**2. Diffusion anisotropy measurement and tensor analysis**

Diffusion is a physical process that involves the translational movement of molecules via thermally driven random motions, the so-called Brownian motion. The factors influencing diffusion in a solution (or self-diffusion in a pure liquid) are molecular weight, intermolecular interactions (viscosity), and temperature [16, 17]. Diffusion is a random transport phenomenon, which describes the transfer of material from one spatial location to other locations over time. The direction of water molecules diffusion in living tissues is always limited to some degree. Water diffusion in biological tissues occurs inside and outside of cellular structures, and it is caused primarily by random thermal fluctuations. The water diffusion is affected by the interaction with cellular and subcellular membranes and with organelles. Cellular membranes deter water diffusion, decreasing the water mean squared displacement. The diffusion hindering and corresponding apparent diffusivity may increase by either cellular swelling or increased cellular density [3].

Previously, the anatomy of the cerebral white matter tracts could only be studied by postmortem dissection or through invasive methods, and said methods could only reveal a few tracts in vivo (neurosurgery) and no tracts could be observed in vivo via conventional imaging

Diffusion tensor tractography (DTT) is a useful noninvasive imaging technique that can identify and represent fiber tracts of the cerebral white matter and their connections in the brain in vivo [1]; also, it can give us information that cannot be achieved by conventional anatomical MRI or histology. In addition to displaying specific cerebral white matter fiber tracts, this technique can also improve the quantification of diffusion characteristics within

DTT provides a three-dimensional representation of diffusion tensor imaging (DTI), and data can be displayed on a colored map obtained from information on the directionality of the

DTI uses the property of the water diffusion anisotropy in axonal fibers allowing the analysis

DTI permits the exploration of microstructural tissue features through the observation of water molecular diffusion, thus furnishing information about the anatomy, microstructural features, and damage of the main brain bundles, useful in several pathological animal models. DTIbased tractography permits the virtual reconstruction of the white matter fiber bundles in-

This technique is commonly used in human medicine to study the anatomy and maturation of the normal, aging brain, but it also can be used to help diagnose neurological conditions, including brain ischemia, multiple sclerosis, diffuse axonal injury, epilepsy, metabolic disorders, certain mental illnesses, and brain tumors, as well as establish a prognosis for patients with these conditions [14, 15]. Though DTI has been extensively used to investigate brains of the dogs ex vivo [11]; there is only one report of the in vivo use of DTT to study cerebral white

The ability to trace cerebral white matter fibers in the dog generates a number of opportunities

Diffusion is a physical process that involves the translational movement of molecules via thermally driven random motions, the so-called Brownian motion. The factors influencing diffusion in a solution (or self-diffusion in a pure liquid) are molecular weight, intermolecular interactions (viscosity), and temperature [16, 17]. Diffusion is a random transport phenomenon, which describes the transfer of material from one spatial location to other locations over

for potential clinical applications, and has both diagnostic and prognostic [1].

**2. Diffusion anisotropy measurement and tensor analysis**

movement of water molecules along the main fiber tracts of cerebral white matter [1].

studies [1–6].

these fibers [1, 7–9].

**1.1. Diffusion tensor imaging**

182 Canine Medicine - Recent Topics and Advanced Research

matter fiber tracts in dogs [1].

and tracking of said fibers in the brain [1, 4, 10, 11].

vivo, following the principal diffusion direction [12, 13].

On the other hand, breakdown of cellular membranes caused by necrosis or other ailments increases the apparent diffusivity. Intracellular water tends to be more contained by cellular membranes, rather than deterred. This restricted diffusion also decreases the apparent diffusivity, but plateaus with increasing diffusion time [3]. In fibrous tissues, including white matter, water diffusion is relatively unimpeded in the parallel direction to the fiber orientation. On the contrary, water diffusion is highly restricted and deterred in directions perpendicular to the fibers. Hence, the diffusion in fibrous tissues is anisotropic [3, 18].

The property by which the rate of diffusion varies with direction is called diffusion anisotropy or anisotropic diffusion [4]. Isotropic diffusion occurs when the magnitude of diffusion is the same in all directions. Conversely, anisotropic diffusion is when the magnitudes of diffusion are significantly different [19].

In some tissues, for example cerebrospinal fluid (CSF), Brownian motion leads water molecules to diffuse freely in any direction. For other tissues, like white matter, water diffusion occurs along the fiber orientation rather than across it due to the highly organized fibrous structure that restricts water diffusion [20]. The underlying tissue cellular microstructure influences the overall mobility of the diffusing molecules by providing numerous barriers and by creating various individual compartments (e.g., intracellular, extracellular, neurons, glial cells, axons) within the tissue [16]. Early diffusion imaging experiments used measurements of parallel and perpendicular diffusion components to characterize the diffusion anisotropy [3].

The behavior of the anisotropic diffusion using diffusion tensor (DT) is described by a multivariate normal distribution, which describes the covariance of diffusion displacements in three dimensions normalized by the diffusion time [3]. Water diffusion cannot be characterized by a single value in an anisotropic voxel given its directional dependence; thus, the tensor model was developed. A tensor may assist in obtaining different parameters. For example, a threedimensional principal eigenvector indicates the gradient of water diffusion within a voxel. In a similar manner, scalar eigenvalues signify the magnitude of the diffusivities along the principal and two orthogonal eigenvectors [21]. The diagonal elements are the diffusion variances along the axes x, y, and z, and the off-diagonal elements are the covariance terms and are symmetric about the diagonal [21]. The diffusion tensor can be represented as an ellipsoid, with its principal axis being defined by the eigenvectors and the ellipsoidalradii defined by the eigenvalues. If the eigenvalues are nearly equal, the diffusion is considered isotropic; if significantly different, anisotropic. Local tissue microstructure modifications such as injury, disease, or normal physiological changes may alter the eigenvalue magnitudes. Hence, the diffusion tensor allows the characterization of both normal and abnormaltissue microstructure [3].IntheCNS,waterdiffusionisusuallymore anisotropic inwhitematterregions andisotropic in both grey matter and cerebrospinal fluid (CSF). The major diffusion eigenvector is assumed to be parallel to the tract orientation in regions of homogeneous white matter [3].

Diffusion-weighted imaging (DWI) is an important technique of functional magnetic resonance (fMR) imaging, which has the ability to assess changes in random motion of water protons in vivo. It is useful to diagnose several diseases in the central nervous system of humans and animals, specially canines [2, 22]. To detect lesions by DWI, the anisotropy is deliberately reduced using imaging techniques and processing to avoid detecting the signals from normal white matter [4].

DWI can be used to detect and visualize water molecules diffusion in tissues by adding a bipolar gradient pulse called a motion-proving gradient (MPG). Diffusion-weighted MRI differs from conventional MRI in that it provides high-contrast resolution based on diffusion, which allows new information on lesions to be obtained [4]. In the 1970s, water diffusion MRI was introduced and later used for medical applications [5]. Reports on diffusion MRI of the brain for neurological disorders were first published in the 1980s [23]. In the 1990s, its use was extended [4]. With the introduction of DTI, it was proposed to represent the water diffusion coefficient distribution in all the directions of space as a tensor in each voxel. A reconstruction of the white matter pathways was later proposed based on this tensor model [5].

DTI is an advanced technique of DWI sequence that displays vectors corresponding to the strength and direction of the movement of water molecules [2]. Recently, the DTI technique has permitted the detailed visualization of white matter structural integrity and connectivity [24]. One of the advantages of DTI is the reconstruction of axonal tracts in the brain in vivo [10]. DTI uses water diffusion anisotropy in axonal fibers allowing the analysis and tracking of said fibers in cerebral white matter.

Cerebral white matter anatomy can be studied in detail using DTI; it shows a complete anatomical and statistical fiber atlas of the white matter [15]; and it can explain, in combination with functional MRI, some anatomical and functional connectivity between different parts of the brain [11].

Pathologic conditions such as edema, inflammation, myelin loss, and gliosis may cause disruption in white matter tracts or changes in the membrane permeability which can alter DTI measurements, such as fractional anisotropy (FA) and apparent diffusion coefficient (ADC) [25].

Several studies have demonstrated the validity of quantitative diffusion imaging of the large white matter tracts in the brain in vivo [2]. FA provides information about the shape of the diffusion tensor at each voxel. The FA relates the differences between isotropic and anisotropic diffusion and is a scalar value between 0 and 1 indicating the degree of anisotropy in water diffusion. If FA value is close to 0, the diffusion is isotropic or random, and if it is close to 1, the diffusion is highly directional. The diffusion coefficient measured by nuclear magnetic resonance is best known as apparent diffusion coefficient (ADC). ADC depends greatly on the interactions of the diffusing molecule with the cellular structures over a given time; it could also be influenced by active processes within the tissue. ADC is calculated by acquiring two or more images with a different gradient duration and amplitudes, quantified as b-values. Also, one can calculate the eigenvalues corresponding the various imaging axis in order to find if the water diffusion is either anisotropic or not. With the obtained data, a tensor map is generated and tractography can be performed. This entire process is called DTI [2, 3, 16, 25, 26]. DWI uses an ADC map; given that DTI is an extension of DWI, it also uses an ADC map [16]. The difference between DWI and DTI is that in DWI encodes water diffusion in three spatial directions and DTI uses up to six directions.

The strength of the signal in FA maps represents the magnitude of FA, and, unlike conventional DWI, it is quantitative. FA decreases at lesion sites. Diffusion tensor analysis has the novel feature of not only quantifying anisotropy by FA and other parameters, but also of analyzing directionality.

Colored FA maps represent anisotropy in different colors according to the direction of the principal axis. These maps make it possible to differentiate fibers based on the direction in which they run. The colors are assigned to nerve fiber tracts depending on the direction of water displacement. The colors represent the predominant orientation of the fibers in a threedimensional coordinate system in the three axes of space (x, y, and z); where red indicates a right-left direction, green indicates a dorsoventral direction, and blue indicates a rostrocaudal direction. This type of representation is called an anisotropic [1, 4, 27].
