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A direct link between the DKI model and the sub-diffusion process

Qianqian Yang¹ and Viktor Vegh^2,3
¹Queensland University of Technology, Brisbane, Australia, ²The University of Queensland, Brisbane, Australia, ³Centre for Innovation in Biomedical Imaging Technology, Brisbane, Australia

We derived a direct mathematical link between DKI and anomalous sub-diffusion models and provided a new alternative and explicit way to compute kurtosis, leading to superior grey-white matter contrast compared to traditional DKI metric.

Figure 3. Comparison of diffusivity and kurtosis estimated from (a) the sub-diffusion and (b) DKI models. Top row: axial view; bottom row: mid-sagittal view.

$D^*$ and

$K^*$ have been computed based on sub-diffusion model parameters

$D_{SUB}$ and

$\beta$ ;

$D_{DKI}$ and

$K_{DKI}$ have been estimated by fitting the standard DKI model to the data.

Figure 2. Link between sub-diffusion and DKI models: (a) plot of the natural logarithm of the sub-diffusion model and its approximations. Mono-exponential (MONO) and DKI are the first- and second-order approximations of the sub-diffusion model, respectively; (b) relationship between kurtosis

$K^*$ and

$\beta$ ; (c) relationship between the ratio

$D^*/D_{SUB}$ and

$\beta$ .

$D^*$ and

$K^*$ are the diffusivity and kurtosis computed from sub-diffusion model parameters

$D_{SUB}$ and

$\beta$ .