Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

An objective anisotropic elastic plastic model and Algorithm applicable to bone mechanics

The implicit projection algorithm of isotropic plasticity is extended to an objective anisotropic elastic perfectly plastic model. The recursion formula developed to project the trial stress on the yield surface, is applicable to any non linear elastic law and any plastic yield function.A curvilinear transverse isotropic model based on a quadratic elastic potential and on Hill's quadratic yield criterion is then developed and implemented in a computer program for bone mechanics perspectives. The paper concludes with a numerical study of a schematic bone-prosthesis system to illustrate the potential of the model.

Permeability estimates from poro-elastic dispersion analyses of sonic logs

Modern sonic logging tools designed for shallow environmental and engineering applications allow for P-wave phase velocity measurements over a wide frequency band. Methodological considerations indicate that, for saturated unconsolidated sediments in the silt to sand range and source frequencies ranging from approximately 1 to 30 kHz, the observable poro-elastic P-wave velocity dispersion is sufficiently pronounced to allow for reliable first-order estimations of the underlying permeability structure. These predictions have been tested on and verified for a surficial alluvial aquifer. Our results indicate that, even without any further calibration, the thus obtained permeability estimates as well as their variabilities within the pertinent lithological units are remarkably close to those expected based on the corresponding granulometric characteristics.

Quantitative comparison of reconstruction methods for intra-voxel fiber recovery from diffusion MRI.

Validation is arguably the bottleneck in the diffusion magnetic resonance imaging (MRI) community. This paper evaluates and compares 20 algorithms for recovering the local intra-voxel fiber structure from diffusion MRI data and is based on the results of the "HARDI reconstruction challenge" organized in the context of the "ISBI 2012" conference. Evaluated methods encompass a mixture of classical techniques well known in the literature such as diffusion tensor, Q-Ball and diffusion spectrum imaging, algorithms inspired by the recent theory of compressed sensing and also brand new approaches proposed for the first time at this contest. To quantitatively compare the methods under controlled conditions, two datasets with known ground-truth were synthetically generated and two main criteria were used to evaluate the quality of the reconstructions in every voxel: correct assessment of the number of fiber populations and angular accuracy in their orientation. This comparative study investigates the behavior of every algorithm with varying experimental conditions and highlights strengths and weaknesses of each approach. This information can be useful not only for enhancing current algorithms and develop the next generation of reconstruction methods, but also to assist physicians in the choice of the most adequate technique for their studies.

PGC1alpha expression is controlled in skeletal muscles by PPARbeta, whose ablation results in fiber-type switching, obesity, and type 2 diabetes.

Mice in which peroxisome proliferator-activated receptor beta (PPARbeta) is selectively ablated in skeletal muscle myocytes were generated to elucidate the role played by PPARbeta signaling in these myocytes. These somatic mutant mice exhibited a muscle fiber-type switching toward lower oxidative capacity that preceded the development of obesity and diabetes, thus demonstrating that PPARbeta is instrumental in myocytes to the maintenance of oxidative fibers and that fiber-type switching is likely to be the cause and not the consequence of these metabolic disorders. We also show that PPARbeta stimulates in myocytes the expression of PGC1alpha, a coactivator of various transcription factors, known to play an important role in slow muscle fiber formation. Moreover, as the PGC1alpha promoter contains a PPAR response element, the effect of PPARbeta on the formation and/or maintenance of slow muscle fibers can be ascribed, at least in part, to a stimulation of PGC1alpha expression at the transcriptional level.

Response to comment on "the geometric structure of the brain fiber pathways".

In response to Catani et al., we show that corticospinal pathways adhere via sharp turns to two local grid orientations; that our studies have three times the diffusion resolution of those compared; and that the noted technical concerns, including crossing angles, do not challenge the evidence of mathematically specific geometric structure. Thus, the geometric thesis gives the best account of the available evidence.

Bilateral dorsal and ventral fiber pathways for the processing of affective prosody identified by probabilistic fiber tracking.

Dorsal and ventral pathways for syntacto-semantic speech processing in the left hemisphere are represented in the dual-stream model of auditory processing. Here we report new findings for the right dorsal and ventral temporo-frontal pathway during processing of affectively intonated speech (i.e. affective prosody) in humans, together with several left hemispheric structural connections, partly resembling those for syntacto-semantic speech processing. We investigated white matter fiber connectivity between regions responding to affective prosody in several subregions of the bilateral superior temporal cortex (secondary and higher-level auditory cortex) and of the inferior frontal cortex (anterior and posterior inferior frontal gyrus). The fiber connectivity was investigated by using probabilistic diffusion tensor based tractography. The results underscore several so far underestimated auditory pathway connections, especially for the processing of affective prosody, such as a right ventral auditory pathway. The results also suggest the existence of a dual-stream processing in the right hemisphere, and a general predominance of the dorsal pathways in both hemispheres underlying the neural processing of affective prosody in an extended temporo-frontal network.

Traitement des fractures de l'enfant par enclouage centro-médullaire élastique stable (ECMES) [Treatment of pediatric fractures by intramedullary stable elastic pinning]

During the past decade several new techniques for the treatment of children's fractures respecting the specificity of the growing bone have been described. The goal of all these techniques was to mechanically stabilise the fracture however to preserve a certain instability of the fracture gap itself inducing early callus formation and subsequent consolidation. The dynamic external fixation as well as the elastic stable intramedullary pinning have become accepted means in the treatment of long bone fractures in the paediatric age group. We report our experience of the last seven years with the intramedullary pinning of 105 fractures. Eighty-four were fractures of the femur, 9 of the humerus, 8 of the forearm, and a further 4 of the tibial shaft. The intramedullary elastic pinning represents a simple technique which supports or even enhances the natural process of fracture healing of the growing bone. The method is not very invasive, is cost effective, and allows short hospitalisation. Early physical activity is guaranteed due to early consolidation of the fracture. Complications are rare and the final orthopedic and cosmetic outcome is excellent.

A pseudo-spectral method for the simulation of poro-elastic seismic wave propagation in 2D polar coordinates using domain decomposition

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in 2D polar coordinates. An important application of this method and its extensions will be the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh, which can be arbitrarily heterogeneous, consisting of two or more concentric rings representing the fluid in the center and the surrounding porous medium. The spatial discretization is based on a Chebyshev expansion in the radial direction and a Fourier expansion in the azimuthal direction and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method is used to match the fluid-solid boundary conditions based on the method of characteristics. This multi-domain approach allows for significant reductions of the number of grid points in the azimuthal direction for the inner grid domain and thus for corresponding increases of the time step and enhancements of computational efficiency. The viability and accuracy of the proposed method has been rigorously tested and verified through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently bench-marked solution for 2D Cartesian coordinates. Finally, the proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is adequately handled.

Quantitative comparison of simulations of seismic wave propagation in heterogeneous poro-elastic media involving fluid-solid interfaces and in equivalent visco-elastic solids

There is increasing evidence to suggest that the presence of mesoscopic heterogeneities constitutes the predominant attenuation mechanism at seismic frequencies. As a consequence, centimeter-scale perturbations of the subsurface physical properties should be taken into account for seismic modeling whenever detailed and accurate responses of the target structures are desired. This is, however, computationally prohibitive since extremely small grid spacings would be necessary. A convenient way to circumvent this problem is to use an upscaling procedure to replace the heterogeneous porous media by equivalent visco-elastic solids. In this work, we solve Biot's equations of motion to perform numerical simulations of seismic wave propagation through porous media containing mesoscopic heterogeneities. We then use an upscaling procedure to replace the heterogeneous poro-elastic regions by homogeneous equivalent visco-elastic solids and repeat the simulations using visco-elastic equations of motion. We find that, despite the equivalent attenuation behavior of the heterogeneous poro-elastic medium and the equivalent visco-elastic solid, the seismograms may differ due to diverging boundary conditions at fluid-solid interfaces, where there exist additional options for the poro-elastic case. In particular, we observe that the seismograms agree for closed-pore boundary conditions, but differ significantly for open-pore boundary conditions. This is an interesting result, which has potentially important implications for wave-equation-based algorithms in exploration geophysics involving fluid-solid interfaces, such as, for example, wave field decomposition.

A pseudo-spectral method for simulating of poro-elastic seismic wave propagation in complex borehole environments

We present a novel numerical approach for the comprehensive, flexible, and accurate simulation of poro-elastic wave propagation in cylindrical coordinates. An important application of this method is the modeling of complex seismic wave phenomena in fluid-filled boreholes, which represents a major, and as of yet largely unresolved, computational problem in exploration geophysics. In view of this, we consider a numerical mesh consisting of three concentric domains representing the borehole fluid in the center, the borehole casing and the surrounding porous formation. The spatial discretization is based on a Chebyshev expansion in the radial direction, Fourier expansions in the other directions, and a Runge-Kutta integration scheme for the time evolution. A domain decomposition method based on the method of characteristics is used to match the boundary conditions at the fluid/porous-solid and porous-solid/porous-solid interfaces. The viability and accuracy of the proposed method has been tested and verified in 2D polar coordinates through comparisons with analytical solutions as well as with the results obtained with a corresponding, previously published, and independently benchmarked solution for 2D Cartesian coordinates. The proposed numerical solution also satisfies the reciprocity theorem, which indicates that the inherent singularity associated with the origin of the polar coordinate system is handled adequately.

Large A-fiber activity is required for microglial proliferation and p38 MAPK activation in the spinal cord: different effects of resiniferatoxin and bupivacaine on spinal microglial changes after spared nerve injury.

BACKGROUND: After peripheral nerve injury, spontaneous ectopic activity arising from the peripheral axons plays an important role in inducing central sensitization and neuropathic pain. Recent evidence indicates that activation of spinal cord microglia also contributes to the development of neuropathic pain. In particular, activation of p38 mitogen-activated protein kinase (MAPK) in spinal microglia is required for the development of mechanical allodynia. However, activity-dependent activation of microglia after nerve injury has not been fully addressed. To determine whether spontaneous activity from C- or A-fibers is required for microglial activation, we used resiniferatoxin (RTX) to block the conduction of transient receptor potential vanilloid subtype 1 (TRPV1) positive fibers (mostly C- and Adelta-fibers) and bupivacaine microspheres to block all fibers of the sciatic nerve in rats before spared nerve injury (SNI), and observed spinal microglial changes 2 days later. RESULTS: SNI induced robust mechanical allodynia and p38 activation in spinal microglia. SNI also induced marked cell proliferation in the spinal cord, and all the proliferating cells (BrdU+) were microglia (Iba1+). Bupivacaine induced a complete sensory and motor blockade and also significantly inhibited p38 activation and microglial proliferation in the spinal cord. In contrast, and although it produced an efficient nociceptive block, RTX failed to inhibit p38 activation and microglial proliferation in the spinal cord. CONCLUSION: (1) Blocking peripheral input in TRPV1-positive fibers (presumably C-fibers) is not enough to prevent nerve injury-induced spinal microglial activation. (2) Peripheral input from large myelinated fibers is important for microglial activation. (3) Microglial activation is associated with mechanical allodynia.