Static and dynamic error of a biplanar videoradiography system using marker-based and markerless tracking techniques

The use of biplanar videoradiography technology has become increasingly popular for evaluating joint function in vivo. Two fundamentally different methods are currently employed to reconstruct 3D bone motions captured using this technology. Marker-based tracking requires at least three radio-opaque markers to be implanted in the bone of interest. Markerless tracking makes use of algorithms designed to match 3D bone shapes to biplanar videoradiography data. In order to reliably quantify in vivo bone motion, the systematic error of these tracking techniques should be evaluated. Herein, we present new markerless tracking software that makes use of modern GPU technology, describe a versatile method for quantifying the systematic error of a biplanar videoradiography motion capture system using independent gold standard instrumentation, and evaluate the systematic error of the W.M. Keck XROMM Facility's biplanar videoradiography system using both marker-based and markerless tracking algorithms under static and dynamic motion conditions. A polycarbonate flag embedded with 12 radio-opaque markers was used to evaluate the systematic error of the marker-based tracking algorithm. Three human cadaveric bones (distal femur, distal radius, and distal ulna) were used to evaluate the systematic error of the markerless tracking algorithm. The systematic error was evaluated by comparing motions to independent gold standard instrumentation. Static motions were compared to high accuracy linear and rotary stages while dynamic motions were compared to a high accuracy angular displacement transducer. Marker-based tracking was shown to effectively track motion to within 0.1?mm and 0.1 deg under static and dynamic conditions. Furthermore, the presented results indicate that markerless tracking can be used to effectively track rapid bone motions to within 0.15 deg for the distal aspects of the femur, radius, and ulna. Both marker-based and markerless tracking techniques were in excellent agreement with the gold standard instrumentation for both static and dynamic testing protocols. Future research will employ these techniques to quantify in vivo joint motion for high-speed upper and lower extremity impacts such as jumping, landing, and hammering.     

Soft-tissue artefact assessment during step-up using fluoroscopy and skin-mounted markers

When measuring knee kinematics with skin-mounted markers, soft tissue and structures surrounding the knee hide the actual underlying segment kinematics. Soft-tissue artefacts can be reduced when plate-mounted markers or marker trees are used instead of individual unconstrained mounted markers. The purpose of this study was to accurately quantify the soft-tissue artefacts and to compare two marker cluster fixation methods by using fluoroscopy of knee motion after total knee arthroplasty during a step-up task. Ten subjects participated 6 months after their total knee arthroplasty. The patients were randomised into (1) a plate-mounted marker group and (2) a strap-mounted marker group. Fluoroscopic data were collected during a step-up motion. A three-dimensional model fitting technique was used to reconstruct the in vivo 3-D positions of the markers and the implants representing the bones. The measurement errors associated with the thigh were generally larger (maximum translational error: 17mm; maximum rotational error 12 degrees ) than the measurement errors for the lower leg (maximum translational error: 11mm; maximum rotational error 10 degrees ). The strap-mounted group showed significant more translational errors than the plate-mounted group for both the shank (respectively, 3+/-2.2 and 0+/-2.0mm, p = 0.025) and the thigh (2+/-2.0 and 0+/-5.9mm, p = 0.031). The qualitative conclusions based on interpretation of the calculated estimates of effects within the longitudinal mixed-effects modelling evaluation of the data for the two groups (separately) were effectively identical. The soft-tissue artefacts across knee flexion angle could not be distinguished from zero for both groups. For all cases, recorded soft-tissue artefacts were less variable within subjects than between subjects. The large soft-tissue artefacts, when using clustered skin markers, irrespective of the fixation method, question the usefulness of parameters found with external movement registration and clinical interpretation of stair data in small patient groups.     

Tracking the motion of hidden segments using kinematic constraints and Kalman filtering

Motion capture for biomechanical applications involves in almost all cases sensors or markers that are applied to the skin of the body segments of interest. This paper deals with the problem of estimating the movement of connected skeletal segments from 3D position data of markers attached to the skin. The use of kinematic constraints has been shown previously to reduce the error in estimated segment movement that are due to skin and muscles moving with respect to the underlying segment. A kinematic constraint reduces the number of degrees of freedom between two articulating segments. Moreover, kinematic constraints can help reveal the movement of some segments when the 3D marker data otherwise are insufficient. Important cases include the human ankle complex and the phalangeal segments of the horse, where the movement of small segments is almost completely hidden from external observation by joint capsules and ligaments. This paper discusses the use of an extended Kalman filter for tracking a system of connected segments. The system is modeled using rigid segments connected by simplified joint models. The position and orientation of the mechanism are specified by a set of generalized coordinates corresponding to the mechanism's degrees of motion. The generalized coordinates together with their first time derivatives can be used as the state vector of a state space model governing the kinematics of the mechanism. The data collected are marker trajectories from skin-mounted markers, and the state vector is related to the position of the markers through a nonlinear function. The Jacobian of this function is derived. The practical use of the method is demonstrated on a model of the distal part of the limb of the horse. Monte Carlo simulations of marker data for a two-segment system connected by a joint with three degrees of freedom indicate that the proposed method gives significant improvement over a method, which does not make use of the joint constraint, but the method requires that the model is a good approximation of the true mechanism. Applying the method to data on the movement of the four distal-most segments of the horse's limb shows good between trial consistency and small differences between measured marker positions and marker positions predicted by the model.     

Minimizing fiducial localization error using sphere-based registration in jaw tracking

Some of the jaw tracking methods may be limited in terms of their accuracy or clinical applicability. This article introduces the sphere-based registration method to minimize the fiducial (reference landmark) localization error (FLE) in tracking and coregistration of physical and virtual dental models, to enable an effective clinical analysis of the patient’s masticatory functions. In this method, spheres (registration fiducials) are placed on the corresponding polygonal concavities of the physical and virtual dental models based on the geometrical principle that establishes a unique spatial position for a sphere inside an infinite trihedron. The experiments in this study were implemented using an optical system which tracked active tracking markers connected to the upper and lower dental casts. The accuracy of the tracking workflow was confirmed in vitro, based on comparing virtually calculated interocclusal regions of close proximity against the physical interocclusal impressions. The target registration error of the tracking was estimated based on the leave-one-sphere-out method to be the sum of the error of the sensors, i.e., the FLE was negligible. Moreover, based on a user study, the FLE of the proposed method was confirmed to be 5 and 10 times smaller than the FLE of conventional fiducial selections on the physical and virtual models, respectively. The proposed tracking method is non-invasive and appears to be sufficiently accurate. To conclude, the proposed registration and tracking principles can be extended to track any biomedical and non-biomedical geometries that contain polygonal concavities.     

How Fast Is Your Body Motion? Determining a Sufficient Frame Rate for an Optical Motion Tracking System Using Passive Markers

This paper addresses how to determine a sufficient frame (sampling) rate for an optical motion tracking system using passive reflective markers. When using passive markers for the optical motion tracking, avoiding identity confusion between the markers becomes a problem as the speed of motion increases, necessitating a higher frame rate to avoid a failure of the motion tracking caused by marker confusions and/or dropouts. Initially, one might believe that the Nyquist-Shannon sampling rate estimated from the assumed maximal temporal variation of a motion (i.e. a sampling rate at least twice that of the maximum motion frequency) could be the complete solution to the problem. However, this paper shows that also the spatial distance between the markers should be taken into account in determining the suitable frame rate of an optical motion tracking with passive markers. In this paper, a frame rate criterion for the optical tracking using passive markers is theoretically derived and also experimentally verified using a high-quality optical motion tracking system. Both the theoretical and the experimental results showed that the minimum frame rate is proportional to the ratio between the maximum speed of the motion and the minimum spacing between markers, and may also be predicted precisely if the proportional constant is known in advance. The inverse of the proportional constant is here defined as the tracking efficiency constant and it can be easily determined with some test measurements. Moreover, this newly defined constant can provide a new way of evaluating the tracking algorithm performance of an optical tracking system.     

Static accuracy analysis of Vicon T40s motion capture cameras arranged externally for motion capture in constrained aquatic environments

While the capabilities of land-based motion capture systems in biomechanical applications have been previously reported, the possibility of using motion tracking systems externally to reconstruct markers submerged inside an aquatic environment has been under explored. This study assesses the ability of a motion capture system (Vicon T40s) arranged externally to track a retro-reflective marker inside a glass tank filled with water and without water. The reflective tape used for marker creation in this study was of Safety of Life at Sea (SOLAS) grade as the conventional marker loses its reflective properties when submerged. The overall trueness calculated based on the mean marker distance errors, varied between 0.257 mm and 0.290 mm in different mediums (air, glass and water). The overall precision calculated based on mean standard deviation of mean marker distances at different locations varied between 0.046 mm and 0.360 mm in different mediums. Our results suggest, that there is no significant influence of the presence of water on the overall static accuracy of the marker center distances when markers were made of SOLAS grade reflective tape. Using optical motion tracking systems for evaluating locomotion in aquatic environment can help to better understand the effects of aquatic therapy in clinical rehabilitation, especially in scenarios that involve equipment, such as an underwater treadmill which generally have constrained capture volumes for motion capture.     

Four-dimensional model of the lower extremity after total hip arthroplasty

We have developed a four-dimensional (4D) model of the lower extremities after total hip arthroplasty in patients. The model can aid in preventing complications such as dislocation and wearing of the sliding surface. The skeletal structure and implant alignment were obtained from CT data. We applied registration method using CAD data to estimate accurate implant alignment from scattered CT data. The reconstructed three-dimensional (3D) skeletal model was combined with motion capture data that were acquired by an optical tracking system. We displayed the patient's skeletal movement and analyzed several parameters that relate to complications. The patient's skeletal model was superimposed onto video footage that was taken by a synchronized and calibrated digital video camera. For validation of the measurement error in this system, we used open MRI to evaluate the relative movement between skin markers and bones. This system visually represents not only the 3D anatomical structure, but also 4D dynamic functions that include the time sequential transitions of components and their positions. The open MRI results indicated that the average error in hip angle was within 5° for each static posture. This system enables clinicians to analyze patient's motions on the basis of individual differences. We found that our system was an effective tool in providing precise guidance of daily postoperative motions that was individualized for each patient. This system will be applicable for surgical planning, assessment of postoperative activities, and the development of new surgical techniques, materials, and prosthetic designs.     

Separating brain motion into rigid body displacement and deformation under low-severity impacts

The relative motion of the brain with respect to the skull has been widely studied to investigate brain injury mechanisms under impacts, but the motion patterns are not yet thoroughly understood. This work analyzes brain motion patterns using the most recent and advanced experimental relative brain/skull motion data collected under low-severity impacts. With a minimum total pseudo-strain energy, the closed-form solutions for rigid body translation and rotation were obtained by matching measured neutral density target (NDT) positions with initial NDT positions. The brain motion was thus separated into rigid body displacement and deformation. The results show that the brain has nearly pure rigid body displacement at low impact speed. As the impact becomes more severe, the increased brain motion primarily is due to deformation, while the rigid body displacement is limited in magnitude for both translation and rotation. Under low-severity impacts in the sagittal plane, the rigid body brain translation has a magnitude of 4-5 mm, and the whole brain rotation is on the order of +/-5 degrees.     

A cine-EPID based method for jaw detection and quality assurance for tracking jaw in IMRT/VMAT treatments

A new tool with the potential to verify and track jaw position during delivery has been developed. The method should be suitable for independent quality assurance for jaw position during jaw tracking dynamic IMRT and VMAT treatments. The jaw detection and tracking algorithm developed consists of five main steps. Firstly, the image is enhanced by removing a normalised predicted EPID image (that does not include the collimator transmission) from each cine EPID image. Then, using a histogram clustering technique a global intensity threshold level was determined. This threshold level was used to classify each pixel of the image as either under the jaws or under the MLC. Additionally, the collimator angle was automatically detected and used to rotate the image to vertical direction. Finally, this rotation allows the jaw positions to be determined using vertical and horizontal projection profiles. Nine IMRT fields (with static jaws) and a single VMAT clinical field (with dynamic jaws) were tested by determining the root mean square difference between planned and detected jaw positions. The test results give a detection accuracy of ±1 mm RMS error for static jaw IMRT treatments and ±1.5 mm RMS error for the dynamic jaw VMAT treatment. This method is designed for quality assurance and verification in modern radiation therapy; to detect the position of static jaws or verify the position of tracking jaws in more complex treatments. This method uses only information extracted from EPID images and it is therefore independent from the linear accelerator.     

An ultrasound based non-invasive method for the measurement of intrinsic foot kinematics during gait

Soft tissue artefact (STA) and marker placement variability are sources of error when measuring the intrinsic kinematics of the foot. This study aims to demonstrate a non-invasive, combined ultrasound and motion capture (US/MC) technique to directly measure foot skeletal motion. The novel approach is compared to a standard motion capture protocol. Fourteen participants underwent instrumented barefoot analysis of foot motion during gait. Markers were attached to foot allowing medial longitudinal arch angle and navicular height to be determined. For the US/MC technique, the navicular marker was replaced by an ultrasound transducer which was secured to the foot allowing the skeletal landmark to be imaged. Ultrasound cineloops showing the location of the navicular tuberosity during the walking trials were synchronised with motion capture measurements and markers mounted on the probe allowed the true position of the bony landmark to be determined throughout stance phase. Two discrete variables, minimum navicular height and maximum MLA angle, were compared between the standard and US/MC protocols. Significant differences between minimum navicular height (P=0.004, 95% CI (1.57, 6.54)) and maximum medial longitudinal arch angle (P=0.0034, 95% CI (13.8, 3.4)) were found between the measurement methods. The individual effects of STA and marker placement error were also assessed. US/MC is a non-invasive technique which may help to provide more accurate measurements of intrinsic foot kinematics.     

The effect of anisotropic systematic errors in estimating helical angles

A common question in movement studies is how the results should be interpreted with respect to systematic and random errors. In this study, simulations are made in order to see how a rigid body's orientation in space (i.e. helical angle between two orientations) is affected by (1) a systematic error added to a single marker (2) a combination of this systematic error and Gaussian white noise. The orientation was estimated after adding a systematic error to one marker within the rigid body. This procedure was repeated with Gaussian noise added to each marker. In conclusion, results show that the systematic error's effect on estimated orientation depends on number of markers in the rigid body and also on which direction the systematic error is added. The systematic error has no effect if the error is added along the radial axis (i.e. the line connecting centre of mass and the affected marker).     

The effect of anisotropic systematic errors in estimating helical angles

A common question in movement studies is how the results should be interpreted with respect to systematic and random errors. In this study, simulations are made in order to see how a rigid body's orientation in space (i.e. helical angle between two orientations) is affected by (1) a systematic error added to a single marker (2) a combination of this systematic error and Gaussian white noise. The orientation was estimated after adding a systematic error to one marker within the rigid body. This procedure was repeated with Gaussian noise added to each marker.

In conclusion, results show that the systematic error's effect on estimated orientation depends on number of markers in the rigid body and also on which direction the systematic error is added. The systematic error has no effect if the error is added along the radial axis (i.e. the line connecting centre of mass and the affected marker).     

Motion analysis of an articulated locomotion model by video and telemetric data.

Traditional techniques of human motion analysis use markers located on body articulations. The position of each marker is extracted from each image. Temporal and kinematic analysis is given by matching these data with a reference model of the human body. However, as human skin is not rigidly linked with the skeleton, each movement causes displacements of the markers and induces uncertainty in results. Moreover, the experiments are mostly conducted in restricted laboratory conditions. The aim of our project was to develop a new method for human motion analysis which needs non-sophisticated recording devices, avoids constraints to the subject studied, and can be used in various surroundings such as stadiums or gymnasiums. Our approach consisted of identifying and locating body parts in image, without markers, by using a multi-sensory sensor. This sensor exploits both data given by a video camera delivering intensity images, and data given by a 3D sensor delivering in-depth images. Our goal, in this design, was to show up the feasibility of our approach. In any case the hardware we used could facilitate an automated motion analysis. We used a linked segment model which referred to Winter's model, and we applied our method not on a human subject but on a life size articulated locomotion model. Our approach consists of finding the posture of this articulated locomotion model in the image. By performing a telemetric image segmentation, we obtained an approximate correspondence between linked segment model position and locomotion model position. This posture was then improved by injecting segmentation results in an intensity image segmentation algorithm. Several tests were conducted with video/telemetric images taken in an outdoor surrounding with the articulated model. This real life-size model was equipped with movable joints which, in static positions, described two strides of a runner. With our fusion method, we obtained relevant limbs identification and location for most postures.     

In situ comparison of A-mode ultrasound tracking system and skin-mounted markers for measuring kinematics of the lower extremity

Skin-mounted marker based motion capture systems are widely used in measuring the movement of human joints. Kinematic measurements associated with skin-mounted markers are subject to soft tissue artifacts (STA), since the markers follow skin movement, thus generating errors when used to represent motions of underlying bone segments. We present a novel ultrasound tracking system that is capable of directly measuring tibial and femoral bone surfaces during dynamic motions, and subsequently measuring six-degree-of-freedom (6-DOF) tibiofemoral kinematics. The aim of this study is to quantitatively compare the accuracy of tibiofemoral kinematics estimated by the ultrasound tracking system and by a conventional skin-mounted marker based motion capture system in a cadaveric experimental scenario. Two typical tibiofemoral joint models (spherical and hinge models) were used to derive relevant kinematic outcomes. Intra-cortical bone pins equipped with optical markers were inserted in the tibial and femoral bones to serve as a reference to provide ground truth kinematics. The ultrasound tracking system resulted in lower kinematic errors than the skin-mounted markers (the ultrasound tracking system: maximum root-mean-square (RMS) error 3.44° for rotations and 4.88 mm for translations, skin-mounted markers with the spherical joint model: 6.32° and 6.26 mm, the hinge model: 6.38° and 6.52 mm). Our proposed ultrasound tracking system has the potential of measuring direct bone kinematics, thereby mitigating the influence and propagation of STA. Consequently, this technique could be considered as an alternative method for measuring 6-DOF tibiofemoral kinematics, which may be adopted in gait analysis and clinical practice.     

Difference between palpation and optoelectronics recording of scapular motion

The aim of this study is to determine the errors of scapular localisation due to skin relative to bone motion with an optoelectronic tracking system. We compared three-dimensional (3D) scapular positions obtained with skin markers to those obtained through palpation of three scapular anatomical landmarks. The scapular kinematics of nine subjects were collected. Static positions of the scapula were recorded with the right arm elevated at 0°, 40°, 80°, 120° and 160° in the sagittal plane. Palpation and subsequent digitisation of anatomical landmarks on scapula and thorax were done at the same positions. Scapular 3D orientation was also computed during 10 repeated movements of arm elevation between 0° and 180°. Significant differences in scapular kinematics were seen between static positions and palpation when considering anterior/posterior tilt and upward/downward rotation at angles over 120° of humeral elevation and only at 120° for internal/external rotation. There was no significant difference between positions computed during static positions and during the movement for the three scapular orientations. A rotation correction model is presented in order to reduce the errors between static position and palpation measurement.     

Fusion of radiostereometric analysis data into computed tomography space: application to the elbow joint

Improvement of joint prostheses is dependent upon information concerning the biomechanical properties of the joint. Radiostereometric analysis (RSA) and electromagnetic techniques have been applied in previous cadaver and in vivo studies on the elbow joint to provide valuable information concerning joint motion axes. However, such information is limited to mathematically calculated positions of the axes according to an orthogonal coordinate system and is difficult to relate to individual skeletal anatomy. The aim of this study was to evaluate the in vivo application of a new fusion method to provide three-dimensional (3D) visualization of flexion axes according to bony landmarks. In vivo RSA data of the elbow joint's flexion axes was combined with data obtained by 3D computed tomography (CT). Results were obtained from five healthy subjects after one was excluded due to an instable RSA marker. The median error between imported and transformed RSA marker coordinates and those obtained in the CT volume was 0.22 mm. Median maximal rotation error after transformation of the rigid RSA body to the CT volume was 0.003 degrees . Points of interception with a plane calculated in the RSA orthogonal coordinate system were imported into the CT volume, facilitating the 3D visualization of the flexion axes. This study demonstrates a successful fusion of RSA and CT data, without significant loss of RSA accuracy. The method could be used for relating individual motion axes to a 3D representation of relevant joint anatomy, thus providing important information for clinical applications such as the development of joint prostheses.     

Effects of trunk deformation on trunk center of mass mechanical energy estimates in the moving horse,Equus caballus

The estimation of the position of the center of mass (CM) is essential in a wide range of biomechanical analyses. In horses, the majority of the body mass is contained in the trunk and in most studies, the trunk is assumed to be rigid. However, this rigidity assumption has not been tested. We quantified changes in the position of the trunk CM due to external shape changes by measuring the kinematics of a mesh encompassing the trunk. Using a frame of reference fixed to the horse's spine, we described the shape deformation of the trunk during walking. In addition, we tested for speed and individual differences. The significance of any trunk deformation was illustrated by calculating mechanical energy profiles. Errors in the estimation of the trunk CM due to a rigid body approach were always small in the vertical direction, but can be significant in the transverse direction and in the longitudinal direction at high walking speeds. This is enough to change the mechanical energy expenditure estimates up to 25%. When extrapolating the position of the trunk CM from cadaver data, one should be aware of this extra source of error, separated from the measurement error of the cadaver CM. We also found considerable inter-individual variation, which complicates theoretical correction routines. We suggest using extra markers on the trunk during gait analysis to correct this CM shift experimentally.     

The utility of the acromion marker cluster (AMC) in a clinical population

IntroductionThe acromion marker cluster (AMC) is a non-invasive scapular motion tracking method. However, it lacks testing in clinical populations, where unique challenges may present. This investigation resolved the utility of the AMC approach in a compromised clinical population.MethodsThe upper body of breast cancer survivors (BCS) and controls were tracked via motion capture and scapular landmarks palpated and recorded using a digitizer at static neutral to maximum elevation postures. The AMC tracked the scapula during dynamic maximum arm abduction. Both single (SC) and double calibration (DC) methods were applied to calculate scapular angles. The influences of calibration method, elevation, and group on mean and absolute error with two-way fixed ANOVAs with interactions (p < 0.05). Root mean square errors (RMSE) were calculated and compared.ResultsDC improved AMC estimation of palpated scapular orientation over SC, especially at higher arm elevations; RMSE averaged 11° higher for SC than DC at maximum elevation, but the methods were only 2.2° different at 90° elevation. DC of the AMC yielded mean error values of ∼5–10°. These approximate errors reported for AMC with young, lean adults.ConclusionsThe AMC with DC is a non-invasive method with acceptable error for measuring scapular motion of BCS and age-matched controls.     

A comparison of two non-invasive methods for measuring scapular orientation in functional positions

Identification of scapular dyskinesis and evaluation of interventions depend on the ability to properly measure scapulothoracic (ST) motion. The most widely used measurement approach is the acromion marker cluster (AMC), which can yield large errors in extreme humeral elevation and can be inaccurate in children and patient populations. Recently, an individualized regression approach has been proposed as an alternative to the AMC. This technique utilizes the relationship between ST orientation, humerothoracic orientation and acromion process position derived from calibration positions to predict dynamic ST orientations from humerothoracic and acromion process measures during motion. These individualized regressions demonstrated promising results for healthy adults; however, this method had not yet been compared to the more conventional AMC. This study compared ST orientation estimates by the AMC and regression approaches to static ST angles determined by surface markers placed on palpated landmarks in typically developing adolescents performing functional tasks. Both approaches produced errors within the range reported in the literature for skin-based scapular measurement techniques. The performance of the regression approach suffered when applied to positions outside of the range of motion in the set of calibration positions. The AMC significantly underestimated ST internal rotation across all positions and overestimated posterior tilt in some positions. Overall, root mean square errors for the regression approach were smaller than the AMC for every position across all axes of ST motion. Accordingly, we recommend the regression approach as a suitable technique for measuring ST kinematics in functional motion.