Vector field statistical analysis of kinematic and force trajectories

When investigating the dynamics of three-dimensional multi-body biomechanical systems it is often difficult to derive spatiotemporally directed predictions regarding experimentally induced effects. A paradigm of ‘non-directed’ hypothesis testing has emerged in the literature as a result. Non-directed analyses typically consist of ad hoc scalar extraction, an approach which substantially simplifies the original, highly multivariate datasets (many time points, many vector components). This paper describes a commensurately multivariate method as an alternative to scalar extraction. The method, called ‘statistical parametric mapping’ (SPM), uses random field theory to objectively identify field regions which co-vary significantly with the experimental design. We compared SPM to scalar extraction by re-analyzing three publicly available datasets: 3D knee kinematics, a ten-muscle force system, and 3D ground reaction forces. Scalar extraction was found to bias the analyses of all three datasets by failing to consider sufficient portions of the dataset, and/or by failing to consider covariance amongst vector components. SPM overcame both problems by conducting hypothesis testing at the (massively multivariate) vector trajectory level, with random field corrections simultaneously accounting for temporal correlation and vector covariance. While SPM has been widely demonstrated to be effective for analyzing 3D scalar fields, the current results are the first to demonstrate its effectiveness for 1D vector field analysis. It was concluded that SPM offers a generalized, statistically comprehensive solution to scalar extraction's over-simplification of vector trajectories, thereby making it useful for objectively guiding analyses of complex biomechanical systems.     

Poisson's ratio of bovine meniscus determined combining unconfined and confined compression

Poisson's ratio has not been experimentally measured earlier for meniscus in compression. It is however an important intrinsic material property needed in biomechanical analysis and computational models. In this study, equilibrium Poisson's ratio of bovine meniscus (n = 6) was determined experimentally by combining stress-relaxation measurements in unconfined and confined compression geometries. The average Young's modulus, aggregate modulus and Poisson's ratio were 0.182 ± 0.086 MPa, 0.252 ± 0.089 MPa and 0.316 ± 0.040, respectively. These moduli are consistent with previously determined values, but the Poisson’s ratio is higher than determined earlier for meniscus in compression through biomechanical modelling analysis. This new experimentally determined Poisson’s ratio value could be used in the analysis of biomechanical data as well as in computational finite element analysis when the Poisson’s ratio is needed as an input for the analysis.     

Tree Branching: Leonardo da Vinci's Rule versus Biomechanical Models

This study examined Leonardo da Vinci''s rule (i.e., the sum of the cross-sectional area of all tree branches above a branching point at any height is equal to the cross-sectional area of the trunk or the branch immediately below the branching point) using simulations based on two biomechanical models: the uniform stress and elastic similarity models. Model calculations of the daughter/mother ratio (i.e., the ratio of the total cross-sectional area of the daughter branches to the cross-sectional area of the mother branch at the branching point) showed that both biomechanical models agreed with da Vinci''s rule when the branching angles of daughter branches and the weights of lateral daughter branches were small; however, the models deviated from da Vinci''s rule as the weights and/or the branching angles of lateral daughter branches increased. The calculated values of the two models were largely similar but differed in some ways. Field measurements of Fagus crenata and Abies homolepis also fit this trend, wherein models deviated from da Vinci''s rule with increasing relative weights of lateral daughter branches. However, this deviation was small for a branching pattern in nature, where empirical measurements were taken under realistic measurement conditions; thus, da Vinci''s rule did not critically contradict the biomechanical models in the case of real branching patterns, though the model calculations described the contradiction between da Vinci''s rule and the biomechanical models. The field data for Fagus crenata fit the uniform stress model best, indicating that stress uniformity is the key constraint of branch morphology in Fagus crenata rather than elastic similarity or da Vinci''s rule. On the other hand, mechanical constraints are not necessarily significant in the morphology of Abies homolepis branches, depending on the number of daughter branches. Rather, these branches were often in agreement with da Vinci''s rule.     

Copula‐based semiparametric models for spatiotemporal data

The joint analysis of spatial and temporal processes poses computational challenges due to the data's high dimensionality. Furthermore, such data are commonly non‐Gaussian. In this paper, we introduce a copula‐based spatiotemporal model for analyzing spatiotemporal data and propose a semiparametric estimator. The proposed algorithm is computationally simple, since it models the marginal distribution and the spatiotemporal dependence separately. Instead of assuming a parametric distribution, the proposed method models the marginal distributions nonparametrically and thus offers more flexibility. The method also provides a convenient way to construct both point and interval predictions at new times and locations, based on the estimated conditional quantiles. Through a simulation study and an analysis of wind speeds observed along the border between Oregon and Washington, we show that our method produces more accurate point and interval predictions for skewed data than those based on normality assumptions.     

A comparison of methods for classifying clinical samples based on proteomics data: a case study for statistical and machine learning approaches

The discovery of protein variation is an important strategy in disease diagnosis within the biological sciences. The current benchmark for elucidating information from multiple biological variables is the so called “omics” disciplines of the biological sciences. Such variability is uncovered by implementation of multivariable data mining techniques which come under two primary categories, machine learning strategies and statistical based approaches. Typically proteomic studies can produce hundreds or thousands of variables, p, per observation, n, depending on the analytical platform or method employed to generate the data. Many classification methods are limited by an n≪p constraint, and as such, require pre-treatment to reduce the dimensionality prior to classification. Recently machine learning techniques have gained popularity in the field for their ability to successfully classify unknown samples. One limitation of such methods is the lack of a functional model allowing meaningful interpretation of results in terms of the features used for classification. This is a problem that might be solved using a statistical model-based approach where not only is the importance of the individual protein explicit, they are combined into a readily interpretable classification rule without relying on a black box approach. Here we incorporate statistical dimension reduction techniques Partial Least Squares (PLS) and Principal Components Analysis (PCA) followed by both statistical and machine learning classification methods, and compared them to a popular machine learning technique, Support Vector Machines (SVM). Both PLS and SVM demonstrate strong utility for proteomic classification problems.     

Assessing the significance of pedobarographic signals using random field theory

Traditional pedobarographic statistical analyses are conducted over discrete regions. Recent studies have demonstrated that regionalization can corrupt pedobarographic field data through conflation when arbitrary dividing lines inappropriately delineate smooth field processes. An alternative is to register images such that homologous structures optimally overlap and then conduct statistical tests at each pixel to generate statistical parametric maps (SPMs). The significance of SPM processes may be assessed within the framework of random field theory (RFT). RFT is ideally suited to pedobarographic image analysis because its fundamental data unit is a lattice sampling of a smooth and continuous spatial field. To correct for the vast number of multiple comparisons inherent in such data, recent pedobarographic studies have employed a Bonferroni correction to retain a constant family-wise error rate. This approach unfortunately neglects the spatial correlation of neighbouring pixels, so provides an overly conservative (albeit valid) statistical threshold. RFT generally relaxes the threshold depending on field smoothness and on the geometry of the search area, but it also provides a framework for assigning p values to suprathreshold clusters based on their spatial extent. The current paper provides an overview of basic RFT concepts and uses simulated and experimental data to validate both RFT-relevant field smoothness estimations and RFT predictions regarding the topological characteristics of random pedobarographic fields. Finally, previously published experimental data are re-analysed using RFT inference procedures to demonstrate how RFT yields easily understandable statistical results that may be incorporated into routine clinical and laboratory analyses.     

A Toolbox for Spatiotemporal Analysis of Voltage-Sensitive Dye Imaging Data in Brain Slices

Voltage-sensitive dye imaging (VSDI) can simultaneously monitor the spatiotemporal electrical dynamics of thousands of neurons and is often used to identify functional differences in models of neurological disease. While the chief advantage of VSDI is the ability to record spatiotemporal activity, there are no tools available to visualize and statistically compare activity across the full spatiotemporal range of the VSDI dataset. Investigators commonly analyze only a subset of the data, and a majority of the dataset is routinely excluded from analysis. We have developed a software toolbox that simplifies visual inspection of VSDI data, and permits unaided statistical comparison across spatial and temporal dimensions. First, the three-dimensional VSDI dataset (x,y,time) is geometrically transformed into a two-dimensional spatiotemporal map of activity. Second, statistical comparison between groups is performed using a non-parametric permutation test. The result is a 2D map of all significant differences in both space and time. Here, we used the toolbox to identify functional differences in activity in VSDI data from acute hippocampal slices obtained from epileptic Arx conditional knock-out and control mice. Maps of spatiotemporal activity were produced and analyzed to identify differences in the activity evoked by stimulation of each of two axonal inputs to the hippocampus: the perforant pathway and the temporoammonic pathway. In mutant hippocampal slices, the toolbox identified a widespread decrease in spatiotemporal activity evoked by the temporoammonic pathway. No significant differences were observed in the activity evoked by the perforant pathway. The VSDI toolbox permitted us to visualize and statistically compare activity across the spatiotemporal scope of the VSDI dataset. Sampling error was minimized because the representation of the data is standardized by the toolbox. Statistical comparisons were conducted quickly, across the spatiotemporal scope of the data, without a priori knowledge of the character of the responses or the likely differences between them.     

Évaluation de l’exactitude de latéralisation du foyer épileptogène par la tomographie par émission de positons au 18f-fluorodésoxyglucose dans le bilan préopératoire de l’épilepsie temporale : analyse visuelle simple et par index d’asymétrie inter-hémisphérique par soustraction d’images,analyse quantitative par statistical parametric mapping

IntroductionInter-ictal 18F-2-fluoro-deoxy-D-glucose-positron emission tomography (FDG-PET) plays a key role for the preoperative evaluation of patients with pharmacoresistant temporal lobe epilepsy. PET images are usually analyzed visually, a way that is reported to provide a high diagnostic value but that remains subjective, depending on the expertise and experience of the observer. By contrast, the voxel-based quantitative analyses, such as statistical parametric mapping (SPM), are objective and therefore, observer independent methods of analyses. In this study, the accuracy of the analyses of brain FDG-PET images to lateralize the temporal lobe epileptogenic zone was compared between: (1) a conventional visual method, (2) a quantitative SPM analysis, and (3) a visual analysis of inter-hemispheric asymmetry (IHA) obtained after images substraction.Materials and methodsFDG-PET scans of 31 patients presenting a severe temporal epilepsy and whom the temporal foci had been accurately lateralized (successful subsequent surgical treatment) were retrospectively analysed by (1) a consensual visual analysis from two experienced observers; (2) SPM analysis with voxel-wise comparisons of FDG-PET images of patients with those of age-matched healthy controls, using various statistical threshold (P) and cluster (k) values; and (3) visual assessment by the two same observers of images obtained for assessing the IHA. For this purpose, a flipped image was initially obtained by reversing in the left-right direction the FDG-PET images, which had been previously spacially normalized with the SPM template. Then, flipped and non-flipped images were substracted.ResultsThe temporal hypometabolic area was accurately identified: (1) by the conventional visual analysis in 87 % of patients and with a satisfactory interobserver reproducibility (interobserver Cohen's coefficient = 0.79); (2) by SPM analysis, in 90 % of patients (when using optimal thresholds of 0.01 for P value and of 50 voxels (400 mm³) for k value); and (3) with the visual analysis of IHA in 97 % of patients with an excellent interobserver reproductibility (interobserver Cohen's coefficient = 1).ConclusionIn patients presenting severe temporal epilepsy, visual assessment of FDG-PET images from IHA seems more accurate for lateralizing the epileptogenic temporal areas when compared with either conventional visual or quantitative SPM analyses. Moreover, this method is very easy to use in clinical practice, contrary to the quantitative method using SPM     

Biaxial biomechanical properties of the nonpregnant murine cervix and uterus

From a biomechanical perspective, female reproductive health is an understudied area of research. There is an incomplete understanding of the complex function and interaction between the cervix and uterus. This, in part, is due to the limited research into multiaxial biomechanical functions and geometry of these organs. Knowledge of the biomechanical function and interaction between these organs may elucidate etiologies of conditions such as preterm birth. Therefore, the objective of this study was to quantify the multiaxial biomechanical properties of the murine cervix and uterus using a biaxial testing set-up. To accomplish this, an inflation-extension testing protocol (n = 15) was leveraged to quantify biaxial biomechanical properties while preserving native matrix interactions and geometry. Ultrasound imaging and histology (n = 10) were performed to evaluate regional geometry and microstructure, respectively. Histological analysis identified a statistically significant greater collagen content and significantly smaller smooth muscle content in the cervix as compared to the uterus. No statistically significant differences in elastic fibers were identified. Analysis of bilinear fits revealed a significantly stiffer response from the circumferentially orientated ECM fibers compared to axially orientated fibers in both organs. Bilinear fits and a two-fiber family constitutive model showed that the cervix was significantly less distensible than the uterus. We submit that the regional biaxial information reported in this study aids in establishing an appropriate reference configuration for mathematical models of the uterine-cervical complex. Thus, may aid future work to elucidate the biomechanical mechanisms leading to cervical or uterine conditions.     

Automatic ROI Selection in Structural Brain MRI Using SOM 3D Projection

This paper presents a method for selecting Regions of Interest (ROI) in brain Magnetic Resonance Imaging (MRI) for diagnostic purposes, using statistical learning and vector quantization techniques. The proposed method models the distribution of GM and WM tissues grouping the voxels belonging to each tissue in ROIs associated to a specific neurological disorder. Tissue distribution of normal and abnormal images is modelled by a Self-Organizing map (SOM), generating a set of representative prototypes, and the receptive field (RF) of each SOM prototype defines a ROI. Moreover, the proposed method computes the relative importance of each ROI by means of its discriminative power. The devised method has been assessed using 818 images from the Alzheimer''s disease Neuroimaging Initiative (ADNI) which were previously segmented through Statistical Parametric Mapping (SPM). The proposed algorithm was used over these images to parcel ROIs associated to the Alzheimer''s Disease (AD). Additionally, this method can be used to extract a reduced set of discriminative features for classification, since it compresses discriminative information contained in the brain. Voxels marked by ROIs which were computed using the proposed method, yield classification results up to 90% of accuracy for controls (CN) and Alzheimer''s disease (AD) patients, and 84% of accuracy for Mild Cognitive Impairment (MCI) and AD patients.     

Biomechanical and morphological properties of the multiparous ovine vagina and effect of subsequent pregnancy

Pelvic floor soft tissues undergo changes during the pregnancy. However, the degree and nature of this process is not completely characterized. This study investigates the effect of subsequent pregnancy on biomechanical and structural properties of ovine vagina. Vaginal wall from virgin, pregnant (in their third pregnancy) and parous (one year after third vaginal delivery) Swifter sheep (n = 5 each) was harvested. Samples for biomechanics and histology, were cut in longitudinal axis (proximal and distal regions). Outcome measurements describing Young’s modulus, ultimate stress and elongation were obtained from stress-strain curves. For histology samples were stained with Miller's Elastica staining. Collagen, elastin and muscle cells and myofibroblasts contents were estimated, using image processing techniques. Statistical analyses were performed in order to determine significant differences among experimental groups. Significant regional differences were identified. The proximal vagina was stiffer than distal, irrespective the reproductive status. During the pregnancy proximal vagina become more compliant than in parous (+47.45%) or virgin sheep (+64.35%). This coincided with lower collagen (−15 to −21%), higher elastin (+30 to +60%), and more smooth muscle cells (+17 to +37%). Vaginal tissue from parous ewes was weaker than of virgins, coinciding with lower collagen (−10%), higher elastin (+50%), more smooth muscle cells (+20%). It could be proposed that after pregnancy biomechanical properties of vagina do not recover to those of virgins. Since elastin has a significant influence on the compliance of soft tissues and collagen is the main “actor” regarding strength, histological analysis performed in this study justifies the mechanical behavior observed.     

Elimination of inbreeding depression from a captive population of Speke's gazelle: Validity of the original statistical analysis and confirmation by permutation testing

The Speke's gazelle captive breeding program was designed in the early 1980s to simultaneously maintain the population's genetic diversity while reducing the severity of the inbreeding depression in a situation in which inbreeding could not be avoided. Statistical analyses of the resulting data using both regression techniques and nonparametric exact contingency tests revealed that the inbreeding depression was indeed reduced, and genetic surveys revealed that high levels of nuclear genetic diversity had indeed been maintained. Hence, the twin goals of the breeding program appeared to have been achieved. Recently, several papers have been published that question the validity of the original statistical analyses and resulting biological conclusions. Specifically, these papers raise three major issues: (1) that a small sample correction factor used in the regression analysis represents a statistical “flaw,” (2) that new analyses of the data do not confirm the original conclusion of a significant reduction in the level of inbreeding depression, and (3) that the biological conclusions about the program are not justified. In this paper we show (1) that there is no “flaw” in the small sample correction, (2) that the recent permutational test given by Willis and Wiese seriously violates standard procedures and has no statistical validity, (3) that the regression procedures used by Ballou are inappropriate because the data seriously violate the underlying statistical assumptions and that the statistically valid components of Ballou's work strongly confirm the validity of the Speke's gazelle program, (4) that permutational tests done in accordance with standard statistical practice strongly confirm the results of the original analysis, and (5) that the original biological conclusions are fully justified by multiple types of statistical analyses. Zoo Biol 17:77–94, 1998. © 1998 Wiley-Liss, Inc.     

Spatio-Temporal Regularization for Longitudinal Registration to Subject-Specific 3d Template

Neurodegenerative diseases such as Alzheimer''s disease present subtle anatomical brain changes before the appearance of clinical symptoms. Manual structure segmentation is long and tedious and although automatic methods exist, they are often performed in a cross-sectional manner where each time-point is analyzed independently. With such analysis methods, bias, error and longitudinal noise may be introduced. Noise due to MR scanners and other physiological effects may also introduce variability in the measurement. We propose to use 4D non-linear registration with spatio-temporal regularization to correct for potential longitudinal inconsistencies in the context of structure segmentation. The major contribution of this article is the use of individual template creation with spatio-temporal regularization of the deformation fields for each subject. We validate our method with different sets of real MRI data, compare it to available longitudinal methods such as FreeSurfer, SPM12, QUARC, TBM, and KNBSI, and demonstrate that spatially local temporal regularization yields more consistent rates of change of global structures resulting in better statistical power to detect significant changes over time and between populations.     

Anti-inflammatory activity of Tetragronula species from Indonesia

Anti-inflammatory drugs inhibit inflammation, particularly those classified as nonsteroidal anti-inflammatory drugs (NSAIDs). Several studies have reported that propolis has both anti-ulcerogenic and anti-inflammatory effects. In this study, we investigated the bioactive compound and in vivo anti-inflammatory properties of both smooth and rough propolis from Tetragronula sp. To further identify anti-inflammatory markers in propolis, LC-MS/MS was used, and results were analyzed by Mass Lynx 4.1. Rough and smooth propolis of Tetragonula sp. were microcapsulated with maltodextrin and arabic gum. Propolis microcapsules at dose 25–200 mg/kg were applied for carrageenan-induced rat’s paw-inflammation model. Data were analyzed by one-way ANOVA and Kruskal–Wallis statistical tests. LC-MS/MS experiments identified seven anti-inflammatory compounds, including [6]-dehydrogingerdione, alpha-tocopherol succinate, adhyperforin, 6-epiangustifolin, deoxypodophyllotoxin, kurarinone, and xanthoxyletin. Our results indicated that smooth propolis at 50 mg/kg inhibited inflammation to the greatest extent, followed by rough propolis at a dose of 25 mg/kg. SPM and RPM with the dose of 25 mg/kg had inflammatory inhibition value of 62.24% and 58.12%, respectively, which is comparable with the value 70.26% of sodium diclofenac with the dose of 135 mg/kg. This study suggests that propolis has the potential candidate to develop as a non-steroid anti-inflammatory drug.     

A generalized spatial niche model for aquatic macrophytes

The spatial niches of submerged macrophytes and some relevant statistics for niche extensions and boundaries are described. An interpretation of the potential niche as a probability measure of survival over an n-dimensional gradient space is given. To this end a set of probability measure of is introduced. It is shown that these measures closely relate to statistical concepts found in survival and failure time analysis. By this approach, potential niches are wholly defined as a statistical concept. Realized niches then arise as samples from the specified statistical model: hence appropriate niche location and size measures can be derived.The conceptualized model of the survival niche extends to a general model which describes the shape of realized spatial niches for aquatic macrophytes. This general model was derived from actual vegetation data sampled by diving in many Norwegian lakes. Spatial performance on the vertical gradient can be described by a product of doubly exponential functions. Each of these corresponds to a Gumbel EV1 distribution and expresses the probability distribution of the species' up- and downslope niche boundaries, respectively. Theoretically, both potential and realized niches separate into a persistent and a transient region, each related to ddifferent time scales. The deep-water patchiness, commonly observed for submerged macrophytes, might indicate the transient domain of a realized niche. Published data indicate that the proposed model had widespread applicability, and also relevance to, for example, periphyton.     

Patterns of density dependence in measles dynamics.

An important question in metapopulation dynamics is the influence of external perturbations on the population''s long-term dynamic behaviour. In this paper we address the question of how spatiotemporal variations in demographic parameters affect the dynamics of measles populations in England and Wales. Specifically, we use nonparametric statistical methods to analyse how birth rate and population size modulate the negative density dependence between successive epidemics as well as their periodicity. For the observed spatiotemporal data from 60 cities, and for simulated model data, the demographic variables act as bifurcation parameters on the joint density of the trade-off between successive epidemics. For increasing population size, a transition occurs from an irregular unpredictable pattern in small communities towards a regular, predictable endemic pattern in large places. Variations in the birth rate parameter lead to a bifurcation from annual towards biennial cyclicity in both observed data and model data.