Artur Krzyżak

Improving the accuracy of PGSE DTI experiments using the spatial distribution of b matrix

A novel method for improving the accuracy of diffusion tensor imaging (DTI) is proposed. It takes into account the b matrix spatial variations, which can be easily determined using a simple anisotropic diffusion phantom. In opposite to standard numerical procedure of the b matrix calculation that requires the exact knowledge of amplitudes, shapes and time dependencies of diffusion gradients, the new method, which we call BSD-DTI (B-matrix spatial distribution in DTI), relies on direct measurements of its space-dependent components. The proposed technique was demonstrated on the Bruker Biospec 94/20USR system, using the spin echo diffusion sequence to image an isotropic water phantom and an anisotropic capillary phantom. The accuracy of the diffusion tensor determination was improved by an overall factor of about 8 for the isotropic water phantom.

ZTE imaging of tight sandstone rocks at 9.4T - Comparison with standard NMR analysis at 0.05T.

Zero echo time (ZTE) imaging at 9.4T was used to assess local water saturation level in the tight sandstone rocks. The results were compared with the industry standard porosity estimation basing on T2 relaxation analysis at 0.05T. A linear dependence between the two was achieved. This suggests the possibility to use 3D ZTE method for assessment of local amount of water in rocks. The method can be applicable in investigation of water saturation processes in tight rocks, where imaging methods based on spin echo like RARE failed due to short T2, while single point imaging (SPI) is impractical due to long acquisition time.

Innovative anisotropic phantoms for calibration of diffusion tensor imaging sequences

The paper describes a novel type of anisotropic phantoms designed for b-matrix spatial distribution diffusion tensor imaging (BSD-DTI). Cubic plate anisotropic phantom, cylinder capillary phantom and water reference phantom are described as a complete set necessary for calibration, validation and normalization of BSD-DTI. An innovative design of the phantoms basing on enclosing the anisotropic cores in glass balls filled with liquid made for the first time possible BSD calibration with usage of echo planar imaging (EPI) sequence. Susceptibility artifacts prone to occur in EPI sequences were visibly reduced in the central region of the phantoms. The phantoms were designed for usage in a clinical scanners head coil, but can be scaled for other coil or scanner types. The phantoms can be also used for a pre-calibration of imaging of other types of phantoms having more specific applications.

Anisotropic phantoms in Magnetic Resonance Imaging.

Even though Magnetic Resonance Imaging (MRI) gives possibility to obtain qualitatively very good images, most quantitative results obtained by means of MRI are biased with high dependence on particular hardware parameters, imaging sequence used, and properties of analysed sample. Thus to enable comparison between results obtained on different scanners a calibration is needed. In one of the approaches to Diffusion Tensor Imaging (DTI), a B-matrix Spatial Distribution DTI (BSD-DTI) anisotropic phantoms are crucial in precise determination of the diffusion tensor. Anisotropic phantoms can be also useful as a porosity models or rock models in geology. The paper focuses on characterization of several anisotropic phantoms and describes their applications in DTI, and other domains related to MRI.

Theoretical analysis of phantom rotations in BSD-DTI.

A novel method of improving accuracy of diffusion tensor imaging (DTI), called BSD-DTI (B-spatial distribution in DTI), has been recently proposed. Determination of the b matrix components using an anisotropic phantom, and derivation of the spatial distribution are of the essence in this approach. So far, a sufficient uniformity of the diffusion properties across the entire phantom has been assumed. Nevertheless, BSD-DTI is not limited only to highly homogeneous phantoms. This study describes a procedure which allows to use basically any anisotropic phantom of a precisely defined structure.

A theoretical validation of the B-matrix spatial distribution approach to diffusion tensor imaging

The recently presented B-matrix Spatial Distribution (BSD) approach is a calibration technique which derives the actual distribution of the B-matrix in space. It is claimed that taking into account the spatial variability of the B-matrix improves the accuracy of diffusion tensor imaging (DTI). The purpose of this study is to verify this approach theoretically through computer simulations. Assuming three different spatial distributions of the B-matrix, diffusion weighted signals were calculated for the six orientations of a model anisotropic phantom. Subsequently two variants of the BSD calibration were performed for each of the three cases; one with the assumption of high uniformity of the model phantom (uBSD-DTI) and the other taking into account imperfections in phantom structure (BSD-DTI). Several cases of varying degrees of phantom uniformity were analyzed and the distributions of the B-matrix obtained were used for the calculation of the diffusion tensor of a model isotropic phantom. The results were compared with standard diffusion tensor calculation. The simulations confirmed the improvement of accuracy in the determination of the diffusion tensor after the calibration. BSD-DTI improves accuracy independent of both the degree of uniformity of the phantom and the inhomogeneity of the B-matrix. In cases of a relatively good uniformity of the phantom and minor distortions in the spatial distribution of the B-matrix, the uBSD-DTI approach is sufficient.

The b matrix calculation using the anisotropic phantoms for DWI and DTI experiments.

B-matrix Spatial Distribution Diffusion Tensor Imaging (BSD-DTI) is a novel approach to imaging of the diffusion tensor. By means of the method a spatial distribution of the b matrices is determined and subsequently incorporated into diffusion tensor calculation. This paper presents experimental verification of the method. Statistical analysis of the results shows significant variation of the b matrix components through the slices and spatial b matrix maps depict inhomogeneity of the gradient distribution for MRI scanners equipped with wide bore magnets. The accuracy of the diffusion tensor determination was improved by the factor of about 3 for the isotropic phantom using the Spin Echo Diffusion sequence.

ZTE MRI in high magnetic field as a time effective 3D imaging technique for monitoring water ingress in porous rocks at sub-millimetre resolution

Zero echo time magnetic resonance imaging (ZTE MRI) at 9.4T was used to assess the local distribution of water in dolomite rocks under different saturation conditions. The results were compared with the industry standard Single Point Imaging (SPI) at 0.6T. 3D maps of the local amount of water saturating heterogeneous rock were obtained from the imaging data, and correlated with the corresponding structural images from high resolution micro-CT (μCT). The method can be applicable in the investigation of spatial kinetics of water saturation processes in porous, heterogeneous rocks where imaging methods based on spin echo, such as RARE, have failed due to short T2, while SPI is often impractical due to its long acquisition time.

The generalized Stejskal-Tanner equation for non-uniform magnetic field gradients

The intensity of the diffusion weighted NMR signal is described by the Stejskal-Tanner equation, which was derived under the assumption that the gradients are uniform throughout the sample. Nevertheless, it has been demonstrated numerous times that this condition is not fulfilled in the cases of virtually any clinical or research MRI scanners. Therefore, technically, the Stejskal-Tanner equation is valid only for a very specific case of homogeneous gradients. In this paper the Stejskal-Tanner equation was derived for the general case on non-uniform diffusion gradients. To this end, the magnetic field was expressed as linear in a curvilinear coordinate system defined by a vector function p(r). Thereafter, the expression for the non-linear magnetic field was put into the Bloch-Torrey equation and solved. Moreover, the meaning of so-called coil tensor, which is used for the gradients inhomogeneity correction, was explained. It was proven that in the case of the spin echo-based sequences, the Stejskal-Tenner equation is still valid, even if the diffusion gradients are non-uniform. However, in such a case, the b-matrix should be derived for each voxel separately. For other sequence, the derived relation possesses an imaginary term, which corresponds do the phase shift of the diffusion weighted signal.

Analysis and correction of errors in DTI-based tractography due to diffusion gradient inhomogeneity

The DTI-based tractography, despite its restrictions, is the most widely utilized fiber tracking method in clinical practice. Its fidelity is strictly dependent on the precision and accuracy of the DTI measurement, which in turn is limited by the linearity of the diffusion sensitizing gradient. The influence of the gradient distortions on the differences between the real and measured orientation of fibers was investigated by computer simulations. In addition, the potential of the b-matrix Spatial Distribution in DTI (BSD-DTI) technique in correcting such kind of errors was demonstrated experimentally. The simulations revealed that the diffusion gradient inhomogeneity, if not corrected, leads to the erroneous indication of the fiber direction. The average and maximum deviations were about 1° and 15°, respectively. Remarkably, the deviation between the real and measured orientation of fibers is directionally dependent, what was confirmed in MRI measurement. The deviation errors can be effectively corrected by preceding the DTI measurement with the BSD-DTI calibration.