Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Criteria for hitting probabilities with applications to systems of stochastic wave equations

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and Bessel-Riesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k >- 1 driven by a d-dimensional spatially homogeneous additive Gaussian noise that is white in time and colored in space.

Stochastic differential equations with random coefficients

In this paper we establish the existence and uniqueness of a solution for different types of stochastic differential equation with random initial conditions and random coefficients. The stochastic integral is interpreted as a generalized Stratonovich integral, and the techniques used to derive these results are mainly based on the path properties of the Brownian motion, and the definition of the Stratonovich integral.

Large deviations for stochastic Volterra equations

This paper is devoted to prove a large-deviation principle for solutions to multidimensional stochastic Volterra equations.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Magnetic resonance imaging correlates of first-episode psychosis in young adult male patients: combined analysis of grey and white matter.

Background: Several patterns of grey and white matter changes have been separately described in young adults with first-episode psychosis. Concomitant investigation of grey and white matter densities in patients with first-episode psychosis without other psychiatric comorbidities that include all relevant imaging markers could provide clues to the neurodevelopmental hypothesis in schizophrenia. Methods: We recruited patients with first-episode psychosis diagnosed according to the DSM-IV-TR and matched controls. All participants underwent magnetic resonance imaging (MRI). Voxel-based morphometry (VBM) analysis and mean diffusivity voxel-based analysis (VBA) were used for grey matter data. Fractional anisotropy and axial, radial and mean diffusivity were analyzed using tract-based spatial statistics (TBSS) for white matter data. Results: We included 15 patients and 16 controls. The mean diffusivity VBA showed significantly greater mean diffusivity in the first-episode psychosis than in the control group in the lingual gyrus bilaterally, the occipital fusiform gyrus bilaterally, the right lateral occipital gyrus and the right inferior temporal gyrus. Moreover, the TBSS analysis revealed a lower fractional anisotropy in the first-episode psychosis than in the control group in the genu of the corpus callosum, minor forceps, corticospinal tract, right superior longitudinal fasciculus, left middle cerebellar peduncle, left inferior longitudinal fasciculus and the posterior part of the fronto-occipital fasciculus. This analysis also revealed greater radial diffusivity in the first-episode psychosis than in the control group in the right corticospinal tract, right superior longitudinal fasciculus and left middle cerebellar peduncle. Limitations: The modest sample size and the absence of women in our series could limit the impact of our results. Conclusion: Our results highlight the structural vulnerability of grey matter in posterior areas of the brain among young adult male patients with first-episode psychosis. Moreover, the concomitant greater radial diffusivity within several regions already revealed by the fractional anisotropy analysis supports the idea of a late myelination in patients with first-episode psychosis.

Assessment of cardiac ischaemia and viability: role of cardiovascular magnetic resonance.

Over the past years, cardiovascular magnetic resonance (CMR) has proven its efficacy in large clinical trials, and consequently, the assessment of function, viability, and ischaemia by CMR is now an integrated part of the diagnostic armamentarium in cardiology. By combining these CMR applications, coronary artery disease (CAD) can be detected in its early stages and this allows for interventions with the goal to reduce complications of CAD such as infarcts and subsequently chronic heart failure (CHF). As the CMR examinations are robust and reproducible and do not expose patients to radiation, they are ideally suited for repetitive studies without harm to the patients. Since CAD is a chronic disease, the option to monitor CAD regularly by CMR over many decades is highly valuable. Cardiovascular magnetic resonance also progressed recently in the setting of acute coronary syndromes. In this situation, CMR allows for important differential diagnoses. Cardiovascular magnetic resonance also delineates precisely the different tissue components in acute myocardial infarction such as necrosis, microvascular obstruction (MVO), haemorrhage, and oedema, i.e. area at risk. With these features, CMR might also become the preferred tool to investigate novel treatment strategies in clinical research. Finally, in CHF patients, the versatility of CMR to assess function, flow, perfusion, and viability and to characterize tissue is helpful to narrow the differential diagnosis and to monitor treatment.

Cardiac structure and function in the obese: a cardiovascular magnetic resonance imaging study.

BACKGROUND: Obesity is a major health problem in the Western world. Among obese subjects cardiac pathology is common, but conventional noninvasive imaging modalities are often suboptimal for detailed evaluation of cardiac structure and function. We investigated whether cardiovascular magnetic resonance imaging (CMR) can better characterize possible cardiac abnormalities associated with obesity, in the absence of other confounding comorbidities. METHODS: In this prospective cross-sectional study, CMR was used to quantify left and right ventricular volumes, ejection fraction, mass, cardiac output, and apical left ventricular rotation in 25 clinically healthy obese men and 25 age-matched lean controls. RESULTS: Obese subjects had higher left ventricular mass (203 +/- 38 g vs. 163 +/- 22 g, p < 0.001), end-diastolic volume (176 +/- 29 mL vs. 156 +/- 25 mL, p < 0.05), and cardiac output (8.2 +/- 1.2 L/min vs. 6.4 +/- 1.3 L/min, p < 0.001). The obese also had increased right ventricular mass (105 +/- 25 g vs. 87 +/- 18 g, p < 0.005) and end-diastolic volume (179 +/- 36 mL vs. 155 +/- 28 mL, p < 0.05). When indexed for height, differences in left and right ventricular mass, and left ventricular end-diastolic volume remained significant. Apical left ventricular rotation and rotational velocity patterns were also different between obese and lean subjects. CONCLUSIONS: Obesity is independently associated with remodeling of the heart. Cardiovascular magnetic resonance imaging identifies subtle cardiac abnormalities and may be the preferred imaging technique to evaluate cardiac structure and function in the obese.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

High-resolution three-dimensional aortic magnetic resonance angiography and quantitative vessel wall characterization of different atherosclerotic stages in a rabbit model

PURPOSE: Atherosclerosis results in a considerable medical and socioeconomic impact on society. We sought to evaluate novel magnetic resonance imaging (MRI) angiography and vessel wall sequences to visualize and quantify different morphologic stages of atherosclerosis in a Watanabe hereditary hyperlipidemic (WHHL) rabbit model. MATERIAL AND METHODS: Aortic 3D steady-state free precession angiography and subrenal aortic 3D black-blood fast spin-echo vessel wall imaging pre- and post-Gadolinium (Gd) was performed in 14 WHHL rabbits (3 normal, 6 high-cholesterol diet, and 5 high-cholesterol diet plus endothelial denudation) on a commercial 1.5 T MR system. Angiographic lumen diameter, vessel wall thickness, signal-/contrast-to-noise analysis, total vessel area, lumen area, and vessel wall area were analyzed semiautomatically. RESULTS: Pre-Gd, both lumen and wall dimensions (total vessel area, lumen area, vessel wall area) of group 2 + 3 were significantly increased when compared with those of group 1 (all P < 0.01). Group 3 animals had significantly thicker vessel walls than groups 1 and 2 (P < 0.01), whereas angiographic lumen diameter was comparable among all groups. Post-Gd, only diseased animals of groups 2 + 3 showed a significant (>100%) signal-to-noise ratio and contrast-to-noise increase. CONCLUSIONS: A combination of novel 3D magnetic resonance angiography and high-resolution 3D vessel wall MRI enabled quantitative characterization of various atherosclerotic stages including positive arterial remodeling and Gd uptake in a WHHL rabbit model using a commercially available 1.5 T MRI system.

European Cardiovascular Magnetic Resonance (EuroCMR) registry--multi national results from 57 centers in 15 countries.

BACKGROUND: The EuroCMR registry sought to evaluate indications, image quality, safety and impact on patient management of clinical routine CMR in a multi-national European setting. Furthermore, interim analysis of the specific protocols should underscore the prognostic potential of CMR. METHODS: Multi-center registry with consecutive enrolment of patients in 57 centers in 15 countries. More than 27000 consecutive patients were enrolled. RESULTS: The most important indications were risk stratification in suspected CAD/Ischemia (34.2%), workup of myocarditis/cardiomyopathies (32.2%), as well as assessment of viability (14.6%). Image quality was diagnostic in more than 98% of cases. Severe complications occurred in 0.026%, always associated with stress testing. No patient died during or due to CMR. In 61.8% CMR findings impacted on patient management. Importantly, in nearly 8.7% the final diagnosis based on CMR was different to the diagnosis before CMR, leading to a complete change in management. Interim analysis of suspected CAD and risk stratification in HCM specific protocols revealed a low rate of adverse events for suspected CAD patients with normal stress CMR (1.0% per year), and for HCM patients without LGE (2.7% per year). CONCLUSION: The most important indications in Europe are risk stratification in suspected CAD/Ischemia, work-up of myocarditis and cardiomyopathies, as well as assessment of viability. CMR imaging is a safe procedure, has diagnostic image quality in more than 98% of cases, and its results have strong impact on patient management. Interim analyses of the specific protocols underscore the prognostic value of clinical routine CMR in CAD and HCM.

Prospective and retrospective motion correction in diffusion magnetic resonance imaging of the human brain.

Diffusion-weighting in magnetic resonance imaging (MRI) increases the sensitivity to molecular Brownian motion, providing insight in the micro-environment of the underlying tissue types and structures. At the same time, the diffusion weighting renders the scans sensitive to other motion, including bulk patient motion. Typically, several image volumes are needed to extract diffusion information, inducing also inter-volume motion susceptibility. Bulk motion is more likely during long acquisitions, as they appear in diffusion tensor, diffusion spectrum and q-ball imaging. Image registration methods are successfully used to correct for bulk motion in other MRI time series, but their performance in diffusion-weighted MRI is limited since diffusion weighting introduces strong signal and contrast changes between serial image volumes. In this work, we combine the capability of free induction decay (FID) navigators, providing information on object motion, with image registration methodology to prospectively--or optionally retrospectively--correct for motion in diffusion imaging of the human brain. Eight healthy subjects were instructed to perform small-scale voluntary head motion during clinical diffusion tensor imaging acquisitions. The implemented motion detection based on FID navigator signals is processed in real-time and provided an excellent detection performance of voluntary motion patterns even at a sub-millimetre scale (sensitivity≥92%, specificity>98%). Motion detection triggered an additional image volume acquisition with b=0 s/mm2 which was subsequently co-registered to a reference volume. In the prospective correction scenario, the calculated motion-parameters were applied to perform a real-time update of the gradient coordinate system to correct for the head movement. Quantitative analysis revealed that the motion correction implementation is capable to correct head motion in diffusion-weighted MRI to a level comparable to scans without voluntary head motion. The results indicate the potential of this method to improve image quality in diffusion-weighted MRI, a concept that can also be applied when highest diffusion weightings are performed.