Studies on solidification of metals with two dimensional heat flow

Imperial Users onl

On input/output maps for nonlinear systems via continuity in a locally convex topology

In this paper we show that the output of a nonlinear system with inputs in () whose state satisfies a nonlinear differential equation with standard smoothness conditions can be written as the composition of a nonlinear map with a linear Hilbert-Schmidt operator acting on the input. The result also extends to abstract semi-linear infinite dimensional systems. The approach is via the study of the continuity of the solution in a locally convex topology generated by seminorms of Hilbert-Schmidt operators in Hilbert space. The result reveals an entirely new structure related to nonlinear systems which can lead to useful approximation results

Kaempferol Treatment after Traumatic Brain Injury during Early Development Mitigates Brain Parenchymal Microstructure and Neural Functional Connectivity Deterioration at Adolescence.

Targeting mitochondrial ion homeostasis using Kaempferol, a mitochondrial Ca2+ uniporter channel activator, improves energy metabolism and behavior soon after a traumatic brain injury (TBI) in developing rats. Because of broad TBI pathophysiology and brain mitochondrial heterogeneity, Kaempferol-mediated early-stage behavioral and brain metabolic benefits may accrue from diverse sources within the brain. We hypothesized that Kaempferol influences TBI outcome by differentially impacting the neural, vascular, and synaptic/axonal compartments. After TBI at early development (P31), functional magnetic resonance imaging and diffusion tensor imaging (DTI) were applied to determine imaging outcomes at adolescence (2 months post-injury). Vehicle and Kaempferol treatments were made at 1, 24, and 48 h post-TBI, and their effects were assessed at adolescence. A significant increase in neural connectivity was observed after Kaempferol treatment as assessed by the spatial extent and strength of the somatosensory cortical and hippocampal resting-state functional connectivity (RSFC) networks. However, no significant RSFC changes were observed in the thalamus. DTI measures of fractional anisotropy (FA) and apparent diffusion coefficient, representing synaptic/axonal and microstructural integrity, showed significant improvements after Kaempferol treatment, with highest changes in the frontal and parietal cortices and hippocampus. Kaempferol treatment also increased corpus callosal FA, indicating measurable improvement in the interhemispheric structural connectivity. TBI prognosis was significantly altered at adolescence by early Kaempferol treatment, with improved neural connectivity, neurovascular coupling, and parenchymal microstructure in select brain regions. However, Kaempferol failed to improve vasomotive function across the whole brain, as measured by cerebrovascular reactivity. The differential effects of Kaempferol treatment on various brain functional compartments support diverse cellular-level mitochondrial functional outcomes in vivo

Prediction of Task-Related BOLD fMRI with Amplitude Signatures of Resting-State fMRI

Blood oxygen contrast-functional magnetic resonance imaging (fMRI) signals are a convolution of neural and vascular components. Several studies indicate that task-related (T-fMRI) or resting-state (R-fMRI) responses linearly relate to hypercapnic task responses. Based on the linearity of R-fMRI and T-fMRI with hypercapnia demonstrated by different groups using different study designs, we hypothesized that R-fMRI and T-fMRI signals are governed by a common physiological mechanism and that resting-state fluctuation of amplitude (RSFA) should be linearly related to T-fMRI responses. We tested this prediction in a group of healthy younger humans where R-fMRI, T-fMRI, and hypercapnic (breath hold, BH) task measures were obtained form the same scan session during resting state and during performance of motor and BH tasks. Within individual subjects, significant linear correlations were observed between motor and BH task responses across voxels. When averaged over the whole brain, the subject-wise correlation between the motor and BH tasks showed a similar linear relationship within the group. Likewise, a significant linear correlation was observed between motor-task activity and RSFA across voxels and subjects. The linear rest–task (R–T) relationship between motor activity and RSFA suggested that R-fMRI and T-fMRI responses are governed by similar physiological mechanisms. A practical use of the R–T relationship is its potential to estimate T-fMRI responses in special populations unable to perform tasks during fMRI scanning. Using the R–T relationship determined from the first group of 12 healthy subjects, we predicted the T-fMRI responses in a second group of 7 healthy subjects. RSFA in both the lower and higher frequency ranges robustly predicted the magnitude of T-fMRI responses at the subject and voxel levels. We propose that T-fMRI responses are reliably predictable to the voxel level in situations where only R-fMRI measures are possible, and may be useful for assessing neural activity in task non-compliant clinical populations

Effect of Photoinitiator System and Water Content on Dynamic Mechanical Properties of a Light-cured bisGMA/HEMA Dental Resin

The selection of an appropriate photoinitiator system is critical for efficient polymerization of dental resins with satisfactory mechanical and physical properties. The purpose of this study was to evaluate the influence of adding an iodonium salt to two-component photoinitiator systems. Four photoinitiator systems were included in a model bisGMA/HEMA resin and used to prepare samples at different water contents; the dynamic mechanical properties and the final degree of conversion of the samples were then characterized. Addition of the iodonium salt to the two-component photoinitiator systems increased the final degree of conversion, glass transition temperature, rubbery modulus, and crosslink density. The photoinitiator system containing ethyl-4-(dimethylamino) benzoate as a coinitiator and the iodonium salt exhibited the highest rubbery modulus. The enhanced properties in the presence of the iodonium salt can be attributed to the production of an active phenyl radical with regeneration of the original camphorquinone, which may increase the compatibility between monomers and initiators, especially in the presence of water. The results support the hypothesis that a photoinitiator system containing an iodonium salt can increase both mechanical properties and final conversion of model resin polymerized in the presence of water. © 2009 Wiley Periodicals, Inc. J Biomed Mater Res 201

Biophysical Modulations of Functional Connectivity

Resting-state low frequency oscillations have been detected in many functional magnetic resonance imaging (MRI) studies and appear to be synchronized between functionally related areas. Converging evidence from MRI and other imaging modalities suggest that this activity has an intrinsic neuronal origin. Multiple consistent networks have been found in large populations, and have been shown to be stable over time. Further, these patterns of functional connectivity have been shown to be altered in healthy controls under various physiological challenges. This review will present the biophysical characterization of functional connectivity, and examine the effects of physical state manipulations (such as anesthesia, fatigue, and aging) in healthy controls.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90432/1/brain-2E2011-2E0039.pd

Consolidated Biochemical Profile of Subacute Stage Traumatic Brain Injury in Early Development

Traumatic brain injury (TBI) in general has varied neuropathological consequences depending upon the intensity and biomechanics of the injury. Furthermore, in pediatric TBI, intrinsic developmental changes add further complexity, necessitating a biochemical dimension for improved TBI characterization. In our earlier study investigating the subacute stage TBI metabolome (72 h post-injury) in a developmental rat model, significant ipsilateral brain biochemical changes occurred across 25 metabolite sets as determined by metabolite set enrichment analysis (MSEA). The broad metabolic perturbation was accompanied by behavioral deficits and neuronal loss across the ipsilateral hemisphere containing the injury epicenter. In order to obtain a consolidated biochemical profile of the TBI assessment, a subgrouping of the 190 identified brain metabolites was performed. Metabolites were divided into seven major subgroups: oxidative energy/mitochondrial, glycolysis/pentose phosphate pathway, fatty acid, amino acid, neurotransmitters/neuromodulators, one-carbon/folate and other metabolites. Subgroups were based on the chemical nature and association with critically altered biochemical pathways after TBI as obtained from our earlier untargeted analysis. Each metabolite subgroup extracted from the ipsilateral sham and TBI brains were modeled using multivariate partial least square discriminant analysis (PLS-DA) with the model accuracy used as a measurable index of TBI neurochemical impact. Volcano plots of each subgroup, corrected for multiple comparisons, determined the TBI neurochemical specificity. The results provide a ranked biochemical profile along with specificity of changes after developmental TBI, enabling a consolidated biochemical template for future classification of different TBI intensities and injury types in animal models

Global signal modulation of single-trial fMRI response variability: effect on positive vs negative BOLD response relationship

In functional magnetic resonance imaging (fMRI), the relationship between positive BOLD responses (PBRs) and negative BOLD responses (NBRs) to stimulation is potentially informative about the balance of excitatory and inhibitory brain responses in sensory cortex. In this study, we performed three separate experiments delivering visual, motor or somatosensory stimulation unilaterally, to one side of the sensory field, to induce PBR and NBR in opposite brain hemispheres. We then assessed the relationship between the evoked amplitudes of contralateral PBR and ipsilateral NBR at the level of both single-trial and average responses. We measure single-trial PBR and NBR peak amplitudes from individual time-courses, and show that they were positively correlated in all experiments. In contrast, in the average response across trials the absolute magnitudes of both PBR and NBR increased with increasing stimulus intensity, resulting in a negative correlation between mean response amplitudes. Subsequent analysis showed that the amplitude of single-trial PBR was positively correlated with the BOLD response across all grey-matter voxels and was not specifically related to the ipsilateral sensory cortical response. We demonstrate that the global component of this single-trial response modulation could be fully explained by voxel-wise vascular reactivity, the BOLD signal standard deviation measured in a separate resting-state scan (resting state fluctuation amplitude, RSFA). However, bilateral positive correlation between PBR and NBR regions remained. We further report that modulations in the global brain fMRI signal cannot fully account for this positive PBR-NBR coupling and conclude that the local sensory network response reflects a combination of superimposed vascular and neuronal signals. More detailed quantification of physiological and noise contributions to the BOLD signal is required to fully understand the trial-by-trial PBR and NBR relationship compared with that of average responses