Gaussian process regression can turn non-uniform and undersampled diffusion MRI data into diffusion spectrum imaging

We propose to use Gaussian process regression to accurately estimate the diffusion MRI signal at arbitrary locations in q-space. By estimating the signal on a grid, we can do synthetic diffusion spectrum imaging: reconstructing the ensemble averaged propagator (EAP) by an inverse Fourier transform. We also propose an alternative reconstruction method guaranteeing a nonnegative EAP that integrates to unity. The reconstruction is validated on data simulated from two Gaussians at various crossing angles. Moreover, we demonstrate on non-uniformly sampled in vivo data that the method is far superior to linear interpolation, and allows a drastic undersampling of the data with only a minor loss of accuracy. We envision the method as a potential replacement for standard diffusion spectrum imaging, in particular when acquistion time is limited.Comment: 5 page

Stereochemical Studies on a New Ciramadol Analogue by NMR-Spectroscopy

The absol. configuration of a Ciramadol analogue obtained from (-)-menthone is established by 'H-NMR-. simulated NMR-, COSY-90-, and NOEmeasurements. The final compound 2-(a-1 -pyrrolidino)benzy 1-4-isopropyl- 1 -methyl-cyclohexan-3-one (4b), e.g.. has 1R.2S,4S.l IS-configuration due to stereoselective Michael-type addition of pyrrolidine to the pertinent benzylidene intermediate 3. Die absol. Konfiguration einer Ciramadol-analogen Verbindung aus (-)- Menthon wurde durch 'H-NMR-. simulierte NMR-. COSY-90- und NOEUntersuchungen geklärt. Danach hat die als Beispiel untersuchte Verbindung 2-(a-1 -Pyrrolidino)benzyl-4-isopropyl-1 -methyl-cyclohexan-3-on (4b) 1R,2S.4S.l IS-Konfiguration, die durch eine stereoselektive Michael-analoge Addition des Pyrrolidins an die entspr. Benzyliden-Verbindung 3 entsteht

Bayesian uncertainty quantification in linear models for diffusion MRI

Diffusion MRI (dMRI) is a valuable tool in the assessment of tissue microstructure. By fitting a model to the dMRI signal it is possible to derive various quantitative features. Several of the most popular dMRI signal models are expansions in an appropriately chosen basis, where the coefficients are determined using some variation of least-squares. However, such approaches lack any notion of uncertainty, which could be valuable in e.g. group analyses. In this work, we use a probabilistic interpretation of linear least-squares methods to recast popular dMRI models as Bayesian ones. This makes it possible to quantify the uncertainty of any derived quantity. In particular, for quantities that are affine functions of the coefficients, the posterior distribution can be expressed in closed-form. We simulated measurements from single- and double-tensor models where the correct values of several quantities are known, to validate that the theoretically derived quantiles agree with those observed empirically. We included results from residual bootstrap for comparison and found good agreement. The validation employed several different models: Diffusion Tensor Imaging (DTI), Mean Apparent Propagator MRI (MAP-MRI) and Constrained Spherical Deconvolution (CSD). We also used in vivo data to visualize maps of quantitative features and corresponding uncertainties, and to show how our approach can be used in a group analysis to downweight subjects with high uncertainty. In summary, we convert successful linear models for dMRI signal estimation to probabilistic models, capable of accurate uncertainty quantification.Comment: Added results from a group analysis and a comparison with residual bootstra

Some families of generating functions for the multiple orthogonal polynomials associated with modified Bessel K-functions

AbstractThe main object of this paper is to derive several substantially more general families of bilinear, bilateral, and mixed multilateral finite-series relationships and generating functions for the multiple orthogonal polynomials associated with the modified Bessel K-functions also known as Macdonald functions. Some special cases of the above statements are also given