Diffusion MRI is a technique used to measure the water displacement in tissues. Basically, the displaced water molecules produce an attenuated signal during diffusion MR scanning. As a result, the axonal architecture in the white matter of the central nervous system promotes diffusion of water in a parallel manner, rather than perpendicular to the axon fibre (Vedantam et al. 1). Currently, diffusion MRI applications include methods such as the contrast in relaxation times for T1 or T2 weighted MR imaging, in the analysis of blood oxygen level dependency for functional MR imaging, in the time of flight MR angiography, and in the diffusion for apparent diffusion coefficient (ADC) imaging (Hagmann et al. S206).
The Physics and Representation of Diffusion
Diffusion is the random motion of any particle in a fluid when agitated by thermal energy (Hagmann et al. S207). This erratic movement can be described using the displacement distribution, which means the number of molecules that are displace in a specific direction distance. In order to observe this phenomena, a simple analogy of diffusion can be observed when a drop of dye falls into a glass of water. When a photograph is taken at time t= ∆, the dye will have been diluted in a manner that will indicate varying relative colour density of the displaced dye molecules.
Basically, diffusion in a homogeneous medium can be described using a Gaussian distribution. Depending on the temperature, molecule, medium, and time allowed for diffusion, the spread may be wide or narrow. The variance (∂2 ) parameter is the one that controls the spread of the Gaussian distribution. In turn, variance depends on the diffusion coefficient (D), which is characterized by viscosity of the medium and time. Therefore, variance is given as ∂2 =2.D. ∆. The diffusion coefficient of water at 370 C is D= 3.10-9 m2 /sec (Hagmann et al. S208). Notably, the longer the diffusion time interval, the larger will be the variance since there is more time for displacing the molecules.
Diffusion in a Complex Media
In a restricted media, such as in a glass, the displacement distribution is associated with similar volume that contains the impermeable solution. Accordingly, the displacement distribution associated with the voxel will be different from that associated with the same volume before the sphere was introduced. This difference is due to water restriction since molecules inside the container cannot move out while those outside cannot move in. as a result, the expected displacement distance is reduced. In a biological reality, the glass container can be replaced with a semipermeable container (Hagmann et al. S209).
Basically, the movement of water molecules during diffusion–driven random displacement is restrained by the semipermeable molecular obstacles, which reduce the diffusion distance. Noteworthy, the neuron tissues are highly packaged and coherently aligned axons. They are also surrounded by glia cells that are organized in bundles. Therefore, the micrometric movements in these cells are mostly restrained to a direction that is perpendicular to the axonal orientation that is parallel to it. Therefore, this distribution is not isotropic and Gaussian like, rather it is cigar shaped (Hagmann et al. S210).
Importance of Diffusion-Weighted MRI
Basically, diffusion-weighted MRI is the unprocessed result of the application of a single pulsed gradient SE sequence in one gradient direction. In addition, it corresponds to the one point in q-space. Notably, such an image can be used to gather crucial information on a patient who has stroke.
 
Figure 1: Diffusion-weighted MRI at a single point 3D q-space of the brain area
Source: Hagman et al. 213
Figure 1 above shows that the right corpus callosum is bright while the right splenium is dark. In areas like the right splenium, where the main diffusion direction is aligned with the applied diffusion gradient, the intensity of the signal is greatly decreased. Therefore, the region appears darker on the image. The ventricles have a free diffusion that is substantial in all directions, such as the applied gradient direction. Consequently, the ventricles appear dark. Majorly, diffusion-weighted imaging is used to investigate for the presence of stroke. In acute stroke, the local cells swell and result in increased restriction of water mobility (Hagmanm et al. S215). As a result, bright images appear in the area of the lesion due to the high presence of signals in the regions that have lesion.
Application of Diffusion Magnetic Resonance in Imaging in MS
DW-MRI is an effective tool for examining multiple sclerosis (MS) because MS damages the integration of the white matter pathways, inside and outside the white matter lesions, are visible using MR images (Voddini and Ciccarelli 249). According to Roosendaal et al., 2009, healthy controls have led to a reduction of the FA in the white matter tracts of patients with MS. Raz et al. 2010, was able to show that a reduction in the diffuse significant FA using TBSS in patients with Clinically Isolated Syndrome (CIS). Yu et al. 2012, was able to show there is a correlation between the FA reduction and cognitive impairment in cognitively relevant tracts mostly in the posterior thalamic radiation, the corpus callosum, and sagittal stratum. Further, Bodini et al., 2013 reported there is a relationship between the damage in the callosal fibers in determining the occurrence of MS. Specifically, a low FA along the the entire corpus callosum is associated with poor verbal memory, executive functioning after five years, and poor speed of information processing.
In a study by Dineen et al., it was found that there is a correlation between the the fornix FA with controls. In particular, individuals who had a low visual memory were found to also have low fornix FA. In support of Dineen et al. research, Kern et al, 2012 found that an increase in the fornix FA correlated with an improved MRI activity in this region, and better memory performance.
In a research done by Bodini et al. 2009, it was found that there is a quantitative relationship between reduced FA and increased atrophy of the connected gray matter. Patients with a lot of gray matter atrophy in the right sensory motor cortex had greater upper limb disability when measured using the 9-peg hole test. In light of the above, DW-MRI is an important tool in evaluating and testing for the presence of MS.
Diffusion Tensor Imaging
Developed from a technique known as diffusion-weighted imaging, Diffusion Tensor Imaging (DTI) is a magnetic resonance technique that can measure the magnitude, as well as the direction of the diffusion water in various body tissues (Vedantam et al. 1). Naturally, water moves freely on any direction through unrestricted/ isotropic diffusion. However, in most cell structures, the biological barrier of the cell itself restrain such movement. Accordingly, nerve fibres, the cell membrane, and myelin sheath prevent water from having a perpendicular diffusion. Nevertheless, it allows for a longitudinal axis along the axon bundle’s (Hendrix et al. 88).
The Physics and Representation of Diffusion Tensor Imaging
In mathematics, a tensor can represent the probability density function of water diffusing. Basically, this method is defined in space by using three orthogonal vectors. An equal norm of all vectors enables for the representation using a sphere. In addition, the diffusion is isotropic. Basically, as water moves in a specific direction due to restricted diffusion, the shape of the tensor representation shifts from that of a sphere to that of an ellipsoid. The long vector originated along the axonal bundle which signifies the high diffusivity. On the other hand, the other two bundles, which are oriented in a perpendicular or radial manner to the axonal bundle are shorter. Generally, this characteristics indicate decreased diffusivity. Therefore, the level of change of the tensor quantifies anisotropy (Hendrix et al. 88).
Fractional anisotropy (FA), which is the most common metric for measuring anisotropy, uses a value of zero to indicate isotropic diffusion whereas 1 signifies near perfect linear diffusion along the eigenvector. Accordingly, diffusion tensor imaging (DTI) is a technique that maps the diffusion tensor.
Importance of using DTI
According to Yamada et al. 89, DTI is able to collect information that enables for the creation of a three-dimensional visualization of fibre tracts/ tractography. Various deterministic and probabilistic methods are used to assess the direction of the fibre. In the deterministic method, the fibre tractography starts and targets the white matter locations to be defined. Tracts are propagated from the start location and target the white matter to be defined. The tracts propagate form the starting location till the white bundles as long as the adjacent tensors are strongly aligned. Finally, the tractography ends at the point of low FA (Hendrix et al. 89)
Clinical Applications of Tractography
Spinal Cord Injury
According to Hendrix et al. 91, the non-invasive imaging technique is important in the management of spinal cord injury (SCI). Although conventional MRI is the most common method, it has the ability of delineating the axonal integrity. DTI and tractography have been used to show axonal integrity in SCI. In most cases, this methods use axial diffusivity (AD), radial diffusivity (RD), FA, and apparent diffusion coefficient (ADC). In a research by Chang et al., it was found out that ADC values did not vary between control individuals and patients at either the site of lesion or in the adjacent cervical spinal cord (Chang et al., 2010). Muganatthan et al., reported that ADC had the highest sensitivity to SCI (Shanmuganathan et al., 2008).
According to Song et al. and Kim et al., the axial and orthogonal diffusivity are sensitive, specific, and non-invasive biomarkers of axonal and myelin damage (Song et al., 2003; Kim et al., 2006). Loy et al., reported that DTI is capable of predicting severity of a damage between 0-6 hrs after the SCI. Basically, the DTI measurements of the axial diffusivity were correlated to the degree of axonal injury on histology. While assessing the locomotor recovery in mice that underwent contusive SCI, Kim et al. were able to observe that the extent of spared white matter correlates with the axial diffusivity, as well as the locomotor recovery after two weeks. In turn, they concluded that DTI conducted at 3 hrs after a traumatic SCI is a valuable prognostic tool.
Rajasekaran et al. and Vedantam et al. established that tractography is capable of delineating the unilateral fibre disruptions that correspond to neurological defects such as the Brown-Sequard Syndrome (Rajasekaran et al., 2010; Vedantam et al.,2012). The Brown-Sequard Syndrome is a hemicord injury that is occasioned by ipsilateral motor weakness and hypoesthesia and loss of pain and temperature sensation on areas below the injury.
Figure 2: Tractography of a Traumatic Spinal Cord Injury
Source: Hendrix et al. 91
Importance of DTI in Multiple Sclerosis
Multiple sclerosis (MS) is an inflammatory condition characterized by demyelination, gliosis, and axonal degeneration in the central nervous system. According to DeBoy et al. 2007, the DTI parameters significantly correlate with the axon degeneration and loss within the site of the lesion and in the adjacent areas. In a study by Theaudin et al. 2012, they found that MRI may at times underestimates the size of lesions in MS. Accordingly, lower FA and ADC values were generally found in lesions than in the normal appearing white matter. Setzer et al. 2010, reported that tractography fibres can be traced through inactive T2 hyperintense multiple sclerosis plaques, which was contrary to other types of lesions that either displaced, interrupted, or deformed the fibres. In a research conducted by Renoux et al. 2006, it was found out that DTI has the ability of identifying white matter abnormalities that are not evident in routine MR imaging. In their research, the FA values were similar to the T2 abnormalities in patients with myelitis.
DTI has been found to be effective in analysing amyotrophic lateral sclerosis. Amyotrophic lateral sclerosis is a fatal neurodegenerative disease that is characterized by a combination of negative effects on the upper motor neurons and lower motor neurons. Cohen-Adad et al. 2013 reported that FA in the spinal cortico-spinal tract correlates with the severity of the disease. In addition, they also found that larger DTI abnormalities caudally to the spinal cord, imply that the degeneration of the corticospinal tracts follows a retrograde pattern.
Neurite Orientation Dispersion and Density Imaging (NODDI)
Neurite Orientation Dispersion and Density Imaging (NODDI) is an advanced diffusion MRI model that overcomes the limitations of DTI. The main limitation of DTI is the assumption made by the tensor model that water diffusion in voxel can be described by a Gaussian displacement in each compartment. To overcome this limitation, the NODDI model uses vivo quantification of microstructural tissue features and neurite morphology by developing advanced models that are able to measure multiple diffusion compartments. To facilitate a detailed description of the tissue microstructures, NODDI provides a quantification of the relative contribution of each voxel to the overall signal in each voxel (Caverzasi et al. 495). These compartments are the isotropic, anisotropic Gaussian, and anisotropic non-Gaussian diffusion.
The NODDI framework acquires DW data and parametric maps that describe the properties of the compartments within which water pools diffuse that fit the model data are obtained. Notably, these maps represent indices such as the neurite density and the neurite orientation dispersion. Neurite density is used to estimate the fraction of axons and dendrites in a tissue. The latter evaluates how parallel the neurites are to each other. Low orientation dispersion indicates there is a coherent organization while high orientation indicates that the neurites are dispersed (Grussu et al. 590). In the interpretation of the gray-scale images, the output maps showing the contribution of compartment to the total diffusion signal represent relative values. In addition, NODDI uses the following steps:

  • Identifying the relative contribution of the isotropic water diffusion compartment from the total signal (VISO )
  • Finding the value of the relative contribution made by anisotropic component (VEC) to get the value of the NODDI toolbox (Caverzasi et al. 495).

Although it was initially developed for brain imaging, NODDi has been found to be useful in imaging the spine. Basically, the importance of the use of NODDI in treating diseases that alter the normal structure of the spinal cord such as MS is due to its ability to use high resolution required to precisely locate the grey and white matter (GM/WM) (Mohammadi et al., 591). According to Lukas et al. 2013, the neurite density estimates in WM may be used to characterize the axonal loss in the provision of new knowledge about the pathological mechanism in the spinal cord atrophy in MS. Noteworthy, the spinal cord atrophy is closely linked to MS.
In a research conducted by Grussu et al. to evaluate the applicability of NODDI to the spinal cord in vivo. In the first step, the published NODDI diffusion encoding protocol used for brain imaging was used to acquire data at cervical level of five healthy adults. These results were routinely compared with those obtained from DTI. The research investigated the following issues:

  • NODDI metrics, which was composed of the region of interest (ROI)
  • The reproducibility of NODDI in GM and WM
  • The relationship between NODDI and DTI indices
  • The goodness of fit for both NODDI and DTI from the resulting data (Grussue et al. 591)

The research results showed that NODDI provides metrics that directly map neurite architecture. Importantly, the NODDI’s ability to map architecture can be useful in the treatment of SCI. Moreover, NODDI was able to disclose several anatomical features which can be related to real microstructural characteristics of the spinal cord. In addition, they can also be related to diffusion DW MRI models used in brain applications such as the “ball and stick” (Grussue et al. 596). Further still, the trends of the DTI indices were consistent with the previous findings, as well as the tract-specific measures in the lateral and dorsal columns of the cervical cord WM (Smith et al., 2010).
The research by Grussue et al. 597, showed that NODDI ODI had the highest contrast between GM and WM on all the fitted metrics. Notably, these figures were higher than those of the DTI. ODI in GM was three times greater than that in the WM, which was in line with well-known differences in the neurite architecture as well as the brains qualitative findings (Zhang et al., 2012). The volume fractions vin and vr showed less contrast between GM and WM. These results suggested that the spinal cord’s vin and vr are more homogeneous between GM and WM than those of the brain. These outcomes may be due to the partial volume effect occasioned by a small number of voxel in each tissue type (GM/WM). On the contrary, since vin is designed to map the density of axons and dendrites, the contrast between these two tissue types may be an indication of axons in GM and dendrites in WM. Consequently, the reduced heterogeneity between these two tissue types, the GM and WM, in the spinal cord as compared to those in the brain possibly contribute to the high FA in GM (Grussu et al. 597).
In addition, the CNR levels in NODDI were similar to those in DTI. Additionally, despite the high contrast levels in oODI among all metrics, its CNR was lower than the FA and AD. Generally, this may be due to the high variability of the NODDI indices when compared to those of DTI, which affect the reproducibility scores (Grussu et al. 597). Given the contrast levels and the CNR score, NODDI can be effectively applied in the examination of the spinal cord due to its ability to clearly differentiate the microstructural differences of WM and GM with regards to the neurite orientation dispersion.
According to Zhang et al., 2012, NODDI can be applied in the standard clinical system. Moreover, it has similar findings as those of the brain. Better still, NODDI acquires its data better than DTI and its neurite orientation dispersion differentiate the WM from the GM more clearly. In fact, the ability to differentiate fibre orientation is an essential feature in highly organized areas such as the human corpus callosum (Ferizi et al. 2013). Additionally, the ability to reproduce NODDI can allow for application in studies that have larger cohorts of subjects.
To conclude, NODDI is a feasible alternative to DTI in the in vivo spinal cord imaging. Similarly, it has an advantage of measuring indices specific to neurite morphology that reveal the factors contributing to various DTI-derived anisotropy. In light of this, there should be more research to investigate the viability of this technique to evaluate and confirm the models specificity and assumption in cases of SCI by analysing the DW MRI ex vivo spinal cord samples.
 
 
 
 
 
 
 
Works Cited
Hagmann, P., et al. Understanding Diffusion MR Imaging Techniques: From Scalar Diffusion-weighted Imaging to Diffusion Tensor Imaging and Beyond: RadioGraphics, 2006, 26:S205-S203. Print.
Hendrix, P. et al. Spinal Diffusion Tensor Imaging: A Comprehensive Review With Emphasis on Spinal Cord Anatomy and Clinical Applications. Clinical Anatomy, 28, 88-95. (2015). Print.
Grussu, F. et al. Neurite orientation dispersion and density imaging of the healthy cervical spinal cord in vivo. Neurolmage, 111:590-601. (2015)
Bodini, B. and Ciccarelli, O. Diffusion MRI in Neurological Disorders. Diffusion MRI for Quantitative Measurement.