Assessing diffusion using Magnetic Resonance Imaging
3.6 Diffusion Tensor Imaging (DTI)
The mobility of water molecules in organized tissue is not necessarily the same in all directions but can occur in one of three ways (i) bulk flow, (ii) isotropic diffusion where motion is random and (iii) restricted diffusion where random motion is constrained by physical barriers. In the kidney, whose function is to transport water, renal structures such as vessel, tubules and collecting ducts are oriented in a radial fashion, resulting in anisotropic diffusion properties [12] .
In a DWI scheme, the diffusion gradients can be applied in at least six directions yielding a diffusion tensor image (DTI) to obtain information on the orientation of water molecule diffusion. In anisotropic tissues, ADC will vary depending on the direction in which it is measured. DTI provides further information on the degree of diffusion anisotropy in the tissue’s microstructure. To measure the ADC values in an anisotropic tissue all tensor components and an unweighted (b=0) image are required. The diffusion properties can then be described mathematically by a tensor which has nine matrix values (3x3), each corresponding to a gradient orientation and a cell orientation (equation (3.10)).
D =
DOO DOY DOZ DOY DYY DYZ DOZ DYZ DZZ
(3.10)
The diffusion tensor results in a three-dimension (3D) ellipsoid. The physical process of diffusion causes water molecules to move out from a central point, and gradually reach in the surface of an ellipsoid if the medium is anisotropic (Figure3.10 (b)) and in the surface of a sphere for an isotropic medium (Figure 3.10 (a)). The ellipsoid has three principle primary axes which describe its length, width and depth properties. These are determined by the eigenvectors (v1,v2 and v3) and eigenvalues (λ1, λ2, and λ3) that describe the orientation and magnitude of diffusion along the principle axes (Figure 3.10). All three of these are perpendicular to each other and cross at the centre point of the ellipsoid. The diffusivity along the principle axis, λ1 is also called the longitudinal diffusivity or the axial diffusivity (AD). The diffusivities in the two minor axes (λ2 and λ3) are often averaged to provide a measure of radial diffusivity (RD) (Equation (3.11)). Mean diffusivity (MD) is a scalar measure of the total diffusion within a voxel (Equation (3.12)). The other parameter involved in
diffusion anisotropy measurements is the fractional anisotropy (FA) (Equation (3.13)), an index scaled from 0 (isotropic: no preferred direction) to 1 (full anisotropy: only one direction).
RD = λ/+ λ9 2 (3.11) MD =λ^+ λ/+ λ9 3 (3.12) FA = 3 λ^− MD /+ λ/− MD / + λ9− MD / 2 λ^/ + λ//+ λ9/ (3.13)
DTI has been applied to renal tissue in a small number of studies [25-27] to measure anisotropic diffusion in the kidney. FA has been shown to be low in the renal cortex suggesting that diffusion in the renal cortex can be coherent in
v1 v2 v3 v1 v2 v3 (a) (b)
Figure 3.10: Three principle directions are coincident with the eigenvector of D, v1,v2, and v3 in (a) an isotropic medium which has spherical diffusion ellipsoid and (b) in an anisotropic medium which has a prolate or oblate diffusion ellipsoid.
direction but relatively isotropic in magnitude [25]. In contrast, recent studies have shown that the directionality of diffusion (FA) is higher in the renal medulla than in the cortex [24, 28, 29], which probably reflects the radial arrangement of tubules, vessels, and collecting ducts and blood vessel [26, 30, 31], suggesting a coherent flow along the axial direction and restricted diffusion in the radial direction. DTI has also been used in the liver [13], and results show that the liver has a near isotropic diffusion. DTI has detected progressive changes in water diffusivities and diffusion anisotropy in tissues with liver fibrosis [32].
In addition, the impact of renal blood flow on FA values of kidneys has been reported [28]. In the human kidney, a significant correlation between renal ADC and blood flow in renal artery [33] has also been demonstrated, with ADC of renal cortex being significantly higher at maximal than minimal blood flow [28]. The potential influence of pulsatile blood flow on ADC and FA values has to be considered when interpreting DWI and DTI data. However, whilst the measured ADC values are highly dependent on the choice of b-values [24], FA values are not, suggesting that FA is a more stable parameter than ADC [10]. Moreover, IVIM and DTI methodology can be combined to distinguish structural from flow effects [34].
This chapter has presented an overview of diffusion imaging which will be applied in Chapters 4 and 6.
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