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Accuracy and repeatability of Roentgen stereophotogrammetric analysis (RSA) for measuring knee laxity in longitudinal studies.

Roentgen stereophotogrammetric analysis (RSA) can be used to assess temporal changes in anterior-posterior (A-P) knee laxity. However, the accuracy and precision of RSA is dependent on many factors and should be independently evaluated for a particular application. The objective of this study was to evaluate the use of RSA for measuring A-P knee laxity. The specific aims were to assess the variation or "noise" inherent to RSA, to determine the reproducibility of RSA for repeated A-P laxity testing, and to assess the accuracy of these measurements. Two experiments were performed. The first experiment utilized three rigid models of the tibiofemoral joint to assess the noise and to compare digitization errors of two independent examiners. No differences were found in the kinematic outputs of the RSA due to examiner, repeated trials, or the model used. In a second experiment, A-P laxity values between the A-P shear load limits of +/-60 N of five cadaver goat knees were measured to assess the error associated with repeated testing. The RSA laxity values were also compared to those obtained from a custom designed linkage system. The mean A-P laxity values with the knee 30 degrees, 60 degrees, and 90 degrees of flexion for the ACL-intact goat knee (+/-95% confidence interval) were 0.8 (+/-0.25), 0.9 (+/-0.29), and 0.4 (+/-0.22) mm, respectively. In the ACL-deficient knee, the A-P laxity values increased by an order of magnitude to 8.8 (+/-1.39), 7.6 (+/-1.32), and 3.1 (+/-1.20)mm, respectively. No significant differences were found between the A-P laxity values measured by RSA and the independent measurement technique. A highly significant linear relationship (r(2)=0.83) was also found between these techniques. This study suggests that the RSA method is an accurate and precise means to measure A-P knee laxity for repeated testing over time.

Animals↗

Estimation of the longitudinal axis of line symmetrical soft bodies by stereophotogrammetry.

The three-dimensional (3-D) position of rigid body segments is generally determined by stereophotogrammetry: the position of markers or marker-trees, fixed onto the rigid body, is identified in each of at least 2 images. Soft bodies like the tongue of a snake are not rigid and difficult to attach marker onto. Therefore, a method is developed to estimate the 3-D position of the central axis from the digitised contours. The 3-D finite spatial curve representing the tongue axis is described by a function of a fourth variable t,tin[0,1]. The projection of this line [x(t),y(t),z(t)], a polynomial curve of a user-defined order, was fitted onto minimally 2 recorded images by means of direct linear transformation. The result is an optimally estimated finite spatial curve defined by the polynomial parameters. The method is applicable for all line symmetrical organs or segments.

Algorithms↗

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.

Algorithms↗

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.

Algorithms↗

An approach for hip joint center calculation for use in seated postures.

In seated postures, such as those in office or automotive seats, locating the hip joint center (HJC) using three markers on the pelvis has been difficult if not impossible. A two-target approach by Bell et al. (J. Biomech. 23 (1990) 617) has been used, however, this method was shown to have inaccuracies when compared to the three-target method developed by Seidel et al. (J. Biomech. 28 (1995) 995). A new two-target method that is specific to the seated environment, has better accuracy than the Bell et al. approach, and is based on the Seidel et al. approach was developed and tested on 13 seated subjects. This new method used three targets and an initial reference file to estimate the HJC location. Once the HJC was located, assumptions were made that the magnitudes between the HJC and the respective anterior superior iliac spine, and the HJC and the respective lateral epicondyle remained constant. The primary concern when evaluating this new method was the affect of seated posture movement, in particular leg splay and spinal flexion on the assumptions. The results obtained with the new approach were compared to Seidel et al. and provided HJC locations with average differences of 3.8, 1.2 and 2.8mm for spinal flexion in the anterior/posterior, medial/lateral and superior/inferior directions, respectively, and 2.3, 1.0 and 1.4mm for knee splay. The proposed method provided better HJC estimation than the Bell et al. approach particularly in the superior/inferior dimensions.

Adult↗

Estimation of the centre of rotation: a methodological contribution.

The location of the centre of rotation of human joints that can be modelled as a spherical hinge can be estimated using kinematics information about the two adjacent bony segments involved recorded while the subject makes them move one relative to the other (functional method). In order to solve the relevant analytical problem, several algorithms have been proposed. Most recently, two methods, one based on a spherical best-fit approach and another based on the Reuleaux construction, have been presented as being different and submitted to comparative evaluation. This paper modifies the second method taking all information in the data set into account and shows that, having done this, the two methods coincide analytically.

Algorithms↗

An inverse dynamics modeling approach to determine the restraining function of human knee ligament bundles.

During knee motion, the fiber bundles of ligaments are nonuniformly loaded in a recruitment pattern which is different for successive knee-joint positions. As a result, the restraining functions of these ligaments are variable. To analyze the relative restraint contributions of the fiber bundles in different knee-joint positions, a new method was developed. Its application was illustrated for the cruciate ligaments of one knee-joint specimen. The methods developed to estimate bundle forces comprise five steps. First, the three-dimensional motions of a knee specimen are measured for anterior-posterior forces, using Röntgen Stereophotogrammetric Analysis. Second, bone-ligament-bone tensile tests are performed to evaluate the mechanical properties of these structures in several relative orientations of the bones. Third, multiple fiber bundles are identified in each ligament, based on the main fiber orientations. Fourth, the nonlinear force-length relationship of each functional bundle, as defined by a stiffness and a recruitment parameter, is determined by combining the multidirectional tensile tests with a multiline-element ligament model. Finally, the information obtained is combined in a whole-joint computer model of the knee, to determine the internal forces in the initial kinematic experiment, using an inverse dynamics approach. The technique appeared to be extremely time consuming and technologically involved. However, it was demonstrated to be useful and effective. The preliminary results reveal that the fiber bundle restraints are extremely sensitive to the knee flexion angle and the restraining forces are highly variable within the ligaments. For both cruciate ligaments, a gradual transition was demonstrated in load transfer from the posterior bundles to the more anteriorly positioned ones during knee flexion. Furthermore, it appeared that relatively high forces were carried by only a few fiber bundles at each flexion angle. Based on these preliminary results, it is concluded that the determination of forces in multiple ligament bundles is important for the understanding of failure mechanisms of ligaments. In particular, alternate loading of different fiber bundles suggests that successful operative reconstruction of the cruciate ligaments may not be achieved simply by a one-bundle preparation.

Algorithms↗

Statistical comparison of DLT versus ILSSC in the calibration of a photogrammetric stereo-system.

This paper compares the DLT and ILSSC approaches in the geometrical calibration of a photogrammetric stereo-system in terms of accuracy and speed. To come up with an unbiased quantitative evaluation of the accuracy of the algorithms, the concept of reliable estimate has been introduced: the statistical distribution of the accuracy is assessed over different calibration experiments performed with the same data but with different noise distribution and different test sets. Results show that in the simulations where the only error on the two-dimensional points was Gaussian, zero mean, and on real data which were corrected for distortions through polynomial or linear interpolation, the accuracy of the two methods was quite similar. DLT showed more accurate than ILSSC on simulated data with residual distortion errors and on real data which were not corrected for distortions. As far as speed is concerned, a fast triangulation algorithm is associated with ILSSC while the simultaneous solution of two pairs of DLT equations is associated to DLT. The first algorithm is much faster, requiring 113 flops per point versus 259 of DLT; the fast triangulation with DLT parameters does not achieve the same accuracy on the reconstructed three-dimensional position. Taken all together the results suggest that ILSSC can be theoretically considered the best approach to three-dimensional reconstruction, provided that distortions are corrected in advance. The statistical evaluation of the accuracy allows a fair judgement of the performances of the algorithms to be obtained, unbiased by particular distributions of measurement errors and test points.

Algorithms↗

Conjugate imagery in the automated reproduction of three dimensional coordinates from two dimensional coordinate data.

The three-dimensional video analysis of human motion commonly utilises automated image processing and digitisation processes to produce real-time unidentified two-dimensional coordinate data of segmental markers. In what can be a time-consuming process the two-dimensional data are then identified and tracked to produce three-dimensional coordinates. This paper presents an approach to the automated reproduction of three-dimensional coordinates from two-dimensional coordinates data. Conjugate imaging techniques were utilised in the development of four criterion measures for determining the validity of conjugate (corresponding) image points. An algorithm based on the criterion measures was then developed for the automated reproduction of three dimensional coordinates from camera image coordinate data. The algorithm was tested with a 55 point marker system viewed in four video cameras (digitisation error approx. 0.2%, lab point separation > or = 6 cm). The success of the algorithm was dependent on the closeness of markers, the accuracy of the photogrammetric system, and the number of markers visible in two camera images. The present research has developed techniques based on conjugate imagery for the automated reproduction of three-dimensional coordinates from two-dimensional data, and provided a bases for further development of automated three-dimensional tracking.

Algorithms↗

Roentgen stereophotogrammetric analysis using computer-based image-analysis.

The two-dimensional position of markers in radiographs for Roentgen Stereophotogrammetric Analysis (RSA) is usually determined using a measuring table. The purpose of this study was to evaluate the reproducibility and the accuracy of a new RSA system using digitized radiographs and image-processing algorithms to determine the marker position in the radiographs. Four double-RSA examinations of a phantom and 18 RSA examinations from six patients included in different RSA-studies of knee prostheses were used to test the reproducibility and the accuracy of the system. The radiographs were scanned at 600 dpi resolution and 256 gray levels. The center of each of the tantalum-markers in the radiographs was calculated by the computer program from the contour of the marker with the use of an edge-detection software algorithm after the marker was identified on a PC monitor. The study showed that computer-based image analysis can be used in RSA-examinations. The advantages of using image-processing software in RSA are that the marker positions are determined in an objective manner, and that there is no need for a systematic manual identification of all the markers on the radiograph before the actual measurement.

Arthrography↗

Fast and accurate automated measurements in digitized stereophotogrammetric radiographs.

Until recently, Roentgen Stereophotogrammetric Analysis (RSA) required the manual definition of all markers using a high-resolution measurement table. To automate this tedious and time-consuming process and to eliminate observer variabilities, an analytical software package has been developed and validated for the detection, identification, and matching of markers in RSA radiographs. The digital analysis procedure consisted of the following steps: (1) the detection of markers using a variant of the Hough circle-finder technique; (2) the identification and labeling of the detected markers; (3) the reconstruction of the three-dimensional position of the bone markers and the prosthetic markers; and (4) the computation of micromotion. To assess the influence of film digitization, the measurements obtained from nine phantom radiographs using two different film scanners were compared with the results obtained by manual processing. All markers in the phantom radiographs were automatically detected and correctly labeled. The best results were obtained with a Vidar VXR-12 CCD scanner, for which the measurement errors were comparable to the errors associated with the manual approach. To assess the in vivo reproducibility, 30 patient radiographs were analyzed twice with the manual as well as with the automated procedure. Approximately, 85% of all calibration markers and bone markers were automatically detected and correctly matched. The calibration errors and the rigid-body errors show that the accuracy of the automated procedure is comparable to the accuracy of the manual procedure. The rigid-body errors had comparable mean values for both techniques: 0.05 mm for the tibia and 0.06 mm for the prosthesis. The reproducibility of the automated procedure showed to be slightly better than that of the manual procedure. The maximum errors in the computed translation and rotation of the tibial component were 0.11 mm and 0.24, compared to 0.13 mm and 0.27 for the manual RSA procedure. The total processing time is less than 10 min per radiograph, including interactive corrections, compared to approximately 1 h for the manual approach. In conclusion, a new and widely applicable, computer-assisted technique has become available to detect, identify, and match markers in RSA radiographs and to assess the micromotion of endoprostheses. This new technique will be used in our clinic for our hip, knee, and elbow studies.

Automation↗

Complete calibration of a stereo photogrammetric system through control points of unknown coordinates.

This paper presents a new method for calibrating a video 3D stereo-photogrammetric system. The external parameters and the focal lengths of the cameras are determined from the epipolar constraint and the principal points are computed through the minimisation of a cost function carried out through an evolutionary optimisation. The method has been made more robust with a deterministic annealing procedure of the search region amplitude. Calibration is carried out by moving a rigid bar, carrying two markers on its extremities, inside the working volume. The distance between the two markers is the only measure required. Tests on real data are reported which show that the obtained accuracy is comparable to the one achieved calibrating with control points of known 3D coordinates.

Calibration↗

Validation of a functional method for the estimation of hip joint centre location.

The present study assesses the accuracy with which the subject specific coordinates of the hip joint centre (HJC) in a pelvic anatomical frame can be estimated using different methods. The functional method was applied by calculating the centre of the best sphere described by the trajectory of markers placed on the thigh during several trials of hip rotations. Different prediction methods, proposed in the literature and in the present investigation, which estimate the HJC of adult subjects using regression equations and anthropometric measurements, were also assessed. The accuracy of each of the above-mentioned methods was investigated by comparing their predictions with measurements obtained on a sample of 11 male adult able-bodied volunteers using roentgen stereophotogrammetric analysis (RSA), assumed to provide the true HJC locations. Prediction methods estimated the HJC location at an average rms distance of 25-30 mm. The functional method performed significantly better and estimated HJCs within a rms distance of 13 mm on average. This result may be confidently generalised if the photogrammetric experiment is carefully conducted and an optimal analytical approach used. The method is therefore suggested for use in motion analysis when the subject's hip range of motion is not limited. In addition, the facts that it is not an invasive technique and that it has relatively small and un-biased errors, make it suitable for regression equations identification with no limit to sample size and population typology.

Adult↗

Accuracy analysis for RSA: a computer simulation study on 3D marker reconstruction.

In this paper, error analysis of three-dimensional marker coordinates reconstructed from noisy two-dimensional measurement in RSA was performed. Mathematical models to predict error propagation of focus position and object points were derived and computer simulations were performed to validate these models. Two clinical calibration cages were compared by testing the error propagation at each RSA step. The results revealed that errors of reconstructed object points were related to the focus position error, two-dimensional measurement error, position of focus and positions of object points, while errors of reconstructed focus position were determined by the two-dimensional measurement error, number of control points and location of the focus. The maximum difference between the mathematical model and the simulation for the assessment of errors of focus position was 14 microm and the maximum difference of object point positions was 1.1 microm. These differences were small and judged irrelevant, hence the simulations indicated that our models were accurate.

Computer Simulation↗

Moiré phototopography in the evaluation of anterior chest wall deformities.

One of the major remaining problems in the management of children with anterior chest wall deformities is the lack of a widely accepted objective method of evaluating the severity of the deformity. This deficiency has made it difficult to evaluate indications for operation or the results of operative repair. Moiré phototopography is a new method of accurately measuring human body contours utilizing recent developments in applied optics and has been used successfully in scoliosis screening programs. This technique has been applied to the evaluation of anterior chest wall deformities and the initial results of this study are presented. Moiré phototopography has proven to be a sensitive, reproducible, and easy to perform method of quantitating pectus deformities. While further evaluation is required, this early experience suggests this technique may provide a means of accurately and objectively measuring chest wall deformities so that their physiologic significance can be precisely investigated and the results of therapy critically reviewed.

Adolescent↗

Surgical correction of pectus carinatum.

Pectus carinatum is an infrequent but eminently correctable chest wall deformity. It is encountered much less frequently than pectus excavatum. In 12 years, from 1973 to 1985, 152 pectus carinatum (16.7%) and 758 pectus excavatum deformities (83.3%) were corrected. It occurs more frequently in boys (119 patients) than girls (33 patients). The majority, 89 cases, were symmetric, while 49 were asymmetric, and 14 were mixed deformities (ipsilateral carinatum, contralateral excavatum). In almost half the patients the deformity was not identified until after the 11th birthday. A family history of chest wall deformities was present in 26%, and of scoliosis in 12%. Associated musculoskeletal abnormalities were identified in 34 patients (scoliosis 23, Poland's syndrome 4, neurofibromatosis 2, Morquio's disease 2, vertebral anomalies 1, hyperlordosis 1, and kyphosis 1). Surgical correction required bilateral resection of the third through seventh costal cartilages in 143 patients, and unilateral resection in nine patients with an isolated abnormality. A single osteotomy was used in 88 patients and a double osteotomy in 53 patients. In 11 cases no osteotomy was required. Mixed deformity with posterior angulation of the sternum was managed by osteotomy and anterior displacement. The remaining cases had sternal osteotomy and fracture of the posterior cortex to correct anterior angulation. The operation was completed with a low complication rate 3.9% (pneumothorax 4, wound infection 1, atelectasis 1, and local tissue necrosis 1). Three patients required revision with additional unilateral lower cartilage resection for persistent malformation of the costal arch. All patients ultimately had a satisfactory result.

Adolescent↗

Surgical correction of chondromanubrial deformity (Currarino Silverman syndrome).

Chondromanubrial (arcuate) pectus carinatum is the rarest protrusion deformity of the chest. Its surgical correction was first described by Ravitch in 1952. We have recently encountered five patients with this deformity who have provided additional insight into the anatomy and optimal repair of this condition. It is notable for a short nonsegmented sternum with marked posterior angulation at the site of the normal chondromanubrial junction. It is optimally corrected by subperichondrial resection of the second to the seventh costal cartilages with a broad wedge-shaped osteotomy through the anterior cortex of the sternum at the point of maximal angulation. Anterior displacement of the sternum is achieved by closing the osteotomy with heavy silk sutures while the costal cartilages are regenerating.

Adolescent↗

Clinical study of location and reproducibility of three mandibular positions in relation to body posture and muscle function.

Clinical studies have confirmed the adequate reproducibility of both centric occlusion and centric relation when used as reference positions during treatment; however, the reproducibility of the neuromuscular position has been found inadequate. This study evaluated the location and reproducibility of these three mandibular positions in relation to body posture, sitting and supine, and bilateral muscle activity before and after the insertion of a flat mandibular positioning device equilibrated to balance the muscle functions, as shown by two electromyography biofeedback instruments. Intraoral recordings were made in 11 young subjects with complete natural dentition. Acrylic resin clutches that supported a screw point in the maxillary arch and painted glass in the mandibular arch were used and positioned not to interfere with the occlusion. The distances of the screw scratch from two of the edges of the painted glass were used to measure the anteroposterior and mediolateral locations with a micrometer. The reproducibility was evaluated by measuring the scratch surface by measuring the weight of the print cutouts made from photographs of the scratches taken with a stereoscope. The location and reproducibility of centric occlusion and centric relation were not affected by body posture. A more precise posterior neuromuscular position was obtained in the supine position. The insertion of a mandibular positioning device did not affect centric occlusion but gave a more precise centric relation. Neuromuscular position became as precise as centric occlusion and was located anteroposteriorly between centric occlusion and centric relation.

Acrylic Resins↗