Propagation of soft tissue artifacts to the center of rotation: A model for the correction of functional calibration techniques

This paper presents a mathematical model for the propagation of errors in body segment kinematics to the location of the center of rotation. Three functional calibration techniques, usually employed for the gleno-humeral joint, are studied: the methods based on the pivot of the instantaneous helical axis (PIHA) or the finite helical axis (PFHA), and the “symmetrical center of rotation estimation” (SCoRE). A procedure for correcting the effect of soft tissue artifacts is also proposed, based on the equations of those techniques and a model of the artifact, like the one that can be obtained by double calibration. An experiment with a mechanical analog was performed to validate the procedure and compare the performance of each technique. The raw error (between 57 and 68 mm) was reduced by a proportion of between 1:6 and less than 1:15, depending on the artifact model and the mathematical method. The best corrections were obtained by the SCoRE method. Some recommendations about the experimental setup for functional calibration techniques and the choice of a mathematical method are derived from theoretical considerations about the formulas and the results of the experiment.     

Analytical study of the effects of soft tissue artefacts on functional techniques to define axes of rotation

The accurate location of the main axes of rotation (AoR) is a crucial step in many applications of human movement analysis. There are different formal methods to determine the direction and position of the AoR, whose performance varies across studies, depending on the pose and the source of errors. Most methods are based on minimizing squared differences between observed and modelled marker positions or rigid motion parameters, implicitly assuming independent and uncorrelated errors, but the largest error usually results from soft tissue artefacts (STA), which do not have such statistical properties and are not effectively cancelled out by such methods. However, with adequate methods it is possible to assume that STA only account for a small fraction of the observed motion and to obtain explicit formulas through differential analysis that relate STA components to the resulting errors in AoR parameters. In this paper such formulas are derived for three different functional calibration techniques (Geometric Fitting, mean Finite Helical Axis, and SARA), to explain why each technique behaves differently from the others, and to propose strategies to compensate for those errors. These techniques were tested with published data from a sit-to-stand activity, where the true axis was defined using bi-planar fluoroscopy. All the methods were able to estimate the direction of the AoR with an error of less than 5°, whereas there were errors in the location of the axis of 30–40 mm. Such location errors could be reduced to less than 17 mm by the methods based on equations that use rigid motion parameters (mean Finite Helical Axis, SARA) when the translation component was calculated using the three markers nearest to the axis.     

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.     

Instantaneous centers of rotation for lumbar segmental extension in vivo

The study aimed to map instantaneous centers of rotation (ICRs) of lumbar motion segments during a functional lifting task and examine differences across segments and variations caused by magnitude of weight lifted. Eleven healthy participants lifted loads of three different magnitudes (4.5, 9, and 13.5 kg) from a trunk-flexed (~75°) to an upright position, while being imaged by a dynamic stereo X-ray (DSX) system. Tracked lumbar vertebral (L2-S1) motion data were processed into highly accurate 6DOF intervertebral (L2L3, L3L4, L4L5, L5S1) kinematics. ICRs were computed using the finite helical axis method. Effects of segment level and load magnitude on the anterior-posterior (AP) and superior-inferior (SI) ICR migration ranges were assessed with a mixed-effects model. Further, ICRs were averaged to a single center of rotation (COR) to assess segment-specific differences in COR AP- and SI-coordinates. The AP range was found to be significantly larger for L2L3 compared to L3L4 (p=0.02), L4L5 and L5S1 (p<0.001). Average ICR SI location was relatively higher – near the superior endplate of the inferior vertebra – for L4L5 and L5SI compared to L2L3 and L3L4 (p≤0.001) – located between the mid-transverse plane and superior endplate of the inferior vertebra – but differences were not significant amongst themselves (p>0.9). Load magnitude had a significant effect only on the SI component of ICR migration range (13.5 kg>9 kg and 4.5 kg; p=0.049 and 0.017 respectively). The reported segment-specific ICR data exemplify improved input parameters for lumbar spine biomechanical models and design of disc replacements, and base-line references for potential diagnostic applications.     

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.     

Comparison of three formal methods used to estimate the functional axis of rotation: an extensive in-vivo analysis performed on the knee joint

Estimating the main axis of rotation (AoR) of a human joint represents an important issue in biomechanics. This study compared three formal methods used to estimate functional AoR, namely a cylindrical fitting method, a mean helical axis transformation, and a symmetrical axis approach. These methods were tested on 106 subjects undergoing navigated total knee arthroplasty. AoR orientation in 3D and in the frontal and coronal planes provided by each method was compared to the transepicondylar axis direction. Although all the methods resulted effective, significant differences were identified among them, relatively to the orientation in 3D and in the frontal plane projection. This was probably due to the presence of secondary rotations during the first degrees of knee flexion.     

Refining the structure of the Halobacterium salinarum flagellar filament using the iterative helical real space reconstruction method: insights into polymorphism

The eubacterial flagellar filament is an external, self-assembling, helical polymer approximately 220 A in diameter constructed from a highly conserved monomer, flagellin, which polymerizes externally at the distal end. The archaeal filament is only approximately 100 A in diameter, assembles at the proximal end and is constructed from different, glycosylated flagellins. Although the phenomenology of swimming is similar to that of eubacteria, the symmetry of the archebacterial filament is entirely different. Here, we extend our previous study on the flagellar coiled filament structure of strain R1M1 of Halobacterium salinarum. We use strain M175 of H.salinarum, which forms poly-flagellar bundles at high yield which, under conditions of relatively low ionic-strength (0.8 M versus 5 M) and low pH ( approximately 2.5 versus approximately 6.8), form straight filaments. We demonstrated previously that a single-particle approach to helical reconstruction has many advantages over conventional Fourier-Bessel methods when dealing with variable helical symmetry and heterogeneity. We show here that when this method is applied to the ordered helical structure of the archebacterial uncoiled flagellar filament, significant extensions in resolution can be obtained readily when compared to applying traditional helical techniques. The filament population can be separated into classes of different morphologies, which may represent polymorphic states. Using cryo-negatively stained images, a resolution of approximately 10-15 A has been achieved. Single alpha-helices can be fit into the reconstruction, supporting the proposed similarity of the structure to that of type IV bacterial pili.     

Modelling the dynamic margins of stability for use in evaluations of balance following a support-surface perturbation

The dynamic margin of stability provides a method that captures the center of mass (CoM) state (position-velocity) in relation to the base of support (BoS). However, the model upon which this concept was derived does not consider how the inertial characteristics of forced support-surface perturbations would influence balance control. Within the current article, the inverted pendulum model was restructured to account for fixed, piecewise accelerations of the BoS. From this logic, two variations of the adjusted margin of stability, each maintaining a similar definition of extrapolated CoM, are proposed; one ignoring horizontal ground contact and inertial forces applied to the BoS, the other incorporating these forces. Unique within the proposed models is the time-variant BoS boundaries that depend on the perturbation applied. Verification of the solution for each model is provided, along with a comparison of obtained values to previous methods of defining CoM position-velocity stability metrics using a computational model and optimal control. For the simpler model variation (ignoring forces), we also assessed how CoM position and perturbation parameter selection over/underestimate the predicted maximal permissible velocity. The results of these analyses suggest that factors which increase the acceleration impulse decrease the difference between the two models; the opposite was observed for factors increasing displacements between the CoM and BoS boundary. Lastly, use of the proposed adjusted margin of stability within an experimental data set highlights the ability of our model to predict instability (stepping strategies; negative margin of stability) relative to the use of the extrapolated CoM alone.     

Centre of resistance and centre of rotation of a tooth: experimental determination,computer simulation and the effect of tissue nonlinearity

The centre of resistance and centre of rotation of a tooth are key concepts in orthodontics. Determining the coordinates of these points is essential for planning orthodontic tooth movement. The paper proposes a procedure for experimental determination of the two centres, verifies a previously developed mathematical theory through computer simulations and evaluates the effect of nonlinearity of the periodontal ligament on the parameters related to the centres. The paper relies on the mathematical theory of a rigid body embedded in an elastic medium, physical experiment, finite element method and a simple nonlinear theory of the tooth. The concept of the centre of resistance requires a revision if nonlinearity is taken into account.     

Fibers of tau fragments, but not full length tau, exhibit a cross beta-structure: implications for the formation of paired helical filaments

We have used X-ray fiber diffraction to probe the structure of fibers of tau and tau fragments. Fibers of fragments from the microtubule binding domain had a cross beta-structure that closely resembles that reported both for neurofibrillary tangles found in Alzheimer's disease brain and for fibrous lesions from other protein folding diseases. In contrast, fibers of full-length tau had a different, more complex structure. Despite major differences at the molecular level, all fiber types exhibited very similar morphology by electron microscopy. These results have a number of implications for understanding the etiology of Alzheimer's and other tauopathic diseases. The morphology of the peptide fibers suggests that the region in tau corresponding to the peptides plays a critical role in the nucleation of fiber assembly. The dramatically different structure of the full length tau fibers suggests that some region in tau has enough inherent structure to interfere with the formation of cross beta-fibers. Additionally, the similar appearance by electron microscopy of fibrils with varying molecular structure suggests that different molecular arrangements may exist in other samples of fibers formed from tau.     

有机无机肥配施提高麦-稻轮作系统中水稻氮肥利用率的机制

采用盆栽试验,研究了有机无机肥配施对麦-稻轮作系统中水稻氮素累积动态和土壤氮素供应动态的影响,并从微生物学角度探讨了有机无机肥协同提高水稻氮肥利用率的机制.结果表明：有机无机肥配施处理的土壤微生物生物量碳、氮和矿质态氮在水稻分蘖期前低于化肥处理,而在抽穗期至灌浆期显著高于其他处理.土壤氮素供应动态与水稻吸收利用氮素规律吻合程度最高,促进了水稻产量、生物量和氮素累积量的增加,显著提高了水稻的氮肥利用率.其主要机制是有机无机肥配施促进了土壤微生物繁殖,使其在水稻生育前期固持了较多的矿质氮,在水稻生育中、后期这些氮素逐渐被释放以供水稻吸收利用,较好地满足了水稻各阶段生长发育对氮素养分的需求.     

A kinematic method for computing the motion of the body centre-of-mass (CoM) during walking: a Bayesian approach

The gait pattern of a particular patient can be altered in a large set of pathologies. Tracking the body centre-of-mass (CoM) during the gait allows a quantitative evaluation of these diseases at comparing the gait with normal patterns. A correct estimation of this variable is still an open question because of its non-linearity and inaccurate location. This paper presents a novel strategy for tracking the CoM, using a biomechanical gait model whose parameters are determined by a Bayesian strategy. A particle filter is herein implemented for predicting the model parameters from a set of markers located at the sacral zone. The present approach is compared with other conventional tracking methods and decreases the calculated root mean squared error in about a 56% in the x-axis and 59% in the y-axis.     

Evaluation of a two‐part regression calibration to adjust for dietary exposure measurement error in the Cox proportional hazards model: A simulation study

Dietary questionnaires are prone to measurement error, which bias the perceived association between dietary intake and risk of disease. Short‐term measurements are required to adjust for the bias in the association. For foods that are not consumed daily, the short‐term measurements are often characterized by excess zeroes. Via a simulation study, the performance of a two‐part calibration model that was developed for a single‐replicate study design was assessed by mimicking leafy vegetable intake reports from the multicenter European Prospective Investigation into Cancer and Nutrition (EPIC) study. In part I of the fitted two‐part calibration model, a logistic distribution was assumed; in part II, a gamma distribution was assumed. The model was assessed with respect to the magnitude of the correlation between the consumption probability and the consumed amount (hereafter, cross‐part correlation), the number and form of covariates in the calibration model, the percentage of zero response values, and the magnitude of the measurement error in the dietary intake. From the simulation study results, transforming the dietary variable in the regression calibration to an appropriate scale was found to be the most important factor for the model performance. Reducing the number of covariates in the model could be beneficial, but was not critical in large‐sample studies. The performance was remarkably robust when fitting a one‐part rather than a two‐part model. The model performance was minimally affected by the cross‐part correlation.     

A method for studying tissue specificity of maternally affected Drosophila melanogaster mutants: mosaic analysis of cinnamon.

Mosaic analysis is introduced to study tissue specificity of the maternal effect which characterizes the wild-type allele of cinnamon (=cin). The methodology presented is applicable to studies of other maternal effect mutations, as well as to female or male sterility mutations. One hundred and forty-three pal-induced fertile cin-mosaic females were obtained, and the degree to which they were capable of maternally affecting their homozygous cin daughters was correlated to their cuticular and germinal genetic constitution. From this analysis the following conclusions are drawn: (1) The presence of a wild-type (cin⁺) allele in maternal germ cells constitutes a sufficient condition for the full expression of the cin⁺ characteristic maternal effect: All cin offspring derived from such cells have normal viability and eye color. (2) This effect is confined to the descendants of a particular germ cell and does not extend to the descendants of other non-cin⁺ germ cells in the same or in a neighboring ovary. (3) A wild-type allele in a germ cell constitutes a necessary condition for the eye color maternal effect. (4) When a maternal germ line is wholly mutant, nonmutant constitution of an additional focus may result in rescue of more than half of the homozygous cin offspring (all with mutant eye color). Mosaic analysis suggests that this somatic viability focus originates from the posterior region of the blastoderm. These conclusions were tested and confirmed by transplanting heterozygous cin ovaries, wild-type Malphigian tubes, and wild-type fat body into homozygous cin hosts. In addition, transplantations of homozygous cin ovaries into wild-type hosts suggest that the posterior maternal viability focus corresponds to the mesodermal components of the ovaries.     

Leveling the playing field: Evaluation of a portable instrument for quantifying balance performance

Balance is a complex, sensorimotor task requiring an individual to maintain the center of gravity within the base of support. Quantifying balance in a reliable and valid manner is essential to evaluating disease progression, aging complications, and injuries in clinical and research settings. Typically, researchers use force plates to track motion of the center of gravity during a variety of tasks. However, limiting factors such as cost, portability, and availability have hindered postural stability evaluation in these settings. This study compared the “gold standard” for assessing postural stability (i.e., the laboratory-grade force plate) to a more affordable and portable assessment tool (i.e., BTrackS balance plate) in healthy young adults. Correlations and Bland-Altman plots between the center of pressure outcome measures derived from these two instruments were produced. Based on the results of this study, the measures attained from the portable balance plate objectively quantified postural stability with high validity on both rigid and compliant surfaces, demonstrated by thirty-five out of thirty-eight observed postural stability metrics in both surface conditions with a correlation of 0.98 or greater. The low cost, portable system performed similarly to the lab-grade force plate indicating the potential for practitioners and researchers to use the BTrackS balance plate as an alternative to the more expensive force plate option for assessing postural stability, whether in the lab setting or in the field.     

Evaluating the performance of sampling plans for phycotoxins in shellfish: Improvement of an existing method

According to the EU Regulation 854/2004, sampling plans must be set up to monitor production areas for the level of okadaic acid (OA) equivalents in live mussel. The level of these toxins, which are produced by harmful algal blooms, must not exceed 160 μg/kg of raw meat (Regulation 853/2004/EC). A sampling plan assessment consists in obtaining an OC (Operating Characteristic) curve showing both consumer and producer risks. The first risk is the risk of opening a shellfish area for harvest while the contamination level is above the threshold; whereas the second risk is the risk of closing a shellfish area having a contamination level under the threshold.For sampling plan validation purposes, a classical mathematical method was improved for the prediction of variance as function of the mean contamination level thanks to prior knowledge of the theoretical distribution fitting the observed OA levels among individual mussels. Indeed, knowing that, thanks to a regression analysis of literature data, for the lognormal distribution the scale parameter was observed to be directly proportional to the location parameter, the regression bias could be lowered. Literature data from Norway and Sweden showed different levels of variability between contamination events and depuration. However, the highest variability level was chosen to propose a best fit sampling plan in order to have a better approach of reality. It consisted of taking two samples of 50 mussels (Mytilus sp.) for this geographic location (Norway and Sweden).     

New method of three-dimensional analysis of bipedal locomotion for the study of displacements of the body and body-parts centers of mass in man and non-human primates: Evolutionary framework

The current biomechanical interpretation of the chimpanzee's bipedal walking argues that larger lateral and vertical displacements of the body center of mass occur in the chimpanzee's “side-to-side” gait than in the human striding gait. The evolutionary hypothesis underlying this study is the following: during the evolution of human bipedalism one of the necessary changes could have been the progressive reduction of these displacements of the body center of mass. In order to quantitatively test this hypothesis, it is necessary to obtain simultaneously the trajectories of the centers of mass of the whole body and of the different body parts. To solve this problem, a new method of three-dimensional analysis of walking, associated with a volumetric modelling of the body, has been developed based on finite-element modelling. An orthogonal synchrophotographic device yielding four synchronous pictures of the walking subject allows a qualitative analysis of the photographic sequences together with the results of their quantitative analysis. This method was applied to an adult man, a 3-year-old girl and a 9-year-old male chimpanzee. Our results suggest that the trajectory of the body center of mass of the human is distinguished from that of the chimpanzee not by a lower movement amplitude but by the synchronization of the transverse and vertical displacements into two periodic curves in phase with one another. The non-human primate uses its repertoire of arboreal movements in its bipedal terrestrial gait, provisionally referred to as a “rope-walker” gait. We show that the interpretation of a “side-to-side” gait is not applicable to the chimpanzee. We argue that similarly this interpretation and the initial hypothesis presuppose a basic symmetric structure of the gait, in relation to the sagittal plane of progression, similar to the human one. This lateral symmetry of the right and left displacements of the center of gravity, in phase with the right and left single supports of walking, is probably a very derived feature of the human gait. We suggest that low lateral and vertical displacements of the body center of mass are not indicative of a progressive bipedal gait and we discuss the new evolutionary implications of our results. © 1993 Wiley-Liss, Inc.     

A calibration method to generate seasonal hatching profiles for the fiddler crabs Uca pugnax (Smith, 1870) and Uca minax (LeConte, 1855) (Decapoda : Brachyura)

A statistical method for generating seasonal egg hatching profiles is applied to the brachyuran crabs Uca pugnax (Smith) and U. minax (LeConte) in New Jersey. Calibration experiments quantified the time course of egg development, using serial egg sampling at 1- to 2- day intervals from marked ovigerous females maintained in cages in the field. Egg stage was ranked from 1 to 10, based on morphological changes during development. Equations for predicting the number of days remaining until hatching from egg developmental stage were obtained from the calibration experiments, using stepwise polynomial regression. To cover the reproductive season, three consecutive calibration experiments using 15 or more females were run for U. pugnax; two for U. minax. Significant seasonal differences in the time course of egg development were detected. Weekly collections of females for each species were made; the date of larval release for each ovigerous female was predicted from the proximate calibration equation, yielding weekly hatching profiles. Weekly hatching profiles were summed to obtain seasonal hatching profiles. The average number of broods produced per female over the reproductive season was 1.9 for U. pugnax and 1.6 for U. minax. Hatching peaks for both species were associated with spring tides. The merits of this and other methods used to estimate daily variation in egg hatching of crabs are discussed.