Equivalence of double and single wave vector diffusion contrast at low diffusion weighting

2011 ◽  
Vol 25 (6) ◽  
pp. 813-818 ◽  
Author(s):  
Sune Nørhøj Jespersen
Keyword(s):  
Wave Vector ◽  
Single Wave ◽  
Diffusion Weighting

Modulated Atomic Displacement Description and Easy Structural Factor Computing

1982 ◽  
Vol 21 ◽  
Author(s):  
P. Wolfers
Keyword(s):  
Wave Vector ◽  
Atomic Displacement ◽  
Crystallographic Structure ◽  
General Description ◽  
Single Wave ◽  
Scattering Center ◽  
Displacement Vectors ◽  
Vector Approximation ◽  
Vector Case ◽  
Modulated Phase

ABSTRACTThe displacement of a particular atom in a modulated crystallographic structure can be described in terms of a Fourier Series. In the harmonic single wave vector approximation, the structure factor can be written as a function of the atomic displacement vectors. Such expressions are however not valid in the multi-wave-vector case. We propose a general description for the modulation of displacement where each scattering center (atom) is distributed on several sites whose population is modulated. In the paper, we will show that approach is well suited for computing. We have developed a general least squares program which has been applied to the modulated phase of αU(T < 43 K) [2].

scholarly journals Studying the extracellular contribution to the double wave vector diffusion-weighted signal

2015 ◽  
Vol 1 (1) ◽  
pp. 240-244 ◽  
Author(s):  
Patricia Ulloa ◽  
Viktor Wottschel ◽  
Martin A. Koch
Keyword(s):  
Pore Size ◽  
Wave Vector ◽  
Corticospinal Tract ◽  
Structural Information ◽  
Double Diffusion ◽  
Pore Shape ◽  
Size And Shape ◽  
Yield Information ◽  
Diffusion Weighting

AbstractThe use of two independent diffusion periods between excitation and acquisition, known as double wave vector (DWV) diffusion-weighting or double diffusion encoding, was proven to yield structural information that it is otherwise not easily available in vivo. Comparing the signal difference between relative diffusion gradient orientations, the antiparallel-parallel and the parallel-perpendicular differences yield information on pore size and shape, respectively. However, results in vivo provided larger pore sizes than expected for axons in the corticospinal tract. This study exploits DWV sensitivity to pore shape and aims to obtain information on the extracellular contributions to the DWV pore size results presented here. The in vivo DWV experiments resulted in a positive parallel-perpendicular difference which is consistent with an irregularly shaped pore dominating the origin of the signal.

Towards compartment size estimationin vivobased on double wave vector diffusion weighting

2011 ◽  
Vol 24 (10) ◽  
pp. 1422-1432 ◽  
Author(s):  
Martin A. Koch ◽  
Jürgen Finsterbusch
Keyword(s):  
Wave Vector ◽  
Diffusion Weighting

Effects of Higher-Order Laue Zone reflections on structure images

1993 ◽  
Vol 51 ◽  
pp. 450-451
Author(s):  
H. S. Kim ◽  
S. S. Sheinin
Keyword(s):  
Wave Vector ◽  
Theoretical Calculations ◽  
Reciprocal Lattice ◽  
Image Plane ◽  
Bloch Wave ◽  
Dynamical Theory ◽  
Higher Order ◽  
Lattice Image ◽  
Lattice Vector ◽  
Image Position

The importance of image simulation in interpreting experimental lattice images is well established. Normally, in carrying out the required theoretical calculations, only zero order Laue zone reflections are taken into account. In this paper we assess the conditions for which this procedure is valid and indicate circumstances in which higher order Laue zone reflections may be important. Our work is based on an analysis of the requirements for obtaining structure images i.e. images directly related to the projected potential. In the considerations to follow, the Bloch wave formulation of the dynamical theory has been used.The intensity in a lattice image can be obtained from the total wave function at the image plane is given by: where ϕg(z) is the diffracted beam amplitide given by In these equations,the z direction is perpendicular to the entrance surface, g is a reciprocal lattice vector, the Cg(i) are Fourier coefficients in the expression for a Bloch wave, b(i), X(i) is the Bloch wave excitation coefficient, ϒ(i)=k(i)-K, k(i) is a Bloch wave vector, K is the electron wave vector after correction for the mean inner potential of the crystal, T(q) and D(q) are the transfer function and damping function respectively, q is a scattering vector and the summation is over i=l,N where N is the number of beams taken into account.

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