Correcting out-of-plane errors in two-dimensional imaging using nonimage-related information

Two-dimensional imaging with a single camera assumes that the motion occurs in a calibrated plane perpendicular to the camera axis. It is well known that kinematic errors result if the object fails to remain in this plane and that if both the distance to the calibration plane from the camera and the distance out-of-plane are known, an analytical correction for the out-of-plane error can be made. Less well appreciated is that out-of-plane distance can frequently be acquired from other, nonimage-related information. In the two examples given, the mediolateral center of pressure coordinate of the foot measured from a force plate and the measured landing point of a shot put throw were used. In both cases, the resulting out-of-plane correction improved the accuracy of the 2-D kinematic data dramatically. These examples also demonstrate that the use of nonimage-related data can increase the accuracy of kinematic data without an increase in the complexity of the experiment.     

Cross-Talk Correction Method for Knee Kinematics in Gait Analysis Using Principal Component Analysis (PCA): A New Proposal

Background

In 3D gait analysis, the knee joint is usually described by the Eulerian way. It consists in breaking down the motion between the articulating bones of the knee into three rotations around three axes: flexion/extension, abduction/adduction and internal/external rotation. However, the definition of these axes is prone to error, such as the “cross-talk” effect, due to difficult positioning of anatomical landmarks. This paper proposes a correction method, principal component analysis (PCA), based on an objective kinematic criterion for standardization, in order to improve knee joint kinematic analysis.

Methods

The method was applied to the 3D gait data of two different groups (twenty healthy subjects and four with knee osteoarthritis). Then, this method was evaluated with respect to three main criteria: (1) the deletion of knee joint angle cross-talk (2) the reduction of variance in the varus/valgus kinematic profile (3) the posture trial varus/valgus deformation matching the X-ray value for patients with knee osteoarthritis. The effect of the correction method was tested statistically on variabilities and cross-talk during gait.

Results

Cross-talk was lower (p<0.05) after correction (the correlation between the flexion-extension and varus-valgus kinematic profiles being annihilated). Additionally, the variance in the kinematic profile for knee varus/valgus and knee flexion/extension was found to be lower and higher (p<0.05), respectively, after correction for both the left and right side. Moreover, after correction, the posture trial varus/valgus angles were much closer to x-ray grading.

Conclusion

The results show that the PCA correction applied to the knee joint eliminates the cross-talk effect, and does not alter the radiological varus/valgus deformation for patients with knee osteoarthritis. These findings suggest that the proposed correction method produces new rotational axes that better fit true knee motion.     

Propagation of errors from skull kinematic measurements to finite element tissue responses

Real-time quantification of head impacts using wearable sensors is an appealing approach to assess concussion risk. Traditionally, sensors were evaluated for accurately measuring peak resultant skull accelerations and velocities. With growing interest in utilizing model-estimated tissue responses for injury prediction, it is important to evaluate sensor accuracy in estimating tissue response as well. Here, we quantify how sensor kinematic measurement errors can propagate into tissue response errors. Using previous instrumented mouthguard validation datasets, we found that skull kinematic measurement errors in both magnitude and direction lead to errors in tissue response magnitude and distribution. For molar design instrumented mouthguards susceptible to mandible disturbances, 150–400% error in skull kinematic measurements resulted in 100% error in regional peak tissue response. With an improved incisor design mitigating mandible disturbances, errors in skull kinematics were reduced to <50%, and several tissue response errors were reduced to <10%. Applying 30\(^{\circ }\) rotations to reference kinematic signals to emulate sensor transformation errors yielded below 10% error in regional peak tissue response; however, up to 20% error was observed in peak tissue response for individual finite elements. These findings demonstrate that kinematic resultant errors result in regional peak tissue response errors, while kinematic directionality errors result in tissue response distribution errors. This highlights the need to account for both kinematic magnitude and direction errors and accurately determine transformations between sensors and the skull.     

Sampling frequencies and measurement error for linear and temporal gait parameters in primate locomotion

Quantitative analyses of animal motion are increasingly easy to conduct using simple video equipment and relatively inexpensive software packages. With careful use, such analytical tools have the potential to quantify differences in movement between individuals or species and to allow insights into the behavioral consequences of morphological differences between taxa. However, as with any other type of measurement, there are errors associated with kinematic measurements. Because normative kinematic data on human and nonhuman primate locomotion are used to model aspects of gait of fossil hominins, errors in the extant data influence the accuracy of fossil gait reconstructions. The principal goal of this paper is to illustrate the effect of camera speeds (frame rates) on kinematic measurement errors, and to demonstrate how these errors vary with subject size, movement velocity, and sample size. Kinematic data for human walking and running (240 Hz), as well as data for primate quadrupedal walking and running (180 Hz) were used as inputs for a simulation of the measurement errors associated with various linear and temporal kinematic variables. Measurement errors were shown to increase as camera speed, subject body size, and interval duration all decrease, and as movement velocity increases. These results have implications for the methods used to calculate subject velocity and suggest that using a moving marker to measure the linear displacements of the body is preferable to the use of a stationary marker. Finally, while slower camera speeds will always result in higher measurement errors than do faster camera speeds, this effect can be moderated to some extent by collecting sufficiently large samples of data.     

Algorithms to determine event timing during normal walking using kinematic data

Algorithms to predict heelstrike and toeoff times during normal walking using only kinematic data are presented. The accuracy of these methods was compared with the results obtained using synchronized force platform recordings of two subjects walking at a variety of speeds for a total of 12 trials. Using a 60Hz data collection system, the absolute value errors (AVE) in predicting heelstrike averaged 4.7ms, while the AVE in predicting toeoff times averaged 5.6ms. True average errors (negative for an early prediction) were +1.2ms for both heelstrike and toeoff, indicating that no systematic errors occurred. It was concluded that the proposed algorithms provide an easy and reliable method of determining event times during walking when kinematic data are collected, with a considerable improvement in resolution over visual inspection of video records, and could be utilized in conjunction with any 2-D or 3-D kinematic data collection system.     

Bayesian inverse kinematics vs. least-squares inverse kinematics in estimates of planar postures and rotations in the absence of soft tissue artifact

A variety of inverse kinematics (IK) algorithms exist for estimating postures and displacements from a set of noisy marker positions, typically aiming to minimize IK errors by distributing errors amongst all markers in a least-squares (LS) sense. This paper describes how Bayesian inference can contrastingly be used to maximize the probability that a given stochastic kinematic model would produce the observed marker positions. We developed Bayesian IK for two planar IK applications: (1) kinematic chain posture estimates using an explicit forward kinematics model, and (2) rigid body rotation estimates using implicit kinematic modeling through marker displacements. We then tested and compared Bayesian IK results to LS results in Monte Carlo simulations in which random marker error was introduced using Gaussian noise amplitudes ranging uniformly between 0.2 mm and 2.0 mm. Results showed that Bayesian IK was more accurate than LS-IK in over 92% of simulations, with the exception of one center-of-rotation coordinate planar rotation, for which Bayesian IK was more accurate in only 68% of simulations. Moreover, while LS errors increased with marker noise, Bayesian errors were comparatively unaffected by noise amplitude. Nevertheless, whereas the LS solutions required average computational durations of less than 0.5 s, average Bayesian IK durations ranged from 11.6 s for planar rotation to over 2000 s for kinematic chain postures. These results suggest that Bayesian IK can yield order-of-magnitude IK improvements for simple planar IK, but also that its computational demands may make it impractical for some applications.     

Error in the description of foot kinematics due to violation of rigid body assumptions

Kinematic data from rigid segment foot models inevitably includes errors because the bones within each segment move relative to each other. This study sought to define error in foot kinematic data due to violation of the rigid segment assumption. The research compared kinematic data from 17 different mid and forefoot rigid segment models to kinematic data of the individual bones comprising these segments. Kinematic data from a previous dynamic cadaver model study was used to derive individual bone as well as foot segment kinematics.Mean and maximum errors due to violation of the rigid body assumption varied greatly between models. The model with least error was the combination of navicular and cuboid (mean errors <=1.3°, average maximum error <=2.4°). Greatest error was seen for the model combining all the ten bones (mean errors <=4.4°, average maximum errors <=6.9°). Based on the errors reported a three segment mid and forefoot model is proposed: (1) Navicular and cuboid, (2) cuneiforms and metatarsals 1, 2 and 3, and (3) metatarsals 4 and 5. However the utility of this model will depend on the precise purpose of the in vivo foot kinematics research study being undertaken.     

Effects of femoral component placement on the balancing of a total knee at surgery

Misalignment and soft-tissue imbalance in total knee arthroplasty (TKA) can cause discomfort, pain, inadequate motion and instability that may require revision surgery. Balancing can be defined as equal collateral ligament tensions or equal medial and lateral compartmental forces during the flexion range. Our goal was to study the effects on balancing of linear femoral component misplacements (proximal, distal, anterior, posterior); and different component rotations in mechanical alignment compared to kinematic alignment throughout the flexion path. A test rig was constructed such that the position of a standard femoral component could be adjusted to simulate the linear and rotational positions. With the knee in neutral reference values of the collateral tensions were adjusted to give anatomic contact force patterns, measured with an instrumented tibial trial. The deviations in the forces for each femoral component position were then determined. Compartmental forces were significantly influenced by 2 mm linear errors in the femoral component placement. However, the errors were least for a distal error, equivalent to undercutting the distal femur. The largest errors mainly increase the lateral condyle force, occurred for proximal and posterior component errors. There were only small contact force differences between kinematic and mechanical alignment. Based on these results, surgeons should avoid overcutting the distal femur and undercutting the posterior femur. However, the 2–3 degrees varus slope of the joint line as in kinematic alignment did not have much effect on balancing, so mechanical or kinematic alignment were equivalent.     

Whole body inverse dynamics over a complete gait cycle based only on measured kinematics

This paper presents a three-dimensional (3D) whole body multi-segment model for inverse dynamics analysis over a complete gait cycle, based only on measured kinematic data. The sequence of inverse dynamics calculations differs significantly from the conventional application of inverse dynamics using force plate data. A new validated "Smooth Transition Assumption" was used to solve the indeterminacy problem in the double support phase. Kinematic data is required for all major body segments and, hence, a whole body gait measurement protocol is presented. Finally, sensitivity analyses were conducted to evaluate the effects of digital filtering and body segment parameters on the accuracy of the prediction results. The model gave reasonably good estimates of sagittal plane ground forces and moment; however, the estimates in the other planes were less good, which we believe is largely due to their small magnitudes in comparison to the sagittal forces and moment. The errors observed are most likely caused by errors in the kinematic data resulting from skin movement artefact and by errors in the estimated body segment parameters. A digital filtering cut-off frequency of 4.5Hz was found to produce the best results. It was also shown that errors in the mass properties of body segments can play a crucial role, with changes in properties sometimes having a disproportionate effect on the calculated ground reactions. The implication of these results is that, even when force plate data is available, the estimated joint forces are likely to suffer from similar errors.     

Kinematic simulation of fracture reduction and bone deformity correction under unilateral external fixation

Combined kinematic analysis and graphic models of two unilateral external fixators are presented to simulate and visualize the correction of bone fracture deformities through systematic adjustments of the fixator joints. The models were developed as rigid linkage systems, and the analysis utilized the 4x4 transformation matrices and the kinematic chain theory to obtain the necessary rotations and translations at each joint of the fixator to correct bone deformities at the fracture site. Three-dimensional malalignments with fracture gaps were simulated to correct the deformities. Due to the redundant pair variables in the fixator joints and other problems in obtaining unique solutions, an optimization technique was used to solve the governing linkage loop equations. For each adjustment solution, the bone correction paths were infinite but a unique and optimal reduction path was obtained by applying corrections to all joints simultaneously and in small increments. When the deformity exceeded a certain range, no admissible solution could be obtained, partially due to the limitation of the unilateral fixator configuration and partially due to the restricted joint rotation and translation in the fixator design. The present models and analysis technique can be used to investigate a fixator's adjustability to correct a 3-D bone deformity at a fracture or lengthening site facilitating patient care planning and medical personnel training.     

Aberration-corrected ultrafine analysis of miRNA reads at single-base resolution: a k-mer lattice approach

Raw sequencing reads of miRNAs contain machine-made substitution errors, or even insertions and deletions (indels). Although the error rate can be low at 0.1%, precise rectification of these errors is critically important because isoform variation analysis at single-base resolution such as novel isomiR discovery, editing events understanding, differential expression analysis, or tissue-specific isoform identification is very sensitive to base positions and copy counts of the reads. Existing error correction methods do not work for miRNA sequencing data attributed to miRNAs’ length and per-read-coverage properties distinct from DNA or mRNA sequencing reads. We present a novel lattice structure combining kmers, (k – 1)mers and (k + 1)mers to address this problem. The method is particularly effective for the correction of indel errors. Extensive tests on datasets having known ground truth of errors demonstrate that the method is able to remove almost all of the errors, without introducing any new error, to improve the data quality from every-50-reads containing one error to every-1300-reads containing one error. Studies on experimental miRNA sequencing datasets show that the errors are often rectified at the 5′ ends and the seed regions of the reads, and that there are remarkable changes after the correction in miRNA isoform abundance, volume of singleton reads, overall entropy, isomiR families, tissue-specific miRNAs, and rare-miRNA quantities.     

Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set. We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush-Kuhn-Tucker optimality conditions. The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment. The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.     

HTS-Corrector: software for the statistical analysis and correction of experimental high-throughput screening data

MOTIVATION: High-throughput screening (HTS) plays a central role in modern drug discovery, allowing for testing of >100,000 compounds per screen. The aim of our work was to develop and implement methods for minimizing the impact of systematic error in the analysis of HTS data. To the best of our knowledge, two new data correction methods included in HTS-Corrector are not available in any existing commercial software or freeware. RESULTS: This paper describes HTS-Corrector, a software application for the analysis of HTS data, detection and visualization of systematic error, and corresponding correction of HTS signals. Three new methods for the statistical analysis and correction of raw HTS data are included in HTS-Corrector: background evaluation, well correction and hit-sigma distribution procedures intended to minimize the impact of systematic errors. We discuss the main features of HTS-Corrector and demonstrate the benefits of the algorithms.     

Stance and swing phase detection during level and slope walking in the cat: effects of slope, injury, subject and kinematic detection method

In quadrupeds, there have been limited comparisons of gait timing events detection (e.g., paw contact, PC and paw-off, PO) determined from kinematics and forceplates. The goal of this study was to investigate the effect of different slopes (0, -27, +27°), recovery times after ankle extensor nerve injury and repair (2, 6, 12 weeks), subjects and detection methods on accuracy of kinematically derived PC and PO timings during feline walking. Right hindlimb kinematics and ground reaction forces (GRF) of 4 cats walking along a sloped walkway with embedded forceplates were recorded. A total of 963 walking cycles were analyzed. Gait timings were determined from five kinematic methods based on displacements, velocities or accelerations of hindlimb markers. GRF based 'gold standard' timings for PC and PO were used to determine the systematic and random error of kinematic timing. Systematic errors between the kinematic methods differed significantly (p<0.05). Methods based on vertical paw peak acceleration and velocity gave the smallest systematic errors for PC and PO, respectively. The smallest random errors (standard deviations) for PC and PO were demonstrated by method based on paw horizontal displacement relative to greater trochanter: 13.4ms and 6.6ms, respectively. Effects of slope and subject on systematic errors of kinematic methods were significant, whereas effects of recovery time after nerve injury were not. It was concluded that timing of gait events can be determined consistently using kinematics, although adjustments must be made to account for the systematic error which varies according to subject and slope condition.     

Validation of imaging-based quantification of glenohumeral joint kinematics using an unmodified clinical biplane fluoroscopy system

Model-based tracking, using CT and biplane fluoroscopy, allows highly accurate quantification of glenohumeral motion and changes in the subacromial space. Previous investigators have used custom-built biplane fluoroscopes designed specifically for kinematic applications, which are available at few institutions and require FDA approval prior to clinical use. The aim of this study was to demonstrate the utility of an off-the-shelf clinical biplane fluoroscope for kinematic applications by validating model-based tracking for measurement of glenohumeral motion using an unmodified clinical system. Biplane images of each shoulder of a cadaver torso were acquired at various joint positions and during simulated movements along anatomical planes of motion. The pose of each humerus and scapula was determined using model-based tracking and compared to a bead-based gold standard. Error due to a temporal-offset between corresponding biplane images, characteristic of clinical biplane systems, was determined by comparison of measured and known relative position of 2 bead clusters of a phantom that was imaged while moved throughout the fluoroscopy image volume. Model-based tracking had global kinematic mean absolute errors of 0.27 mm and 0.29° (static), and 0.22–0.32 mm and 0.12–0.45° (dynamic). Glenohumeral mean absolute errors were 0.39 mm and 0.45° (static), and 0.36–0.42 mm and 0.41–0.48° (dynamic). The temporal-offset was predicted to add errors of 0.06–0.85 mm and 0.05–0.28° for cadaveric trials for the speeds examined. For defined speeds, sub-millimeter and sub-degree kinematic accuracy and precision were achieved using an unmodified clinical biplane fluoroscope for quantification of glenohumeral motion.     

Kinematic analysis of over-determinate biomechanical systems

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set.

We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush–Kuhn–Tucker optimality conditions.

The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment.

The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.     

Determination of patient-specific multi-joint kinematic models through two-level optimization

Dynamic patient-specific musculoskeletal models have great potential for addressing clinical problems in orthopedics and rehabilitation. However, their predictive capability is limited by how well the underlying kinematic model matches the patient's structure. This study presents a general two-level optimization procedure for tuning any multi-joint kinematic model to a patient's experimental movement data. An outer level optimization modifies the model's parameters (joint position and orientations) while repeated inner level optimizations modify the model's degrees of freedom given the current parameters, with the goal of minimizing errors between model and experimental marker trajectories. The approach is demonstrated by fitting a 27 parameter, three-dimensional, 12 degree-of-freedom lower-extremity kinematic model to synthetic and experimental movement data for isolated joint (hip, knee, and ankle) and gait (full leg) motions. For noiseless synthetic data, the approach successfully recovered the known joint parameters to within an arbitrarily tight tolerance. When noise was added to the synthetic data, root-mean-square (RMS) errors between known and recovered joint parameters were within 10.4 degrees and 10 mm. For experimental data, RMS marker distance errors were reduced by up to 62% compared to methods that estimate joint parameters from anatomical landmarks. Optimized joint parameters found using a loaded full-leg gait motion differed significantly from those found using unloaded individual joint motions. In the future, this approach may facilitate the creation of dynamic patient-specific musculoskeletal models for predictive clinical applications.     

Robustness of kinematic weighting and scaling concepts for musculoskeletal simulation

Musculoskeletal modelling is widely used to estimate internal loading conditions. In order to optimise robustness and reduce errors between the subject-specific reference motion data (RMD) and the musculoskeletal simulation, 90 permutations of kinetic and kinematic data were analysed during split squats. A ranking for the scaling and kinematic weighting concepts based on the RMS errors when including functional centres of rotation (fCoRs), joint angles, and skin markers, revealed that analyses should include fCoR in the scaling and the simulation processes, as well as an automated weighting procedure including all attached skin markers for optimal registration of the musculoskeletal model to the RMD.