The classical DTI model [2] assumes that the measured diffusion signal belongs to the set of Gaussian distributions. While DTI has well-known limitations with respect to the modeling of crossing tissue configurations and restricted diffusion,

Fig. 1 Regions of interest for biomarker estimation on the registered FA map of rat 1. We mark the cingulate cortex (green), corpus callosum (blue) and hippocampus (red)

its derived metrics FA and MD have been found useful to classify AD patients [4]. Using signal attenuation E(b) = S(b)/S(0), the DTI model describes the diffusion signal as E(b) = exp(— bg^{T}Dg) with D a 3 x 3 symmetric positive-definite matrix and g the gradient direction. Estimating the eigenvalues of D as {Ai, A_{2}, A_{3}} the FA and MD are given as

In accordance with DTI’s Gaussian diffusion assumption, we only use the b0 and b = 1000 s/mm^{2} data when fitting DTI. The FA and MD in our slice of interest are shown in Fig. 2.

NODDI Metrics

The more advanced multi-compartment NODDI model [3] separates the signal contribution of different tissues by fitting a combination of intra-cellular, extracellular and free-water models.

The intra-cellular signal E_{ic} is modeled as a set of dispersed sticks, i.e., cylinders of zero radius, to capture the highly restricted nature of diffusion perpendicular to neurites and unhindered diffusion along them. The amount of dispersion is given by the orientation dispersion index (ODI), which is defined by a Watson distribution. The extra-cellular signal E_{ec} is described as a dispersed mixture of Gaussian anisotropic diffusion, and an isotropic Gaussian compartment E_{iso} represents free diffusion. Similarly as in [7], we study the ODI, the neurite density index NDI = (1 — v_{iso})v_{ic} and the isotropic volume fraction IsoVF = v_{iso}.

In accordance with NODDI’s recommended acquisition scheme [3], we fit NODDI only using the b0 and b = {1000,3000} s/mm^{2} data. Furthermore, as water diffusivity changes in ex-vivo tissue, we set the intra-cellular and isotropic

Fig. 2 Illustrations of a DTI and NODDI metrics in the same coronal slice for the three time points

diffusivity to 0.6x10 ^{9}m^{2}s ^{1} and 2.0x10 ^{9}m^{2}s ^{1} [13]. An illustration of the ODI, NDI and IsoVF can be seen in Fig. 2.