6R instrumented spatial linkages for anatomical joint motion measurement--Part 2: Calibration

An instrumented spatial linkage for measuring knee joint kinematics

BACKGROUND

In this study, the design and development of a highly accurate instrumented spatial linkage (ISL) for kinematic analysis of the ovine stifle joint is described. The ovine knee is a promising biomechanical model of the human knee joint.

METHODS

The ISL consists of six digital rotational encoders providing six degrees of freedom (6-DOF) to its motion. The ISL makes use of the complete and parametrically continuous (CPC) kinematic modeling method to describe the kinematic relationship between encoder readings and the relative positions and orientation of its two ends. The CPC method is useful when calibrating the ISL, because a small change in parameters corresponds to a small change in calculated positions and orientations and thus a smaller optimization error, compared to other kinematic models. The ISL is attached rigidly to the femur and the tibia for motion capture, and the CPC kinematic model is then employed to transform the angle sensor readings to relative motion of the two ends of the linkage, and thereby, the stifle joint motion.

RESULTS

The positional accuracy for ISL after calibration and optimization was 0.3±0.2mm (mean +/- standard deviation). The ISL was also evaluated dynamically to ensure that accurate results were maintained, and achieved an accuracy of 0.1mm.

CONCLUSIONS

Compared to the traditional motion capture methods, this system provides increased accuracy, reduced processing time, and ease of use. Future work will be on the application of the ISL to the ovine gait and determination of in vivo joint motions and tissue loads.

CLINICAL RELEVANCE

Accurate measurement of knee joint kinematics is essential in understanding injury mechanisms and development of potential preventive or treatment strategies.

Design, Calibration and Validation of a Novel 3D Printed Instrumented Spatial Linkage that Measures Changes in the Rotational Axes of the Tibiofemoral Joint

An accurate axis-finding technique is required to measure any changes from normal caused by total knee arthroplasty in the flexion–extension (F–E) and longitudinal rotation (LR) axes of the tibiofemoral joint. In a previous paper, we computationally determined how best to design and use an instrumented spatial linkage (ISL) to locate the F–E and LR axes such that rotational and translational errors were minimized. However, the ISL was not built and consequently was not calibrated; thus the errors in locating these axes were not quantified on an actual ISL. Moreover, previous methods to calibrate an ISL used calibration devices with accuracies that were either undocumented or insufficient for the device to serve as a gold-standard. Accordingly, the objectives were to (1) construct an ISL using the previously established guidelines,(2) calibrate the ISL using an improved method, and (3) quantify the error in measuring changes in the F–E and LR axes. A 3D printed ISL was constructed and calibrated using a coordinate measuring machine, which served as a gold standard. Validation was performed using a fixture that represented the tibiofemoral joint with an adjustable F–E axis and the errors in measuring changes to the positions and orientations of the F–E and LR axes were quantified. The resulting root mean squared errors (RMSEs) of the calibration residuals using the new calibration method were 0.24, 0.33, and 0.15 mm for the anterior–posterior, medial–lateral, and proximal–distal positions, respectively, and 0.11, 0.10, and 0.09 deg for varus–valgus, flexion–extension, and internal–external orientations, respectively. All RMSEs were below 0.29% of the respective full-scale range. When measuring changes to the F–E or LR axes, each orientation error was below 0.5 deg; when measuring changes in the F–E axis, each position error was below 1.0 mm. The largest position RMSE was when measuring a medial–lateral change in the LR axis (1.2 mm). Despite the large size of the ISL, these calibration residuals were better than those for previously published ISLs, particularly when measuring orientations, indicating that using a more accurate gold standard was beneficial in limiting the calibration residuals. The validation method demonstrated that this ISL is capable of accurately measuring clinically important changes (i.e. 1 mm and 1 deg) in the F–E and LR axes.

Design and evaluation of a new general-purpose device for calibrating instrumented spatial linkages

Because instrumented spatial linkages (ISLs) have been commonly used in measuring joint rotations and must be calibrated before using the device in confidence, a calibration device design and associated method for quantifying calibration device error would be useful. The objectives of the work reported by this paper were to (1) design an ISL calibration device and demonstrate the design for a specific application, (2) describe a new method for calibrating the device that minimizes measurement error, and (3) quantify measurement error of the device using the new method. Relative translations and orientations of the device were calculated via a series of transformation matrices containing inherent fixed and variable parameters. These translations and orientations were verified with a coordinate measurement machine, which served as a gold standard. Inherent fixed parameters of the device were optimized to minimize measurement error. After parameter optimization, accuracy was determined. The root mean squared error (RMSE) was 0.175 deg for orientation and 0.587 mm for position. All RMSE values were less than 0.8% of their respective full-scale ranges. These errors are comparable to published measurement errors of ISLs for positions and lower by at least a factor of 2 for orientations. These errors are in spite of the many steps taken in design and manufacturing to achieve high accuracy. Because it is challenging to achieve the accuracy required for a custom calibration device to serve as a viable gold standard, it is important to verify that a calibration device provides sufficient precision to calibrate an ISL.

Development and evaluation of an instrumented linkage system for total knee surgery

The principles and application of total knee surgery using optical tracking have been well demonstrated, but electromagnetic tracking may offer further advantages. We asked whether an instrumented linkage that attaches directly to the bone can maintain the accuracy of the optical and electromagnetic systems but be quicker, more convenient, and less expensive to use. Initial testing using a table-mounted digitizer to navigate a drill guide for placing pins to mount a cutting guide demonstrated the feasibility in terms of access and availability. A first version (called the Mark 1) instrumented linkage designed to fix directly to the bone was constructed and software was written to carry out a complete total knee replacement procedure. The results showed the system largely fulfilled these goals, but some surgeons found that using a visual display for pin placement was difficult and time consuming. As a result, a second version of a linkage system (called the K-Link) was designed to further develop the concept. User-friendly flexible software was developed for facilitating each step quickly and accurately while the placement of cutting guides was facilitated. We concluded that an instrumented linkage system could be a useful and potentially lower-cost option to the current systems for total knee replacement and could possibly have application to other surgical procedures.

Design and demonstration of a new instrumented spatial linkage for use in a dynamic environment: application to measurement of ankle rotations during snowboarding

Joint injuries during sporting activities might be reduced by understanding the extent of the dynamic motion of joints prone to injury during maneuvers performed in the field. Because instrumented spatial linkages (ISLs) have been widely used to measure joint motion, it would be useful to extend the functionality of an ISL to measure joint motion in a dynamic environment. The objectives of the work reported by this paper were to (i) design and construct an ISL that will measure dynamic joint motion in a field environment, (ii) calibrate the ISL and quantify its static measurement error, (iii) quantify dynamic measurement error due to external acceleration, and (iv) measure ankle joint complex rotation during snowboarding maneuvers performed on a snow slope. An "elbow-type" ISL was designed to measure ankle joint complex rotation throughout its range (+/-30 deg for flexion/extension, +/-15 deg for internal/external rotation, and +/-15 deg for inversion/eversion). The ISL was calibrated with a custom six degree-of-freedom calibration device generally useful for calibrating ISLs, and static measurement errors of the ISL also were evaluated. Root-mean-squared errors (RMSEs) were 0.59 deg for orientation (1.7% full scale) and 1.00 mm for position (1.7% full scale). A custom dynamic fixture allowed external accelerations (5 g, 0-50 Hz) to be applied to the ISL in each of three linear directions. Maximum measurement deviations due to external acceleration were 0.05 deg in orientation and 0.10 mm in position, which were negligible in comparison to the static errors. The full functionality of the ISL for measuring joint motion in a field environment was demonstrated by measuring rotations of the ankle joint complex during snowboarding maneuvers performed on a snow slope.

Validation of a calibration technique for 6-DOF instrumented spatial linkages

This paper presents a practical and effective approach to the calibration of instrumented spatial linkages for biomechanical applications. A 6-DOF mechanical linkage with rotational transducers is designed and in-house manufactured for this purpose. In order to assess the validity of the proposed calibration technique and to distinguish between geometrical and electrical parameters uncertainties, high-precision optical encoders are used and calibration is addressed from a kinematic point of view only. The proposed technique is based on a closed-loop method, in which the end segments of the linkage are connected to each other by revolute joints. A parametrical model of the system is formulated using a standard link-to-link transformation matrices approach. Continuous data collection is carried out and a recursive identification of kinematic parameters is implemented by the use of an extended Kalman filter algorithm. Results shows that the proposed technique, despites its simplicity, is effective in improving the accuracy of the system up to its theoretically computed resolution, which limits the performance of the real system.

Simultaneous Measurement of Three-Dimensional Joint Kinematics and Ligament Strains With Optical Methods

The objective of this study was to assess the precision and accuracy of a nonproprietary, optical three-dimensional (3D) motion analysis system for the simultaneous measurement of soft tissue strains and joint kinematics. The system consisted of two high-resolution digital cameras and software for calculating the 3D coordinates of contrast markers. System precision was assessed by examining the variation in the coordinates of static markers over time. Three-dimensional strain measurement accuracy was assessed by moving contrast markers fixed distances in the field of view and calculating the error in predicted strain. Three-dimensional accuracy for kinematic measurements was assessed by simulating the measurements that are required for recording knee kinematics. The field of view (190 mm) was chosen to allow simultaneous recording of markers for soft tissue strain measurement and knee joint kinematics. Average system precision was between ±0.004 mm and ±0.035 mm, depending on marker size and camera angle. Absolute error in strain measurement varied from a minimum of ±0.025% to a maximum of ±0.142%, depending on the angle between cameras and the direction of strain with respect to the camera axes. Kinematic accuracy for translations was between ±0.008 mm and ±0.034 mm, while rotational accuracy was ±0.082 deg to ±0.160 deg. These results demonstrate that simultaneous optical measurement of 3D soft tissue strain and 3D joint kinematics can be performed while achieving excellent accuracy for both sets of measurements.

Towards understanding the workspace of human limbs

Significant attention in recent years has been given towards obtaining a better understanding of human joint ranges, measurement, and functionality, especially in conjunction with commands issued by the central nervous system. Studies of those commands often include computer algorithms to describe path trajectories. These are typically in "open-form" with specific descriptions of motions, but not "closed form" mathematical solutions of the full range of possibilities. This paper proposes a rigorous "closed form" kinematic formulation to model human limbs, understand their workspace (also called the reach envelope), and delineate barriers therein where a path becomes difficult or impossible owing to physical constraints. The novel ability to visualize barriers in the workspace emphasizes the power of these closed form equations. Moreover, this formulation takes into account joint limits in terms of ranges of motion and identifies barriers therein where a person is required to attain a different posture. Examples include the workspaces of a typical forearm and a typical finger. The wrist's range of motion is used to illustrate the visualization of the progress in the functionality of a wrist undergoing rehabilitation.

In vivo elbow biomechanical analysis during flexion: three-dimensional motion analysis using magnetic resonance imaging

The purpose of this article is to evaluate in vivo 3-dimensional kinematics of the elbow joint during elbow flexion. We studied the ulnohumeral and radiohumeral joint noninvasively in 3 elbows in healthy volunteers using a markerless bone registration algorithm. Magnetic resonance images were acquired in 6 positions of elbow flexion. The inferred contact areas on the ulna against the trochlea tended to occur only on the medial facet of the trochlear notch in all of the elbow positions we tested. The inferred contact areas on the radial head against the capitellum occurred on the central depression of the radial head in all of the tested elbow positions except for 135 degrees flexion, where the anterior rim of the radial head articulates with the capitellum.

Calibration and validation of 6 DOFs instrumented spatial linkage for biomechanical applications. A practical approach

A method for both calibration and validation of a 6 DOF electrogoniometer is presented. A 6 Revolute Instrumented Spatial Linkage (6R-ISL) and a three-dimensional digitizer (3DD) were used simultaneously to collect both static and continuous poses of unconstrained or constrained motions. Validation occurred using a calibrated ball-and-socket joint. A parametrical model of the 6R-ISL (i.e. Virtual Goniometer or VG) was designed using a standard multibody system geometry. Two approaches were used to adjust the VG parameters: a parametrical adjustment of the VG linkage geometry, and a functional adjustment of the potentiometer calibration curves (angle-voltage) in a predefined range of motion. After calibration, 6R-ISL accuracy was better than 1 mm and 1 degrees for translation and orientation, respectively. The functional method presented in this paper can be suggested as a practical approach, which allows on-line checking and calibration of 6R-ISL within the specific range of interest of a particular anatomical joint. In addition, improving the potentiometer calibration curves was less time consuming than the parametrical adjustment.

Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading

The objectives of this study were (1) to develop subject-specific experimental and finite element (FE) techniques to study the three-dimensional stress-strain behavior of ligaments, with application to the human medial collateral ligament (MCL), and (2) to determine the importance of subject-specific material properties and initial (in situ) strain distribution for prediction of the strain distribution in the MCL under valgus loading. Eight male knees were subjected to varus-valgus loading at flexion angles of 0 degrees, 30 degrees, and 60 degrees. Three-dimensional joint kinematics and MCL strains were recorded during kinematic testing. Following testing, the MCL of each knee was removed to allow measurement of the in situ strain distribution and to perform material testing. A FE model of the femur-MCL-tibia complex was constructed for each knee to simulate valgus loading at each flexion angle, using subject-specific bone and ligament geometry, material properties, and joint kinematics. A transversely isotropic hyperelastic material model was used to represent the MCL. The MCL in situ strain distribution at full extension was used to apply in situ strain to each MCL FE model. FE predicted MCL strains during valgus loading were compared to experimental measurements using regression analysis. The subject-specific FE predictions of strain correlated reasonably well with experimentally measured MCL strains (R(2)=0.83, 0.72, and 0.66 at 0 degrees, 30 degrees, and 60 degrees, respectively). Despite large inter-subject variation in MCL material properties, MCL strain distributions predicted by individual FE models that used average MCL material properties were strongly correlated with subject-specific FE strain predictions (R(2)=0.99 at all flexion angles). However, predictions by FE models that used average in situ strain distributions yielded relatively poor correlations with subject-specific FE predictions (R(2)=0.44, 0.35, and 0.33 at flexion angles of 0 degrees, 30 degrees, and 60 degrees, respectively). The strain distribution within the MCL was nonuniform and changed with flexion angle. The highest MCL strains occurred at full extension in the posterior region of the MCL proximal to the joint line during valgus loading, suggesting this region may be most vulnerable to injury under these loading conditions. This work demonstrates that subject-specific FE models can predict the complex, nonuniform strain fields that occur in ligaments due to external loading of the joint.

Comparison of three kinematic analyses of the knee: determination of intrinsic features and applicability to intraoperative procedures

The evaluation of knee motion is an important step for correct diagnoses and optimal surgical reconstructions, but controversial opinions still remain about the most suitable numerical method for the elaboration of clinical kinematic tests. In this paper, we present a comparison of three methods applied to an experimental animal study (Grood and Suntay method [Grood, E.S. and Suntay, W.J. (1983) "A coordinate system for the clinical description of three-dimensional motions: application to the knee", J. Biomech. Engng, 105, pp. 136-144], Helical Axes method [Blankevoort, L., Huiskes, R. and de Lange, A. (1990). "Helical axes of passive knee joint motions", J. Biomech., 23 pp. 1219-1229] and Functional method [Martelli, S., Zaffagnini, S., Falcioni, B. and Marcacci, M. (2000). "Intraoperative kinematic protocol for knee joint evaluation", Comput. Methods Programs Biomed., 62 pp. 77-86]). The study shows the numerical differences among the three protocols and evaluates their performances and repeatability during clinical tests, i.e. laxity measurements and passive range of motion. The Functional method gives the optimal compromise among accuracy, clinical interpretability and ease of use for intraoperative kinematic evaluations.

A method for measuring joint kinematics designed for accurate registration of kinematic data to models constructed from CT data

A method for measuring three-dimensional kinematics that incorporates the direct cross-registration of experimental kinematics with anatomic geometry from Computed Tomography (CT) data has been developed. Plexiglas registration blocks were attached to the bones of interest and the specimen was CT scanned. Computer models of the bone surface were developed from the CT image data. Determination of discrete kinematics was accomplished by digitizing three pre-selected contiguous surfaces of each registration block using a three-dimensional point digitization system. Cross-registration of bone surface models from the CT data was accomplished by identifying the registration block surfaces within the CT images. Kinematics measured during a biomechanical experiment were applied to the computer models of the bone surface. The overall accuracy of the method was shown to be at or below the accuracy of the digitization system used. For this experimental application, the accuracy was better than +/-0.1mm for position and 0.1 degrees for orientation for linkage digitization and better than +/-0.2mm and +/-0.2 degrees for CT digitization. Surface models of the radius and ulna were constructed from CT data, as an example application. Kinematics of the bones were measured for simulated forearm rotation. Screw-displacement axis analysis showed 0.1mm (proximal) translation of the radius (with respect to the ulna) from supination to neutral (85.2 degrees rotation) and 1.4mm (proximal) translation from neutral to pronation (65.3 degrees rotation). The motion of the radius with respect to the ulna was displayed using the surface models. This methodology is a useful tool for the measurement and application of rigid-body kinematics to computer models.

Knee joint motion: description and measurement

Knee joint motion has been described in various ways in the literature. These are explained and commented on. Two methods for describing knee joint motion with 6 degrees of freedom (DOF)--Euler angle and the helical axis of motion--are discussed. Techniques to measure joint motion which can either approximate the motion to less than 6 DOF or fully measure the spatial motion are identified. These include electrical linkage methods, radiographic and video techniques, fluoroscopic techniques and electromagnetic devices. In those cases where the full spatial motion is measured, the data are available to describe the motion in simpler terms (or with less DOF) than three rotations with three translations. This is necessary for clinical application and to facilitate communication between the clinician and the engineer.

Mechanics of the anterior drawer and talar tilt tests. A cadaveric study of lateral ligament injuries of the ankle

We analyzed the changes in lateral ligament forces during anterior drawer and talar tilt testing and examined ankle joint motion during testing, following an isolated lesion of the anterior talofibular ligament (ATFL) or a combined lesion of the ATFL and calcaneofibular ligament (CFL). 8 cadaver specimens were held in a specially designed testing apparatus in which the ankle position (dorsiflexion-plantarflexion and supination-pronation) could be varied in a controlled manner. Ligament forces were measured with buckle transducers, and joint motion was measured with an instrumented spatial linkage. An anterior drawer test was performed using an 80 N anterior translating force, and a talar tilt test was performed using a 5.7 Nm supination torque with intact ligaments, after sectioning of the ATFL, and again after sectioning of the CFL. The tests were repeated at 10 degrees dorsiflexion, neutral, and 10 degrees and 20 degrees plantarflexion. In the intact ankle, the largest increases in ATFL force were observed during testing in plantarflexion, whereas the largest increases in CFL force were observed in dorsiflexion. Isolated ATFL injury caused only small laxity changes, but a pronounced increase in laxity was observed after a combined CFL and ATFL injury.

Biomechanics of ankle ligament reconstruction. An in vitro comparison of the Broström repair, Watson-Jones reconstruction, and a new anatomic reconstruction technique

We wanted to use biomechanical testing in a cadaveric model to compare the Broström repair, the Watson-Jones reconstruction, and a new anatomic reconstruction method. Eight specimens were held in a specially designed testing apparatus in which the ankle position (dorsiflexion-plantar flexion and supination-pronation) could be varied in a controlled manner. Testing was done with intact ligaments and was repeated after sectioning of the anterior talofibular ligament and the calcaneofibular ligament and after a Broström repair, a Watson-Jones reconstruction, and a new anatomic reconstruction were performed. An anterior drawer test was performed using an anterior translating force of 10 to 50 N, and a talar tilt test was performed using a supination torque of 1.1 to 3.4 N-m. The forces in the anterior talofibular ligament and calcaneofibular ligament were measured with buckle transducers, and tibiotalar motion and total ankle joint motion were measured with an instrumented spatial linkage. The increase in ankle joint laxity observed after sectioning of both the anterior talofibular and calcaneofibular ligaments was significantly reduced by the three reconstructive techniques, although not always to the level of the intact ankle. Joint motion was restricted after the Watson-Jones procedure compared with that in the intact ankle. Unlike the Watson-Jones procedure, the ligament or graft force patterns observed during loading after the Broström repair and the new anatomic technique resembled those observed in the intact ankle.

On improving the accuracy of instrumented spatial linkage system

Calibration is important for improving the accuracy of instrumented spatial linkage (ISL) in the application of biomechanical studies. The assumption of the linear performance of the potentiometer transducer has limited the improvement of the linkage accuracy. We present a non-linear numerical calibration procedure and double potentiometer design to improve the accuracy of ISL. Through the use of a three-degree-of-freedom linkage, the non-linear calibration procedure and the double potentiometer design were shown to be effective in reducing the ISL errors. The error, i.e. standard deviation for the angle decreased from +/-0.38 degree to +/-0.12 degree while the same for the translation decreased from +/-0.41 to +/-0.16 mm. A high-accuracy linkage system using low-cost potentiometers could be constructed by using our calibration method and double potentiometer design.