A model to predict canine pelvic limb musculoskeletal geometry

We developed a model to predict the three-dimensional canine pelvic limb muscular geometry (i.e., all muscle moment arms during any instant in gait). Forty-one muscle origins and insertions, as well as external landmarks (to obtain anthropometric dimensions) were marked on both pelvic limbs of five dogs and digitized on biplanar radiographs. Reference frames in the pelvis, femur, and tibia established the three-dimensional coordinates of each origin, insertion, and landmark. A set of dimensionless 'scaled coordinates' was created by dividing the actual origin and insertion coordinates by selected anthropometric dimensions of each animal. Combining scaled coordinates from all ten limbs produced an averaged 'template' of scaled coordinates. To provide limited validation of the scaling procedure, we measured the anthropometric dimensions between externally palpable landmarks of two additional pelvic limbs. The anthropometric dimensions were multiplied by the averaged template coordinates to calculate two new sets of hindlimb muscle coordinates within the three bony reference frames. The two limbs then were dissected, muscle endpoints were marked, and biplanar radiographs of each of the limb segments were digitized. The actual coordinates so obtained were similar to those predicted by the template and anthropometric measures.     

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.     

Muscle parameters estimation based on biplanar radiography

The evaluation of muscle and joint forces in vivo is still a challenge. Musculo-Skeletal (musculo-skeletal) models are used to compute forces based on movement analysis. Most of them are built from a scaled-generic model based on cadaver measurements, which provides a low level of personalization, or from Magnetic Resonance Images, which provide a personalized model in lying position. This study proposed an original two steps method to access a subject-specific musculo-skeletal model in 30 min, which is based solely on biplanar X-Rays. First, the subject-specific 3D geometry of bones and skin envelopes were reconstructed from biplanar X-Rays radiography. Then, 2200 corresponding control points were identified between a reference model and the subject-specific X-Rays model. Finally, the shape of 21 lower limb muscles was estimated using a non-linear transformation between the control points in order to fit the muscle shape of the reference model to the X-Rays model. Twelfth musculo-skeletal models were reconstructed and compared to their reference. The muscle volume was not accurately estimated with a standard deviation (SD) ranging from 10 to 68%. However, this method provided an accurate estimation the muscle line of action with a SD of the length difference lower than 2% and a positioning error lower than 20 mm. The moment arm was also well estimated with SD lower than 15% for most muscle, which was significantly better than scaled-generic model for most muscle. This method open the way to a quick modeling method for gait analysis based on biplanar radiography.     

Finger Muscle Attachments for an OpenSim Upper-Extremity Model

We determined muscle attachment points for the index, middle, ring and little fingers in an OpenSim upper-extremity model. Attachment points were selected to match both experimentally measured locations and mechanical function (moment arms). Although experimental measurements of finger muscle attachments have been made, models differ from specimens in many respects such as bone segment ratio, joint kinematics and coordinate system. Likewise, moment arms are not available for all intrinsic finger muscles. Therefore, it was necessary to scale and translate muscle attachments from one experimental or model environment to another while preserving mechanical function. We used a two-step process. First, we estimated muscle function by calculating moment arms for all intrinsic and extrinsic muscles using the partial velocity method. Second, optimization using Simulated Annealing and Hooke-Jeeves algorithms found muscle-tendon paths that minimized root mean square (RMS) differences between experimental and modeled moment arms. The partial velocity method resulted in variance accounted for (VAF) between measured and calculated moment arms of 75.5% on average (range from 48.5% to 99.5%) for intrinsic and extrinsic index finger muscles where measured data were available. RMS error between experimental and optimized values was within one standard deviation (S.D) of measured moment arm (mean RMS error = 1.5 mm < measured S.D = 2.5 mm). Validation of both steps of the technique allowed for estimation of muscle attachment points for muscles whose moment arms have not been measured. Differences between modeled and experimentally measured muscle attachments, averaged over all finger joints, were less than 4.9 mm (within 7.1% of the average length of the muscle-tendon paths). The resulting non-proprietary musculoskeletal model of the human fingers could be useful for many applications, including better understanding of complex multi-touch and gestural movements.     

Muscle forces predicted using optimization methods are coordinate system dependent

Optimization methods are widely used to predict in vivo muscle forces in musculoskeletal joints. Moment equilibrium at the joint center (usually chosen as the origin of the joint coordinate system) has been used as a constraint condition for optimization procedures and the joint reaction moments were assumed zero. This study, through the use of a three-dimensional elbow model, investigated the effect of coordinate system origin (joint center) location on muscle forces predicted using a nonlinear static optimization method. The results demonstrated that moving the origin of the coordinate system medially and laterally along the flexion-extension axis caused dramatic variations in the predicted muscle forces. For example, moving the origin of the coordinate system from a position 5mm medial to 5mm lateral of the geometric elbow center caused the predicted biceps force to vary from 12% to 46% and the brachialis force to vary from 80% to 34% of the total muscle loading. The joint reaction force reduced by 24% with this medial to lateral variation of the coordinate system origin location. This data revealed that the muscle forces predicted using the optimization method are sensitive to the coordinate system origin location due to the zero joint reaction moment assumption in the moment constraint condition. For accurate prediction of muscle load distributions using optimization methods, it is necessary to determine the accurate coordinate system origin location where the condition of a zero joint reaction moment is satisfied.     

3D reconstruction of the ribs from lateral and frontal X-rays in comparison to 3D CT-scan reconstruction

Subject-specific three-dimensional (3D) reconstructions of the ribs can be obtained from biplanar X-rays. The goal of this study was to evaluate the accuracy and the inter-observer reproducibility of this technique in comparison to CT-scan reconstructions. CT scans and biplanar X-rays were obtained from 50 ribs (from three cadaveric rib cages). Three experienced experimenters reconstructed each rib from biplanar X-rays. Morphometric parameters were then computed from the rib midlines. Differences were computed between parameters obtained from the 3D reconstructions based on biplanar X-rays and from CT scans. The accuracy was computed as the mean of this difference for the 50 ribs from all three experimenters. The inter-observer variability was assessed using the coefficient of variation (CV) between the three observers. The CT-scan reconstructions were considered to be the gold standard in spite of their limitations for rib reconstructions. According to the different linear parameters, the accuracy of the reconstructions was found to be between -6mm (-2%) and 3mm, (4%). The accuracy of the current method was close to that of CT-scan reconstructions. The inter-observer variability was between 3% and 6%. Frontal and lateral X-rays are commonly obtained clinically, so 3D reconstructions can be used without increased radiation exposure to the patient.     

A three-dimensional model of the rat hindlimb: musculoskeletal geometry and muscle moment arms

As a first step towards developing a dynamic model of the rat hindlimb, we measured muscle attachment and joint center coordinates relative to bony landmarks using stereophotogrammetry. Using these measurements, we analyzed muscle moment arms as functions of joint angle for most hindlimb muscles, and tested the hypothesis that postural change alone is sufficient to alter the function of selected muscles of the leg. We described muscle attachment sites as second-order curves. The length of the fit parabola and residual errors in the orthogonal directions give an estimate of muscle attachment sizes, which are consistent with observations made during dissection. We modeled each joint as a moving point dependent on joint angle; relative endpoint errors less than 7% indicate this method as accurate. Most muscles have moment arms with a large range across the physiological domain of joint angles, but their moment arms peak and vary little within the locomotion domain. The small variation in moment arms during locomotion potentially simplifies the neural control requirements during this phase. The moment arms of a number of muscles cross zero as angle varies within the quadrupedal locomotion domain, indicating they are intrinsically stabilizing. However, in the bipedal locomotion domain, the moment arms of these muscles do not cross zero and thus are no longer intrinsically stabilizing. We found that muscle function is largely determined by the change in moment arm with joint angle, particularly the transition from quadrupedal to bipedal posture, which may alter an intrinsically stabilizing arrangement or change the control burden.     

A finite element model of the human knee joint for the study of tibio-femoral contact

As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior, and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (ie., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 mm by 5 mm to 1 mm by 1 mm. The solution was considered converged for an average element size of 2 mm by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.     

Twente spine model: A complete and coherent dataset for musculo-skeletal modeling of the lumbar region of the human spine

Musculo-skeletal modeling can greatly help in understanding normal and pathological functioning of the spine. For such models to produce reliable muscle and joint force estimations, an adequate set of musculo-skeletal data is necessary. In this study, we present a complete and coherent dataset for the lumbar spine, based on medical images and dissection measurements from one embalmed human cadaver. We divided muscles into muscle-tendon elements, digitized their attachments at the bones and measured morphological parameters. In total, we measured 11 muscles from one body side, using 96 elements. For every muscle element, we measured three-dimensional coordinates of its attachments, fiber length, tendon length, sarcomere length, optimal fiber length, pennation angle, mass, and physiological cross-sectional area together with the geometry of the lumbar spine. Results were consistent with other anatomical studies and included new data for the serratus posterior inferior muscle. The dataset presented in this paper enables a complete and coherent musculo-skeletal model for the lumbar spine and will improve the current state-of-the art in predicting spinal loading.     

Centers and angles of rotation of body joints: A study of errors and optimization

Large variations are generally reported in the locations of centers of rotation (CR) for each of various joints in the human body. Some of these reports present conflicting results. This paper shows that this may be due in part to suboptimal experimental design as well as the phenomenon of error magnification. An algorithm is presented for computing the coordinates of the CR and the angle of rotation from the x, y coordinate measurements of two point markers on a moving body in two different positions. Error analysis is performed using a mathematical model that introduces systematically a positive or a negative error into each of the 8 x, y coordinates in all possible combinations, resulting in 256 CR locations. CR error zones are computed and graphed. Parametric analysis of the experimental set-up leads to optimization of the set-up. A typical case is analyzed and its errors computed. It is shown that small errors present in the measurements of the x, y coordinates of the markers are magnified to relatively large errors in the CR coordinates. In a suboptimal case, this magnification may be 30–50 times or more. The results show that, besides the magnitude of x, y coordinate errors, other factors responsible for determining the magnitude of errors in the location of the CR are: the magnitude of angle of rotation, the orientation of the markers with respect to the CR and their distances from the CR. In conjunction with the CR, the angle of rotation is also analyzed. Guidelines for optimal experimental set-up for minimizing the output errors are presented.     

Analysis of humeral head displacements from sequences of biplanar X-rays: repeatability study and preliminary results in healthy subjects

This work presents an accurate method to measure gleno-humeral translations in a controlled pseudo-kinematic environment. Low-dose biplanar X-rays were acquired from nine healthy subjects at three elevations of the arm in the scapular plane. On each set of images, shoulder bony landmarks were manually located in 3D using a dedicated software. Intra-observer and inter-observer repeatability of landmark identification, as well as humeral head center (GH) translations, were studied. Repeatability for the identification of GH in the global coordinate system (CS) was good with 95% confidence intervals (CIs) ranging from 0.57 to 2.25 mm. Scapular landmark CIs ranged from 0.80 to 12 mm. Gleno-humeral translations of small amplitude ( < 6 mm) were detected in seven out of nine subjects. The results obtained here confirm that calibrated low-dose stereo-radiography is a promising tool for the functional analysis of the shoulder.     

Algorithm and validation of a computer method for quantifying attachment locus of glenohumeral ligament in vivo

The aim of this work is to validate an algorithm that quantifies the locus of glenohumeral ligament (GHL) attachments on glenohumeral joint (GHJ) bones.

A computed tomography scan of a GHJ was segmented to reconstruct the humerus, scapula, anatomical neck (AN) and glenoid rim (GR) into 3D meshes of interconnecting nodal vectors. These were applied to construct a ‘clock face’ coordinate system in which 3 o'clock points anteriorly.

Based on the assigned clock face coordinate frame and the fitted plane, the error between the fitted plane and the actual bony node was quantified through manual data extraction. This was tested on 50 specimens.

Mean algorithm quantification errors for GHL attachments were 4.8 (SD 2.2 mm) and 4.5 mm (1.7 mm) for the humerus and glenoid, respectively. Further studies would apply this to investigate GHL length changes during function and may suggest how these structures should be handled during surgical repairs.     

Analysis of humeral head displacements from sequences of biplanar X-rays: repeatability study and preliminary results in healthy subjects

This work presents an accurate method to measure gleno-humeral translations in a controlled pseudo-kinematic environment. Low-dose biplanar X-rays were acquired from nine healthy subjects at three elevations of the arm in the scapular plane. On each set of images, shoulder bony landmarks were manually located in 3D using a dedicated software. Intra-observer and inter-observer repeatability of landmark identification, as well as humeral head center (GH) translations, were studied. Repeatability for the identification of GH in the global coordinate system (CS) was good with 95% confidence intervals (CIs) ranging from 0.57 to 2.25 mm. Scapular landmark CIs ranged from 0.80 to 12 mm. Gleno-humeral translations of small amplitude ( < 6 mm) were detected in seven out of nine subjects. The results obtained here confirm that calibrated low-dose stereo-radiography is a promising tool for the functional analysis of the shoulder.     

Algorithm and validation of a computer method for quantifying attachment locus of glenohumeral ligament in vivo

The aim of this work is to validate an algorithm that quantifies the locus of glenohumeral ligament (GHL) attachments on glenohumeral joint (GHJ) bones. A computed tomography scan of a GHJ was segmented to reconstruct the humerus, scapula, anatomical neck (AN) and glenoid rim (GR) into 3D meshes of interconnecting nodal vectors. These were applied to construct a 'clock face' coordinate system in which 3 o'clock points anteriorly. Based on the assigned clock face coordinate frame and the fitted plane, the error between the fitted plane and the actual bony node was quantified through manual data extraction. This was tested on 50 specimens. Mean algorithm quantification errors for GHL attachments were 4.8 (SD 2.2?mm) and 4.5?mm (1.7?mm) for the humerus and glenoid, respectively. Further studies would apply this to investigate GHL length changes during function and may suggest how these structures should be handled during surgical repairs.     

Quantification of meniscal volume by segmentation of 3T magnetic resonance images

Meniscal injuries place the knee at risk for early osteoarthritis (OA) because they disrupt their load-bearing capabilities. Partial resection is routinely performed to alleviate symptomatic meniscal tears. While the removal of meniscal tissue may not be the only factor associated with partial meniscectomy outcome, the amount removed certainly contributes to functional loss. It is unknown, however, whether there is a critical amount of meniscal tissue that can be removed without diminishing the structure's chondroprotective role. In order to examine the existence of such a threshold, it is necessary to accurately quantify meniscal volume both before and after partial meniscectomy to determine the amount of meniscal tissue removed. Therefore, our goal was to develop and validate an MR-based method for assessing meniscal volume. The specific aims were: (1) to evaluate the feasibility of the MR-based segmentation method; (2) to determine the method's reliability for repeated measurements; and (3) to validate its accuracy in situ. MR images were obtained on a 3T magnet, and each scan was segmented using a biplanar approach. The MR-based volumes for each specimen were compared to those measured by water displacement. The results indicate that the biplanar approach of measuring meniscal volumes is accurate and reliable. The calculated volumes of the menisci were within 5% of the true values, the coefficients of variation were 4%, and the intraclass correlation coefficients were greater than 0.96. These data demonstrate that this method could be used to measure the amount of meniscal tissue excised during partial meniscectomy to within 125.7 mm(3).     

Availability of applying diaphragm matching with the breath-holding technique in stereotactic body radiation therapy for liver tumors

PurposeImage-guided radiotherapy (IGRT) based on bone matching can produce large target-positioning errors because of expiration breath-hold reproducibility during stereotactic body radiation therapy (SBRT) for liver tumors. Therefore, the feasibility of diaphragm-based 3D image matching between planning computed tomography (CT) and pretreatment cone-beam CT was investigated.MethodsIn 59 liver SBRT cases, Lipiodol uptake after transarterial chemoembolization was defined as a tumor marker. Further, the relative isocenter coordinate that was obtained by Lipiodol matching was defined as the reference coordinate. The distance between the relative isocenter coordinate and reference coordinate, which was obtained from diaphragm matching and bone matching techniques, was defined as the target positioning error. Furthermore, the target positioning error between liver matching and Lipiodol matching was evaluated.ResultsThe positioning errors in all directions by the diaphragm matching were significantly smaller than those obtained by using by the bone matching technique (p < 0.05). Further, the positioning errors in the A-P and C-C directions that were obtained by using liver matching were significantly smaller than those obtained by using bone matching (p < 0.05). The estimated PTV margins calculated by the formula proposed by van Herk for diaphragm matching, liver matching, and bone matching were 5.0 mm, 5.0 mm, and 11.6 mm in the C-C direction; 3.6 mm, 2.4 mm, and 6.9 mm in the A-P direction; and 2.6 mm, 4.1 mm, and 4.6 mm in the L-R direction, respectively.ConclusionsDiaphragm matching-based IGRT may be an alternative image matching technique for determining liver tumor positions in patients.     

Feasibility of using a magnetic tracking device for measuring carpal kinematics

While several different methods have been used to measure carpal kinematics, biplanar radiography is generally considered to be the most accurate and popular one. However, biplanar radiography is tedious and so only pseudo-dynamic kinematics can be measured. Recently, magnetic tracking system has been developed for the measurement of joint kinematics which is versatile and easy to use and so the possibility of measuring motions dynamically. In this study, the capability of a magnetic tracking device to accurately measure carpal kinematics was investigated by comparing it with biplanar radiography. The kinematics of the third metacarpal, scaphoid, and lunate in five fresh cadaveric specimens were measured using both methods as the wrists were placed in eight positions. The finite screw rotation of each bone with respect to the distal radius during selecting the seven wrist motions was calculated for both measuring techniques and compared. In general, the kinematics for all three bones measured by using either magnetic tracking device or biplanar radiography was identical and showed no statistical difference. The averaged differences ranged from 0.0 to 2.0°. These differences were due to the potential effect of the weight of the sensors and the interference of the attaching rod to the surrounding tissue. It is concluded that the application of the magnetic tracking device to carpal kinematics is warranted, if proper technical procedures as suggested are followed.     

Estimating muscle attachment contours by transforming geometrical bone models

For individualization of a biomechanical model, it is necessary to estimate the muscle attachments of the person to whom it is to be adapted. One of the methods to estimate muscle attachments is to use model transformations to transform a model with known muscle attachments to the bones of a person. We hypothesize that the location and shape of muscle attachment sites correlate with the shape of the bones they are attached to. If this hypothesis holds, it is possible to predict the location of muscle attachments when the shape of the bones is known. To validate this hypothesis, geometric models of three sets of shoulder bones were built. These models consist of 3-D surface models of the scapula, clavicle, and humerus, with the muscle attachment contours connected to them. By means of geometric transformations, the models were transformed, so the muscle attachments of the different data sets could be compared. Using these techniques, 50 per cent of the muscle attachment contours could be predicted with high accuracy. The muscle attachment contours that could not be predicted were all influenced by measurement errors. For 30 per cent of the muscle attachment contours, it was not possible to distinguish the interindividual differences from the inaccuracies of the method used. From this study, we concluded that most muscle attachment contours can be predicted by means of geometric models of the bones.     

A comprehensive analysis of translational missense errors in the yeast Saccharomyces cerevisiae

The process of protein synthesis must be sufficiently rapid and sufficiently accurate to support continued cellular growth. Failure in speed or accuracy can have dire consequences, including disease in humans. Most estimates of the accuracy come from studies of bacterial systems, principally Escherichia coli, and have involved incomplete analysis of possible errors. We recently used a highly quantitative system to measure the frequency of all types of misreading errors by a single tRNA in E. coli. That study found a wide variation in error frequencies among codons; a major factor causing that variation is competition between the correct (cognate) and incorrect (near-cognate) aminoacyl-tRNAs for the mutant codon. Here we extend that analysis to measure the frequency of missense errors by two tRNAs in a eukaryote, the yeast Saccharomyces cerevisiae. The data show that in yeast errors vary by codon from a low of 4 × 10⁻⁵ to a high of 6.9 × 10⁻⁴ per codon and that error frequency is in general about threefold lower than in E. coli, which may suggest that yeast has additional mechanisms that reduce missense errors. Error rate again is strongly influenced by tRNA competition. Surprisingly, missense errors involving wobble position mispairing were much less frequent in S. cerevisiae than in E. coli. Furthermore, the error-inducing aminoglycoside antibiotic, paromomycin, which stimulates errors on all error-prone codons in E. coli, has a more codon-specific effect in yeast.