Comparative accuracy of radiostereometric and optical tracking systems

This study aims to quantify and compare the accuracy of traditional radiostereometric analysis (RSA), fluoroscopic RSA (fRSA), and optical tracking systems. Three phantoms were constructed, each having three stainless steel spheres and three reflective markers. One phantom was mounted to the base of a precision cross-slide table, one to the base of a precision rotation table, and the third was mounted to each moveable tabletop. Two dial-gauges, rigidly mounted to the cross-slide table and rotation table, quantified translations and rotations. Two fluoroscopy units placed orthogonally tracked the steel spheres while a four-camera optical motion capture system tracked the reflective markers in three-dimensional space. RSA was performed with both digital radiography and fluoroscopy. Three axes of translation were tested: parallel to one fluoroscopy image, parallel to the other fluoroscopy image, and at approximately 45° to each image. One axis of rotation was tested. Intraclass correlation coefficients indicated excellent agreement between the actual (dial-gauge) and measured translations for all modalities (ICCs>0.99) and excellent agreement between actual and measured rotations for RSA and fRSA (ICCs>0.99). Standard errors of measurement ranged from 0.032 mm and 0.121° for RSA, to 0.040 mm and 0.229° for fRSA, and to 0.109 mm and 0.613° for optical tracking. Differences between actual and measured translations along the 45° axis were significantly smaller than the two parallel axes. These findings suggest that under ideal conditions, accuracy of fRSA is comparable to traditional RSA, and superior to optical tracking. Accuracy is highest when measured at 45° to the fluoroscopy units.     

In vitro assessment of a motion-based optimization method for locating the talocrural and subtalar joint axes

The locations of the joint axes of the ankle complex vary considerably between subjects, yet no noninvasive method with demonstrated accuracy exists for locating these axes. The moments of muscle and ground reaction forces about the joint axes are dependent on axis locations, making knowledge of these locations critical to accurate musculoskeletal modeling of the foot and ankle. The accuracy of a computational optimization method that fits a two-revolute model to measured motion was assessed using computer-generated data, a two-revolute mechanical linkage, and three lower-leg cadaver specimens. Motions were applied to cadaver specimens under axial load while bone-mounted markers attached to the tibia, talus, and calcaneus were tracked using a video-based motion analysis system. Estimates of the talocrural and subtalar axis locations were computed from motions of the calcaneus relative to the tibia using the optimization method. These axes were compared to mean helical axes computed directly from tibia, talus, and calcaneus motions. The optimization method performed well when the motions were computer-generated or measured in the mechanical linkage, with angular differences between optimization and mean helical axes ranging from 1 deg to 5 deg. In the cadaver specimens, however, these differences exceeded 20 deg. Optimization methods that locate the anatomical joint axes of the ankle complex by fitting two revolute joints to measured tibia-calcaneus motions may be limited because of problems arising from non-revolute behavior.     

Validation of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics

Shoulder motion is complex and significant research efforts have focused on measuring glenohumeral joint motion. Unfortunately, conventional motion measurement techniques are unable to measure glenohumeral joint kinematics during dynamic shoulder motion to clinically significant levels of accuracy. The purpose of this study was to validate the accuracy of a new model-based tracking technique for measuring three-dimensional, in vivo glenohumeral joint kinematics. We have developed a model-based tracking technique for accurately measuring in vivo joint motion from biplane radiographic images that tracks the position of bones based on their three-dimensional shape and texture. To validate this technique, we implanted tantalum beads into the humerus and scapula of both shoulders from three cadaver specimens and then recorded biplane radiographic images of the shoulder while manually moving each specimen's arm. The position of the humerus and scapula were measured using the model-based tracking system and with a previously validated dynamic radiostereometric analysis (RSA) technique. Accuracy was reported in terms of measurement bias, measurement precision, and overall dynamic accuracy by comparing the model-based tracking results to the dynamic RSA results. The model-based tracking technique produced results that were in excellent agreement with the RSA technique. Measurement bias ranged from -0.126 to 0.199 mm for the scapula and ranged from -0.022 to 0.079 mm for the humerus. Dynamic measurement precision was better than 0.130 mm for the scapula and 0.095 mm for the humerus. Overall dynamic accuracy indicated that rms errors in any one direction were less than 0.385 mm for the scapula and less than 0.374 mm for the humerus. These errors correspond to rotational inaccuracies of approximately 0.25 deg for the scapula and 0.47 deg for the humerus. This new model-based tracking approach represents a non-invasive technique for accurately measuring dynamic glenohumeral joint motion under in vivo conditions. The model-based technique achieves accuracy levels that far surpass all previously reported non-invasive techniques for measuring in vivo glenohumeral joint motion. This technique is supported by a rigorous validation study that provides a realistic simulation of in vivo conditions and we fully expect to achieve these levels of accuracy with in vivo human testing. Future research will use this technique to analyze shoulder motion under a variety of testing conditions and to investigate the effects of conservative and surgical treatment of rotator cuff tears on dynamic joint stability.     

Accuracy of a CT-based bone contour registration method to measure relative bone motions in the hindfoot

For measuring the in-vivo range of motion of the hindfoot, a CT-based bone contour registration method (CT-BCM) was developed to determine the three-dimensional position and orientation of bones. To validate this technique, we hypothesized that the range of motion in the hindfoot is equally, accurately measured by roentgen stereophotogrammetric analysis (RSA) as by the CT-BCM technique.Tantalum bone markers were placed in the distal tibia, talus and calcaneus of one cadaver specimen. With a fixed lower leg, the cadaveric foot was held in neutral and subsequently loaded in eight extreme positions. Immediately after acquiring a CT-scan with the foot in a position, RSA radiographs were made. Bone contour registration and RSA was performed. Helical axis parameters were calculated for talocrural and subtalar joint motion from neutral to extreme positions and between opposite extreme positions. Differences between CT-BCM and RSA were calculated.Compared with RSA, the CT-BCM data registered an overall root mean square difference (RMSd) of 0.21° for rotation about the helical axis, and 0.20 mm translation along the helical axis for the talocrural and subtalar joint and for all motions combined. The RMSd of the position and direction of the helical axes was 3.3 mm and 2.4°, respectively. The latter errors were larger with smaller helical rotations.The differences are similar to those reported for validated RSA and thus are not clinically relevant. Concluding, CT-BCM is an accurate and accessible alternative for studying joint motion, as it does not have the risk of infection and overlapping bone markers.     

A finite helical axis as a landmark for kinematic reference of the knee

Reference coordinates based on the finite helical axis for flexion of the knee from 0 to 90 deg are proposed. Six degree-of-freedom tracking allows the use of such a helical axis as a kinematic landmark for knee motion representation. Data from five human subjects in vivo are presented as a path of finite helical axes for flexion of the knee from 20 to 80 deg. The finite helical axis rotates by an average of 11.4 deg, the centrode translates an average of 19.8 mm, and the total axial translation averages 0.1 mm during flexion from 20 to 80 deg. Error due to the transducer was measured on a fixed-pivot pendulum and found to be 1.0 deg and 1.9 mm rms for the helical axis orientation and position, respectively, and 0.1 mm for the axial translation. Reproducibility and soft tissue effects on the measurements were repeatable to 4.0 deg and 2.7 mm rms in orientation and position, respectively, and 0.1 mm for the axial translations. Soft tissue errors averaged 4.9 deg and 3.6 mm in position and orientation, and 0.3 mm in the axial translations.     

Fusion of radiostereometric analysis data into computed tomography space: application to the elbow joint

Improvement of joint prostheses is dependent upon information concerning the biomechanical properties of the joint. Radiostereometric analysis (RSA) and electromagnetic techniques have been applied in previous cadaver and in vivo studies on the elbow joint to provide valuable information concerning joint motion axes. However, such information is limited to mathematically calculated positions of the axes according to an orthogonal coordinate system and is difficult to relate to individual skeletal anatomy. The aim of this study was to evaluate the in vivo application of a new fusion method to provide three-dimensional (3D) visualization of flexion axes according to bony landmarks. In vivo RSA data of the elbow joint's flexion axes was combined with data obtained by 3D computed tomography (CT). Results were obtained from five healthy subjects after one was excluded due to an instable RSA marker. The median error between imported and transformed RSA marker coordinates and those obtained in the CT volume was 0.22 mm. Median maximal rotation error after transformation of the rigid RSA body to the CT volume was 0.003 degrees . Points of interception with a plane calculated in the RSA orthogonal coordinate system were imported into the CT volume, facilitating the 3D visualization of the flexion axes. This study demonstrates a successful fusion of RSA and CT data, without significant loss of RSA accuracy. The method could be used for relating individual motion axes to a 3D representation of relevant joint anatomy, thus providing important information for clinical applications such as the development of joint prostheses.     

The effect of decreasing computed tomography dosage on radiostereometric analysis (RSA) accuracy at the glenohumeral joint

Standard, beaded radiostereometric analysis (RSA) and markerless RSA often use computed tomography (CT) scans to create three-dimensional (3D) bone models. However, ethical concerns exist due to risks associated with CT radiation exposure. Therefore, the aim of this study was to investigate the effect of decreasing CT dosage on RSA accuracy. Four cadaveric shoulder specimens were scanned using a normal-dose CT protocol and two low-dose protocols, where the dosage was decreased by 89% and 98%. 3D computer models of the humerus and scapula were created using each CT protocol. Bi-planar fluoroscopy was used to image five different static glenohumeral positions and two dynamic glenohumeral movements, of which a total of five static and four dynamic poses were selected for analysis. For standard RSA, negligible differences were found in bead (0.21±0.31mm) and bony landmark (2.31±1.90mm) locations when the CT dosage was decreased by 98% (p-values>0.167). For markerless RSA kinematic results, excellent agreement was found between the normal-dose and lowest-dose protocol, with all Spearman rank correlation coefficients greater than 0.95. Average root mean squared errors of 1.04±0.68mm and 2.42±0.81° were also found at this reduced dosage for static positions. In summary, CT dosage can be markedly reduced when performing shoulder RSA to minimize the risks of radiation exposure. Standard RSA accuracy was negligibly affected by the 98% CT dose reduction and for markerless RSA, the benefits of decreasing CT dosage to the subject outweigh the introduced errors.     

Validation of radiostereometric analysis in six degrees of freedom for use with reverse total shoulder arthroplasty

A phantom study was conducted to determine bias in motion and bias at zero motion of radiostereometric analysis (RSA) for evaluating implant relative displacement in reverse total shoulder arthroplasty (RTSA). A Sawbones shoulder phantom was fitted with a RTSA implant set and 13 tantalum markers. The model was fixed to a manual micrometer, providing controlled movements though fifteen known increments in translation and twelve increments in rotation (0.02–5.00 mm and 0.1–6.0°), along each translation and rotation axis. Movement between the glenoid and humerus was assessed using beads vs. beads (B/B), model vs. beads (M/B), and model vs. model (M/M) measurement methods in a model-based RSA environment. Bias in motion and bias at zero motion were defined as the difference between measured and accepted reference values, and the difference between double examinations with a theoretical displacement of zero, respectively. Bias in motion ranged from 0.054 ± 0.010 to 0.129 ± 0.014 mm and 0.076 ± 0.025 to 0.126 ± 0.025° (B/B), 0.023 ± 0.009 to 0.126 ± 0.016 mm and 0.111 ± 0.033 to 0.794 ± 0.251° (M/B), and 0.029 ± 0.010 to 0.135 ± 0.030 mm and 0.243 ± 0.088 to 0.384 ± 0.153° (M/M). Bias at zero motion ranged from 0.120 to 0.156 mm and 0.075 to 0.206° (B/B), 0.074 to 0.149 mm and 0.067 to 1.953° (M/B), and 0.069 to 0.259 mm and 0.284 to 1.273° (M/M). This is the first RSA for RTSA study, with results comparable to those validating the use of RSA for hip and knee arthroplasties (accepted as 0.05–0.50 mm and 0.15–1.15°), justifying the potential use of RSA as a tool for measuring implant displacement in the shoulder.     

A new method for estimating joint parameters from motion data

Joint centers and axes of rotation (joint parameters) are central to all branches of movement analysis. In gait analysis, the standard protocol used to determine hip and knee joint parameters is prone to errors arising from palpation, anthropometric regression equations, and misplaced alignment devices. Several alternative methods have been proposed, but to date none have been shown to be accurate and reliable enough for use in the clinical setting. This article describes a new method for joint parameter estimation. The new method can be summarized as follows: (i) the motions of two adjacent segments spanning a single joint are tracked, (ii) the axis of rotation between every pair of observed segment configurations is computed, (iii) the most likely intersection of all axes (effective joint center) and most likely orientation of the axes (effective joint axis) is found. Initial validation of the method was conducted on a hinged mechanical analog and a single healthy adult subject. For the analog, the center was found to be within 3.8 mm of the geometric center and 2.0 degrees of the geometric axis (standard deviation). For the adult subject, hip centers varied on the order of 1-3 mm, knee centers by 3-9 mm, and knee axes by 2.0 degrees. The results suggest that the new method is an objective, precise, and practical alternative to the standard clinical approach.     

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.     

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.     

Measurement of the screw-home motion of the knee is sensitive to errors in axis alignment

Measurements of joint angles during motion analysis are subject to error caused by kinematic crosstalk, that is, one joint rotation (e. g., flexion) being interpreted as another (e.g., abduction). Kinematic crosstalk results from the chosen joint coordinate system being misaligned with the axes about which rotations are assumed to occur. The aim of this paper is to demonstrate that measurement of the so-called "screw-home" motion of the human knee, in which axial rotation and extension are coupled, is especially prone to errors due to crosstalk. The motions of two different two-segment mechanical linkages were examined to study the effects of crosstalk. The segments of the first linkage (NSH) were connected by a revolute joint, but the second linkage (SH) incorporated gearing that caused 15 degrees of screw-home rotation to occur with 90 degrees knee flexion. It was found that rotating the flexion axis (inducing crosstalk) could make linkage NSH appear to exhibit a screw-home motion and that a different rotation of the flexion axis could make linkage SH apparently exhibit pure flexion. These findings suggest that the measurement of screw-home rotation may be strongly influenced by errors in the location of the flexion axis. The magnitudes of these displacements of the flexion axis were consistent with the inter-observer variability seen when five experienced observers defined the flexion axis by palpating the medial and lateral femoral epicondyles. Care should be taken when interpreting small internal-external rotations and abduction-adduction angles to ensure that they are not the products of kinematic crosstalk.     

Implementation and validation of an implant-based coordinate system for RSA migration calculation

An in vitro radiostereometric analysis (RSA) phantom study of a total knee replacement was carried out to evaluate the effect of implementing two new modifications to the conventional RSA procedure: (i) adding a landmark of the tibial component as an implant marker and (ii) defining an implant-based coordinate system constructed from implant landmarks for the calculation of migration results. The motivation for these two modifications were (i) to improve the representation of the implant by the markers by including the stem tip marker which increases the marker distribution (ii) to recover clinical RSA study cases with insufficient numbers of markers visible in the implant polyethylene and (iii) to eliminate errors in migration calculations due to misalignment of the anatomical axes with the RSA global coordinate system. The translational and rotational phantom studies showed no loss of accuracy with the two new measurement methods. The RSA system employing these methods has a precision of better than 0.05 mm for translations and 0.03° for rotations, and an accuracy of 0.05 mm for translations and 0.15° for rotations. These results indicate that the new methods to improve the interpretability, relevance, and standardization of the results do not compromise precision and accuracy, and are suitable for application to clinical data.     

Analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation

The accurate location of the main axes of rotation (AoR) is a crucial step in many applications of human movement analysis. There are different formal methods to determine the direction and position of the AoR, whose performance varies across studies, depending on the pose and the source of errors. Most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters, implicitly assuming independent and uncorrelated errors, but the largest error usually results from soft tissue artefacts (STA), which do not have such statistical properties and are not effectively cancelled out by such methods. However, with adequate methods it is possible to assume that STA only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate STA components to the resulting errors in AoR parameters. In this paper such formulas are derived for three different functional calibration techniques (Geometric Fitting, mean Finite Helical Axis, and SARA), to explain why each technique behaves differently from the others, and to propose strategies to compensate for those errors. These techniques were tested with published data from a sit-to-stand activity, where the true axis was defined using bi-planar fluoroscopy. All the methods were able to estimate the direction of the AoR with an error of less than 5°, whereas there were errors in the location of the axis of 30–40 mm. Such location errors could be reduced to less than 17 mm by the methods based on equations that use rigid motion parameters (mean Finite Helical Axis, SARA) when the translation component was calculated using the three markers nearest to the axis.     

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.     

Knee joint secondary motion accuracy improved by quaternion-based optimizer with bony landmark constraints

Skin marker-based motion analysis has been widely used in biomechanical studies and clinical applications. Unfortunately, the accuracy of knee joint secondary motions is largely limited by the nonrigidity nature of human body segments. Numerous studies have investigated the characteristics of soft tissue movement. Utilizing these characteristics, we may improve the accuracy of knee joint motion measurement. An optimizer was developed by incorporating the soft tissue movement patterns at special bony landmarks into constraint functions. Bony landmark constraints were assigned to the skin markers at femur epicondyles, tibial plateau edges, and tibial tuberosity in a motion analysis algorithm by limiting their allowed position space relative to the underlying bone. The rotation matrix was represented by quaternion, and the constrained optimization problem was solved by Fletcher's version of the Levenberg-Marquardt optimization technique. The algorithm was validated by using motion data from both skin-based markers and bone-mounted markers attached to fresh cadavers. By comparing the results with the ground truth bone motion generated from the bone-mounted markers, the new algorithm had a significantly higher accuracy (root-mean-square (RMS) error: 0.7 ± 0.1 deg in axial rotation and 0.4 ± 0.1 deg in varus-valgus) in estimating the knee joint secondary rotations than algorithms without bony landmark constraints (RMS error: 1.7 ± 0.4 deg in axial rotation and 0.7 ± 0.1 deg in varus-valgus). Also, it predicts a more accurate medial-lateral translation (RMS error: 0.4 ± 0.1 mm) than the conventional techniques (RMS error: 1.2 ± 0.2 mm). The new algorithm, using bony landmark constrains, estimates more accurate secondary rotations and medial-lateral translation of the underlying bone.     

Assessment of screw displacement axis accuracy and repeatability for joint kinematic description using an electromagnetic tracking device

Screw displacement axes (SDAs) have been employed to describe joint kinematics in biomechanical studies. Previous reports have investigated the accuracy of SDAs combining various motion analysis techniques and smoothing procedures. To our knowledge, no study has assessed SDA accuracy describing the relative movement between adjacent bodies with an electromagnetic tracking system. This is important, since in relative motion, neither body is fixed and consequently sensitivity to potential measurement errors from both bodies may be significant. Therefore, this study assessed the accuracy of SDAs for describing relative motion between two moving bodies. We analyzed numerical simulated data, and physical experimental data recorded using a precision jig and electromagnetic tracking device. The numerical simulations demonstrated SDA position accuracy (p=0.04) was superior for single compared to relative body motion, whereas orientation accuracy (p=0.2) was similar. Experimental data showed data-filtering (Butterworth filter) improved SDA position and orientation accuracies for rotation magnitudes smaller or equal to 5.0 degrees, with no effect at larger rotation magnitudes (p<0.05). This suggests that in absence of a filter, SDAs should only be calculated at rotations of greater than 5.0 degrees. For rotation magnitudes of 0.5 degrees (5.0 degrees ) about the SDA, SDA position and orientation error measurements determined from filtered experimental data were 3.75+/-0.30 mm (3.31+/-0.21 mm), and 1.10+/-0.04 degrees (1.04+/-0.03 degrees ), respectively. Experimental accuracy values describing the translation along and rotation about the SDA, were 0.06+/-0.00 mm and 0.09+/-0.01 degrees, respectively. These small errors establish the capability of SDAs to detect small translations, and rotations. In conclusion, application of SDAs should be a useful tool for describing relative motion in joint kinematic studies.     

Evaluation of a robot-assisted testing system for multisegmental spine specimens

Mono- and multi-segmental testing methods are required to identify segmental motion patterns and evaluate the biomechanical behaviour of the spine. This study aimed to evaluate a new testing system for multisegmental specimens using a robot combined with an optical motion analysis system. After validation of the robotic system for accuracy, two groups of calf specimens (six monosegmental vs. six multisegmental) were mounted and the functional unit L3-4 was observed. Using rigid body markers, range of motion (ROM), elastic zone (EZ) and neutral zone (NZ), as well as stiffness properties of each functional spine unit (FSU) was acquired by an optical motion capture system. Finite helical axes (FHA) were calculated to analyse segmental movements. Both groups were tested in flexion and extension. A pure torque of 7.5 Nm was applied. Statistical analyses were performed using the Mann-Whitney U-test. Repeatability of robot positioning was -0.001±0.018 mm and -0.025±0.023° for translations and rotations, respectively. The accuracy of the optical system for the proposed set-up was 0.001±0.034 mm for translations and 0.075±0.12° for rotations. No significant differences in mean values and standard deviations of ROM for L3-4 compared to literature data were found. A robot-based facility for testing multisegmental spine units combined with a motion analysis system was proposed and the reliability and reproducibility of all system components were evaluated and validated. The proposed set-up delivered ROM results for mono- and multi-segmental testing that agreed with those reported in the literature. Representing the FHA via piercing points determined from ROM was the first attempt showing a relationship between ROM and FHA, which could facilitate the interpretation of spine motion patterns in the future.     

System and modelling errors in motion analysis: implications for the measurement of the elbow angle in cricket bowling

The system and modelling errors of two fundamentally different motion capture systems (opto-reflective vs. video-based) were tested under various conditions, to determine their ability to accurately measure flexion-extension of the elbow angle in cricket bowling. A mechanical arm was used for all testing, that enabled known elbow flexion-extension and abduction ("carry") angles to be manually set. The root mean squared (RMS) error of 0.6 degrees for the opto-reflective system (Vicon-612) was more accurate in reconstructing a known angle than the video-based system (Peak Motus) (RMS error 2.3 degrees ) in the laboratory, when the same mathematical procedure (model) was applied to calculate the elbow flexion-extension angle. When different models were applied to the raw marker trajectories collected using the video-based system, RMS was lowest for the external marker segmental cluster models (2.3 degrees ) compared with 9.4 degrees for the vector and 4.5 degrees for the projected vector approaches, where joint centres were visually approximated. Real world, field-based comparisons using the video-based system showed that occluding the arm and therefore the shoulder, elbow and wrist joint centre locations by placing a shirt on the arm, increased RMS error for both vector (7.8 degrees -9.0 degrees ) and projected vector (4.3 degrees -5.1 degrees ) modelling approaches.     

A central role for the nitrate transporter NRT2.1 in the integrated morphological and physiological responses of the root system to nitrogen limitation in Arabidopsis

Up-regulation of the high-affinity transport system (HATS) for NO(3)(-) and stimulation of lateral root (LR) growth are two important adaptive responses of the root system to nitrogen limitation. Up-regulation of the NO(3)(-) HATS by nitrogen starvation is suppressed in the atnrt2.1-1 mutant of Arabidopsis (Arabidopsis thaliana), deleted for both NRT2.1 and NRT2.2 nitrate transporter genes. We then used this mutant to determine whether lack of HATS stimulation affected the response of the root system architecture (RSA) to low NO(3)(-) availability. In Wassilewskija (Ws) wild-type plants, transfer from high to low NO(3)(-) medium resulted in contrasting responses of RSA, depending on the level of nitrogen limitation. Moderate nitrogen limitation (transfer from 10 mm to 1 or 0.5 mm NO(3)(-)) mostly led to an increase in the number of visible laterals, while severe nitrogen stress (transfer from 10 mm to 0.1 or 0.05 mm NO(3)(-)) promoted mean LR length. The RSA response of the atnrt2.1-1 mutant to low NO(3)(-) was markedly different. After transfer from 10 to 0.5 mm NO(3)(-), the stimulated appearance of LRs was abolished in atnrt2.1-1 plants, whereas the increase in mean LR length was much more pronounced than in Ws. These modifications of RSA mimicked those of Ws plants subjected to severe nitrogen stress and could be fully explained by the lowered NO(3)(-) uptake measured in the mutant. This suggests that the uptake rate of NO(3)(-), rather than its external concentration, is the key factor triggering the observed changes in RSA. However, the mutation of NRT2.1 was also found to inhibit initiation of LR primordia in plants subjected to nitrogen limitation independently of the rate of NO(3)(-) uptake by the whole root system and even of the presence of added NO(3)(-) in the external medium. This indicates a direct stimulatory role for NRT2.1 in this particular step of LR development. Thus, it is concluded that NRT2.1 has a key dual function in coordinating root development with external NO(3)(-) availability, both indirectly through its role as a major NO(3)(-) uptake system that determines the nitrogen uptake-dependent RSA responses, and directly through a specific action on LR initiation under nitrogen-limited conditions.