Abstract
In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin diffusion in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows to provide analytical expressions for the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.
Highlights
When exposed to an external magnetic field as in magnetic resonance imaging (MRI), spatial variations of magnetic susceptibility in heterogeneous systems such as biological tissue induce local inhomogeneities of the magnetic field that are usually visible for macroscopic structures
Susceptibility differences in biological tissue occur at the interfaces between different tissue structures and/or different types of tissue, generating local magnetic field gradients that lead to a dephasing of the magnetization
An increase of spin dephasing through diffusion effects may lead to a characteristic loss of inter-spin coherence: a spin that diffuses around these magnetic field perturbers experiences the local magnetic field inhomogeneities even though the applied external field is homogeneous
Summary
When exposed to an external magnetic field as in magnetic resonance imaging (MRI), spatial variations of magnetic susceptibility in heterogeneous systems such as biological tissue induce local inhomogeneities of the magnetic field that are usually visible for macroscopic structures. Susceptibility differences in biological tissue occur at the interfaces between different tissue structures and/or different types of tissue, generating local magnetic field gradients that lead to a dephasing of the magnetization. This effect can be used to obtain quantifiable information. Due to the BOLD effect [7], capillaries containing erythrocytes with deoxygenated hemoglobine possess an inherent paramagnetic susceptibility that is different to that of the surrounding tissue For such magnetized spherical and cylindrical subvoxel structures, diffusion effects due to spin movements are not negligible. Some authors suggest that anomalous or non-Gaussian diffusion in biological tissue is due to dephasing effects that are promoted by both diffusion multi-compartmentalization and magnetic susceptibility [10, 11]
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