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Validation of Blood Flow Simulations in Intracranial Aneurysms

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Validation of Blood Flow Simulations in Intracranial Aneurysms Final-Project Presentation (Registration) Yue Yu Brown University – PowerPoint PPT presentation

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Title: 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!
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