In vivo NMR T2 relaxation of experimental brain tumors in the cat: a multiparameter tissue characterization.

Experimental gliomas (F98) were inoculated in cat brain for the systematic study of their in vivo T₂ relaxation time behavior. With a CPMG multi-echo imaging sequence, a train of 16 echoes was evaluated to obtain the transverse relaxation time and the magnetization M(0) at time T = 0. The magnetization decay curves were analyzed for biexponentiality. All tissues showed monoexponential T₂, only that of the ventricular fluid and part of the vital tumor tissue were biexponential. Based on these NMR relaxation parameters the tissues were characterized, their correct assignment being assured by comparison with histological slices. T₂ of normal grey and white matter was 74 ± 6 and 72 ± 6 msec, respectively. These two tissue types were distinguished through M(0) which for white matter was only 0.88 of the intensity of grey matter in full agreement with water content, determined from tissue specimens. At the time of maximal tumor growth and edema spread a tissue differentiation was possible in NMR relaxation parameter images. Separation of the three tissue groups of normal tissue, tumor and edema was based on T₂ with T_2(normal) < T_2(tumor) < T_2(edema). Using M(0) as a second parameter the differentiation was supported, in particular between white matter and tumor or edema. Animals were studied at 1–4 wk after tumor implantation to study tumor development. The magnetization M(0) of both tumor and peritumoral edema went through a maximum between the second and third week of tumor growth. T₂ of edema was maximal at the same time with 133 ± 4 msec, while the relaxation time of tumor continued to increase during the whole growth period, reaching values of 114 ± 12 msec at the fourth week. Thus, a complete characterization of pathological tissues with NMR relaxometry must include a detailed study of the developmental changes of these tissues to assure correct experimental conditions for the goal of optimal contrast between normal and pathological regions in the NMR images.     

Further Saponins from Phytolacca dodecandra L′HERIT

Three new bidesmosidic saponins 1 – 3 have been isolated from the berries of Phytolacca dodecandra L′HERIT (Phytolaccaeae). The structures have been established by spectroscopic (¹H-NMR, ¹³C-NMR, FAB-MS, DCI-MS, and GC/MS) and chemical methods (acid, basic, and enzymatic hydrolysis). Saponins 1 and 3 are tetra- and pentaglycosides of oleanolic acid, whereas 2 is a tetraglycoside of bayogenin. The corresponding prosapogenins 1a - 3a , obtained by cleavage of a glucose unit esterified at C(28), exhibited strong molluscicidal activity against schistosomiasis-transmitting snails.     

The potts glass in uniform and random fields: a monte carlo investigation

As a simple model of an anisotropic orientational glass with short range forces, the 3-state Potts model on the simple cubic lattice with nearest neighbor interactions drawn from a Gaussian distribution is considered. With Monte Carlo methods we study the response of the system to a uniform “field” which favors one of the states. This is motivated by experiments which apply stress that favors one molecular orientation of the quadrupolar glass. The responsem to that fieldh=H/k _BT is analyzed in terms of an expansionm= χ₁ h+χ₁ h ²+χ₁ h ³+..., where χ₁ is the linear susceptibility, and χ₂,χ₁₃ are nonlinear susceptibilities. Unlike the case of spin glasses, where the spin inversion symmetry of the system in the absence of fields implies χ₂≡0,χ₂ is nonzero here and diverges to −∞ at the zero temperature transition of the model, while χ₃ diverges to +∞ as in spin glasses. At inifinite temperature, however, χ₁=1/3, χ₂=1/18 and χ₃=-1/54, i.e. the nonlinear susceptibilities have a different sign as at low temperature. In contrast, a random field does not induce a uniform order parameterm but only a glass order parameterq. The temperature dependence of this glass order parameterq(T) shows for intermediate field strength order parameterq(T) shows for intermediate field strength a maximum of the slopedq(T)/dT very similar to corresponding experiments.     

Photoionization of 1,1-difluoroethane: The structure of the C2H3F2+ ions

In order to explain the photoionization efficiency curve of the ions with m/e = 65 from CH₃CHF₂, we have carried out ab initio calculations predicting energy differences and structural parameters for different isomers and conformers of both the neutral system and the ion. Also, some heats of formation are estimated.     

Zur Affinoberfläche konvexer Körper

Ohne ZusammenfassungHerrn Martin Barner zum 65. Geburtstag gewidmet     

Logical Processing for Integer Programming

This paper reviews tools which have great potential for reducing the difficulty of solving IP (and also MIP) problems, if well implemented in solvers. Recent experiments with Branch and Bound solvers, in connection with “Short Start Features”, have shown that implementations need and can still be improved. Concepts which are likely to be specially important for (0,1) MIP are pointed out.     

Linear minimax estimation with ellipsoidal constraints

We consider the simultaneous linear minimax estimation problem in linear models with ellipsoidal constraints imposed on an unknown parameter. Using convex analysis, we derive necessary and sufficient optimality conditions for a matrix to define the linear minimax estimator. For certain regions of the set of characteristics of linear models and constraints, we exploit these optimality conditions and get explicit formulae for linear minimax estimators.