In vivo estimation of the glenohumeral joint centre by functional methods: Accuracy and repeatability assessment

Several algorithms have been proposed for determining the centre of rotation of ball joints. These algorithms are used rather to locate the hip joint centre. Few studies have focused on the determination of the glenohumeral joint centre. However, no studies have assessed the accuracy and repeatability of functional methods for glenohumeral joint centre.This paper aims at evaluating the accuracy and the repeatability with which the glenohumeral joint rotation centre (GHRC) can be estimated in vivo by functional methods. The reference joint centre is the glenohumeral anatomical centre obtained by medical imaging. Five functional methods were tested: the algorithm of Gamage and Lasenby (2002), bias compensated (Halvorsen, 2003), symmetrical centre of rotation estimation (Ehrig et al., 2006), normalization method (Chang and Pollard, 2007), helical axis (Woltring et al., 1985). The glenohumeral anatomical centre (GHAC) was deduced from the fitting of the humeral head.Four subjects performed three cycles of three different movements (flexion/extension, abduction/adduction and circumduction). For each test, the location of the glenohumeral joint centre was estimated by the five methods. Analyses focused on the 3D location, on the repeatability of location and on the accuracy by computing the Euclidian distance between the estimated GHRC and the GHAC. For all the methods, the error repeatability was inferior to 8.25 mm. This study showed that there are significant differences between the five functional methods. The smallest distance between the estimated joint centre and the centre of the humeral head was obtained with the method of Gamage and Lasenby (2002).     

Repeatability assessment of functional methods to estimate the glenohumeral joint centre

Functional methods can be used to determine the centre of rotation (CoR) of a ball-and-socket joint. The algorithms are used to locate rather the hip joint centre than the glenohumeral joint centre. The choice of the most suitable method depends especially on the intra- and inter-session repeatability of these methods. This paper aims at evaluating the intra- and inter-session repeatability of functional methods with which the glenohumeral joint rotation centre (GHRC) can be estimated in vivo. It also estimates the most suitable amplitude of functional movements. Five functional methods were tested: the algorithms of Gamage and Lasenby, bias compensation, symmetrical CoR estimation, normalisation method and helical axis. Ten subjects performed three cycles of three different movements (flexion–extension, abduction–adduction and circumduction). These movements were repeated three times with three different ranges of motion. Six subjects came back in order to evaluate the inter-session repeatability. For each test, the location of the GHRC was estimated by the five methods. The method to solve the functional problem and the range of functional movement affected the GHRC location. The results showed a good to excellent intra-session repeatability. The lowest repeatability error was found for the high amplitude whatever the methods used. The inter-session reliability was moderate. Finally, we suggest the use of functional methods with high amplitude movement in order to locate the GHRC with the best reliability.     

The SCoRE residual: a quality index to assess the accuracy of joint estimations

The determination of an accurate centre of rotation (CoR) from skin markers is essential for the assessment of abnormal gait patterns in clinical gait analysis. Despite the many functional approaches to estimate CoRs, no non-invasive analytical determination of the error in the reconstructed joint location is currently available. The purpose of this study was therefore to verify the residual of the symmetrical centre of rotation estimation (SCoRE) as a reliable indirect measure of the error of the computed joint centre. To evaluate the SCoRE residual, numerical simulations were performed to evaluate CoR estimations at different ranges of joint motion. A statistical model was developed and used to determine the theoretical relationships among the SCoRE residual, the magnitude of the skin marker artefact, the corrections to the marker positions, and the error of the CoR estimations to the known centre of rotation. We found that the equation err=0.5r(s) provides a reliable relationship among the CoR error, err, and the scaled SCoRE residual, r(s), providing that any skin marker artefact is first minimised using the optimal common shape technique (OCST). Measurements on six healthy volunteers showed a reduction of SCoRE residual from 11 to below 6mm and therefore demonstrated consistency of the theoretical considerations and numerical simulations with the in vivo data. This study also demonstrates the significant benefit of the OCST for reducing skin marker artefact and thus for predicting the accuracy of determining joint centre positions in functional gait analysis. For the first time, this understanding of the SCoRE residual allows a measure of error in the non-invasive assessment of joint centres. This measure now enables a rapid assessment of the accuracy of the CoR as well as an estimation of the reproducibility and repeatability of skeletal motion patterns.     

The glenohumeral joint rotation centre in vivo

Within the framework of the current call for standardization in upper extremity research, three methods to determine the glenohumeral joint rotation centre in vivo were tested. Therefore, subjects performed humeral movements, while a 3D electromagnetic tracking device registered the motion of the humerus with respect to the scapula. For the first method to estimate the glenohumeral joint rotation centre five scapular bony landmarks served as input to regression equations. The second method fitted a sphere through the humeral position data and the third method calculated the rotation centre determining an optimal helical axis. The experiment consisted of two parts, at first one subject was measured 10 times, subsequently one observer measured 10 subjects twice and another observer measured these subjects once. The first part of the experiment demonstrated that all methods are capable to reproduce the rotation centre within 4 mm, but the location of the centre differed significantly between methods (p<0.001). The second part, showed that inter- and intra-observer reliability was sufficiently for the sphere-fitting method and for the helical-axes method. The two observations of one observer differed significantly (p<0.008) using the regression method. The authors prefer the helical-axes method, it is a reliable and valid method which can be applied in movement registration of healthy subjects and patients with a shoulder endoprosthesis, it can be applied in hinge joints to determine a rotation axis instead of a rotation centre which is desirable in standardized upper extremity research, and calculation time is short.     

Effects of gleno-humeral joint centre mislocation on gleno-humeral kinematics and kinetics

The gleno-humeral (GH) rotation centre is typically estimated using predictive or functional methods, however these methods may lead to location errors. This study aimed at determining a location error threshold above which statistically significant changes in the values of kinematic and kinetic GH parameters occur. The secondary aims were to quantify the effects of the direction of mislocation (X, Y or Z axis) of the GH rotation centre on GH kinematic and kinetic parameters.

Shoulder flexion and abduction movements of 11 healthy volunteers were recorded using a standard motion capture system (Vicon, Oxford Metrics Ltd, Oxford, UK), then GH kinematic and kinetic parameters were computed. The true position of the GH rotation centre was determined using a low dose x-ray scanner (EOS? imaging, France) and this position was transferred to the motion data. GH angles and moments were re-computed for each position of the GH rotation centre after errors of up to ± 20?mm were added in increments of ± 5?mm to each axis. The three-dimensional error range was 5?mm to 34.65?mm.

GH joint angle and moment values were significantly altered from 10?mm of three-dimensional error, and from 5?mm of error on individual axes. However, errors on the longitudinal and antero-posterior axes only caused very small alterations of GH joint angle and moment values respectively. Future research should develop methods of GH rotation centre estimation that produce three-dimensional location errors of less than 10?mm to reduce error propagation on GH kinematics and kinetics.     

Hip joint centre location: An ex vivo study

The human hip joint is normally represented as a spherical hinge and its centre of rotation is used to construct femoral anatomical axes and to calculate hip joint moments. The estimate of the hip joint centre (HJC) position using a functional approach is affected by stereophotogrammetric errors and soft tissue artefacts. The aims of this study were (1) to assess the accuracy with which the HJC position can be located using stereophotogrammetry and (2) to investigate the effects of hip motion amplitude on this accuracy. Experiments were conducted on four adult cadavers. Cortical pins, each equipped with a marker cluster, were implanted in the pelvis and femur, and eight skin markers were attached to the thigh. Recordings were made while an operator rotated the hip joint exploiting the widest possible range of motion. For HJC determination, a proximal and a distal thigh skin marker cluster and two recent analytical methods, the quartic sphere fit (QFS) method and the symmetrical centre of rotation estimation (SCoRE) method, were used. Results showed that, when only stereophotogrammetric errors were taken into account, the analytical methods performed equally well. In presence of soft tissue artefacts, HJC errors highly varied among subjects, methods, and skin marker clusters (between 1.4 and 38.5 mm). As expected, larger errors were found in the subject with larger soft tissue artefacts. The QFS method and the distal cluster performed generally better and showed a mean HJC location accuracy better than 10 mm over all subjects. The analysis on the effect of hip movement amplitude revealed that a reduction of the amplitude does not improve the HJC location accuracy despite a decrease of the artefact amplitude.     

A survey of formal methods for determining the centre of rotation of ball joints

The determination of an accurate centre of rotation (CoR) from segment marker positions is of interest across a wide range of applications, but particularly for clinical gait analysis and for estimating the hip joint centre during surgical intervention of the knee, for limb alignment purposes. For the first time in this survey of formal methods, we classify, analyse and compare different methods (geometric, algebraic, bias compensated algebraic, and Pratt sphere fit methods, as well as the centre transformation technique, the Holzreiter approach, the helical pivot technique, the Schwartz transformation techniques, the minimal amplitude point method and the Stoddart approach) for the determination of spherical joint centres from marker position data. In addition, we propose a new method, the symmetrical CoR estimation or SCoRE, in which the coordinates of the joint centre must only remain constant relative to each segment, thus not requiring the assumption that one segment should remain at rest. For each method, 1000 CoR estimations were analysed with the application of isotropic, independent and identically distributed Gaussian noise (standard deviation 0.1cm) to each of the marker positions, to all markers on the segment simultaneously and the two in combination. For the test conditions used here, most techniques were capable of determining the CoR to within 0.3 cm, as long as the spherical range of motion (RoM) of the joint was 45 degrees or more. Under the most stringent conditions tested, however, the SCoRE was capable of best determining the CoR, to within approximately 1.2mm with a RoM of 20 degrees . The correct selection and application of these methodologies should help improve the accuracy of surgical navigation and clinical kinematic measurement.     

The position of the rotation center of the glenohumeral joint

To validate the assumption that the center of rotation in the glenohumeral (GH) joint can be described based on the geometry of the joint, two methods for calculation of the GH rotation center were compared. These are a kinematic estimation based on the calculation of instantaneous helical axes, and a geometric estimation based on a spherical fit through the surface of the glenoid. Four fresh cadaver arms were fixed at the scapula and fitted with electromagnetic sensors. Each arm was moved in different directions while at the same time the orientation of the humerus was recorded. Subsequently, each specimen was dissected and its glenoid and humeral head surfaces were digitized. Results indicate no differences between the methods. It is concluded that the method to estimate the GH center of rotation as the center of a sphere through the glenoid surface, with the radius of the humeral head, appears to be valid.     

Comparison of two methods for in vivo estimation of the glenohumeral joint rotation center (GH-JRC) of the patients with shoulder hemiarthroplasty

Determination of an accurate glenohumeral-joint rotation center (GH-JRC) from marker data is essential for kinematic and dynamic analysis of shoulder motions. Previous studies have focused on the evaluation of the different functional methods for the estimation of the GH-JRC for healthy subjects. The goal of this paper is to compare two widely used functional methods, namely the instantaneous helical axis (IHA) and symmetrical center of rotation (SCoRE) methods, for estimating the GH-JRC in vivo for patients with implanted shoulder hemiarthroplasty. The motion data of five patients were recorded while performing three different dynamic motions (circumduction, abduction, and forward flexion). The GH-JRC was determined using the CT-images of the subjects (geometric GH-JRC) and was also estimated using the two IHA and SCoRE methods. The rotation centers determined using the IHA and SCoRE methods were on average 1.47±0.62 cm and 2.07±0.55 cm away from geometric GH-JRC, respectively. The two methods differed significantly (two-tailed p-value from paired t-Test ～0.02, post-hoc power ～0.30). The SCoRE method showed a significant lower (two-tailed p-value from paired t-Test ～0.03, post-hoc power ～0.68) repeatability error calculated between the different trials of each motion and each subject and averaged across all measured subjects (0.62±0.10 cm for IHA vs. 0.43±0.12 cm for SCoRE). It is concluded that the SCoRE appeared to be a more repeatable method whereas the IHA method resulted in a more accurate estimation of the GH-JRC for patients with endoprostheses.     

Propagation of soft tissue artifacts to the center of rotation: A model for the correction of functional calibration techniques

This paper presents a mathematical model for the propagation of errors in body segment kinematics to the location of the center of rotation. Three functional calibration techniques, usually employed for the gleno-humeral joint, are studied: the methods based on the pivot of the instantaneous helical axis (PIHA) or the finite helical axis (PFHA), and the “symmetrical center of rotation estimation” (SCoRE). A procedure for correcting the effect of soft tissue artifacts is also proposed, based on the equations of those techniques and a model of the artifact, like the one that can be obtained by double calibration. An experiment with a mechanical analog was performed to validate the procedure and compare the performance of each technique. The raw error (between 57 and 68 mm) was reduced by a proportion of between 1:6 and less than 1:15, depending on the artifact model and the mathematical method. The best corrections were obtained by the SCoRE method. Some recommendations about the experimental setup for functional calibration techniques and the choice of a mathematical method are derived from theoretical considerations about the formulas and the results of the experiment.     

MRI development and validation of two new predictive methods of glenohumeral joint centre location identification and comparison with established techniques

Identification of the centre of the glenohumeral joint (GHJ) is essential for three-dimensional (3D) upper limb motion analysis. A number of convenient, yet un-validated methods are routinely used to estimate the GHJ location in preference to the International Society of Biomechanics (ISB) recommended methods. The current study developed a new regression model, and simple 3D offset method for GHJ location estimation, employing easy to administer measures, and compared the estimates with the known GHJ location measured with magnetic resonance imaging (MRI). The accuracy and reliability of the new regression and simple 3D offset techniques were compared with six established predictive methods. Twenty subjects wore a 3D motion analysis marker set that was also visible in MRI. Immediately following imaging, they underwent 3D motion analysis acquisition. The GHJ and anatomical landmark positions of 15 participants were used to determine the new regression and simple 3D generic offset methods. These were compared for accuracy with six established methods using 10 subject's data. A cross validation on 5 participants not used for regression model development was also performed. Finally, 10 participants underwent a further two MRI's and subsequent 3D motion analysis analyses for inter-tester and intra-tester reliability quantification. When compared with any of the other established methods, our newly developed regression model found an average GHJ location closer to the actual MRI location, having an GHJ location error of 13±2 mm, and had significantly lower inter-tester reliability error, 6±4 mm (p<0.01).     

Modeling the stability of the human glenohumeral joint during external rotation

An analytical model of the human glenohumeral joint was developed to predict glenohumeral kinematics and investigate how the glenohumeral capsule and articular contact between the humeral head and the glenoid stabilize the joint. This was performed during a simulation of an apprehension clinical exam or the cocked phase of throwing, when the humerus is susceptible to anterior instability or dislocation. Contact between the joint surfaces was modeled using a deformable articular contact method and the capsule was modeled as five elements with the ability to wrap around the surface of the humeral head. Experimental measurements (Novotny et al., Journal of Shoulder and Elbow surgery, 1998, 7, 629-639) provided geometric data from four in vitro specimens and kinematic results to validate model predictions. Material properties were taken from the literature. An equilibrium approach was used with the forces and moments produced by the ligaments and surface contact balanced against those applied externally to the humerus during external rotation of the abducted and extended humerus. The six equilibrium equations were solved for the position and orientation of the humerus. The center of the humeral head translated posteriorly and superiorly with external rotation. Model predictions for translational and rotational ranges of motion were not significantly different from experimental findings; however, at individual moment increments, the model underestimated the external rotation and overestimated the superior-inferior position of the humerus relative to the glenoid. The anterior band of the inferior glenohumeral ligament increased in tension with external rotation, while the axillary pouch and posterior band decreased in tension. Contact area, stress and force increased with external rotation and the contact area moved posteriorly and inferiorly around the rim of the glenoid. The model results provide information on how the relationship between the ligament element tensions and contact forces may act to avoid glenohumeral instability.     

A musculoskeletal shoulder simulation of moment arms and joint reaction forces after medialization of the supraspinatus footprint in rotator cuff repair

A non-anatomical reinsertion of the supraspinatus medially to the original footprint to avoid over-tensioning of the tendon in large and retracted tears is one surgical option in rotator cuff (RC) repair. The purpose of the study was to determine the biomechanical effects on the glenohumeral joint with regard to this surgical technique. A modified musculoskeletal computational shoulder model was used to evaluate the change in moment arms and muscle forces of the RC and the co-contracting muscles and the alteration of the joint reaction forces (compressive and shear forces) after reinsertion of the supraspinatus 5?mm, 10?mm, 15?mm and 20?mm medially to the original footprint. A medialization of the supraspinatus reduces its moment arm in glenohumeral abduction. In case of a medialization of the attachment of 15?mm and 20?mm, the supraspinatus restricts glenohumeral abduction at 54° and 68°. In glenohumeral forward flexion and in lower degrees of internal rotation the moment arm of the supraspinatus increases for a medialized tendon attachment and decreases in external rotation in relation to the anatomical condition. A medialization of the supraspinatus insertion point yields in an increase in muscle force for abduction, internal and external rotation. In the present model a medially non-anatomic reinsertion reduces significantly the compressive glenohumeral joint reaction and the glenohumeral stability. Moreover, the results show that a medialization of the supraspinatus leads to a reduction of the supraspinatus moment arm especially in abduction. This leads to an increase of a compensatory supraspinatus load for stabilization the humerus in space, which may potentially cause a postoperative overload of the tendon-bone-complex.     

Glenohumeral joint cartilage contact in the healthy adult during scapular plane elevation depression with external humeral rotation

The shoulder (glenohumeral) joint has the greatest range of motion of all human joints; as a result, it is particularly vulnerable to dislocation and injury. The ability to non-invasively quantify in-vivo articular cartilage contact patterns of joints has been and remains a difficult biomechanics problem. As a result, little is known about normal in-vivo glenohumeral joint contact patterns or the consequences that surgery has on altering them. In addition, the effect of quantifying glenohumeral joint contact patterns by means of proximity mapping, both with and without cartilage data, is unknown. Therefore, the objectives of this study are to (1) describe a technique for quantifying in-vivo glenohumeral joint contact patterns during dynamic shoulder motion, (2) quantify normal glenohumeral joint contact patterns in the young healthy adult during scapular plane elevation depression with external humeral rotation, and (3) compare glenohumeral joint contact patterns determined both with and without articular cartilage data. Our results show that the inclusion of articular cartilage data when quantifying in-vivo glenohumeral joint contact patterns has significant effects on the anterior–posterior contact centroid location, the superior–inferior contact centroid range of travel, and the total contact path length. As a result, our technique offers an advantage over glenohumeral joint contact pattern measurement techniques that neglect articular cartilage data. Likewise, this technique may be more sensitive than traditional 6-Degree-of-Freedom (6-DOF) joint kinematics for the assessment of overall glenohumeral joint health. Lastly, for the shoulder motion tested, we found that glenohumeral joint contact was located on the anterior–inferior glenoid surface.     

An optimized protocol for hip joint centre determination using the functional method

The functional method identifies the hip joint centre (HJC) as the centre of rotation of the femur relative to the pelvis during an ad hoc movement normally recorded using stereophotogrammetry. This method may be used for the direct determination of subject-specific HJC coordinates or for creating a database from which regression equations may be derived that allow for the prediction of those coordinates. In order to contribute to the optimization of the functional method, the effects of the following factors were investigated: the algorithm used to estimate the HJC coordinates from marker coordinates, the type and amplitude of the movement of the femur relative to the pelvis, marker cluster location and dimensions, and the number of data samples. This was done using a simulation approach which, in turn, was validated using experiments made on a physical analogue of the pelvis and femur system. The algorithms used in the present context were classified and, in some instances, modified in order to optimize both accuracy and computation time, and submitted to a comparative evaluation. The type of movement that allowed for the most accurate results consisted of several flexion-extension/abduction-adduction movements performed on vertical planes of different orientations, followed by a circumduction movement. The accuracy of the HJC estimate improved, with an increasing rate, as a function of the amplitude of these movements. A sharp improvement was found as the number of the photogrammetric data samples used to describe the movement increased up to 500. For optimal performance with the recommended algorithms, markers were best located as far as possible from each other and with their centroid as close as possible to the HJC. By optimizing the analytical and experimental protocol, HJC location error not caused by soft tissue artefacts may be reduced by a factor of ten with a maximal expected value for such error of approximately 1mm.     

Registration of 6-DOFs electrogoniometry and CT medical imaging for 3D joint modeling

The paper describes a method in which two data-collecting systems, medical imaging and electrogoniometry, are combined to allow the accurate and simultaneous modeling of both the spatial kinematics and the morphological surface of a particular joint. The joint of interest (JOI) is attached to a Plexiglas jig that includes four metallic markers defining a local reference system (R(GONIO)) for the kinematics data. Volumetric data of the JOI and the R(GONIO) markers are collected from medical imaging. The spatial location and orientation of the markers in the global reference system (R(CT)) of the medical-imaging environment are obtained by applying object-recognition and classification methods on the image dataset. Segmentation and 3D isosurfacing of the JOI are performed to produce a 3D model including two anatomical objects-the proximal and distal JOI segments. After imaging, one end of a custom-made 3D electrogoniometer is attached to the distal segment of the JOI, and the other end is placed at the R(GONIO) origin; the JOI is displaced and the spatial kinematics data is recorded by the goniometer. After recording, data registration from R(GONIO) to R(CT) occurred prior to simulation. Data analysis was performed using both joint coordinate system (JCS) and instantaneous helical axis (IHA).Finally, the 3D joint model is simulated in real time using the experimental kinematics data. The system is integrated into a computer graphics interface, allowing free manipulation of the 3D scene.The overall accuracy of the method has been validated with two other kinematics data collection methods including a 3D digitizer and interpolation of the kinematics data from discrete positions obtained from medical imaging. Validation has been performed on both superior and inferior radio-ulna joints (i.e. prono-supination motion). Maximal RMS error was 1 degrees and 1.2mm on the helical axis rotation and translation, respectively. Prono-supination of the forearm showed a total rotation of 132 degrees for 0.8mm of translation. The method reproducibility using JCS parameters was in average 1 degrees (maximal deviation=2 degrees ) for rotation, and 1mm (maximal deviation=2mm) for translation. In vitro experiments have been performed on both knee joint and ankle joint. Averaged JCS parameters for the knee were 109 degrees, 17 degrees and 4 degrees for flexion, internal rotation and abduction, respectively. Averaged maximal translation values for the knee were 12, 3 and 4mm posteriorly, medially and proximally, respectively. Averaged JCS parameters for the ankle were 43 degrees, 9 degrees and 3 degrees for plantarflexion, adduction and internal rotation, respectively. Averaged maximal translation values for the ankle were 4, 2 and 1mm anteriorly, medially and proximally, respectively.     

A rigid-body method for finding centers of rotation and angular displacements of planar joint motion

A rigid-body method for determining the center of rotation (CR) and the angular displacement in a plane is developed. A comparison of this method to the graphical method of Reuleaux (Theoretische Kinematik: Grundzüge einer Theorie des Maschinenwerens, 1875) is found to have fewer constraints while meeting or exceeding the Reuleaux method in accuracy. The rigid-body method is not constrained by the location of the markers, as they can be placed radially or juxtapositioned about the CR. Magnitude of the rotation angle does not affect the accuracy in calculating the rotation angle. When applying both methods to locate the CR in a simulated knee joint, a substantial decrease in error is found with the new method. In a comparison of optimal marker angles used to locate the CR and find the angular displacement, the rigid-body method is found to be more accurate in both the mean and range of error. Effects of parameters specified by Panjabi (J. Biomechanics 12, 911-920, 1979) are applied to both methods. Results are then used in setting up guidelines for increasing accuracy with the rigid-body method.     

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.     

Calculating the 2D motion of lumbar vertebrae using splines

In this study we investigate the use of splines and the ICP method [Besl, P., McKay, N., 1992. A method for registration of 3d shapes. IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 239-256.] for calculating the transformation parameters for a rigid body undergoing planar motion parallel to the image plane. We demonstrate the efficacy of the method by estimating the finite centre of rotation and angle of rotation from lateral flexion/extension radiographs of the lumbar spine. In an in vitro error study, the method displayed an average error of rotation of 0.44 +/- 0.45 degrees, and an average error in FCR calculation of 7.6 +/- 8.5 mm. The method was shown to be superior to that of Crisco et al. [Two-dimensional rigid-body kinematics using image contour registration. Journal of Biomechanics 28(1), 119-124.] and Brinckmann et al. [Quantification of overload injuries of the thoracolumbar spine in persons exposed to heavy physical exertions or vibration at the workplace: Part i - the shape of vertebrae and intervertebral discs - study of a yound, healthy population and a middle-aged control group. Clinical Biomechanics Supplement 1, S5-S83.] for the tests performed here. In general, we believe the use of splines to represent planar shapes to be superior to using digitised curves or landmarks for several reasons. First, with appropriate software, splines require less effort to define and are a compact representation, with most vertebra outlines using less than 30 control points. Second, splines are inherently sub-pixel representations of curves, even if the control points are limited to pixel resolutions. Third, there is a well-defined method (the ICP algorithm) for registering shapes represented as splines. Finally, like digitised curves, splines are able to represent a large class of shapes with little effort, but reduce potential segmentation errors from two dimensions (parallel and perpendicular to the image gradient) to just one (parallel to the image gradient). We have developed an application for performing all the necessary computations which can be downloaded from http://www.claritysmart.com.