Diffusion Magnetic Resonance Imaging: From Isotropic Diffusion - Weighted Imaging to Diffusion Tensor Imaging and Beyond

Diffusion magnetic resonance imaging (dMRI), which was established in the mid 1980ʼs, is an imaging technique that is based on the diffusion of water molecules in tissue. Initially it was an isotropic diffusion-weighted imaging (DWI) technique, and has been widely used mainly for investigating the tissue microstructural changes in neurological abnormalities, especially ischemic stroke. Many studies have been conducted to validate the usefulness of DWI in clinical settings and to improve the technique. Diffusion tensor imaging (DTI) was later introduced to deal with the anisotropic diffusion; the use of an ellipsoid tensor model means that the size and the direction of the water diffusion can be delineated. DTI and its developments are becoming powerful tools, and have become the standard imaging techniques for analyzing white matter fiber structure and connectivity in vivo . Furthermore, to facilitate researchers in applying DTI for multi-subject studies, tract-based spatial statistics (TBSS) was developed. TBSS is a voxelwise statistical analysis that was originally used to evaluate the fractional anisotropy (FA) values in the white matter. Thereafter, diffusion kurtosis imaging (DKI) was developed to overcome the limitations of DTI such as the non-Gaussian characteristics of tissue and the crossing fiber problems. The latest promising technique is neurite orientation dispersion and density imaging (NODDI), which can be used to show the microstructural changes of brain tissue more sensitively and specifically.


Introduction
Diffusion magnetic resonance imaging (dMRI) has been used widely in the clinical setting to analyze the microstructural changes of tissue based on the movement of water molecules 1) . Nowadays, the clinical usage of dMRI is mainly to investigate neurological abnormalities, especially for ischemic stroke 1)-3) . Diffusion tensor imaging (DTI) and DT tractography, which were developed from dMRI, are now becoming powerful tools and have become the standard imaging techniques for analyzing white matter fiber structure and brain connectivity in vivo 4)-6) . More advanced diffusion techniques will be also described in this manuscript.

The history and basic principles of dMRI
Molecular diffusion or Brownian motion was proposed by Einstein in 1905 as a random motion of molecules in a fluid that is induced by thermal energy 1) 6) . In the mid 1980ʼ s, Le Bihan proposed that microstructural information of tissue could be delineated by imaging the water diffusion through intravoxel incoherent motion (IVIM) MR Imaging 1)-3) . To produce diffusion-weighted images (DWI), Le Bihan applied the sequence described by Stejskal and Tanner in 1965, which is a gradient spin echo T2-weighted sequence with two extra gradient pulses or motion-probing gradients (MPGs) that are equal in magnitude but have an opposite effect in direction 1) 7)-9) . These MPGs were applied along the same directional axis before and after the 180°RF pulse 10) . The first of the two gradient pulses acts as a dephasing gradient and the second pulse acts as a rephasing gradient 4) 9)-11) . As the result, in a voxel of tissue with stationary water molecules or stable spins (Figure-1A), the opposite effect of the gradient pulses will cancel each other and strong signal intensity will be produced. However, moving water molecules or moving spins (Figure-1B) will be affected by the opposite effect of gradient pulses in the different locations, so the two gradients no longer have the same magnitude and they cannot cancel out each other, and thus little signal intensity is produced 6) 7) 9) 11) .
The use of dMRI in clinical application was established in 1990 after Michael Moseley discovered that the water diffusion coefficient drops approximately 30-50% in an acute cat brain ischemia model, within several minutes after the occlusion of the middle cerebral artery 1) 2) . Shortly after that, Robert Turner applied echo-planar imaging (EPI) ( Figure-2A), with the result that diffusion images can be obtained in a short enough time to be feasible for clinical application; the motion artifacts were reduced, and sensitivity to signal changes due to the molecular motion was increased 1) 2) 11) 12) . DWI ( Figure-2B) provides an image with a unique contrast, and the diffusion coefficient could be quantitatively evaluated with apparent diffusion coefficients (ADC) 9) 13) . Moreover, an ADC map (Figure-2C) can be created and ADC values can be displayed by drawing a region of interest (ROI) 9) .
The signal intensity (SI) of each voxel of tissue in diffusion weighted image is calculated with the following equation 9) : SI = SI0×exp (-b×ADC),

Figure-1 Sequence chart of diffusion
To produce diffusion weighted images, a pair of motion probing gradients (MPGs) that are equal in magnitude but have an opposite effect in direction are added to the spin echo-echo planar imaging (EPI) sequence. In a voxel of tissue with stable spins (A), the opposite effect of gradient pulses will cancel each other and a strong signal will be produced. However, moving spins (B) will strongly affected by the opposite effect of gradient pulses in the different locations. The two gradients no longer have the same effect due to the different locations, and they cannot cancel each other, and thus little signal intensity is produced 7) . where SI0 is the signal intensity on the T2-weighted (or b = 0 sec/mm 2 or b0 image), b is a diffusion sensitivity factor that consists of γ 2 G 2 δ 2 (Δ-δ/3).
Here, G is the strength of the gradients, Δ (large delta) is the time interval between the gradients, δ (small delta) is the duration of the gradient, Δ-δ/3 is the diffusion time, and γ is the gyromagnetic constant 7) 9) 10) .
Higher ADC values that reflect faster water diffusion appear as lower signal intensity on DW images, while lower ADC values reflect restricted diffusion that is represented as high signal intensity on DW images 14) . It is also important that the contrast of DW images is not only due to the differences in ADC but is also influenced by the T2-weighted contrast. Increased signal intensity on DW images that is caused by T2 prolongation is termed the"T2 shine through effect" 7) 9) 14) .

Clinical applications of isotropic diffusion MRI
Below are some examples of the utilization of DWI in clinical practice:

Acute brain infarction
A rapid disruption of cerebral blood flow will interrupt the energy metabolism and ion exchange pumps and cause cytotoxic edema. This pathology will appear as a high signal intensity on DWI with low ADC value (Figure-3A) 9) 15 ) .

Hemorrhage
The imaging characteristics of hemorrhage lesions on dMRI are dependent on the age of the hemorrhage, which contains different blood products. During the hyperacute stage, intracellular oxyhemoglobin will restrict the water movement inside the red blood cells and cause high signal intensity on DWI and lower ADC (Figure-3B) 9) 15) .

Abscess
The high viscosity of pus causes restricted diffusion that is marked with a strong hyperintensity on DWI and reduced ADC 9) 16) . The characteristics of an abscess on DWI can be used to differentiate the necrotic portion of a tumor which has a lower signal intensity and higher ADC ratios

Figure-3 Example cases that show the utility of isotropic dMRI
The first row is the diffusion-weighted images (DWI) and the second row is the apparent diffusion coefficient (ADC) maps, all the brain pathologies are indicated with red arrows. A. Acute brain infarction, B. Hemorrhage, C. Abscess, D. Herpes encephalitis, and E. Creutzfeldt-Jakob disease (CJD) show high signal intensity on DWI and low signal intensity on the ADC map, which reflects the restricted diffusion. F. Epidermoid cyst has high signal intensity on DWI but is isointense with the gray matter on the ADC map; this might be caused by the"T2-shine through"effect.

Herpes encephalitis
Herpes encephalitis lesions are shown as hyperintense lesions on DWI and hypointense on ADC map that caused by the cytotoxic edema and high cellularity, that reflect irreversible neuronal damage undergoing necrosis (Figure-3D) 9) 15) 17) .

Creutzfeldt-Jakob disease (CJD)
DWI is proposed as the most sensitive imaging technique in the diagnosis of CJD 18) . It will show hyperintense lesions with low ADC value in the cortex and basal ganglia (putamen and caudate nucleus) or thalamus (Figure-3E) 9) 15) 18)-20) . Histopathologically, the hyperintensity is correlated with intraneuronal vacuolation, astrocytic gliosis, and the deposition of prion (PrP Sc ) 19) .

Epidermoid tumor
DWI is an important imaging technique to differentiate between epidermoid and arachnoid cysts. An epidermoid cyst appears hyperintense on DWI, while an arachnoid cyst will not. Epidermoid cysts have almost similar ADC value as the gray and white matter, suggesting that the high signal intensity in DWI is caused by the"T2 shinethrough"effect (Figure-3F) 9) 13) 15) .

Multiple sclerosis (MS)
On DWI, the signal intensity of MS is variable. MS active lesions that have enhanced contrast usually appear with hyperintensity relative to white matter, while chronic lesions were isointense. Some studies showed increasing ADC values in MS lesions and normal-appearing white matter. The "T2 shine-through"effect is predicted as the cause of this increased signal intensity 15) .
8. Other brain lesions that show restricted diffusion Brain tumors with high cellularities, such as glioma, malignant meningioma, and lymphoma might appear as high signal intensity in DWI with low ADC values. However, in many cases these brain tumors might also appear iso-or hypointense 15) 21) . Metabolic brain diseases with white matter abnormalities or leukodystrophies, such as metachromatic leukodystrophy, Krabbe disease, Canavan disease, and phenylketonuria also appear as high signal intensity on DW images with low ADC values 22) .

Diffusion tensor imaging (DTI)
During the development of DTI, Michael Moseley found that water diffusion in a parallel direction to the white matter fibers is faster than in the perpendicular direction 1) . This anisotropic phenomenon of the diffusion in the brain can be seen by comparing images that are acquired in three different gradient directions 9) . Structures that have the same direction as the gradient appear as low signal intensity on the b0 image 9) . In the x-(right-to-left) direction, the corpus callosum is hypointense (Figure-4A), in the y-(anterior-to-posterior) direction, the peritrigonal white matter tracts, including the optic radiation tract and occipito-thalamic tract are hypointense (Figure-4B), and in the z-(superior-to-inferior) direction, the corticospinal tracts are hypointense (Figure-4C). The signal intensities on DWI are the cube root of the multiplication of those three images with different gradient directions (Figure-4D) 7) 9) . To deal with the anisotropic diffusion, Peter Basser introduced diffusion tensor imaging (DTI) as a technique to determine the true directionality of diffusion 1) 9) 23) . Since then, DTI has been widely used for research and clinical applications as it can show the white matter pathologies 4) . DTI is an imaging technique that is represented with a 3D ellipsoid shape model ( Figure-5) with eigenvalues: λ1 (axial diffusivity) the longest axes, reflects the diffusion that parallel to the white matter fibers; λ2 and λ3, the middle and the shortest axes reflects the diffusion that is perpendicular to white matter fibers. The radial diffusivity is the average value of λ2 and λ3 7) 24) . Moreover, eigenvectors; V1, V2, and V3 represent the direction of the diffusion 7) 24) .
The interpretations of DTI parameters are: 1) fractional anisotropy (FA) that describe the degree of anisotropy of a diffusion process, with values from 0 (isotropic) to 1 (anisotropic) 24) ; 2) mean diffusivity (MD); 3) radial diffusivity (RD); and 4) axial diffusivity (AD) 4) . FA reflects the axonal density, axonal integrity, and fiber tract complexity 25) . Reduced FA was found in many diseases, that is attributed to degradation of myelin sheaths and axonal membranes, or reduced density of axonal fibers 4) 25) . MD, which is the mean-squared displacement of water molecules restricted by organelles and membranes, reflects cellular density and extracellular volume and relates to the volume fraction of the interstitial space 25) . Moreover, RD will increase in demyelination, edema will increase the MD, and cell proliferation will decrease the MD 4) .
Below are some developments of DTI:

1) White matter tractography
The major eigenvector of DT is assumed to be parallel to the white matter fibers and can be simply visualized using color maps (Figure-2E) 4) . The connectivity of white matter on the basis of anisotropic diffusion of water can also be visualized using tractography (Figure-2F) 4) . To delineate the white matter tract with tractography, first we have to draw the first region of interest (ROI) in the "seed"point, followed by the second ROI in the "target"point 26) . From the seed, the lines were sequentially along the major eigenvector of the diffusion ellipsoid and only the lines that reached the target will be displayed 26) . Until now, tractography has been used to reconstruct many white matter pathways, such as the corticospinal tract and corona radiata 4) .

2) Tract-based spatial statistics (TBSS)
TBSS is a voxelwise statistical analysis, that was originally used to evaluate FA values in the white matter 23) . The aims of this method are: 1) to provide an appropriate registration algorithm, and In this model, the size and the direction of the diffusion are represented by the eigenvalues (λ) and eigenvectors (V), respectively. λ 1 (the axial diffusivity) with the longest axes, reflects the diffusion that parallel to the white matter fibers, whereas, λ 2 and λ 3 reflects the diffusion that is perpendicular to the white matter fibers.
2) to improve the sensitivity, objectivity, and interpretability of multi-subject analysis studies 27) . Firstly, FA images were co-registered to each other using nonlinear registration (Figure-6A, B). Next, the group mean FA image was created and thinned to create a mean FA skeleton that represents the centers of all tracts common to the group (Figure-6C). Each subjectʼs FA images (that can now also be used for other DTI parameters) was then projected into the skeleton and the resulting data fed into voxelwise cross-subject statistics 25)-28) . As an example, Kamagata, et al. 28) applied TBSS to investigate the white-matter alteration in Parkinson disease with dementia (PDD) and as the results, they found lower FA values in many major tracts in PDD patients.
Recent studies also showed that TBSS can be used to analyze the parameters of more advanced DWI techniques such as diffusion kurtosis imaging (DKI) 28) and neurite orientation dispersion and density imaging (NODDI) 29) , that will be discussed in the next section.

Diffusion kurtosis imaging (DKI)
DWI and DTI are in vivo imaging modalities that are based on the Gaussian distribution of water molecules 8) 23) ; however, biological tissue has a complex microstructure, such that water diffusion is hindered and the distribution of diffusion does not follow a Gaussian distribution or called non-Gaussian 23) 30) . For that reason, diffusion kurtosis imaging (DKI) was introduced to image the non-Gaussian characteristics of water diffusion and reflect the heterogeneity of tissue 23) . Moreover, DKI is sensitive to the alterations in the area of crossing fibers, which FA was not able to measure 30) . The indices of DKI are as follows: 1) mean kurtosis (MK), the average of the diffusion kurtosis along all diffusion directions; 2) axial kurtosis (AK), the kurtosis along the axial direction of the directions of the axons; and 3) radial kurtosis (RK), the kurtosis along the radial direction of the directions of the axons 23) . MK reflects the complexity of the tissue, the axonal water fraction, and the tortuosity of the extracellular space 28) . Kamiya,et al. 30) showed that MK had a significant correlation with clinical severity and provide more information compared to FA in normal pressure hydrocephalus patients.

Neurite orientation dispersion and density imaging (NODDI)
NODDI is an imaging method based on dMRI, and was proposed to overcome the limitations of DTI 29) 31) 32) . NODDI is able to quantify the direction and the structure of neurites (axons and dendrites) by the orientation-dispersed cylinder model and the Watson distribution 29) 31) 32) . Regarding NODDI parameters, the intracellular volume fraction (Vic) represents the neurite density, and the orientation dispersion index (OD) represents the OD of the neurite 32) . The indices of NODDI are assumed to describe the changes in FA 31) 32) . Kamagata, et al. 31) compared DTI and NODDI parameters in diagnosing PD and found that Vic in the substantia nigra pars compacta is the best index for diagnosing PD. Reduced Vic reflects the neuron loss which is the