On intrinsic equivalences of the finite helical axis,the instantaneous helical axis,and the SARA approach. A mathematical perspective

Accurate determination of joint axes is essential for understanding musculoskeletal function. Whilst numerous algorithms to compute such axes exist, the conditions under which each of the methods performs best remain largely unknown. Typically, algorithms are evaluated for specific conditions only limiting the external validity of conclusions regarding their performance. We derive exact mathematical relationships between three commonly used algorithms for computing joint axes from motion data: finite helical axes (FHA), instantaneous helical axes (IHA) and SARA (symmetrical axis of rotation approach), including relationships for an extension to the mean helical axes methods that facilitate determining joint centres and axes. Through the derivation of a sound mathematical framework to objectively compare the algorithms we demonstrate that the FHA and SARA approach are equivalent for the analysis of two time frames. Moreover, we show that the position of a helical axis derived from the IHA using positional data is affected by a systematic error perpendicular to the true axis direction, whereas the axis direction is identical to those computed with either the FHA or SARA approach (true direction). Finally, with an appropriate choice of weighting factors the mean FHA (MFHA) method is equivalent to the Symmetrical Centre of Rotation Estimation (SCoRE) algorithm for determination of a Centre of Rotation (CoR), and similarly, equivalent to the SARA algorithm for determination of an Axis of Rotation (AoR). The deep understanding of the equivalences between methods presented here enables readers to choose numerically efficient, robust methods for determining AoRs and CoRs with confidence.     

Accuracy of a CT-based bone contour registration method to measure relative bone motions in the hindfoot

For measuring the in-vivo range of motion of the hindfoot, a CT-based bone contour registration method (CT-BCM) was developed to determine the three-dimensional position and orientation of bones. To validate this technique, we hypothesized that the range of motion in the hindfoot is equally, accurately measured by roentgen stereophotogrammetric analysis (RSA) as by the CT-BCM technique.Tantalum bone markers were placed in the distal tibia, talus and calcaneus of one cadaver specimen. With a fixed lower leg, the cadaveric foot was held in neutral and subsequently loaded in eight extreme positions. Immediately after acquiring a CT-scan with the foot in a position, RSA radiographs were made. Bone contour registration and RSA was performed. Helical axis parameters were calculated for talocrural and subtalar joint motion from neutral to extreme positions and between opposite extreme positions. Differences between CT-BCM and RSA were calculated.Compared with RSA, the CT-BCM data registered an overall root mean square difference (RMSd) of 0.21° for rotation about the helical axis, and 0.20 mm translation along the helical axis for the talocrural and subtalar joint and for all motions combined. The RMSd of the position and direction of the helical axes was 3.3 mm and 2.4°, respectively. The latter errors were larger with smaller helical rotations.The differences are similar to those reported for validated RSA and thus are not clinically relevant. Concluding, CT-BCM is an accurate and accessible alternative for studying joint motion, as it does not have the risk of infection and overlapping bone markers.     

Joint kinematics estimation using a multi-body kinematics optimisation and an extended Kalman filter,and embedding a soft tissue artefact model

To reduce the impact of the soft tissue artefact (STA) on the estimate of skeletal movement using stereophotogrammetric and skin-marker data, multi-body kinematics optimisation (MKO) and extended Kalman filters (EKF) have been proposed. This paper assessed the feasibility and efficiency of these methods when they embed a mathematical model of the STA and simultaneously estimate the ankle, knee and hip joint kinematics and the model parameters. A STA model was used that provides an estimate of the STA affecting the marker-cluster located on a body segment as a function of the kinematics of the adjacent joints. The MKO and the EKF were implemented with and without the STA model. To assess these methods, intra-cortical pin and skin markers located on the thigh, shank, and foot of three subjects and tracked during the stance phase of running were used. Embedding the STA model in MKO and EKF reduced the average RMS of marker tracking from 12.6 to 1.6 mm and from 4.3 to 1.9 mm, respectively, showing that a STA model trial-specific calibration is feasible. Nevertheless, with the STA model embedded in MKO, the RMS difference between the estimated and the reference joint kinematics determined from the pin markers slightly increased (from 2.0 to 2.1 deg) On the contrary, when the STA model was embedded in the EKF, this RMS difference was slightly reduced (from 2.0 to 1.7 deg) thus showing a better potentiality of this method to attenuate STA effects and improve the accuracy of joint kinematics estimate.     

Effects of data smoothing on the reconstruction of helical axis parameters in human joint kinematics

In biomechanical joint-motion analyses, the continuous motion to be studied is often approximated by a sequence of finite displacements, and the Finite Helical Axis (FHA) or "screw axis" for each displacement is estimated from position measurements on a number of anatomical or artificial landmarks. When FHA parameters are directly determined from raw (noisy) displacement data, both the position and the direction of the FHA are ill-determined, in particular when the sequential displacement steps are small. This implies, that under certain conditions, the continuous pathways of joint motions cannot be adequately described. The purpose of the present experimental study is to investigate the applicability of smoothing (or filtering) techniques, in those cases where FHA parameters are ill-determined. Two different quintic-spline smoothing methods were used to analyze the motion data obtained with Roentgenstereophotogrammetry in two experiments. One concerning carpal motions in a wrist-joint specimen, and one relative to a kinematic laboratory model, in which the axis positions are a priori known. The smoothed and non-smoothed FHA parameter errors were compared. The influences of the number of samples and the size of the sampling interval (displacement step) were investigated, as were the effects of equidistant and nonequidistant sampling conditions and noise invariance.     

Accuracy map of an optical motion capture system with 42 or 21 cameras in a large measurement volume

Optical motion capture is commonly used in biomechanics to measure human kinematics. However, no studies have yet examined the accuracy of optical motion capture in a large capture volume (>100 m³), or how accuracy varies from the center to the extreme edges of the capture volume. This study measured the dynamic 3D errors of an optical motion capture system composed of 42 OptiTrack Prime 41 cameras (capture volume of 135 m³) by comparing the motion of a single marker to the motion reported by a ThorLabs linear motion stage. After spline interpolating the data, it was found that 97% of the capture area had error below 200 μm. When the same analysis was performed using only half (21) of the cameras, 91% of the capture area was below 200 μm of error. The only locations that exceeded this threshold were at the extreme edges of the capture area, and no location had a mean error exceeding 1 mm. When measuring human kinematics with skin-mounted markers, uncertainty of marker placement relative to underlying skeletal features and soft tissue artifact produce errors that are orders of magnitude larger than the errors attributed to the camera system itself. Therefore, the accuracy of this OptiTrack optical motion capture system was found to be more than sufficient for measuring full-body human kinematics with skin-mounted markers in a large capture volume (>100 m³).     

Synergistic fibrinolysis: The combined effects of tissue plasminogen activator and recombinant staphylokinase in vitro

BackgroundMechanisms of fibrin-specificity of tissue plasminogen activator (tPA) and recombinant staphylokinase (STA) are different, therefore we studied in vitro the possibility of the synergy of their combined thrombolytic action.MethodsThrombolytic effects of tPA, STA and their combinations were measured by lysis rate of human plasma clot and side effects were evaluated by decreasing in fibrinogen, plasminogen and α₂-antiplasmin levels in the surrounding plasma at 37 °C in vitro.ResultsSTA and tPA induced dose- and time-dependent clot lysis: 50% lysis in 2 h was obtained with 30 nM tPA and 75 nM STA, respectively. At these concentrations, tPA produced greater degradation of plasma fibrinogen than STA. According to a mathematical analysis of dose–response curves by the isobole method, combinations of tPA and STA caused a considerable synergistic thrombolytic effect. The simultaneous and sequential combinations of tPA (< 4 nM) and STA (< 35 nM) induced a significant fibrin-specific synergistic thrombolysis, which was more pronounced in 2 h at simultaneous combinations than at sequential addition of STA after 30 min of tPA action. Simultaneous combination of 2.5 nM tPA and 15 nM STA showed a maximal 3-fold increase in thrombolytic effect compared to the expected total effect of the individual agents. Sequential combinations caused a lower depletion of plasma proteins compared to simultaneous combinations.ConclusionsThe simultaneous and sequential combinations of tPA and STA possessed synergistic fibrin-specific thrombolytic action on clot lysis in vitro.General significanceThe results show that combined thrombolysis may be more effective and safer than thrombolysis with each activator alone.     

Soft tissue artefacts of skin markers on the lower limb during cycling: Effects of joint angles and pedal resistance

Soft tissue artefacts (STA) are a major error source in skin marker-based measurement of human movement, and are difficult to eliminate non-invasively. The current study quantified in vivo the STA of skin markers on the thigh and shank during cycling, and studied the effects of knee angles and pedal resistance by using integrated 3D fluoroscopy and stereophotogrammetry. Fifteen young healthy adults performed stationary cycling with and without pedal resistance, while the marker data were measured using a motion capture system, and the motions of the femur and tibia/fibula were recorded using a bi-plane fluoroscopy-to-CT registration method. The STAs with respect to crank and knee angles over the pedaling cycle, as well as the within-cycle variations, were obtained and compared between resistance conditions. The thigh markers showed greater STA than the shank ones, the latter varying linearly with adjacent joint angles, the former non-linearly with greater within-cycle variability. Both STA magnitudes and within-cycle variability were significantly affected by pedal resistance (p < 0.05). The STAs appeared to be composed of one component providing the stable and consistent STA patterns and another causing their variations. Mid-segment markers experienced smaller STA ranges than those closer to a joint, but tended to have greater variations primarily associated with pedal resistance and muscle contractions. The current data will be helpful for a better choice of marker positions for data collection, and for developing methods to compensate for both stable and variation components of the STA.     

A constrained extended Kalman filter for the optimal estimate of kinematics and kinetics of a sagittal symmetric exercise

This paper presents a method for real-time estimation of the kinematics and kinetics of a human body performing a sagittal symmetric motor task, which would minimize the impact of the stereophotogrammetric soft tissue artefacts (STA). The method is based on a bi-dimensional mechanical model of the locomotor apparatus the state variables of which (joint angles, velocities and accelerations, and the segments lengths and inertial parameters) are estimated by a constrained extended Kalman filter (CEKF) that fuses input information made of both stereophotogrammetric and dynamometric measurement data. Filter gains are made to saturate in order to obtain plausible state variables and the measurement covariance matrix of the filter accounts for the expected STA maximal amplitudes. We hypothesised that the ensemble of constraints and input redundant information would allow the method to attenuate the STA propagation to the end results. The method was evaluated in ten human subjects performing a squat exercise. The CEKF estimated and measured skin marker trajectories exhibited a RMS difference lower than 4 mm, thus in the range of STAs. The RMS differences between the measured ground reaction force and moment and those estimated using the proposed method (9 N and 10 N m) were much lower than obtained using a classical inverse dynamics approach (22 N and 30 N m). From the latter results it may be inferred that the presented method allows for a significant improvement of the accuracy with which kinematic variables and relevant time derivatives, model parameters and, therefore, intersegmental moments are estimated.     

Effect of various upper limb multibody models on soft tissue artefact correction: A case study

Soft tissue artefacts (STA) introduce errors in joint kinematics when using cutaneous markers, especially on the scapula. Both segmental optimisation and multibody kinematics optimisation (MKO) algorithms have been developed to improve kinematics estimates. MKO based on a chain model with joint constraints avoids apparent joint dislocation but is sensitive to the biofidelity of chosen joint constraints. Since no recommendation exists for the scapula, our objective was to determine the best models to accurately estimate its kinematics. One participant was equipped with skin markers and with an intracortical pin screwed in the scapula. Segmental optimisation and MKO for 24-chain models (including four variations of the scapulothoracic joint) were compared against the pin-derived kinematics using root mean square error (RMSE) on Cardan angles. Segmental optimisation led to an accurate scapula kinematics (1.1° ≤ RMSE ≤ 3.3°) even for high arm elevation angles. When MKO was applied, no clinically significant difference was found between the different scapulothoracic models (0.9° ≤ RMSE ≤ 4.1°) except when a free scapulothoracic joint was modelled (1.9° ≤ RMSE ≤ 9.6°). To conclude, using MKO as a STA correction method was not more accurate than segmental optimisation for estimating scapula kinematics.     

Hip joint centre location: An ex vivo study

The human hip joint is normally represented as a spherical hinge and its centre of rotation is used to construct femoral anatomical axes and to calculate hip joint moments. The estimate of the hip joint centre (HJC) position using a functional approach is affected by stereophotogrammetric errors and soft tissue artefacts. The aims of this study were (1) to assess the accuracy with which the HJC position can be located using stereophotogrammetry and (2) to investigate the effects of hip motion amplitude on this accuracy. Experiments were conducted on four adult cadavers. Cortical pins, each equipped with a marker cluster, were implanted in the pelvis and femur, and eight skin markers were attached to the thigh. Recordings were made while an operator rotated the hip joint exploiting the widest possible range of motion. For HJC determination, a proximal and a distal thigh skin marker cluster and two recent analytical methods, the quartic sphere fit (QFS) method and the symmetrical centre of rotation estimation (SCoRE) method, were used. Results showed that, when only stereophotogrammetric errors were taken into account, the analytical methods performed equally well. In presence of soft tissue artefacts, HJC errors highly varied among subjects, methods, and skin marker clusters (between 1.4 and 38.5 mm). As expected, larger errors were found in the subject with larger soft tissue artefacts. The QFS method and the distal cluster performed generally better and showed a mean HJC location accuracy better than 10 mm over all subjects. The analysis on the effect of hip movement amplitude revealed that a reduction of the amplitude does not improve the HJC location accuracy despite a decrease of the artefact amplitude.     

MRI development and validation of two new predictive methods of glenohumeral joint centre location identification and comparison with established techniques

Identification of the centre of the glenohumeral joint (GHJ) is essential for three-dimensional (3D) upper limb motion analysis. A number of convenient, yet un-validated methods are routinely used to estimate the GHJ location in preference to the International Society of Biomechanics (ISB) recommended methods. The current study developed a new regression model, and simple 3D offset method for GHJ location estimation, employing easy to administer measures, and compared the estimates with the known GHJ location measured with magnetic resonance imaging (MRI). The accuracy and reliability of the new regression and simple 3D offset techniques were compared with six established predictive methods. Twenty subjects wore a 3D motion analysis marker set that was also visible in MRI. Immediately following imaging, they underwent 3D motion analysis acquisition. The GHJ and anatomical landmark positions of 15 participants were used to determine the new regression and simple 3D generic offset methods. These were compared for accuracy with six established methods using 10 subject's data. A cross validation on 5 participants not used for regression model development was also performed. Finally, 10 participants underwent a further two MRI's and subsequent 3D motion analysis analyses for inter-tester and intra-tester reliability quantification. When compared with any of the other established methods, our newly developed regression model found an average GHJ location closer to the actual MRI location, having an GHJ location error of 13±2 mm, and had significantly lower inter-tester reliability error, 6±4 mm (p<0.01).     

Soft tissue artifact compensation by linear 3D interpolation and approximation methods

Several compensation methods estimate bone pose from a cluster of skin-mounted makers, each influenced by soft tissue artifact (STA). In this study, linear 3D interpolation and approximation methods (affine mapping, Kriging and radial basis function (RBF)) and the conventional singular value decomposition (SVD) method were examined to determine their suitability for STA compensation. The ability of these four methods to estimate knee angles and displacements was compared using simulated gait data with and without added STA. The knee angle and the displacement estimates of all four methods were similar with root-mean-square errors (RMSEs) near 1.5° and 4 mm, respectively. The 3D interpolation and approximation methods were more complicated to implement than the conventional SVD method. However, these non-standard methods provided additional geometric (homothety, stretch) and time functions that model the deformation of the cluster of markers. This additional information may be useful to model and compensate the STA.     

The effects of wrist motion and hand orientation on muscle forces: A physiologic wrist simulator study

Although the orientations of the hand and forearm vary for different wrist rehabilitation protocols, their effect on muscle forces has not been quantified. Physiologic simulators enable a biomechanical evaluation of the joint by recreating functional motions in cadaveric specimens. Control strategies used to actuate joints in physiologic simulators usually employ position or force feedback alone to achieve optimum load distribution across the muscles. After successful tests on a phantom limb, unique combinations of position and force feedback – hybrid control and cascade control – were used to simulate multiple cyclic wrist motions of flexion-extension, radioulnar deviation, dart thrower’s motion, and circumduction using six muscles in ten cadaveric specimens. Low kinematic errors and coefficients of variation of muscle forces were observed for planar and complex wrist motions using both novel control strategies. The effect of gravity was most pronounced when the hand was in the horizontal orientation, resulting in higher extensor forces (p < 0.017) and higher out-of-plane kinematic errors (p < 0.007), as compared to the vertically upward or downward orientations. Muscle forces were also affected by the direction of rotation during circumduction. The peak force of flexor carpi radialis was higher in clockwise circumduction (p = 0.017), while that of flexor carpi ulnaris was higher in anticlockwise circumduction (p = 0.013). Thus, the physiologic wrist simulator accurately replicated cyclic planar and complex motions in cadaveric specimens. Moreover, the dependence of muscle forces on the hand orientation and the direction of circumduction could be vital in the specification of such parameters during wrist rehabilitation.     

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

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

Phosphorus mass load and outflow concentration relationships in stormwater treatment areas for Everglades restoration

Mass loading and outflow phosphorus (P) relationships were investigated for four stormwater treatment area (STA) wetlands in south Florida. These systems, ranging in size from 350 to 2670 ha, were constructed by the South Florida Water Management District (SFWMD) for Everglades restoration, and approaches currently are being investigated for optimizing their design and management. We analyzed 2–7 years of P removal data from 10 independent STA process trains using system classifications based on dominant vegetation type, which was either emergent aquatic vegetation (EAV) or submerged aquatic vegetation (SAV), and prior land use, which was either recently farmed (RF) or historic wetland (HW). We found that a 1–2 year history of mass loading rates (MLR) at or below ∼1.3 g P/m²/year in STA process trains provided a high likelihood of achieving outflow total P (TP) concentrations less than ∼30 μg/L. Statistical analyses revealed that P removal performance of SAV and EAV-HW systems was generally superior to that of EAV-RF systems. These performance differences were corroborated with data from seven other non-STA Florida-based treatment wetlands. Furthermore, in the subset of SAV and continuously flooded EAV-HW data with P MLRs at or below ∼2 g/m²/year, outflow P concentrations were consistently between 10 and 20 μg/L, mass removal efficiencies were consistently above 85%, and the wetlands demonstrated a substantial resilience to small-to-moderate pulsed inflow P loads. Despite 16 occurrences in these full-scale STA data of annual flow-weighted mean outflow P concentrations between 10 and 20 μg/L, no significant MLR–P relationships were identified for targeting specific P concentrations in this range.     

Impact of physiological breathing motion for breast cancer radiotherapy with proton beam scanning – An in silico study

This study investigates the impact of breathing motion on proton breast treatment plans. Twelve patients with CT datasets acquired during breath-hold-at-inhalation (BHI), breath-hold-at-exhalation (BHE) and in free-breathing (FB) were included in the study. Proton plans were designed for the left breast for BHI and subsequently recalculated for BHE or designed for FB and recalculated for the extreme breath-hold phases. The plans were compared from the point of view of their target coverage and doses to organs-at-risk. The median amplitude of breathing motion determined from the positions of the sternum was 4.7 mm (range 0.5–14.6 mm). Breathing motion led to a degradation of the dose coverage of the target (heterogeneity index increased from 4–7% to 8–11%), but the degraded values of the dosimetric parameters of interest fulfilled the clinical criteria for plan acceptance. Exhalation decreased the lung burden [average dose 3.1–4.5 Gy (RBE)], while inhalation increased it [average dose 5.8–6.8 Gy (RBE)]. The individual values depended on the field arrangement. Smaller differences were seen for the heart [average dose 0.1–0.2 Gy (RBE)] and the LAD [1.9–4.6 Gy (RBE)]. Weak correlations were generally found between changes in dosimetric parameters and respiratory motion. The differences between dosimetric parameters for various breathing phases were small and their expected clinical impact is consequently quite small. The results indicated that the dosimetric parameters of the plans corresponding to the extreme breathing phases are little affected by breathing motion, thus suggesting that this motion might have little impact for the chosen beam orientations with scanned proton beams.     

Bone orientation and position estimation errors using Cosserat point elements and least squares methods: Application to gait

The aim of this study was to analyze the accuracy of bone pose estimation based on sub-clusters of three skin-markers characterized by triangular Cosserat point elements (TCPEs) and to evaluate the capability of four instantaneous physical parameters, which can be measured non-invasively in vivo, to identify the most accurate TCPEs. Moreover, TCPE pose estimations were compared with the estimations of two least squares minimization methods applied to the cluster of all markers, using rigid body (RBLS) and homogeneous deformation (HDLS) assumptions. Analysis was performed on previously collected in vivo treadmill gait data composed of simultaneous measurements of the gold-standard bone pose by bi-plane fluoroscopy tracking the subjects' knee prosthesis and a stereophotogrammetric system tracking skin-markers affected by soft tissue artifact. Femur orientation and position errors estimated from skin-marker clusters were computed for 18 subjects using clusters of up to 35 markers. Results based on gold-standard data revealed that instantaneous subsets of TCPEs exist which estimate the femur pose with reasonable accuracy (median root mean square error during stance/swing: 1.4/2.8 deg for orientation, 1.5/4.2 mm for position). A non-invasive and instantaneous criteria to select accurate TCPEs for pose estimation (4.8/7.3 deg, 5.8/12.3 mm), was compared with RBLS (4.3/6.6 deg, 6.9/16.6 mm) and HDLS (4.6/7.6 deg, 6.7/12.5 mm). Accounting for homogeneous deformation, using HDLS or selected TCPEs, yielded more accurate position estimations than RBLS method, which, conversely, yielded more accurate orientation estimations. Further investigation is required to devise effective criteria for cluster selection that could represent a significant improvement in bone pose estimation accuracy.     

Continuous thickness measurement of rectus femoris muscle in ultrasound image sequences: A completely automated approach

Muscle thickness is one of the most widely used parameters for quantifying muscle function in both diagnosis and rehabilitation assessment. Ultrasound imaging has been frequently used to non-invasively study the thickness of human muscles as a reliable method. However, the measurement is traditionally conducted by manual digitization of reference points at the superior and inferior muscle fascias, thus it is subjective and time-consuming. In this paper, a novel method is proposed to detect the muscle thickness automatically. The superficial and deep fascias of a muscle are detected by line detection algorithm at the first ultrasound frame, and the image regions of interest (ROI) for the fascias are subsequently located and tracked by optical flow technique. The muscle thickness is geometrically obtained based on the location of the fascias for each frame. Six ultrasound sequences (250 frames in each sequence) are used to evaluate this method. The correlation coefficient of the detection results between the proposed method and manual method is 0.95 ± 0.01, and the difference is ?0.05 ± 0.22 mm. The linear regression of the total 1500 detections show that a good linear correlation between the results of the two methods is obtained (R² = 0.981). The automated method proposed here provides an accurate, high repeatable and efficient approach for estimating fascicle thickness during human motion, thus justifying its application in biological sciences.     

A three dimensional finite element study on dental implant design

Implant diameter and length are the most effective parameters affecting stress distribution in surrounding bones. In order to extract simplified design equations to better understand implants behavior, 25 different implant designs with gradual increase in diameter and length were analyzed in 3D using Finite Element Method. Four types of loadings were applied on each design: tension of 50 N, compression of 100 N, bending of 20 N, and torque of 2 Nm to derive design curves.Analysis of results showed that increasing implant diameter and length generate better stress distribution on spongy and cortical bones. Approximate design equations and curves were obtained as a result of this study.