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Research Papers

Use of Robotic Manipulators to Study Diarthrodial Joint Function OPEN ACCESS

[+] Author and Article Information
Richard E. Debski

Orthopaedic Robotics Laboratory,
Departments of Bioengineering
and Orthopaedic Surgery,
University of Pittsburgh,
408 Center for Bioengineering,
300 Technology Drive,
Pittsburgh, PA 15219
e-mail: genesis1@pitt.edu

Satoshi Yamakawa, Hiromichi Fujie

Tokyo Metropolitan University,
6-6 Asahigaoka, Hino,
Tokyo 191-0065, Japan

Volker Musahl

Orthopaedic Robotics Laboratory,
Departments of Orthopaedic Surgery
and Bioengineering,
University of Pittsburgh,
408 Center for Bioengineering,
300 Technology Drive,
Pittsburgh, PA 15219

1Corresponding author.

Manuscript received July 9, 2016; final manuscript received December 23, 2016; published online January 19, 2017. Assoc. Editor: Beth A. Winkelstein.

J Biomech Eng 139(2), 021010 (Jan 19, 2017) (7 pages) Paper No: BIO-16-1288; doi: 10.1115/1.4035644 History: Received July 09, 2016; Revised December 23, 2016

Diarthrodial joint function is mediated by a complex interaction between bones, ligaments, capsules, articular cartilage, and muscles. To gain a better understanding of injury mechanisms and to improve surgical procedures, an improved understanding of the structure and function of diarthrodial joints needs to be obtained. Thus, robotic testing systems have been developed to measure the resulting kinematics of diarthrodial joints as well as the in situ forces in ligaments and their replacement grafts in response to external loading conditions. These six degrees-of-freedom (DOF) testing systems can be controlled in either position or force modes to simulate physiological loading conditions or clinical exams. Recent advances allow kinematic, in situ force, and strain data to be measured continuously throughout the range of joint motion using velocity-impedance control, and in vivo kinematic data to be reproduced on cadaveric specimens to determine in situ forces during physiologic motions. The principle of superposition can also be used to determine the in situ forces carried by capsular tissue in the longitudinal direction after separation from the rest of the capsule as well as the interaction forces with the surrounding tissue. Finally, robotic testing systems can be used to simulate soft tissue injury mechanisms, and computational models can be validated using the kinematic and force data to help predict in vivo stresses and strains present in these tissues. The goal of these analyses is to help improve surgical repair procedures and postoperative rehabilitation protocols. In the future, more information is needed regarding the complex in vivo loads applied to diarthrodial joints during clinical exams and activities of daily living to serve as input to the robotic testing systems. Improving the capability to accurately reproduce in vivo kinematics with robotic testing systems should also be examined.

FIGURES IN THIS ARTICLE
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A complex interaction between bones, ligaments and capsules, articular cartilage, and muscles mediates the function of diarthrodial joints. Due to the interdependence of these structures, overall joint function can deteriorate due to injury or failure of any individual component. Ligaments and capsular tissues are particularly vulnerable, as they are subjected to frequent sprains and strains, and in many cases can be completely ruptured. For example, the annual frequency of injury to knee ligaments in the U.S. was estimated to be approximately 80/100,000 and is growing annually [14]. Anterior cruciate ligament (ACL) injuries alone have an annual incidence of 200,000 per year with a lifetime burden of $7.6 billion annually in the U.S. [5].

To gain a better understanding of injury mechanisms, improve surgical procedures, and design better postsurgical rehabilitation protocols, scientific knowledge on the biomechanics of diarthrodial joints and the function of the ligaments and other connective tissues can be helpful. Specifically, the kinematics of normal and surgically reconstructed diarthrodial joints in multiple degrees-of-freedom and the in situ forces experienced by ligaments and their replacement grafts have been a major interest [68]. To facilitate these objectives, robotic testing systems (coupling of a robotic manipulator with a universal force–moment sensor (UFS)) are frequently used [922]. These systems have been designed to measure joint kinematics and the in situ forces in the ligaments and their replacements using cadaveric diarthrodial joints. In vitro data for the major ligaments in diarthrodial joints in response to various external loading conditions combined with simulated muscle loads have also been obtained [8,2329]. The data are collected without constraining joint motion and attaching mechanical devices to soft tissues for force measurements. This testing system and methodology also have the potential to study the function of these ligaments and their replacement grafts during various in vivo activities.

In this article, the principles of joint kinematics and the in situ forces of individual ligaments as well as the latest advances with robotic testing systems will be described. Current applications of robotic testing systems to study knee kinematics and in situ forces of connective tissues throughout a continuous range of motion will also be discussed. In addition, robotic testing systems combined with optical tracking systems have been used to collect data on the strain within capsular tissue of both knees and shoulders. Furthermore, robotic testing systems have also been used to replay in vivo kinematics, yielding the possibility to measure in situ forces and strains present in the connective tissues during physiologic motion. This testing system in combination with appropriate computational models can help to gain data on the stress and strain in connective tissues in vivo, to examine the mechanisms of injury to the ligaments as well as to improve surgical procedures and rehabilitation protocols. Thus, improving patient outcomes.

With the combination of a robotic manipulator and a universal force and moment sensor (UFS), multi-axial force and position control can be used to apply loads and produce motions of diarthrodial joints in multiple degrees-of-freedom (DOF) [12,19,20,3033]. In addition, the robotic testing system can record the resulting 6DOF motions and then reproduce the identical path of motion in a ligament deficient or reconstructed specimen in order to apply the principle of superposition to determine the in situ forces in a ligament or other structures [18,30]. Since identical loading conditions are applied to the intact, ligament deficient, and reconstructed states of the same specimen, interspecimen variability can be minimized to increase the statistical power in each study. For example, the testing system can be used to quantitatively compare the magnitude and direction of in situ forces in intact ligaments with those in replacement grafts [34,35]. This enables investigators to determine the efficacy of reconstruction procedures in reproducing normal force transmission through the replacement graft. Throughout the remainder of this section, the knee will be used to illustrate the principles and use of robotic testing systems.

To understand the control of the robotic testing system, it is important to define the coordinate systems of the testing system: (1) end-effector coordinate system attached to the manipulator; (2) a sensor coordinate system fixed to the UFS; and (3) coordinate systems attached to the tibia and femur (Fig. 1). One rigid body (femur) is typically fixed to the base of the testing system and the other rigid body (tibia) fixed to the manipulator. The coordinate systems of the femur and tibia allow anatomical joint motion between the two rigid bodies to be defined.

For example, the joint motion at the knee is typically described using the Grood and Suntay motion description [36]. Briefly, the Grood and Suntay motion description defines the femoral coordinate system using the long axis of the femur, a flexion extension axis through the lateral collateral ligament (LCL) and the medial collateral ligament (MCL) insertion sites, and a third axis is defined as the cross product of the other two axes. The tibial coordinate system is defined by the long axis of the tibia, with the other axes coincident with the femoral coordinate system at full extension. To describe motion, flexion/extension rotation and medial/lateral displacement are taken about the femoral flexion axis, internal/external rotation and proximal/distal displacement are taken about the long axis of the tibia, and varus/valgus rotation and anterior/posterior movement are taken about a floating axis that is the cross product of the other two axes (Fig. 2).

To relate the forces and moments measured by the UFS to the forces present in the joint coordinate systems, Jacobian matrices are used [31,37]. The Jacobian matrix to relate the differential motion at the knee coordinate system to the coordinate system of the tibia is (J1), and the Jacobian matrix to relate the differential motion at the tibial coordinate system to the UFS is (J2) (Fig. 3). Therefore, the differential motion at the knee joint, dΘ, can be created by the differential motion at the UFS, dy, using the relationship of dy = J2 J1dΘ. Differentiation of this relationship by time provides the relationship of velocity at the joint and the UFS. The force and moment at the knee, F, were transformed from the force and moment measured at the UFS, Fs, using the relationship of F = −J1T J2TFs. With this information, the robotic testing system is able to move the knee through a series of positions or apply external loading conditions. Thus, a robotic testing system can be operated in two modes in each DOF of the knee, i.e., position control or force control mode.

For position control, the robotic testing system is asked to accurately reproduce joint positions that represent any sequence of positions defining a path of motion of a diarthrodial joint. The coordinate systems associated with the robotic testing system and the joint are used to move the knee through the paths of motion. This methodology takes advantage of the manipulators capabilities to precisely reproduce defined paths of motion.

To determine the in situ force in a ligament, the forces and moments at the joint with an intact ligament are measured during a recorded path of motion (F1) using position control. The ligament is subsequently transected, and the robotic testing system reproduces the previously recorded joint motion again in the ligament deficient knee. A new set of force data is obtained (F2). If the knee experiences identical conditions, the principle of superposition can be applied and the in situ force in the ligament is the vectorial difference in recorded forces (F = F1 − F2). The principle of superposition is satisfied as long as: (1) there is no interaction between the structures or the force in the structure is only dependent on the position of its bony attachments, (2) the bony tissue can be considered rigid relative to the ligaments, and (3) the positions of the bones are repeatable [18,30]. For capsular tissue, it is important to distinguish individual components of the capsular tissue by separation from each other in order to satisfy the principle of superposition. Thus, eliminating interaction between components. Once the tissues have been separated, subsequent cutting of the structures can be performed to determine the in situ force of the capsular regions in the longitudinal direction. The separation procedure determines the interaction forces between each region of the capsule [11,34].

For force control, a given external load or a set of desired forces and moments are applied to the joint via one of several methodologies and the resulting joint kinematics are recorded. Under stiffness force control, the resulting movement of the robotic manipulator is determined by comparing the current forces and moments measured by the UFS to the target, or desired, forces and moments. The robotic testing system is then instructed to perform a movement in order to achieve these target forces and moments. A movement to achieve target forces and moments is calculated by multiplying the inverse of the joint stiffness by the difference between the target forces and moments and the current forces and moments measured by the UFS. This iterative process allows the robotic testing system to move the knee through the appropriate motions such that a series of target forces and moments are achieved. Stiffness control uses simple algorithms to produce adequate joint motion reproduction, but the control is slow and unsmooth.

A method that utilizes velocity-impedance control has been implemented for robotic testing systems [38] and has been subsequently used with parallel robots/hexapods for spine testing [39,40]. This control strategy, originally developed in the field of robotics as “virtual compliance control,” compares the velocity of the manipulator via Jacobian matrices to the velocity of the joint [41]. Velocity-impedance control relies on velocity, acceleration, and displacement error to determine the applied forces and moments without having to make stepwise changes in position to target forces. The governing equation for velocity-impedance control is Display Formula

(1)[M]dv/dt+[K]dx+[C]v=F

where [M] is a virtual mass, dv/dt is the acceleration, [K] is the virtual stiffness, dx is the displacement error, [C] is the virtual viscosity, v is the velocity, and F is the applied force/moment to the joint. This equation can be reduced to a discrete expression shown below under the assumption that velocity change is relatively small and that effect of stiffness can be neglected Display Formula

(2)v=Δt[M]1F+Rv(R=[I]Δt[M]1[C])

Here, Δt represents the iterative cycle of control, and [I] represents a unit matrix. The coefficient, R, is the reference rate for determining the updated velocity. Based on the current velocity, v, the velocity in the next step (v′) can be calculated from Eq. (2). This method of control relies on the velocity of the robotic manipulator to accurately control forces during kinematic data collection in real time. Velocity-impedance control also allows for accurate force control while placing diarthrodial joints through their whole range of motion. This control method is simple, fast, and smooth.

All the force control methods can be used to apply an identical external load to a specimen in the intact, ligament deficient, and reconstructed states. Therefore, the differences in the resulting joint kinematics between these states can then be determined. These tests can be similar to clinical examinations used to diagnose ligament deficiency.

To illustrate the performance of each force control method, a stifle joint from an immature pig was fixed to the clamps of a robotic testing system (FRS2010, Technology Service, China, Japan). After the knee joint coordinate system [36] was established based on the anatomical landmarks of the insertion sites of medial collateral and lateral collateral ligaments [38], a step-function of 20 N of proximal force (joint compressive force) was input using velocity-impedance control mode to the knee at 30 deg of flexion, while the resultant force output was recorded. At this time, a variety of parameter sets of [M] and [C] ([R]) in Eq. (2) were commanded to the robotic testing system and the best set of parameters that results in approximately 20% of force overshoot was determined. The step-function test was then repeated in stiffness control mode while determining the best set of stiffness parameters that results in approximately 20% of force overshoot.

Differences were found between the temporal changes of the proximal force in response to the step-input (Fig. 4). In stiffness control, the best setting of [K] was 100 N/mm, and proximal force reached the prescribed value at approximately 0.4 s and fluctuated thereafter. In velocity-impedance control, the best setting of [M] and [R] was 0.056 kg and 25%, and proximal force reached the prescribed value at only 0.1 s and was constant afterward. These results suggest that velocity-impedance control is faster and more stable as compared with stiffness control in applying forces to the knee.

Traditional 6DOF robotic testing systems rely on modified, commercially available 6DOF manipulators in combination with a universal force–moment sensor [812,18,22,24,25,32,33,4245]. These robotic testing systems use a series of position regulated actuators in combination with a UFS to control forces/moments and displacements/rotations of a diarthrodial joint. These articulated manipulators were originally developed for industrial applications and suffer several limitations for the purpose of diarthrodial joint testing. The manipulators were designed to perform tasks in a large work space at very high speeds. One concern in the use of systems adapted from industrial robotic testing systems is that the position repeatability and stiffness are generally lower than other types of robotic testing systems such as orthogonal ones, due to their clamp-to-clamp compliance for mechanical tests. This becomes a concern when studying joint kinematics and forces because precise control and repeatability are required to determine ligament and other soft tissue function.

An orthogonal 6DOF robotic testing system was developed with two movable mechanisms [31] (Fig. 5). The first mechanism is connected to a fixation clamp via a universal force–moment sensor and consists of two translational (X, Z) and three rotational axes (U, V, W) in series. The second mechanism has one translational axis (Y) and another fixation point. Three translational axes are orthogonal to each other and each of the three rotation axes cross through one point. The translational axes are driven by AC servomotors with screw mechanisms, while the rotational axes are driven by AC servomotors with harmonic gear mechanisms. This system differs from the traditional robotic manipulators which have six serially linked rotational axes. This configuration increases the reliability and repeatability of motion reproduction.

Continuous Joint Loading.

A new method to apply consistent loads throughout the range of flexion has recently been reported and compared to applying loads at discrete flexion angles [46]. Previous research has utilized robotic testing systems to examine joint kinematics and in situ forces in response to loads applied at discrete flexion angles due to limitations of robotic control (static method), as well as to simulate static clinical tests such as the Lachman or Anterior-Drawer test [34,35,42,47,48]. Recently, studies have applied loads continuously throughout flexion, as some clinical exams such as the pivot shift rely on flexion under loading conditions (continuous flexion method) [29,49]. However, the joint kinematics resulting from each of these methods have not been directly compared. Therefore, a robotic testing system was used to compare kinematics and in situ forces of porcine knees between static and continuous loading methodologies. Both methods were found to be comparable in detecting significant differences (p < 0.05) between intact and ACL deficient knee states (Fig. 6). However, the continuous flexion method presents several advantages over the static method. Utilizing velocity-impedance control for the continuous testing method allows for greater control throughout the full range of motion and enabling robotic testing conditions such as a simulated pivot shift to be applied throughout a full flexion/extension cycle are two advantages. The continuous motion of the joint also enables more conditioning of the tissue to minimize viscoelastic effects during loading. Finally, collection of kinematic and/or in situ force data throughout all of flexion can occur, providing more insight into joint behavior throughout its whole range of motion.

Capsular Strain.

Quantification of the deformation of soft tissue structures is important to understand their function due to their complex geometry, nonhomogeneous properties, and wrapping around bony contours. Therefore, robotic testing systems have also been used in conjunction with motion capture systems in order to quantify strain in capsular tissues (shoulder and knee). The strain in the glenohumeral capsule was quantified during simulated clinical exams since the glenohumeral joint is the most commonly dislocated joint in the body [43,50,51]. Strain in the glenohumeral capsule was quantified by placing a grid of strain markers on the capsule (Fig. 7). A reference configuration was determined by inflating the capsule to minimize folds and wrinkles, and then, the location of strain markers was captured with a motion tracking system while simulating a clinical exam (external rotation at 60 deg of abduction). The maximum principle strain of each element created by four neighboring strain markers was determined at the centroid of each element, while the direction was determined at each node to determine the amount of deformation present in the capsule. The positions of the glenohumeral joint can also be reproduced to quantify the magnitudes of force transmitted by the capsule between the scapula and humerus. The previously described regions of the inferior glenohumeral ligament were not identified with a qualitative evaluation of the strain distribution pattern quantified for each specimen. Thus, the findings suggest that future studies should treat the inferior glenohumeral capsule as a continuous sheet of fibrous tissue.

Due to the recent interest in the anterolateral capsule of the knee and reports of a proposed anterolateral ligament, the deformation and forces in the anterolateral capsule of the knee were evaluated since capsule tissue can transmit forces in a multi-axial manner [5254]. Strain markers were placed onto the capsule to determine the strain distribution in the capsule in response to external loading conditions. A robotic testing system was used to place the knee under anterior loading (134 N), posterior loading (134 N), internal rotation torque (7 N·m), and external rotation torque (7 N·m) at 30, 60, and 90 deg of knee flexion. During the loading conditions, a motion capture system was used to track motion of the strain markers attached to the surface of the capsule (Fig. 7). The positions of the strain markers were compared between loaded conditions and a nonstrained reference configuration to determine the magnitude and direction of the maximum principal strain present in the midsubstance of the anterolateral capsule. Following measurement of strain, the capsule was separated from the LCL by three vertical cuts. This method allows for the determination of the interaction between capsular regions and the forces transmitted along the longitudinal direction of each region. The magnitude and direction of the maximum principal strain in the anterolateral capsule suggest that the anterolateral capsule does not function like a traditional ligament.

Reproduction of In Vivo Kinematics.

Knowledge of the forces in connective tissues during in vivo joint motion is important for the development of improved reconstruction procedures and rehabilitation protocols. Thus, three methodologies have been developed to estimate these forces using robotic testing systems. Initially, an attempt was made to record motion of a group of knees and then reproduce the average motion on another group of knees [55]. Thus, this process simulates recording of in vivo kinematics from human subjects and then reproducing the motion on a set of cadaveric knees. Porcine knees were placed into a 6DOF robotic testing system and kinematics were recorded during application of: (1) a 100 N anterior load and (2) a 5 N·m valgus torque. These kinematics were then averaged and replayed on “target” porcine knees. The in situ forces in the ACL were determined for both sets of knees and compared. Significant differences were found between the source knees and the target knees for all the flexion angles in response to an anterior load. However, in response to valgus loads, there was no significant difference between the source knees and the target knees at 30 and 90 deg of flexion. It was noted that there was a correlation between anterior knee laxity (the distance along the displacement axis from the origin to the beginning of the linear region of the load–displacement curve) and internal–external rotation. These data suggest that in order to obtain reproducible results, one needs to first match knees to knees with comparable anterior knee laxity. Thus, an estimate of the in situ forces in the ACL during in vivo activities might be obtainable using this novel methodology.

To further study in situ forces during in vivo motion, in vivo kinematics of the stifle joint of sheep were measured during “normal gait,” then the in vivo motions were reproduced on the same joints using a robotic testing system to determine the relationship between the loading of the anterior and posterior cruciate ligaments [56]. To measure the in vivo motion for replay purposes, surgical plates were implanted onto the proximolateral aspect of the tibia and the distolateral aspect of the femur. An instrumented spatial linkage (ISL) consisting of six rotational encoders was then mounted onto these plates. This linkage was used to record three-dimensional motion of the femur relative to the tibia while the sheep walked on a treadmill. Following kinematic testing, the hind limbs were disarticulated and mounted on a 6DOF robotic testing system which then replayed the in vivo motion data collected from the ISL. The major ligaments were subsequently sectioned in turn with replay of the kinematic data after each to determine the loads present in the ligaments during the in vivo motion. The loads borne by the cruciate ligaments were determined using the principle of superposition. This is a novel study quantifying the function of the cruciate ligaments during gait by directly capturing gait information from sheep and reproducing the same motion in their own knees to directly measure in vivo forces.

Injury Models.

Instability due to permanent deformation of the glenohumeral capsule is a common pathology at the glenohumeral joint due to dislocation [57]. The change in joint kinematics and magnitude of nonrecoverable strain in the glenohumeral capsule due to dislocation has implications for the ideal location and extent of plication, which is a common clinical procedure used to repair the capsule. Therefore, a robotic testing system was used to anteriorly dislocate the glenohumeral joint, and the kinematics of the intact and injured joint in response to an anterior load with the joint abducted and externally rotated (apprehension position) were quantified [5860]. In addition, the amount of nonrecoverable strain, or injury to the capsule, was determined. Significant increases in anterior translation between intact and injured states were found at 0, 30, and 60 deg of external rotation. This type of information may help to standardize physical exams based on joint position and could also help surgeons identify specific locations of capsular injury that may have been previously ignored.

Computational Models.

Joint kinematics in response to applied external loading conditions and the corresponding ligament and bony contact forces obtained from robotic testing systems as well as the strain distribution in soft tissue structures are essential elements to validate computational models of diarthrodial joints [28,51,61]. Loading conditions can be applied to the cadaveric joint using a robotic testing system, while the resulting joint kinematics, ligament and bony contact forces, and surface strain in soft tissue structures are determined. A magnetic resonance image and/or CT scan of cadaveric joints can be used to create a finite-element model (FEM) of the diarthrodial joint including bones, ligaments, and their insertion sites, cartilage, and menisci. The mechanical properties for each tissue obtained from the literature or mechanical testing of the tissues can serve as additional inputs to the FEM, and then, identical loading conditions from the experiments can be applied to the FEM. When the model's predictions of resulting joint kinematics, in situ forces in soft tissue structures, or strain in soft tissues compare well with experimental data, the FEM is considered validated for that loading condition. Typical validation criteria might include 10% error or within the experimental repeatability of the measurement technique. The models are also able to provide more insight into the stresses and strains experienced by the ligaments, cartilage, capsule, and other connective tissues at each joint. These models can be used in the future to apply more complex loading conditions or help with patient outcome predictions.

To date, most research accomplished involves applying relatively simple loading conditions (constant loads and torques applied at either fixed flexion angles or throughout the range of flexion) to cadaveric joints using robotic testing systems. In the future, more information is needed regarding the complex in vivo loads applied to joints during clinical exams such as the pivot shift test to examine knee stability and activities of daily living to serve as input to the testing systems. These loads can vary as a function of flexion angle and time and are relatively unknown. In addition, a wide variation of loads are experienced between individuals that might also require knowledge of variations in joint geometry.

More research should also go into accurately reproducing in vivo kinematics with the use of robotic testing systems to estimate the forces with the proper use of the principle of superposition and strains during activities of daily living. The accuracy of robotic testing systems to reproduce in vivo joint kinematics of a diarthrodial joint is primarily limited by the accuracy of the in vivo motion measurement system and the registration process that relates joint geometry between the in vivo motion measurement system and the robotic testing system. Improvements need to be made in this methodology. Further improvements can then be made to surgical procedures and rehabilitation protocols. Thus, patient outcomes can be improved as well as time and cost can be saved.

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Zantop, T. , Lenschow, S. , Lemburg, T. , Weimann, A. , and Petersen, W. , 2004, “ Soft-Tissue Graft Fixation in Posterior Cruciate Ligament Reconstruction: Evaluation of the Effect of Tibial Insertion Site on Joint Kinematics and In Situ Forces Using a Robotic/UFS Testing System,” Arch. Orthop. Trauma Surg., 124(9), pp. 614–620. [CrossRef] [PubMed]
Gill, T. J. , DeFrate, L. E. , Wang, C. , Carey, C. T. , Zayontz, S. , Zarins, B. , and Li, G. , 2003, “ The Biomechanical Effect of Posterior Cruciate Ligament Reconstruction on Knee Joint Function. Kinematic Response to Simulated Muscle Loads,” Am. J. Sports Med., 31(4), pp. 530–536. [PubMed]
Gill, T. J. , DeFrate, L. E. , Wang, C. , Carey, C. T. , Zayontz, S. , Zarins, B. , and Li, G. , 2004, “ The Effect of Posterior Cruciate Ligament Reconstruction on Patellofemoral Contact Pressures in the Knee Joint Under Simulated Muscle Loads,” Am. J. Sports Med., 32(1), pp. 109–115. [CrossRef] [PubMed]
Li, G. , DeFrate, L. E. , Zayontz, S. , Park, S. E. , and Gill, T. J. , 2004, “ The Effect of Tibiofemoral Joint Kinematics on Patellofemoral Contact Pressures Under Simulated Muscle Loads,” J. Orthop. Res., 22(4), pp. 801–806. [CrossRef] [PubMed]
Li, G. , Most, E. , Sultan, P. G. , Schule, S. , Zayontz, S. , Park, S. E. , and Rubash, H. E. , 2004, “ Knee Kinematics With a High-Flexion Posterior Stabilized Total Knee Prosthesis: An In Vitro Robotic Experimental Investigation,” J. Bone Jt. Surg., 86(8), pp. 1721–1729. [CrossRef]
Li, G. , Rudy, T. W. , Sakane, M. , Kanamori, A. , Ma, C. B. , and Woo, S. L. , 1999, “ The Importance of Quadriceps and Hamstring Muscle Loading on Knee Kinematics and In-Situ Forces in the ACL,” J. Biomech., 32(4), pp. 395–400. [CrossRef] [PubMed]
Li, G. , Suggs, J. , and Gill, T. , 2002, “ The Effect of Anterior Cruciate Ligament Injury on Knee Joint Function Under a Simulated Muscle Load: A Three-Dimensional Computational Simulation,” Ann. Biomed. Eng., 30(5), pp. 713–720. [CrossRef] [PubMed]
Markolf, K. L. , O'Neill, G. , Jackson, S. R. , and McAllister, D. R. , 2004, “ Effects of Applied Quadriceps and Hamstrings Muscle Loads on Forces in the Anterior and Posterior Cruciate Ligaments,” Am. J. Sports Med., 32(5), pp. 1144–1149. [CrossRef] [PubMed]
Fujie, H. , Livesay, G. A. , Woo, S. L. , Kashiwaguchi, S. , and Blomstrom, G. , 1995, “ The Use of a Universal Force-Moment Sensor to Determine In-Situ Forces in Ligaments: A New Methodology,” ASME J. Biomech. Eng., 117(1), pp. 1–7. [CrossRef]
Fujie, H. , Sekito, T. , and Orita, A. , 2004, “ A Novel Robotic System for Joint Biomechanical Tests: Application to the Human Knee Joint,” ASME J. Biomech. Eng., 126(1), pp. 54–61. [CrossRef]
Gilbertson, L. G. , Doehring, T. C. , Livesay, G. A. , Rudy, T. W. , Kang, J. D. , and Woo, S. L. , 1999, “ Improvement of Accuracy in a High-Capacity, Six Degree-of-Freedom Load Cell: Application to Robotic Testing of Musculoskeletal Joints,” Ann. Biomed. Eng., 27(6), pp. 839–843. [CrossRef] [PubMed]
Woo, S. L. , Wu, C. , Dede, O. , Vercillo, F. , and Noorani, S. , 2006, “ Biomechanics and Anterior Cruciate Ligament Reconstruction,” J. Orthop. Surg. Res., 1(1), p. 2. [CrossRef] [PubMed]
Livesay, G. A. , Fujie, H. , Kashiwaguchi, S. , Morrow, D. A. , Fu, F. H. , and Woo, S. L. , 1995, “ Determination of the In Situ Forces and Force Distribution Within the Human Anterior Cruciate Ligament,” Ann. Biomed. Eng., 23(4), pp. 467–474. [CrossRef] [PubMed]
Livesay, G. A. , Rudy, T. W. , Woo, S. L. , Runco, T. J. , Sakane, M. , Li, G. , and Fu, F. H. , 1997, “ Evaluation of the Effect of Joint Constraints on the In Situ Force Distribution in the Anterior Cruciate Ligament,” J. Orthop. Res., 15(2), pp. 278–284. [CrossRef] [PubMed]
Grood, E. S. , and Suntay, W. J. , 1983, “ A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee,” ASME J. Biomech. Eng., 105(2), pp. 136–144. [CrossRef]
Fujie, H. , Livesay, G. A. , Fujita, M. , and Woo, S. L. , 1996, “ Forces and Moments in Six-DOF at the Human Knee Joint: Mathematical Description for Control,” J. Biomech., 29(12), pp. 1577–1585. [CrossRef] [PubMed]
Fujie, H. , and Yagi, H. , 2011, “ Novel Robotic System for Joint Mechanical Tests Using Velocity-Impedance Control,” ASME Paper No. SBC2011-53884.
Goertzen, D. J. , and Kawchuk, G. N. , 2009, “ A Novel Application of Velocity-Based Force Control for Use in Robotic Biomechanical Testing,” J. Biomech., 42(3), pp. 366–369. [CrossRef] [PubMed]
Lawless, I. M. , Ding, B. , Cazzolato, B. S. , and Costi, J. J. , 2014, “ Adaptive Velocity-Based Six Degree of Freedom Load Control for Real-Time Unconstrained Biomechanical Testing,” J. Biomech., 47(12), pp. 3241–3247. [CrossRef] [PubMed]
Hirabayashi, H. , Sugimoto, K. , Enomoto, A. , and Ishimaru, I. , 2000, “ Robot Manipulation Using Virtual Compliance Control,” J. Rob. Mechantronics, 12(5), pp. 567–576. [CrossRef]
Kanamori, A. , Woo, S. L. , Ma, C. B. , Zeminski, J. , Rudy, T. W. , Li, G. , and Livesay, G. A. , 2000, “ The Forces in the Anterior Cruciate Ligament and Knee Kinematics During a Simulated Pivot Shift Test: A Human Cadaveric Study Using Robotic Technology,” Arthroscopy, 16(6), pp. 633–639. [CrossRef] [PubMed]
Moore, S. M. , Stehle, J. H. , Rainis, E. J. , McMahon, P. J. , and Debski, R. E. , 2008, “ The Current Anatomical Description of the Inferior Glenohumeral Ligament Does Not Correlate With Its Functional Role in Positions of External Rotation,” J. Orthop. Res., 26(12), pp. 1598–1604. [CrossRef] [PubMed]
Fujie, H. , Mabuchi, K. , Tsukamoto, Y. , Yamamoto, M. , and Sasada, T. , 1987, “ Application of Robotics to the Knee Instability Test—Preliminary Experiment of Canine Knee Joints,” Annual Meeting of Japanese Society for Orthopaedic Biomechanics, pp. 105–110.
Fujie, H. , Mabuchi, K. , Tsukamoto, Y. , Yamamoto, M. , and Sasada, T. , 1989, “ Application of Robotics to Palpation of Injury of Ligaments—Development of a New Method of Knee Instability Test,” American Society of Mechanical Engineers—Bioengineering Division, San Francisco, CA, pp. 119–121.
Bell, K. M. , Arilla, F. V. , Rahnemai-Azar, A. A. , Fu, F. H. , Musahl, V. , and Debski, R. E. , 2015, “ Novel Technique for Evaluation of Knee Function Continuously Through the Range of Flexion,” J. Biomech., 48(13), pp. 3728–3731. [CrossRef] [PubMed]
Ma, C. B. , Janaushek, M. A. , Vogrin, T. M. , Rudy, T. W. , Harner, C. D. , and Woo, S. L. , 2000, “ Significance of Changes in the Reference Position for Measurements of Tibial Translation and Diagnosis of Cruciate Ligament Deficiency,” J. Orthop. Res., 18(2), pp. 176–182. [CrossRef] [PubMed]
Woo, S. L. , Chan, S. S. , and Yamaji, T. , 1997, “ Biomechanics of Knee Ligament Healing, Repair and Reconstruction,” J. Biomech., 30(5), pp. 431–439. [CrossRef] [PubMed]
Markolf, K. L. , Jackson, S. R. , Foster, B. , and McAllister, D. R. , 2014, “ ACL Forces and Knee Kinematics Produced by Axial Tibial Compression During a Passive Flexion-Extension Cycle,” J. Orthop. Res., 32(1), pp. 89–95. [CrossRef] [PubMed]
Malicky, D. M. , Kuhn, J. E. , Frisancho, J. C. , Lindholm, S. R. , Raz, J. A. , and Soslowsky, L. J. , 2002, “ Neer Award 2001: Nonrecoverable Strain Fields of the Anteroinferior Glenohumeral Capsule Under Subluxation,” J. Shoulder Elbow Surg., 11(6), pp. 529–540. [CrossRef] [PubMed]
Moore, S. M. , Ellis, B. , Weiss, J. A. , McMahon, P. J. , and Debski, R. E. , 2010, “ The Glenohumeral Capsule Should Be Evaluated as a Sheet of Fibrous Tissue: A Validated Finite Element Model,” Ann. Biomed. Eng., 38(1), pp. 66–76. [CrossRef] [PubMed]
Claes, S. , Vereecke, E. , Maes, M. , Victor, J. , Verdonk, P. , and Bellemans, J. , 2013, “ Anatomy of the Anterolateral Ligament of the Knee,” J. Anat., 223(4), pp. 321–328. [CrossRef] [PubMed]
Guenther, D. , Rahnemai-Azar, A. A. , Bell, K. M. , Irarrazaval, S. , Fu, F. H. , Musahl, V. , and Debski, R. E. , 2016, “ The Anterolateral Capsule of the Knee Behaves Like a Sheet of Fibrous Tissue,” Am. J. Sports Med. (epub).
Sexton, S. L. , Guenther, D. , Bell, K. M. , Irarrazaval, S. , Rahnemai-Azar, A. A. , Fu, F. H. , Musahl, V. , and Debski, R. E. , 2016, “ Anterolateral Capsule of the Knee Functions as a Sheet of Tissue Based on Tissue Strain,” Summer Biomechanics, Bioengineering and Biotransport Conference, National Harbor, MD, p. SB3C2016-2096. http://www.engineering.pitt.edu/Departments/Bioengineering/_.../Sexton_Stephanie/
Darcy, S. P. , Kilger, R. H. , Woo, S. L. , and Debski, R. E. , 2006, “ Estimation of ACL Forces by Reproducing Knee Kinematics Between Sets of Knees: A Novel Non-Invasive Methodology,” J. Biomech., 39(13), pp. 2371–2377. [CrossRef] [PubMed]
Nesbitt, R. J. , Herfat, S. T. , Boguszewski, D. V. , Engel, A. J. , Galloway, M. T. , and Shearn, J. T. , 2014, “ Primary and Secondary Restraints of Human and Ovine Knees for Simulated In Vivo Gait Kinematics,” J. Biomech., 47(9), pp. 2022–2027. [CrossRef] [PubMed]
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Browe, D. P. , Rainis, C. A. , McMahon, P. J. , and Debski, R. E. , 2013, “ Injury to the Anteroinferior Glenohumeral Capsule During Anterior Dislocation,” Clin. Biomech., 28(2), pp. 140–145. [CrossRef]
Browe, D. P. , Voycheck, C. A. , McMahon, P. J. , and Debski, R. E. , 2014, “ Changes to the Mechanical Properties of the Glenohumeral Capsule During Anterior Dislocation,” J. Biomech., 47(2), pp. 464–469. [CrossRef] [PubMed]
Rainis, C. A. , Browe, D. P. , McMahon, P. J. , and Debski, R. E. , 2013, “ Capsule Function Following Anterior Dislocation: Implications for Diagnosis of Shoulder Instability,” J. Orthop. Res., 31(6), pp. 962–968. [CrossRef] [PubMed]
Li, G. , Gil, J. , Kanamori, A. , and Woo, S. L. , 1999, “ A Validated Three-Dimensional Computational Model of a Human Knee Joint,” ASME J. Biomech. Eng., 121(6), pp. 657–662. [CrossRef]
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References

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Rudy, T. W. , Livesay, G. A. , Woo, S. L. , and Fu, F. H. , 1996, “ A Combined Robotic/Universal Force Sensor Approach to Determine In Situ Forces of Knee Ligaments,” J. Biomech., 29(10), pp. 1357–1360. [CrossRef] [PubMed]
Woo, S. L. , Debski, R. E. , Wong, E. K. , Yagi, M. , and Tarinelli, D. , 1999, “ Use of Robotic Technology for Diarthrodial Joint Research,” J. Sci. Med. Sport, 2(4), pp. 283–297. [CrossRef] [PubMed]
Woo, S. L. , and Fisher, M. B. , 2009, “ Evaluation of Knee Stability With Use of a Robotic System,” J. Bone Jt. Surg., 91(Suppl. 1), pp. 78–84. [CrossRef]
Woo, S. L. , Kanamori, A. , Zeminski, J. , Yagi, M. , Papageorgiou, C. , and Fu, F. H. , 2002, “ The Effectiveness of Reconstruction of the Anterior Cruciate Ligament With Hamstrings and Patellar Tendon. A Cadaveric Study Comparing Anterior Tibial and Rotational Loads,” J. Bone Jt. Surg., 84(6), pp. 907–914. [CrossRef]
Zantop, T. , Lenschow, S. , Lemburg, T. , Weimann, A. , and Petersen, W. , 2004, “ Soft-Tissue Graft Fixation in Posterior Cruciate Ligament Reconstruction: Evaluation of the Effect of Tibial Insertion Site on Joint Kinematics and In Situ Forces Using a Robotic/UFS Testing System,” Arch. Orthop. Trauma Surg., 124(9), pp. 614–620. [CrossRef] [PubMed]
Gill, T. J. , DeFrate, L. E. , Wang, C. , Carey, C. T. , Zayontz, S. , Zarins, B. , and Li, G. , 2003, “ The Biomechanical Effect of Posterior Cruciate Ligament Reconstruction on Knee Joint Function. Kinematic Response to Simulated Muscle Loads,” Am. J. Sports Med., 31(4), pp. 530–536. [PubMed]
Gill, T. J. , DeFrate, L. E. , Wang, C. , Carey, C. T. , Zayontz, S. , Zarins, B. , and Li, G. , 2004, “ The Effect of Posterior Cruciate Ligament Reconstruction on Patellofemoral Contact Pressures in the Knee Joint Under Simulated Muscle Loads,” Am. J. Sports Med., 32(1), pp. 109–115. [CrossRef] [PubMed]
Li, G. , DeFrate, L. E. , Zayontz, S. , Park, S. E. , and Gill, T. J. , 2004, “ The Effect of Tibiofemoral Joint Kinematics on Patellofemoral Contact Pressures Under Simulated Muscle Loads,” J. Orthop. Res., 22(4), pp. 801–806. [CrossRef] [PubMed]
Li, G. , Most, E. , Sultan, P. G. , Schule, S. , Zayontz, S. , Park, S. E. , and Rubash, H. E. , 2004, “ Knee Kinematics With a High-Flexion Posterior Stabilized Total Knee Prosthesis: An In Vitro Robotic Experimental Investigation,” J. Bone Jt. Surg., 86(8), pp. 1721–1729. [CrossRef]
Li, G. , Rudy, T. W. , Sakane, M. , Kanamori, A. , Ma, C. B. , and Woo, S. L. , 1999, “ The Importance of Quadriceps and Hamstring Muscle Loading on Knee Kinematics and In-Situ Forces in the ACL,” J. Biomech., 32(4), pp. 395–400. [CrossRef] [PubMed]
Li, G. , Suggs, J. , and Gill, T. , 2002, “ The Effect of Anterior Cruciate Ligament Injury on Knee Joint Function Under a Simulated Muscle Load: A Three-Dimensional Computational Simulation,” Ann. Biomed. Eng., 30(5), pp. 713–720. [CrossRef] [PubMed]
Markolf, K. L. , O'Neill, G. , Jackson, S. R. , and McAllister, D. R. , 2004, “ Effects of Applied Quadriceps and Hamstrings Muscle Loads on Forces in the Anterior and Posterior Cruciate Ligaments,” Am. J. Sports Med., 32(5), pp. 1144–1149. [CrossRef] [PubMed]
Fujie, H. , Livesay, G. A. , Woo, S. L. , Kashiwaguchi, S. , and Blomstrom, G. , 1995, “ The Use of a Universal Force-Moment Sensor to Determine In-Situ Forces in Ligaments: A New Methodology,” ASME J. Biomech. Eng., 117(1), pp. 1–7. [CrossRef]
Fujie, H. , Sekito, T. , and Orita, A. , 2004, “ A Novel Robotic System for Joint Biomechanical Tests: Application to the Human Knee Joint,” ASME J. Biomech. Eng., 126(1), pp. 54–61. [CrossRef]
Gilbertson, L. G. , Doehring, T. C. , Livesay, G. A. , Rudy, T. W. , Kang, J. D. , and Woo, S. L. , 1999, “ Improvement of Accuracy in a High-Capacity, Six Degree-of-Freedom Load Cell: Application to Robotic Testing of Musculoskeletal Joints,” Ann. Biomed. Eng., 27(6), pp. 839–843. [CrossRef] [PubMed]
Woo, S. L. , Wu, C. , Dede, O. , Vercillo, F. , and Noorani, S. , 2006, “ Biomechanics and Anterior Cruciate Ligament Reconstruction,” J. Orthop. Surg. Res., 1(1), p. 2. [CrossRef] [PubMed]
Livesay, G. A. , Fujie, H. , Kashiwaguchi, S. , Morrow, D. A. , Fu, F. H. , and Woo, S. L. , 1995, “ Determination of the In Situ Forces and Force Distribution Within the Human Anterior Cruciate Ligament,” Ann. Biomed. Eng., 23(4), pp. 467–474. [CrossRef] [PubMed]
Livesay, G. A. , Rudy, T. W. , Woo, S. L. , Runco, T. J. , Sakane, M. , Li, G. , and Fu, F. H. , 1997, “ Evaluation of the Effect of Joint Constraints on the In Situ Force Distribution in the Anterior Cruciate Ligament,” J. Orthop. Res., 15(2), pp. 278–284. [CrossRef] [PubMed]
Grood, E. S. , and Suntay, W. J. , 1983, “ A Joint Coordinate System for the Clinical Description of Three-Dimensional Motions: Application to the Knee,” ASME J. Biomech. Eng., 105(2), pp. 136–144. [CrossRef]
Fujie, H. , Livesay, G. A. , Fujita, M. , and Woo, S. L. , 1996, “ Forces and Moments in Six-DOF at the Human Knee Joint: Mathematical Description for Control,” J. Biomech., 29(12), pp. 1577–1585. [CrossRef] [PubMed]
Fujie, H. , and Yagi, H. , 2011, “ Novel Robotic System for Joint Mechanical Tests Using Velocity-Impedance Control,” ASME Paper No. SBC2011-53884.
Goertzen, D. J. , and Kawchuk, G. N. , 2009, “ A Novel Application of Velocity-Based Force Control for Use in Robotic Biomechanical Testing,” J. Biomech., 42(3), pp. 366–369. [CrossRef] [PubMed]
Lawless, I. M. , Ding, B. , Cazzolato, B. S. , and Costi, J. J. , 2014, “ Adaptive Velocity-Based Six Degree of Freedom Load Control for Real-Time Unconstrained Biomechanical Testing,” J. Biomech., 47(12), pp. 3241–3247. [CrossRef] [PubMed]
Hirabayashi, H. , Sugimoto, K. , Enomoto, A. , and Ishimaru, I. , 2000, “ Robot Manipulation Using Virtual Compliance Control,” J. Rob. Mechantronics, 12(5), pp. 567–576. [CrossRef]
Kanamori, A. , Woo, S. L. , Ma, C. B. , Zeminski, J. , Rudy, T. W. , Li, G. , and Livesay, G. A. , 2000, “ The Forces in the Anterior Cruciate Ligament and Knee Kinematics During a Simulated Pivot Shift Test: A Human Cadaveric Study Using Robotic Technology,” Arthroscopy, 16(6), pp. 633–639. [CrossRef] [PubMed]
Moore, S. M. , Stehle, J. H. , Rainis, E. J. , McMahon, P. J. , and Debski, R. E. , 2008, “ The Current Anatomical Description of the Inferior Glenohumeral Ligament Does Not Correlate With Its Functional Role in Positions of External Rotation,” J. Orthop. Res., 26(12), pp. 1598–1604. [CrossRef] [PubMed]
Fujie, H. , Mabuchi, K. , Tsukamoto, Y. , Yamamoto, M. , and Sasada, T. , 1987, “ Application of Robotics to the Knee Instability Test—Preliminary Experiment of Canine Knee Joints,” Annual Meeting of Japanese Society for Orthopaedic Biomechanics, pp. 105–110.
Fujie, H. , Mabuchi, K. , Tsukamoto, Y. , Yamamoto, M. , and Sasada, T. , 1989, “ Application of Robotics to Palpation of Injury of Ligaments—Development of a New Method of Knee Instability Test,” American Society of Mechanical Engineers—Bioengineering Division, San Francisco, CA, pp. 119–121.
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Figures

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Fig. 1

A schematic diagram of an articulated robotic manipulator combined with a UFS, as well as the coordinate systems of the femur, tibia, UFS, and robotic end-effector

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Fig. 2

The Grood and Suntay description of tibiofemoral motion

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Fig. 3

Typical coordinate systems associated with a robotic testing system and the Jacobian matrices that relate the forces and motions between each coordinate system

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Fig. 4

Proximal force applied to a porcine knee as a function of time using the stiffness and velocity-impedance control methodologies

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Fig. 5

An orthogonal robotic testing system with a femur mounted to the lower mechanism and tibia attached to the upper mechanism. (X, Y, Z are the translational degrees-of-freedom; U, V, W are the rotational degrees-of-freedom).

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Fig. 7

Inferior view of the glenohumeral joint with strain markers attached to the inferior glenohumeral capsule to allow the determination of capsular strain [43]

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Fig. 6

Anterior tibial translation and in situ forces in the ACL during static and continuous testing methods [46]

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