Diffusion-weighted imaging

Diffusion-weighted imaging is a specific MRI modality that produces in vivo magnetic resonance images of biological tissues weighted with the local characteristics of water diffusion.

Overview

DWI is a modification of regular MRI techniques, and is an approach which utilizes the measurement of Brownian (or random walk) motion of molecules. Regular MRI acquisition utilizes the behaviour of protons in water to generate contrast between clinically relevant features of a particular subject. The versatile nature of MRI is due to this capability of producing contrast, called weighting. In a typical $T_{1}$-weighted image, water molecules in a sample are excited with the imposition of a strong magnetic field. This causes the millions of water molecules to precess simultaneously, and it is this precession of protons which produces signals in MRI. In $T_{2}$-weighted images, contrast is produced by measuring the loss of coherence or synchrony between the water protons. When water is in an environment where it can freely tumble, relaxation tends to take longer. In certain clinical situations, this can generate contrast between an area of pathology and the surrounding healthy tissue.

In diffusion-weighted images, instead of a homogenous magnetic field, the homogeneity is varied linearly by a pulsed field gradient. Since precession is proportional to the magnet strength, the protons begin to precess at different rates, resulting in dispersion of the phase and signal loss. Another gradient pulse is applied in the same direction but with opposite magnitude to refocus or rephase the spins. The refocusing will not be perfect for protons that have moved during the time interval between the pulses, and the signal measured by the MRI machine is reduced. This reduction in signal due to the application of the pulse gradient can be related to the amount of diffusion that is occurring through the following equation:

${\frac {S}{S_{0}}}=e^{-\gamma ^{2}G^{2}\delta ^{2}\left(\Delta -\delta /3\right)D}=e^{-bD}\,$

where $S_{0}$ is the signal intensity without the diffusion weighting, $S$ is the signal with the gradient, $\gamma$ is the gyromagnetic ratio, $G$ is the strength of the gradient pulse, $\delta$ is the duration of the pulse, $\Delta$ is the time between the two pulses, and finally, $D$ is the diffusion constant.

By rearranging the formula to isolate the diffusion-coefficient, it is possible to obtain an idea of the properties of diffusion occurring within a particular voxel (volume picture element). These values, called apparent diffusion coefficient (ADC) can then be mapped as an image, using diffusion as the contrast.

The first successful clinical application of DWI was in imaging the brain following stroke in adults. Areas which were injured during a stroke showed up "darker" on an ADC map compared to healthy tissue. At about the same time as it became evident to researchers that DWI could be used to assess the severity of injury in adult stroke patients, they also noticed that ADC values varied depending on which way the pulse gradient was applied. This orientation-dependant contrast is generated by diffusion anisotropy, meaning that the diffusion in parts of the brain has directionality. This may be useful for determining structures in the brain which could restrict the flow of water in one direction, such as the myleinated axons of nerve cells (which is affected by multiple sclerosis). However, in an imaging the brain following a stroke, it may actually prevent the injury from being seen. To compensate for this, it is necessary to apply a tensor to fully characterize the motion of water in all directions. This tensor is called a diffusion tensor: ${\bar {D}}={\begin{vmatrix}D_{xx}&D_{xy}&D_{xz}\\D_{yx}&D_{yy}&D_{yz}\\D_{zx}&D_{zy}&D_{zz}\end{vmatrix}}$

Diffusion-weighted images are very useful to diagnose vascular strokes in the brain, to study the diseases of the white matter or to (try to) infer the connectivity of the brain (i.e. tractography; try to see which part of the cortex is connected to another one, and so on).

References

Carano AD, van Bruggen N, de Crespigny AJ. MRI measurement of cerebral water diffusion and its application to experimental research. Printed in Biomedical Imaging in Experimental Neuroscience. Boca Raton, FL: CRC Press, 2003. pp 21-54.

Mori S, Barker PB (1999) Diffusion magnetic resonance imaging: its principle and applications. Anat Rec B New Anat 257:102-109.

Koyama T, Tamai K, Togashi K (2006) Current status of body MR imaging : fast MR imaging and diffusion-weighted imaging. Int J Clin Oncol 11:278-285.

See also

• Diffusion MRI
• IRC: About Diffusion MRI