Validation of Blood Flow Simulations in Intracranial Aneurysms

1
Validation of Blood Flow Simulations in
Intracranial Aneurysms
Final-Project Presentation (Registration)?

• Yue Yu

Brown University
2
Objective

• Finished
• Generate 3d patient-specific mesh from Dicom
  files.
• Simulate concentration field inside with the
  mesh.
• Now
• Fit the 3d results with 2d dye-injection image by
  2d-3d image registration technique.

3
Registration

• For every iteration of the registration algorithm
  a 3D rigid-body geometric transform is applied to
  the CT volume to produce a change in the 3D
  position of the arteries.
• The 3D volume is then reduced to a 2D digitally
  reconstructed radiograph (DRR) by summing the
  voxel values of the transformed CT volume in the
  z direction.

z
Compare with
y
rotate translate
x
project
2d fluoroscopy frame
3d object
DRR
4
Registration

• Assume pixel values of the filtered DRR are
  denoted by Ii and pixel values of the fluoroscopy
  frame are denoted by Ri, by minimizing the
  objective function
• where
• and is the histogram bin which includes
  Ri.

. I_i
. R_i

• NOTE
• I didn't filter the data, because in our case
  not only the shape should match, the density on
  each pixel should also match.
• Since the data size is huge (536by536by536), I
  took the R_i instead of its average.

5
Registration

• To optimize the objective function S(m), with
  Taylor expansion for the update vector p,
• we can get an approximation for p as
• where m(Tx,Ty,Tz,Rx,Ry,Rz) contains the
  information for translation (T) and rotation (R).
• In the implementation, I use the matlab
  optimization function
• x
  fminunc(fun,x0)?
• Instead of optimizing all six parameters at
  one time, I optimize S with respect to rotation R
  first, then to translation T, and repeat this
  process for five times.

6
Simple Tests

• Translation only
• Rotation only

3D DATA size 656565 when 32ltx,y,zlt40 density1
2D DATA size 3535 when 17ltx,y,zlt25 density1
FITTING RESULT T(15, 15, 0.111) s2.58e-13
Initial T(17, 17, 1)?
2D DATA size 3535 when 17ltx,y,zlt25 density1,
rotate pi/3
3D DATA size 656565 when 32ltx,y,zlt40 density1
FITTING RESULT R(1.047, -5e-5, -5e-6) s2.54e-7
Initial T(17, 17, 1)?
7
Simple Tests

• Translation and rotation

FITTING RESULT T(14.5, 15.3, 0.082) R(6.95,
-2.91, 0.45)? s3.56
2D DATA size 3535 created by 3D DATA rotating
with R(pi/3,pi/4,0)?
Initial T(15, 15, 1/9)? R(0, 0, 0)?
3D DATA size 656565 when 32ltx,y,zlt40 density1
FITTING RESULT T(22.5, 17, 0.083) R(0.52,
0.79, 0)? s6.79e-3
Initial T(15, 15, 1/9)? R(pi/3, pi/4, 0)?
8
Comparison for arterial data qualitative

• Computational results

• CT results

T0.22 (sec)?
T0.72 (sec)?
T0.22 (sec)?
T0.72 (sec)?
T1.22 (sec)?
T1.72 (sec)?
T1.22 (sec)?
T1.72 (sec)?
9
Quantitative comparison Prepare Data

• 2D data
• Considering the geometric differences near the
  aneurysm part, we cut upstream areas in 2d
  angiograms for comparison.

• 3D data
• Invert plt concentration field data into
  536by536by536 matlab 3d matrix.

For easier comparison, change the 2d and 3d data
to black background, that is, the values for
background pixels are zero.
10
Quantitative comparison Coarse to fine

• Coarse
• Condense both the 2d and 3d data into 1/16 of
  their original sizes and apply the fitting
  algorithm, get optimal parameters T_small and
  R_small.

• Fine
• Now apply the algorithm to data with original
  size, with initial values for T and R as
• T16T_small
• RR_small
• Because of the lack of time, we use data with
  ¼ of the original size as our fine results.

11
Quantitative comparison Results
T0.22 (sec)?
T0.72 (sec)?
T1.22 (sec)?
2D data
Fitted 3D data
Relative error I-R
5.61
5.80
4.05
12
Conclusions

• Conclusion
• For rotation or translation only, the fitting
  algorithm gives satisfying results for different
  initial values. However, to fit with both
  rotation and translation effects, a good guess
  for initial values is important for reasonable
  results.
• The concentration field calculated from simulated
  velocity field matches well with the angiograms
  from dye injection (relative error I-R around
  5).

13
References

• Juan R. Cebral, Alessandro Radaelli, Alejandro
  Frangi, and Christopher M. Putman, Qualitative
  Comparison of Intra-aneurysmal Flow Structures
  Determined from Conventional and Virtual
  Angiograms, Medical Imaging 2007 Physiology,
  Function, and Structure from Medical Images.
• Matthew D. Ford, Gordan R. Stuhne, Hristo N.
  Nikolov, Damiaan F. Habets, Stephen P. Lownie,
  David W. Holdsworth, and David A. Steinman,
  Virtual Angiography for Visualization and
  Validation of Computational Models of Aneurysm
  Hemodynamics, IEEE Transactions on Medical
  Imaging, Vol. 25, No. 12, 2005.
• M. Pickering, A. Muhit, J. Scarvell, and P.
  Smith, A new multimodal similarity measure for
  fast gradient-based 2D-3D image registration, in
  Proc. IEEE Int. Conf. on Engineering in Medicine
  and Biology (EMBC), Minneapolis, USA, 2009, pp.
  5821-5824.

Thank you!