Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Diffusion-weighted MRI in metastatic gastrointestinal tumors (GIST): A pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT

Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumor (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT. Methods and materials: Five patients (3W/2M, aged 56 ± 13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analyzed blindly, then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analyzed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analyzed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2 ± 7.7 g/mL to 5.9 ± 5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

Diffusion-weighted MRI in metastatic gastrointestinal tumours (GIST): a pilot study on the assessment of treatment response in comparison with 18 F-FDG PET/CT

Purpose: To evaluate the clinical potential of diffusion-weighted MR imaging with apparent diffusion coefficient (ADC) mapping for the assessment of gastrointestinal stromal tumour (GIST) response to targeted therapy in comparison with 18F-FDG PET/CT Methods and Materials: Five patients (3 W/2M, aged 56±13 y) with metastatic GIST underwent both a 18F-FDG PET/CT (Discovery LS, GE Healthcare) and a MRI (VIBE T1 Gd, DWI [b = 50,300,600] and ADC mapping) before and after change in therapy. Exams were first analysed blindly and then PET/CT images were coregistered to T1 Gd MR images for lesion detection. SUVmax and ADC were measured for the six largest lesions on MRI. The relationship between SUVmax and ADC was analysed using Spearman's correlation. Results: Altogether, 24 lesions (15 hepatic and 9 non-hepatic) were analysed on both modalities. Three PET/CT lesions (12.5%) were initially not considered on ADC and 4 lesions on the second PET/CT were excluded because of hepatic vascular activity spillover. SUVmax decreased from 7.2±7.7 g/mL to 5.9±5.9 g/mL (P = 0.53) and ADC increased from 1.2x10-3 mm2/s ± 0.4 to 1.4x10-3 mm2/s ± 0.4 (P = 0.07). There was a significant association between SUVmax decrease and ADC increase (rho= -0.64, P = 0.004). Conclusion: Changes in ADC from diffusion-weighted MRI reflect response of 18F-FDG-avid GIST to therapy. The exact diagnostic value of DWI needs to be investigated further, as well as the effect of lesion size and time under therapy before imaging. Furthermore, the proven association between SUVmax and ADC may be useful for the assessment of treatment response in 18F-FDG non-avid GIST.

Perfusion and diffusion MRI of glioblastoma progression in a four-year prospective temozolomide clinical trial.

PURPOSE: This study was performed to determine the impact of perfusion and diffusion magnetic resonance imaging (MRI) sequences on patients during treatment of newly diagnosed glioblastoma. Special emphasis has been given to these imaging technologies as tools to potentially anticipate disease progression, as progression-free survival is frequently used as a surrogate endpoint. METHODS AND MATERIALS: Forty-one patients from a phase II temolozomide clinical trial were included. During follow-up, images were integrated 21 to 28 days after radiochemotherapy and every 2 months thereafter. Assessment of scans included measurement of size of lesion on T1 contrast-enhanced, T2, diffusion, and perfusion images, as well as mass effect. Classical criteria on tumor size variation and clinical parameters were used to set disease progression date. RESULTS: A total of 311 MRI examinations were reviewed. At disease progression (32 patients), a multivariate Cox regression determined 2 significant survival parameters: T1 largest diameter (p < 0.02) and T2 size variation (p < 0.05), whereas perfusion and diffusion were not significant. CONCLUSION: Perfusion and diffusion techniques cannot be used to anticipate tumor progression. Decision making at disease progression is critical, and classical T1 and T2 imaging remain the gold standard. Specifically, a T1 contrast enhancement over 3 cm in largest diameter together with an increased T2 hypersignal is a marker of inferior prognosis.

Comparative testing of a miniature diffusion size classifier to assess airborne ultrafine particles under field conditions

Miniature diffusion size classifiers (miniDiSC) are novel handheld devices to measure ultrafine particles (UFP). UFP have been linked to the development of cardiovascular and pulmonary diseases; thus, detection and quantification of these particles are important for evaluating their potential health hazards. As part of the UFP exposure assessments of highwaymaintenance workers in western Switzerland, we compared a miniDiSC with a portable condensation particle counter (P-TRAK). In addition, we performed stationary measurements with a miniDiSC and a scanning mobility particle sizer (SMPS) at a site immediately adjacent to a highway. Measurements with miniDiSC and P-TRAK correlated well (correlation of r = 0.84) but average particle numbers of the miniDiSC were 30%âeuro"60% higher. This difference was significantly increased for mean particle diameters below 40 nm. The correlation between theminiDiSC and the SMPSduring stationary measurements was very high (r = 0.98) although particle numbers from the miniDiSC were 30% lower. Differences between the three devices were attributed to the different cutoff diameters for detection. Correction for this size dependent effect led to very similar results across all counters.We did not observe any significant influence of other particle characteristics. Our results suggest that the miniDiSC provides accurate particle number concentrations and geometric mean diameters at traffic-influenced sites, making it a useful tool for personal exposure assessment in such settings.

Diffusion-weighted spectroscopy: a novel approach to determine macromolecule resonances in short-echo time 1H-MRS.

Quantification of short-echo time proton magnetic resonance spectroscopy results in >18 metabolite concentrations (neurochemical profile). Their quantification accuracy depends on the assessment of the contribution of macromolecule (MM) resonances, previously experimentally achieved by exploiting the several fold difference in T(1). To minimize effects of heterogeneities in metabolites T(1), the aim of the study was to assess MM signal contributions by combining inversion recovery (IR) and diffusion-weighted proton spectroscopy at high-magnetic field (14.1 T) and short echo time (= 8 msec) in the rat brain. IR combined with diffusion weighting experiments (with δ/Δ = 1.5/200 msec and b-value = 11.8 msec/μm(2)) showed that the metabolite nulled spectrum (inversion time = 740 msec) was affected by residuals attributed to creatine, inositol, taurine, choline, N-acetylaspartate as well as glutamine and glutamate. While the metabolite residuals were significantly attenuated by 50%, the MM signals were almost not affected (< 8%). The combination of metabolite-nulled IR spectra with diffusion weighting allows a specific characterization of MM resonances with minimal metabolite signal contributions and is expected to lead to a more precise quantification of the neurochemical profile.

Cationic Diffusion in La2/3Ca1/3MnO3 Thin Films Grown on LaAlO3 (001) Substrates.

Microstructural features of La2/3Ca1/3MnO3 layers of various thicknesses grown on top of 001 LaAlO3 substrates are studied by using transmission electron microscopy and electron energy loss spectroscopy. Films are of high microstructural quality but exhibit some structural relaxation and mosaicity both when increasing thickness or after annealing processes. The existence of a cationic segregation process of La atoms toward free surface has been detected, as well as a Mn oxidation state variation through layer thickness. La diffusion would lead to a Mn valence change and, in turn, to reduced magnetization.

Nutrient supply by mass flow and diffusion to maize plants in response to soil aggregate size and water potential

Nutrients are basically transported to the roots by mass flow and diffusion. The aim of this study was to quantify the contribution of these two mechanisms to the acquisition of macronutrients (N, P, K, Ca, Mg, and S) and cationic micronutrients (Fe, Mn, Zn, and Cu) by maize plants as well as xylem exudate volume and composition in response to soil aggregate size and water availability. The experiment was conducted in a greenhouse with samples of an Oxisol, from under two management systems: a region of natural savanna-like vegetation (Cerradão, CER) and continuous maize under conventional management for over 30 years (CCM). The treatments were arranged in a factorial [2 x (1 + 2) x 2] design, with two management systems (CER and CCM), (1 + 2) soil sifted through a 4 mm sieve and two aggregate classes (< 0.5 mm and 0.5 - 4.0 mm) and two soil matric potentials (-40 and -10 kPa). These were evaluated in a randomized block design with four replications. The experiment was conducted for 70 days after sowing. The influence of soil aggregate size and water potential on the nutrient transport mechanisms was highest in soil samples with higher nutrient concentrations in solution, in the CER system; diffusion became more relevant when water availability was higher and in aggregates < 0.5 mm. The volume of xylem exudate collected from maize plants increased with the decrease in aggregate size and the increased availability of soil water in the CER system. The highest Ca and Mg concentrations in the xylem exudate of plants grown on samples from the CER system were related to the high concentrations of these nutrients in the soil solution of this management system.

l0-deconvolution for compressive diffusion MRI

Diffusion MRI is a well established imaging modality providing a powerful way to non-invasively probe the structure of the white matter. Despite the potential of the technique, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a wide variety of methods have been proposed to shorten acquisition times. [...] We here review a recent work where we propose to further exploit the versatility of compressed sensing and convex optimization with the aim to characterize the fiber orientation distribution sparsity more optimally. We re-formulate the spherical deconvolution problem as a constrained l0 minimization.

Diffusion tensor imaging shows structural remodeling of stroke mirror region: results from a pilot study.

Background: The role of the non-injured hemisphere in stroke recovery is poorly understood. In this pilot study, we sought to explore the presence of structural changes detectable by diffusion tensor imaging (DTI) in the contralesional hemispheres of patients who recovered well from ischemic stroke. Methods: We analyzed serial DTI data from 16 stroke patients who had moderate initial neurological deficits (NIHSS scores 3-12) and good functional outcome at 3-6 months (NIHSS score 0 or modified Rankin Score ≤1). We segmented the brain tissue in gray and white matter (GM and WM) and measured the apparent diffusion coefficient (ADC) and fractional anisotropy in the infarct, in the contralesional infarct mirror region as well as in concentrically expanding regions around them. Results: We found that GM and WM ADC significantly increased in the infarct region (p < 0.01) from acute to chronic time points, whereas in the infarct mirror region, GM and WM ADC increased (p < 0.01) and WM fractional anisotropy decreased (p < 0.05). No significant changes were detected in other regions. Conclusion: DTI-based metrics are sensitive to regional structural changes in the contralesional hemisphere during stroke recovery. Prospective studies in larger cohorts with varying levels of recovery are needed to confirm our findings.

Accelerated Microstructure Imaging via Convex Optimization (AMICO) from diffusion MRI data.

Microstructure imaging from diffusion magnetic resonance (MR) data represents an invaluable tool to study non-invasively the morphology of tissues and to provide a biological insight into their microstructural organization. In recent years, a variety of biophysical models have been proposed to associate particular patterns observed in the measured signal with specific microstructural properties of the neuronal tissue, such as axon diameter and fiber density. Despite very appealing results showing that the estimated microstructure indices agree very well with histological examinations, existing techniques require computationally very expensive non-linear procedures to fit the models to the data which, in practice, demand the use of powerful computer clusters for large-scale applications. In this work, we present a general framework for Accelerated Microstructure Imaging via Convex Optimization (AMICO) and show how to re-formulate this class of techniques as convenient linear systems which, then, can be efficiently solved using very fast algorithms. We demonstrate this linearization of the fitting problem for two specific models, i.e. ActiveAx and NODDI, providing a very attractive alternative for parameter estimation in those techniques; however, the AMICO framework is general and flexible enough to work also for the wider space of microstructure imaging methods. Results demonstrate that AMICO represents an effective means to accelerate the fit of existing techniques drastically (up to four orders of magnitude faster) while preserving accuracy and precision in the estimated model parameters (correlation above 0.9). We believe that the availability of such ultrafast algorithms will help to accelerate the spread of microstructure imaging to larger cohorts of patients and to study a wider spectrum of neurological disorders.

Estimation of jump-diffusion processes via empirical characteristic functions

Preface The starting point for this work and eventually the subject of the whole thesis was the question: how to estimate parameters of the affine stochastic volatility jump-diffusion models. These models are very important for contingent claim pricing. Their major advantage, availability T of analytical solutions for characteristic functions, made them the models of choice for many theoretical constructions and practical applications. At the same time, estimation of parameters of stochastic volatility jump-diffusion models is not a straightforward task. The problem is coming from the variance process, which is non-observable. There are several estimation methodologies that deal with estimation problems of latent variables. One appeared to be particularly interesting. It proposes the estimator that in contrast to the other methods requires neither discretization nor simulation of the process: the Continuous Empirical Characteristic function estimator (EGF) based on the unconditional characteristic function. However, the procedure was derived only for the stochastic volatility models without jumps. Thus, it has become the subject of my research. This thesis consists of three parts. Each one is written as independent and self contained article. At the same time, questions that are answered by the second and third parts of this Work arise naturally from the issues investigated and results obtained in the first one. The first chapter is the theoretical foundation of the thesis. It proposes an estimation procedure for the stochastic volatility models with jumps both in the asset price and variance processes. The estimation procedure is based on the joint unconditional characteristic function for the stochastic process. The major analytical result of this part as well as of the whole thesis is the closed form expression for the joint unconditional characteristic function for the stochastic volatility jump-diffusion models. The empirical part of the chapter suggests that besides a stochastic volatility, jumps both in the mean and the volatility equation are relevant for modelling returns of the S&P500 index, which has been chosen as a general representative of the stock asset class. Hence, the next question is: what jump process to use to model returns of the S&P500. The decision about the jump process in the framework of the affine jump- diffusion models boils down to defining the intensity of the compound Poisson process, a constant or some function of state variables, and to choosing the distribution of the jump size. While the jump in the variance process is usually assumed to be exponential, there are at least three distributions of the jump size which are currently used for the asset log-prices: normal, exponential and double exponential. The second part of this thesis shows that normal jumps in the asset log-returns should be used if we are to model S&P500 index by a stochastic volatility jump-diffusion model. This is a surprising result. Exponential distribution has fatter tails and for this reason either exponential or double exponential jump size was expected to provide the best it of the stochastic volatility jump-diffusion models to the data. The idea of testing the efficiency of the Continuous ECF estimator on the simulated data has already appeared when the first estimation results of the first chapter were obtained. In the absence of a benchmark or any ground for comparison it is unreasonable to be sure that our parameter estimates and the true parameters of the models coincide. The conclusion of the second chapter provides one more reason to do that kind of test. Thus, the third part of this thesis concentrates on the estimation of parameters of stochastic volatility jump- diffusion models on the basis of the asset price time-series simulated from various "true" parameter sets. The goal is to show that the Continuous ECF estimator based on the joint unconditional characteristic function is capable of finding the true parameters. And, the third chapter proves that our estimator indeed has the ability to do so. Once it is clear that the Continuous ECF estimator based on the unconditional characteristic function is working, the next question does not wait to appear. The question is whether the computation effort can be reduced without affecting the efficiency of the estimator, or whether the efficiency of the estimator can be improved without dramatically increasing the computational burden. The efficiency of the Continuous ECF estimator depends on the number of dimensions of the joint unconditional characteristic function which is used for its construction. Theoretically, the more dimensions there are, the more efficient is the estimation procedure. In practice, however, this relationship is not so straightforward due to the increasing computational difficulties. The second chapter, for example, in addition to the choice of the jump process, discusses the possibility of using the marginal, i.e. one-dimensional, unconditional characteristic function in the estimation instead of the joint, bi-dimensional, unconditional characteristic function. As result, the preference for one or the other depends on the model to be estimated. Thus, the computational effort can be reduced in some cases without affecting the efficiency of the estimator. The improvement of the estimator s efficiency by increasing its dimensionality faces more difficulties. The third chapter of this thesis, in addition to what was discussed above, compares the performance of the estimators with bi- and three-dimensional unconditional characteristic functions on the simulated data. It shows that the theoretical efficiency of the Continuous ECF estimator based on the three-dimensional unconditional characteristic function is not attainable in practice, at least for the moment, due to the limitations on the computer power and optimization toolboxes available to the general public. Thus, the Continuous ECF estimator based on the joint, bi-dimensional, unconditional characteristic function has all the reasons to exist and to be used for the estimation of parameters of the stochastic volatility jump-diffusion models.

Diffusion Spectrum Imaging after stroke shows structural changes in the contra-lateral motor network correlating with functional recovery

There is growing interest in understanding the role of the non-injured contra-lateral hemisphere in stroke recovery. In the experimental field, histological evidence has been reported that structural changes occur in the contra-lateral connectivity and circuits during stroke recovery. In humans, some recent imaging studies indicated that contra-lateral sub-cortical pathways and functional and structural cortical networks are remodeling, after stroke. Structural changes in the contra-lateral networks, however, have never been correlated to clinical recovery in patients. To determine the importance of the contra-lateral structural changes in post-stroke recovery, we selected a population of patients with motor deficits after stroke affecting the motor cortex and/or sub-cortical motor white matter. We explored i) the presence of Generalized Fractional Anisotropy (GFA) changes indicating structural alterations in the motor network of patientsâeuro? contra-lateral hemisphere as well as their longitudinal evolution ii) the correlation of GFA changes with patientsâeuro? clinical scores, stroke size and demographics data iii) and a predictive model.

Contrasting diffusion of Quaternary gene pools across Europe: the case of the arctic-alpine Gentiana nivalis L. (Gentianaceae).

The fate of European arctic-alpine species during Pleistocene climatic oscillations still remains debated. Did these cold-adapted species invade much of the continental steppe or did they remain restricted to warmer slopes of inner mountain massifs? To examine this question, we investigated the phylogeography of Gentiana nivalis, a typical European arctic-alpine plant species. Genome fingerprinting analyses revealed that four genetic pools are actually unevenly distributed across the continent. One cluster covers almost all mountain massifs as well as northern areas, and thus coincides with a scenario of past distribution covering a large part of the European glacial steppe. In contrast, the three other lineages are strongly restricted spatially to western, central, and eastern Alps, respectively, thus arguing towards a scenario of in situ glacial survival. The coexistence of lineages with such contrasting demographic histories in Europe challenges our classical view of refugia and corroborates several hypotheses of biogeographers from the twentieth century.

A multimodality vascular imaging phantom with fiducial markers visible in DSA, CTA, MRA, and ultrasound.

The objective was to design a vascular phantom compatible with digital subtraction angiography, computerized tomography angiography, ultrasound and magnetic resonance angiography (MRA). Fiducial markers were implanted at precise known locations in the phantom to facilitate identification and orientation of plane views from three-dimensional (3-D) reconstructed images. A vascular conduit connected to tubing at the extremities of the phantom ran through an agar-based gel filling it. A vessel wall in latex was included around the conduit to avoid diffusion of contrast agents. Using a lost-material casting technique based on a low melting point metal, geometries of pathological vessels were modeled. During the experimental testing, fiducial markers were detectable in all modalities without distortion. No leak of gadolinium through the vascular wall was observed on MRA after 5 hours. Moreover, no significant deformation of the vascular conduit was noted during the fabrication process (confirmed by microtome slicing along the vessel). The potential use of the phantom for calibration, rescaling, and fusion of 3-D images obtained from the different modalities as well as its use for the evaluation of intra- and inter-modality comparative studies of imaging systems are discussed. In conclusion, the vascular phantom can allow accurate calibration of radiological imaging devices based on x-ray, magnetic resonance and ultrasound and quantitative comparisons of the geometric accuracy of the vessel lumen obtained with each of these methods on a given well defined 3-D geometry.