The partially alternating ternary sum in an associative dialgebra

The alternating ternary sum in an associative algebra, $abc - acb - bac + bca + cab - cba$, gives rise to the partially alternating ternary sum in an associative dialgebra with products $\dashv$ and $\vdash$ by making the argument $a$ the center of each term: $a \dashv b \dashv c - a \dashv c \dashv b - b \vdash a \dashv c + c \vdash a \dashv b + b \vdash c \vdash a - c \vdash b \vdash a$. We use computer algebra to determine the polynomial identities in degree $\le 9$ satisfied by this new trilinear operation. In degrees 3 and 5 we obtain $[a,b,c] + [a,c,b] \equiv 0$ and $[a,[b,c,d],e] + [a,[c,b,d],e] \equiv 0$; these identities define a new variety of partially alternating ternary algebras. We show that there is a 49-dimensional space of multilinear identities in degree 7, and we find equivalent nonlinear identities. We use the representation theory of the symmetric group to show that there are no new identities in degree 9.Comment: 14 page

Comprehensive 4D velocity mapping of the heart and great vessels by cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>Phase contrast cardiovascular magnetic resonance (CMR) is able to measure all three directional components of the velocities of blood flow relative to the three spatial dimensions and the time course of the heart cycle. In this article, methods used for the acquisition, visualization, and quantification of such datasets are reviewed and illustrated.</p> <p>Methods</p> <p>Currently, the acquisition of 3D cine (4D) phase contrast velocity data, synchronized relative to both cardiac and respiratory movements takes about ten minutes or more, even when using parallel imaging and optimized pulse sequence design. The large resulting datasets need appropriate post processing for the visualization of multidirectional flow, for example as vector fields, pathlines or streamlines, or for retrospective volumetric quantification.</p> <p>Applications</p> <p>Multidirectional velocity acquisitions have provided 3D visualization of large scale flow features of the healthy heart and great vessels, and have shown altered patterns of flow in abnormal chambers and vessels. Clinically relevant examples include retrograde streams in atheromatous descending aortas as potential thrombo-embolic pathways in patients with cryptogenic stroke and marked variations of flow visualized in common aortic pathologies. Compared to standard clinical tools, 4D velocity mapping offers the potential for retrospective quantification of flow and other hemodynamic parameters.</p> <p>Conclusions</p> <p>Multidirectional, 3D cine velocity acquisitions are contributing to the understanding of normal and pathologically altered blood flow features. Although more rapid and user-friendly strategies for acquisition and analysis may be needed before 4D velocity acquisitions come to be adopted in routine clinical CMR, their capacity to measure multidirectional flows throughout a study volume has contributed novel insights into cardiovascular fluid dynamics in health and disease.</p

A Three-Dimensional Atlas of the Honeybee Neck

Three-dimensional digital atlases are rapidly becoming indispensible in modern biology. We used serial sectioning combined with manual registration and segmentation of images to develop a comprehensive and detailed three-dimensional atlas of the honeybee head-neck system. This interactive atlas includes skeletal structures of the head and prothorax, the neck musculature, and the nervous system. The scope and resolution of the model exceeds atlases previously developed on similar sized animals, and the interactive nature of the model provides a far more accessible means of interpreting and comprehending insect anatomy and neuroanatomy

Stridulations Reveal Cryptic Speciation in Neotropical Sympatric Ants

The taxonomic challenge posed by cryptic species underlines the importance of using multiple criteria in species delimitation. In the current paper we tested the use of acoustic analysis as a tool to assess the real diversity in a cryptic species complex of Neotropical ants. In order to understand the potential of acoustics and to improve consistency in the conclusions by comparing different approaches, phylogenetic relationships of all the morphs considered were assessed by the analysis of a fragment of the mitochondrial DNA cytochrome b. We observed that each of the cryptic morph studied presents a morphologically distinct stridulatory organ and that all sympatric morphs produce distinctive stridulations. This is the first evidence of such a degree of specialization in the acoustic organ and signals in ants, which suggests that stridulations may be among the cues used by these ants during inter-specific interactions. Mitochondrial DNA variation corroborated the acoustic differences observed, confirming acoustics as a helpful tool to determine cryptic species in this group of ants, and possibly in stridulating ants in general. Congruent morphological, acoustic and genetic results constitute sufficient evidence to propose each morph studied here as a valid new species, suggesting that P. apicalis is a complex of at least 6 to 9 species, even if they present different levels of divergence. Finally, our results highlight that ant stridulations may be much more informative than hitherto thought, as much for ant communication as for integrative taxonomists

4D cardiovascular magnetic resonance velocity mapping of alterations of right heart flow patterns and main pulmonary artery hemodynamics in tetralogy of Fallot

<p>Abstract</p> <p>Background</p> <p>To assess changes in right heart flow and pulmonary artery hemodynamics in patients with repaired Tetralogy of Fallot (rTOF) we used whole heart, four dimensional (4D) velocity mapping (VM) cardiovascular magnetic resonance (CMR).</p> <p>Methods</p> <p>CMR studies were performed in 11 subjects with rTOF (5M/6F; 20.1 ± 12.4 years) and 10 normal volunteers (6M/4F; 34.2 ± 13.4 years) on clinical 1.5T and 3.0T MR scanners. 4D VM-CMR was performed using PC VIPR (Phase Contrast Vastly undersampled Isotropic Projection Reconstruction). Interactive streamline and particle trace visualizations of the superior and inferior vena cava (IVC and SVC, respectively), right atrium (RA), right ventricle (RV), and pulmonary artery (PA) were generated and reviewed by three experienced readers. Main PA net flow, retrograde flow, peak flow, time-to-peak flow, peak acceleration, resistance index and mean wall shear stress were quantified. Differences in flow patterns between the two groups were tested using Fisher's exact test. Differences in quantitative parameters were analyzed with the Kruskal-Wallis rank sum test.</p> <p>Results</p> <p>4D VM-CMR was successfully performed in all volunteers and subjects with TOF. Right heart flow patterns in rTOF subjects were characterized by (a) greater SVC/IVC flow during diastole than systole, (b) increased vortical flow patterns in the RA and in the RV during diastole, and (c) increased helical or vortical flow features in the PA's. Differences in main PA retrograde flow, resistance index, peak flow, time-to-peak flow, peak acceleration and mean wall shear stress were statistically significant.</p> <p>Conclusions</p> <p>Whole heart 4D VM-CMR with PC VIPR enables detection of both normal and abnormal right heart flow patterns, which may allow for comprehensive studies to evaluate interdependencies of post-surgically altered geometries and hemodynamics.</p

Hemodynamic predictors of aortic dilatation in bicuspid aortic valve by velocity-encoded cardiovascular magnetic resonance

<p>Abstract</p> <p>Background</p> <p>Congenital Bicuspid Aortic Valve (BAV) is a significant risk factor for serious complications including valve dysfunction, aortic dilatation, dissection, and sudden death. Clinical tools for identification and monitoring of BAV patients at high risk for development of aortic dilatation, an early complication, are not available.</p> <p>Methods</p> <p>This paper reports an investigation in 18 pediatric BAV patients and 10 normal controls of links between abnormal blood flow patterns in the ascending aorta and aortic dilatation using velocity-encoded cardiovascular magnetic resonance. Blood flow patterns were quantitatively expressed in the angle between systolic left ventricular outflow and the aortic root channel axis, and also correlated with known biochemical markers of vessel wall disease.</p> <p>Results</p> <p>The data confirm larger ascending aortas in BAV patients than in controls, and show more angled LV outflow in BAV (17.54 ± 0.87 degrees) than controls (10.01 ± 1.29) (p = 0.01). Significant correlation of systolic LV outflow jet angles with dilatation was found at different levels of the aorta in BAV patients STJ: r = 0.386 (N = 18, p = 0.048), AAO: r = 0.536 (N = 18, p = 0.022), and stronger correlation was found with patients and controls combined into one population: SOV: r = 0.405 (N = 28, p = 0.033), STJ: r = 0.562 (N = 28, p = 0.002), and AAO r = 0.645 (N = 28, p < 0.001). Dilatation and the flow jet angle were also found to correlate with plasma levels of matrix metallo-proteinase 2.</p> <p>Conclusions</p> <p>The results of this study provide new insights into the pathophysiological processes underlying aortic dilatation in BAV patients. These results show a possible path towards the development of clinical risk stratification protocols in order to reduce morbidity and mortality for this common congenital heart defect.</p

Altered aortic 3D hemodynamics and geometry in pediatric Marfan syndrome patients

BACKGROUND: Blood flow dynamics make it possible to better understand the development of aortopathy and cardiovascular events in patients with Marfan syndrome (MFS). Aortic 3D blood flow characteristics were investigated in relation to aortic geometry in children and adolescents with MFS. METHODS: Twenty-five MFS patients (age 15.6 ± 4.0 years; 11 females) and 21 healthy controls (age 16.0 ± 2.6 years; 12 females) underwent magnetic resonance angiography and 4D flow CMR for assessment of thoracic aortic size and 3D blood flow velocities. Data analysis included calculation of aortic diameter and BSA-indexed aortic dimensions (Z-score) along the thoracic aorta, 3D mean systolic wall shear stress (WSS(mean)) in ten aortic segments and assessment of aortic blood flow patterns. RESULTS: Aortic root (root), ascending (AAo) and descending (DAo) aortic size was significantly larger in MFS patients than healthy controls (Root Z-score: 3.56 ± 1.45 vs 0.49 ± 0.78, p < 0.001; AAo Z-score 0.21 ± 0.95 vs −0.54 ± 0.64, p = 0.004; proximal DAo Z-score 2.02 ± 1.60 vs 0.56 ± 0.66, p < 0.001). A regional variation in prevalence and severity of flow patterns (vortex and helix flow patterns) was observed, with the aortic root and the proximal DAo (pDAo) being more frequently affected in MFS. MFS patients had significantly reduced WSS(mean) in the proximal AAo (pAAo) outer segment (0.65 ± 0.12 vs. 0.73 ± 0.14 Pa, p = 0.029) and pDAo inner segment (0.74 ± 0.17 vs. 0.87 ± 0.21 Pa, p = 0.021), as well as higher WSS(mean) in the inner segment of the distal AAo (0.94 ± 0.14 vs. 0.84 ± 0.15 Pa, p = 0.036) compared to healthy subjects. An inverse relationship existed between pDAo WSS(mean) and both pDAo diameter (R = −0.53, p < 0.001) and % diameter change along the pDAo segment (R = −0.64, p < 0.001). CONCLUSIONS: MFS children and young adults have altered aortic flow patterns and differences in aortic WSS that were most pronounced in the pAAo and pDAo, segments where aortic dissection or rupture often originate. The presence of vortex flow patterns and abnormal WSS correlated with regional size of the pDAo and are potentially valuable additional markers of disease severity. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12968-017-0345-7) contains supplementary material, which is available to authorized users