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.     

A closer look at the distribution of number needed to treat (NNT): a Bayesian approach

In this paper, I present a Bayesian approach to estimation of the number needed to treat (NNT). The use of NNT as a measure of clinical benefit is now becoming commonplace. Various methods of estimation have been proposed, but none of them seem to provide entirely good estimates. Very little has been done to understand the statistical properties of NNT. Here, I derive the posterior distribution of NNT and use simulations to investigate the general behaviour of the distribution. The posterior mode of the distribution is proposed as a point estimate and results are compared with the conventional method of estimation of NNT done by inversion.     

A multi-segment kinematic model of the foot with a novel definition of forefoot motion for use in clinical gait analysis during walking

A multi-segment kinematic model of the foot was developed for use in a gait analysis laboratory. The foot was divided into hindfoot, talus, midfoot and medial and lateral forefoot segments. Six functional joints were defined: ankle and subtalar joints, frontal and transverse plane motions of the hindfoot relative to midfoot, supination/pronation twist of the forefoot relative to midfoot and medial longitudinal arch height-to-length ratio. Twelve asymptomatic subjects were tested during barefoot walking with a six-camera optical stereometric system and auto-reflective markers organized in triads. Repeatability of the joint motions was tested using coefficients of multiple correlation. Ankle and subtalar joint motions and twisting of the forefoot were most repeatable. Hindfoot motions were least repeatable both within-subjects and between-subjects. Hindfoot and forefoot pronation in the frontal plane was found to coincide with dropping of the medial longitudinal arch between early to mid-stance, followed by supination and rising of the arch in late stance and swing phase. This multi-segment foot model addresses an unfortunate shortcoming in current gait analysis practice-the inability to measure motion within the foot. Such measurements are crucial if gait analysis is to remain relevant in the orthopaedic and rehabilitative treatment of the foot and ankle.     

A Bayesian method for classification of images from electron micrographs

Particle classification is an important component of multivariate statistical analysis methods that has been used extensively to extract information from electron micrographs of single particles. Here we describe a new Bayesian Gibbs sampling algorithm for the classification of such images. This algorithm, which is applied after dimension reduction by correspondence analysis or by principal components analysis, dynamically learns the parameters of the multivariate Gaussian distributions that characterize each class. These distributions describe tilted ellipsoidal clusters that adaptively adjust shape to capture differences in the variances of factors and the correlations of factors within classes. A novel Bayesian procedure to objectively select factors for inclusion in the classification models is a component of this procedure. A comparison of this algorithm with hierarchical ascendant classification of simulated data sets shows improved classification over a broad range of signal-to-noise ratios.     

BGX: a fully Bayesian integrated approach to the analysis of Affymetrix GeneChip data

We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common statistically coherent framework, allowing all components and thus associated errors to be considered simultaneously. Secondly, inference is based on the full posterior distribution of gene expression indices and derived quantities, such as fold changes or ranks, rather than on single point estimates. Measures of uncertainty on these quantities are thus available. The models presented represent the first building block for integrated Bayesian Analysis of Affymetrix GeneChip data: the models take into account additive as well as multiplicative error, gene expression levels are estimated using perfect match and a fraction of mismatch probes and are modeled on the log scale. Background correction is incorporated by modeling true signal and cross-hybridization explicitly, and a need for further normalization is considerably reduced by allowing for array-specific distributions of nonspecific hybridization. When replicate arrays are available for a condition, posterior distributions of condition-specific gene expression indices are estimated directly, by a simultaneous consideration of replicate probe sets, avoiding averaging over estimates obtained from individual replicate arrays. The performance of the Bayesian model is compared to that of standard available point estimate methods on subsets of the well known GeneLogic and Affymetrix spike-in data. The Bayesian model is found to perform well and the integrated procedure presented appears to hold considerable promise for further development.     

On the limitations of standard statistical modeling in biological systems: A full Bayesian approach for biology

One of the most important scientific challenges today is the quantitative and predictive understanding of biological function. Classical mathematical and computational approaches have been enormously successful in modeling inert matter, but they may be inadequate to address inherent features of biological systems. We address the conceptual and methodological obstacles that lie in the inverse problem in biological systems modeling. We introduce a full Bayesian approach (FBA), a theoretical framework to study biological function, in which probability distributions are conditional on biophysical information that physically resides in the biological system that is studied by the scientist.     

A general Bayesian method for an automated signal class recognition in 2D NMR spectra combined with a multivariate discriminant analysis

Summary A generally applicable method for the automated classification of 2D NMR peaks has been developed, based on a Bayesian approach coupled to a multivariate linear discriminant analysis of the data. The method can separate true NMR signals from noise signals, solvent stripes and artefact signals. The analysis relies on the assumption that the different signal classes have different distributions of specific properties such as line shapes, line widths and intensities. As to be expected, the correlation network of the distributions of the selected properties affects the choice of the discriminant function and the final selection of signal properties. The classification rule for the signal classes was deduced from Bayes's theorem. The method was successfully tested on a NOESY spectrum of HPr protein from Staphylococcus aureus. The calculated probabilities for the different signal class memberships are realistic and reliable, with a high efficiency of discrimination between peaks that are true NOE signals and those that are not.     

Evaluating the performance of a multilocus Bayesian method for the estimation of migration rates

Bayesian methods have become extremely popular in molecular ecology studies because they allow us to estimate demographic parameters of complex demographic scenarios using genetic data. Articles presenting new methods generally include sensitivity studies that evaluate their performance, but they tend to be limited and need to be followed by a more thorough evaluation. Here we evaluate the performance of a recent method, bayesass , which allows the estimation of recent migration rates among populations, as well as the inbreeding coefficient of each local population. We expand the simulation study of the original publication by considering multi-allelic markers and scenarios with varying number of populations. We also investigate the effect of varying migration rates and F _ST more thoroughly in order to identify the region of parameter space where the method is and is not able to provide accurate estimates of migration rate. Results indicate that if the demographic history of the species being studied fits the assumptions of the inference model, and if genetic differentiation is not too low ( F _ST ≥ 0.05), then the method can give fairly accurate estimates of migration rates even when they are fairly high (about 0.1). However, when the assumptions of the inference model are violated, accurate estimates are obtained only if migration rates are very low ( m  = 0.01) and genetic differentiation is high ( F _ST ≥ 0.10). Our results also show that using posterior assignment probabilities as an indication of how much confidence we can place on the assignments is problematical since the posterior probability of assignment can be very high even when the individual assignments are very inaccurate.     

A Bayesian analysis of the effect of selection for growth rate on growth curves in rabbits

Gompertz growth curves were fitted to the data of 137 rabbits from control (C) and selected (S) lines. The animals came from a synthetic rabbit line selected for an increased growth rate. The embryos from generations 3 and 4 were frozen and thawed to be contemporary of rabbits born in generation 10. Group C was the offspring of generations 3 and 4, and group S was the contemporary offspring of generation 10. The animals were weighed individually twice a week during the first four weeks of life, and once a week thereafter, until 20 weeks of age. Subsequently, the males were weighed weekly until 40 weeks of age. The random samples of the posterior distributions of the growth curve parameters were drawn by using Markov Chain Monte Carlo (MCMC) methods. As a consequence of selection, the selected animals were heavier than the C animals throughout the entire growth curve. Adult body weight, estimated as a parameter of the Gompertz curve, was 7% higher in the selected line. The other parameters of the Gompertz curve were scarcely affected by selection. When selected and control growth curves are represented in a metabolic scale, all differences disappear.     

A Monte Carlo method for Bayesian analysis of linkage between single markers and quantitative trait loci. II. A simulation study

A Bayesian approach to the statistical mapping of Quantitative Trait Loci (QTLs) using single markers was implemented via Markov Chain Monte Carlo (MCMC) algorithms for parameter estimation and hypothesis testing. Parameters were estimated by marginal posterior means computed with a Gibbs sampler with data augmentation. Variables sampled included the augmented data (marker-QTL genotypes, polygenic effects), the event of linkage or nonlinkage, and the parameters (allele frequencies, QTL substitution effect, recombination rate, polygenic and residual variances). The analysis was evaluated empirically via application to simulated granddaughter designs consisting of 2000 sons, 20 related sires and their ancestors. Results obtained in this study and preliminary work on multiple linked markers and multiple QTLs support the usefulness of the Bayesian method for the statistical mapping of QTLs.     

Single-cell recordings: a method for investigating the brain's activation pattern during exercise

The precision of human movements to generate skills as accurate as the exercises performed by athletes are the consequence of a long and complex learning process. These processes involve a great amount of the nervous system’s structures. Electrophysiological techniques have been largely used to highlight brain functions related to the control of these kinds of movements. These methods cover invasive and non-invasive techniques which have been applied to humans and experimental animals. We describe here electrophysiological techniques that are used in behaving animals. Especially, we will focus on the analysis and results obtained from single-cell recording in the prefrontal cortex to explain the relationship between single neuronal activity and movement during locomotion. In addition, we will show how, analyzing these results, that we can characterize the integrative role of neurons involved in the control of locomotion. The objective is to demonstrate single-cell recording techniques as suitable methods to study, in experimental animals, the brain’s activation pattern during exercise.     

A method for computing the three-dimensional angular velocity and acceleration of a body segment from three-dimensional position data

A theoretical technique, based on the Method of Least Squares, was employed to solve for the three-dimensional components of the angular velocity and acceleration of a limb segment directly from experimentally recorded three-dimensional position data. Results showed that a minimum of four targets placed on the body segment, forming six relative position vector equations, were required to produce the most accurate results. It was also found that this method eliminates the errors due to soft tissue motion and system noise.     

A Bayesian approach to estimate the age-specific prevalence of Schistosoma mansoni and implications for schistosomiasis control

Models that accurately estimate the age-specific infection prevalence of Schistosoma mansoni can be useful for schistosomiasis control programmes, particularly with regard to whether mass drug administration or selected treatment should be employed. We developed a Bayesian formulation of an immigration-death model that has been previously proposed, which used maximum likelihood inference for estimating the age-specific S. mansoni prevalence in a dataset from Egypt. For comparative purposes, we first applied the Bayesian formulation of the immigration-death model to the dataset from Egypt. We further analysed data obtained from a cross-sectional parasitological survey that determined the infection prevalence of S. mansoni among 447 individuals in a village in C?te d'Ivoire. Three consecutive stool samples were collected from each participant and analysed by the Kato-Katz technique. In the C?te d'Ivoire study, the observed S. mansoni infection prevalence was 41.6% and varied with age. The immigration-death model was able to correctly predict 50% of the observed age group-specific point prevalences. The model presented here can be utilized to estimate S. mansoni community infection prevalences, which in turn helps in the strategic planning of schistosomiasis control.     

A spatial analysis method (SAM) to detect candidate loci for selection: towards a landscape genomics approach to adaptation

The detection of adaptive loci in the genome is essential as it gives the possibility of understanding what proportion of a genome or which genes are being shaped by natural selection. Several statistical methods have been developed which make use of molecular data to reveal genomic regions under selection. In this paper, we propose an approach to address this issue from the environmental angle, in order to complement results obtained by population genetics. We introduce a new method to detect signatures of natural selection based on the application of spatial analysis, with the contribution of geographical information systems (GIS), environmental variables and molecular data. Multiple univariate logistic regressions were carried out to test for association between allelic frequencies at marker loci and environmental variables. This spatial analysis method (SAM) is similar to current population genomics approaches since it is designed to scan hundreds of markers to assess a putative association with hundreds of environmental variables. Here, by application to studies of pine weevils and breeds of sheep we demonstrate a strong correspondence between SAM results and those obtained using population genetics approaches. Statistical signals were found that associate loci with environmental parameters, and these loci behave atypically in comparison with the theoretical distribution for neutral loci. The contribution of this new tool is not only to permit the identification of loci under selection but also to establish hypotheses about ecological factors that could exert the selection pressure responsible. In the future, such an approach may accelerate the process of hunting for functional genes at the population level.     

A general-purpose framework to simulate musculoskeletal system of human body: using a motion tracking approach*

Computation of muscle force patterns that produce specified movements of muscle-actuated dynamic models is an important and challenging problem. This problem is an undetermined one, and then a proper optimization is required to calculate muscle forces. The purpose of this paper is to develop a general model for calculating all muscle activation and force patterns in an arbitrary human body movement. For this aim, the equations of a multibody system forward dynamics, which is considered for skeletal system of the human body model, is derived using Lagrange–Euler formulation. Next, muscle contraction dynamics is added to this model and forward dynamics of an arbitrary musculoskeletal system is obtained. For optimization purpose, the obtained model is used in computed muscle control algorithm, and a closed-loop system for tracking desired motions is derived. Finally, a popular sport exercise, biceps curl, is simulated by using this algorithm and the validity of the obtained results is evaluated via EMG signals.     

A cladistic and comparative analysis of kinematic components of the fast-start of fishes,with a note on body size constraints

The fast-start is an ecologically relevant behavior pattern in fishes. The present article analyses the distribution of five continuous kinematic traits (latency for response initiation, time to maximum angular velocity, time to maximum displacement velocity, maximum angular velocity, and maximum displacement velocity) in eight of the eleven species described in Eaton (66:65–81, 1977). Phylogenetic generalized least square estimation of ancestor states demonstrated evolutionary changes in maximum angular velocity and maximum displacement velocity, consistent with species differences in the same variables. These changes in maximum velocity are also correlated (phylogenetically independent contrasts) with the mean body sizes of all species, pointing to the possibility that body size was an evolutionary constraint on maximum velocities. The conservation of the other traits suggest that they are mainly constrained by neural control, and a trade-off between neural and body size-constraints is proposed ex hypothesi. An erratum to this article can be found at     

The evolution of ecomorphological traits within the Abrothrichini (Rodentia: Sigmodontinae): a Bayesian phylogenetics approach

The generally accepted hypothesis regarding the origin of fossorial mammals proposes adaptive convergence from open environments towards the use of subterranean environments. We evaluated this hypothesis for South American mole-mice using conventional and Bayesian frameworks, with independent evidence. By using a molecular approach based on Cytochrome b and IRBP sequences, we evaluated phylogenetic relationships, time of origin, the ancestral trait of fossoriality, and ancestral distributions of species belonging to the Andean Clade (Rodentia: Sigmodontinae). Our results indicate that the Andean Clade is highly sustained; with one clade grouping all fossorial forms and another grouping all cursorial species. We hypothesized that fossoriality originated in the Miocene/Pliocene transition, in the Temperate Forests of southern South America. We conclude that the origin of fossorial ecomorphological traits did not necessarily occur under a general model of open environments, the origin of these traits depends on the ecological-historical relationship of the taxon with the environment.     

Accounting for phylogenetic uncertainty in biogeography: a Bayesian approach to dispersal-vicariance analysis of the thrushes (Aves: Turdus)

The phylogeny of the thrushes (Aves: Turdus) has been difficult to reconstruct due to short internal branches and lack of node support for certain parts of the tree. Reconstructing the biogeographic history of this group is further complicated by the fact that current implementations of biogeographic methods, such as dispersal-vicariance analysis (DIVA; Ronquist, 1997), require a fully resolved tree. Here, we apply a Bayesian approach to dispersal-vicariance analysis that accounts for phylogenetic uncertainty and allows a more accurate analysis of the biogeographic history of lineages. Specifically, ancestral area reconstructions can be presented as marginal distributions, thus displaying the underlying topological uncertainty. Moreover, if there are multiple optimal solutions for a single node on a certain tree, integrating over the posterior distribution of trees often reveals a preference for a narrower set of solutions. We find that despite the uncertainty in tree topology, ancestral area reconstructions indicate that the Turdus clade originated in the eastern Palearctic during the Late Miocene. This was followed by an early dispersal to Africa from where a worldwide radiation took place. The uncertainty in tree topology and short branch lengths seems to indicate that this radiation took place within a limited time span during the Late Pliocene. The results support the role of Africa as a probable source area for intercontinental dispersals as suggested for other passerine groups, including basal diversification within the songbird tree.