Diffusion-weighted magnetic resonance imaging (DWI or DW-MRI) is the use of specific MRI sequences as well as software that generates images from the resulting data that uses the diffusion of water molecules to generate contrast in MR images. It allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and non-invasively. Molecular diffusion in tissues is not random, but reflects interactions with many obstacles, such as macromolecules, fibers, and membranes. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state. A special kind of DWI, diffusion tensor imaging (DTI), has been used extensively to map white matter tractography in the brain.
Introduction In diffusion weighted imaging (DWI), the intensity of each image element (voxel) reflects the best estimate of the rate of water diffusion at that location. Because the mobility of water is driven by thermal agitation and highly dependent on its cellular environment, the hypothesis behind DWI is that findings may indicate (early) pathologic change. For instance, DWI is more sensitive to early changes after a stroke than more traditional MRI measurements such as T1 or T2 relaxation rates. A variant of diffusion weighted imaging, diffusion spectrum imaging (DSI), was used in deriving the Connectome data sets; DSI is a variant of diffusion-weighted imaging that is sensitive to intra-voxel heterogeneities in diffusion directions caused by crossing fiber tracts and thus allows more accurate mapping of axonal trajectories than other diffusion imaging approaches.
Diffusion-weighted images are very useful to diagnose vascular strokes in the brain. It is also used more and more in the staging of non-small-cell lung cancer, where it is a serious candidate to replace positron emission tomography as the 'gold standard' for this type of disease. Diffusion tensor imaging is being developed for studying the diseases of the white matter of the brain as well as for studies of other body tissues (see below). DWI is most applicable when the tissue of interest is dominated by isotropic water movement e.g. grey matter in the cerebral cortex and major brain nuclei, or in the body—where the diffusion rate appears to be the same when measured along any axis. However, DWI also remains sensitive to T1 and T2 relaxation. To entangle diffusion and relaxation effects on image contrast, one may obtain quantitative images of the diffusion coefficient, or more exactly the apparent diffusion coefficient (ADC). The ADC concept was introduced to take into account the fact that the diffusion process is complex in biological tissues and reflects several different mechanisms.
Diffusion tensor imaging (DTI) is important when a tissue—such as the neural axons of white matter in the brain or muscle fibers in the heart—has an internal fibrous structure analogous to the anisotropy of some crystals. Water will then diffuse more rapidly in the direction aligned with the internal structure (axial diffusion), and more slowly as it moves perpendicular to the preferred direction (radial diffusion). This also means that the measured rate of diffusion will differ depending on the direction from which an observer is looking.
Diffusion Basis Spectrum Imaging (DBSI) further separates DTI signals into discrete anisotropic diffusion tensors and a spectrum of isotropic diffusion tensors to better differentiate sub-voxel cellular structures. For example, anisotropic diffusion tensors correlate to axonal fibers, while low isotropic diffusion tensors correlate to cells and high isotropic diffusion tensors correlate to larger structures (such as the lumen or brain ventricles). DBSI has been shown to differentiate some types of brain tumors and multiple sclerosis with higher specificity and sensitivity than conventional DTI. DBSI has also been useful in determining microstructure properties of the brain.
Traditionally, in diffusion-weighted imaging (DWI), three gradient-directions are applied, sufficient to estimate the trace of the diffusion tensor or 'average diffusivity', a putative measure of edema. Clinically, trace-weighted images have proven to be very useful to diagnose vascular strokes in the brain, by early detection (within a couple of minutes) of the hypoxic edema.
More extended DTI scans derive neural tract directional information from the data using 3D or multidimensional vector algorithms based on six or more gradient directions, sufficient to compute the diffusion tensor. The diffusion tensor model is a rather simple model of the diffusion process, assuming homogeneity and linearity of the diffusion within each image voxel. From the diffusion tensor, diffusion anisotropy measures such as the fractional anisotropy (FA), can be computed. Moreover, the principal direction of the diffusion tensor can be used to infer the white-matter connectivity of the brain (i.e. tractography; trying to see which part of the brain is connected to which other part).
More advanced models of the diffusion process have been proposed that aim to overcome the weaknesses of the diffusion tensor model. Amongst others, these include q-space imaging and generalized diffusion tensor imaging.
Mechanism Diffusion imaging is an MRI method that produces in vivo magnetic resonance images of biological tissues sensitized with the local characteristics of molecular diffusion, generally water (but other moieties can also be investigated using MR spectroscopic approaches). MRI can be made sensitive to the motion of molecules. Regular MRI acquisition utilizes the behavior 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 related to the structure of tissues at the microscopic level. In a typical T1-weighted image, water molecules in a sample are excited with the imposition of a strong magnetic field. This causes many of the protons in water molecules to precess simultaneously, producing signals in MRI. In T2-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.
To sensitize MRI images to diffusion, the magnetic field strength (B1) 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 magnitude but with opposite direction 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 "field gradient pulse" method was initially devised for NMR by Stejskal and Tanner who derived the reduction in signal due to the application of the pulse gradient related to the amount of diffusion that is occurring through the following equation:
where is the signal intensity without the diffusion weighting, is the signal with the gradient, is the gyromagnetic ratio, is the strength of the gradient pulse, is the duration of the pulse, is the time between the two pulses, and finally, is the diffusion-coefficient.
In order to localize this signal attenuation to get images of diffusion one has to combine the pulsed magnetic field gradient pulses used for MRI (aimed at localization of the signal, but those gradient pulses are too weak to produce a diffusion related attenuation) with additional "motion-probing" gradient pulses, according to the Stejskal and Tanner method. This combination is not trivial, as cross-terms arise between all gradient pulses. The equation set by Stejskal and Tanner then becomes inaccurate and the signal attenuation must be calculated, either analytically or numerically, integrating all gradient pulses present in the MRI sequence and their interactions. The result quickly becomes very complex given the many pulses present in the MRI sequence, and as a simplification, Le Bihan suggested gathering all the gradient terms in a " factor" (which depends only on the acquisition parameters) so that the signal attenuation simply becomes:
Also, the diffusion coefficient, , is replaced by an apparent diffusion coefficient, , to indicate that the diffusion process is not free in tissues, but hindered and modulated by many mechanisms (restriction in closed spaces, tortuosity around obstacles, etc.) and that other sources of IntraVoxel Incoherent Motion (IVIM) such as blood flow in small vessels or cerebrospinal fluid in ventricles also contribute to the signal attenuation. At the end, images are "weighted" by the diffusion process: In those diffusion-weighted images (DWI) the signal is more attenuated the faster the diffusion and the larger the factor is. However, those diffusion-weighted images are still also sensitive to T1 and T2 relaxivity contrast, which can sometimes be confusing. It is possible to calculate "pure" diffusion maps (or more exactly ADC maps where the ADC is the sole source of contrast) by collecting images with at least 2 different values, and , of the factor according to:
Although this ADC concept has been extremely successful, especially for clinical applications, it has been challenged recently, as new, more comprehensive models of diffusion in biological tissues have been introduced. Those models have been made necessary, as diffusion in tissues is not free. In this condition, the ADC seems to depend on the choice of values (the ADC seems to decrease when using larger b values), as the plot of ln(S/So) is not linear with the factor, as expected from the above equations. This deviation from a free diffusion behavior is what makes diffusion MRI so successful, as the ADC is very sensitive to changes in tissue microstructure. On the other hand, modeling diffusion in tissues is becoming very complex. Among most popular models are the biexponential model, which assumes the presence of 2 water pools in slow or intermediate exchange and the cumulant-expansion (also called Kurtosis) model, which does not necessarily require the presence of 2 pools.
Diffusion model
Given the concentration and flux , Fick's first law gives a relationship between the flux and the concentration gradient:
where D is the diffusion coefficient. Then, given conservation of mass, the continuity equation relates the time derivative of the concentration with the divergence of the flux:
Putting the two together, we get the diffusion equation:
Magnetization dynamics
With no diffusion present, the change in nuclear magnetization over time is given by the classical Bloch equation
which has terms for precession, T2 relaxation, and T1 relaxation.
In 1956, H.C. Torrey mathematically showed how the Bloch equations for magnetization would change with the addition of diffusion. Torrey modified Bloch's original description of transverse magnetization to include diffusion terms and the application of a spatially varying gradient. Since the magnetization is a vector, there are 3 diffusion equations, one for each dimension. The Bloch-Torrey equation is:
where is now the diffusion tensor.
For the simplest case where the diffusion is isotropic the diffusion tensor is a multiple of the identity:
then the Bloch-Torrey equation will have the solution
The exponential term will be referred to as the attenuation . Anisotropic diffusion will have a similar solution for the diffusion tensor, except that what will be measured is the apparent diffusion coefficient (ADC). In general, the attenuation is:
where the terms incorporate the gradient fields , , and .