High-resolution MR venography of cerebral arteriovenous malformations

The purpose of this study was to evaluate the diagnostic potential of a high-resolution magnetic resonance (MR) venography technique in patients with cerebral arteriovenous malformations (AVMs). A high-resolution 3D gradient echo sequence was used with a long echo time TE to obtain venous information down to sub-pixel sized vessel diameters of several hundred microns. The method is based on the paramagnetic property of deoxyhemoglobin, and the resulting developing phase difference between veins and brain parenchyma at long echo times which leads to signal cancellation. The reconstructed venograms were compared with time-of-flight (TOF)-MR angiography using qualitative and quantitative criteria with the conventional digital subtraction angiography serving as the reference gold standard. In 17 patients with angiographically proven cerebral AVMs, the method indicates its potential in clinical applications. Venography was able to detect all AVMs whereas TOF-MRA failed in three patients. In the delineation of venous drainage patterns MR venography was superior to TOF-MRA, however, the method failed in the detection of about half of the main feeding arteries, as expected. Due to susceptibility artifacts at air/tissue boundaries and interference with paramagnetic hemosiderin, venography was limited with respect to the delineation of the exact nidus sizes and shapes in ten patients with AVMs located close to the skull base or having suffered from previous bleeding. Although the visualization of draining veins represents an important prerequisite in the surgical and radiosurgical treatment planning of cerebral AVMs, application of high resolution MR venography may be limited in the diagnostic work-up in some of these patients. On the other hand, it may be of special importance in the early detection and assessment of small AVMs that are difficult to diagnose with other MR methods.     

The perfectB-splines and a time-optimal control problem

Letx _v =cos (πν/n) (v=0, 1, …,n). It is shown that theB-splineM(x)=M(x; x ₀ ,x ₁ ,…, x _n ) is such thatM _n ⁽ⁿ⁾ (x) has a constant absolute value (=2 ⁿ⁻² (n−1)!) in [−1, 1]. Its integralf ₀(x)=∫ ₋₁ ^x M(t)dt is shown to have an optimal property that allows to solveexplicitly a certain time-optimal control problem.     

Disappearance of tumor contrast on contrast-enhanced FLAIR imaging of cerebral gliomas

Contrast-enhanced fluid-attentuated inversion recovery (FLAIR) magnetic resonance (MR) imaging has shown to be a valuable diagnostic modality in the assessment of cerebral gliomas. In this study we report of a potential pitfall regarding the delineation of enhancing tumor parts on contrast enhanced FLAIR imaging. In a limited number of patients, the administration of gadolinium obscures the area of contrast enhancement on contrast enhanced FLAIR images. Therefore the delineation of the macroscopic tumor parts, which are of great importance for the treatment planning is substantially worsened.     

Zur Abzählung der reellen Wurzeln algebraischer Gleichungen

Ohne Zusammenfassung     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Über variationsvermindernde lineare Transformationen

Ohne Zusammenfassung     

On Rescaled Poisson Processes and the Brownian Bridge

The process obtained by rescaling a homogeneous Poisson process by the maximum likelihood estimate of its intensity is shown to have surprisingly strong self-correcting behavior. Formulas for the conditional intensity and moments of the rescaled Poisson process are derived, and its behavior is demonstrated using simulations. Relationships to the Brownian bridge are explored, and implications for point process residual analysis are discussed.