Determination of 3D spinal kinematics without defining a local vertebral coordinate system

In this paper a method is presented to calculate Euler's angles of rotation of a body segment during locomotion without a priori defining the location of the center of rotation, and without defining a local vertebral coordinate system. The method was applied to in vivo spinal kinematics. In this method, the orientation of each segment is identified by a set of three markers. The orientation of the axes of rotation is calculated based on the average position of the markers during one stride cycle. Some restrictions and assumptions should be made. The approach is viable only when the average orientation of the anatomical axes of rotation of each spinal segment during a stride cycle coincides with the three axes of the laboratory coordinate system. Furthermore, the rotations should be symmetrical with respect to both sides of the plane of symmetry of the spinal segment, and the subject should move parallel to one axis of the laboratory coordinate system. Since in experimental conditions these assumptions will only be met approximately, errors will be introduced in the calculated angles of rotation. The magnitude of the introduced errors was investigated in a computer simulation experiment. Since the maximal errors did not exceed 0.7° in a range of misalignments up to 10° between the two coordinate systems, the approach proved to be a valid method for the estimation of spinal kinematics.     

The Spherical Expansion of H2 Dimer Interaction Energy by Double Symmetry-Adapted Perturbation Theory

Abstract

The weak interaction energy of H₂ dimer is studied by double symmetry-adapted perturbation theory (SAPT) within second-order of intermolecular and intramonomer perturbation for molecular simulations. The assumed orientations of H₂ dimer are linear, parallel, T type and X type. Among four orientations T orientation is the most stable, while linear orientation is the most repulsive. The second-order dispersion energy E _disp ⁽²⁾ is the most attractive contribution in all orientations. The interaction energy has the anisotropy, so we expressed our total interaction energy by the spherical expansion to compare with the experimental value. The isotropic interaction energy is about 85% of the experimental value.     

A joint coordinate system proposal for the study of the trapeziometacarpal joint kinematics

The International Society of Biomechanics (ISB) has recommended a standardisation for the motion reporting of almost all human joints. This study proposes an adaptation for the trapeziometacarpal joint.

The definition of the segment coordinate system of both trapezium and first metacarpal is based on functional anatomy. The definition of the joint coordinate system (JCS) is guided by the two degrees of freedom of the joint, i.e. flexion–extension about a trapezium axis and abduction–adduction about a first metacarpal axis. The rotations obtained using three methods are compared on the same data: the fixed axes sequence proposed by Cooney et al., the mobile axes sequence proposed by the ISB and our alternative mobile axes sequence. The rotation amplitudes show a difference of 9° in flexion–extension, 2° in abduction–adduction and 13° in internal–external rotation.

This study emphasizes the importance of adapting the JCS to the functional anatomy of each particular joint.     

The conformation and orientation of copper(II)-bleomycin intercalated with DNA

EPR data are used to describe the conformation and identity of the atoms coordinated to Cu(II) in Cu(II)-bleomycin bound to oriented DNA fibers. The fibers were slowly drawn from viscous solutions of Cu(II)-bleomycin-DNA containing one Cu(II)-bleomycin to 200 basepairs. EPR measurements were made at room temperature and 90 K for different orientations of the external magnetic field with respect to the helical axes of the fibers. The g-values ($\text{g}{}_{\mathrm{}}\text{=2.21}$, g_⊥ =2.04) and the hyperfine constant ($\text{A}{}_{\mathrm{}}\text{=175}\text{G}$) are consistent with values expected for Cu(II) chelated to a square planar array of ligands. In the oriented fibers, the square planar arrays do not all have the same orientations with respect to the fiber axes. At room temperature the chelated ions have rotational freedom in which the normal to the planar array has almost complete freedom of rotation about axes perpendicular to the DNA fiber axes. The normal maintains an angle of 75° with respect to the axis, in the plane of the basepair, about which it rotates. Nine superhyperfine peaks on the high field side of the EPR spectrum were partially resolved. The number and splitting (12 G) of these superhyperfine peaks indicate that four nitrogen atoms are chelated to Cu(II) in a square planar array. These data on Cu(II)-bleomycin bound to DNA give information on the orientation of the metal-containing portion of bleomycin which lies outside the double helix.     

Anatomically-based skeletal coordinate systems for use with impact biomechanics data intended for anthropomorphic test device development

Post-mortem human subjects (PMHS) are frequently used to characterize biomechanical response and injury tolerance of humans to various types of loading by means of instrumentation installed directly on the skeleton. Data extracted from such tests are often used to develop and validate anthropomorphic test devices (ATDs), which function as human surrogates in tests for injury assessment. Given that the location and orientation of installed instrumentation differs between subjects, nominally similar measurements made on different PMHS must be transformed to standardized, skeletal-based local coordinate systems (LCS) before appropriate data comparisons can be made. Standardized PMHS LCS that correspond to ATD instrumentation locations and orientations have not previously been published. This paper introduces anatomically-defined PMHS LCS for body regions in which kinematic measurements are made using ATDs. These LCS include the head, sternum, single vertebrae, pelvis, femurs (distal and proximal), and tibiae (distal and proximal) based upon skeletal landmarks extracted from whole body CT scans. The proposed LCS provide a means to standardize the reporting of PMHS data, and facilitate both the comparison of PMHS impact data across institutions and the application of PMHS data to the development and validation of ATDs.     

Incorporation of tumor motion directionality in margin recipe: The directional MidP strategy

PurposePlanning target volume (PTV) definition based on Mid-Position (Mid-P) strategy typically integrates breathing motion from tumor positions variances along the conventional axes of the DICOM coordinate system. Tumor motion directionality is thus neglected even though it is one of its stable characteristics in time. We therefore propose the directional MidP approach (MidP dir), which allows motion directionality to be incorporated into PTV margins. A second objective consists in assessing the ability of the proposed method to better take care of respiratory motion uncertainty.Methods11 lung tumors from 10 patients with supra-centimetric motion were included. PTV were generated according to the MidP and MidP dir strategies starting from planning 4D CT.ResultsPTV_{MidP dir} volume didn’t differ from the PTV_MidP volume: 31351 mm³ IC95% [17242–45459] vs. 31003 mm³ IC95% [ 17347–44659], p = 0.477 respectively. PTV_{MidP dir} morphology was different and appeared more oblong along the main motion axis. The relative difference between 3D and 4D doses was on average 1.09%, p = 0.011 and 0.74%, p = 0.032 improved with directional MidP for D_99% and D_95%. D_2% was not significantly different between both approaches. The improvement in dosimetric coverage fluctuated substantially from one lesion to another and was all the more important as motion showed a large amplitude, some obliquity with respect to conventional axes and small hysteresis.ConclusionsDirectional MidP method allows tumor motion to be taken into account more tightly as a geometrical uncertainty without increasing the irradiation volume.     

On the estimation of joint kinematics during gait.

In gait analysis, the concepts of Euler and helical (screw) angles are used to define the three-dimensional relative joint angular motion of lower extremities. Reliable estimation of joint angular motion depends on the accurate definition and construction of embedded axes within each body segment. In this paper, using sensitivity analysis, we quantify the effects of uncertainties in the definition and construction of embedded axes on the estimation of joint angular motion during gait. Using representative hip and knee motion data from normal subjects and cerebral palsy patients, the flexion-extension axis is analytically perturbed +/- 15 degrees in 5 degrees steps from a reference position, and the joint angles are recomputed for both Euler and helical angle definitions. For the Euler model, hip and knee flexion angles are relatively unaffected while the ab/adduction and rotation angles are significantly affected throughout the gait cycle. An error of 15 degrees in the definition of flexion-extension axis gives rise to maximum errors of 8 and 12 degrees for the ab/adduction angle, and 10-15 degrees for the rotation angles at the hip and knee, respectively. Furthermore, the magnitude of errors in ab/adduction and rotation angles are a function of the flexion angle. The errors for the ab/adduction angles increase with increasing flexion angle and for the rotation angle, decrease with increasing flexion angle. In cerebral palsy patients with flexed knee pattern of gait, this will result in distorted estimation of ab/adduction and rotation. For the helical model, similar results are obtained for the helical angle and associated direction cosines.(ABSTRACT TRUNCATED AT 250 WORDS)     

Computed tomography analysis of radiostereometric data to determine flexion axes after total joint replacement: Application to the elbow joint

Kinematic analysis for in vivo assessment of elbow endoprostheses requires knowledge of the exact positions of motion axes relative to bony landmarks or the prosthesis. A prosthesis-based reference system is required for comparison between individuals and studies. The primary aim of this study was to further develop an earlier described algorithm for fusion of radiostereometric analysis (RSA) data and data obtained in 3D computed tomography (CT) for application to the elbow after total joint replacement. The secondary aim was to propose a method for marking of prostheses in 3D CT, enabling definition of a prosthesis-based reference system. Six patients with elbow endoprostheses were investigated.The fusion of data made it possible to visualize the motion axes in relation to the prostheses in the 3D CT volume. The differences between two repeated positioning repetitions of the longitudinal prosthesis axis were less than 0.6° in the frontal and sagittal planes. Corresponding values for the transverse axis were less than 0.6° in the frontal and less than 1.4° (in four out of six less than 0.6°) in the horizontal plane.This study shows that by fusion of CT and RSA data it is possible to determine the accurate position of the flexion axes of the elbow joint after total joint replacement in vivo. The proposed method for implant marking and registration of reference axes enables comparison of prosthesis function between patients and studies.     

Validation of a model-based inverse kinematics approach based on wearable inertial sensors

Abstract

Wearable inertial measurement units (IMUs) are a promising solution to human motion estimation. Using IMUs 3D orientations, a model-driven inverse kinematics methodology to estimate joint angles is presented. Estimated joint angles were validated against encoder-measured kinematics (robot) and against marker-based kinematics (passive mechanism). Results are promising, with RMS angular errors respectively lower than 3 and 6?deg over a minimum range of motion of 50?deg (robot) and 160?deg (passive mechanism). Moreover, a noise robustness analysis revealed that the model-driven approach reduces the effects of experimental noises, making the proposed technique particularly suitable for application in human motion analysis.     

Oppugning the assumptions of spatial averaging of segment and joint orientations

Movement scientists frequently calculate “arithmetic averages” when examining body segment or joint orientations. Such calculations appear routinely, yet are fundamentally flawed. Three-dimensional orientation data are computed as matrices, yet three-ordered Euler/Cardan/Bryant angle parameters are frequently used for interpretation. These parameters are not geometrically independent; thus, the conventional process of averaging each parameter is incorrect. The process of arithmetic averaging also assumes that the distances between data are linear (Euclidean); however, for the orientation data these distances are geodesically curved (Riemannian). Therefore we question (oppugn) whether use of the conventional averaging approach is an appropriate statistic. Fortunately, exact methods of averaging orientation data have been developed which both circumvent the parameterization issue, and explicitly acknowledge the Euclidean or Riemannian distance measures. The details of these matrix-based averaging methods are presented and their theoretical advantages discussed. The Euclidian and Riemannian approaches offer appealing advantages over the conventional technique. With respect to practical biomechanical relevancy, examinations of simulated data suggest that for sets of orientation data possessing characteristics of low dispersion, an isotropic distribution, and less than 30° second and third angle parameters, discrepancies with the conventional approach are less than 1.1°. However, beyond these limits, arithmetic averaging can have substantive non-linear inaccuracies in all three parameterized angles. The biomechanics community is encouraged to recognize that limitations exist with the use of the conventional method of averaging orientations. Investigations requiring more robust spatial averaging over a broader range of orientations may benefit from the use of matrix-based Euclidean or Riemannian calculations.     

Automatic determination of anatomical coordinate systems for three-dimensional bone models of the isolated human knee

The combination of three-dimensional (3-D) models with dual fluoroscopy is increasingly popular for evaluating joint function in vivo. Applying these modalities to study knee motion with high accuracy requires reliable anatomical coordinate systems (ACSs) for the femur and tibia. Therefore, a robust method for creating ACSs from 3-D models of the femur and tibia is required. We present and evaluate an automated method for constructing ACSs for the distal femur and proximal tibia based solely on 3-D bone models. The algorithm requires no observer interactions and uses model cross-sectional area, center of mass, principal axes of inertia, and cylindrical surface fitting to construct the ACSs. The algorithm was applied to the femur and tibia of 10 (unpaired) human cadaveric knees. Due to the automated nature of the algorithm, the within specimen variability is zero for a given bone model. The algorithm’s repeatability was evaluated by calculating variability in ACS location and orientation across specimens. Differences in ACS location and orientation between specimens were low (<1.5 mm and <2.5°). Variability arose primarily from natural anatomical and morphological differences between specimens. The presented algorithm provides an alternative method for automatically determining subject-specific ACSs from the distal femur and proximal tibia.     

Estimating joint kinematics from skin motion observation: modelling and validation

Modelling of soft tissue motion is required in many areas, such as computer animation, surgical simulation, 3D motion analysis and gait analysis. In this paper, we will focus on the use of modelling of skin deformation during 3D motion analysis. The most frequently used method in 3D human motion analysis involves placing markers on the skin of the analysed segment which is composed of the rigid bone and the surrounding soft tissues. Skin and soft tissue deformations introduce a significant artefact which strongly influences the resulting bone position, orientation and joint kinematics. For this study, we used a statistical solid dynamics approach which is a combination of several previously reported tools: the point cluster technique (PCT) and a Kalman filter which was added to the PCT. The methods were tested and evaluated on controlled human-arm motions, using an optical motion capture system (Vicon^TM).

The addition of a Kalman filter to the PCT for rigid body motion estimation results in a smoother signal that better represents the joint motion. Calculations indicate less signal distortion than when using a digital low-pass filter. Furthermore, adding a Kalman filter to the PCT substantially reduces the dispersion of the maximal and minimal instantaneous frequencies. For controlled human movements, the result indicated that adding a Kalman filter to the PCT produced a more accurate signal. However, it could not be concluded that the proposed Kalman filter is better than a low-pass filter for estimation of the motion. We suggest that implementation of a Kalman filter with a better biomechanical motion model will be more likely to improve the results.     

Comparison of three local frame definitions for the kinematic analysis of the fingers and the wrist

Because the hand is a complex poly-articular limb, numerous methods have been proposed to investigate its kinematics therefore complicating the comparison between studies and the methodological choices. With the objective of overcoming such issues, the present study compared the effect of three local frame definitions on local axis orientations and joint angles of the fingers and the wrist. Three local frames were implemented for each segment. The “Reference” frames were aligned with global axes during a static neutral posture. The “Landmark” frames were computed using palpated bony landmarks. The “Functional” frames included a flexion–extension axis estimated during functional movements. These definitions were compared with regard to the deviations between obtained local segment axes and the evolution of joint (Cardan) angles during two test motions. Each definition resulted in specific local frame orientations with deviations of 15° in average for a given local axis. Interestingly, these deviations produced only slight differences (below 7°) regarding flexion–extension Cardan angles indicating that there is no preferred method when only interested in finger flexion–extension movements. In this case, the Reference method was the easiest to implement, but did not provide physiological results for the thumb. Using the Functional frames reduced the kinematic cross-talk on the secondary and tertiary Cardan angles by up to 20° indicating that the Functional definition is useful when investigating complex three-dimensional movements. Globally, the Landmark definition provides valuable results and, contrary to the other definitions, is applicable for finger deformities or compromised joint rotations.     

The orientation of transition moments of dye molecules used in fluorescence studies of muscle systems

Fluorescence and phosphorescence depolarization techniques can provide information on orientational order and rotational motion of crossbridges in muscle fibres. However the depolarization experiment monitors the orientation and motion of the crossbridges indirectly. The changes in depolarization arise from a change in the orientation of the transition dipoles of the dye attached to the crossbridge. In order to extract the physiologically relevant orientations from the data it is therefore necessary to characterize the orientation of the dye molecule relative to the crossbridge and the orientation of the transition moments in the frame of the dyes. The dyes 1,5-1-AEDANS and eosin-5-maleimide are commonly used for labelling the crossbridge in muscle fibres. The orientations of the absorption and fluorescence emission dipoles of these two dyes in the molecular frame were determined. Angle resolved fluorescence depolarization experiments on the dyes, macroscopically aligned in a stretched polymer matrix of poly vinyl alcohol, were carried out. The data were analyzed in terms of an orientational distribution of the dye molecules in the film and the orientations of the absorption and emission dipoles in the frame of the dye molecule. Experimental data, obtained from a given sample at different excitation wavelengths, were analyzed simultaneously in a global target approach. This leads to a reduction in the number of independent parameters optimized by the non-linear least squares procedure.Abbreviations 1,5-I-AEDANS 5-iodoacetamido-ethyl-aminonaphthalene-a-sulfonic acid - IATR iodoacetamido-tetra-methylrhodamine - E5M Eosin-5-Maleimide - ATP adenosine tri phosphate - -ATP 1:N⁶-ethano-ATP - -2-aza-ATP 1:N⁶-etheno-2-aza-ATP - ant-ATP anthraniloyl-ATP     

Repeatability,reproducibility, and agreement of three computational methods to approximate the functional flexion-extension axis of the tibiofemoral joint using 3D bone models of the femur

Abstract

Background: Closely approximating the functional flexion-extension (FE) axis of the tibiofemoral joint in 3D models of the femur is important when computing joint motions which are physiologic. The objectives were to 1) develop methods to approximate the functional FE axis based on fitting circles, a tapered cylinder, and spheres to the posterior condyles, 2) determine the repeatability and reproducibility of each method, and 3) determine limits of agreement between pairs of axes.

Methods: For each method, the respective axis was determined in forty 3D bone models of the distal femur. Varus-valgus angles and internal-external axial angles were computed relative to standard planes.

Results: Repeatability and reproducibility were comparable for the tapered cylinder-based and sphere-based methods and better than that for the circle-based method. Limits of agreement were tightest when comparing the sphere-based and tapered cylinder-based axes. However, limits of agreement for the internal-external axial angle were wide at +3.6° to ?3.9° whereas limits of agreement were tighter at +1.4° to ?0.7° for the varus-valgus angle.

Conclusion: The tapered cylinder-based and sphere-based methods offer advantages of better repeatability and reproducibility over the circle-based method. However, the sphere-based and tapered cylinder-based axes are not interchangeable owing to wide limits of agreement for the internal-external axial angle. The tapered cylinder-based axis is preferred intuitively over the sphere-based axis because the spheres require fitting in both the sagittal and coronal planes whereas the tapered cylinder requires fitting in the sagittal plane only which is the plane of motion in flexion-extension.     

The association of urbanicity and travel time with lung cancer screening utilization

BackgroundTo examine 1) the rate of lung cancer screening (LCS) utilization in a large healthcare system in South Carolina; 2) associations of urbanicity and travel time with LCS utilization.MethodsLCS-eligible patients from 2019 were identified. The outcome was LCS utilization. The exposures were zip-code level urbanicity and travel time from the centroid of zip-code area to the nearest screening site (<10,10-<20, ≥20 min). Covariates included age, sex, race, marital status, insurance, body mass index, chronic obstructive pulmonary disease, Charlson Comorbidity Index (0, 1, 2, ≥3), and zip-code level median income. Chi-square tests and logistic regressions were employed.ResultsThe analysis included 6930 patients, among whom 1432 (20.66%) received LCS. After adjusting for covariates, living in a non-metropolitan area (adjusted odds ratio: 0.32; 95% confidence interval: 0.26–0.40) and having longer travel time (0.80 [0.65–0.98] and 0.68 [0.54–0.86] for 10-<20 and ≥20 min travel time, respectively, compared to <10 min travel time) were significantly associated with lower odds of LCS utilization.ConclusionsThe LCS utilization rate of a healthcare system was about 20% in 2019. Living in non-metropolitan areas or having longer travel time to LCS site were associated with lower LCS utilization.     

Method for the estimation of a double hinge kinematic model for the trapeziometacarpal joint using MR imaging

In this paper, we propose a method to estimate the parameters of a double hinge model of the trapeziometacarpal joint (TMC) by MRI-based motion analysis. The model includes two non-orthogonal and non-intersecting rotation axes accounting for flexion–extension (F–E) and adduction–abduction (A–A). We evaluated the quality of the estimated model parameters in the prediction of the relative motion of the first metacarpal bone with respect to the trapezium. As a result, we obtained that: (a) the estimated location and orientation of the F–E and A–A axes were in agreement with previous in vitro studies, (b) the motion of the first metacarpal predicted by the 2 degrees of freedom (2DoF) model exhibits a maximum surface distance error in the range of about 2 mm and (c) four thumb postures at the boundary of the TMC range of motion are sufficient to provide a good estimation of the 2DoF TMC kinematic model and good reproducibility (～1.7 mm) of the real thumb motion at TMC level.     

A method for three-dimensional quantification of vascular smooth muscle orientation: application in viable murine carotid arteries

When studying in vivo arterial mechanical behaviour using constitutive models, smooth muscle cells (SMCs) should be considered, while they play an important role in regulating arterial vessel tone. Current constitutive models assume a strictly circumferential SMC orientation, without any dispersion. We hypothesised that SMC orientation would show considerable dispersion in three dimensions and that helical dispersion would be greater than transversal dispersion. To test these hypotheses, we developed a method to quantify the 3D orientation of arterial SMCs. Fluorescently labelled SMC nuclei of left and right carotid arteries of ten mice were imaged using two-photon laser scanning microscopy. Arteries were imaged at a range of luminal pressures. 3D image processing was used to identify individual nuclei and their orientations. SMCs showed to be arranged in two distinct layers. Orientations were quantified by fitting a Bingham distribution to the observed orientations. As hypothesised, orientation dispersion was much larger helically than transversally. With increasing luminal pressure, transversal dispersion decreased significantly, whereas helical dispersion remained unaltered. Additionally, SMC orientations showed a statistically significant (\(p < 0.05\)) mean right-handed helix angle in both left and right arteries and in both layers, which is a relevant finding from a developmental biology perspective. In conclusion, vascular SMC orientation (1) can be quantified in 3D; (2) shows considerable dispersion, predominantly in the helical direction; and (3) has a distinct right-handed helical component in both left and right carotid arteries. The obtained quantitative distribution data are instrumental for constitutive modelling of the artery wall and illustrate the merit of our method.     

A joint coordinate system proposal for the study of the trapeziometacarpal joint kinematics

The International Society of Biomechanics (ISB) has recommended a standardisation for the motion reporting of almost all human joints. This study proposes an adaptation for the trapeziometacarpal joint. The definition of the segment coordinate system of both trapezium and first metacarpal is based on functional anatomy. The definition of the joint coordinate system (JCS) is guided by the two degrees of freedom of the joint, i.e. flexion-extension about a trapezium axis and abduction-adduction about a first metacarpal axis. The rotations obtained using three methods are compared on the same data: the fixed axes sequence proposed by Cooney et al., the mobile axes sequence proposed by the ISB and our alternative mobile axes sequence. The rotation amplitudes show a difference of 9 degrees in flexion-extension, 2 degrees in abduction-adduction and 13 degrees in internal-external rotation. This study emphasizes the importance of adapting the JCS to the functional anatomy of each particular joint.