Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Alveolar echinococcosis of the liver: Diffusion-weighted MRI findings and potential role in lesion characterisation

PURPOSE: To report the diffusion-weighted MRI findings in alveolar echinococcosis (AE) of the liver and evaluate the potential role of apparent diffusion coefficients (ADCs) in the characterisation of lesions. MATERIALS AND METHODS: We retrospectively included 22 patients with 63 AE liver lesions (≥1cm), examined with 3-T liver MRI, including a free-breathing diffusion-weighted single-shot echo-planar imaging sequence (b-values=50, 300 and 600s/mm(2)). Two radiologists jointly assessed the following lesion features: size, location, presence of cystic and/or solid components (according to Kodama's classification system), relative contrast enhancement, and calcifications (on CT). The ADCtotal, ADCmin and ADCmax were measured in each lesion and the surrounding liver parenchyma. RESULTS: Three type 1, 19 type 2, 17 type 3, three type 4 and 21 type 5 lesions were identified. The mean (±SD) ADCtotal, ADCmin and ADCmax for all lesions were 1.73±0.50, 0.76±0.38 and 2.63±0.76×10(-3)mm(2)/s, respectively. The mean ADCtotal for type 1, type 2, type 3, type 4 and type 5 lesions were 1.97±1.01, 1.76±0.53, 1.73±0.41, 1.15±0.42 and 1.76±0.44×10(-3)mm(2)/s, respectively. No significant differences were found between the five lesion types, except for type 4 (p=0.0363). There was a significant correlation between the presence of a solid component and low ADCmin (r=0.39, p=0.0016), whereas an inverse correlation was found between the relative contrast enhancement and ADCtotal (r=-0.34, p=0.0072). CONCLUSION: The ADCs of AE lesions are relatively low compared to other cystic liver lesions, which may help in the differential diagnosis. Although ADCs are of little use to distinguish between the five lesion types, their low value reflects the underlying solid component.

Diffusion-weighted MR imaging of the spine at 3-T: feasibility, optimization of b-value and utility to differentiate benign from pathological vertebral compression fractures

Purpose: To evaluate the feasibility, determine the optimal b-value, and assess the utility of 3-T diffusion-weighted MR imaging (DWI) of the spine in differentiating benign from pathologic vertebral compression fractures.Methods and Materials: Twenty patients with 38 vertebral compression fractures (24 benign, 14 pathologic) and 20 controls (total: 23 men, 17 women, mean age 56.2years) were included from December 2010 to May 2011 in this IRB-approved prospective study. MR imaging of the spine was performed on a 3-T unit with T1-w, fat-suppressed T2-w, gadolinium-enhanced fat-suppressed T1-w and zoomed-EPI (2D RF excitation pulse combined with reduced field-of-view single-shot echo-planar readout) diffusion-w (b-values: 0, 300, 500 and 700s/mm2) sequences. Two radiologists independently assessed zoomed-EPI image quality in random order using a 4-point scale: 1=excellent to 4=poor. They subsequently measured apparent diffusion coefficients (ADCs) in normal vertebral bodies and compression fractures, in consensus.Results: Lower b-values correlated with better image quality scores, with significant differences between b=300 (mean±SD=2.6±0.8), b=500 (3.0±0.7) and b=700 (3.6±0.6) (all p<0.001). Mean ADCs of normal vertebral bodies (n=162) were 0.23, 0.17 and 0.11×10-3mm2/s with b=300, 500 and 700s/mm2, respectively. In contrast, mean ADCs were 0.89, 0.70 and 0.59×10-3mm2/s for benign vertebral compression fractures and 0.79, 0.66 and 0.51×10-3mm2/s for pathologic fractures with b=300, 500 and 700s/mm2, respectively. No significant difference was found between ADCs of benign and pathologic fractures.Conclusion: 3-T DWI of the spine is feasible and lower b-values (300s/mm2) are recommended. However, our preliminary results show no advantage of DWI in differentiating benign from pathologic vertebral compression fractures.

Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method.

We present a method for segmenting white matter tracts from high angular resolution diffusion MR. images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.

Diffusion-weighted magnetic resonance imaging in metastatic gastrointestinal stromal tumor (GIST): a pilot study on the assessment of treatment response in comparison with 18F-FDG PET/CT.

BACKGROUND: Diffusion-weighted magnetic resonance imaging (MRI) is increasingly being used for assessing the treatment succes in oncology, but the real clinical value needs to evaluated by comparison with other, already established, metabolic imaging techniques. PURPOSE: To prospectively evaluate the clinical potential of diffusion-weighted MRI with apparent diffusion coefficient (ADC) mapping for gastrointestinal stromal tumor (GIST) response to targeted therapy compared with 18F-fluorodeoxyglucose positron emission tomography/computed tomography (18F-FDG PET/CT). MATERIAL AND METHODS: Eight patients (mean age, 56 ± 11 years) known to have metastatic GIST underwent 18F-FDG PET/CT and MRI (T1Gd, DWI [b = 50,300,600], ADC mapping) simultaneously, before and after change in targeted therapy. MR and PET/CT examinations were first analyzed blindly. Second, PET/CT images were co-registered with T1Gd-MR images for lesion detection. Only 18F-FDG avid lesions were considered. Maximum standardized uptake value (SUVmax) and the corresponding minimum ADCmin were measured for the six largest lesions per patient, if any, on baseline and follow-up examinations. The relationship between changes in SUVmax and ADCmin was analyzed (Spearman's correlation). RESULTS: Twenty-four metastases (12 hepatic, 12 extra-hepatic) were compared on PET/CT and MR images. SUVmax decreased from 7.7 ± 8.1 g/mL to 5.5 ± 5.4 g/mL (P = 0.20), while ADCmin increased from 1.2 ± 0.3 × 10(-3)mm(2)/s to 1.5 ± 0.3 × 10(-3)mm(2)/s (P = 0.0002). There was a significant association between changes in SUVmax and ADCmin (rho = - 0.62, P = 0.0014), but not between changes in lesions size (P = 0.40). CONCLUSION: Changes in ADCmin correlated with the response of 18F-FDG avid GIST to targeted therapy. Thus, diffusion-weighted MRI may represent a radiation-free alternative for follow-up treatment for metastatic GIST patients.

3-d residual eddy current field characterisation: applied to diffusion weighted magnetic resonance imaging.

Clinical use of the Stejskal-Tanner diffusion weighted images is hampered by the geometric distortions that result from the large residual 3-D eddy current field induced. In this work, we aimed to predict, using linear response theory, the residual 3-D eddy current field required for geometric distortion correction based on phantom eddy current field measurements. The predicted 3-D eddy current field induced by the diffusion-weighting gradients was able to reduce the root mean square error of the residual eddy current field to ~1 Hz. The model's performance was tested on diffusion weighted images of four normal volunteers, following distortion correction, the quality of the Stejskal-Tanner diffusion-weighted images was found to have comparable quality to image registration based corrections (FSL) at low b-values. Unlike registration techniques the correction was not hindered by low SNR at high b-values, and results in improved image quality relative to FSL. Characterization of the 3-D eddy current field with linear response theory enables the prediction of the 3-D eddy current field required to correct eddy current induced geometric distortions for a wide range of clinical and high b-value protocols.

Influence of initial foot dorsal flexion on vertical jump and running performance.

Several studies (on an inclined platform or with special shoes) have reported improved jump performance when the ankle was in a dorsiflexion (DF) position. The present study aims to test whether shoes inducing moderate DF modify vertical jump performance and energy cost. Twenty-one young, healthy female subjects (30 +/- 6 yr, 58 +/- 6 kg, O2max 45 +/- 3 mLxkg-1xmin-1, mean +/- SD) participated in the study. Jump performance was tested with subjects either wearing 4 degrees DF or standard (S) shoes. The jump tests (performed on a force platform) consisted of squat jump (SJ), countermovement jump (CMJ), and continuous jumps (CJ) during 15 seconds. Measured parameters were jump height, speed at take off, and maximal and average power. Oxygen uptake was measured on a treadmill while subjects ran at 95% of the anaerobic threshold during a 7-minute steady-state period. As compared with S shoes, DF shoes significantly improved the height of SJ (31 +/- 4 cm vs. 34 +/- 4 cm, p = 0.0001), CMJ (32 +/- 4 cm vs. 34 +/- 4 cm, p = 0.0004), and CJ (17.5 +/- 4.2 cm vs. 22.0 +/- 6.0 cm, p = 0.0001). Speed at take off was also significantly higher. Mean power significantly increased in SJ and CJ but not in CMJ. Oxygen uptake was not different between conditions (p = 0.40). Dorsiflexion shoes induce a significant increase in jump performance. These results are in accordance with the concept that a DF of the ankle may induce an increase of the length and strength of the triceps surae (higher torque). However, wearing DF shoes did not require more energy during running. Dorsiflexion shoes could be used to increase jump performance in several sports such as volleyball in which jump height is essential.

Altered structural connectivity in patients with medial temporal lobe epilepsy: A Diffusion Spectrum Imaging and Graph Analysis study

In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the nodes represents the anatomical ROIs and the edges are the connections between any pair of ROIs weighted by the mean GFA/FA values. A significant difference was found between the patient group vs control group in characteristic path length, clustering coefficient and small-worldness. This suggests that the MTLE network is less efficient compared to the network of the control group.

Quantitative Assessment of T1 Relaxation and Diffusion as a Prognostic Tool for Brain Development: A Longitudinal Preliminary Study on Preterm Babies

BACKGROUND: Despite major advances in care of premature infants, survivors exhibit mild cognitive deficits in around 40%. Beside severe intraventricular haemorrhages (IVH) and cystic periventricular leucomalacia (PVL), more subtle patterns such as grade I and II IVH, punctuate WM lesions and diffuse PVL might be linked to the cognitive deficits. Grey matter disease is also recognized to contribute to long-term cognitive impairment.¦OBJECTIVE: We intend to use novel MR techniques to study more precisely the different injury patterns. In particular MP2RAGE (magnetization prepared dual rapid echo gradient) produces high-resolution quantitative T1 relaxation maps. This contrast is known to reflect tissue anomalies such as white matter injury in general and dysmyelination in particular. We also used diffusion tensor imaging, a quantitative technique known to reflect white matter maturation and disease.¦DESIGN/METHODS: All preterm infants born under 30 weeks of GA were included. Serial 3T MR-imaging using a neonatal head-coil at DOL 3, 10 and at term equivalent age (TEA), using DTI and MP2RAGE sequences was performed. MP2RAGE generates a T1 map and allows calculating the relaxation time T1. Multiple measurements were performed for each exam in 12 defined white and grey matter ROIs.¦RESULTS: 16 patients were recruited: mean GA 27 2/7 w (191,2d SD±10,8), mean BW 999g (SD±265). 39 MRIs were realized (12 early: mean 4,83d±1,75, 13 late: mean 18,77d±8,05 and 14 at TEA: 88,91d±8,96). Measures of relaxation time T1 show a gradual and significant decrease over time (for ROI PLIC mean±SD in ms: 2100.53±102,75, 2116,5±41,55 and 1726,42±51,31 and for ROI central WM: 2302,25±79,02, 2315,02±115,02 and 1992,7±96,37 for early, late and TEA MR respectively). These trends are also observed in grey matter area, especially in thalamus. Measurements of ADC values show similar monotonous decrease over time.¦CONCLUSIONS: From these preliminary results, we conclude that quantitative MR imaging in very preterm infants is feasible. On the successive MP2RAGE and DTI sequences, we observe a gradual decrease over time in the described ROIs, representing the progressive maturation of the WM micro-structure and interestingly the same evolution is observed in the grey matter. We speculate that our study will provide normative values for T1map and ADC and might be a predictive factor for favourable or less favourable outcome.

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.

Atomic diffusion induced by stress relaxation in InGaAs/GaAs epitaxial layers

The origin of the microscopic inhomogeneities in InxGa12xAs layers grown on GaAs by molecular beam epitaxy is analyzed through the optical absorption spectra near the band gap. It is seen that, for relaxed thick layers of about 2.8 mm, composition inhomogeneities are responsible for the band edge smoothing into the whole compositional range (0.05,x,0.8). On the other hand, in thin enough layers strain inhomogeneities are dominant. This evolution in line with layer thickness is due to the atomic diffusion at the surface during growth, induced by the strain inhomogeneities that arise from stress relaxation. In consequence, the strain variations present in the layer are converted into composition variations during growth. This process is energetically favorable as it diminishes elastic energy. An additional support to this hypothesis is given by a clear proportionality between the magnitude of the composition variations and the mean strain.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

Self and cross-velocity correlation functions and diffusion coefficients in liquids: a molecular dynamics study of binary mixtures of soft spheres

Molecular dynamics simulation is applied to the study of the diffusion properties in binary liquid mixtures made up of soft-sphere particles with different sizes and masses. Self- and distinct velocity correlation functions and related diffusion coefficients have been calculated. Special attention has been paid to the dynamic cross correlations which have been computed through recently introduced relative mean molecular velocity correlation functions which are independent on the reference frame. The differences between the distinct velocity correlations and diffusion coefficients in different reference frames (mass-fixed, number-fixed, and solvent-fixed) are discussed.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.