## Diffusion Studies

The random diffusion of water molecules in the presence of a strong magnetic gradient results in a reduction of the MR signal caused by the loss of spin coherence.

As mentioned above diffusion sensitization, or diffusion weighting, consists of the application of a pair of strong gradients to elicit differences in the diffusion of water molecules within different biological compartments [3]. The application of a second gradient oriented in the same spatial direction but with inverse polarity, or with the same polarity but applied on the other side of the 180° refocusing pulse, restores the phase coherence of stationary protons, while the randomly diffusing molecules lose phase coherence proportionally to their displacement in the gradient direction.

The degree of diffusion weighting is given by the b value, a parameter that is determined by the mode of application of the diffusion-sensitizing gradient scheme. The most commonly implemented modality in clinical MR scanners is the Stejskal-Tanner spin-echo scheme [3], which consists of a pulsed pair of approximately rectangular gradients before and after a 180° RF pulse. In this case, the b value depends on the duration (d) and strength (G) of the sensitizing pulsed gradients, and on the time interval between the two pulsed gradients (A), according to the equation:

where is the gyromagnetic ratio. Thus, the b value, and so the diffusion sensitization, can be increased by using stronger (G) and longer (d) pulsed gradients or by increasing the time between the pulsed gradients (D) [3].

Adding diffusion-sensitizing gradients to an imaging sequence constitutes the basis for diffusion weighted MRI. In these MR images, the signal intensity (S) of each voxel is influenced by two sequence parameters, b value and echo time, and by two parameters intrinsic to biological tissues: the apparent diffusion coefficient (ADC) and the transverse relaxation time (T2). ADC is a measure of molecular diffusion and reflects the presence of restrictions, such as viscosity and spatial barriers.

The following formula [3] describes the relationship between signal intensity in a diffusion-weighted MR image and molecular diffusivity:

where S0 is the signal intensity at b = 0; or using the natural logarithm:

Given the mixed dependence of the signal intensity on tissue ADC and T2, it is necessary to use an acquisition strategy to highlight the effect of diffusion. Indeed, acquiring images with at least two different b values (commonly 0-20 and 1,000 s/mm2) to vary the diffusion weighting, but with the same TE so as to obtain a stable T2 weighting, allows determination of the ADC value of each voxel. The lower b value is often selected to be slightly greater than zero to eliminate the effects of large vessels and flow [3].

Molecular diffusion within a given voxel is generally assumed to have a single diffusion coefficient. In fact, most tissues contain multiple subcompartments. At least the intra- and extracellular compartment are always present, whose contribution is estimated to be respectively 82.5% and 17.5% of the brain tissue; they have basically different intrinsic ADC values, the extracellular diffusion being much faster. The measured ADC can depend on the b value used, as data obtained with low b values (up to 1,000 s/mm2) would be more sensitive to fast diffusion components and thus to extracellular compartment dynamics. In clinical studies and most animal experiments, especially when data are fitted with a single exponent, the diffusion patterns observed in tissues thus need to be explained in terms of extracellular space dynamics, even though this compartment is physically the smaller one. Changes in ADC calculated in this way should thus be interpreted as changes in ADC of the extracellular space (tortuosity) and in its fractional variation relative to the intra-cellular volume. This explains why diffusion studies have immediately been recognized as sensitive probes of the changes taking place in the extracellular/intracel-lular volume ratio, as observed in brain ischaemia, spreading depression [1-4, 6] and status epilepticus [1-7].

It is important to note that diffusion imaging is a quantitative method. The diffusion coefficient is a physical parameter that reflects directly the physical properties of tissues in terms of random molecular translation. This entails that, in principle, diffusion coefficients obtained at different times in a given patient, in different patients, or even at different hospitals can be compared without need for normalization [1].

MR measurement ofthe Brownian movement ofwa-ter molecules can be applied at different, increasingly complex levels: (1) DWI, (2) ADC maps, (3) DTI and TI (Fig. 7.1).

Fig. 7.1. Different MR diffusion imaging techniques. a EPI T2 with b value = 0. b Diffusion weighted imaging (Tr/TE 11,000/ min, matrix 164x192, 1 Nex, FOV 32 cm, thickness 5 mm, b value = 1,000, 0:44). c ADC map

Fig. 7.1. Different MR diffusion imaging techniques. a EPI T2 with b value = 0. b Diffusion weighted imaging (Tr/TE 11,000/ min, matrix 164x192, 1 Nex, FOV 32 cm, thickness 5 mm, b value = 1,000, 0:44). c ADC map

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