DWI evaluates the mean molecular diffusivity from the average diffusion coefficients in all directions. Evaluation of the mean diffusivity must avoid anisotropic diffusion effects and make the results independent of the orientation of the reference frame [1]. Such an evalua tion can be performed by calculating the trace of the diffusion tensor, Tr(D) = Dxx + Dyy + Dzz [1], where Dxx, Dyy and Dzz are the diffusion coefficients along the three axes. The mean diffusivity is then given by Tr(D)/3. The procedure generally adopted to calculate the mean diffusivity in clinical settings is to average the DW images or diffusion coefficients obtained by separately acquiring data with gradient pulses added along the x, y, and z axes. Nonetheless, the diffusion coefficients measured in this way do not usually coincide exactly with Dxx, Dyy, and Dzz, unless the diffusion is iso-tropic and the contribution of each gradient pulse to the other two axes is negligible. Correct Tr(D) estimation would require complete determination of the diffusion tensor [1]. The mean diffusivity, as obtained from the trace of the diffusion tensor, corresponds to the overall water molecule displacements, which are similar in grey and white matter. This results in the typically low grey/white matter contrast of DW images, which makes pathological changes in diffusivity clear and easy to detect. Tissue components with free or elevated diffusion, like cerebrospinal fluid, exhibit hypo-intense signal, whereas those restricting diffusion are hyperintense.

Potential clinical applications of water-diffusion MRI were suggested very early after its introduction [8]. DWI is widely used in clinical practice, its most successful application being in the study of brain is-chaemia [9]; in particular, it has a fundamental role in the diagnosis of hyperacute ischaemia, where no other MR imaging modality provides comparable results (Fig. 7.2).

Fig. 7.1. d Tensor imaging. e Main eigenvector map (area of interest genu of the corpus callosum). f Tracto-graphy (cingulum)

Moseley et al. reported that in cat brain water diffusion decreases in a very early phase of the ischaemic event

[10], and that it can drop to 50% of the normal value

[11]. This finding is related to the cytotoxic oedema, which in turn is induced by the energy failure of the cell membrane Na/K pump system, although the exact mechanism underpinning such decreased diffusion at the molecular level is still unclear. Changes in water compartmentalization in brain tissue determined by the cytotoxic oedema, with a reduction of the fast extracellular compartment and an increase of the slow-diffusion intracellular volume fraction might explain it. While changes in membrane permeability [12] are a prerequisite for changes in water compartmentaliza-tion, two events concur to reduce molecular diffusion. The first is the volume increase of the slower intracellu lar compartment at the expense of the faster extracellular one, resulting in reduced average water diffusion; the second is the reduced water diffusion in the faster compartment itself, through the shrinkage of the extracellular space, resulting in increased tortuosity and impairment the Brownian displacement of water molecules [1-14]. The results from animal studies have been confirmed in human stroke, where DWI has been able to detect the ischaemic regions within the first few hours, or even minutes, of the ischaemic event. In this very early phase, well before standard MRI can depict the vasogenic oedema, the ischaemic tissue may still be rescued [1-16] with appropriate therapies. DWI appears to be particularly useful in combination with perfusion MRI, making it possible to distinguish the ischa-emic tissue from the penumbra, optimize the therapeu

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Fig. 7.2. Right occipital hyperacute cerebral ischaemia: DWI (in a b value = 0; in b b value = 1,000)

Fig. 7.2. Right occipital hyperacute cerebral ischaemia: DWI (in a b value = 0; in b b value = 1,000)

tic approach [17], monitor patient progress and predict outcome [18,19].

Despite the high sensitivity and specificity of DWI for ischaemia, anisotropic diffusion effects may sometimes mimic ischaemic regions, especially near ventricular cavities. In fact, if diffusion sensitization is applied in only one direction, the compact white matter bundles that run perpendicular to the gradient sensitiza-tion direction will appear artefactually brighter due to restriction of diffusion by membranes and myelin. It is, therefore, necessary to use mean diffusivity or the trace of the diffusion tensor to remove these artefacts [20].

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