## 1 Introduction
### Diffusion Tensor Imaging  
In diffusion-weighted MRI, a gradient is applied in a given direction; if protons diffuse along the gradient direction, dephasing will be accelerated, attenuating the MR signal. Areas with more free diffusion of water will have a reduced MR signal due to the greater movement of the protons; e.g., CSF will appear dark compared to grey matter as CSF contains minimal obstructive microstructure. Some tissues such as white matter will have preferential diffusion in a particular direction, which is known as anisotropic diffusion. This is due to the WM axons restricting the diffusion of water perpendicular to them, but diffusion parallel to their orientation being unrestricted. The imaging gradient direction can be changed, and the DWI signal would be expected to be higher if perpendicular to a WM tract and lower if parallel to it [12]. If DWI images are obtained with at least six gradient directions, the orientation or overall direction of diffusion in the voxel can be calculated and is known as diffusion tensor imaging (DTI). If the voxel is in WM, then the diffusion direction can be assumed to be the orientation of the WM tract. The amount to which that diffusion is preferential to one direction can be quantified and is known as fraction anisotropy (FA), where 0 is completely equal diffusion in all directions and 1 is completely uniform diffusion in only one direction. The overall diffusion of a voxel is known as mean diffusivity (MD). Another set of similar metrics to MD and FA are p and q maps, which refer to the isotropic and anisotropy components of the voxel, respectively [13]. A diagram displaying the effects of tissue microstructure on diffusion measurements is shown in Figure 2.  
As displayed in Figure 2, DTI can capture microstructural changes of white matter, as damage leads to reduced FA and increased MD values due to a reduction in axon density and reduced myelination. This has been shown to be useful in detecting tumoural invasion, which can be observed as reduced FA or q values and has additionally been shown to be potentially useful in differentiating glioma reoccurrence from radiation necrosis after radiotherapy [14]. MD or p values will also increase with tumour invasion and have been suggested to be useful in defining glioma margins [15]. Other DTI measures have additionally been suggested to have potential in the diagnosis of intracranial malignancies, with ADC being shown to be useful in differentiating brain stem gliomas from medulloblastoma [16; 17]. The information from DTI can be used to model whole WM tracts and is known as tractography. This is where each voxel is followed from a seed point and walks in the orientation or tract direction of each voxel; this is repeated for a set number of steps, and a tract is formed. Then, this is done for each voxel in a seed region. When a single tract is taken from each seed voxel, this is known as deterministic tractography. An issue with this method is that a false tract may be followed by accident. Another method known as probabilistic tractography repeats the tract formation multiple times, and a probability distribution of potential tracts is taken. Probabilistic tractography is usually more accurate, as it incorporates an amount of error, and tracts with a lower probability, that are likely false positives, can be filtered out [18]. Figure 3 displays an example of tractography forming a tract. Figure 3: Diagram explaining the tractography process showing an example of how the voxel tensors (**left**) can be tracked from a seed point to form a tract (**middle**) and performed multiple times to produce a virtually dissected white matter tract (**right**). Figure 2: Diagram displaying tensors from different microstructures and how this would affect the isotropic tensor derivatives (p and MD) and the anisotropic components (q and FA). Selecting a seed point to form a desired tract is usually done based on structural anatomy likely to only contain the tract.