Computed tomography analysis of radiostereometric data to determine flexion axes after total joint replacement: Application to the elbow joint

Kinematic analysis for in vivo assessment of elbow endoprostheses requires knowledge of the exact positions of motion axes relative to bony landmarks or the prosthesis. A prosthesis-based reference system is required for comparison between individuals and studies. The primary aim of this study was to further develop an earlier described algorithm for fusion of radiostereometric analysis (RSA) data and data obtained in 3D computed tomography (CT) for application to the elbow after total joint replacement. The secondary aim was to propose a method for marking of prostheses in 3D CT, enabling definition of a prosthesis-based reference system. Six patients with elbow endoprostheses were investigated.The fusion of data made it possible to visualize the motion axes in relation to the prostheses in the 3D CT volume. The differences between two repeated positioning repetitions of the longitudinal prosthesis axis were less than 0.6° in the frontal and sagittal planes. Corresponding values for the transverse axis were less than 0.6° in the frontal and less than 1.4° (in four out of six less than 0.6°) in the horizontal plane.This study shows that by fusion of CT and RSA data it is possible to determine the accurate position of the flexion axes of the elbow joint after total joint replacement in vivo. The proposed method for implant marking and registration of reference axes enables comparison of prosthesis function between patients and studies.     

A new non-orthogonal decomposition method to determine effective torques for three-dimensional joint rotation

This paper describes a new non-orthogonal decomposition method to determine effective torques for three-dimensional (3D) joint rotation. A rotation about a joint coordinate axis (e.g. shoulder internal/external rotation) cannot be explained only by the torque about the joint coordinate axis because the joint coordinate axes usually deviate from the principal axes of inertia of the entire kinematic chain distal to the joint. Instead of decomposing torques into three orthogonal joint coordinate axes, our new method decomposes torques into three "non-orthogonal effective axes" that are determined in such a way that a torque about each effective axis produces a joint rotation only about one of the joint coordinate axes. To demonstrate the validity of this new method, a simple internal/external rotation of the upper arm with the elbow flexed at 90 degrees was analyzed by both orthogonal and non-orthogonal decomposition methods. The results showed that only the non-orthogonal decomposition method could explain the cause-effect mechanism whereby three angular accelerations at the shoulder joint are produced by the gravity torque, resultant joint torque, and interaction torque. The proposed method would be helpful for biomechanics and motor control researchers to investigate the manner in which the central nervous system coordinates the gravity torque, resultant joint torque, and interaction torque to control 3D joint rotations.     

Imaging knee position using MRI, RSA/CT and 3D digitisation

The purpose of this study was to compare 3 methods of imaging knee position. Three fresh cadaver knees were imaged at 6 flexion angles between 0 degrees and 120 degrees by MRI, a combination of RSA and CT and 3D digitisation (in two knees). Virtual models of all 42 positions were created using suitable computer software. Each virtual model was aligned to a newly defined anatomically based Cartesian coordinate system. The angular rotations around the 3 coordinate system axes were calculated directly from the aligned virtual models using rigid body kinematics and found to be equally accurate for the 3 methods. The 3 rotations in each knee could be depicted using anatomy-based diagrams for all 3 methods. We conclude that the 3 methods of data acquisition are equally and adequately accurate in vitro. MRI may be the most useful in vivo.     

A joint coordinate system proposal for the study of the trapeziometacarpal joint kinematics

The International Society of Biomechanics (ISB) has recommended a standardisation for the motion reporting of almost all human joints. This study proposes an adaptation for the trapeziometacarpal joint.

The definition of the segment coordinate system of both trapezium and first metacarpal is based on functional anatomy. The definition of the joint coordinate system (JCS) is guided by the two degrees of freedom of the joint, i.e. flexion–extension about a trapezium axis and abduction–adduction about a first metacarpal axis. The rotations obtained using three methods are compared on the same data: the fixed axes sequence proposed by Cooney et al., the mobile axes sequence proposed by the ISB and our alternative mobile axes sequence. The rotation amplitudes show a difference of 9° in flexion–extension, 2° in abduction–adduction and 13° in internal–external rotation.

This study emphasizes the importance of adapting the JCS to the functional anatomy of each particular joint.     

Expression of joint moment in the joint coordinate system

The question of using the nonorthogonal joint coordinate system (JCS) to report joint moments has risen in the literature. However, the expression of joint moments in a nonorthogonal system is still confusing. The purpose of this paper is to present a method to express any 3D vector in a nonorthogonal coordinate system. The interpretation of these expressions in the JCS is clarified and an example for the 3D joint moment vector at the shoulder and the knee is given. A nonorthogonal projection method is proposed based on the mixed product. These nonorthogonal projections represent, for a 3D joint moment vector, the net mechanical action on the JCS axes. Considering the net mechanical action on each axis seems important in order to assess joint resistance in the JCS. The orthogonal projections of the same 3D joint moment vector on the JCS axes can be characterized as "motor torque." However, this interpretation is dependent on the chosen kinematic model. The nonorthogonal and orthogonal projections of shoulder joint moment during wheelchair propulsion and knee joint moment during walking were compared using root mean squares (rmss). rmss showed differences ranging from 6 N?m to 22.3 N?m between both projections at the shoulder, while differences ranged from 0.8 N?m to 3.0 N?m at the knee. Generally, orthogonal projections were of lower amplitudes than nonorthogonal projections at both joints. The orthogonal projection on the proximal or distal coordinates systems represents the net mechanical actions on each axis, which is not the case for the orthogonal projection (i.e., motor torque) on JCS axes. In order to represent the net action at the joint in a JCS, the nonorthogonal projection should be used.     

Quantifying translations in the radiohumeral joint: application of a floating axis analysis

The purpose of this study was to apply the Floating Axis analysis technique to the elbow joint, and to verify its ability to quantify clinically relevant radiohumeral translation in vitro using an electromagnetic tracking device. Of particular interest was the ability to quantify changes in anterior-posterior radial head translation, which is associated with the clinical condition of posterolateral rotatory instability of the elbow. Following the method proposed by Grood and Suntay to determine motions in the knee, an elbow coordinate system with axes representing the flexion-extension axis of the humerus, the long axis of the radius, and their mutual perpendicular, was developed. The algorithm was tested using a mechanical articulator that modeled the Floating Axis approach. Translation errors using this articulator were 0.1+/-0.1mm. The algorithm was applied to kinematic data collected from 12 cadaveric elbows that underwent a pivot shift test prior and subsequent to transection of the lateral collateral ligament. Anterior-posterior radiohumeral translation increased significantly in these elbows following the ligament sectioning (p<0.0001), with the average magnitude of posterior translation increasing from 0.9 to 19.8mm at 90 degrees of flexion. This approach will provide valuable information related to alterations in elbow motion pathways, especially for studies aimed at quantifying changes in joint stability.     

In vivo determination of the direction of rotation and moment-angle relationship of individual elbow muscles.

The direction of rotation (DOR) of individual elbow muscles, defined as the direction in which a muscle rotates the forearm relative to the upper arm in three-dimensional space, was studied in vivo as a function of elbow flexion and forearm rotation. Electrical stimulation was used to activate an individual muscle selectively, and the resultant flexion-extension, supination-pronation, and varus-valgus moments were used to determine the DOR. Furthermore, multi-axis moment-angle relationships of individual muscles were determined by stimulating the muscle at a constant submaximal level across different joint positions, which was assumed to result in a constant level of muscle activation. The muscles generate significant moments about axes other than flexion-extension, which is potentially important for actively controlling joint movement and maintaining stability about all axes. Both the muscle DOR and the multi axis moments vary with the joint position systematically. Variations of the DOR and moment-angle relationship across muscle twitches of different amplitudes in a subject were small, while there were considerable variations between subjects.     

Image-based RSA: Roentgen stereophotogrammetric analysis based on 2D-3D image registration

Image-based Roentgen stereophotogrammetric analysis (IBRSA) integrates 2D-3D image registration and conventional RSA. Instead of radiopaque RSA bone markers, IBRSA uses 3D CT data, from which digitally reconstructed radiographs (DRRs) are generated. Using 2D-3D image registration, the 3D pose of the CT is iteratively adjusted such that the generated DRRs resemble the 2D RSA images as closely as possible, according to an image matching metric. Effectively, by registering all 2D follow-up moments to the same 3D CT, the CT volume functions as common ground. In two experiments, using RSA and using a micromanipulator as gold standard, IBRSA has been validated on cadaveric and sawbone scapula radiographs, and good matching results have been achieved. The accuracy was: |mu |< 0.083 mm for translations and |mu| < 0.023 degrees for rotations. The precision sigma in x-, y-, and z-direction was 0.090, 0.077, and 0.220 mm for translations and 0.155 degrees , 0.243 degrees , and 0.074 degrees for rotations. Our results show that the accuracy and precision of in vitro IBRSA, performed under ideal laboratory conditions, are lower than in vitro standard RSA but higher than in vivo standard RSA. Because IBRSA does not require radiopaque markers, it adds functionality to the RSA method by opening new directions and possibilities for research, such as dynamic analyses using fluoroscopy on subjects without markers and computer navigation applications.     

Calculating the axes of rotation for the subtalar and talocrural joints using 3D bone reconstructions

Orientation of the subtalar joint axis dictates inversion and eversion movements of the foot and has been the focus of evolutionary and clinical studies for a number of years. Previous studies have measured the subtalar joint axis against the axis of the whole foot, the talocrural joint axis and, recently, the principal axes of the talus. The present study introduces a new method for estimating average joint axes from 3D reconstructions of bones and applies the method to the talus to calculate the subtalar and talocrural joint axes. The study also assesses the validity of the principal axes as a reference coordinate system against which to measure the subtalar joint axis. In order to define the angle of the subtalar joint axis relative to that of another axis in the talus, we suggest measuring the subtalar joint axis against the talocrural joint axis. We present corresponding 3D vector angles calculated from a modern human skeletal sample. This method is applicable to virtual 3D models acquired through surface-scanning of disarticulated 'dry' osteological samples, as well as to 3D models created from CT or MRI scans.     

In vivo measurements of moment arm lengths of three elbow flexors at rest and during isometric contractions

The purpose of this study was to determine in vivo moment arm lengths (MAs) of three elbow flexors at rest and during low- and relatively high-intensity contractions, and to examine the contraction intensity dependence of MAs at different joint positions. At 50°, 80° and 110° of elbow flexion, MAs of the biceps brachii, brachialis and brachioradialis were measured in 10 young men using sagittal images of the right arm obtained by magnetic resonance imaging, at rest and during 20% and 60% of isometric maximal voluntary elbow flexion. In most conditions, MAs increased with isometric contractions, which is presumably due to the contraction-induced thickening of the muscles. This phenomenon was especially evident in the flexed elbow positions. The influence of the contraction intensities on the increases in MAs varied across the muscles. These results suggest that in vivo measurements of each elbow flexor MA during contractions are essential to properly examine the effects on the interrelationships between elbow flexion torque and individual muscle forces.     

Comparison of the hindfoot axes of a multi-segment foot model to the underlying bony anatomy

Musculoskeletal models used in gait analysis require coordinate systems to be identified for the body segments of interest. It is not obvious how hindfoot (or rearfoot) axes defined by skin-mounted markers relate to the anatomy of the underlying bones. The aim of this study was to compare the marker-based axes of the hindfoot in a multi-segment foot model to the orientations of the talus and calcaneus as characterized by their principal axes of inertia. Twenty adult females with no known foot deformities had radio-opaque markers placed on their feet and ankles at the foot model marker locations. CT images of the feet were acquired as the participants lay supine with their feet in a semi-weight bearing posture. The spatial coordinates of the markers were obtained from the images and used to define the foot model axes. Segmented masks of the tali and calcanei were used to create 3D bone models, from which the principal axes of the bones were obtained. The orientations of the principal axes were either within the range of typical values reported in the imaging literature or differed in ways that could be explained by variations in how the angles were defined. The model hindfoot axis orientations relative to the principal axes of the bones had little bias but were highly variable. Consideration of coronal plane hindfoot alignment as measured clinically and radiographically suggested that the model hindfoot coordinate system represents the posterior calcaneal tuberosity, rather than the calcaneus as a whole.     

Evaluation of a 3D object registration method for analysis of humeral kinematics

In 3D image-based studies of joint kinematics, 3D registration methods should be automatic, insensitive to segmentation inconsistencies and use coordinate systems that have clinically relevant orientations and locations because this is important for analyzing rotation angles and translation directions. We developed and evaluated a registration method, which is based on the cylindrical geometry of the humerus shaft and an analysis of the inertia moments of the humerus head, in order to consistently and automatically orient the humerus coordinate system according to its anatomy. Registration techniques must be thoroughly evaluated. In this study we used a well-detectable marker as reference, from which coordinate system determination errors of a 3D object could be measured. This allowed us to quantify by means of unique error analysis the translational and rotational errors in terms of how much and about/along which humeral axis errors occurred. The evaluation experiments were performed using virtual rotations of 3D humeral binary image, a humerus model and a 3D image of a volunteer's shoulder. They indicated that the humeral coordinate system determination errors primarily originated from segmentation inconsistencies, which influenced mostly the humeral transverse axes orientation. The error analysis revealed that the developed registration method reduced the effect of manual segmentation inconsistencies on the orientation of the humeral transverse axes up to 37%, in comparison to the commonly used inertia registration.     

A technical method using musculoskeletal model to analyse dynamic properties of muscles during human movement

An effective way to avoid invading or injuring the subjects is to use the musculoskeletal model when studying the dynamic properties of muscles in vivo. So, we put forward a joint coordinate system-based method, which mainly focuses on the coordinate's transformation of corresponding muscle attachment points, respectively, in the model and the subject in order to reproduce the movement of the subject on the model. As muscle moment arm is usually used to evaluate the dynamic properties of muscles, the moment arms in elbow flexion for each of the major muscles crossing the elbow in 50 healthy subjects (25 males and 25 females), ranging in height from 1.50 to 1.80 m (mean 1.6542 m) are calculated and compared with the measured data obtained from anatomical studies reported in the literature. The trends of the value basically coincide with each other. So, this novel method can be valid.     

Sensitivity of the knee joint kinematics calculation to selection of flexion axes

Various flexion axes have been used in the literature to describe knee joint kinematics. This study measured the passive knee kinematics of six cadaveric human knee specimens using two widely accepted flexion axes; transepicondylar axis and the geometric center axis. These two axes were found to form an angle of 4.0 degrees +/- 0.8 degrees. The tibial rotation calculated using the transepicondylar axis was significantly different than the rotation obtained using the geometric center axis for the same knee motion. At 90 degrees of flexion, the tibial rotation obtained using the transepicondylar axis was 4.8 degrees +/- 9.4 degrees whereas the rotation recorded using the geometric center axis at the same flexion angle was 13.8 degrees +/- 10.2 degrees. At 150 degrees of knee flexion, the rotations obtained from the transepicondylar and the geometric center axes were 7.2 degrees +/- 5.7 degrees and 19.9 degrees +/- 6.9 degrees, respectively. The data suggest that a clear definition of the flexion axis is necessary when reporting knee joint kinematics.     

Problems in reconstruction of fossil anatomy and locomotor behaviour: The Dryopithecus elbow complex

Problems in reconstruction of Dryopithecus elbow anatomy are presented. The articular surfaces in the Dryopithecus elbow complex are missing in fossil specimens with the exception of the D. (Proconsul) africanus distal humerus and movement capabilities must be reconstructed (KNM-RU2036). Particular attention is paid to the anatomical relationships of the capitulum and the bi-epicondylar breadth. Lacking structure of the joint surfaces and data concerning the direction and range of joint movements in most taxa, interpretation of associated inferred positional behaviour is premature.     

A technical method using musculoskeletal model to analyse dynamic properties of muscles during human movement

An effective way to avoid invading or injuring the subjects is to use the musculoskeletal model when studying the dynamic properties of muscles in vivo. So, we put forward a joint coordinate system-based method, which mainly focuses on the coordinate's transformation of corresponding muscle attachment points, respectively, in the model and the subject in order to reproduce the movement of the subject on the model. As muscle moment arm is usually used to evaluate the dynamic properties of muscles, the moment arms in elbow flexion for each of the major muscles crossing the elbow in 50 healthy subjects (25 males and 25 females), ranging in height from 1.50 to 1.80 m (mean 1.6542 m) are calculated and compared with the measured data obtained from anatomical studies reported in the literature. The trends of the value basically coincide with each other. So, this novel method can be valid.     

A joint coordinate system proposal for the study of the trapeziometacarpal joint kinematics

The International Society of Biomechanics (ISB) has recommended a standardisation for the motion reporting of almost all human joints. This study proposes an adaptation for the trapeziometacarpal joint. The definition of the segment coordinate system of both trapezium and first metacarpal is based on functional anatomy. The definition of the joint coordinate system (JCS) is guided by the two degrees of freedom of the joint, i.e. flexion-extension about a trapezium axis and abduction-adduction about a first metacarpal axis. The rotations obtained using three methods are compared on the same data: the fixed axes sequence proposed by Cooney et al., the mobile axes sequence proposed by the ISB and our alternative mobile axes sequence. The rotation amplitudes show a difference of 9 degrees in flexion-extension, 2 degrees in abduction-adduction and 13 degrees in internal-external rotation. This study emphasizes the importance of adapting the JCS to the functional anatomy of each particular joint.     

Surface EMG force modeling with joint angle based calibration

In this paper, a calibration method to compensate for changes in SEMG amplitude with joint angle is introduced. Calibration factors were derived from constant amplitude surface electromyogram (SEMG) recordings from the biceps brachii (during elbow flexion) and the triceps brachii (during elbow extension) across seven elbow joint angles. SEMG data were then recorded from the elbow flexors (biceps brachii and brachioradialis) and extensors (triceps brachii) during isometric, constant force flexion and extension contractions at the same joint angles. The resulting force at the wrist was measured. The fast orthogonal search method was used to find a mapping between the system inputs – estimated SEMG amplitudes and joint angle – and the system output – measured force, for both calibrated and non-calibrated SEMG data. Models developed with calibrated data yielded a statistically significant improvement in force estimation compared to models developed with non-calibrated data, suggesting that the calibration method can compensate for changes in the SEMG–force relationship with changing joint angle. It was also found that the number of non-linear, joint angle-dependent terms used in the SEMG–force model was reduced with calibration. Additionally, initial inter-session analysis performed for four subjects suggests that calibration values can be used for subsequent recording sessions, and different output force levels.     

Orientation and location of the finite helical axis of the equine forelimb joints

To reduce anatomically unrealistic limb postures in a virtual musculoskeletal model of a horse's forelimb, accurate knowledge on forelimb joint constraints is essential. The aim of this cadaver study is to report all orientation and position changes of the finite helical axes (FHA) as a function of joint angle for different equine forelimb joints. Five horse cadaver forelimbs with standardized cuts at the midlevel of each segment were used. Bone pins with reflective marker triads were drilled into the forelimb bones. Unless joint angles were anatomically coupled, each joint was manually moved independently in all three rotational degrees of freedom (flexion–extension, abduction–adduction, internal–external rotation). The 3D coordinates of the marker triads were recorded using a six infra-red camera system. The FHA and its orientational and positional properties were calculated and expressed against joint angle over the entire range of motion using a finite helical axis method. When coupled, joint angles and FHA were expressed in function of flexion–extension angle. Flexion–extension movement was substantial in all forelimb joints, the shoulder allowed additional considerable motion in all three rotational degrees of freedoms. The position of the FHA was constant in the fetlock and elbow and a constant orientation of the FHA was found in the shoulder. Orientation and position changes of the FHA over the entire range of motion were observed in the carpus and the interphalangeal joints. We report FHA position and orientation changes as a function of flexion–extension angle to allow for inclusion in a musculoskeletal model of a horse to minimize calculation errors caused by incorrect location of the FHA.     

The effect of patient positioning on the precision of model-based radiostereometric analysis

A repeatable method for in vivo and in vitro measurement of polyethylene wear in total knee replacement (TKA) is needed. This research examines the model-based radiostereometric analysis’ (MBRSA) in vitro precision under different patient-radiograph orientations and flexion angles of the knee using a TKA phantom. Anterior–posterior and medial–lateral imaging orientations showed the highest precision; better than 0.036 mm (3-dimensional translation) and 0.089° (3-dimensional rotation). Flexion of the knee did not affect MBRSA precision. Medial–lateral imaging is advantageous as it allows for flexion of the knee joint during an RSA examination, thus providing greater information for wear measurement.