alonso ramírez-manzanares , ramón aranda mariano rivera and...

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Alonso Ramírez-Manzanares 1 , Ramón Aranda 2 , Mariano Rivera 2 and Omar Ocegueda 2 1. University of Guanajuato 2. Centro de Investigación en Matemáticas (CIMAT)

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Page 1: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

Alonso Ramírez-Manzanares1, Ramón Aranda2, Mariano Rivera2 and Omar Ocegueda2

1. University of Guanajuato 2. Centro de Investigación en Matemáticas (CIMAT)

Page 2: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

}  B=1500 }  NS=48

Intention: realistic clinical scenario

Page 3: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

3

MRI signal for a single fiber MRI signal for a 2 fiber crossing

Set of signals for the basis of DBFs

Page 4: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

Each signal is modeled as a positive linear combination of the DBFs

This leads to a non-negative least squares problem for each voxel v

Page 5: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas
Page 6: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

Homogeneity criterion 1:

Homogeneity criterion 2:

Page 7: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas
Page 8: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas
Page 9: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas
Page 10: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas
Page 11: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas
Page 12: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

}  We applied the same approach as published in 2007 plus a different spatial regularization

}  Spatial regularization should be used provided we have evidence that the local anatomical structure is sufficiently homogeneous ◦  Challenge: how can we infer that the anatomical

structure of a region is sufficiently homogeneous?

Page 13: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas

b-value should be taken into account In the evaluation

Two-fiber crossing? Four-fiber crossing?

Accurate Diff. profile needed?

Page 14: Alonso Ramírez-Manzanares , Ramón Aranda Mariano Rivera and …hardi.epfl.ch/static/events/2012_ISBI/_static/Talks/... · 2012. 5. 7. · Centro de Investigación en Matemáticas