# A restriction-spectrum sparse-fascicle model for diffusion MRI

### Ariel Rokem*, Christian Pötter, Robert F. Dougherty

Center for Cognitive and Neurobiological Imaging, Stanford University
*Now at the University of Washington eScience Institute

## RS-SFM Combines two different ideas:

• ### Sparse Fascicle Model (Rokem et al., 2015)

• The signal is modeled as a combination of tensor response functions:
...

• The active set of 'fascicles' is selected using non-negative least-squares regression regularized with Elastic Net
• The direction-independent ("isotropic") signal is modeled separately as a multi-exponential: $$f(b) = \beta_1 e^{-bD_1} + \beta_2 e^{-bD_2} + \epsilon$$
• ### Restriction Spectrum Imaging (White et al. 2013)

• Each fascicle is repeated with different combinations of λ12,3
• Accounts for different restriction conditions within each voxel
• A multi-exponential decay profile for every fascicle

### But also (high gradient strength):

$$Still, \: overall \: R^2 = 98.8$$

## Reproducible research

"...an article about computational result is advertising, not scholarship. The actual scholarship is the full software environment, code and data, that produced the result..." -- Buckheit and Donoho (1995)

All the code used to fit the model is available at