such a force on the edge of the glenoid prosthesis would, therefore, generate a torque of 1.8 kN × 2.5 cm = 45 N·m. For dynamic simulations, it was also assumed that the subject did not exceed speeds of 30 rpm (half a revolution per second). To fulfill these constraints, two identical electrical brushed DC motors (RE50, 200 W, Maxon Motor AG, Sachseln, Switzerland) were chosen (Eα, Eβ). Both motors were customized with a planetary reducer (1:74) and a transmission belt, further reducing the speed by a ratio 1:2.4. This allowed the motor to develop moments up to 45 N·m. With this level of reduction, the final rotation speed was still adequate, with 31 rpm in the free rotation (theoretical value).

Eα and Eβ were equipped with a 500-impulsion encoder on the motor shaft. Since a turn of the prosthesis corresponded (due to the transmission system) to 177.6 turns of the motor shaft, it was equivalent to 355,200 impulsions (4 × 500 quadcounts × 74 × 2.4 tours after transmission system) and therefore a theoretical resolution of 0.001 deg. Nonetheless, the errors due to internal contact motions between all the components of the transmission chain were factored in, reducing this theoretical precision.

Controller.

Hx, Hy, and Hz were controlled through MTS proprietary software (FlexTest 793.00) using a proportional-integral derivative controller with feedforward (FF) compensatory term (PID-FF). During most tests the actuators were used in displacement control mode to place the humeral head 1 cm above the center of the glenoid component. Then, the axial actuator Hz was switched to force control with a command of 10 N to push at the center of the glenoid implant. Next, the simulation started and all hydraulic actuators were switched to force control in order to replicate the internal 3D force of the simulated subject. The range of the Hx and Hy was programmed to keep the glenoid implant within [−17.1; 21.1] mm and [−20.1; 32.1] mm respectively which was enough to study the stability of the implant.

The force control PID gains were manually fine-tuned to obtain a settling time less than 0.2 s and critically damped or overdamped, but close to critically damped behavior when tested with a number of control commands from different initial states. Two FF gains were added to improve the tracking. The following gains obtained for different actuators control; axial actuator: P: 30; I: 5; D: 0.1; F: 0.5; F: 0.5; inferior–superior actuator: P: 20; I: 5; D: 0.1; F: 0.3; F: 0.4; anterior–superior actuator: P: 20; I: 5; D: 0.1; F: 0.3; F: 0.4.

The rotary motors Eα and Eβ were position-controlled using a customized software developed in LabVIEW 2015 version 15.0f2 (National Instruments, Austin, TX). The control was done with two PIDs, using the gains: P: 271; I: 165; D: 1417 and P: 688; I: 1477; D: 1565 for the rotations about the inferior–superior axis (angle α) and the anterior–posterior axis (angle β), respectively. To avoid oscillatory behaviors the motor speeds were limited to a maximum value of 4000 rpm on the motor shaft, allowing for the prosthesis to rotate at top speeds of 22.5 rpm (135 deg/s) on the shaft of the glenoid implant. The maximum acceleration and deceleration of the motors were limited to 10,000 rpm/s on the motor shaft (337.8 deg/s2 on the shaft of the glenoid implant). To avoid internal impacts within different components of the simulator the Eα and Eβ was limited to ±40 deg.

The control interface (Fig. 2) offered several advantages: (i) correction of the homing offset; (ii) recording the angular value of the glenoid shaft in an external file for further analysis; and (iii) ability to reconfigure the controller while running in order to reproduce a complex motion sequence.

For practical reasons, the control of the hydraulic actuators was decoupled from the control of the electric motors and managed by two different computers and different controllers (Fig. 3). On both setups, the computers sent target positions or forces to the controllers, as well as the control parameters (PID-FF/PID gains). Then, the controllers ran the control loop with the actuators at 1 kHz frequency.

General Performance Evaluation.

The robustness of the robot's control was assessed through the ability to replicate a step response and maintain a specified position under varying torques. For the step response, the hydraulic actuators (Hx, Hy, Hz) were evaluated independently through the application of a preload of 10 N, followed by steps of different amplitudes (±50 N, ±100 N, ±150 N), every time returning to 10 N before applying the next step. The ability of the rotatory motors (Eα, Eβ) to maintain a specified position under varying torques was tested. After applying a short preloading of 0.1 N·m on the glenoid implant, larger torques were applied as a sequence of forces with magnitudes of (±0.5 N·m, ±1 N·m, ±1.5 N·m), respectively (every time returning to 0.1 N·m before applying the next step). These torques were obtained by using similar forces (±50 N, ±100 N, ±150 N) and preloading of 10 N applied at ±0.01 m of the glenoid implant center. The prosthesis rotation caused by these sudden torques was recorded by the motor's encoders.

Since the transmission chain between the rotatory motors and the glenoid implant degrades the angular measurement accuracy, the latter was concurrently tested against a reference system: the motion-capture system VICON (Vicon Motion Systems, Oxford, UK). This test was performed by comparing the angular command value with the value measured on the platform supporting the glenoid implant through a set of VICON markers. The difference (i.e., the angular accuracy of the system) was tested for static angles with all the 81 combinations of motors' rotation between −40 deg and +40 deg by steps of 10 deg.

Standardized Test for Dislocation Force Estimation.

The ASTM F2028-14 standardized test [38] was applied on the AEQUALIS™ PERFORM M35 pegged glenoid implant (Tornier-Wright Medical, Montbonnot-Saint-Martin, France) to measure how much an anatomical glenoid component rocks or pivots following cyclic displacements of the humeral implant, here the AEQUALIS™ Humeral Head (Φ = 46 mm, H = 17 mm, Ecc = 1.5 mm, Type = CoCr, Tornier-Wright Medical, Montbonnot-Saint-Martin, France). The first part of the test consisted of quantifying the magnitude of the lateral force (Fx, Fy) that could cause prosthetic dislocation. Dislocation was defined as the case where the humeral head left the glenoid cavity and slid away from the glenoid implant.

In standardized conditions, the axis of the glenoid implant and the humeral head component had to be aligned (α = β = 0 deg). The procedure was as follows:

  • application of an axial force of 750 N;

  • shifting the humeral head laterally until dislocation;

  • the force needed to cause the luxation was then retained as dislocation force.

To avoid mixing the effects of the robot's inertia with the dislocation force in our simulator shifting, the humeral head sideways was replaced by the application of a slowly increasing force until the center of the humeral head passed over the edge of the glenoid implant.

This protocol was repeated three times to test for the anterior, superior, and inferior directions of dislocation. Since the prosthesis is symmetric about its inferior–superior axis, the force associated with posterior dislocation was assumed to be the same as the anterior one.

Simulation With Realistic Forces.

Three series of tests were performed to assess the simulator performance in reproducing shoulder contact force patterns and joint translations. First, a pattern of 3D joint contact forces as recorded by in vivo instrumented prosthesis (Orthoload patient S1R_300605_1_20 [33]) during a countered external rotation of the arm with no humerus movement was modeled using Fourier series of order 20. Then, the patterns were fed to the PID-FF controller and reproduced by the simulator. Force tracking performance was evaluated using the embedded force sensors. During this test, the unconstrained displacements of the humeral head over the glenoid cavity were measured using the linear resistance transducers of Eα and Eβ actuators. The first test was performed at the arbitrary orientation α = 0 and β = 0. However, the test in the Orthoload database has been performed in a posture close to anatomical position, but no information about GH orientation was available.

Therefore, in the second test, the values of α and β were measured from a set of 11 TSA patients using postoperative shoulder computed tomography scans performed in the anatomical position. Approval from the institutional ethics committee was obtained (CER-VD protocol 395/15), and all patients gave written informed consent. Based on these measurements (α: 41.7±7.3 deg and β: –10.2±17.6 δεγ), the GH was set to α = 40 deg and β = −10 deg.

In the third test, we checked the possibility to detect dislocation by changing GH orientation. For this purpose, five samples of force data from the Orthoload dataset were selected and used in a quasi-static test where for each force, GH orientation was changed from (0 deg, 0 deg) to (αstable, βstable) corresponding the dislocation or transducer range. A dislocation was detected when the estimated point of contact of the humeral head reached out of the glenoid rim, therefore switching from a stable equilibrium to an unstable one.

Results

Dynamic Performance.

In Fig. 4, the step responses of the three linear actuators are presented. Results showed that transient errors lower than 1% of the command position could be reached in less than a second of settlement time (see Appendix  A, Table 1). As shown in Fig. 4, no overshoot or oscillatory behaviors were observed in any condition, further validating this controller for the use of static simulations.

Static Performance.

In addition to the linear actuators, the rotatory motors were evaluated (Appendix  B, Tables 2 and 3). The steady-state errors were consistently low, with both the mean and median in the order of 0.1 deg for α and 0.5 deg for β.

The ability of the robot to maintain a requested angle independent from the application of external moments of force is an important characteristic of the system. No perturbation was able to significantly alter the angular position (Appendix  B, Table 4), with angle variations never larger than 0.005 deg.

Standardized Test for Dislocation Force Estimation.

Under a compressive force of 750 N, horizontal forces of 1300 N and 1250 N were necessary to cause prosthetic dislocation in the anterior–posterior and superior directions, respectively (Fig. 5(a)). Aiming to induce a dislocation in the inferior direction, forces up to 1750 N were applied but no dislocation was observed. The application of these forces over the rim of the glenoid implant also caused large nonreversible deformations of the polyethylene (Fig. 5(b)).

Simulation With Realistic Forces.

Dynamic test. The robot was able to reproduce the requested pattern in real-time with a coefficient of correlation (R) of more than 0.98 and a root-mean-square error (RMSE) of 6.2 N for the Hz actuator and less than 5 N for the Hx and Hy actuators (Fig. 6(a)). Figure 6(b) shows the GH translation of the humeral head over the glenoid cavity for [α = 0 deg; β = 0 deg]. Using more realistic GH orientations of [α = −10 deg; β = 40 deg] still resulted in a clean control of the forces (R > 0.95, RMSE < 11.5 N, Fig. 7(a)) and GH translations of less than 3.0 mm (Fig. 7(b)). In both situations the prosthesis had a stable behavior. The range of translations were [−0.1 mm; 1.25 mm] for [α = 0 deg; β = 0 deg] and [−0.1 mm; 3.0 mm] for [α = −10 deg; β = 40 deg].

Quasi-static test. The limit of stability (αstable, βstable) of GH orientations during the application of realistic force was explored for five static sample forces extracted at a regular sampling interval from the previous force patterns (Fig. 6(a)): F1(−7.9, −14.9, −42.0), F2(−21.2, −39.7, −93.6), F3(−88.4, −68.4, −238.9), F4(−26.6, −2.0, −57.5), F5(−4.2, −0.5, −21.3) N. For each of these forces, GH orientation was changed while keeping one or the other angle (i.e., α or β) at zero degrees. The range of stable angle found for every combination is reported in Table 5. In general, αstable was in the range of [−40 deg; +40 deg] and βstable within [−39 deg; +38 deg], which was also close to the limit of the actuators (Appendix  C, Table 5).

Discussion

A 5DoF robotic simulator was designed and built to model GH instability. The system was able to reproduce the internal net force of the joint for 3D forces up to 2 kN, which are sufficient to reproduce most activities of daily living of the shoulder. Moreover, the simulator was able to control the rotations about the inferosuperior and anteroposterior axes. The mediolateral (or axial) axis was neglected as equivalent to rotations around the centerline of a perfectly hemispheric prosthetic humeral head. As far as linear motions are concerned, the simulator was able to test the stability of an anatomic GH implant composed of a humeral metallic (CoCr) head and a polyethylene glenoid implant when applying realistic force and replicate GH possible dislocation when some particular combinations of orientations and trajectories were set.

Using three hydraulic actuators, the triaxial forces could be controlled with a settling time (within 1% error) of 0.6 s and translation could be measured with a high precision (25.4 μm), which is quite enough to simulate shoulder stability in most activity of daily life. Testing for the effective angular accuracy of the simulator against a reference system demonstrated expected errors less than 0.5 deg, even in the presence of external perturbations. Hence, this resulted in reliable control of the simulated GH angles.

Compared to existing simulators, this novel simulator used a set of orthonormal actuators, as suggested by Ref. [31], but in addition had the ability to generate actuated rotations over two axis, which were not produced with some other robotic simulators [10,21,22]. Moreover, unlike existing simulators [24,32] where the force was limited (e.g., to 200 N), it was possible to produce enough load on the prosthesis (e.g., up to 2 kN) to simulate situations found in diverse activities of daily living. Actually, the force range of the proposed simulator fit the same range as observed in real patients [33] allowing to simulate better activities of daily living.

Ideally, the robotic simulations should be compared to actual situation measured with real subjects. Due to difficulty of measuring GH forces or translations in vivo a direct comparison is practically impossible. Therefore, we designed several tests to verify if the outcomes of the simulator are meaningful and consistent in extreme situations leading to dislocation and in realistic movement where shoulder stability is expected. The first test as defined by ASTM F2028-14 [38] aimed at determining the dislocation force (minimum force needed to push the humeral head out of the glenoid rim) while maintaining the joint under a constant axial load of 750 N. It also aimed to determine the extent of the robotic simulator achievement of the similar results as those of a wear test machine used by shoulder prosthesis manufacturers. It measured higher amplitude of force, with 1250 N and 1750 N for superior and inferior dislocation, compared to the measurements of Tornier-Wright Medical which were 351.1 N and 442.3 N, respectively [39]. The reasons for this difference may be related to a stiffer support for the prosthesis (polyamide 2200 in our case versus a cemented block of polyurethane foam in the case of Tornier-Wright Medical), allowing for less compression under the edge of the glenoid implant. Moreover, in the case of Tornier-Wright Medical, AEQUALIS™ PERFORM glenoid component had a 5 mm larger curvature radius (keeled M40 glenoid) than us (keeled M35 glenoid). More trials with different support materials are needed to point out the potential impact of the quality of the support material under the glenoid implant on joint stability.

In the second and third tests, a force-tracking task was executed at natural speed with realistic data. An excellent performance (RMSE < 6 N, R2 > 0.98 for all actuators) was obtained, indicating that the motor control is reliable in these conditions. Moreover, this test allowed us to measure GH translations at an arbitrary position [α = 0 deg; β = 0 deg] and a realistic position [α = −10 deg; β = 40 deg]. The measured translations were small and close to the center of the glenoid (less than 1.25 mm at α = 0 and β = 0 and less than 3.0 mm at α = −10 deg and β = 40 deg). As expected in the case of a stable shoulder joint, the results were consistently stable when realistic forces and GH orientation were applied.

In the third test, the joint was pushed to the extreme values of GH orientation to determine possible dislocations. The robotic simulator was able to replicate dislocation situations, showing that the choice of the GH angles, which are underreported in the literature, play an important role in GH translations. Even though more tests will be necessary to draw a definitive conclusion, this result puts forward the importance of choosing correctly the version and inclination angle of the glenoid implant to maintain joint stability. For this reason, a patient-specific set of GH forces and angles will be necessary for future simulations.

One of the main applications of this robotic simulator is to evaluate the importance of glenoid implant orientation to better balance potential eccentric loadings in a subject specific case. For this purpose, a customized numerical patient-specific simulator for the prediction of internal forces [20] may be coupled with the robotic simulator for the overall predictions of implant stability before surgery. This robot may also become useful for other applications, such as simulation of the causes of GH subluxation/dislocation or the design of new prostheses by evaluation of the shoulder stability behavior and tuning of relevant parameters used for the design purpose.

Conclusion

A novel 5DoFs robotic simulator for the modeling of the GH joint was designed and realized. The simulator was able to control the net forces and orientations of a prosthetic GH joint and measure accurately the GH translation associated with prosthesis stability. The simulator controlled and reproduced realistic force patterns derived from in vivo measurements. The results open new possibilities to study the impact of different GH angles on joint stability and to measure GH translations resulting from the application of specific GH contact forces and angles. Combined with a numeric simulator, this robotic model could have the potential to be used as a tool to improve the surgical planning and outcome in TSA, as well as the prosthetic design.

Acknowledgment

The authors would like to thank Pascal Morel for his valuable help in the design of mechanical components. Additionally, the authors would like to thank Tornier-Wright Medical, for donation of all shoulder prosthetic implants used in this study.

Funding Data

  • Swiss National Science Foundation (SNSF) (Grant No. CR32I2_162766; Funder ID: 10.13039/501100001711).

  • Lausanne Orthopedic Research Foundation (LORF).

Nomenclature

     
  • CAP =

    custom actuator products

  •  
  • DoF =

    degrees-of-freedom

  •  
  • FF =

    feedforward (loop)

  •  
  • GH =

    glenohumeral

  •  
  • PID =

    proportional-integral derivative (control loop)

  •  
  • PID-FF =

    combined use of PID and FF

  •  
  • RMSE =

    root-mean-square error

  •  
  • TSA =

    total shoulder arthroplasty

Footnotes

Appendix

Step Force Responses of Hydraulic Actuators

Position Robustness of Electrical Actuators

Stability Ranges of Glenohumeral Rotation
in Quasi-Static Test

References

References
1.
Day
,
J. S.
,
Lau
,
E.
,
Ong
,
K. L.
,
Williams
,
G. R.
,
Ramsey
,
M. L.
, and
Kurtz
,
S. M.
,
2010
, “
Prevalence and Projections of Total Shoulder and Elbow Arthroplasty in the United States to 2015
,”
J. Shoulder Elb. Surg.
,
19
(
8
), pp.
1115
1120
.10.1016/j.jse.2010.02.009
2.
Terrier
,
A.
,
Ramondetti
,
S.
,
Merlini
,
F.
,
Pioletti
,
D. D.
, and
Farron
,
A.
,
2010
, “
Biomechanical Consequences of Humeral Component Malpositioning After Anatomical Total Shoulder Arthroplasty
,”
J. Shoulder Elbow Surg.
,
19
(
8
), pp.
1184
1190
.10.1016/j.jse.2010.06.006
3.
Walch
,
G.
,
Badet
,
R.
,
Boulahia
,
A.
, and
Khoury
,
A.
,
1999
, “
Morphologic Study of the Glenoid in Primary Glenohumeral Osteoarthritis
,”
J. Arthroplast.
,
14
(
6
), pp.
756
760
.10.1016/S0883-5403(99)90232-2
4.
Terrier
,
A.
,
Ston
,
J.
, and
Farron
,
A.
,
2015
, “
Importance of a Three-Dimensional Measure of Humeral Head Subluxation in Osteoarthritic Shoulders
,”
J. Shoulder Elb. Surg.
,
24
(
2
), pp.
295
301
.10.1016/j.jse.2014.05.027
5.
Bercik
,
M. J.
,
Kruse
,
K.
,
Yalizis
,
M.
,
Gauci
,
M. O.
,
Chaoui
,
J.
, and
Walch
,
G.
,
2016
, “
A Modification to the Walch Classification of the Glenoid in Primary Glenohumeral Osteoarthritis Using Three-Dimensional Imaging
,”
J. Shoulder Elb. Surg.
,
25
(
10
), pp.
1601
1606
.10.1016/j.jse.2016.03.010
6.
Kidder
,
J. F.
,
Rouleau
,
D.
,
Pons-Villanueva
,
J.
,
Dynamidis
,
S.
,
Defranco
,
M.
, and
Walch
,
G.
,
2010
, “
Humeral Head Posterior Subluxation on CT Scan: Validation and Comparison of 2 Methods of Measurement
,”
Tech. Shoulder Elb. Surg.
,
11
(
3
), pp.
72
76
.10.1097/BTE.0b013e3181e5d742
7.
Sabesan
,
V. J.
,
Callanan
,
M.
,
Youderian
,
A.
, and
Iannotti
,
J. P.
,
2014
, “
3D CT Assessment of the Relationship Between Humeral Head Alignment and Glenoid Retroversion in Glenohumeral Osteoarthritis
,”
J. Bone Jt. Surg. Am.
,
96
(
8
), p.
64
.10.2106/JBJS.L.00856
8.
Gerber
,
C.
, and
Nyffeler
,
R. W.
,
2002
, “
Classification of Glenohumeral Joint Instability
,”
Clin. Orthop. Relat. Res.
,
400
, pp.
65
76
.10.1097/00003086-200207000-00009
9.
Franklin
,
J. L.
,
Barrett
,
W. P.
,
Jackins
,
S. E.
, and
Matsen
,
F. A.
,
1988
, “
Glenoid Loosening in Total Shoulder Arthroplasty. Association With Rotator Cuff Deficiency
,”
J. Arthroplast.
,
3
(
1
), pp.
39
46
.10.1016/S0883-5403(88)80051-2
10.
Terrier
,
A.
,
Ston
,
J.
,
Dewarrat
,
A.
,
Becce
,
F.
, and
Farron
,
A.
,
2017
, “
A Semi-Automated Quantitative CT Method for Measuring Rotator Cuff Muscle Degeneration in Shoulders With Primary Osteoarthritis
,”
Orthop. Traumatol. Surg. Res.
,
103
(
2
), pp.
151
157
.10.1016/j.otsr.2016.12.006
11.
Wirth
,
M. A.
, and
Rockwood
,
C. A. J.
,
1996
, “
Complications of Total Shoulder-Replacement Arthroplasty
,”
J. Bone Jt. Surg. Am.
,
78
(
4
), pp.
603
616
.10.2106/00004623-199604000-00018
12.
Prinold
,
J. A.
,
Masjedi
,
M.
,
Johnson
,
G. R.
, and
Bull
,
A. M.
,
2013
, “
Musculoskeletal Shoulder Models: A Technical Review and Proposals for Research Foci
,”
Proc. Inst. Mech. Eng., Part H
,
227
(
10
), pp.
1041
1057
.10.1177/0954411913492303
13.
Quental
,
C.
,
Folgado
,
J.
,
Ambrósio
,
J.
, and
Monteiro
,
J.
,
2013
, “
Critical Analysis of Musculoskeletal Modelling Complexity in Multibody Biomechanical Models of the Upper Limb
,”
Comput. Methods Biomech. Biomed. Eng.
,
18
(
7
), pp.
37
41
.10.1080/10255842.2013.845879
14.
Charlton
,
I. W.
, and
Johnson
,
G. R.
,
2006
, “
A Model for the Prediction of the Forces at the Glenohumeral Joint
,”
Proc. Inst. Mech. Eng., Part H
,
220
(
8
), pp.
801
812
.10.1243/09544119JEIM147
15.
Helm
,
F. C. T. V D.
,
1994
, “
A Finite Element Musculoskeletal Model of the Shoulder Mechanism
,”
J. Biomech.
,
27
(
5
), pp.
551
569
.10.1016/0021-9290(94)90065-5
16.
Sins
,
L.
,
Tétreault
,
P.
,
Hagemeister
,
N.
, and
Nuño
,
N.
,
2015
, “
Adaptation of the AnyBodyTM Musculoskeletal Shoulder Model to the Nonconforming Total Shoulder Arthroplasty Context
,”
ASME J. Biomech. Eng.
,
137
(
10
), p.
101006
.10.1115/1.4031330
17.
Quental
,
C.
,
Folgado
,
J.
,
Ambrósio
,
J.
, and
Monteiro
,
J.
,
2016
, “
A New Shoulder Model With a Biologically Inspired Glenohumeral Joint
,”
Medical Eng. Phys.
,
38
(
9
), pp.
969
977
.10.1016/j.medengphy.2016.06.012
18.
Terrier
,
A.
,
Larrea
,
X.
,
Malfroy Camine
,
V.
,
Pioletti
,
D. P.
, and
Farron
,
A.
,
2013
, “
Importance of the Subscapularis Muscle After Total Shoulder Arthroplasty
,”
Clin. Biomech.
,
28
(
2
), pp.
146
150
.10.1016/j.clinbiomech.2012.11.010
19.
Favre
,
P.
,
Senteler
,
M.
,
Hipp
,
J.
,
Scherrer
,
S.
,
Gerber
,
C.
, and
Snedeker
,
J. G.
,
2012
, “
An Integrated Model of Active Glenohumeral Stability
,”
J. Biomech.
,
45
(
13
), pp.
2248
2255
.10.1016/j.jbiomech.2012.06.010
20.
Sarshari
,
E.
,
Farron
,
A.
,
Terrier
,
A.
,
Pioletti
,
D.
, and
Mullhaupt
,
P.
,
2017
, “
A Simulation Framework for Humeral Head Translations
,”
Med. Eng. Phys.
,
49
, pp.
140
147
.10.1016/j.medengphy.2017.08.013
21.
Smith
,
S. L.
,
Li
,
L.
,
Johnson
,
G.
, and
Joyce
,
T.
,
2012
, “
Commissioning of a Multi-Station Shoulder Joint Wear Simulator
,” Annual Conference, British Orthopaedic Research Society.
22.
Gregory
,
T.
,
Hansen
,
U.
,
Taillieu
,
F.
,
Baring
,
T.
,
Brassart
,
N.
,
Mutchler
,
C.
,
Amis
,
A.
,
Augereau
,
B.
, and
Emery
,
R.
,
2009
, “
Glenoid Loosening After Total Shoulder Arthroplasty: An In Vitro CT-Scan Study
,”
J. Orthop. Res.
,
27
(
12
), pp.
1589
1595
.10.1002/jor.20912
23.
Virani
,
N. A.
,
Harman
,
M.
,
Li
,
K.
,
Levy
,
J.
,
Pupello
,
D. R.
, and
Frankle
,
M. A.
,
2008
, “
In Vitro and Finite Element Analysis of Glenoid Bone/Baseplate Interaction in the Reverse Shoulder Design
,”
J. Shoulder Elbow Surg.
,
17
(
3
), pp.
509
521
.10.1016/j.jse.2007.11.003
24.
Favre
,
P.
,
Sussmann
,
P. S.
, and
Gerber
,
C.
,
2010
, “
The Effect of Component Positioning on Intrinsic Stability of the Reverse Shoulder Arthroplasty
,”
J. Shoulder Elbow Surg.
,
19
(
4
), pp.
550
556
.10.1016/j.jse.2009.11.044
25.
Karduna
,
A. R.
,
Williams
,
G. R.
,
Williams
,
J. L.
, and
Iannotti
,
J. P.
,
1997
, “
Joint Stability After Total Shoulder Arthroplasty in a Cadaver Model
,”
J. Shoulder Elb. Surg.
,
6
(
6
), pp.
506
511
.10.1016/S1058-2746(97)90082-3
26.
Wuelker
,
N.
,
Korell
,
M.
, and
Thren
,
K.
,
1998
, “
Dynamic Glenohumeral Joint Stability
,”
J. Shoulder Elb. Surg.
,
7
(
1
), pp.
43
52
.10.1016/S1058-2746(98)90182-3
27.
Kido
,
T.
,
Itoi
,
E.
,
Lee
,
S.
,
Neale
,
P. G.
, and
An
,
K.-N.
,
2003
, “
Dynamic Stabilizing Function of the Deltoid Muscle in Shoulders With Anterior Instability
,”
Am. J. Sports Med.
,
31
(
3
), pp.
399
403
.10.1177/03635465030310031201
28.
Sodeyama
,
Y.
,
Nishino
,
T.
,
Namiki
,
Y.
,
Nakanishi
,
Y.
,
Mizuuchi
,
I.
, and
Inaba
,
M.
,
2008
, “
The Designs and Motions of a Shoulder Structure With a Spherical Thorax, Scapulas and Collarbones for Humanoid ‘Kojiro
,’”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), San Diego, CA, Sept. 22–26, pp.
1465
1470
.10.1109/IROS.2008.4651221
29.
Sodeyama
,
Y.
,
Yoshikai
,
T.
,
Nishino
,
T.
,
Mizuuchi
,
I.
, and
Inaba
,
M.
,
2007
, “
The Designs and Motions of a Shoulder Structure With a Wide Range of Movement Using Bladebone-Collarbone Structures
,”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Nice, France, Oct. 29–Nov. 2, pp.
3629
3634
.10.1109/IROS.2007.4399241
30.
Mizuuchi
,
I.
,
Tajima
,
R.
,
Yoshikai
,
T.
,
Sato
,
D.
,
Nagashima
,
K.
,
Inaba
,
M.
,
Kuniyoshi
,
Y.
, and
Inoue
,
H.
,
2002
, “
The Design and Control of the Flexible Spine of a Fully Tendon-Driven Humanoid ‘Kenta
,’”
IEEE/RSJ International Conference on Intelligent Robots and Systems
(
IROS
), Lausanne, Switzerland, Sept. 30–Oct. 4, pp.
2527
2532
.10.1109/IRDS.2002.1041649
31.
Fujie
,
H.
,
Mabuchi
,
K.
,
Woo
,
S. L. Y.
,
Livesay
,
G. A.
,
Shinji
,
A.
, and
Tsukamoto
,
Y.
,
1993
, “
The Use of Robotics Technology to Study Human Joint Kinematics: A New Methodology
,”
ASME J. Biomech. Eng.
,
115
(
3
), pp.
211
217
.10.1115/1.2895477
32.
Debski
,
R. E.
,
Yamakawa
,
S.
,
Musahl
,
V.
, and
Fujie
,
H.
,
2017
, “
Use of Robotic Manipulators to Study Diarthrodial Joint Function
,”
ASME J. Biomech. Eng.
,
139
(2), p. 021010.10.1115/1.4035644
33.
Bergmann
,
G.
,
2009
, “
Orthoload Database
,” Orthoload, Berlin, Germany, accessed Aug. 30, 2018, https://orthoload.com/database/
34.
Suárez
,
D. R.
,
van der Linden
,
J. C.
,
Valstar
,
E. R.
,
Broomans
,
P.
,
Poort
,
G.
,
Rozing
,
P. M.
, and
van Keulen
,
F.
,
2009
, “
Influence of the Positioning of a Cementless Glenoid Prosthesis on Its Interface Micromotions
,”
Proc. Inst. Mech. Eng., Part H
,
223
(
7
), pp.
795
804
.10.1243/09544119JEIM545
35.
Terrier
,
A.
,
Merlini
,
F.
,
Pioletti
,
D. P.
, and
Farron
,
A.
,
2009
, “
Total Shoulder Arthroplasty: Downward Inclination of the Glenoid Component to Balance Supraspinatus Deficiency
,”
J. Shoulder Elb. Surg.
,
18
(
3
), pp.
360
365
.10.1016/j.jse.2008.11.008
36.
Wong
,
A. S.
,
Gallo
,
L.
,
Kuhn
,
J. E.
,
Carpenter
,
J. E.
, and
Hughes
,
R. E.
,
2003
, “
The Effect of Glenoid Inclination on Superior Humeral Head Migration
,”
J. Shoulder Elb. Surg.
,
12
(
4
), pp.
360
364
.10.1016/S1058-2746(03)00026-0
37.
Wu
,
G.
,
van der Helm
,
F. C. T.
,
(DirkJan) Veeger
,
H. E. J.
,
Makhsous
,
M.
,
Van Roy
,
P.
,
Anglin
,
C.
,
Nagels
,
J.
,
Karduna
,
A. R.
,
McQuade
,
K.
,
Wang
,
X.
,
Werner
,
F. W.
, and
Buchholz
,
B.
,
2005
, “
ISB Recommendation on Definitions of Joint Coordinate Systems of Various Joints for the Reporting of Human Joint Motion—Part II: Shoulder, Elbow, Wrist and Hand
,”
J. Biomech.
,
38
(
5
), pp.
981
992
.10.1016/j.jbiomech.2004.05.042
38.
ASTM International
,
2014
, “
Standard Test Methods for Dynamic Evaluation of Glenoid Loosening or Disassociation
,” ASTM International, West Conshohocken, PA, Standard No. F2028-14.
39.
Tornier's_Test_Laboratory
,
2011
, “Subluxation and Loosening on Keeled Glenoid Component (RF/11640) (Following ASTM-F2028-08),” Tornier's_Test_Laboratory, Montbonnot-Saint-Martin, France, Report No. E1364-A.