Developments in dairy cow fertility research.

Accurate mass and MS/MS fragmentation data for (a) kynurenine, (b) melatonin, and (c) tryptophan. (TIF 191 kb

Additional file 7: Figure S3. of Urinary metabolomics of young Italian autistic children supports abnormal tryptophan and purine metabolism

ROC curve for the top 25 most discriminating metabolites between ASD cases and controls, displayed in Fig. 2. (TIF 131 kb

4D-Analysis of Left Ventricular Heart Cycle Using Procrustes Motion Analysis

<div><p>The aim of this study is to investigate human left ventricular heart morphological changes in time among 17 healthy subjects. Preliminarily, 2 patients with volumetric overload due to aortic insufficiency were added to our analyses. We propose a special strategy to compare the shape, orientation and size of cardiac cycle’s morphological trajectories in time. We used 3D data obtained by Speckle Tracking Echocardiography in order to detect semi-automated and homologous landmarks clouds as proxies of left ventricular heart morphology. An extended Geometric Morphometrics toolkit in order to distinguish between intra- and inter-individual shape variations was used. Shape of trajectories with inter-individual variation were compared under the assumption that trajectories attributes, estimated at electrophysiologically homologous times are expressions of left ventricular heart function. We found that shape analysis as commonly applied in Geometric Morphometrics studies fails in identifying a proper morpho-space to compare the shape of morphological trajectories in time. To overcome this problem, we performed a special type of Riemannian Parallel Transport, called “linear shift”. Whereas the two patients with aortic insufficiency were not differentiated in the static shape analysis from the healthy subjects, they set apart significantly in the analyses of motion trajectory’s shape and orientation. We found that in healthy subjects, the variations due to inter-individual morphological differences were not related to shape and orientation of morphological trajectories. Principal Component Analysis showed that volumetric contraction, torsion and twist are differently distributed on different axes. Moreover, global shape change appeared to be more correlated with endocardial shape change than with the epicardial one. Finally, the total shape variation occurring among different subjects was significantly larger than that observable across properly defined morphological trajectories.</p></div

Pictorial view of the Parallel Transport of tangent spaces.

<p>Our procedure is aimed at comparing motion trajectories’ shapes once removed the effect of inter-individual differences. In this picture it is shown the parallel transport of two different euclidean planes on the tangent plane of the Grand Mean. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0094673#pone-0094673-g002" target="_blank">Figure 4</a> to test the eligibility of a common euclidean plane.</p

Pictorial view of the Parallel Transport of tangent spaces.

<p>Our procedure is aimed at comparing motion trajectories’ shapes once removed the effect of inter-individual differences. In this picture it is shown the parallel transport of two different euclidean planes on the tangent plane of the Grand Mean. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086896#pone-0086896-g004" target="_blank">Figure 4</a> to test the eligibility of a common euclidean plane.</p

GPA performed on trajectories shapes using the PC values interpolated as explained above and treated as homologous landmarks.

<p>Median points were excluded during Procrustes Distance minimization process and were passively appended to transformations (translation, scaling and rotation) estimated using PC values estimated only at the homologous electromechanical moments. This strategy allows to compare relatively complete estimated shapes without adding noise due to non perfectly homologous physiologically-based event estimation. a) Aligned PC values-based shapes; only first two PCs are showed here, while the actual alignment was performed using first three PCs, b) the shapes of trajectories in the PCA shape space. This PCA is performed on aligned values of first three PCs extracted from the actual LV shape analysis.</p

The effect of interpolation.

<p>a) a PC1/PC2 scatterplot for one motion trajectory is illustrated, b) the corresponding shape change is plotted on the PC1/PC2 scatterplot, c) basing on the interpolation procedure described in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086896#pone-0086896-g004" target="_blank">Fig. 4</a>, all interpolated trajectories are depicted here.</p

Inter-individual variability at R peak of the electrocardiogram.

<p>PC 1 and PC 2 are shown.</p

PCA shape space for the 11 interpolated trajectories after the linear shift.

<p>a) PC1/PC2 scatterplot, b) PC1/PC3 scatterplot.</p

Physiological parameters for the subjects analyzed in this study.

<p>Physiological parameters for the subjects analyzed in this study.</p