Prediction of joint center location by customizable multiple regressions: Application to clavicle,scapula and humerus

Accurate spatial location of joint center (JC) is a key issue in motion analysis since JC locations are used to define standardized anatomical frames, in which results are represented. Accurate and reproducible JC location is important for data comparison and data exchange. This paper presents a method for JC locations based on the multiple regression algorithms without preliminary assumption on the behavior of the joint-of-interest. Regression equations were obtained from manually palpable ALs on each bone-of-interest. Results are presented for all joint surfaces found on the clavicle, scapula and humeral bone. Mean accuracy errors on the JC locations obtained on dry bones were 5.2±2.5 mm for the humeral head, 2.5±1.1 mm for the humeral trochlea, 2.3±0.9 mm for the humeral capitulum, 8.2±3.9 mm for the scapula glenoid cavity, 7.2±3.2 mm for the scapular aspect of the acromio-clavicular joint, 3.5±1.8 mm for the clavicular aspect of the sternoclavicular joint and 3.2±1.4 mm for the clavicular aspect of the acromio-clavicular joint. In-vitro and in-vivo validation accuracy was 5.3 and 8.5 mm, respectively, for the humeral head center location. Regression coefficients for joint radius dimension and joint surface orientation were also processed and reported in this paper.     

Prediction of the hip joint centre in adults, children, and patients with cerebral palsy based on magnetic resonance imaging

The location of the hip joint centre (HJC) is required for calculations of hip moments, the location and orientation of the femur, and muscle lengths and lever arms. In clinical gait analysis, the HJC is normally estimated using regression equations based on normative data obtained from adult populations. There is limited relevant anthropometric data available for children, despite the fact that clinical gait analysis is predominantly used for the assessment of children with cerebral palsy. In this study, pelvic MRI scans were taken of eight adults (ages 23-40), 14 healthy children (ages 5-13) and 10 children with spastic diplegic cerebral palsy (ages 6-13). Relevant anatomical landmarks were located in the scans, and the HJC location in pelvic coordinates was found by fitting a sphere to points identified on the femoral head. The predictions of three common regression equations for HJC location were compared to those found directly from MRI. Maximum absolute errors of 31 mm were found in adults, 26 mm in children, and 31 mm in the cerebral palsy group. Results from regression analysis and leave-one-out cross-validation techniques on the MRI data suggested that the best predictors of HJC location were: pelvic depth for the antero-posterior direction; pelvic width and leg length for the supero-inferior direction; and pelvic depth and pelvic width for the medio-lateral direction. For single-variable regression, the exclusion of leg length and pelvic depth from the latter two regression equations is proposed. Regression equations could be generalised across adults, children and the cerebral palsy group.     

Subject-specific hip geometry and hip joint centre location affects calculated contact forces at the hip during gait

Hip loading affects the development of hip osteoarthritis, bone remodelling and osseointegration of implants. In this study, we analyzed the effect of subject-specific modelling of hip geometry and hip joint centre (HJC) location on the quantification of hip joint moments, muscle moments and hip contact forces during gait, using musculoskeletal modelling, inverse dynamic analysis and static optimization. For 10 subjects, hip joint moments, muscle moments and hip loading in terms of magnitude and orientation were quantified using three different model types, each including a different amount of subject-specific detail: (1) a generic scaled musculoskeletal model, (2) a generic scaled musculoskeletal model with subject-specific hip geometry (femoral anteversion, neck-length and neck-shaft angle) and (3) a generic scaled musculoskeletal model with subject-specific hip geometry including HJC location. Subject-specific geometry and HJC location were derived from CT. Significant differences were found between the three model types in HJC location, hip flexion–extension moment and inclination angle of the total contact force in the frontal plane. No model agreement was found between the three model types for the calculation of contact forces in terms of magnitude and orientations, and muscle moments. Therefore, we suggest that personalized models with individualized hip joint geometry and HJC location should be used for the quantification of hip loading. For biomechanical analyses aiming to understand modified hip joint loading, and planning hip surgery in patients with osteoarthritis, the amount of subject-specific detail, related to bone geometry and joint centre location in the musculoskeletal models used, needs to be considered.     

Defining and evaluating wrapping surfaces for MRI-derived spinal muscle paths

Muscle paths can be approximated in biomechanical models by wrapping the path around geometric objects; however, the process for selecting and evaluating wrapping surface parameters is not well defined, especially for spinal muscles. In this study, we defined objective methods to select the shape, orientation, size and location of wrapping surfaces and evaluated the wrapping surfaces using an error metric based on the distance between the modeled muscle path and the centroid path from magnetic resonance imaging (MRI). We applied these methods and the error metric to a model of the neck musculature, where our specific goals were (1) to optimize the vertebral level at which to place a single wrapping surface per muscle; and (2) to define wrapping surface parameters in the neutral posture and evaluate them in other postures. Detailed results are provided for the sternocleidomastoid and the semispinalis capitis muscles. For the sternocleidomastoid, the level where the wrapping surface was placed did not significantly affect the error between the modeled path and the centroid path; use of wrapping surfaces defined from the neutral posture improved the representation of the muscle path compared to a straight line in all postures except contralateral rotation. For the semispinalis capitis, wrapping surfaces placed at C3 or C4 resulted in lower error compared to other levels; and the use of wrapping surfaces significantly improved the muscle path representation in all postures. These methods will be used to improve the estimates of muscle length, moment arm and moment-generating capacity in biomechanical models.     

Automated muscle wrapping using finite element contact detection

Realistic muscle path representation is essential to musculoskeletal modeling of joint function. Algorithms predicting these muscle paths typically rely on a labor intensive predefinition of via points or underlying geometries to guide wrapping for given joint positions. While muscle wrapping using anatomically precise three-dimensional (3D) finite element (FE) models of bone and muscle has been achieved, computational expense and pre-processing associated with this approach exclude its use in applications such as subject-specific modeling. With the intention of combining advantageous features of both approaches, an intermediate technique relying on contact detection capabilities of commercial FE packages is presented. We applied the approach to the glenohumeral joint, and validated the method by comparison against existing experimental data. Individual muscles were modeled as a straight series of deformable beam elements and bones as anatomically precise 3D rigid bodies. Only the attachment locations and a default orientation of the undeformed muscle segment were pre-defined. The joint was then oriented in a static position of interest. The muscle segment free end was then moved along the shortest Euclidean path to its origin on the scapula, wrapping the muscle along bone surfaces by relying on software contact detection. After wrapping for a given position, the resulting moment arm was computed as the perpendicular distance from the line of action vector to the humeral head center of rotation.This approach reasonably predicted muscle length and moment arm for 27 muscle segments when compared to experimental measurements over a wide range of shoulder motion. Artificial via points or underlying contact geometries were avoided, contact detection and multiobject wrapping on the bone surfaces were automatic, and low computational cost permitted wrapping of individual muscles within seconds on a standard desktop PC. These advantages may be valuable for both general and subject-specific musculoskeletal modeling.     

Precision and accuracy of bone landmarks in characterizing hand and wrist position

Characterization of the motion of the hand and wrist requires reference to the underlying bones which, for three-dimensional analyses, are assumed to be rigid bodies. Stereoradiogrammetric techniques involving the identification of prominent bone landmarks have been used as the standard against which surface markers used for in vivo testing have been evaluated. The precision and accuracy with which the 3D positions of bone landmarks in the hand and wrist could be determined was evaluated in a small inter-observer and inter-cadaver study and compared to the precision and accuracy with which implanted lead markers could be located. A subset of landmarks suitable for evaluating wrist and metacarpal-phalangeal joint motion was identified; the mean precison for identifying these points was better than 1.1 mm in all hand positions with a mean inter-observer accuracy of 2.3 mm. These values show that the average uncertainty in locating bone landmarks is at best roughly twice that for implanted markers.     

A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints

This study describes a genera] set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean ± stand, dev. error in translation: 0.63 ± 1.19 mm, 0.10 ± 0.71 mm, -0.29 ± 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 ± 1.71°, 0.27 ±2.38°, -1.13 ± 1.83° in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room.     

A Mathematical Formulation for 3D Quasi-Static Multibody Models of Diarthrodial Joints

This study describes a general set of equations for quasi-static analysis of three-dimensional multibody systems, with a particular emphasis on modeling of diarthrodial joints. The model includes articular contact, muscle forces, tendons and tendon pulleys, ligaments, and the wrapping of soft tissue structures around bone and cartilage surfaces. The general set of equations governing this problem are derived using a consistent notation for all types of links, which can be converted conveniently into efficient computer codes. The computational efficiency of the model is enhanced by the use of analytical Jacobians, particularly in the analysis of articular surface contact and wrapping of soft tissue structures around bone and cartilage surfaces. The usefulness of the multibody model is demonstrated by modeling the patellofemoral joint of six cadaver knees, using cadaver-specific data for the articular surface and bone geometries, as well as tendon and ligament insertions and muscle lines of actions. Good accuracy was observed when comparing the model patellar kinematic predictions to experimental data (mean +/- stand. dev. error in translation: 0.63 +/- 1.19 mm, 0.10 +/- 0.71 mm, -0.29 +/- 0.84 mm along medial, proximal, and anterior directions, respectively; in rotation: -1.41 +/- 1.71 degrees, 0.27 +/- 2.38 degrees, -1.13 +/- 1.83 degrees in flexion, tilt and rotation, respectively). The accuracy which can be achieved with this type of model, and the computational efficiency of the algorithm employed in this study may serve in many applications such as computer-aided surgical planning, and real-time computer-assisted surgery in the operating room.     

Statistical shape modelling versus linear scaling: Effects on predictions of hip joint centre location and muscle moment arms in people with hip osteoarthritis

Marker-based dynamic functional or regression methods are used to compute joint centre locations that can be used to improve linear scaling of the pelvis in musculoskeletal models, although large errors have been reported using these methods. This study aimed to investigate if statistical shape models could improve prediction of the hip joint centre (HJC) location. The inclusion of complete pelvis imaging data from computed tomography (CT) was also explored to determine if free-form deformation techniques could further improve HJC estimates. Mean Euclidean distance errors were calculated between HJC from CT and estimates from shape modelling methods, and functional- and regression-based linear scaling approaches. The HJC of a generic musculoskeletal model was also perturbed to compute the root-mean squared error (RMSE) of the hip muscle moment arms between the reference HJC obtained from CT and the different scaling methods. Shape modelling without medical imaging data significantly reduced HJC location error estimates (11.4 ± 3.3 mm) compared to functional (36.9 ± 17.5 mm, p = <0.001) and regression (31.2 ± 15 mm, p = <0.001) methods. The addition of complete pelvis imaging data to the shape modelling workflow further reduced HJC error estimates compared to no imaging (6.6 ± 3.1 mm, p = 0.002). Average RMSE were greatest for the hip flexor and extensor muscle groups using the functional (16.71 mm and 8.87 mm respectively) and regression methods (16.15 mm and 9.97 mm respectively). The effects on moment-arms were less substantial for the shape modelling methods, ranging from 0.05 to 3.2 mm. Shape modelling methods improved HJC location and muscle moment-arm estimates compared to linear scaling of musculoskeletal models in patients with hip osteoarthritis.     

A three-dimensional musculoskeletal model for gait analysis. Anatomical variability estimates

Three-dimensional coordinates defining the origin and insertion of 40 muscle units, and bony landmarks for osteometric scaling were identified on dry bone specimens. Interspecimen coordinate differences along the anterior-posterior axis of the pelvis and the long bone axes of the pelvis, femur and leg were reduced by scaling but landmark differences along the other axes were not. The coordinates were mapped to living subjects using close-range photogrammetry to locate superficial reference markers. The error of predicting the positions of internal coordinates was assessed by comparing joint centre locations calculated from local axes defining the orientation of segments superior and inferior to a joint. A difference was attributed to: anatomical variability not accounted for by scaling; errors in identifying and placing reference landmarks; the accuracy of locating markers using photogrammetry and error introduced by marker oscillation during movement. Anatomical differences between specimens are one source of error in defining a musculoskeletal model but larger errors are introduced when such models are mapped to living subjects.     

Accuracy of femur reconstruction from sparse geometric data using a statistical shape model

Sparse geometric information from limited field-of-view medical images is often used to reconstruct the femur in biomechanical models of the hip and knee. However, the full femur geometry is needed to establish boundary conditions such as muscle attachment sites and joint axes which define the orientation of joint loads. Statistical shape models have been used to estimate the geometry of the full femur from varying amounts of sparse geometric information. However, the effect that different amounts of sparse data have on reconstruction accuracy has not been systematically assessed. In this study, we compared shape model and linear scaling reconstruction of the full femur surface from varying proportions of proximal and distal partial femur geometry in combination with morphometric and landmark data. We quantified reconstruction error in terms of surface-to-surface error as well as deviations in the reconstructed femur’s anatomical coordinate system which is important for biomechanical models. Using a partial proximal femur surface, mean shape model-based reconstruction surface error was 1.8 mm with 0.15° or less anatomic axis error, compared to 19.1 mm and 2.7–5.6° for linear scaling. Similar results were found when using a partial distal surface. However, varying amounts of proximal or distal partial surface data had a negligible effect on reconstruction accuracy. Our results show that given an appropriate set of sparse geometric data, a shape model can reconstruct full femur geometry with far greater accuracy than simple scaling.     

Determining skeletal muscle architecture with Laplacian simulations: a comparison with diffusion tensor imaging

Determination of skeletal muscle architecture is important for accurately modeling muscle behavior. Current methods for 3D muscle architecture determination can be costly and time-consuming, making them prohibitive for clinical or modeling applications. Computational approaches such as Laplacian flow simulations can estimate muscle fascicle orientation based on muscle shape and aponeurosis location. The accuracy of this approach is unknown, however, since it has not been validated against other standards for muscle architecture determination. In this study, muscle architectures from the Laplacian approach were compared to those determined from diffusion tensor imaging in eight adult medial gastrocnemius muscles. The datasets were subdivided into training and validation sets, and computational fluid dynamics software was used to conduct Laplacian simulations. In training sets, inputs of muscle geometry, aponeurosis location, and geometric flow guides resulted in good agreement between methods. Application of the method to validation sets showed no significant differences in pennation angle (mean difference \(0.5{^{\circ }})\) or fascicle length (mean difference 0.9 mm). Laplacian simulation was thus effective at predicting gastrocnemius muscle architectures in healthy volunteers using imaging-derived muscle shape and aponeurosis locations. This method may serve as a tool for determining muscle architecture in silico and as a complement to other approaches.     

Development and validation of ultrasound speckle tracking to quantify tendon displacement

Ultrasound can be used to study tendon movement. However, measurement of tendon movement is mostly based on manual tracking of anatomical landmarks such as the musculo-tendinous junction, limiting the applicability to a small number of muscle-tendon units. The aim of this study was to quantify tendon displacement without anatomical landmarks using a speckle tracking algorithm optimized for tendons in long B-mode image sequences. A dedicated two-dimensional multi-kernel block-matching scheme with subpixel motion estimation was devised to handle large displacements over long sequences. The accuracy of the tracking on porcine tendons was evaluated during different displacements and velocities. Subsequently, the accuracy of tracking the flexor digitorum superficialis (FDS) of a human cadaver hand was evaluated. Finally, the in-vivo accuracy of the tendon tracking was determined by measuring the movement of the FDS at the wrist level. For the porcine experiment and the human cadaver arm experiment tracking errors were, on average, 0.08 and 0.05 mm, respectively (1.3% and 1.0%). For the in-vivo experiment the tracking error was, on average, 0.3 mm (1.6%). This study demonstrated that our dedicated speckle tracking can quantify tendon displacement at different physiological velocities without anatomical landmarks with high accuracy. The technique allows tracking over large displacements and in a wider range of tendons than by using anatomical landmarks.     

Identification of scapular kinematics using surface mapping: a validation study

The immediate goal of this study was to develop and validate a noninvasive, computational surface mapping approach for measuring scapular kinematics by using available motion capture technology in an innovative manner. The long-term goal is to facilitate clinical determination of the role of the scapula in children with brachial plexus birth palsy (BPBP). The population for this study consisted of fourteen healthy adults with prominent scapulae. Subject-specific scapular templates were created using the coordinates of five scapular landmarks obtained from palpation with subjects seated and arms relaxed in a neutral position. The scapular landmarks were re-palpated and their locations recorded in the six arm positions of the modified Mallet classification. The six Mallet positions were repeated with approximately 300 markers covering the scapula. The markers formed a surface map covering the tissue over the scapula. The scapular template created in the neutral position was iteratively fit to the surface map of each trial, providing an estimate of the orientation of the scapula. These estimates of scapular orientation were compared to the known scapular orientation determined from the scapular landmarks palpated in each Mallet position. The magnitude of the largest mean difference about an anatomical axis between the two measures of scapular orientation was 3.8° with an RMS error of 5.9°. This technique is practical for populations with visibly prominent scapulae (e.g., BPBP patients), for which it is a viable alternative to existing clinical methods with comparable accuracy.     

Assessment of the functional method of hip joint center location subject to reduced range of hip motion

Motion analysis of the lower extremities usually requires determination of the location of the hip joint center. The results of several recent studies have suggested that kinematic and kinetic variables calculated from motion analysis data are highly sensitive to errors in hip joint center location. "Functional" methods in which the location of the hip joint center is determined from the relative motion of the thigh and pelvis, rather than from the locations of bony landmarks, are promising but may be ineffective when motion is limited. The aims of the present study were to determine whether the accuracy of the functional method is compromised in young and elderly subjects when limitations on hip motion are imposed and to investigate the possibility of locating the hip joint center using data collected during commonly studied motions (walking, sit-to-stand, stair ascent, stair descent) rather than using data from an ad hoc trial in which varied hip motions are performed. The results of the study suggested that functional methods would result in worst-case hip joint center location errors of 26mm (comparable to the average errors previously reported for joint center location based on bony landmarks) when available hip motion is substantially limited. Much larger errors ( approximately 70mm worst-case), however, resulted when hip joint centers were located from data collected during commonly performed motions, perhaps because these motions are, for the most part, restricted to the sagittal plane. It appears that the functional method can be successfully implemented when range of motion is limited but still requires collection of a special motion trial in which hip motion in both the sagittal and frontal planes is recorded.     

Movement of the human pelvis and displacement of related anatomical landmarks on the body surface

Anatomical landmarks on the body surface can be measured with high accuracy by using rasterstereography and surface curvature analysis. The present study shows that the lumbar dimples can be localized with a statistical error of about 1 mm. It is generally assumed that the dimples are in close relation to the pelvis (in particular to the PSISs) and may thus be taken as indicators for pelvis movements. By introducing an artificial pelvis tilt of up to +/- 10 degrees this relation was examined. In fact, a nearly perfect correlation (r approximately equal to 0.99) between landmark and pelvis movements was observed. Asymmetries of pelvis motion due to scoliotic deformity were not observed. There was, however, a systematic lag of the dimple movements, resulting in a displacement of the dimples of up to +/- 1.5 mm relative to the pelvis (for +/- 10 degrees pelvis tilt). Either a soft tissue effect or a torsion of the pelvis may be responsible for this behaviour. The theory of pelvis torsion is confirmed by the fact that the orientation of the back surface at the locus of the dimples reveals a corresponding torsion of similar magnitude and sign. A torsion angle of about +/- 1.5 degrees in either sacro-iliac joint is sufficient to explain the observed dimple lag and the surface torsion. An independent measurement (e.g. using roentgenphotogrammetry) would be desirable to further validate this theory. According to our measurements the dimples of the PSISs cannot be taken as exact indicators for orientation and movement of the pelvis.(ABSTRACT TRUNCATED AT 250 WORDS)     

Sensitivity of insertion locations on length patterns of anterior cruciate ligament fibers

A technique is demonstrated, employing an instrumented spatial linkage, for the determination of the length patterns of discrete fiber bundles within a ligament under controlled loading conditions. The instrumented spatial linkage was used to measure the three-dimensional joint motion. The linkage was also used as a three-dimensional coordinate digitizer to determine the spatial location of bony landmarks and the ligament's insertion areas. The length of pseudo fiber bundles was determined as the straight line distance between bone attachments. A comparison is presented, showing good agreement, between elongation patterns obtained from this method and those measured using an instrumented fine wire cable fiber. A sensitivity analysis was performed to evaluate the influence of tibial and femoral attachment location on the length pattern of fiber bundles of the anterior cruciate ligament. It was found that the relationship between fiber elongation and knee flexion depended strongly on the fibers femoral attachment location but not on its tibial attachment location.     

Accuracy of the functional method of hip joint center location: effects of limited motion and varied implementation.

Accurate location of the hip joint center is essential for computation of hip kinematics and kinetics as well as for determination of the moment arms of muscles crossing the hip. The functional method of hip joint center location involves fitting a pelvis-fixed sphere to the path traced by a thigh-fixed point while a subject performs hip motions; the center of this sphere is the hip joint center. The aim of the present study was to evaluate the potential accuracy of the functional method and the dependence of its accuracy on variations in its implementation and the amount of available hip motion. The motions of a mechanical linkage were studied to isolate the factors of interest, removing errors due to skin movement and the palpation of bony landmarks that are always present in human studies. It was found that reducing the range of hip motion from 30 degrees to 15 degrees did significantly increase hip joint center location errors, but that restricting motion to a single plane did not. The magnitudes of these errors, however, even in the least accurate cases, were smaller than those previously reported for either the functional method or other methods based on pelvis measurements of living subjects and cadaver specimens. Neither increasing the number of motion data observations nor analyzing the motion of a single thigh marker (rather than the centroid of multiple markers) was found to significantly increase error. The results of this study (1) imply that the limited range of motion that is often evident in subjects with hip pathology does not preclude accurate determination of the hip joint center when the functional method is used; and (2) provide guidelines for the use of the functional method in human subjects.     

Stereotaxic map of the muscle fibers in the indirect flight muscles of Drosophila melanogaster

It is possible to monitor the electrical activity of the motor neurons of Drosophila by recording the electrical activity of the muscle fibers. We have found that it is possible to specify the location of the subcuticular terminations and to describe the orientation within the thorax for the individual muscle fibers, because of the large size of the fibers and because the surface anatomy of Drosophila is known in detail. A map has been made to indicate the location of the muscle fibers with respect to superficial landmarks. The importance of the stereotaxic map for physiological studies is discussed.