Serial manipulator functional calibration for in vitro biomechanical testing

Serial manipulators are often used in biomechanical testing of human joints because they are precise, repeatable instruments that can create interesting loading scenarios. Unfortunately, commercial serial manipulators often do not have acceptable global positional accuracy due to manufacturing tolerances, assembly errors, and other mechanical imperfections. Numerous calibration methods have been reported which calibrate geometric and non-geometric parameters to reduce static position errors under constant loading conditions. However, the manipulator's global accuracy during continuous motion with time-varying external loading conditions is often not addressed but is necessary for joint biomechanical testing. Using the Mitsubishi PA10-6CE as a case study, a novel functional calibration procedure was developed that performs both static and dynamic calibration. The calibration uses optimization techniques to populate a 34-parameter model that accounts for the robot's geometric and non-geometric parameters and significantly reduces the mean/peak static and dynamic position errors to 0.368/0.67 mm and 0.353/0.81 mm, respectively, while externally loaded.     

Thermal melting and circular dichroism of DNA complexes with (Lys-Ala-Ala)10 and (Lys-Ala-Ala)n: effect of polypeptide chain length

DNA complexes with polypeptides (Lys-Ala-Ala)₁)] and (Lys-Ala-Ala)₃₄ have been studied using the methods of thermal melting and circular dichroism. Derivative melting curves of (Lys-Ala-Ala)₁₀ DNA differed substantially from those of (Lys-Ala-Ala)₃₄ prepared either by salt gradient dialysis or by direct mixing. Melting curves of the former complex were unimodal or bimodal with T_m increasing continuously withn input lysin-to-DNA phosphate ratio (r); those of the latter complex consisted of three separate transitions with T_m values almost independent of r. Complete reversibility of binding in the (Lys-Ala-Ala)₁₀-DNA system but a slow redistribution of (Lys-Ala-Ala)₃₄ on DNA at low temperature were found in the redistribution experiments Much faster redistribution from denatured to native DNA occurs at the temperature of melting, contributing to the unusual trimodal melting pattern. Circular dichroism curves are very similar for both complexes and indicate little change of DNA conformation upon polypeptide binding.     

Estimation of Individual Growth Curves by Empirically Weighted Least Squares

The simultaneous estimation of individual growth curves and a mean growth curve is accomplished by weighted least squares. A polynomial curve is fitted for each individual and the polynomial parameters are linear functions of parameters corresponding to covariates. A simple, computationally efficient variance-covariance estimator is derived. The resultant estimate is used in the weighted least squares estimation. The results are compared to empirical Bayes estimation.     

Prediction of yield in the Rothamsted Park Grass Experiment by Ellenberg indicator values

Abstract. The Rothamsted Park Grass Experiment was established in 1856, with experimental plots subjected to annual applications of fertilizer and twice-yearly cutting of hay. There were two major responses to fertilizer, one reflecting high ammonium-nitrogen and increased acidity and the other reflecting high herbage yield without increased acidity. We calculated mean Ellenberg indicator values for N (nitrogen) and R (soil reaction) for the hay harvested between 1948 and 1975, using both unweighted and abundance-weighted means. Plot Ellenberg values were compared with herbage yield and with fertilizer application rates and published soil data. Annual yield of hay varied from 1.5 to 7.4 t/ha and was well predicted by the unweighted mean Ellenberg N-values (r = 0.91). Relatively large negative residuals from the relationship were found in plots whose soil combined low K and low pH. Soil pH was poorly predicted by the unweighted mean R-value, but showed a moderately good relation with weighted mean R (r = 0.73). The fact that Ellenberg N-values correlated better with yield than with applied nitrogen suggests that they might rather be called productivity values.     

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.     

A method to measure predictive ability of an injury risk curve using an observation-adjusted area under the receiver operating characteristic curve

Area under the receiver operating characteristic curve (AROC) is commonly used to choose a biomechanical metric from which to construct an injury risk curve (IRC). However, AROC may not handle censored datasets adequately. Survival analysis creates robust estimates of IRCs which accommodate censored data. We present an observation-adjusted ROC (oaROC) which uses the survival-based IRC to estimate the AROC. We verified and evaluated this method using simulated datasets of different censoring statuses and sample sizes. For a dataset with 1000 left and right censored observations, the median AROC closely approached the oaROC_True, or the oaROC calculated using an assumed “true” IRC, differing by a fraction of a percent, 0.1%. Using simulated datasets with various censoring, we found that oaROC converged onto oaROC_True in all cases. For datasets with right and non-censored observations, AROC did not converge onto oaROC_True. oaROC for datasets with only non-censored observations converged the fastest, and for a dataset with 10 observations, the median oaROC differed from oaROC_True by 2.74% while the corresponding median AROC with left and right censored data differed from oaROC_True by 9.74%. We also calculated the AROC and oaROC for a published side impact dataset, and differences between the two methods ranged between −24.08% and 24.55% depending on metric. Overall, when compared with AROC, we found oaROC performs equivalently for doubly censored data, better for non-censored data, and can accommodate more types of data than AROC. While more validation is needed, the results indicate that oaROC is a viable alternative which can be incorporated into the metric selection process for IRCs.     

Evaluation of knee functional calibration with and without the effect of soft tissue artefact

Functional calibration methods were devised to improve repeatability and accuracy of the knee flexion–extension axis, which is used to define the medio-lateral axis of the femur coordinate system in gait analysis. Repeatability of functional calibration methods has been studied extensively in healthy individuals, but not accuracy in the absence of a benchmark knee axis. We captured bi-plane fluoroscopy data of the knee joint in 17 subjects with unilateral total knee arthroplasty during treadmill walking. The prosthesis provided a benchmark knee axis to evaluate the functional calibration methods. Stereo-photogrammetry data of thigh and shank marker clusters were captured simultaneously to investigate the effect of soft tissue artefact (STA). Three methods were tested, the Axis Transformation Technique (ATT) finds the best single fixed axis of rotation, 2DofKnee finds the axis that minimises knee varus–valgus and trajAJC finds the axis perpendicular to the trajectory, in the transverse plane of the femur, of a point located on the longitudinal axis of the tibia. Using fluoroscopy data, functional axes formed an angle of less than 2° in the transverse plane with the benchmark axis. True internal–external range of movement was correlated with decreased accuracy for ATT, while varus–valgus range of movement was correlated with decreased accuracy for 2DofKnee and trajAJC. STA had negative impact on accuracy and variability. Using stereo-photogrammetry data, the accuracy of 2DofKnee was 1.7°(SD: 5.1°), smaller than ATT 2.9°(SD: 5.1°) but not to trajAJC 1.7°(SD: 5.2°). Our results confirm that of previous studies, which utilised the femur condylar axis as reference.     

A Growth Curve Analysis for Bulls Tested at Station

Data on 2712 bulls tested at station were analysed to study the effect of certain external variables on growth traits of bulls. Most of the animals were Ayrshires (2136). Otherwise Finncattle bulls and Frisian bulls were involved. The testing covers the interval 60–365 days of age, although in part of the data the period is 30–365. Bulls were weighted every 30th day (between 1965 and 1970), or at the ages of 60 and 180 days, and thereafter every 30 days up to the age of 365 days (between 1971 and 1977). Also birth weight was available for 1250 calves. Feeding and general treatment of bulls at station was as uniform as possible for all animals. Conseqúently it can be assumed that effects of non-genetic factors on the growth traits of bulls are minimized. One of the objectives of this study was to compare the growth curves for the three breeds. In our data measurements at certain time-points have dropped out during the course of data collection. Therefore we study the influence of deleting measurements. We also consider the problem of influential measurements at both the design level and the inference level. Several types of growth curves are fitted to the data in order to find the most appropriate model.     

Shapes and functions of species–area curves (II): a review of new models and parameterizations

This paper has extended and updated my earlier list and analysis of candidate models used in theoretical modelling and empirical examination of species–area relationships (SARs). I have also reviewed trivariate models that can be applied to include a second independent variable (in addition to area) and discussed extensively the justifications for fitting curves to SARs and the choice of model. There is also a summary of the characteristics of several new candidate models, especially extended power models, logarithmic models and parameterizations of the negative-exponential family and the logistic family. I have, moreover, examined the characteristics and shapes of trivariate linear, logarithmic and power models, including combination variables and interaction terms. The choice of models according to best fit may conflict with problems of non-normality or heteroscedasticity. The need to compare parameter estimates between data sets should also affect model choice. With few data points and large scatter, models with few parameters are often preferable. With narrow-scale windows, even inflexible models such as the power model and the logarithmic model may produce good fits, whereas with wider-scale windows where inflexible models do not fit well, more flexible models such as the second persistence (P2) model and the cumulative Weibull distribution may be preferable. When extrapolations and expected shapes are important, one should consider models with expected shapes, e.g. the power model for sample area curves and the P2 model for isolate curves. The choice of trivariate models poses special challenges, which one can more effectively evaluate by inspecting graphical plots.