The precision of DCE-MRI using the tissue homogeneity model with continuous formulation of the perfusion parameters

The present trend in dynamic contrast-enhanced MRI is to increase the number of estimated perfusion parameters using complex pharmacokinetic models. However, less attention is given to the precision analysis of the parameter estimates. In this paper, the distributed capillary adiabatic tissue homogeneity pharmacokinetic model is extended by the bolus arrival time formulated as a free continuous parameter. With the continuous formulation of all perfusion parameters, it is possible to use standard gradient-based optimization algorithms in the approximation of the tissue concentration time sequences. This new six-parameter model is investigated by comparing Monte-Carlo simulations with theoretically derived covariance matrices. The covariance-matrix approach is extended from the usual analysis of the primary perfusion parameters of the pharmacokinetic model to the analysis of the perfusion parameters derived from the primary ones. The results indicate that the precision of the estimated perfusion parameters can be described by the covariance matrix for signal-to-noise ratio higher than ~ 20 dB. The application of the new analysis model on a real DCE-MRI data set is also presented.     

FINITE ELEMENT APPROXIMATION OF A NONLINEAR STEADY-STATE HEAT CONDUCTION PROBLEM

1. Introduction Anciellt Chinese mathematicians have done many fund~al discoveries, even thoughmad of them are now usually called by western names, e.g., the Pascal triangle, the HornerIcheme, the Gaussian elimination, see [231. In the modern era3 Chinese mathematiciare have.jalso got many priorities. For instance, the fast Proof Of convergence of the finite element methodfor a linear elliptic boundary vajue problem was done in the pioneering work [61 by K. Feng in1965 (for the English tra…     

On the existence of solutions of nonlinear equations

Results on the existence of solutions are derived for asymptotically quasilinear, nonlinear operator equations. Applications are given to implicit nonlinear integral equations.

     

Ultrafast all-optical modulation on a silicon chip

We experimentally demonstrate ultrafast all-optical modulation using a micrometer-sized silicon photonic integrated device. The device transmission is strongly modulated by photoexcited carriers generated by low-energy pump pulses. A p-i-n junction is integrated on the structure to permit control of the generated carrier lifetimes. When the junction is reverse biased, carriers are extracted from the device in a time as short as 50 ps, permitting greater than 5 Gbit/s modulation of optical signals on a silicon chip.     

Learning beginning algebra in a computer-intensive environment

We present a design research on learning beginning algebra in an environment where spreadsheets were available at all times but the decision about using them or not, and how, in any particular situation was left to the students. Students’ activity is analyzed in Kieran’s framework of generational, transformational and global/meta-level activity, and compared to the designers’ intentions. We do this by focusing on the activity of one student in four sessions spread over several months and discussing the activity of 51 additional students in view of the analysis of the focus student. We show that the environment enables a number of different entries into algebra and as such supports students in becoming autonomous learners of algebra, and in making the shift from arithmetic to algebra via generational and global/meta-level activity before dealing with the more technical transformational activities.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.     

Modification of PP fibres with alkaline copolyamides

Copolyamides with 5.9‐19.7 wt.% of nylon salt ADETA (adipic acid + diethylenetriamine) and 94.1‐80.3 wt.% of ϵ‐caprolactam were synthesized and their properties were estimated. Blended polypropylene/copolyamides fibres containing 5‐15 wt.% of copolyamides were prepared and their properties were evaluated. The electrical properties, hydrophilicity and especially dyeability of modified PP fibres are positively influenced by a higher amount of the copolyamide in the PP and also by a higher amount of the nylon salt ADETA in the copolyamide.     

Development of metallocomplex amino acids synthons for the asymmetric preparation of α-amino acids by stereoselective introduction of a side chain. Evaluation of the model asymmetric preparation of alanine and β-13C monolabelled α-aminoisobutyric acid

In this communication the evaluation of eleven new metallocomplex alanine synthons bearing C₂-symmetric benzyl groups with electron-donating and electron-withdrawing substituents is described. α-Methylated glycine synthons (alanine complexes) were evaluated alongside alanine synthons in order to obtain a deeper understanding of the relationship between their structures and stereochemistry of monoalkylated products and to choose several candidates for their further tests for stereospecific preparation of 6-[¹⁸F]FDOPA. Glycine-derived analogues of the complexes 3–5 are the best candidates for the development of a 6-[¹⁸F]FDOPA preparation procedure. In the model epimerisation reaction they demonstrated the best performance, much better compared to the previously described compound 2. Complexes 3, 5 and 8 are the best in asymmetric preparation of β-¹³C monolabelled α-aminoisobutyric acid. They have to be tested in the preparation of α-methyl amino acids like 6-[¹⁸F]-α-methylDOPA and 2-[¹⁸F]-α-methyltyrosine.     

Ab initio calculation of structure and transport properties of He…X (X = Zn, Cd, Hg) van der Waals complexes

The ground state ab initio CCSD(T) potential curves using various basis sets (aug-cc-pVXZ-PP (X = D, T, Q, 5)) is obtained for the dimers of helium with IIb group metals. The effect of the position of the (mid) bond-functions on the interaction energy is discussed. A Symmetry Adapted Perturbation Theory decomposition of the interaction energy is provided and the trends in the dimer stabilizing and destabilizing contributions are depicted. The spline fitted potential curves are applied together with rigorous statistical formulae in order to obtain the transport coefficients (viscosity coefficients, diffusion coefficients) and the second virial coefficient both for pure constituents and mixtures. The obtained theoretical results are compared with available experimental data. Molecular dynamics is used to obtain reliable values of the diffusion coefficients for all the systems under study.