Real-time magnetic resonance imaging in pediatric radiology — new approach to movement and moving children

The recent development of highly undersampled radial gradient echo sequences in combination with nonlinear inverse image reconstruction now allows for MRI examinations in real time. Image acquisition times as short as 20 ms yield MRI videos with rates of up to 50 frames per second with spin density, T1- and T2-type contrast. The addition of an initial 180° inversion pulse achieves accurate T1 mapping within only 4 s. These technical advances promise specific advantages for studies of infants and young children by eliminating the need for sedation or anesthesia. Our preliminary data demonstrate new diagnostic opportunities ranging from dynamic studies of speech and swallowing processes and body movements to a rapid volumetric assessment of brain cerebrospinal fluid spaces in only few seconds. Real-time MRI of the heart and blood flow can be performed without electrocardiogram gating and under free breathing. The present findings support the idea that real-time MRI will complement existing methods by providing long-awaited diagnostic options for patients in early childhood. Major advantages are the avoidance of sedation or anesthesia and the yet unexplored potential to gain insights into arbitrary body functions.

Residual and fixed modules

The article presents some sufficient conditions for the commutativity of transvections with elements of linear groups over division ring in the language of residual and fixed submodules. The residual and fixed submodules of the element $\sigma $ of the linear group are defined as the image and nucleus of the element $\sigma -1$ and are denoted by $R(\sigma)$ and $P(\sigma)$ respectively. It is proved that transvection ${\sigma }_1$ over an arbitrary body commutes with an element ${\sigma }_2$ for which $\mathop{\rm dim}R({\sigma }_2)=\mathop{\rm dim}R({\sigma }_2)\cap P({\sigma }_2)+l$, $l\le 1$, if and only if the inclusion system $R({\sigma }_1)\subseteq P({\sigma }_2)$, $R({\sigma }_2)\subseteq P({\sigma }_1)$. It is shown that for $l>1$ this statement is not always true.

Reduction of Arbitrary Rigid Bodies to Inertially Equivalent Discrete Systems of Material Points

In a previous paper of the authors, a general method was presented for the reduction of a rigid plane plate to a discrete system of material points, with equivalent inertial properties (mass, center of mass, tensor of inertia). The present paper generalizes the method for rigid bodies of arbitrary shape, i.e. for material volumes, as well as for curved shells. It is shown that a homogenous ellipsoid can be reduced to a system of seven material points placed in significant geometrical points of the body. Next, starting from the concept of ellipsoid of inertia, an equivalent homogenous ellipsoid is determined for an arbitrary body. The method simplifies considerably the calculation of various mechanical quantities, such as moments and products of inertia with respect to rotated Cartesian coordinate systems, angular momentum and kinetic energy, of rigid bodies part of all types of mechanical devices or structures.

Inverse problems and invisibility cloaking for FEM models and resistor networks

In this paper we consider inverse problems for resistor networks and for models obtained via the finite element method (FEM) for the conductivity equation. These correspond to discrete versions of the inverse conductivity problem of Calderón. We characterize FEM models corresponding to a given triangulation of the domain that are equivalent to certain resistor networks, and apply the results to study nonuniqueness of the discrete inverse problem. It turns out that the degree of nonuniqueness for the discrete problem is larger than the one for the partial differential equation. We also study invisibility cloaking for FEM models, and show how an arbitrary body can be surrounded with a layer so that the cloaked body has the same boundary measurements as a given background medium.