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In-Vivo Quantification of Brain
Microstructure: a Preliminary
Analysis using SHORE Diffusion
Model
L. Brusini1, M. Zucchelli1, G.K. Ricciardi2, F. Pizzini2, S. Montemezzi2, G.
Menegaz1
1 Dept.
of Computer Science, University of Verona
2 Dept. of Neuroradiology, AOUI of Verona
From Diffusion Signal to Water
Molecules PDF
E(q)
2/8
From Diffusion Signal to Water
Molecules PDF
E(q)
The Ensemble Average
Propagator (EAP) represents
the probability of a net
displacement r in the unit time
P(r)
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From Diffusion Signal to Water
Molecules PDF
E(q)
The Ensemble Average
Propagator (EAP) represents
the probability of a net
displacement r in the unit time
P(r)
ODF(u)
The Orientation Distribution
Function (ODF) represents the
probability of diffusion in each
direction u
2/8
Diffusion Tensor Imaging (DTI)
3/8
Diffusion Tensor Imaging (DTI)
✓ Fast acquisition
✓ Efficient reconstruction
3/8
Diffusion Tensor Imaging (DTI)
✓ Fast acquisition
✓ Efficient reconstruction
☓ Since the EAP is modeled as
a single tensor, DTI is not
able to resolve complex fibers
architectures like fannings
and crossings
3/8
Simple Harmonic Oscillator based
Reconstruction and Estimation (SHORE)
Signal approximated using a combination of orthonormal
functions which are the solutions of the 3D quantum
mechanical harmonic oscillator
4/8
Simple Harmonic Oscillator based
Reconstruction and Estimation (SHORE)
Signal approximated using a combination of orthonormal
functions which are the solutions of the 3D quantum
mechanical harmonic oscillator
Continuous analytical basis
✓ Continuous analytical signal representation in q-space
independently from the acquisition sampling scheme
✓ Possibility to calculate the EAP and the ODF
analytically, obtaining an exact solution for all the
computations
4/8
Propagator Anisotropy (PA) and
Mean Squared Displacement (MSD)
GFA
5/8
Propagator Anisotropy (PA) and
Mean Squared Displacement (MSD)
PA
GFA
Measure of the
angular similarity
between the
propagator and its
isotropic part
5/8
Propagator Anisotropy (PA) and
Mean Squared Displacement (MSD)
PA
Measure of the
angular similarity
between the
propagator and its
isotropic part
GFA
MSD
Degree of diffusivity
of the water
molecules in the
voxel
5/8
Measures of Zero Net Displacement
● Restricted diffusion in pores
● gradient duration very small
● time between gradients is
large
figure refers
to
L. Avram et
al., NMR
Biomed.
2008; 21:
888–898
6/8
Measures of Zero Net Displacement
● Restricted diffusion in pores
● gradient duration very small
● time between gradients is
large
figure refers
to
L. Avram et
al., NMR
Biomed.
2008; 21:
888–898
Return To the Origin
Probability (RTOP)
6/8
Measures of Zero Net Displacement
● Restricted diffusion in pores
● gradient duration very small
● time between gradients is
large
figure refers
to
L. Avram et
al., NMR
Biomed.
2008; 21:
888–898
Return To the Origin
Probability (RTOP)
Return To the Axis
Probability (RTAP)
6/8
Measures of Zero Net Displacement
● Restricted diffusion in pores
● gradient duration very small
● time between gradients is
large
figure refers
to
L. Avram et
al., NMR
Biomed.
2008; 21:
888–898
Return To the Origin
Probability (RTOP)
Return To the Plane
Probability (RTPP)
Return To the Axis
Probability (RTAP)
6/8
From RTOP, RTAP and RTPP to
Physical Measures
Probability for molecules to undergo no net displacement between the
application of the two diffusion sensitizing gradients
RTOP
reciprocal of the
volume
7/8
From RTOP, RTAP and RTPP to
Physical Measures
Probability for molecules to undergo no net displacement between the
application of the two diffusion sensitizing gradients
RTAP
reciprocal of the
mean crosssectional area
RTOP
reciprocal of the
volume
7/8
From RTOP, RTAP and RTPP to
Physical Measures
Probability for molecules to undergo no net displacement between the
application of the two diffusion sensitizing gradients
RTAP
reciprocal of the
mean crosssectional area
RTOP
reciprocal of the
volume
RTPP
reciprocal of the
mean length of the
pores
7/8
Conclusions and Future Works
8/8
Conclusions and Future Works
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Conclusions and Future Works
8/8
Conclusions and Future Works
8/8