Finsler geometry on higher order tensor fields and applications to high angular resolution diffusion imaging.

We study 3D-multidirectional images, using Finsler geometry. The application considered here is in medical image analysis, specifically in High Angular Resolution Diffusion Imaging (HARDI) (Tuch et al. in Magn. Reson. Med. 48(6):1358–1372, 2004) of the brain. The goal is to reveal the architecture of the neural fibers in brain white matter. To the variety of existing techniques, we wish to add novel approaches that exploit differential geometry and tensor calculus. In Diffusion Tensor Imaging (DTI), the diffusion of water is modeled by a symmetric positive definite second order tensor, leading naturally to a Riemannian geometric framework. A limitation is that it is based on the assumption that there exists a single dominant direction of fibers restricting the thermal motion of water molecules. Using HARDI data and higher order tensor models, we can extract multiple relevant directions, and Finsler geometry provides the natural geometric generalization appropriate for multi-fiber analysis. In this paper we provide an exact criterion to determine whether a spherical function satisfies the strong convexity criterion essential for a Finsler norm. We also show a novel fiber tracking method in Finsler setting. Our model incorporates a scale parameter, which can be beneficial in view of the noisy nature of the data. We demonstrate our methods on analytic as well as simulated and real HARDI data

Extended Birkhoff's Theorem in the f(T) Gravity

The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011), arXiv:1107.0629v1], we prove that the Birkhoff's theorem holds in a more general context, specifically with the off diagonal tetrad case, in this communication letter. Then, we discuss respectively the results of the external vacuum and internal gravitational field in the f(T) gravity framework, as well as the extended meaning of this theorem. We also investigate the validity of the Birkhoff's theorem in the frame of f(T) gravity via conformal transformation by regarding the Brans-Dicke-like scalar as effective matter, and study the equivalence between both Einstein frame and Jordan frame.Comment: 7 pages, 1 figure, submitted to EPJ-C. arXiv admin note: substantial text overlap with arXiv:1107.062

Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order

f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation field. In this present work, we investigate specifically the range of validity of Birkhoff's theorem with the general tetrad field via perturbative approach. At zero order, Birkhoff's theorem is valid and the solution is the well known Schwarzschild-(A)dS metric. Then considering the special case of the diagonal tetrad field, we present a new spherically symmetric solution in the frame of f(T) gravity up to the perturbative order. The results with the diagonal tetrad field satisfy the physical equivalence between the Jordan and the so-called Einstein frames, which are realized via conformal transformation, at least up to the first perturbative order.Comment: 8 pages, no figure. Final version, accepted for publication in EPJ

Reconstruction of some cosmological models in f(R,T) gravity

In this paper, we reconstruct cosmological models in the framework of $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. We show that the dust fluid reproduces $\Lambda$CDM, phantom-non-phantom era and the phantom cosmology. Further, we reconstruct different cosmological models including, Chaplygin gas, scalar field with some specific forms of $f(R,T)$. Our numerical simulation for Hubble parameter shows good agreement with the BAO observational data for low redshifts $z<2$.Comment: 12 pages, 2 figure

Scalar models for the generalized Chaplygin gas and the structure formation constraints

The generalized Chaplygin gas model represents an attempt to unify dark matter and dark energy. It is characterized by a fluid with an equation of state $p = - A/\rho^\alpha$. It can be obtained from a generalization of the DBI action for a scalar, tachyonic field. At background level, this model gives very good results, but it suffers from many drawbacks at perturbative level. We show that, while for background analysis it is possible to consider any value for $\alpha$, the perturbative analysis must be restricted to positive values of $\alpha$. This restriction can be circumvented if the origin of the generalized Chaplygin gas is traced back to a self-interacting scalar field, instead of the DBI action. But, in doing so, the predictions coming from formation of large scale structures reduce the generalized Chaplygin gas model to a kind of quintessence model, and the unification scenario is lost, if the scalar field is the canonical one. However, if the unification condition is imposed from the beginning as a prior, the model may remain competitive. More interesting results, concerning the unification program, are obtained if a non-canonical self-interacting scalar field, inspired by Rastall's theory of gravity, is imposed. In this case, an agreement with the background tests is possible.Comment: Latex file, 25 pages, 33 figures in eps format. New section on scalar models. Accepted for publication in Gravitation&Cosmolog

Comprehensive in vivo Mapping of the Human Basal Ganglia and Thalamic Connectome in Individuals Using 7T MRI

Basal ganglia circuits are affected in neurological disorders such as Parkinson's disease (PD), essential tremor, dystonia and Tourette syndrome. Understanding the structural and functional connectivity of these circuits is critical for elucidating the mechanisms of the movement and neuropsychiatric disorders, and is vital for developing new therapeutic strategies such as deep brain stimulation (DBS). Knowledge about the connectivity of the human basal ganglia and thalamus has rapidly evolved over recent years through non-invasive imaging techniques, but has remained incomplete because of insufficient resolution and sensitivity of these techniques. Here, we present an imaging and computational protocol designed to generate a comprehensive in vivo and subject-specific, three-dimensional model of the structure and connections of the human basal ganglia. High-resolution structural and functional magnetic resonance images were acquired with a 7-Tesla magnet. Capitalizing on the enhanced signal-to-noise ratio (SNR) and enriched contrast obtained at high-field MRI, detailed structural and connectivity representations of the human basal ganglia and thalamus were achieved. This unique combination of multiple imaging modalities enabled the in-vivo visualization of the individual human basal ganglia and thalamic nuclei, the reconstruction of seven white-matter pathways and their connectivity probability that, to date, have only been reported in animal studies, histologically, or group-averaged MRI population studies. Also described are subject-specific parcellations of the basal ganglia and thalamus into sub-territories based on their distinct connectivity patterns. These anatomical connectivity findings are supported by functional connectivity data derived from resting-state functional MRI (R-fMRI). This work demonstrates new capabilities for studying basal ganglia circuitry, and opens new avenues of investigation into the movement and neuropsychiatric disorders, in individual human subjects

Deep brain stimulation for refractory obsessive-compulsive disorder (OCD): emerging or established therapy?

A consensus has yet to emerge whether deep brain stimulation (DBS) for treatment-refractory obsessive-compulsive disorder (OCD) can be considered an established therapy. In 2014, the World Society for Stereotactic and Functional Neurosurgery (WSSFN) published consensus guidelines stating that a therapy becomes established when “at least two blinded randomized controlled clinical trials from two different groups of researchers are published, both reporting an acceptable risk-benefit ratio, at least comparable with other existing therapies. The clinical trials should be on the same brain area for the same psychiatric indication.” The authors have now compiled the available evidence to make a clear statement on whether DBS for OCD is established therapy. Two blinded randomized controlled trials have been published, one with level I evidence (Yale-Brown Obsessive Compulsive Scale (Y-BOCS) score improved 37% during stimulation on), the other with level II evidence (25% improvement). A clinical cohort study (N = 70) showed 40% Y-BOCS score improvement during DBS, and a prospective international multi-center study 42% improvement (N = 30). The WSSFN states that electrical stimulation for otherwise treatment refractory OCD using a multipolar electrode implanted in the ventral anterior capsule region (including bed nucleus of stria terminalis and nucleus accumbens) remains investigational. It represents an emerging, but not yet established therapy. A multidisciplinary team involving psychiatrists and neurosurgeons is a prerequisite for such therapy, and the future of surgical treatment of psychiatric patients remains in the realm of the psychiatrist

Basal ganglia dysfunction in OCD: subthalamic neuronal activity correlates with symptoms severity and predicts high-frequency stimulation efficacy

Functional and connectivity changes in corticostriatal systems have been reported in the brains of patients with obsessive–compulsive disorder (OCD); however, the relationship between basal ganglia activity and OCD severity has never been adequately established. We recently showed that deep brain stimulation of the subthalamic nucleus (STN), a central basal ganglia nucleus, improves OCD. Here, single-unit subthalamic neuronal activity was analysed in 12 OCD patients, in relation to the severity of obsessions and compulsions and response to STN stimulation, and compared with that obtained in 12 patients with Parkinson's disease (PD). STN neurons in OCD patients had lower discharge frequency than those in PD patients, with a similar proportion of burst-type activity (69 vs 67%). Oscillatory activity was present in 46 and 68% of neurons in OCD and PD patients, respectively, predominantly in the low-frequency band (1–8 Hz). In OCD patients, the bursty and oscillatory subthalamic neuronal activity was mainly located in the associative–limbic part. Both OCD severity and clinical improvement following STN stimulation were related to the STN neuronal activity. In patients with the most severe OCD, STN neurons exhibited bursts with shorter duration and interburst interval, but higher intraburst frequency, and more oscillations in the low-frequency bands. In patients with best clinical outcome with STN stimulation, STN neurons displayed higher mean discharge, burst and intraburst frequencies, and lower interburst interval. These findings are consistent with the hypothesis of a dysfunction in the associative–limbic subdivision of the basal ganglia circuitry in OCD's pathophysiology