Quantitation of treatment volumes from CT and MRI in high-grade gliomas: implications for radiotherapy.

Long-term survival of patients with high-grade gliomas remains extremely poor. The main reason for such an outcome is local failure, or recurrence, after surgery and/or radiotherapy. Higher doses of radiation may result in decreased local failure rates provided that the location (and extent) of gross tumor and microscopic disease can be defined accurately. The abnormalities appearing in images from diagnostic modalities, such as CT and MRI, are being used as a starting point and as a guide for the clinical definition of tumor and its extensions. However, some recent studies on two-dimensional specimens, correlating histopathological findings to CT and MRI images, showed that the resulting definition of tumor cell extensions was unsatisfactory, different, and in need of ample margins. We carried out a retrospective analysis to compare the target volumes that would have been defined by CT, T2-weighted MRI, and T1-weighted postgadolinium MRI images of the same individual and to explore the implications of the resulting volume definitions for radiotherapy. The results of our limited study, based on the margins used, indicate that the CT-defined target volume is consistently larger than that from either of the two MRI modalities and suggest that noncoplanar approaches for its treatment and other local approaches for tumor boost should be considered. We conclude that until more definitive histopathological guidelines correlated to image features have been formulated and agreed upon, one should try to make full use of all available diagnostic information in order to minimize the possibility of geographical miss of target extensions.     

Natural frequencies of rectangular orthotropic plates with a pair of parallel edges simply supported

Solutions of the exact characteristic equations for the title problem derived earlier by an extension of Bolotin's asymptotic method are considered. These solutions, which correspond to flexural modes with frequency factor, R, greater than unity, are expressed in convenient forms for all combinations of clamped, simply supported and free conditions at the remaining pair of parallel edges. As in the case of uniform beams, the eigenvalues in the CC case are found to be equal to those of elastic modes in the FF case provided that the Kirchoff's shear condition at a free edge is replaced by the condition $\text{?M}{}_{\mathrm{n}}\text{?n = 0}$. The flexural modes with frequency factor less than unity are also investigated in detail by introducing a suitable modification in the procedure. When Poisson's ratios are not zero, it is shown that the frequency factor corresponding to the first symmetric mode in the free-free case is less than unity for all values of side ratio and rigidity ratios. In the case of one edge clamped and the other free it is found that modes with frequency factor less than unity exist for certain dimensions of the plate—a fact hitherto unrecognized in the literature.     

High pressure phase transitions in organic solids I:α → β transition in resorcinol

An experimental program has been started to study polymorphic phase transitions under pressure in organic solids using the Be gasketing technique developed by us. This allows us to obtain x-ray diffraction patterns of low symmetry organic solids with high resolution, employing CuK _α radiation. The first organic solid studied is α-resorcinol. At 0.5 GPa, it transforms to its high temperature and denser modification, β-resorcinol. The transformation mechanism is discussed with the help of molecular packing calculations.     

Synthesis of audio spectra using a diffraction model

It is shown that the intensity variations of an audio signal in the frequency domain can be obtained by using a mathematical function containing a series of weighted complex Bessel functions. With proper choice of values for two parameters, this function can transform an input spectrum of discrete frequencies of unit intensity into the known spectra of different musical instruments. Specific examples of musical instruments are considered for evaluating the performance of this method. It is found that this function yields musical spectra with a good degree of accuracy.     

Existence of Global Solutions for a Class of Abstract Second-Order Nonlocal Cauchy Problem with Impulsive Conditions in Banach Spaces

In this paper, we are concerned with a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. First, we study the existence of mild solutions for a class of second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces on an interval [0,a]. Later, we study a couple of cases where we can establish the existence of global solutions for a class of abstract second-order nonlocal Cauchy problem with impulsive conditions in Banach spaces. We apply our theory to study the existence of solutions for impulsive partial differential equations.     

Controllability for a class of second-order evolution differential inclusions without compactness

In this paper, we discuss the existence and controllability for a class of second-order evolution differential inclusions without compactness in Banach spaces. By applying the technique of weak topology and Glicksberg–Ky Fan fixed point theorem, we prove our main results without the hypotheses of compactness on the operator generated by the linear part and any conditions on the multivalued nonlinearity expressed in terms of measures of noncompactness. Further, we extend our study to existence and controllability of second-order evolution differential inclusions with nonlocal conditions and impulses. Finally, an example is given for the illustration of the obtained theoretical results.