Marker Configuration Model-Based Roentgen Fluoroscopic Analysis

It remains unknown if and how the polyethylene bearing in mobile bearing knees moves during dynamic activities with respect to the tibial base plate. Marker Configuration Model-Based Roentgen Fluoroscopic Analysis (MCM-based RFA) uses a marker configuration model of inserted tantalum markers in order to accurately estimate the pose of an implant or bone using single plane Roentgen images or fluoroscopic images. The goal of this study is to assess the accuracy of (MCM-Based RFA) in a standard fluoroscopic set-up using phantom experiments and to determine the error propagation with computer simulations. The experimental set-up of the phantom study was calibrated using a calibration box equipped with 600 tantalum markers, which corrected for image distortion and determined the focus position. In the computer simulation study the influence of image distortion, MC-model accuracy, focus position, the relative distance between MC-models and MC-model configuration on the accuracy of MCM-Based RFA were assessed. The phantom study established that the in-plane accuracy of MCM-Based RFA is 0.1 mm and the out-of-plane accuracy is 0.9 mm. The rotational accuracy is 0.1 degrees. A ninth-order polynomial model was used to correct for image distortion. Marker-Based RFA was estimated to have, in a worst case scenario, an in vivo translational accuracy of 0.14 mm (x-axis), 0.17 mm (y-axis), 1.9 mm (z-axis), respectively, and a rotational accuracy of 0.3 degrees. When using fluoroscopy to study kinematics, image distortion and the accuracy of models are important factors, which influence the accuracy of the measurements. MCM-Based RFA has the potential to be an accurate, clinically useful tool for studying kinematics after total joint replacement using standard equipment.     

Model-based Roentgen stereophotogrammetry of orthopaedic implants

Attaching tantalum markers to prostheses for Roentgen stereophotogrammetry (RSA) may be difficult and is sometimes even impossible. In this study, a model-based RSA method that avoids the attachment of markers to prostheses is presented and validated. This model-based RSA method uses a triangulated surface model of the implant. A projected contour of this model is calculated and this calculated model contour is matched onto the detected contour of the actual implant in the RSA radiograph. The difference between the two contours is minimized by variation of the position and orientation of the model. When a minimal difference between the contours is found, an optimal position and orientation of the model has been obtained. The method was validated by means of a phantom experiment. Three prosthesis components were used in this experiment: the femoral and tibial component of an Interax total knee prosthesis (Stryker Howmedica Osteonics Corp., Rutherfort, USA) and the femoral component of a Profix total knee prosthesis (Smith & Nephew, Memphis, USA). For the prosthesis components used in this study, the accuracy of the model-based method is lower than the accuracy of traditional RSA. For the Interax femoral and tibial components, significant dimensional tolerances were found that were probably caused by the casting process and manual polishing of the components surfaces. The largest standard deviation for any translation was 0.19mm and for any rotation it was 0.52 degrees. For the Profix femoral component that had no large dimensional tolerances, the largest standard deviation for any translation was 0.22mm and for any rotation it was 0.22 degrees. From this study we may conclude that the accuracy of the current model-based RSA method is sensitive to dimensional tolerances of the implant. Research is now being conducted to make model-based RSA less sensitive to dimensional tolerances and thereby improving its accuracy.     

Migration of radio-opaque markers injected into tendon grafts: a study using roentgen stereophotogrammetric analysis (RSA)

An increase in anterior laxity following reconstruction of the anterior cruciate ligament (ACL) can result from lengthening of the graft construct either at the sites of fixation and/or between the sites of fixation (i.e., graft substance). Roentgen stereophotogrammetric analysis (RSA), which requires that radio-opaque markers be attached to the graft, has been shown to be a useful technique in determining lengthening in these regions. Previous methods have been used for attaching radio-opaque markers to the graft, but they all have limitations particularly for single-loop grafts. Therefore, the objective of this study was to evaluate injecting markers directly into the substance of a tendon as a viable method for measuring lengthening of single-loop graft constructs by determining the maximum amount of migration after cyclic loading. Tantalum spheres of 0.8 mm diameter were used as tendon markers. Ten single-loop tendon grafts were passed through tibial tunnels drilled in calf tibias and fixed with a tibial fixation device. Two tendon markers were inserted in one tendon bundle of each graft and the grafts were cyclically loaded for 225,000 cycles from 20 N to 170 N. At specified intervals, simultaneous radiographs were obtained of the tendon markers. Marker migration was computed as the change in distance between the two tendon markers parallel to the axis of the tibial tunnel. Marker migration had a root mean square (RMS) value of less than 0.1 mm. Because the RMS value indicates the error introduced into measurements of lengthening and because this error is negligible, the method described for attaching markers to single-loop ACL grafts has the potential to be useful for determining lengthening of single-loop ACL graft constructs in in vivo studies in humans.     

Precision measurements of the RSA method using a phantom model of hip prosthesis

Radiostereometric analysis (RSA) has become one of the recommended techniques for pre-market evaluation of new joint implant designs. In this study we evaluated the effect of repositioning of X-ray tubes and phantom model on the precision of the RSA method. In precision measurements, we utilized mean error of rigid body fitting (ME) values as an internal control for examinations. ME value characterizes relative motion among the markers within each rigid body and is conventionally used to detect loosening of a bone marker. Three experiments, each consisting of 10 double examinations, were performed. In the first experiment, the X-ray tubes and the phantom model were not repositioned between one double examination. In experiments two and three, the X-ray tubes were repositioned between one double examination. In addition, the position of the phantom model was changed in experiment three. Results showed that significant differences could be found in 2 of 12 comparisons when evaluating the translation and rotation of the prosthetic components. Repositioning procedures increased ME values mimicking deformation of rigid body segments. Thus, ME value seemed to be a more sensitive parameter than migration values in this study design. These results confirmed the importance of standardized radiographic technique and accurate patient positioning for RSA measurements. Standardization and calibration procedures should be performed with phantom models in order to avoid unnecessary radiation dose of the patients. The present model gives the means to establish and to follow the intra-laboratory precision of the RSA method. The model is easily applicable in any research unit and allows the comparison of the precision values in different laboratories of multi-center trials.     

A new model-based RSA method validated using CAD models and models from reversed engineering

Roentgen stereophotogrammetric analysis (RSA) was developed to measure micromotion of an orthopaedic implant with respect to its surrounding bone. A disadvantage of conventional RSA is that it requires the implant to be marked with tantalum beads. This disadvantage can potentially be resolved with model-based RSA, whereby a 3D model of the implant is used for matching with the actual images and the assessment of position and rotation of the implant. In this study, a model-based RSA algorithm is presented and validated in phantom experiments. To investigate the influence of the accuracy of the implant models that were used for model-based RSA, we studied both computer aided design (CAD) models as well as models obtained by means of reversed engineering (RE) of the actual implant. The results demonstrate that the RE models provide more accurate results than the CAD models. If these RE models are derived from the very same implant, it is possible to achieve a maximum standard deviation of the error in the migration calculation of 0.06 mm for translations in x- and y-direction and 0.14 mm for the out of plane z-direction, respectively. For rotations about the y-axis, the standard deviation was about 0.1 degrees and for rotations about the x- and z-axis 0.05 degrees. Studies with clinical RSA-radiographs must prove that these results can also be reached in a clinical setting, making model-based RSA a possible alternative for marker-based RSA.     

Markerless Roentgen Stereophotogrammetric Analysis for in vivo implant migration measurement using three dimensional surface models to represent bone

Recent studies have shown that model-based RSA using implant surface models to detect in vivo migration is as accurate as the classical marker-based RSA method. Use of bone surface models would be a further advancement of the model-based method by decreasing complications arising from marker insertion. The aim of this pilot investigation was to assess the feasibility of a "completely markerless" model-based RSA in detecting migration of an implant using bone surface models instead of bone markers. A total knee arthroplasty (TKA) was performed on a human cadaver knee, which was subsequently investigated by repeated RSA measurements performed by one observer. The cadaver knee was CT scanned prior to implantation of the TKA. Tibia-fibular surface models were created using two different commercially available software packages to investigate the effect of segmentation software on the accuracy of repeated migration measures of zero displacement by one observer. Reverse engineered surface models of the TKA tibial component were created. The analysis of the RSA images was repeated 10 times by one individual observer. For the markerless method, the greatest apparent migration observed about the three anatomical axes investigated was between -2.08 and 1.35 mm (SD ≤ 0.88) for z-axis translation, and -4.57° to 7.86° (SD ≤ 3.17) for R(y)-axis rotation, which were well beyond out of the range of what is typically considered adequate for clinically relevant RSA measurements. Use of tibia-fibular surface models of the bone instead of markers could provide practical advantages in evaluating implant migration. However, we found the accuracy and precision of the markerless approach to be lower than that of marker-based RSA, to a degree which precludes the use of this method for measuring implant migration in its present form.     

Validation of a low-dose hybrid RSA and fluoroscopy technique: Determination of accuracy, bias and precision

Analyzing skeletal kinematics with radiostereometric analysis (RSA) following corrective orthopedic surgery allows the quantitative comparison of different implant designs. The purpose of this study was to validate a technique for dynamically estimating the relative position and orientation of skeletal segments using RSA and single plane X-ray fluoroscopy. Two micrometer-based in vitro phantom models of the skeletal segments in the hip and knee joints were used. The spatial positions of tantalum markers that were implanted into each skeletal segment were reconstructed using RSA. The position and orientation of each segment were determined in fluoroscopy images by minimizing the difference between the markers measured and projected in the image plane. Accuracy was determined in terms of bias and precision by analyzing the deviation between the applied displacement protocol and measured pose estimates. Measured translational accuracy was less than 100 microm parallel to the image plane and less than 700 microm in the direction orthogonal to the image plane. The measured rotational error was less than 1 degrees . Measured translational and rotational bias was not statistically significant at the 95% level of confidence. The technique allows real-time kinematic skeletal measurements to be performed on human subjects implanted with tantalum markers for quantitatively measuring the motion of normal joints and different implant designs.     

Digital automated RSA compared to manually operated RSA

The accuracy of digital Roentgen stereophotogrammetric analysis (RSA) was compared to the accuracy of a manually operated RSA system. For this purpose, we used radiographs of a phantom and radiographs of patients. The radiographs of the patients consisted of double examinations of 12 patients that had a tibial osteotomy and of double examinations of 12 patients that received a total hip prosthesis. First, the radiographs were measured manually with an accurate measurement table. Subsequently, the images were digitized by a film scanner at 150 DPI and 300 DPI resolutions and analyzed with the RSA-CMS software. In the phantom experiment, the manually operated system produced significantly better results than the digital system, although the maximum difference between the median values of the manually operated system and the digital system was as low as 0.013 mm for translations and 0.033° for rotations. In the radiographs of the patients, the manually operated system and the digital system produced equally accurate results: no significant differences in translations and rotations were found. We conclude that digital RSA is an accurate, fast, and user friendly alternative for manually operated RSA. Currently, digital RSA systems are being used in a growing number of clinical RSA-studies.     

How cyclic loading affects the migration of radio-opaque markers attached to tendon grafts using a new method: a study using roentgen stereophotogrammetric analysis (RSA)

An increase in anterior laxity following reconstruction of the anterior cruciate ligament (ACL) can result from lengthening of the graft construct in either the regions of fixation and/or the region of the graft substance between the fixations. RSA could be a useful technique to determine lengthening in these regions if a method can be devised for attaching radio-opaque markers to soft tissue grafts so that marker migration from repeated loading of the graft is limited. Therefore, the objectives of this study were 1) to develop a method for attaching radio-opaque markers to an ACL graft that limits marker migration within the graft, 2) to characterize the error of an RSA system used to study migration, and 3) to determine the maximum amount of migration and the time when it occurs during cyclic loading of ACL grafts. Tendon markers were constructed from a 0.8-mm tantalum ball and a stainless steel suture. Ten double-looped tendon grafts were passed through tibial tunnels drilled in bovine tibias and fixed with a tibial fixation device. Two tendon markers were sewn to one tendon bundle of each graft and the grafts were cyclically loaded for 225,000 cycles from 20 N to 170 N. At specified intervals, simultaneous radiographs were obtained of the tendon markers and a radiographic standard of known length. The bias and imprecision in measuring the length of the radiographic standard were 0.0 and 0.046 mm respectively. Marker migration was computed as the change in distance between the two tendon markers along the axis of the tibial tunnel. Marker migration was greatest after 225,000 cycles with a root mean square (RMS) value of less than 0.2 mm. Because the RMS value indicates the error introduced into measurements of lengthening and because this error is small, the method described for attaching markers to an ACL graft has the potential to be useful for determining lengthening of ACL graft constructs in in vivo studies in humans.     

Lengthening of a single-loop tibialis tendon graft construct after cyclic loading: a study using Roentgen stereophotogrammetric analysis

Although single-loop tibialis tendon allografts have increased in popularity owing to their many advantages over patellar tendon and double-loop hamstring tendon autografts, some percentage of the patient population do not have clinically stable knees following anterior cruciate ligament reconstruction with single-loop tibialis tendon allografts. Therefore, it would be advantageous to determine the causes of increased anterior laxity which ultimately must be traced to lengthening of the graft construct. One objective of this study was to demonstrate the feasibility of using Roentgen stereophotogrammetric analysis (RSA) to determine the causes of lengthening of a single-loop graft construct subjected to cyclic loading. A second objective was to determine which cause(s) contributes most to an increase in length of this graft construct. Radio-opaque markers were inserted into ten grafts to measure the lengthening at the sites of the tibial and femoral fixations and between the sites of fixation. Each graft was passed through a tibial tunnel in a calf tibia, looped around a rigid cross-pin, and fixed to the tibia with a Washerloc fixation device. The grafts were cyclically loaded for 225,000 cycles from 20 to 170 N. Prior to and at intervals during the cyclic loading, simultaneous radiographs were taken. RSA was used to determine the three-dimensional coordinates of the markers from which the lengthening at the sites of fixation and between the sites of fixation was computed at each interval. The sites of the femoral and tibial fixations were the largest contributors to the increase in length of the graft construct, with maximum average values of 0.68 and 0.55 mm, respectively, after 225,000 cycles. The graft substance between the sites of fixation contributed least to lengthening of the graft, with a maximum average value of 0.31 mm. Ninety percent of the maximum average values occurred before 100,000 cycles of loading for the largest contributors. RSA proved to be a useful method for measuring lengthening due to all three causes. Lengthening of the graft construct at the sites of both fixations is sufficiently large that the combined contributions may manifest as a clinically important increase in anterior laxity.     

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.     

RSA wear measurements with or without markers in total hip arthroplasty

Novel algorithms for radiostereometric (RSA) measurements of the femoral head and metal-backed, hemi-spherical cups of a total hip replacement are presented and evaluated on phantom images and clinical double examinations of 20 patients. The materials were analysed with classical RSA and three novel algorithms: (1) a dual-projection head algorithm using the outline of the femoral head together with markers in the cup; (2) a marker-less algorithm based on measurements of the outline of the femoral head, the cup shell and opening circle of the cup; and (3) a combination of both methods. The novel algorithms improve current, marker-based, RSA measurements, as well as allows studies without marked cups. This opens the possibility of performing wear measurements on larger group of patients, in clinical follow-ups, even retrospective studies. The novel algorithms may help to save patient data in current RSA studies lost due to insufficiently marked cups. Finally, the novel algorithms simplify the RSA procedure and allow new studies without markers, saving time, money, and reducing safety concerns. Other potential uses include migration measurements of re-surfacing heads and measuring spherical sections as implant landmarks instead of markers.     

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.     

Improved RSA accuracy with DLT and balanced calibration marker distributions with an assessment of initial-calibration

Roentgen stereophotogrammetric analysis (RSA) has been used for over 25 years for accurate micromotion measurement in a wide variety of orthopaedic applications. This study investigated two possible improvements to the method. First, direct linear transformation (DLT) was compared to the traditional RSA reconstruction algorithm. The two methods were considered with respect to standard extrapolation and interpolation calibration cages. Matlab simulations showed that reconstruction accuracy was greatly improved (>60%) by combining DLT with an even distribution of enclosing calibration markers. Second, a benchtop study using phantoms translated at 0.0254-mm intervals showed initial-calibration, followed by removal of the interpolation cage for subsequent exposures, was potentially twice as accurate as self-calibration with an extrapolation cage. These results showed optimizations for the application of RSA when unobstructed space is required.     

Using an extended kalman filter for rigid body pose estimation

Rigid body pose is commonly represented as the rigid body transformation from one (often reference) pose to another This is usually computed for each frame of data without any assumptions or restrictions on the temporal change of the pose. The most common algorithm was proposed by S?derkvist and Wedin (1993, "Determining the Movements of the Skeleton Using Well-configured Markers," J. Biomech., 26, pp. 1473-1477), and implies the assumption that measurement errors are isotropic and homogenous. This paper describes an alternative method based on a state space formulation and the application of an extended Kalman filter (EKF). State space models are formulated, which describe the kinematics of the rigid body. The state vector consists of six generalized coordinates (corresponding to the 6 degrees of freedom), and their first time derivatives. The state space models have linear dynamics, while the measurement function is a non-linear relation between the state vector and the observations (marker positions). An analytical expression for the linearized measurement function is derived. Tracking the rigid body motion using an EKF enables the use of a priori information on the measurement noise and type of motion to tune the filter. The EKF is time variant, which allows for a natural way of handling temporarily missing marker data. State updates are based on all the information available at each time step, even when data from fewer than three markers are available. Comparison with the method of S?derkvist and Wedin on simulated data showed a considerable improvement in accuracy with the proposed EKF method when marker data was temporarily missing. The proposed method offers an improvement in accuracy of rigid body pose estimation by incorporating knowledge of the characteristics of the movement and the measurement errors. Analytical expressions for the linearized system equations are provided, which eliminate the need for approximate discrete differentiation and which facilitate a fast implementation.     

Validation of a non-invasive fluoroscopic imaging technique for the measurement of dynamic knee joint motion

The accurate measurement of the in vivo knee joint kinematics in six degrees-of-freedom (6DOF) remains a challenge in biomedical engineering. We have adapted a dual fluoroscopic imaging system (DFIS) to investigate the various in vivo dynamic knee joint motions. This paper presents a thorough validation of the accuracy and repeatability of the DFIS system when used to measure 6DOF dynamic knee kinematics. First, the validation utilized standard geometric spheres made from different materials to demonstrate the capability of the DFIS technique to determine the object positions under changing speeds. The translational pose of the spheres could be recreated to less than 0.15±0.09 mm for velocities below 300 mm/s. Next, tantalum beads were inserted into the femur and tibia of two fresh frozen cadaver knees to compare the dynamic kinematics measured by matching knee models to the kinematics from the tantalum bead matching—a technique similar to Roentgen stereophotogrammetric analysis (RSA). Each cadaveric knee was attached to the crosshead of a tensile testing machine and vertically translated at a rate of 16.66 mm/s while images were captured with the DFIS. Subsequently, the tibia was held fixed and the femur manually flexed from full extension to 90° of flexion, as the DFIS acquired images. In vitro translation of the cadaver knee using the tensile testing machine deviated from predicted values by 0.08±0.14 mm for the matched knee models. The difference between matching the knee and tantalum bead models during the dynamic flexion–extension motion of the knee was 0.1±0.65°/s in flexion speed; 0.24±0.16 mm in posterior femoral translation; and 0.16±0.61° in internal–external tibial rotation. Finally, we applied the method to investigate the knee kinematics of a living subject during a step ascent and treadmill gait. High repeatability was demonstrated for the in vivo application. Thus, the DFIS provides an easy and powerful tool for accurately determining 6DOF positions of the knee when performing daily functional activities.     

Effect of segmentation errors on 3D-to-2D registration of implant models in X-ray images

In many biomedical applications, it is desirable to estimate the three-dimensional (3D) position and orientation (pose) of a metallic rigid object (such as a knee or hip implant) from its projection in a two-dimensional (2D) X-ray image. If the geometry of the object is known, as well as the details of the image formation process, then the pose of the object with respect to the sensor can be determined. A common method for 3D-to-2D registration is to first segment the silhouette contour from the X-ray image; that is, identify all points in the image that belong to the 2D silhouette and not to the background. This segmentation step is then followed by a search for the 3D pose that will best match the observed contour with a predicted contour. Although the silhouette of a metallic object is often clearly visible in an X-ray image, adjacent tissue and occlusions can make the exact location of the silhouette contour difficult to determine in places. Occlusion can occur when another object (such as another implant component) partially blocks the view of the object of interest. In this paper, we argue that common methods for segmentation can produce errors in the location of the 2D contour, and hence errors in the resulting 3D estimate of the pose. We show, on a typical fluoroscopy image of a knee implant component, that interactive and automatic methods for segmentation result in segmented contours that vary significantly. We show how the variability in the 2D contours (quantified by two different metrics) corresponds to variability in the 3D poses. Finally, we illustrate how traditional segmentation methods can fail completely in the (not uncommon) cases of images with occlusion.     

Can markers injected into a single-loop anterior cruciate ligament graft define the axes of the tibial and femoral tunnels? A cadaveric study using roentgen stereophotogrammetric analysis

Lengthening of a soft-tissue anterior cruciate ligament (ACL) graft construct over time, which leads to an increase in anterior laxity following ACL reconstruction, can result from relative motions between the graft and fixation devices and between the fixation devices and bone. To determine these relative motions using Roentgen stereophotogrammetry (RSA), it is first necessary to identify the axes of the tibial and femoral tunnels. The purpose of this in vitro study was to determine the error in using markers injected into the portions of a soft-tissue tendon graft enclosed within the tibial and femoral tunnels to define the axes of these tunnels. Markers were injected into the tibia, femur, and graft in six cadaveric legs the knees of which were reconstructed with single-loop tibialis grafts. The axes of the tunnels were defined by marker pairs that were injected into the bones on lines parallel to the walls of the tibial and femoral tunnels (i.e., standard). By using marker pairs injected into the portions of the graft enclosed within the tibial and femoral tunnels and the marker pairs aligned with the tunnel axes, the directions of vectors were determined by using RSA, while a 150 N anterior force was transmitted at the knee. The average and standard deviations of the angle between the two vectors were 5.5+/-3.3 deg. This angle translates into an average error and standard deviation of the error in lengthening quantities (i.e., relative motions along the tunnel axes) at the sites of fixation of (0.6+/-0.8)%. Identifying the axes of the tunnels by using marker pairs in the graft rather than marker pairs in the walls of the tunnels will shorten the surgical procedure by eliminating the specialized tools and time required to insert marker pairs in the tunnel walls and will simplify the data analysis in in vivo studies.     

Multibody kinematics optimization with marker projection improves the accuracy of the humerus rotational kinematics

Markers put on the arm undergo large soft tissue artefact (STA). Using markers on the forearm, multibody kinematics optimization (MKO) helps improve the accuracy of the arm kinematics especially its longitudinal rotation. However deleterious effect of STA may persist and affect other segment estimate. The objective was to present an innovative multibody kinematics optimization algorithm with projection of markers onto a requested axis of the local system of coordinates, to cancel their deleterious effect on this degree-of-freedom. Four subjects equipped with markers put on intracortical pins inserted into the humerus, on skin (scapula, arm and forearm) and subsequently on rigid cuffs (arm and forearm) performed analytic, daily-living, sports and range-of-motion tasks. Scapulohumeral kinematics was estimated using 1) pin markers (reference), 2) single-body optimization, 3) MKO, 4) MKO with projection of all arm markers and 5) MKO with projection of a selection of arm markers. Approaches 2–4 were applied to markers put on the skin and the cuff. The main findings were that multibody kinematics optimization improved the accuracy of 40–50% and the projection algorithm added an extra 20% when applied to cuff markers or a selection of skin markers (all but the medial epicondyle). Therefore, the projection algorithm performed better than multibody and single-body optimizations, especially when using markers put on a cuff. Error of humerus orientation was reduced by half to finally be less than 5°. To conclude, this innovative algorithm is a promising approach for estimating accurate upper-limb kinematics.     

Determination of rigid body registration marker error from edge error

Registration markers affixed to rigid bodies (fixed to bone as opposed to skin) are commonly used when tracking 3D rigid body motion. The measured positions of registration markers are subject to unavoidable errors, both systematic and non-systematic. Prior studies have investigated the error propagated to such derived properties as rigid body positions and helical axes, while others have focused on the error associated with a specific position tracking system under restricted conditions. Theoretical and simulation-based error propagation requires knowledge of the variation due to individual registration markers; however, the variation in registration marker position measurement has previously been either assumed or determined from static cases. The objective of this paper is the introduction of a method for determining individual marker variation irrespective of change in rigid body position or motion by utilizing the distances between the markers (edge lengths), which are invariant under rotation and translation. Simulations were used to validate and characterize the introduced technique, demonstrating that the predictions improve with greater edge length and additional markers, converge on reference values where the edge length is at least 4 times the magnitude of the maximum vertex variation, and that under ideal conditions the confidence interval about the predicted variation is within 7% of the maximum variation associated with that marker set. The introduced technique was tested on the results of a motion tracking experiment to demonstrate the wide disparity in vertex variation between static and non-static measurements of the same registration markers, where the non-static variation exceeded the static variation by an average factor of 12.7.