Optimal B-Spline Mapping of Flow Imaging Data for Imposing Patient-Specific Velocity Profiles in Computational Hemodynamics

Figures

• 

  Fig. 1. Method overview. Through-plane velocity is extracted from 3D colour Doppler or 2D flow MRI data (left). For each temporal phase i in the velocity data, a velocity contour cυi⊂πυ defining the boundary of the vessel is obtained (left). A separate model contour cm⊂πm is defined in the face of the geometric model, built from the anatomy image data (CT or MRI; right). In this work, cm is not time-dependent, but this need not be the case in general. In order to co-register cυi and cm, the user must define landmarks in both velocity and anatomy images. The velocity profiles between each of the n cardiac phases are temporally interpolated to produce the required resolution for the CFD analysis

• 

  Fig. 2. Rotational contour alignment using a reference landmark. In what follows, the difference in shape and size between the cm and cυi the figures in this section is exaggerated for ease of visualisation.

• 

  Fig. 3. Non rigid alignment between the velocity image derived contour and the model contour at the inlet. Left: point-wise correspondence between points defining equal angular increments in the two contours (only every fifth point is labelled). Right: the corresponding points specify the contour deformation vectors that will define the mapping.

• 

  Fig. 4. Mapping from model inlet to velocity profile, using the proposed method (top) and the Schwarz-Christoffel method (bottom). The difference in shape between the two contours has been exaggerated for better visualisation of the smooth transition between contours offered by the proposed method.

• 

  Fig. 5. Test synthetic profile types, representing a variety of shapes that model simplified normal and abnormal aortic inlet velocity profiles.

• 

  Fig. 6. Quantitative analysis of profile mapping using synthetic data. (a) Execution time, per case, using the proposed method (left) compared to the SC method (right). (b) Point-wise difference in mapped velocity values between the proposed method and the SC method, using the three profile types from Fig. 5 (adapted to randomly generated contours). The error values in cm/s can also be read as % since the maximum velocity value was set to 100cm/s.

• 

  Fig. 7. Mapped synthetic profiles for the case with highest dissimilarity between the SC method and the proposed method. The first row shows the original velocity from the synthetic imaging data, for three profile types. The second and third row show the velocities mapped to the model inlet (contoured in red). A notable difference is the angled profile in the slit-like profile (central column) which is observed in the SC method but not in the proposed method.

• 

  Fig. 8. Velocity profile mapping addressing orientation and shape changes between the model and the velocity data. a) Profiles obtained from CDI images from a healthy volunteer. b) Profiles obtained from Flow MRI images from a cardiac patient

• 

  Fig. 9. Quantitative analysis of the effect of the trade-off factor λ. (top) Relative absolute error in stroke volume (SV) for λ∈[0.1]. (middle) Relative absolute error in flow rate (FR), for the volunteer, showing the median and quantiles (25% and 75%) of the error distribution over the cardiac cycle. (bottom) Relative error in FR for the patient.

• 

  Fig. 10. Blood velocity distribution (in m/s) of the mapped profile over time from a) imaging data, compared to the imaging data for different trade-off value λ, from b) matching the velocity distribution (λ = 0) to c) matching the flow rate (λ = 1).

• 

  Fig. 11. Visualisation of the profile mapping results in the CRIMSON softwareExample of visualization of the systolic profile prescribed on the inlet of the geometric model in CRIMSON [16]. b) Flow waveform illustrating the cyclic temporal interpolation GUI.

• 

  Fig. 12. CRIMSON GUI overview. a) 1. Data manager with all the loaded objects, 2. Display area used for data visualisation, and 3. Activity-specific GUI controls are located on the right side. In this example the selected activity is velocity profile mapping. b) Detailed view of the CRIMSON velocity profile mapping GUI, which includes: A) Model face selection. B) Specification of velocity and anatomy images and geometric model. C) Vessel lumen segmentation in the velocity images. D) Positioning of landmarks in both model and velocity images. E) Additional information related to the velocity image in the context of PC-MRI (such as velocity encoding). F) Advanced settings.