Dependence of the frequency distribution around a vessel on the voxel orientation.

In this work the frequency distribution around a vessel inside a cubic voxel is investigated. Therefore, the frequency distribution is calculated in dependence on the orientation of the voxel according to the external magnetic field. The frequency distribution exhibits an interesting peak structure that cannot be explained by the established Krogh's vessel model. The results were validated with phantom measurements and in vivo measurements that agree very well with the developed theory.

Pseudo-diffusion effects in lung MRI.

Magnetic resonance imaging of lung tissue is strongly influenced by susceptibility effects between spin-bearing water molecules and air-filled alveoli. The measured lineshape, however, also depends on the interplay between susceptibility effects and blood-flow around alveoli that can be approximated as pseudo-diffusion. Both effects are quantitatively described by the Bloch-Torrey-equation, which was so far only solved for dephasing on the alveolar surface. In this work, we extend this model to the whole range of physiological relevant air volume fractions. The results agree very well with in vivo measurements in human lung tissue.

Spin dephasing around randomly distributed vessels.

We analyze the gradient echo signal in the presence of blood vessel networks. Both, diffusion and susceptibility effects are analytically emphasized within the Bloch-Torrey equation. Solving this equation, we present the first exact description of the local magnetization around a single vessel. This allows us to deduce the gradient echo signal of parallel vessels randomly distributed in a plane, which is valid for arbitrary mean vessel diameters in the range of physiological relevant blood volume fractions. Thus, the results are potentially relevant for gradient echo measurements of blood vessel networks with arbitrary vessel size.

Diffusion effects in myelin sheath free induction decay.

Myelin sheath microstructure and composition produce MR signal decay characteristics that can be used to evaluate status and outcome of demyelinating disease. We extend a recently proposed model of neuronal magnetic susceptibility, that accounts for both the structural and inherent anisotropy of the myelin sheath, by including the whole dynamic range of diffusion effects. The respective Bloch-Torrey equation for local spin dephasing is solved with a uniformly convergent perturbation expansion method, and the resulting magnetization decay is validated with a numerical solution based on a finite difference method. We show that a variation of diffusion strengths can lead to substantially different MR signal decay curves. Our results may be used to adjust or control simulations for water diffusion in neuronal structures.

The influence of spatial patterns of capillary networks on transverse relaxation.

Tissue-inherent relaxation parameters offer valuable information about the arrangement of capillaries: in an external field, capillaries act as magnetic perturbers to generate local inhomogeneous fields due to the susceptibility difference of deoxygenated blood and the surrounding tissue. These field inhomogeneities influence the free induction decay in a characteristic way, and, conversely, the above tissue parameters can be recovered by multi-parametric fits of adequate theoretical models to experimentally sampled free induction decays. In this work we study the influence of different spatial patterns of capillary positions on the free induction decay. Starting from the standard single capillary approximation (Krogh cylinder) for a symmetric array of capillaries, the free induction decay is analyzed for increasingly random capillary positions, using a previously described Gibbs point field model. The effects of diffusion are implemented with a flexible and fast random walk simulation. We find that the asymmetric form of the obtained frequency distribution is more robust against variations of capillary radii than against shifts of capillary positions, and further that, for an inclusion of diffusion effects, the single capillary approximation models the uniform alignment of capillaries in the hexagonal lattice to great accuracy. An increase in randomization of capillary positions then leads to a significant change in relaxation times. This effect, however, is found less pronounced than that of changes in the off-resonance field strengths which are controlled by the oxygen extraction fraction, thus indicating that observed changes in BOLD imaging are more likely to be attributed to changes in oxygenation than to capillary alignment.

Dephasing and diffusion on the alveolar surface.

We propose a surface model of spin dephasing in lung tissue that includes both susceptibility and diffusion effects to provide a closed-form solution of the Bloch-Torrey equation on the alveolar surface. The nonlocal susceptibility effects of the model are validated against numerical simulations of spin dephasing in a realistic lung tissue geometry acquired from synchotron-based µCT data sets of mouse lung tissue, and against simulations in the well-known Wigner-Seitz model geometry. The free induction decay is obtained in dependence on microscopic tissue parameters and agrees very well with in vivo lung measurements at 1.5 Tesla to allow a quantification of the local mean alveolar radius. Our results are therefore potentially relevant for the clinical diagnosis and therapy of pulmonary diseases.

Spin dephasing in a magnetic dipole field around large capillaries: Approximative and exact results.

We present an analytical solution of the Bloch-Torrey equation for local spin dephasing in the magnetic dipole field around a capillary and for ensembles of capillaries, and adapt this solution for the study of spin dephasing around large capillaries. In addition, we provide a rigorous mathematical derivation of the slow diffusion approximation for the spin-bearing particles that is used in this regime. We further show that, in analogy to the local magnetization, the transverse magnetization of one MR imaging voxel in the regime of static dephasing (where diffusion effects are not considered) is merely the first term of a series expansion that constitutes the signal in the slow diffusion approximation. Theoretical results are in agreement with experimental data for capillaries in rat muscle at 7T.

CPMG relaxation rate dispersion in dipole fields around capillaries.

Transverse relaxation rates for Carr-Purcell-Meiboom-Gill (CPMG) sequences increase with inter-echo time in presence of microscopic magnetic field inhomogeneities due to nuclear spin diffusion. For a weak field approximation that includes diffusion effects, the CPMG relaxation rate shift for proton diffusion around capillaries in muscle tissue can be expressed in terms of a frequency correlation function and the inter-echo time. The present work provides an analytical expression for the local relaxation rate shift that is dependent on local blood volume fraction, diffusion coefficient, capillary radius, susceptibility difference and inter-echo time. Asymptotic regions of the model are in agreement with previous modeling results of Brooks et al., Luz et al. and Ziener et al. In comparison with simulation data, the model shows an equal or better accuracy than established approximations. Also, model behavior coincides with experimental data for rat heart and skeletal muscle. The present work provides analytical tools to extract sub-voxel information about uniform capillary networks that can be used to study capillary organization or micro-circulatory remodeling.

[Principles and applications of susceptibility weighted imaging]. / Grundlagen und Anwendungen der suszeptibilitätsgewichteten Bildgebung.

BACKGROUND: Susceptibility-weighted imaging (SWI), initially developed to provide an improved method for cerebral magnetic resonance (MR) venography, is now an integral part of neuroradiological diagnostics and is steadily gaining importance in non-cerebral imaging. PRINCIPLES: Tissue-inherent susceptibility differences generate a local magnetic field in which the dephasing of signal-producing protons occurs. This leads to a characteristic phase shift that can be used as a means to enhance contrast in the well-known T2*-weighted imaging. APPLICATION IN CLINICAL ROUTINE: Many medically relevant pathologies induce tissue alterations that also influence the magnetic properties of tissue. Thus, the detection of blood residues and calcifications in SWI is superior to conventional MR sequences. FUTURE PROSPECTS: New techniques, such as quantitative susceptibility mapping (QSM) and susceptibility tensor imaging (STI) allow improved differentiation between blood residues and calcifications and provide an alternative imaging method for fiber tractography with respect to diffusion tensor imaging.

Free induction decay caused by a dipole field.

We analyze the free induction decay of nuclear spins under the influence of restricted diffusion in a magnetic dipole field around cylindrical objects. In contrast to previous publications no restrictions or simplifications concerning the diffusion process are made. By directly solving the Bloch-Torrey equation, analytical expressions for the magnetization are given in terms of an eigenfunction expansion. The field strength-dependent complex nature of the eigenvalue spectrum significantly influences the shape of the free induction decay. As the dipole field is the lowest order of the multipole expansion, the obtained results are important for understanding fundamental mechanisms of spin dephasing in many other applied fields of nuclear magnetic resonance such as biophysics or material science. The analytical methods are applied to interpret the spin dephasing in the free induction decay in cardiac muscle and skeletal muscle. A simple expression for the relevant transverse relaxation time is found in terms of the underlying microscopic parameters of the muscle tissue. The analytical results are in agreement with experimental data. These findings are important for the correct interpretation of magnetic resonance images for clinical diagnosis at all magnetic field strengths and therapy of cardiovascular diseases.