Validation of Blood Flow Simulations in Intracranial Aneurysms

Yue YuBrown University

Final-Project Presentation(Registration)

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.

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.

3d object

rotate translate

project

Compare with

DRR

2d fluoroscopy

frame

x

y

z

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.

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.

Simple Tests• Translation only:

• Rotation only:

3D DATAsize: 65*65*65

when 32<x,y,z<40density=1

2D DATAsize: 35*35

when 17<x,y,z<25density=1

Initial T=(17, 17, 1)

FITTING RESULTT=(15, 15, 0.111)

s=2.58e-13

FITTING RESULTR=(1.047, -5e-5, -5e-6)

s=2.54e-7

3D DATAsize: 65*65*65

when 32<x,y,z<40density=1

2D DATAsize: 35*35

when 17<x,y,z<25density=1, rotate pi/3

Initial T=(17, 17, 1)

Simple Tests

• Translation and rotation:

3D DATAsize: 65*65*65

when 32<x,y,z<40density=1

2D DATAsize: 35*35

created by 3D DATA rotating with R=(pi/3,pi/4,0)

Initial T=(15, 15, 1/9)R=(pi/3, pi/4, 0)

FITTING RESULTT=(14.5, 15.3, 0.082) R=(6.95, -2.91, 0.45)

s=3.56

FITTING RESULTT=(22.5, 17, 0.083)

R=(0.52, 0.79, 0)s=6.79e-3

Initial T=(15, 15, 1/9)

R=(0, 0, 0)

Comparison for arterial data: qualitative

Computational results: CT results:T=0.22 (sec) T=0.72 (sec)

T=1.22 (sec) T=1.72 (sec)

T=0.22 (sec) T=0.72 (sec)

T=1.22 (sec) T=1.72 (sec)

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.

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

T=16*T_small

R=R_small

Because of the lack of time, we use data with ¼ of the original size as our fine results.

Quantitative comparison: Results

T=0.22 (sec) T=0.72 (sec) T=1.22 (sec)

2D data

Fitted3D data

Relative error |I-R| 5.61% 5.80%4.05%

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%).

• 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.

References

Thank you!