Mathematical description of bacterial traveling pulses

The Keller-Segel system has been widely proposed as a model for bacterial waves driven by chemotactic processes. Current experiments on E. coli have shown precise structure of traveling pulses. We present here an alternative mathematical description of traveling pulses at a macroscopic scale. This modeling task is complemented with numerical simulations in accordance with the experimental observations. Our model is derived from an accurate kinetic description of the mesoscopic run-and-tumble process performed by bacteria. This model can account for recent experimental observations with E. coli. Qualitative agreements include the asymmetry of the pulse and transition in the collective behaviour (clustered motion versus dispersion). In addition we can capture quantitatively the main characteristics of the pulse such as the speed and the relative size of tails. This work opens several experimental and theoretical perspectives. Coefficients at the macroscopic level are derived from considerations at the cellular scale. For instance the stiffness of the signal integration process turns out to have a strong effect on collective motion. Furthermore the bottom-up scaling allows to perform preliminary mathematical analysis and write efficient numerical schemes. This model is intended as a predictive tool for the investigation of bacterial collective motion.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Reduced fronto-temporal and limbic connectivity in the 22q11.2 deletion syndrome: vulnerability markers for developing schizophrenia?

The 22q11.2 deletion syndrome (22q11DS) is a widely recognized genetic model allowing the study of neuroanatomical biomarkers that underlie the risk for developing schizophrenia. Recent advances in magnetic resonance image analyses enable the examination of structural connectivity integrity, scarcely used in the 22q11DS field. This framework potentially provides evidence for the disconnectivity hypothesis of schizophrenia in this high-risk population. In the present study, we quantify the whole brain white matter connections in 22q11DS using deterministic tractography. Diffusion Tensor Imaging was acquired in 30 affected patients and 30 age- and gender-matched healthy participants. The Human Connectome technique was applied to register white matter streamlines with cortical anatomy. The number of fibers (streamlines) was used as a measure of connectivity for comparison between groups at the global, lobar and regional level. All statistics were corrected for age and gender. Results showed a 10% reduction of the total number of fibers in patients compared to controls. After correcting for this global reduction, preserved connectivity was found within the right frontal and right parietal lobes. The relative increase in the number of fibers was located mainly in the right hemisphere. Conversely, an excessive reduction of connectivity was observed within and between limbic structures. Finally, a disproportionate reduction was shown at the level of fibers connecting the left fronto-temporal regions. We could therefore speculate that the observed disruption to fronto-temporal connectivity in individuals at risk of schizophrenia implies that fronto-temporal disconnectivity, frequently implicated in the pathogenesis of schizophrenia, could precede the onset of symptoms and, as such, constitutes a biomarker of the vulnerability to develop psychosis. On the contrary, connectivity alterations in the limbic lobe play a role in a wide range of psychiatric disorders and therefore seem to be less specific in defining schizophrenia.

Quantitative ultrasound of the heel and fracture risk assessment: an updated meta-analysis.

Meta-analysis of prospective studies shows that quantitative ultrasound of the heel using validated devices predicts risk of different types of fracture with similar performance across different devices and in elderly men and women. These predictions are independent of the risk estimates from hip DXA measures.Introduction Clinical utilisation of heel quantitative ultrasound (QUS) depends on its power to predict clinical fractures. This is particularly important in settings that have no access to DXA-derived bone density measurements. We aimed to assess the predictive power of heel QUS for fractures using a meta-analysis approach.Methods We conducted an inverse variance random effects meta-analysis of prospective studies with heel QUS measures at baseline and fracture outcomes in their follow-up. Relative risks (RR) per standard deviation (SD) of different QUS parameters (broadband ultrasound attenuation [BUA], speed of sound [SOS], stiffness index [SI], and quantitative ultrasound index [QUI]) for various fracture outcomes (hip, vertebral, any clinical, any osteoporotic and major osteoporotic fractures) were reported based on study questions.Results Twenty-one studies including 55,164 women and 13,742 men were included in the meta-analysis with a total follow-up of 279,124 person-years. All four QUS parameters were associated with risk of different fracture. For instance, RR of hip fracture for 1 SD decrease of BUA was 1.69 (95% CI 1.43-2.00), SOS was 1.96 (95% CI 1.64-2.34), SI was 2.26 (95%CI 1.71-2.99) and QUI was 1.99 (95% CI 1.49-2.67). There was marked heterogeneity among studies on hip and any clinical fractures but no evidence of publication bias amongst them. Validated devices from different manufacturers predicted fracture risks with similar performance (meta-regression p values > 0.05 for difference of devices). QUS measures predicted fracture with a similar performance in men and women. Meta-analysis of studies with QUS measures adjusted for hip BMD showed a significant and independent association with fracture risk (RR/SD for BUA = 1.34 [95%CI 1.22-1.49]).Conclusions This study confirms that heel QUS, using validated devices, predicts risk of different fracture outcomes in elderly men and women. Further research is needed for more widespread utilisation of the heel QUS in clinical settings across the world.

Long-term follow-up of four patients with Langer-Giedion syndrome: clinical course and complications.

Long-term observations of individuals with the so-called Langer-Giedion (LGS) or tricho-rhino-phalangeal type II (TRPS2) are scarce. We report here a on follow-up of four LGS individuals, including one first described by Andres Giedion in 1969, and review the sparse publications on adults with this syndrome which comprises ectodermal dysplasia, multiple cone-shaped epiphyses prior to puberty, multiple cartilaginous exostoses, and mostly mild intellectual impairment. LGS is caused by deletion of the chromosomal segment 8q24.11-q24.13 containing among others the genes EXT1 and TRPS1. Most patients with TRPS2 are only borderline or mildly cognitively delayed, and few are of normal intelligence. Their practical skills are better than their intellectual capability, and, for this reason and because of their low self-esteem, they are often underestimated. Some patients develop seizures at variable age. Osteomas on processes of cervical vertebrae may cause pressure on cervical nerves or dissection of cerebral arteries. Joint stiffness is observed during childhood and changes later to joint laxity causing instability and proneness to trauma. Perthes disease is not rare. Almost all males become bald at or soon after puberty, and some develop (pseudo) gynecomastia. Growth hormone deficiency was found in a few patients, TSH deficiency so far only in one. Puberty and fertility are diminished, and no instance of transmission of the deletion from a non-mosaic parent to a child has been observed so far. Several affected females had vaginal atresia with consequent hydrometrocolpos.

Confounding effects of heart rate on pulse wave velocity in paced patients with a low degree of atherosclerosis.

BACKGROUND: Pulse wave velocity (PWV), an index of arterial wall stiffness, is modulated by blood pressure (BP). Whether heart rate (HR) is also a modulator of PWV is controversial. Recent research involving mainly patients with high aortic PWV have found either no change or a positive correlation between the two. Given that PWV is increasingly being measured in cardiovascular studies, the relationship between HR and PWV should be known in patients with preserved arterial wall elasticity. OBJECTIVE: The aim of this study was to evaluate the importance of HR as a determinant of the variability in PWV in patients with a low degree of atherosclerosis. DESIGN AND METHODS: Fourteen patients (five female, nine male; aged 68 +/- 8 years) were evaluated post pacemaker implantation due to sick sinus or carotid hypersensitivity syndromes. Carotid-femoral PWV was measured at rest and during atrial pacing at 80, 90 and 100 bpm (paced HR). Arterial femoral blood flow (AFBF) was measured by echodoppler. RESULTS: PWV increased from 6.2 +/- 1.5 m/s (mean +/- SD) during resting sinus rhythm (HR 62 +/- 8 bpm; mean +/- SD) to 6.8 +/- 1.0, 7.0 +/- 0.9, and 7.6 +/- 1.1 m/s at pacing rates of 80, 90 and 100 bpm, respectively (P < 0.0001). Systolic (SBP) and mean blood pressure (MBP) remained constant at all HR levels, whereas AFBF increased in a linear fashion. CONCLUSIONS: These results demonstrate that even in patients with a low degree of atherosclerosis, HR is a potential modulator of carotid-femoral PWV.

Magnetic resonance imaging determinants of intraindividual variability in the elderly: combined analysis of grey and white matter.

Elderly individuals display a rapid age-related increase in intraindividual variability (IIV) of their performances. This phenomenon could reflect subtle changes in frontal lobe integrity. However, structural studies in this field are still missing. To address this issue, we computed an IIV index for a simple reaction time (RT) task and performed magnetic resonance imaging (MRI) including voxel based morphometry (VBM) and the tract based spatial statistics (TBSS) analysis of diffusion tensor imaging (DTI) in 61 adults aged from 22 to 88 years. The age-related IIV increase was associated with decreased fractional anisotropy (FA) as well as increased radial (RD) and mean (MD) diffusion in the main white matter (WM) fiber tracts. In contrast, axial diffusion (AD) and grey matter (GM) densities did not show any significant correlation with IIV. In multivariate models, only FA has an age-independent effect on IIV. These results revealed that WM but not GM changes partly mediated the age-related increase of IIV. They also revealed that the association between WM and IIV could not be only attributed to the damage of frontal lobe circuits but concerned the majority of interhemispheric and intrahemispheric corticocortical connections.

Estrategies per la inversió tridimensional de dades magnetotel.lúriques:

Projecte de recerca elaborat a partir d’una estada a la Dublin Institute for Advanced Studies, Irlanda, entre setembre i desembre del 2009.En els últims anys s’ha realitzat un important avanç en la modelització tridimensional en magnetotel•lúrica (MT) gracies a l'augment d’algorismes d’inversió tridimensional disponibles. Aquests codis utilitzen diferents formulacions del problema (diferències finites, elements finits o equacions integrals), diverses orientacions del sistema de coordenades i, o bé en el conveni de signe, més o menys, en la dependència temporal. Tanmateix, les impedàncies resultants per a tots els valors d'aquests codis han de ser les mateixes una vegada que es converteixen a un conveni de signe comú i al mateix sistema de coordenades. Per comparar els resultats dels diferents codis hem dissenyat models diferents de resistivitats amb estructures tridimensional incrustades en un subsòl homogeni. Un requisit fonamental d’aquests models és que generin impedàncies amb valors importants en els elements de la diagonal, que no són menyspreables. A diferència dels casos del modelització de dades magnetotel.lúriques unidimensionals i bidimensionals, pel al cas tridimensional aquests elements de les diagonals del tensor d'impedància porten informació sobre l'estructura de la resistivitat. Un dels models de terreny s'utilitza per comparar els diferents algoritmes que és la base per posterior inversió dels diferents codis. Aquesta comparació va ser seguida de la inversió per recuperar el conjunt de dades d'una estructura coneguda.

Recovering the Elliott invariant from the Cuntz semigroup

Let A be a simple, separable C*-algebra of stable rank one. We prove that the Cuntz semigroup of C (T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yields a description of the Cuntz semigroup of C (T, A) in terms of the Elliott invariant of A. Second, suitably interpreted, it shows that the Elliott functor and the functor defined by the Cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent.

Atomic force and electron microscopic-based study of sarcolemmal surface of living cardiomyocytes unveils unexpected mitochondrial shift in heart failure.

Loss of T-tubules (TT), sarcolemmal invaginations of cardiomyocytes (CMs), was recently identified as a general heart failure (HF) hallmark. However, whether TT per se or the overall sarcolemma is altered during HF process is still unknown. In this study, we directly examined sarcolemmal surface topography and physical properties using Atomic Force Microscopy (AFM) in living CMs from healthy and failing mice hearts. We confirmed the presence of highly organized crests and hollows along myofilaments in isolated healthy CMs. Sarcolemma topography was tightly correlated with elasticity, with crests stiffer than hollows and related to the presence of few packed subsarcolemmal mitochondria (SSM) as evidenced by electron microscopy. Three days after myocardial infarction (MI), CMs already exhibit an overall sarcolemma disorganization with general loss of crests topography thus becoming smooth and correlating with a decreased elasticity while interfibrillar mitochondria (IFM), myofilaments alignment and TT network were unaltered. End-stage post-ischemic condition (15days post-MI) exacerbates overall sarcolemma disorganization with, in addition to general loss of crest/hollow periodicity, a significant increase of cell surface stiffness. Strikingly, electron microscopy revealed the total depletion of SSM while some IFM heaps could be visualized beneath the membrane. Accordingly, mitochondrial Ca(2+) studies showed a heterogeneous pattern between SSM and IFM in healthy CMs which disappeared in HF. In vitro, formamide-induced sarcolemmal stress on healthy CMs phenocopied post-ischemic kinetics abnormalities and revealed initial SSM death and crest/hollow disorganization followed by IFM later disarray which moved toward the cell surface and structured heaps correlating with TT loss. This study demonstrates that the loss of crest/hollow organization of CM surface in HF occurs early and precedes disruption of the TT network. It also highlights a general stiffness increased of the CM surface most likely related to atypical IFM heaps while SSM died during HF process. Overall, these results indicate that initial sarcolemmal stress leading to SSM death could underlie subsequent TT disarray and HF setting.

Prospective evaluation of risk of vertebral fractures using quantitative ultrasound measurements and bone mineral density in a population-based sample of postmenopausal women: results of the Basel Osteoporosis Study.

OBJECTIVE: Prospective studies have shown that quantitative ultrasound (QUS) techniques predict the risk of fracture of the proximal femur with similar standardised risk ratios to dual-energy x-ray absorptiometry (DXA). Few studies have investigated these devices for the prediction of vertebral fractures. The Basel Osteoporosis Study (BOS) is a population-based prospective study to assess the performance of QUS devices and DXA in predicting incident vertebral fractures. METHODS: 432 women aged 60-80 years were followed-up for 3 years. Incident vertebral fractures were assessed radiologically. Bone measurements using DXA (spine and hip) and QUS measurements (calcaneus and proximal phalanges) were performed. Measurements were assessed for their value in predicting incident vertebral fractures using logistic regression. RESULTS: QUS measurements at the calcaneus and DXA measurements discriminated between women with and without incident vertebral fracture, (20% height reduction). The relative risks (RRs) for vertebral fracture, adjusted for age, were 2.3 for the Stiffness Index (SI) and 2.8 for the Quantitative Ultrasound Index (QUI) at the calcaneus and 2.0 for bone mineral density at the lumbar spine. The predictive value (AUC (95% CI)) of QUS measurements at the calcaneus remained highly significant (0.70 for SI, 0.72 for the QUI, and 0.67 for DXA at the lumbar spine) even after adjustment for other confounding variables. CONCLUSIONS: QUS of the calcaneus and bone mineral density measurements were shown to be significant predictors of incident vertebral fracture. The RRs for QUS measurements at the calcaneus are of similar magnitude as for DXA measurements.

Confirmation of functional zones within the human subthalamic nucleus: patterns of connectivity and sub-parcellation using diffusion weighted imaging.

The subthalamic nucleus (STN) is a small, glutamatergic nucleus situated in the diencephalon. A critical component of normal motor function, it has become a key target for deep brain stimulation in the treatment of Parkinson's disease. Animal studies have demonstrated the existence of three functional sub-zones but these have never been shown conclusively in humans. In this work, a data driven method with diffusion weighted imaging demonstrated that three distinct clusters exist within the human STN based on brain connectivity profiles. The STN was successfully sub-parcellated into these regions, demonstrating good correspondence with that described in the animal literature. The local connectivity of each sub-region supported the hypothesis of bilateral limbic, associative and motor regions occupying the anterior, mid and posterior portions of the nucleus respectively. This study is the first to achieve in-vivo, non-invasive anatomical parcellation of the human STN into three anatomical zones within normal diagnostic scan times, which has important future implications for deep brain stimulation surgery.

The generator problem for Z-stable C*-algebras

The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebra A is singly generated, which means that there exists an element x є A that is not contained in any proper sub-C*- algebra of A. To give applications of our result, we observe that Z can be embedded into the reduced group C*-algebra of a discrete group that contains a non-cyclic, free subgroup. It follows that certain tensor products with reduced group C*-algebras are singly generated. In particular, C*r (F ∞) ⨂ C*r (F ∞) is singly generated.

Targetting of the ventro-intermediate nucleus using ultra-high field (7T) MRI for gamma knife surgery purposes: A pilot in vivo study on healthy subjects.

INTRODUCTION: Gamma Knife surgery (GKS) is a non-invasive neurosurgical stereotactic procedure, increasingly used as an alternative to open functional procedures. This includes targeting of the ventro-intermediate nucleus of the thalamus (e.g. Vim) for tremor. We currently perform an indirect targeting, as the Vim is not visible on current 3Tesla MRI acquisitions. Our objective was to enhance anatomic imaging (aiming at refining the precision of anatomic target selection by direct visualisation) in patients treated for tremor with Vim GKS, by using high field 7T MRI. MATERIALS AND METHODSH: Five young healthy subjects were scanned on 3 (T1-w and diffusion tensor imaging) and 7T (high-resolution susceptibility weighted images (SWI)) MRI in Lausanne. All images were further integrated for the first time into the Gamma Plan Software(®) (Elekta Instruments, AB, Sweden) and co-registered (with T1 was a reference). A simulation of targeting of the Vim was done using various methods on the 3T images. Furthermore, a correlation with the position of the found target with the 7T SWI was performed. The atlas of Morel et al. (Zurich, CH) was used to confirm the findings on a detailed analysis inside/outside the Gamma Plan. RESULTS: The use of SWI provided us with a superior resolution and an improved image contrast within the basal ganglia. This allowed visualization and direct delineation of some subgroups of thalamic nuclei in vivo, including the Vim. The position of the target, as assessed on 3T, perfectly matched with the supposed one of the Vim on the SWI. Furthermore, a 3-dimensional model of the Vim-target area was created on the basis of the obtained images. CONCLUSION: This is the first report of the integration of SWI high field MRI into the LGP, aiming at the improvement of targeting validation of the Vim in tremor. The anatomical correlation between the direct visualization on 7T and the current targeting methods on 3T (e.g. quadrilatere of Guyot, histological atlases) seems to show a very good anatomical matching. Further studies are needed to validate this technique, both by improving the accuracy of the targeting of the Vim (potentially also other thalamic nuclei) and to perform clinical assessment.

Cardiac Lineage Protein-1 (CLP-1) Regulates Cardiac Remodeling via Transcriptional Modulation of Diverse Hypertrophic and Fibrotic Responses and Angiotensin II-transforming Growth Factor β (TGF-β1) Signaling Axis.

It is well known that the renin-angiotensin system contributes to left ventricular hypertrophy and fibrosis, a major determinant of myocardial stiffness. TGF-β1 and renin-angiotensin system signaling alters the fibroblast phenotype by promoting its differentiation into morphologically distinct pathological myofibroblasts, which potentiates collagen synthesis and fibrosis and causes enhanced extracellular matrix deposition. However, the atrial natriuretic peptide, which is induced during left ventricular hypertrophy, plays an anti-fibrogenic and anti-hypertrophic role by blocking, among others, the TGF-β-induced nuclear localization of Smads. It is not clear how the hypertrophic and fibrotic responses are transcriptionally regulated. CLP-1, the mouse homolog of human hexamethylene bis-acetamide inducible-1 (HEXIM-1), regulates the pTEFb activity via direct association with pTEFb causing inhibition of the Cdk9-mediated serine 2 phosphorylation in the carboxyl-terminal domain of RNA polymerase II. It was recently reported that the serine kinase activity of Cdk9 not only targets RNA polymerase II but also the conserved serine residues of the polylinker region in Smad3, suggesting that CLP-1-mediated changes in pTEFb activity may trigger Cdk9-dependent Smad3 signaling that can modulate collagen expression and fibrosis. In this study, we evaluated the role of CLP-1 in vivo in induction of left ventricular hypertrophy in angiotensinogen-overexpressing transgenic mice harboring CLP-1 heterozygosity. We observed that introduction of CLP-1 haplodeficiency in the transgenic α-myosin heavy chain-angiotensinogen mice causes prominent changes in hypertrophic and fibrotic responses accompanied by augmentation of Smad3/Stat3 signaling. Together, our findings underscore the critical role of CLP-1 in remodeling of the genetic response during hypertrophy and fibrosis.