[Neuroimaging] Dipy - Minimum diffusivity defined in DTI fit reconstruction

[Bago]

The minimum diffusivity values are defined with respect to the maximum
b-values so that dipy will work with b-values inputs in different units.
For example, a data set with 2 diffusion weighted shells might have
b-values of 1000 and 2000 mm^2/s. These b-values can also be expressed as
1e-3 and 2e-3 cm^2/s. The diffusivity values are computed in inverse units
of the b-values, (s/mm^2 and s/cm^2 respectively for the example above) so
we need to define the minimum diffusivity in the appropriate units.

1e-6 is simply an empirical value that worked well, but I guess you could
justify it by saying that it is close to 1 / (2^16) which is the level of
precision in most MRI data sets (raw MRI data most often uses an int16
representation).

Bago

On Tue, Jul 7, 2015 at 7:35 AM, Rafael Henriques <rafaelnh21 at gmail.com>
wrote:

> Hi all,
>
> I understand that the minimum diffusivity in Dipy's dti module is defined
> to avoid problematic causes of zero division. In functions
> *ols_fit_tensor* and *wls_fit_tensor* the minimum diffusivity is
> automatically defined as function of the inverse of the maximum b-value.
> What is the mathematical basis of these lines of code? And why tol variable
> is set to 1e-6?
>
> Thanks,
> Rafael
>
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