## Basic Principles

A brief overview of the structural characteristics of nerve tissue is in order to help understand the rationale of diffusion studies. White matter is mainly composed of myelinated axons with a given orientation, whereas grey matter is made up of cells, principally neurons. Axons have a mean diameter of ~20 ^m and may form parallel, sometimes thick bundles.

The rationale of tractography and DTI is that the random movement of water molecules in tissues (diffusion) is restricted by the presence of cell structures (Fig. 8.1). As a consequence, diffusion perpendicular to axon bundles is hindered by axonal cell membranes and myelin sheaths [7, 8] whereas it is unrestricted along them. Within axons water is surrounded by cell membranes and myelin sheaths; again, its diffusion will be greater parallel to the fibres. Longitudinally oriented axoplasmic neurofilaments do not seem to restrict diffusion [9]. Tissues like cerebral white matter, possessing a microscopic architecture with a specific spatial orientation, will thus exhibit different diffusion values in the different spatial directions. When diffusion exhibits a preferential direction, it is termed an-isotropic.

The diffusion of water molecules in biological tissues can be measured using MR gradients and diffusion-weighted sequences. The acquisition technique consists of „tagging" the water molecules with a very short gradient. Tagged molecules acquire a magnetization and a phase that depend on their spatial position. The natural phenomenon of diffusion causes the displacement of these molecules to areas containing molecules with different magnetization and phase. The presence in a region of signals with different magnetization and phase results in an overall lower signal intensity, as the signal of the diffusing molecules reduces the one of local molecules. Therefore, increasing diffusion of the water molecules induces a reduction in tissue signal. The study of diffusion anisotropy uses the same image acquisition strategies as clinical diffusion studies. Indeed, water molecule diffusion data are actually generated as anisotropic data, because all acquisi

Fig. 8.1. Representation ofthephysi-cal bases of the reconstruction of the diffusion tensor. In homogeneous tissues, the three eigenvalues have similar values and the tensor is spherical. In tissues where barriers restrict water diffusion in a particular direction, the tensor is an ellipsoid and the direction corresponding to the principal eigenvalue represents the direction of the fibres

Fig. 8.1. Representation ofthephysi-cal bases of the reconstruction of the diffusion tensor. In homogeneous tissues, the three eigenvalues have similar values and the tensor is spherical. In tissues where barriers restrict water diffusion in a particular direction, the tensor is an ellipsoid and the direction corresponding to the principal eigenvalue represents the direction of the fibres tions read diffusion along a given spatial direction, coinciding with the direction of the magnetic field gradient used. In clinical diffusion studies, the direction information is lost through the averaging of diffusion values along the three spatial axes; this simplifies the detection of pathological changes in the diffusion coefficient, which are independent of fibre direction.

In DTI studies, this information is retained and the prevalence of diffusion along a direction, e.g. along a fibre bundle, can be expressed in terms of anisotropy. The degree of anisotropy can be quantified using the diffusion tensor [9-11]. A tensor is a complex mathematical entity [12]; when measured with MR, it maybe represented in matrix form using data from diffusion-weighted images to obtain parameters like fractional anisotropy (FA) and the apparent diffusion coefficient (ADC) [13]. The diffusion tensor also contains much additional information. In particular, an algebraic procedure called diagonalization makes it possible to obtain for each image voxel three eigenvalues ( 1, 2, 3) representing the values of diffusion along three spatial directions (eigenvectors). If in a given voxel the three values are similar (A; ^A2^A3), as in grey matter, the water diffuses in a similar manner in all directions and its diffusion in the voxel is called isotropic. If, by contrast, one of the three eigenvalues is much greater than the other two, as in white matter, water diffuses more easily along the direction corresponding with that eigenvalue, and its diffusion in the voxel is termed anisotropic.

It may bear stressing that, unlike MR parameters such as relaxation times, those obtained from the diffusion tensor do not depend directly on the magnetic field and can thus be measured and directly compared between high- and low-field acquisitions. In practice, whereas T1 and T2, and thus the relevant images, change as a function of the magnetic field, water diffu sion in a given space is the same at 1.5, 3.0 and even 7.0 T. Diffusion studies thus fully benefit from the greater signal/noise ratio (SNR) of high-field magnets.

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