Data_Sheet_1_Incomplete spectrum QSM using support information.PDF

IntroductionReconstructing a bounded object from incomplete k-space data is a well posed problem, and it was recently shown that this incomplete spectrum approach can be used to reconstruct undersampled MRI images with similar quality to compressed sensing approaches. Here, we apply this incomplete spectrum approach to the field-to-source inverse problem encountered in quantitative magnetic susceptibility mapping (QSM). The field-to-source problem is an ill-posed problem because of conical regions in frequency space where the dipole kernel is zero or very small, which leads to the kernel's inverse being ill-defined. These “ill-posed” regions typically lead to streaking artifacts in QSM reconstructions. In contrast to compressed sensing, our approach relies on knowledge of the image-space support, more commonly referred to as the mask, of our object as well as the region in k-space with ill-defined values. In the QSM case, this mask is usually available, as it is required for most QSM background field removal and reconstruction methods.MethodsWe tuned the incomplete spectrum method (mask and band-limit) for QSM on a simulated dataset from the most recent QSM challenge and validated the QSM reconstruction results on brain images acquired in five healthy volunteers, comparing incomplete spectrum QSM to current state-of-the art-methods: FANSI, nonlinear dipole inversion, and conventional thresholded k-space division.ResultsWithout additional regularization, incomplete spectrum QSM performs slightly better than direct QSM reconstruction methods such as thresholded k-space division (PSNR of 39.9 vs. 39.4 of TKD on a simulated dataset) and provides susceptibility values in key iron-rich regions similar or slightly lower than state-of-the-art algorithms, but did not improve the PSNR in comparison to FANSI or nonlinear dipole inversion. With added (ℓ1-wavelet based) regularization the new approach produces results similar to compressed sensing based reconstructions (at sufficiently high levels of regularization).DiscussionIncomplete spectrum QSM provides a new approach to handle the “ill-posed” regions in the frequency-space data input to QSM.</p

On the signs of the order parameters

<p>Snapshot of blog post from nmrlipids.blogspot.fi done for citing purposes. See link below for properly archieved webpage.</p> <p> </p

nmrlipids.blogspot.fi — on October 25th 2015

<p>Snapshot of the blog nmrlipids.blogspot.fi on October 25th 2015.</p> <p> </p> <p>The NMRlipids project is an open scientific collaboration to understand the atomistic resolution structures of lipid bilayers through classical molecular dynamics simulations. The project is progressed through the comments in the blog and using the GitHub organization (see links). The main results are also published in traditional peer reviewed scientific journals.</p

Examples of strategies and results for the 2016–2017 edition.

<p>Left panel: Team B implemented an efficient sampling algorithm using a grid representation of the proteins to be docked and FFT. For the scoring, they used evolutionary information extracted from multiple sequence alignments of homologs of the two partners. Right panel: Team D used biological knowledge during the sampling step to filter out conformations early and drastically reduce the search space. The results obtained by the students (Teams B and D) on two complexes (barnase–barstar complex, Protein Data Bank [PDB] code: 1AY7, and an antibody–antigen complex, PDB code: 1JPS, respectively) are comparable to those obtained from state-of-the-art methods, namely ZDOCK [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005992#pcbi.1005992.ref010" target="_blank">10</a>] and ATTRACT [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005992#pcbi.1005992.ref011" target="_blank">11</a>]. ZDOCK relies on efficient sampling using FFT and on an optimized energy function [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005992#pcbi.1005992.ref010" target="_blank">10</a>]. ATTRACT proceeds through minimization steps using an empirical, coarse-grained molecular mechanics potential [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005992#pcbi.1005992.ref011" target="_blank">11</a>]. Candidate conformations for the complexes are represented as cartoons and superimposed onto the known crystallographic structures. The receptor is in black, the ligand from the candidate conformation is colored (in orange for Meet-U students, blue for ZDOCK, and purple for ATTRACT), and that from the crystallographic structure is in grey. With each candidate conformation are associated its rank, according to the scoring function of the method, and its deviation (in Å) from the crystallographic structure. FFT, Fast Fourier Transform; PDB, protein data bank.</p